History of Valence-Bond Theory

WORKSHOP ON STRONGLY CORRELATED SYSTEMS, COOPERATIVITY, AND VALENCE-BOND THEORY

23 – 24 July, 2011 A Coruña, Spain

Program and abstracts book

WORKSHOP ON STRONGLY CORRELATED SYSTEMS, COOPERATIVITY, AND VALENCE-BOND THEORY 23 – 24 July, 2011 A Coruña, Spain

Program and abstracts book

Edited by:

Josep Oliva Consejo Superior de Investigaciones Científicas (CSIC – Madrid)

Moisés Canle Universidade de A Coruña

Arturo Santaballa Universidade de A Coruña

Title/Título:

WORKSHOP

ON

STRONGLY

CORRELATED

SYSTEMS,

COOPERATIVITY, AND VALENCE-BOND THEORY Editores/Edited by: Josep Oliva, Moisés Canle, Arturo Santaballa

2011 Universidade de A Coruña

All rights reserved.

No part of this publication may be reproduced, stored in any

retrieval system, or transmitted, in any form or by any means for commercial reasons without the prior permission of the editors or the owner of the copyright.

Quedan reservados todos los derechos. Esta publicación, total o parcialmente, no puede ser reproducida, almacenada o transmitida, en modo y/o medio alguno para fines comerciales sin el previo consentimiento expreso de los editores o del propietario de los derechos.

ISBN: 978-84-9749-489-2 Depósito legal: C 2255-2011 Imprime: Servicio de Reprografia UDC

Workshop on Strongly Correlated Systems, Cooperativity, and Valence-Bond Theory

http://watoc2011satelliteconferencecoruna.webs.com/

WORKSHOP ON STRONGLY CORRELATED SYSTEMS, COOPERATIVITY, AND VALENCE-BOND THEORY

Table of contents Welcome

3

Meeting information

5

The Tower of Hercules

9

Committees

11

Preface by Ruben Pauncz

13

Preface by Roy Mcweeny

15

Schedule

17

Program

19

Abstracts of Plenary communications

27

Abstracts of Oral communications

51

Abstracts of Poster communications

65

Epilogue by Douglas Klein

79

List of Participants

81

Sponsors

82

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Welcome The organizing committee is pleased to welcome you in A Coruña, the city where nobody is foreigner. We hope that you will enjoy the scientific program dedicated to STRONGLY CORRELATED SYSTEMS, COOPERATIVITY, AND VALENCE-BOND THEORY, and we thank all the participants for their contribution.

Aim of the workshop This workshop is the place to bring together world leader researchers, in a pleasant location, to address difficult problems concerning electronic structure: molecules, nano-structures and beyond, and to create scientific collaborations around the workshops’ topics. We hope that the environment of the workshop will help you to forge new friendship and fruitful collaborations.

Topics •

Strongly correlated (extended) systems and nanostructures

•

Model Hamiltonians for extended systems and nanostructures: Hubbard, tJ, Heisenberg, hard-dimer

•

(Resonating) Valence-Bond theory in chemistry and physics

•

Density-functional theory & correlation

•

Group theoretic approaches for many-body and collective aspects: Lie-algebraic, (density matrix) renormalization group methods

The Local Organizing Committee

Please enjoy the workshop, enjoy A Coruña …

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Meeting Information Workshop Venue: Centro Universitario de Riazor (Calle Almirante Lángara)

Activity

Location

Secretary of the Workshop

Ground floor

Plenary and Oral communications

Main Lecture room – First floor

Posters

Ground floor

Coffee breaks and posters’ Underground

refreshment

Lunches: There are plenty of places, within 5 minutes walking distance, to have a lunch, many of them with prices around 10 euro. Workshop banquet: Restaurante Mirador de San Pedro. Bus transportation will be provided. The bus will depart from the hotel Riazor by 20:15, with one stop at the Workshop Venue. The bus will depart from the restaurant by 23:45 to Hotel Riazor.

Internet facilities Free wireless connection is available in the whole Workshop Venue; please refer to the reception desk.

Badges The name badges have to be worn during the workshop, they allow to identify the participants and the members of the workshop organization.

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Meeting Information

Oral presentations Instructions for speakers Presenters are kindly invited to provide their presentation on a memory stick as soon as possible; and no later than the break before the session of the scheduled talk. Laser pointer is available on request. Presenters can also use their own laptop. For any question or assistance, please refer to the audiovisual assistant. There are two types of oral presentations: plenary (30 min) and oral communication (15 min). Please notice that those times include questions and changeover.

The session chairs will follow the schedule rigorously

Suggested times, in minutes, are as follows: Presentation

Talk

Questions & changeover

Plenary

22 - 23

8-7

Oral communication

10

5

Posters Posters should be placed according their number on Saturday morning, and removed on Sunday during the last coffee-break. Maximun poster size is A0 (i.e. 84.1 cm (width)x118.9 cm (length)).

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The Tower of Hercules (la Torre de Hércules)

The Tower of Hercules is an ancient Roman lighthouse that was inscribed as a UNESCO World Heritage Site during the 33rd session of the World Heritage Committee in Seville, Spain, on 22 - 30 June, 2009. The tower is the oldest fully functioning lighthouse in the world and also a symbol of A Coruna that is synonymous with the province and appears on its heraldry.

The lighthouse stands on an elevated headland a short distance from the center of A Coruna city, and its oldest sections date back 1900 years to the Roman occupation that expanded across most of Europe. The tower faces the Atlantic Ocean and stands approximately fifty seven metres (over 180 feet) high and literally looks like it has occupied this spot forever.

Myths Through the millennia many mythical stories of its origin have been told. According to a myth that blends Celtic and Greco-Roman elements, the hero Hercules slew the giant tyrant Geryon after three days and three nights of continuous battle. Hercules then—in a Celtic gesture— buried the head of Geryon with his weapons and ordered that a city be built on the site. The lighthouse atop a skull and crossbones representing the buried head of Hercules’ slain enemy appears in the coat-of-arms of the city of Corunna.

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Another legend embodied in the 11th-century compilation Lebor Gabala Erren— the "Book of Invasions"— King Breogán, the founding father of the Galician Celtic nation, constructed here a massive tower of such a grand height that his sons could see a distant green shore from its top. The glimpse of that distant green land lured them to sail north to Ireland. A colossal statue of Breogán has been erected near the Tower.

In reality the Tower of Hercules has probably existed in some form or other from the second century onwards, and inscriptions on the foundation base refer to a Roman engineer called "Sevius Lupus". References are also made to the Tower of Hercules as early as 415AD in written texts

It is highly likely that the original tower had an external access ramp and burned a wood fire, but in 1788, under the rule of King Carlos IV, a three year project was undertaken to build an enclosing facade around the structure and that is what can be seen now.

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Committees Honorary Committee P. W. Anderson (Princeton University, USA) R. McWeeny (University of Pisa, Italy) R. Pauncz (Technion, Israel)

International Advisory Board D. R. Alcoba (University of Buenos Aires, Argentina) J. A. Alonso (University of Valladolid, Spain) D. L. Cooper (University of Liverpool, UK) J. Z. Davalos (CSIC, Spain) G. Delgado-Barrio (CSIC, Spain) M. A. Garcia-Bach (University of Barcelona, Spain) H. Lischka (University of Vienna, Austria) N. H. March (University of Oxford, UK) J. Paldus (University of Waterloo, Canada) L. Rincón (University of Los Andes, Venezuela) K. Ruedenberg (Iowa State University, USA) P. von R. Schleyer (University of Georgia, USA) M. Troyer (ETH, Switzerland)

Local committee M. Canle (Universidade de A Coruña) A. Chana (CSIC) M. I. Fernández (Universidade de A Coruña) M. V. García (Universidade de A Coruña) J. M. Oliva (CSIC) J. A. Santaballa (Universidade de A Coruña)

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Preface

Ruben Pauncz Schulich Faculty of Chemistry, Technion, Haifa, Israel I received a kind invitation from D.J. Klein and J.M. Oliva to write a short introduction to the Conference. The subject matter looks very interesting and the list of speakers (many old friends) is excellent. I hope I am allowed to make some personal remarks about my own interest, some of the subjects have close relation to the problems to be discussed in this meeting.

One of my main interests was in the construction of spin eigenfunctions. There are four basic methods for the construction. (a) The branching diagram method, (b) the Serber construction, (c) the projection operator method, (d) the valence bond type spin coupling.. The spin functions generate an irreducible representation of the symmetric group, it corresponds to those Young tableaux which have only two rows. One can also show that the correct spatial eigenfunctions (which are essential in the energy expression) also generate a representation of the symmetric group. These correspond to those Young tableaux which have no more than two columns. Matsen advocated an approach (Spin free quantum chemistry) in which one only uses spatial functions with the correct permutational symmetry.

I published a monograph on the construction of spin eigenfunctions in 1979, published a shorter, updated version (with exercise problems) in 2000. I gave graduate courses in this subject, the last one in 2008, when I was "only" 88 years old.

In 1994 I received an invitation from D.J.Klein to write a monograph on the use of the symmetric group in chemistry. I presented again the construction of spin eigenfunctions and the representations of the symmetric group generated by these functions. A separate chapter treated Matsen's approach in detail. In the last chapter (Spin coupled functions) I drew attention to a very promising approach started by J. Gerratt and co-workers. They use a linear combination of spin eigenfunctions. They optimize separately both the orbitals and the spin coupling coefficients. The simultaneous optimization of the orbitals (through their expansion coefficients) and the search for the best combination of spin eigenfunctions gives a great flexibility and still retains visuality. It is very interesting to follow what happens with the orbitals and the spincoupling coefficients upon dissociation. When the nuclei are well separated the orbitals are

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similar to atomic orbitals and the mode of spin coupling is characteristic of the separated fragments. When the atoms come closer the orbitals deform, they have more contribution from neighboring atoms. The spin-coupling coefficients change first very slowly but they undergo a rapid change when the fragments approach a certain distance. The method is presented very clearly in the paper of Gerratt, Cooper, Kadarakov and Raimondi.

One of the important developments has been the use of the unitary group in the calculation of the matrix elements of the Hamiltonian in the configuration interaction treatment. Moshinsky realized the importance of the unitary group in the theory of the nucleus and in spectroscopic calculations. Matsen advocated the use of unitary group in spin free quantum chemistry. An important step in the theory was the work of Gel'fand who was able to give explicit formulas for the representation of the elementary generators of the unitary group. Paldus made a breakthrough when he realized that Gel'fand's formulas become considerably simpler when one restricts the representations to only those which are physically allowed. The next great improvement was achieved by Shavitt who introduced the graphical unitary group approach. Using these developments it became possible to perform configuration interaction calculation involving many million configurations. Of course only a small number of configurations are really important, see Ruedenberg's paper in this conference.

An alternative approach was developed by Duch and Karwovski. They base the calculation of the matrix elements of the Hamiltonian using the representations of the symmetric group. A similar successful treatment was presented by Sarma and Rettrup.

The mentioned irreducible representation theory of the symmetric and unitary groups is naturally at the core of the program development for quantum chemical computation. But also the workshop holds promise in chemical applications of valence-bond theory, and further some consideration of many-body resonating valence-bond theory of nanoscopic and bulk materials.

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Preface

Roy McWeeny Department of Chemistry, University of Pisa, Pisa, Italy

There used to be two main problems in Quantum Chemistry: the so-called “Correlation problem”, of how best to admit the Coulomb interaction between electrons, and the related problem of how to describe the electronic structure of molecules in bond-breaking geometries. At a fundamental level, both problems are still with us.

My first non-empirical VB calculations were made in the early 1950s, shortly after Slater’s claim that the “non-orthogonality difficulty” could be circumvented simply by orthogonalizing all the AOs at the outset. That was true, but led to the unfortunate result that the formally covalent structures showed no trace of chemical bonds; one had to admit all the ionic structures and perform a large CI calculation to restore the bonds. During a year at MIT (where they had an electronic computer!) I managed to get a decent account of the first few states of the benzene π-electron system (albeit with rough estimates of the many 2-electron integrals). Evidently ab initio VB calculations were feasible – but not easy. Perhaps it would be better to think about the direct calculation of the electron density? Husimi (in 1940), had invented a new concept – the Reduced Density Matrix (RDM) – as a tool for use in Statistical Mechanics. And it was clear that the energy of any N-electron system, with only 1- and 2-body interactions, could be expressed in terms of just two such densities, the 1-RDM and the 2-RDM. What Husimi had discovered was in fact beautifully general; the 2-RDM alone could give both the “electron density”– for a molecule in any geometry – and an energy that included the effects of electron correlation! But how could one calculate the RDMs without first knowing the wave function Ψ, a function of all particle coordinates? That was John Coleman’s famous “N-representability problem” – still awaiting solution.

Between that time and the present day, most quantum chemists spent their time either working with simple ‘semi-empirical’ models or (armed with ever more powerful computers) making rather accurate calculations on very small systems. Just a few concentrated on methodology, borrowing sophisticated techniques from Physics, notably many-body perturbation theory and

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propagator methods, which could sometimes be applied to small molecules with impressive results. It was all good fun! But many chemists saw it as a somewhat sterile exercise.

On reading the list of speakers in the Workshop, and the abstracts of their papers, it is clear how Quantum Chemistry has moved on: the more exciting challenges now range from nanotubes to large and exotic molecules.

I am happy to see the names of so many old friends and colleagues; and I wish all participants a stimulating and productive meeting.

Addendum Ruben Pauncz (a close friend for more than five decades) kindly sent me a copy of his "Preface" -- which had become a nice review of some of the main steps in the development of VB theory! I notice that he made no mention of the Chinese school, led by Professor Zhang, who made outstanding progress in the use of the symmetric group in VB theory. May I add a few words on their brilliant achievements?

Wei Wu (a participant at this meeting) was largely responsible for going beyond the "10electron barrier" (set by the exploding value of N! in fully ab initio classical VB calculations) by developing efficient algorithms for evaluating algebrants.

Another co-worker, Jiabo Li, extended the methodology and combined it with the Group Function approach in which an N-electron system is viewed as a collection of subsystems, containing only N1, N2, N3, ... electrons. Using his widely available program "VB2000" it is possible to perform fully-optimized ab initio computations on rather large molecules, even in bond-breaking geometries, provided no VB-subsystem contains more than about 15 electrons.

Astonishing progress has also been made in obtaininng feasible solutions of Coleman's Nrepresentabilty problem, thanks largely to the work of Carmela Valdemoro (another participant at this meeting), Nakatsuji, Mazziotti and others. It is now possible to perform high precision quantum chemical calculations WITHOUT WAVE FUNCTIONS!

So Quantum Chemistry is moving fast. And you are all just at the beginning.

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Schedule Saturday (23rd July) 9:00 09:30 – 10:00

Sunday (24th July) Chair

Check in

Chair

BARTLETT (PL-10)

Opening

10:00 – 10:30

KLEIN (PL-01)

Delgado-Barrio

CALZADO (PL-11)

Alonso 10:30 – 11:00

SHARMA (PL-02)

11:00 – 11:30

Coffee break

11:30 – 11:45

DELGADO-BARRIO (O-01)

11:45 – 12:00

CHERANOVSKII (PL-12) Coffee break DANOVICH (O-07)

GAO (O-02)

SHURKI (O-08)

Vázquez

Chana

12:00 – 12:30

CIRAC (PL-03)

HIBERTY (PL-13)

12:30 – 13:00

WU (PL-04)

PALDUS (PL-14)

13:00 – 14:30

Lunch

Lunch

14:30 – 14:45

BRAIDA (O-03)

HAVENITH (O-09)

14:45 – 15:00

PANAS (O-04)

ALONSO (O-10)

15:00 – 15:30

García-Bach

MICHL (PL-05)

Klein

MOREIRA (PL-15)

15:30 – 16:00

KAPLAN (PL-06)

PIECUCH (PL-16)

16:00 – 16:30

ORDEJON (PL-07)

VALDEMORO (PL-17)

16:30 – 17:00

Coffee break

17:00 – 17:15 17:15 – 17:30

Coffee break

RUEDENBERG (O-05)

COE (O-11)

LEPETIT (O-06)

DUKE (O-12)

Lago 17:30 – 18:00

NISHINO (PL-08)

18:00 – 18:30

SHAIK (PL-09)

18:30 – 19:00

Ruedenberg

ZAANEN (PL-19) MALRIEU (PL-20)

Poster session

19:00 – 19:30

21:00 – 23:30

VALENTI (PL-18)

Closing remarks (10’) Workshop banquet

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18




Program

19


20




Saturday (23rd July) 9:00

Check in

9:30

Opening Speaker

Title Chair: Alonso

10:00

Klein

PL-01

History of valence-bond theory

10:30

Sharma

PL-02

Spin-adapted DMRG and its application to transition metal chemistry

11:00

Coffee break Chair: Vázquez

11:30

Delgado-B

O-01

Potential energy surfaces and dynamics of small H2n+1 clusters

11:45

Gao

O-02

Multistate density functional theory (MSDFT) for chemical and biological applications

12:00

Cirac

PL-03

Tensor network approach to many-body quantum systems

12:30

Wu

PL-04

Ab initio computational methods for classical valence bond theory

13:00

Lunch Chair: García-Bach O-03

The Jastrow-VBSCF method : presentation, and application to (TCNE)22− anion dimer

Panas

O-04

Superatom representation of high-TC superconductivity

15:00

Michl

PL-05

Singlet fission

15:30

Kaplan

PL-06

Precise ab initio studies of the 3d transition-metal clusters:Mn2 and Sc2

16:00

Ordejón

PL-07

Electronic transport in chemically-modified graphene

14:30

Braida

14:45

16:30

Coffee break Chair: Lago

17:00

Ruedenberg O-05

A priori identification and deletion of configurational deadwood from fullvalence-space correlated wave functions

17:15

Lepetit

O-06

Computing the magneto-electric coupling between atoms with numerous open-shells to experimental accuracy: YMnO3

17:30

Nishino

PL-07

Absence of boundary effect under sine-square deformation

18:00

Shaik

PL-08

The valence bond way in bioinorganic chemistry

18:30

Poster session

21:30

Workshop banquet

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Sunday (24th July)

Speaker

Title Chair: Delgado-Barrio

09:30

Bartlett

PL-10

Does the Random Phase Approximation (RPA) help in describing strongly correlated systems?

10:00

Calzado

PL-11

Evaluation of magnetic terms in Cu4O4 cubane-like systems: A case study of polynuclear transition-metal systems

10:30

Cheranovskii PL-12

Magnetic properties of model Hamiltonians for some quasi-onedimensional transition metal compounds

11:00

Coffee break Chair: Chana

11:30

Danovich

O-07

Why the high spin states of the metal clusters are bound? The valence bond analyse of the no-pair bonding

11:45

Shurki

O-08

Hybrid ab initio Valence Bond / Molecular Mechanics (VB/MM), A new method for calculating biochemical Systems

12:00

Hiberty

PL-13

New concepts in chemical bonding. Charge-shift bonding and its manifestations in Chemistry

12:30

Paldus

PL-14

Symmetry breaking and strongly correlated systems

13:00

Lunch Chair: Klein

14:30

Havenith

O-09

The many-electron band structure approach: Theory and application

14:45

Alonso

O-10

Half-metallicity in finite single wall zigzag carbon nanotubes

15:00

Moreira

PL-15

Valence tautomerism in TiCl4-α-alkiloxyketone derived enolates: paradigmatic biradical intermediates for organic synthesis

15:30

Piecuch

PL-16

Recent advances in renormalized and active-space coupled-cluster methods

16:00

Valdemoro

PL-17

Combining the G-particle-hole hypervirial equation and the Hermitian operator method to study electronic excitations and de-excitations

16:30

Coffee break Chair: Ruedenberg

17:00

Coe

O-11

Investigating the extended Hubbard model as an approximation to the entanglement of a nanostructure system

17:15

Duke

O-12

The extended spin coupled method SC(n,m)

17:30

Valenti

PL-18

Multistep approach to microscopic models for frustated quantum magnets: The case of the natural mineral azurite

18:00

Zaanen

PL-19

Fermionic Quantum criticality and the AdS/CFT correspondence of string theory

18:30

Malrieu

PL-20

Scale changes in quantum chemistry: contraction and renormalization techniques

19:00

Closing remarks (10’)

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Posters P–01

Rashid

Resonance and Aromaticity. An Ab initio Valence Bond Approach

P–02

Dávalos

Anionic polymerization of Li2B12H12 and LiCB11H12: An experimental and computational study

P–03

Delgado-Barrio

Quantum Chemistry Calculations in Helium clusters doped with diatomic molecules

P–04

Eliav

Quantum chemical many-body approach based on QED - double Fock-space Coupled Cluster method

P–05

Garcia-Bach

Dimer-covering RVB treatment of single-walled zigzag carbon nanotubes

P–06

García-Fandiño

Methyl-Blocked α,γ-Peptide Nanotube Segments. A DFT study

P–07

García-Fandiño

Derivatized carbon nanotubes - interactions with membranes, water, and ions. A computational study.

P–08

Humbel

Mesomeric description, ab initio & Hückel derived approaches

P–09

Lago

Theoretical and experimental study of the parabanic acid molecule following VUV excitation and photodissociation

P–10

Lutz

Geometries and Adiabatic Excitation Energies of the Low-Lying States of CNC, C2N, N3, and NCO Studied with the Electron-Attached and Ionized Equation-ofMotion Coupled-Cluster Methodologies

P–11

Ruedenberg

P–12

Sauri

π-bonding and biradical character in the valence iso-electronic series O3, S3, SO2 and OS2 Parametrization of the Extended Hubbard Model for hydrocarbons derived from RASPT2 potential energy curves of stretched ethene

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Abstracts of Plenary communications

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PL-01

Valence-Bond Theory D. J. Klein Texas A&M University at Galveston, Galveston, Texas 77553-1675, USA [email protected]

Abstract The chemical history of valence-bond (VB) theory traces from the valencepatterns of Crum Brown around 1864 through the work of Lewis & Langmuir around 1916-1918 to W. Heitler & F. London in the mid-1920s, who obtained a quantitative description of localized chemical valence. The delocalized case was addressed early on around 1870 for benzene by A. Kekule, with embellishments by several others, on to G. Rumer’s quantum mechanical systematization for conjugated carbon pi-networks as more completely considered by L. Pauling & G. W. Wheland, in the mid-1930s. Thereafter there appeared many VB works by many quantum chemists, including C. Mullen, Vroelant, W. T. Simpson, C. A. Coulson, L. J. Oosterhoff, N. D. Epiotis, J. P. Malrieu, & S. Shaik on the semiempirical side, then F. A. Matsen, W. A. Goddard, J. Gerrat, M. Raimondi, D. Cooper, J. P. Malrieu, & R. McWeeny on the ab initio side. And in fact, especially more recently there have been many contributors (including us in Texas). Much focus has been on “small” molecules (of say up to a few dozen atoms) with a good portion of the work being ab initio, but also a certain amount has been on conceptual interpretations & frameworks, with even some notable many-body work. As the quantitative VB approach entailed explicit spin-coupling, the field overlapped with the idea of configuration-interaction-type computations amongst spin configurations. Such “correlated-electron” schemes (often utilizing irreducible representation theory for the symmetric or unitary groups) then were developed by T. Yamanouchi, M. Kotani, F. A. Matsen, I. G. Kaplan, R. McWeeny, K. Ruedenberg, J. Paldus, I. Shavitt, R. Pauncz, & many others, with ultimate implementation in quantitative computations, but often with difficult classical chemical interpretation. An often very accurate related many-body “density-matrix renormalization group” scheme was developed in the physics literature, by S. R. White. The independently begun semiempirical branch in physics occurred, starting with the Heisenberg spin Hamiltonian in the late 1920s, focusing on the many-body case (allowing unbounded numbers of electrons). Though typically first treated via mean-field approximations, there also was some special-case rigorous work by H. Bethe & L. Hulthen, and more extensively later by E. H. Lieb & a host of others. A few iconoclastic physicists studied resonating VB theory (including M. A. Garcia-Bach & M. Suzuki). But the focus of physicists on systems with application of resonating VB ideas was decisively instigated in 1986 by P. W. Anderson, with a motivation to understand hightemperature superconductivity. A huge number of theoretical works appeared, though no generally accepted view for high-temperature superconductors easily emerged. Here the case with differeing numbers of resonating electrons & sites on which they are localized is of great interest. Ultimately in physics much focus turned to understanding the relevances of “novel” resonating VB ideas for general many-body systems.

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PL-02 Spin-adapted DMRG and its application to transition metal chemistry Sandeep Sharma, Garnet Kin-Lic Chan Department of Chemistry and Chemical Biology, Cornell University, Ithaca NY14853 email: [email protected]

In this talk we will describe the implementation of spin-adapted DMRG along the lines suggested by McCulloch et al.[1] It is seen that the use of spin-adaptation improves efficiency, and for singlet states one often needs only half the number of renormalised states to achieve the same accuracy as with the non-spin adapted DMRG. This roughly corresponds to an order of magnitude improvement in the performance of DMRG. Various research groups [2–4] have started targeting transition metal chemistry as a potential application of DMRG. First row transition metal atoms contain five 3d orbitals which typically need to be included in the active space for a balanced treatment of the electronic structure. In addition often the p orbitals from the ligand atoms should be included in the active space as well. Even for very small molecules these requirements yield an active space which is beyond the scope of conventional CASCI techniques. In the past it has been demonstrated that DMRG can target large active spaces of around 30 orbitals [4] and can give a tight upperbound to the FCI energy. The energy obtained by DMRG is often within chemical accuracy (1 kcal/mol) of the FCI energy. In this work we aim to perform such large scale calculations with our state of the art implementation of spin-adapted DMRG that is efficiently parallelized. For these benchmark calculations we will examine the properties of iron sulphur clusters, specifically Fe2 S2 and Fe4 S4 .

[1] I. P. McCulloch and M. Gulacsi, Europhys. Lett. 57, 852 (2002). [2] G. Moritz, B. A. Hess, and M. Reiher, J. Chem. Phys. 122, 024107 (2005). [3] K. H. Marti, I. M. Ond´ık, G. Moritz, and M. Reiher, J. Chem. Phys. 128, 014104 (2008). [4] Y.Kurashige and T. Yanai, J. Chem. Phys. 130, 234114 (2009).

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PL-03 Tensor network approach to many-body quantum systems J. Ignacio Cirac Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany [email protected]

Tensor networks can be used to describe many-body quantum systems undergoing short-range interactions in thermal equilibrium. In this talk I will introduce some of the most popular tensor network states, among them the matrix product and projected entangled-pair states, and show how they can be used to determine different physical properties of strongly interacting systems in lattices. I will illustrate the methods with some time-dependent calculations simulating ultracold fermions in optical lattices.

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PL-04

Ab initio Computational Methods for Classical Valence Bond Theory Wei Wu The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China,

In this talk, we would report some recent advances in the methodology developments of valence bond theory. This talk will focus on the ab initio VB methods that are based on classical VB theory, which deal with purely localized orbitals and explicit consideration of covalent and ionic structures. Post-VBSCF methods, valence bond configuration interaction method (VBCI) and the valence bond second order perturbation method (VBPT2), will be reported in this talk. In the VBCI method, the VBSCF energy and wave function are improved by configuration interaction (CI). On the other hand, VBPT2 uses perturbation theory, taking the VBSCF wave function as the zeroth order reference. Furthermore, VB approaches for solvent effect were developed in the last few years, including VBPCM, VBSM, and VBEFP methods, which will be reviewed in the talk.

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PL-05 Singlet Fission Josef Michl Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Prague, Czech Republic, and Department of Chemistry and Biochemistry, University of Colorado, Boulder, CO, USA e-mail: [email protected]

Singlet fission is a process in which a singlet excited chromophore shares its energy with a neighboring chromophore to produce a state in which both are excited to their triplet state, and can be viewed as the inverse of triplet-triplet annihilation. It is of interest because in principle, its use would permit the maximum theoretical efficiency of a solar cell to rise from the Shockley-Queisser limit of ~1/3 to ~1/2. Although several materials are known to undergo singlet fission, the quantum yield of triplet formation rarely exceeds a few per cent. The question we ask is "how can one design molecular structures that will produce triplet yields close to 200% and allow the triplets to act independently in order to ultimately produce a 200% yield of electron-hole pairs?".

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PL-06 Precise ab initio studies of the 3d transition-metal clusters: Mn2 and Sc2 Ilya G. Kaplan Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apdo. Postal 70-360, 04510, México D.F., México The problem of calculation of the electronic structure of transition-metal clusters still presents a challenge for computational chemistry. The reason is that the expansion of the ground state wave function on electronic configurations does not contain a principal configuration and a large number of reference configurations must be treated equally. Thus the multi-reference (MR) approaches are, in general, mandatory. A large number of Mn2 calculations were performed by the DFT method. In the most of studies the ferromagnetic ground state was predicted, with S = 5, while experiment and ab initio multireference calculations predict the antiferromagnetic ground state with S = 0. There are two reasons for this contradiction: 1. The 3d clusters should be treated by the multireference methods, although the DFT method is a single reference and what is more, it is a single-determinant approach. 2) As was proved in Ref. 1, the electron density of an arbitrary N-electron system is invariant with respect of the total spin S; hence the conventional Kohn-Sham equations are the same for all values of S, while the spin-multiplet procedures developed in DFT used correlation functionals not corresponding to S. According to our studies of Mn2 [2] by the MR CISD(+Q)/ aug-cc-pVQZ and ACPF approaches, the ground state being the singlet , X 1Σg+ , with the binding energy De = 1.7 kcal/mol (0.07 eV) and Re = 3.6 A. It was proved that the binding in the Mn2 dimer is of the van der Waals type. The calculation of Sc2 at the MR CISD(+Q)/cc-pV5Z level, showed that the its ground state corresponds to a quintet,

5

Σu− , with

an agreement with experiment and previous precise calculations. The triplet 3Σ u state is located about 1.1 kcal/mol above [3]. −

The ground state, X Σ u , of the Sc2 dimer was calculated by the MRCISD(+Q) method at the 5

complete basis set (CBS) limit [4]. This is the first MRCISD(+Q) calculation of 3d transition-metal clusters at the CBS limit. The employment of the C2v symmetry group, allowed us to obtain the Sc atoms in different states at the dissociation limit. From the Mulliken population analysis and comparison with atomic energies follows that in the ground state Sc2 dissociates on one Sc in the ground state and the other in the second excited quartet state, 4Fu. The spectroscopic parameters of the ground potential curve, obtained by the Dunham analysis at the valence MRCISD(+Q)/CBS level, are: Re = 5.20 bohr, De = 50.37 kcal/mol, and ωe = 234.5 cm-1. The obtained value for the harmonic frequency agrees very well with the experimental one, ωe = 239.9 cm-1. The dissociation energy with reference to the dissociation on two Sc in the ground states was estimated as De = 9.98 kcal/mol. In contrast with many other studied transitionmetal dimers, which are attributed to the van der Waals bonded molecules, the Sc2 dimer is stabilized by the covalent bonding on the hybrid atomic orbitals. 1. I.G. Kaplan, J. Mol. Struct. 838, 39 (2007); Int. J. Quant. Chem. 107, 2595 (2007). 2. D. Tzeli, U. Miranda, I.G. Kaplan, and A. Mavridis, J. Chem. Phys. 129, 154310 (2008). 3. A. Kalemos, I.G. Kaplan, and A. Mavridis, J. Chem. Phys. 132, 024309 (2010). 4. U. Miranda and I.G. Kaplan. Eur. Phys. J. D (2011); DOI: 10 1140/epjd/e2010-10607-y.

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PL-07 Electronic transport in chemically-modified graphene N. Leconte1, D. Soriano2, J.J. Palacios3, P. Ordejón4, J.-C. Charlier1 and S. Roche5,6 1 Université Catholique de Louvain, Belgium 2 Departamento de Física Aplicada, Universidad de Alicante, Spain 3 Universidad Autónoma de Madrid, Cantoblanco, Madrid 28049, Spain 4 Centre d'Investigació en Nanociència i Nanotecnologia - CIN2 (CSIC-ICN), Bacelona, Spain 5 CIN2 (ICN-CSIC) and UAB, Catalan Institute of Nanotechnology, Spain 6 ICREA, Institucio Catalana de Recerca i Estudis Avançats, Barcelona, Spain e-mail: [email protected]

Graphene is a new material which holds the promise of revolutionizing technology areas such as electronics, due to its amazing properties. A large amount of activity is now being devoted to determining the effect of chemical functionalization of graphene on its electronic transport properties. The use of first-principles (ab-initio) methods is not straightforward to tackle these problems, since the relevant sizes involved in transport in graphene devices are much larger than those that ab-initio methods can reach. In this talk, I will describe how we are dealing with this problem, by using Density Functional Theory (DFT) calculations to build accurate effective Tight Binding models. These TB models are then used to compute the transport properties in mesoscopic samples by means of an efficient Kubo formulation based on wave packet evolution. In this talk, I will present the results of applying such an approach to graphene functionalized with oxygen and hydrogen. In the first case, we find that a metal-insulator transition can be driven as a function of the concentration of oxygen impurities, explaining recent experimental data [1]. For the case of hydrogen, we have found that the electronic transportis closely linked with the magnetic ordering induced by the presence of hydrogen. In particular, it should possible to obtain measurable magnetoresistance signals by applying a sufficiently largemagnetic field [2], which would pinpoint the presence of localized spins in H-functionalized graphene.Such effects are due to electron correlations in graphene, which translate into magnetic order and distinct transport properties of the different magnetic phases [3]. [1] N. Leconte, J. Moser, P. Ordejon, H. Tao, A. Lherbier, A. Bachtold, F. Alsina, C.M. Sotomayor Torres, J.-C. Charlier, and S. Roche, ACS Nano 4, 7, 4033-4038 (2010) [2] D. Soriano, N. Leconte, P. Ordejon, J.-C. Charlier, J. J. Palacios and S. Roche, Phys. Rev. Lett. (in press) [3] N. Leconte, D. Soriano, S. Roche, P. Ordejon, J.-C. Charlier and J.J. Palacios, ACS Nano (in press)

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PL-08 Absence of Boundary Effect under Sine-Square Deformation Tomotoshi Nishino1, Y. Lee1, Andrej Gendiar2, M. Daniska2 and Toshiya Hikihara3 1 Kobe University, Kobe 657-8501, Japan 2 Slovak Academy of Sciences, SK841-04 Bratislava, Slovakia 3 Gunma University, Gunma 371-8510, Japan e-mail: [email protected].

We consider Fermionic lattice models in one-dimension. When open-boundary conditions are imposed for a finite chain, observables such as particle density and bond energy shows boundary fluctuation. Such effects can be suppressed by the introduction of `smooth boundary conditions’, which is realized by reducing energy scale near the system boundary. We report that a special functional form [sin(j /N)] 2, where j (0 < j < N) represents the lattice index and N the system size, for the position dependent energy scale COMPLETELY remove all the boundary effects from the ground state of free Fermionic systems [1]. In other words, both ends of the system are effectively connected, although those boundary sites are most far apart [2]. The suppression of boundary effect works fairly well even when there are interactions between Fermions, as we will see for the case of (extended) Hubbard model. Geometrical origin of this good reduction of boundary effects would be discussed, based on the system size dependence of the entanglement entropy [2,3].

from Ref.[3]: Nearest neighbour correlation function of the ground-state of the N=1000-site spinless hopping model, when the bond strength is proportional to [sin(j /N)] m. Since the system is gapless, there is large boundary effect if the interaction is uniform (m=0). Sinusoidal deformation (m=1) reduce the effect somehow, and when m=2 the reduction is perfect. For m > 2, again small boundary effect appears. [1] A. Gendiar, R. Krcmar, T. Nishino, Prog. Theor. Phys. 112 (2009) 953-967; arXiv: 0810.0622. [2] T. Hikihara, T. Nishino, Phys. Rev. E83 (2011) 060414; arXiv: 1012.0472. [3] A. Gendiar, M. Daniska, Y. Lee, T. Nishino; arXiv: 1012.1472. [4] Quite recently an analytic proof is given for free Fermionic case: H. Katsura, arXiv:1104.1721.

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PL-09 The Valence Bond Way in Bioinorganic Chemistry S. Shaik1 1 The Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry The Hebrew University of Jerusalem, Givat-Ram Campus, Jerusalme 91904, Israel [email protected].

Valence Bond (VB) theory can create a great deal of order in Chemistry [1]. In this talk I will show its application to bioinorgnic chemisry of iron enzymes. Potentially, if time permits, I may cover the following two stories: (a) The story of the oxy complexes of Myoglobin and Hemoglobin (Mb.O2; Hb.O2), which were “discovered” about 333 years ago, and their bonding features, which were outlined first in 1936, remain disputed for 75 years. We shall see how VB theory resolves the dispute by transforming the CASSCF/MM wave function to a VB/MM wave function, which shows clearly the bonding mechanism of O2 to the ferrous heme complex [2]. (b) The second story concerns the reactivity of the iron-oxo species of Cytochrome P450 in Habstraction, sulfoxidation, and aromatic hydroxylation, and how VB theory creates order and makes predictions in this complex field [3,4]. It will be argued that VB theory and VB reading of the wave function is a productive future paradigm in the field. [1] (a) S. Shaik, Phys. Chem. Chem. Phys. 12 (2010) 8706-8720. (b) S. Shaik, P.C. Hiberty, A Primer on Qualitative Valence Bond Theory: A Theory Coming of Age, Wiley Interdisciplinary Reviews Computational Science, 1 (2011) 18-29. (c) S. Shaik, P.C. Hiberty, A Chemist’s Guide to Valence Bond Theory. Wiley Interscience, New York, 2008. [2] H. Chen, M. Ikeda-Saito, S. Shaik, J. Am. Chem. Soc., 130 (2008) 14778-14790. [3] S. Shaik, W.Z. Lai, H. Chen, Y. Wang, Acc. Chem. Res. 43 (2010) 1154-1165. [4] P. Milko, P. Schyman, U. Dandamundi, H. Chen, S. Shaik, J. Chem. Theory Comput. 7 (2011) 327-339.

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PL-10 Does the Random Phase Approximation (RPA) help in describing strongly correlated systems? Rodney J. Bartlett, Prakash Verma, Ajith Perera, Victor Lotrich Quantum Theory Project, University of Florida, Gainesville, FL 32611-8435, USA [email protected]

We present some studies of RPA as a special case of coupled-cluster theory for some bond breaking systems and others that show strong correlation. RPA in its direct ring form offers a way to better describe the Coulomb perturbation, permitting other effects like exchange and single excitations to be introduced more approximately. This talk will address some of the benefits this 'Coulomb attenuation' can introduce.

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PL-11 Evaluation of magnetic terms in Cu4O4 cubane-like systems: a case study of polynuclear transition-metal systems Carmen J. Calzado1 and Daniel Maynau2 1 Departamento de Química Física. Universidad de Sevilla. Spain. 2 Laboratoire de Chimie et Physique Quantiques. IRSAMC. Université de Toulouse. France e-mail: [email protected]

In this contribution we present some results concerning the evaluation of magnetic terms in Cu4O4 cubane-like systems from truncated CI calculations, as a case study of transition-metal polynuclear complexes [1]. These systems represent a real challenge both from experimental and theoretical points of view. The presence of several active magnetic centres on the molecule introduces a large number of magnetic interactions, involving not only two neighbour sites but also three or four centres at the same time. In most of the systems, too simplified models have been used to analyse the experimental data, which provide fitting of acceptable quality, but hiding in some cases the physics of the problem. Also, as a consequence of the use of oversimplified model Hamiltonians, the resulting magnetic parameters are affected by a larger uncertainty than in the case of binuclear systems. In this context, an unbiased and simultaneous evaluation of all the interactions would be welcome. However, the theoretical evaluation of the magnetic constants in these systems also faces several difficulties: (i) a large number of unpaired electrons, giving a manifold of quasidegenerate low-lying states, with a remarkable multireferential character, (ii) the presence of extended ligands, which represents an additional and not negligible computational cost. To overcome these difficulties we employ a new selectedconfiguration interaction method EXSCI [2,3] based on the use of local orbitals. Taking advantage of the locality and then of the fact that interactions vanish when the distance is large, the dimension of the CI is largely reduced. Once the eigenvalues and eigenvectors of the low-lying magnetic states have been evaluated, the amplitudes of the magnetic parameters are extracted by using the effective Hamiltonian theory [4,5]. The nature and amplitude of all the computed interactions agree with the relative orientation of the magnetic orbitals in the molecule, and correctly reproduce the susceptibility versus temperature curve, although some of them contrast with the values provided by the fittings. The results put in evidence the drawbacks of the fitting based on oversimplified magnetic models and the role that an efficient computational strategy can play in the interpretation of the magnetic data and the validation of the magnetic interaction model. [1] C.J. Calzado and D.Maynau, Dalton Trans. submitted [2] B. Bories, D. Maynau and M.L. Bonet J. Comp. Chem. 2007, 28, 632 [3] N. Ben Amor and D. Maynau, J. Chem. Phys. 2011 in press. [4] C. J. Calzado and J.P. Malrieu, Phys. Rev. B 2001, 63, 214520; Eur. Phys. J. B 2001, 21, 375; Phys. Rev. B 2004, 69, 0944351. [5] C. J. Calzado, C. de Graaf, E. Bordas, R. Caballol, and J. P. Malrieu. Phys. Rev. B 2003, 67, 132409.

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PL-12 MAGNETIC PROPERTIES OF MODEL HAMILTONIANS FOR SOME QUASIONE-DIMENSIONAL TRANSITION METAL COMPOUNDS V.O.Cheranovskii, E.V.Ezerskaya Karazin Kharkov National University [email protected]

We report the results of our analytical and numerical study of three different one-dimensional strongly correlated lattice models describing magnetic properties of some transition metal compounds. These are decorated mixed-spin tube, anisotropic spin delta-chain, and t-J model for the lattices like necklace ladder and diamond chain. First model is a tubular 1D spin systems formed by folding of stripe fragments of a decorated rectangular spin lattice and can be treated as a spin model of “ferromagnetic” nanotube [1]. In order to study the energy spectrum and magnetic properties of the model we use perturbation theory, spin-wave approximation with first order perturbative corrections (SWA) and exact diagonalization method. In particular, for tubes formed by weakly interacted cyclic fragments we show the existence of gapless excitations with decreasing total spin and gapped excitations [2]. This leads to an intermediate plateau in field dependence of tube magnetization. Our study demonstrates high accuracy of SWA estimations for bipartite spin systems and the possibility of quantum phase transitions mediated by frustrated interactions and/or spin anisotropy. For infinite Heisenberg-Ising analog of the decorated tubes we also show the existence of first order quantum phase transitions with macroscopic jump of magnetization mediated by next nearest neighbor coupling in cyclic fragments of the tubes of small diameters. By transfer matrix approach we show numerically that these frustrated interactions may lead to the occurrence of an additional plateau in field dependence of magnetization at low temperatures. Second model is highly frustrated spin system – delta-chain describing magnetic structure of delafossite YCuO2.5 and olivines ZnL2S4 (L=Er, Tm, Yb). For finite and infinite delta chains with XY coupling in the main chain and different Ising couplings in triangles we obtain analytical solutions for the part of exact energy spectrum. On the base of exact diagonalization study and the results from the density matrix renormalization group method (DMRG) we demonstrate strong dependence of the ground state spin structure on coupling parameters. The existence of intermediate magnetization plateau in lowtemperature field dependence of magnetization is shown numerically. Third model is applied to study of the effect of doping on the magnetic energy spectrum of 1D magnets like IPA2CuCL4 (IPA- isopropylammonium) and azurite. On the base of cyclic spin permutation formalism we derive effective low-energy VB Hamiltonians for the lattice formed by weakly interacted unit cells. Numerical calculations demonstrate the absence of magnetic polarons in contrast to rectangular lattice having the same three-site unit cell. For t-J model with one hole in halffilled band we derive effective pure spin Hamiltonian of non-Heisenberg type, which corresponds the exact separation of charge and spin variables. The analytical treatment of this problem for one inverted spin is also given. The exact diagonalization study of finite cyclic systems shows non-monotonic behavior of the model ground state spin as a function of coupling parameter J. [1] V.O. Cheranovskii, E. V. Ezerskaya, Acta Phys. Pol. A. 118 (2010) 946-947. [2] V.O. Cheranovskii, E.V. Ezerskaya, D.J. Klein, A.A. Kravchenko, J. Magn. Magn. Mater. 323 (2011) .1636-1642.

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PL-13 New Concepts in Chemical Bonding. Charge-Shift Bonding and its Manifestations in Chemistry P. C. Hiberty1, S. Shaik2, W. Wu3, B. Silvi4 1 Université de Paris-Sud, Laboratoire de Chimie Physique, UMR CNRS 8000, 91405 Orsay Cédex, France 2 Institute of Chemistry and The Lise Mienter-Minerva Center for Computational Quantum Chemistry, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel 3 State Key Laboratory of Physical Chemistry of Solid Surfaces and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China 4 Laboratoire de Chimie Théorique, UMR CNRS 7616, Université de Paris-6, 4 Place Jussieu, 75252 Paris Cédex, France [email protected]

Valence bond (VB) theory, electron-localization function (ELF) and Atoms-in-Molecules (AIM) calculations of various single bonds demonstrate that along the two classical bond families of covalent and ionic bonds, there exists a class of charge-shift bonds (CS-bonds) in which the fluctuation of the electron pair density plays a dominant role. In VB theory, CS-bonding manifests by large covalent-ionic resonance energy, RECS, and in ELF by a depleted basin population with large variances (fluctuations) [1]. CS-bonding can also be probed by AIM theory. This type of bond can be found in homopolar as well as heteropolar bonds. Atoms that are prone to CS-bonding are compact electronegative and/or electron rich species. An extreme case is the single bond in difluorine, where the purely covalent wave function is repulsive at all distances, while the stability of the molecule is entirely due to covalent-ionic resonance. The difference between covalent and charge-shift bonds, in terms of ELF picture, is illustrated with the examples of ethane and F2 below. C-H bond

C-C covalent bond

Lone pair

F-F charge-shift bond

The CS character of such bonds have some experimental consequences, among which the strange stabilities of some cage compounds like the family of propellanes, which display rather strong bonds between “inverted” carbons despite their pyramidalization in the “wrong” direction [2]. Another experimental consequence, the rarity of silicenium ions in condensed phases [3], will be addressed if there is some time left.

C

C–C chargeshift bond C

C C

C

[1.1.1] propellane

[1] S. Shaik, D. Danovich, B. Silvi, D. Lauvergnat, P.C. Hiberty, Chem. Eur. J. 2005, 11, 658 [2] S. Shaik, D. Danovich, W. Wu, P. C. Hiberty, Nature Chem. 2009, 1, 443. [3] P. Su, L. Song, W. Wu, S. Shaik, P. C. Hiberty, J. Phys. Chem. A 2008, 112, 2988.

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PL-14 Symmetry breaking and strongly correlated systems Josef Paldus, Xiangzhu Li, and Gabriela Thiamová Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada e-mail: [email protected]

We shall address the phenomenon of a spontaneous symmetry breaking (SSB) at both semiempirical and ab initio levels of approximation. In the former case we rely on our earlier work on the singlet stability of the symmetryadapted, restricted Hartree-Fock (RHF) solutions and the implied symmetry breaking in the strongly correlated limit of various planar π-electron systems as described by the Pariser-Parr-Pople Hamiltonian. The occurrence of singlet instabilities implies the appearance of charge density waves (CDWs) or Wigner crystallization. Specifically, we shall report on a recent work addressing the phenomenon that can be referred to as an approximate or implied symmetry breaking that occurs even in the absence of a spatial symmetry of the system [1,2], by exploring various real and hypothetical structures resulting by a systematic deformation of the nuclear framework of cyclic polyenes. Next we will address the SSB in ab initio models of various homonuclear diatomics and symmetric triatomics of the ABA type [3–9] at both the HF and post-HF levels of approximation. In the case of homonuclear diatomics such RHF instabilities are primarily encountered at nonequilibrium geometries and play an important role when generating realistic potential energy curves (PECs). In the case of ABA-type triatomics we shall see that the SSB of the RHF reference can propagate to the post-HF correlated level and may indeed imply broken-symmetry equilibrium geometry. The role of the symmetry breaking of the RHF or UHF reference at the correlated level will also be pointed out. Time permitting, a brief mention will be made concerning the SSB phenomena in quantum dots. [1] J. Paldus, G. Thiamová, J. Math. Chem. 44 (2008) 44-120. [2] G. Thiamová, J. Paldus, Eur. Phys. J. D 46 (2008) 453-461. [3] X. Li, J. Paldus, J. Chem. Phys. 126 (2007) 224304[1-7]. [4] X. Li, J. Paldus, Int. J. Quantum Chem. 108 (2008) 2117–2127. [5] X. Li, J. Paldus, Int. J. Quantum Chem. 109 (2009) 1756–1765. [6] X. Li, J. Paldus, J. Chem. Phys. 130 (2009) 084110[1-9]. [7] X. Li, J. Paldus, Phys. Chem. Chem. Phys. 11 (2009) 5281–5289. [8] X. Li, J. Paldus, J. Chem. Phys. 130 (2009) 164116[1-12]. [9] X. Li, J. Paldus, J. Chem. Phys. 134 (2011) 074301[1-10].

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PL-15 Valence tautomerism in TiCl4-α-alkiloxyketone derived enolates: paradigmatic biradical intermediates for organic synthesis Ibério de P. R. Moreira1, Josep Maria Bofill2 and Josep Maria Anglada3 Departament de Química Física, Universitat de Barcelona, c/ Martí i Franquès 1, 08028 Barcelona, Spain 2 Departament de Química Orgànica, Universitat de Barcelona, c/ Martí i Franquès 1, 08028 Barcelona, Spain 3 Institut de Investigacions Químiques i Ambientals de Barcelona, Consejo Superior de Investigaciones Científicas (CSIC), Jordi Girona Salgado 18-26, 08034 Barcelona, Spain e-mail: [email protected]. 1

Aldolic reactions are essential chemical processes in organic and bioorganic synthesis of polyacetals, polyketides and polyethers. These compounds are precursors of many different natural products, antibiotics and metabolic intermediates [1,2]. Metal enolates derived from TiCl4 complexes have become important intermediates for aldol additions due to the high stereoselectivity control and yield of the processes, their chemical versatility to incorporate additional ligands, inexpensive precursors (TiCl4) and easy and clean elimination of the metal by simple hydrolysis (TiO2) when the aldolic addition is completed [3]. The general process of formation of titanium enolates is depicted in Fig. 1. In this process a TiCl4-carbonyl pre-complex is formed to increase the acidity of an H atom in α position. This H atom can be eliminated by a base (e.g. a ternary amine) to produce the titanium enolate. O

O

TiCl4

TiCl4

R

R

O

Base

TiCl4

+

R

Base-H

Fig. 1 A theoretical study combined with NMR and EPR experiments on titanate enolates derived from TiCl4/α-alkoxyketone complexes have univocally demonstrated that these intermediates posses biradical character [4]. The existence of the biradical titanium enolates has been explained by the existence of a valence tautomerism involving the tetrachlorotitanate(IV) enolate and the tetrachlorotitanate(III) α-carbonyl radical pair shown in Fig. 2. Cl4 Ph

Cl4

Ti O O

Ti O Ph

O

Fig. 2 From the theoretical point of view, the CASSCF(8,10) and MRCI description of the biradical enolate depicted in Fig. 2 corresponds to a Ti(III) complex with an unpaired electron on a d orbital of the Ti atom and the other unpaired electron is delocalized on the tricentric π system of the terminal O-C-C group (3 electrons in 3 pz orbitals). The topology of the natural orbitals of the biradical electronic state can be assigned to an allylic-like π-system (π1, π2, and π3 orbitals) combined with the Ti d orbital, (Ti(d)). The π1 and π3 orbitals are clearly identified because they

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involve the bonding and antibonding combinations of the allyl-like π-system. However, the π2 orbital (nonbonding in the allyl-like π-system) is mixed with the Ti(d) orbital. The orbitals, π2 + Ti(d) and π2 - Ti(d) with occupations of 1.14 and 0.86, fulfil the biradical structure. It is also shown that the description of the biradical character of this kind of titanium enolates requires a careful treatment of static electronic correlation by using a CASSCF wave function using a CAS(4,4) as the minimal active space, and including the dynamic correlation by means of extended multireference CI wavefunctions. DFT based approaches or inclusion of correlation effects by means of perturbation treatments such as CASPT2 incorrectly describe the ground state of system as a closed shell, 40 kcal/mol below the open shell state. The origin of the overstabilization of the closed shell solution can be attributed to the inherent pair excitation structure of the correlation terms considered in these approaches. The existence of this kind of biradical titanium enolates through the valence tautomerism described above has been invoked to explain other important highly stereoselective reactions such as aldol condensations [5] or haloalkylations [6] by the increased reactivity of the biradical tautomer. Similarly, the present results suggest that organometallic analogues of the electrochemically activated radicals proposed by MacMillan and co-workers [7,8] can be produced by a similar valence tautomerism of appropriate titanium enolates. In this presentation we discuss the theoretical model for the valence tautomerism shown in Fig. 2 that explain the experimental detection of a biradical titanium enolate [6], the relevance of static and dynamic correlation effects to correctly describe the biradical pair in the valence tautomerism, and the shortcomings found by standard DFT and CASPT2 methods to describe the experimentally observed biradical complexes. Finally, we explore possible extensions of the theoretical model of a valence tautomerism in a system consisting of a metal center (TiCl4) coupled with an allylic-like π-system (carbonyl, O-C-C) to other allylic-like groups such as the imino ((H)N=C-C) or the thiocarbonyl (S-C-C) or different metal complexes (Cu, V or Ru) [7].

[1] R. Mahrwald (Ed.), Modern Aldol Reactions, Vols. I and II, Wiley-VCH, Weinheim, 2004. [2] B. Schetter and R. Mahrwald, Angew. Chem. Int. Ed. 45 (2006) 7506. [3] J.G. Solsona, P. Romea, F. Urpí and J. Vilarasa, Org. Lett. 5 (2003) 519. [4] I. de P. R. Moreira, J. M. Bofill, J. M. Anglada, J. G. Solsona, J. Nebot, P. Romea, and F. Urpí, J. Am. Chem. Soc. 130 (2008) 3242-3243. [5] R. Spaccini, N. Pastori, A. Clerici, C. Punta, and O. Porta, J. Am. Chem. Soc. 130 (2008) 3242-3243. [6] S. Beaumont, E. A. Ilardi, L. R. Monroe, and A. Zakarian, J. Am. Chem. Soc. 132 (2010) 1482-1483. [7] H. Jang, J. Hong and D. W. C. MacMillan, J. Am. Chem. Soc. 129 (2007) 7004-7005. [8] D. W. C. MacMillan, Nature 455 (2008) 304-308. [9] I. de P. R. Moreira, J. M. Bofill and J. M. Anglada, to be submitted.

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PL-16 Recent Advances in Renormalized and Active-Space Coupled-Cluster Methods Piotr Piecuch1, Wei Li1,2, Jun Shen1, Jeffrey R. Gour1,3, Jesse J. Lutz1, Marta Włoch4 1 Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA 2 School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, Jiangsu 210093, China 3 Department of Chemistry, Stanford University, Stanford, California 94305, USA 4 Department of Chemistry, Michigan Technological University, Houghton, Michigan 49931, USA e-mail: [email protected]

The widely used coupled-cluster (CC) and equation-of-motion (EOM) CC methods, such as CCSD(T) and EOMCCSD, have difficulties with capturing stronger non-dynamic electron correlations characterizing chemical reaction pathways and excited states dominated by twoelectron transitions that can often be addressed by exploiting the completely renormalized (CR) and active-space CC and EOMCC approaches. This talk will discuss recent advances in the development and applications of the CR and active-space CC/EOMCC methods, including the extension of the former approaches to larger reactive molecular systems via the local correlation cluster-in-molecule ansatz and its multi-level extension, and the possibility of merging the CR and active-space methodologies into a single mathematical formalism that leads to further improvements of the results for potential energy surfaces along bond breaking coordinates. The latter idea requires the generalization of the moment energy expansions that are behind the CR-CC methods to non-traditional truncations of the cluster operator and related excitation manifolds.

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PL-17 Combining the G-particle-hole Hypervirial equation and the Hermitian Operator method to study electronic excitations and de-excitations

C. Valdemoro1 , D. R. Alcoba2 , O. B. O˜ na2 , L. M. Tel3 ,E. P´ erez-Romero3 1

Instituto de F´ısica Fundamental,

Consejo Superior de Investigaciones Cient´ıficas, Serrano 123, 28006 Madrid, Spain 2

Departamento de F´ısica, Universidad de Buenos Aires, Buenos Aires, Argentina

3

Departamento de Qu´ımica F´ısica, Universidad de Salamanca,

37008 Salamanca, Spain

The 2-order G-particle-hole hypervirial (GHV) is the most recent member of the family of 2-order Contracted equations. In the GHV method one does not look for an N-electron function but for a 2-order G-particle-hole matrix which is a 2-electron quantum average of the Electronic Correlation of the N-electron state considered. An overview of the contracted equations theory leading to the (GHV) is given in the first part of this talk. The suitability of combining the GHV method with the Hermitian Operator (HO) method for obtaining various energy differences of a system spectrum is then shown. This theoretical part is complemented with the results obtained in a series of calculations. The present status and lines of future development are discussed.

Some References 1.- H. Nakatsuji, Phys. Rev. A 14 (1976) 41. L. Cohen and C. Frishberg, Phys. Rev. A 13 (1976) 927. 2.- C. Valdemoro, Phys. Rev. A 31, 2123 (1985). 3.- M. Bouten, P. Van Leuven, M. V. Mihailovich and M. Rosina, Nucl. Phys. A 202 (1973) 127, 221 (1974) 173. 4.- D. R. Alcoba, C. Valdemoro, L. M. Tel, E. P´erez-Romero and O. O˜ na, J. Math. Chem. xxx (2011) xxxx. (DOI: 10.1007/s10910-011-9810-y).

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PL-18

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PL-19 Fermionic Quantum criticality and the AdS/CFT correspondence of string theory. Jan Zaanen Instituut Lorentz for Theoretical Physics, Leiden University, The Netherlands

The central mystery in quantum matter is the general nature of matter formed from fermions. The methods of many body quantum physics fail and one can only rely on the phenomenological Fermi-liquid and BCS theories. However, in heavy fermion systems and cuprates one deals with non Fermi-liquid quantum critical metals, and to understand their superconductivity one needs to understand these normal states first. Remarkably, it might well be that the mathematics of string theory is capable of describing such states of fermion matter. The AdS/CFT correspondence translates this problem into an equivalent general-relativity problem involving the propagation of classical fields in an Anti-de-Sitter space-time with a black hole in its center. Very recently it was realized thatAdS/CFT has a great potential to process fermions, creating much excitement: it appears that both emergent heavy Fermi-liquids and non Fermi-liquids can be gravitationally encoded, as well as ‘holographic’ superconductors having suggestive traits in common with the real life high Tc variety.

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PL-20 Scale changes in Quantum Chemistry: contraction and renormalization techniques 1

Malrieu Jean-Paul1 Laboratoire de Chimie et Physique Quantiques, UMR 5626 CNRS, IRSAMC, Université Toulouse 3, 118 Rte de Narbonne, 31062 Toulouse Cedex (France) e-mail: [email protected]

The dimension of the working Hilbert space represents the main bottleneck of post meanfield calculations in Quantum Chemistry. This contribution presents two tools which enable one to reduce this size. The first one consists in contracting a series of excitations issued from either a same couple of bond orbitals [1,2] or from excitations inside the same region of space [3]. The method may be applied to multireference problems and excited states, provided that the zero-order description of the excitation may be kept within a Complete Active Space. When the excitation is strongly delocalized, an alternative approach has to be considered, namely an excitonic approach in which the diagonal and off-diagonal terms are renormalized [4]. Illustrations of this Renormalized Excitonic Method to the charge gap of Hubbard Hamiltonians will be presented[5], as well as extensions to ab-initio model problems [6]. [1]P. Reinhardt, H.J. Zhang, J. Ma, J-P Malrieu, J. Chem. Phys. 129 (2008) 164106, [2]H.J. Zhang, J-P Malrieu, P. Reinhardt, J. Ma, J. Chem. Phys. 132 (2010) 034108, [3] S. Hoyau, D. Maynau, J-P Malrieu, J. Chem. Phys. 134 (2011) 054125, [4] M. Al Hajj, J-P Malrieu, N. Guihéry, Phys. Rev. B 72 (2005) 224412 [5 ] M. Kepenekian, V. Robert, J-P Malrieu, submitted [6] H.J. Zhang, H. Ma, J -P Malrieu, J. Ma, submitted

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Abstracts of Oral communications

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POTENTIAL ENERGY SURFACES AND DYNAMICS OF SMALL H2n+1 CLUSTERS

P. Barragán, R. Pérez de Tudela, R. Prosmiti, P. Villarreal and G. Delgado-Barrio Instituto de Física Fundamental, CSIC, Serrano 123, 28006 Madrid, Spain

Results of recent studies on the H2n+1 clusters will be presented. Nowdays for the first members of this series high accurate ab initio electronic structure calculations can be carried out. However, a reliable global representation of even the H5+ PES is still an open and challenging problem [1]. Thus, here an alternative approach following the idea of ab initio molecular dynamics simulations, that combines nuclear dynamics methods with first-principles electronic structure calculations within the DFT framework is adopted. Such DFT approach using the B3(H) hybrid functional, specially designed for hydrogen-only systems, allows to carry out reliable dynamics calculations, classical/quantum mechanical ones, by computing the potential value at a given configuration, on the fly, with both reasonable accuracy and at low computational cost without any posterior parametrization procedure of the surface [2]. It was found that the DFT/B3(H) approach provides a reliable global description of the potential surface of the H5+ cluster Based on the B3(H) surface both classical and path integral Monte Carlo (CMC, PIMC) calculations at low temperature are carried out to investigate quantum effects on the internal proton transfer (see figure (b)), and thermal structural fluctuations on the vibrational zero-point structure of H5+ cluster [3]. Such findings are of particular interest for studying larger species of the Hn+ clusters, as well as gas-phase solvation effects, cluster fragmentation, and collision processes in astrophysical applications[4,6].

References [1] A. Aguado, P. Barragán, R. Prosmiti, G. Delgado-Barrio, P. Villarreal, and O. Roncero J. Chem. Phys. 133, 024306 (2010). [2] P. Barragán, R. Prosmiti, O. Roncero, A. Aguado, P. Villarreal, and G. Delgado-Barrio, J. Chem. Phys. 133, 054303 (2010). [3]R. Pérez de Tudela, P. Barragán, R. Prosmiti, P. Villarreal, and G. DelgadoBarrio, J. Phys. Chem. A 115(2011)2483 [4] P. Barragán et al. Phys.Scr. 2011 In press [5] R. Prosmiti et al., J. Phys. Chem. A 107, 4768 (2003) [6] P. Barragán et al., (in preparation)

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O-01



O-02 Multistate Density Functional Theory (MSDFT) for Chemical and Biological Applications Jiali Gao Department of Chemistry, University of Minnesota Minneapolis, MN 55455, USA e-mail: [email protected]

In this paper, I will present a multistate density functional theory (MSDFT) for the study of chemical reactions, including proton coupled electron transfer (PCET) processes. The method is based on non-orthogonal, block-localized molecular orbital (BLMO) and block-localized density functional theory (BLDFT), in which localized electronic configurations, called diabatic states, are obtained by construction with specific orbital and charge constraints. A key feature of MSDFT is that the electron density of the adiabatic ground state is not directly computed nor used to obtain the ground-state energy. Rather, the ground-state energy is determined by minimization of the valence bond Hamiltonian. The methods of MSDFT and BLDFT are illustrated by applications to chemical and PCET reactions.page. The following figure illustrates the resonance of three pair-wise localized water configurations that are polarized by the other monomer.

[1] A. Cembran, L. Song, Y. Mo, J. Gao, J. Chem. Theory Comput. 5 (2009) 2702-2716. [2] Y. Mo, P. Bao, J. Gao, Phys. Chem. Chem. Phys..13 (2011) 6760-6775.

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O-03 The Jastrow-VBSCF method : presentation, and application to (TCNE)22- anion dimer. Benoît BRAÏDA1, Kevin HENDRICKX1, Julien TOULOUSE1 and Philippe C. HIBERTY2 1 Laboratoire de Chimie Théorique, Université Pierre et Marie Curie and CNRS, 4 place Jussieu 75005 PARIS, FRANCE 2 Laboratoire de Chimie Physique, Université de Paris-Sud and CNRS, 91405 ORSAY, FRANCE e-mail: [email protected]

High level ab initio Valence Bond (VB) methods based on strictly local (one-center atomic) orbitals and including dynamical correlation, like the BOVB or VBCI methods,[1] combine a unique chemical interpretability with reasonable accuracy of the computed quantities. However, because of orbital nonorthogonality their computational cost is very high, and they can only be applied to small model systems (a few heavy atoms and a handful of VB structures). A new Valence Bond method will be presented, which benefits from the advantages of using Quantum Monte-Carlo (QMC) algorithms. The wave function consists of a VBSCF determinantal part, complemented by a Jastrow function, which is a very compact and efficient way of describing correlation, and in particular dynamic correlation. This form of VB wave function combines extreme compactness with good accuracy, and similar interpretative capabilities as other strictly local VB methods, as it preserves the direct correspondence between the bonding patterns (Lewis structures) and the mathematical expressions of the VB structures. In contrast to traditional analytical calculations, nonorthogonal orbitals do not lead to extra computational cost in QMC, and in addition QMC algorithms are particularly well suited to large parallel machines, which opens the possibility of high level VB calculations on larger systems. The benefits of using compact VB wave functions for QMC calculations will be briefly illustrated on some representative diatomic molecules, by comparing with QMC calculations using MO-based wave functions.[2] Application of the Jastrow-VBSCF method on the elucidation of the nature of bonding in tetracyano-ethylene anion dimer will be presented, which represents to our knowledge the largest calculation to date using a strictly local ab initio VB method which includes dynamical correlation (20 heavy atoms).

Fig.1 [1] (a) S. Shaik and P. C. Hiberty, A Chemist’s Guide to Valence Bond Theory. Wiley, New York, 2008. (b) P. C. Hiberty and S. Shaik, J. Comput. Chem. 28 (2007) 137. [2] B. Braïda, J. Toulouse, M. Caffarel and C. J. Umrigar, J. Chem. Phys., 134 (2011) 084108.

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O-04 Superatom Representation of High-TC Superconductivity 1

Itai Panas1 Chalmers University of Technology, Kemivägen 10, S-41296, Gothenburg, Sweden e-mail: [email protected]

High critical temperature superconductivity HTSC is said to reflect cooperative coexistence of two virtual Bose-Einstein condensates comprising virtual super-atom excitations and complementary virtual magnons. "Phase locking" between the two virtual condensates produces the effective superconducting ground state. The required entanglement among superatoms results from non-adiabatic coupling between holes aggregates and anti-ferromagnetic embedding, thus causing virtual excitations in either subsystem due to intersystem coupling. Consequently, the resulting composite Cooper pairs comprise the interaction particles for virtual magnons mediated "selfcoherent entanglement" of superatoms. A resonating valence bond RVB approach is taken to articulate the formation of such nonlocal real-space Cooper pairs. In this formalism the Cooper pair undergoes the analogue of "spin-charge separation" in that the pair state becomes uncharged. Pairing energy as well as resonance stabilization owing to the Bose Einstein condensation are deduced in terms of the super-exchange interaction. Connection is made to an equivalent real-space BCS formulation of HTSC1,2. Claimed "disentangling of Cooper-pairs formation above the transition temperature from the pseudogap state in the cuprates" at "T(pair)"3 is reinterpreted to reflect the onset of a concerted interband- and aggregation redistribution of charge carriers. Having said this, it is true that our deduction of the RVB-BEC includes as a first step the formation of isolated Cooper pairs. Prior to the condensation, each pair is being shared by precisely two superatoms. Said interband excitations and charge carrier segregation phenomenology is substantiated further. Two Bi2201 model systems are employed to demonstrate how, beside the Cu-O band, a second band of purely O2p character can be made to cross the Fermi energy owing to sensitivity to local crystal field. Further instability towards hole clustering is also demonstrated. Analysis based on band structures, partial densities of states and sums-over-states-densities STM-type images is provided4, and employed to explain the particle-hole symmetry breaking across the pseudo-gap recently reported by Shen and co-workers5. Generality of the two-bands scenario is demonstrated by comparing to the Hg-cuprates. A multi-band analogue is offered for the FeSe and Fe-pnictide materials, and the HTSC is again articulated in terms of a superatom representation2. Here the required non-local entanglement is made possible by Hund's rule violation on one Fe sublattice. This is caused by the AFM in the second Fe sublattice. Again, Cooper pairs are articulated in terms of virtual magnons mediated "self-coherent entanglement" of superatoms. [1] I. Panas, B103 (1999) 10767. [2] I. Panas, Phys. Rev. B82:6(2010)064508. [3] T. Kondo et al. Nature Physics 7, (2011) 21 [4] I. Panas, Phys. Rev. B83:2 (2011) 024508. [5] M. Hashimoto et al., Nature Physics 6, (2010) 414.

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O-05 A priori identification and deletion of configurational deadwood from full-valence-space correlated wave functions Laimutis Bytautas and Klaus Ruedenberg Department of Chemistry and Ames Laboratory, Iowa State University Ames, Iowa, 50011, USA ruedenberg@iastate,edu Wave functions that are optimized in the full molecular valence space of all conceptual minimal basis orbitals of a molecule (or occasionally by using N orbitals for N valence electrons) furnish useful, unbiased and size-consistent zeroth-order reference functions for chemical reactions. Even with this orbital limitation and even for moderate-sized molecules, these full optimized reaction spaces still have excessive dimensions and it is imperative to get rid of all configurational deadwood. While a large part of it is eliminated by expansion in terms of successive excitations, the further removal of ineffective configurations within the retained excitation levels still remains essential. Given here is a method for separating deadwood from “livewood” that satisfies the following desiderata: (i) It can be executed a priori, i.e. by modest preliminary calculations without entering the heavy full CI calculation; (ii) it is nonetheless based on a rigorous quantitative assessment and not on an intuitive model. It can therefore also serve to assess the reasonableness of specific intuitive selections. The method identifies those terms in the CI expansion that can be deleted if a given error in the energy is tolerated. It is based on the division into principal and secondary orbitals by split-localization, which the authors have shown to generate a more rapid CI convergence than natural orbitals. The truncations are performed independently for the quadruple, quintuple and sextuple excitations on the basis of information derived from the double and triple excitations. The effectiveness of the method is shown by application to SDTQ56-CI wave functions of the molecules HNO, N2 and NCCN. Work supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. Department of Energy under Contract No. DE-AC02-07CH11358 with Iowa State University through the Ames Laboratory.

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O-06

Computing the magneto-electric coupling between atoms with numerous open-shells to experimental accuracy : YMnO3 Marie-Bernadette LEPETIT CRISMAT UMR6508 CNRS-ENSICAEN, 6 bd Maréchal Juin, 14050 Caen, FRANCE

In strongly correlated systems the electron-electron repulsion between the Fermi level electrons is of larger magnitude than the kinetic energy. It results that the nature of the ground and the low-lying excited-states is thus fundamentally multi-configurational and single-determinant based methods (such as density functional theory) encounter difficulties in properly describing their electronic structure and more specifically their magnetic properties. The multireference CAS+DDCI [1] and related LCAS+S [2] methods proved their high reliability and efficiency for accessing the local physics such as the magnetic exchange within experimental accuracy, however they cannot be used for systems involving more than one or two unpaired electrons per magnetic center. We will use a simple physical criterion in order to propose a new ab initio approach that overcomes this problem [3]. We used this new method to study the magneto-electric coupling in a prototypal magnetoelectric system YMnO3 [4]. Indeed we were able to computed the magnetic exchange as a function of an applied electric field within experimntal accuracy. The importance of the different microscopic contributions (piezzo-magnetic effects, spin-orbit couplign etc. . .) on the magneto-electric coupling will be discussed from he ab-initio results.

(1) J. Miralles, J. P. Daudey and R. Caballol, Chem. Phys. Lett. 198, 555 (1992) ; V. M. García et al., Chem. Phys. Lett. 238, 222 (1995) ; V. M. García, M. Reguero and R. Caballol, Theor. Chem. Acc. 98, 50 (1997). (2) A. Gellé, M. L. Munzarová, M.B. Lepetit and F. Illas, Phys. Rev. B 68, 125103 (2003) ; C J. Calzado, J. F. Sanz and J. P. Malrieu, J. of Chem. Phys. 112, 5158 (2002). (3) Alain GELLÉ, Julien VARIGNON et Marie-Bernadette LEPETIT, EPL 88 37003 (2009). (4) J. Varignon and M.-B. Lepetit, in preparation.

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O-07 Why the High Spin States of the Metal Clusters are Bound? The Valence Bond Analyse of the No-Pair Bonding David Danovich, Sason Shaik The Institute of Chemistry and The Lise Meitner Minerva Center for Computational Quantum Chemistry, The Hebrew University, Jerusalem 91904, Israel e-mail: [email protected]

€

Investigation in the area of atomic clusters focuses at present on the properties of these clusters in their ground states. We expanded this interest to the instigations of the high spin states and presented a bonding model, based on a Valence Bond (VB) approach, which explains and predicts the bonding features in the high spin state of the atomic clusters [1- 3]. The present work discusses bonding in a variety of metal clusters, n+1Mn (M=Li, Na, K, Cu, Ag, Au). These clusters do not possess any electron pairs and are nevertheless strongly bonded. According to the VB model (See scheme) the no-pair bonding originated from bound triplet electron pairs that spread over all the close neighbors of a given atom in the clusters. The bound triplet pair owes its stabilization to the resonance energy provided by the mixing of the local ionic configurations, 3 M(↑↑) − M + and M + 3 M(↑↑) − , and by the various excited configurations into the fundamental repulsive configuration 3 (M↑↑M) with s1s1 electronic configuration. The VB model shows how a weak interaction in the dimer can become a remarkably strong binding force in large clusters without a€single electron pair. €

3Φ zz

We also demonstrate that due to increasing role of the ionic configurations in the mixed clusters, the E no-pair bonding becomes even stronger in 3Φ s,z comparison with homoatomic ones of the same size. Among the investigated mixed clusters the strongest no-pair bonding is found in the 5Cu2Au2 cluster. 3Φ ss Results of the different DFT and ab initio calculations of the no-pair clusters will be δεrep ΔΕmix presented. Differences in the mechanism of the E (2M) bonding between alkali and coinage metal clusters De will be discussed. + 3ψ (3Σ ) 3M The results obtained in the present work u 2 suggest that the bond dissociation energy per atom De = ΔEmix - δεrep ; ΔEmix = Σδεmix,i in the mixed no-pair clusters may even exceed 20 i kcal/mol thus becoming comparable with the strength of the usual bonding due to the spin pairing. 2

[1] D. Danovich, W. Wu, S. Shaik, J. Am. Chem. Soc., 121 (1999), 3165-. [2] D. Danovich, M. Filatov, J. Phys. Chem. A, 112 (2008), 12995-. [3] D. Danovich, S. Shaik, J. Chem. Theor. Comput. 6 (2010), 1479-.

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O-08 Hybrid ab initio Valence Bond / Molecular Mechanics (VB/MM), A New Method for Calculating Biochemical Systems Avital Sharir-Ivry1, Avital Shurki1 1 Department of Medicinal Chemistry, Institute of Drug Research, The Lise Meitner-Minerva Center for Computational Quantum Chemistry The Hebrew University of Jerusalem, Jerusalem 91120, Israel e-mail:[email protected]

The growing demand for realistic methods that would calculate chemical reactions in biological systems resulted with the development of hybrid quantum mechanical (QM) molecular mechanical (MM) schemes. Recent years have proven schemes that are based on concepts from valence bond (VB) methodology, to be beneficial for the description of enzyme catalysis and reactivity. The development of a new hybrid (QM/MM) method where the QM part is treated by ab-initio Valence Bond (VB) theory will be presented[1]. The method considers the effect of the environment on each one of the VB structures separately while the overall adiabatic state is obtained as a result of mixing of these VB structures. Furthermore, it utilizes the simple mechanical embedding scheme to describe the interactions between the QM part and the surrounding. Finally, the off diagonal elements of the VB matrix in the new environment are calculated by using the approximation that both the overlap between the VB configurations and the respective reduced resonance integral are invariant to the environment. The VB/MM method as well as the various approximations ustilized will be explained. It will be shown that examination of these approximations which is based on extension of the method justifies their use.[2,3] The validity of the method will be shown to be successful in several examples including for the description of a reaction in proteins.[4]

[1] A. shurki, H. Crown J. Phys. Chem. B, 109 (2005), 23638-23644 [2] A. Sharir-Ivry, H. A. Crown, W Wu, A. Shurki J. Phys. Chem. A, 112 (2008) 2489 -2496 [3] A. Sharir-Ivry, A. Shurki J. Phys. Chem. B, 112 (2008) 12491-12497 [4] A. Sharir-Ivry , T. Shnerb, M. Strajbl, A. Shurki J. Phys. Chem. B, 114 (2010) 2212–2218

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O-09 The many-electron band structure approach: theory and application Remco W.A. Havenith and Ria Broer Zernike Institute for Advanced Materials, Theoretical Chemistry, Nijenborgh 4, 9747 AG Groningen, The Netherlands e-mail: [email protected] One-electron band structure theory has inadequacies in the prediction of accurate band gaps or excitation energies for systems where electron correlation plays an important role. Examples are extended systems in which ionisations or excitations have a local character. Our approach to overcome this deficiency involves the computation of correlated (MCSCF) cluster-wavefunctions, which serve as a basis for the construction of the delocalised many-electron wavefunctions of the crystal. On this poster an outline of our method is given, together with an example to show its performance for the calculation of the ionisation potential of CuCl. The applicability of this method for the study of hopping in charge-transfer salts and of transition probabilities occurring during singlet-fission and triplet-annihilation processes is also discussed.

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O-10 Half-metallicity in finite single wall zigzag carbon nanotubes A. Mañanes1, P. Alonso-Lanza1, M. J. López2, J. A. Alonso2 1 Departamento de Física Moderna, University of Cantabria, 39005 Santander, Spain 2 Departamento de Física Teórica, Atómica y Optica, University of Valladolid, 47011 Valladolid, Spain e-mail: [email protected].

Density-functional calculations predict half-metallicity in single-walled zigzag carbon nanotubes of finite length with the two ends saturated with hydrogen [1]. We have analyzed the change of the spin-up and spin-down electronic gaps under the influence of an electric field applied along the nanotube axis. For (14,0) nanotubes, the half-metallic behavior, in which the electronic gap is zero for one spin orientation, and nonzero for the opposite spin orientation, is achieved for a critical electric field of 3.0/L V/Å, where L is the length of the nanotube. This critical field is the same as that predicted for graphene nanoribbons [2]. Narrower, (7,0) nanotubes, are also analyzed. A detailed analysis of the spin structure shows the relevance of the edge states, electronic states spatially localized at the carbon atoms of the nanotube boundaries, on the onset of half-metallicity, and on the magnetic properties of the finite zigzag nanotubes.

Fig.1 Net spin density nα(r)-nβ(r) for C128 H28. The net spin density (in a.u.) is indicated by the different colors: 0.0003, red; 0.00015, yellow; 0.00, green; −0.00015, light blue; and −0.00030, dark blue. The left side of the nanotube is dominated by α-, and the right side by β-spin density. The largest net spin densities occur over the carbon atoms at the edges of the nanotube. [1] A. Mañanes, F. Duque, A. Ayuela, M. J. López, and J. A. Alonso. Phys.Rev. B 78 (2008) 035432:1-10. [2] Y. W. Son, M. L. Cohen, and S. G. Louie, Nature 444 (2006) 347-349.

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O-11 Investigating the extended Hubbard model as an approximation to the entanglement of a nanostructure system J. P. Coe1, V. V. França2, I. D’Amico3 1 Department of Chemistry, Heriot-Watt University, Edinburgh, EH14 4AS, UK 2 Department of Physics, University of York, York YO10 5DD, UK 3 Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder Straße 3, D-79104, Freiburg Germany e-mail: [email protected]

Quantum-dot (QD) nanostructures are possible candidates for quantum information processing hardware. Within this context, entanglement is considered one of the main resources. Modelling many-electron systems accurately is usually computationally very demanding so often approximations are used, such as the Hubbard model (HM) and its variants. If these models are proven to be accurate as an approximation to the entanglement of some specific systems, such as chains of nanostructures, then this may allow us to efficiently investigate the entanglement in these systems when a very large number of particles are considered, as density-functional schemes for calculating the entanglement within the HM are available [1]. Ultimately this may help assessing the suitability of nanostructures for use as quantum information devices. We have previously found that the 1D HM is a good approximation to the local entanglement of a system of two-electrons with contact interaction that are trapped in a string of QDs [2]. This is the entanglement between regions ('sites') of the system in the site occupation basis. In this contribution we consider a similar QD chain, but with more realistic long-range interactions. The accuracy of the HM and the extended HM (with or without correlated hopping) to reproduce the local entanglement of this system is then appraised. Surprisingly we find that there exist some typical experimental parameters for which the (extended) HM is not at all a good approximation [3]. Furthermore we propose a method to calculate the spatial entanglement of the HM and extended HM. This is the entanglement between the particles' positions. We compare this approximation with the exact spatial entanglement of the QD system. Even if the HM approximation drastically reduces the degrees of freedom from infinite to the number of sites – just four in our calculations -it reproduces unexpectedly well qualitatively and quantitatively the spatial entanglement of the QD system.

[1] V. V. França, K. Capelle, Phys. Rev. Lett. 100 (2008) 070403. [2] J. P. Coe, V. V. França, I. D'Amico, Phys. Rev. A 81 (2010) 052321. [3] J. P. Coe, V. V. França, I. D'Amico, EPL 93 (2011) 10001.

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O-12 The extended spin coupled method SC(n,m) Brian J. Duke1, Peter B. Karadakov2, Jiabo Li3 and David L. Cooper4 1 Faculty of Pharmacy and Pharmaceutical Sciences, Monash University, 381 Royal Parade, Parkville, VIC 3052, Australia 2 Department of Chemistry, University of York, Heslington, York, YO10 5DD, UK 3 SciNet Technologies, 9943 Fieldthorn St., San Diego, CA 92127, USA 4 Department of Chemistry, University of Liverpool, Liverpool L69 7ZD, UK email: Brian.Salter[email protected].

The spincoupled method has been remarkably successful. As the best single orbital product wavefunction for n electrons in n orbitals, it is the next step after the wellknown HartreeFock method which uses a single orbital product incorporated within a Slater determinant. Significantly, in most cases the spin structures combined with the orbital product can be identified with classical valence bond structures. A key advantage of the method is its description of a system without bias to any particular selection of bonding patterns. This is essential for a consistent description for reaction systems, from reactants to products. However, there are some cases where the “n electrons in n orbitals” model is not really appropriate. Good examples are the π systems of cyclopentadienyl anion and cycloheptatrienyl cation, both with 6 electrons. It is difficult to see how 6 orbitals can be obtained for these systems with C5 and C7 symmetry. Other examples are the 4electron 3centre bonding systems such as the π system of ozone. Spincoupled solutions for 4 electrons in 4 orbitals can be obtained, but there are two quite different solutions for the 4 orbitals. These were designated as SCA and SCB by Thorsteinsson et al [1]. The energies of SCA and SCB are quite close with that of SCA lower than that of SCB for ozone, but higher for some other systems. They can be obtained by projection from two different CASSCF(4,4) functions, CASSCF(4,4)A and CASSCF(4,4)B, where A has 3 symmetric molecular orbitals and 1 asymmetric orbital, while B has 2 symmetric molecular orbitals and 2 asymmetric orbitals. We have developed an extension of the spincoupled method, SC(n,m), for cases that are better represented by a “n electrons in m orbitals” model. SC(n,m) uses several orbital products multiplied by the normal spin terms. The choice of orbitals products is the set that maximises the occupancy of the m orbitals. Thus, for the cyclopentadienyl anion, we have SC(6,5) and the orbitals products are the five that have one of the five orbitals doublyoccupied and the other four singly occupied. For the cycloheptatrienyl cation, we have SC(6,7), and the orbitals products are the seven that have one vacant orbital and six singlyoccupied orbitals. This extension of the spincoupled method retains the consistent description for reaction systems, from reactants to products. The method has been implemented in the VB2000 program which was used for the C5H5, C7H7+ and ozone calculations. Analogous calculations were subsequently carried out using the CASVB code in MOLPRO. [1] Thorstein Thorsteinsson, David L. Cooper, Joseph Gerratt, Peter B. Karadakov and Mario Raimondi, Theor Chim Acta, 93, (1996), 343 366.

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Abstracts of Poster communications

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P-01 Resonance and Aromaticity: An Ab Initio Valence Bond Approach Zahid Rashid1, Joop H. van Lenthe1, Remco W. A. Havenith2 Theoretical Chemistry Group, Department of Chemistry, Debye Institute For Nanomaterials Science, Utrecht University, Princetonplein 1, De Uithof, 3584 CC Utrecht, The Netherlands. 2 Theoretical Chemistry, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands. 1

e-mail: [email protected]

Resonance energy is one of the criteria to measure the aromaticity. The effect of the use of different orbital models is investigated in the calculated resonance energies of cyclic conjugated hydrocarbons within the framework of the ab initio Valence Bond Self-Consistent Field (VBSCF) method. The VB wave function for each system was constructed using a linear combination of the Kekulé valence structures and two types of orbitals, i.e. strictly local and delocal atomic p-orbitals, were used to describe the π-system. It was found that the Pauling Wheland's resonance energy with nonorthogonal structures decreases while the same with orthogonalised structures and the total mean resonance energy (the sum of the weighted off-diagonal contributions in the Hamiltonian matrix of orthogonalised structures) increase when fully optimised delocal orbitals are used compared to local p-orbitals. For linear benzenoids the Pauling Wheland's resonance energy and the total mean resonance energy per π electron decrease with the increasing size of the system using the local orbitals. With delocal orbitals, however, this trend in the Pauling Wheland's resonance energy was not observed. Analysis of the interactions between the different Kekulé valence structures of a system showed that the resonance in the 6π electron conjugated circuits have the largest contributions to the resonance energy. The VBSCF calculations also show that the extra stability of phenanthrene, a kinked or bent benzenoid, compared to its linear counterpart, anthracene, is a consequence of the resonance in the π system rather than the H−H interaction in the bay region as suggested previously. At last, the empirical parameters for the resonance interactions between different (4n+2) or 4n π electron conjugated circuits, used in the Randić's π-electrons conjugated circuit theory or Herdon's semiemprical VB approach, are quantified. These parameters have to be scaled by the structure coefficients (weights) of the contributing Kekulé valence structures.

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P-02 Anionic polymerization of Li2B12H12 and LiCB11H12: An experimental and computational study A. Chana, J.Z. Dávalos, F.J. González, A. Guerrero, J.M. Oliva CSIC, Instituto de Química-Física “Rocasolano”, c/ Serrano 119, Madrid, 28006, Spain [email protected] The polymerization of the lithiated boron cages Li2B12H12 (I) and LiCB11H12 (II) was studied by mass spectrometry using an ESI spectrometer 7T FT-ICR (“Fourier Transform Ion Cyclotron Resonance Spectrometry”) [1]. According to the observed mass spectra, the polymerization of (I) takes place forming, among others, mono charged anions with formulae [Lin−1 (n ≥ 1) while (II) yields mono- and di-charged anions [Li2n-1(B12H12)n]−1, [Li2n1(CB11H12)n+1] −2 (n ≥ 1), respectively. According to these results, (II) shows a bigger affinity for 2(B12H12)n] lithium than (I). The structure of the formed clusters was determined by density-functional theory (DFT) computations. Figure 1 below shows the optimized geometry of the most probable energy minimum for the complex (Li2B12H12)···(LiB12H12)− ≡ [Li2n-1(B12H12)n]−1 with n = 2, using a Hartree-Fock/DFT hybrid model, known as B3LYP/6-31G* [2], which uses a double-ζ basis set with polarization d-functions on Li and B atoms. The bond energy of the lithium linkage in the mono-charged dimers (complexes with n = 2) was estimated by CID (Collision Induced Dissociation) means in an ESI triple quadrupole taking into account the predicted energy minima for LiCB11H12 [3] and Li2B12H12 [4].

Fig.1 Optimized geometry of the (Li2B12H12)···(LiB12H12)− complex with D3d symmetry, corresponding to an energy minimum, using the B3LYP/6-31G* model. [1] A.G. Marshall, C.L. Hendrickson, M.R. Emmett, R.P. Rodgers, G.T. Blakney, C.L. Nilsson. Eur. J. Mass Spectrom. 13 ( 2007) 57 [2] C.J. Cramer, Essentials of Computational Chemistry: Theories and Models. Wiley, Chichester, 2007 . [3] V. Manero, J.M. Oliva, L. Serrano-Andrés, D.J. Klein, J. Chem. Theory Comput. 3 (2007) 1399-1404. [4] J.M. Oliva, A. Fernández-Barbero, L. Serrano-Andrés, M. Canle-L., J.A. Santaballa, M.I. Fernández, Chem. Phys. Lett. 497 (2010) 172-177.

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Quantum Chemistry Calculations in Helium clusters doped with diatomic molecules

P-03

G. Delgado-Barrio, R. Pérez de Tudela, D. López-Durán, R. Prosmiti, P. de Lara-Castells and P. Villarreal Instituto Física Fundamental (CSIC) C/ Serrano 123 28006-Madrid (SPAIN)

Spectroscopic studies of simple molecules surrounded by He atoms show a drastic difference depending on the fermionic or bosonic character of the solvent atoms [1]. A quantum chemistry-like approach has been recently developed in our group to deal with HeN –BC doped helium clusters, where the BC dopant is a conventional di-atomic molecule. The central idea is to consider the He atoms as “electrons” while the B and C atoms play the role of the nuclei in standard electronic structure calculations. The procedure provides spectral simulations and, hence, making feasible to do proper comparisons with current experiments (1). However, due to the big difference of masses of He and electrons, and also to the replacement of Coulomb potentials by molecular interactions, it is worthy to asses at what extent the approximations involved (decoupling of orbital angular momenta of the He atoms from the BC rotation and adiabaticity of the BC stretch versus de He motions) lead to accurate results (2-10). Here, we consider several diatomic molecules as dopants. The model provides the energy levels of the cluster and the intensities of the main lines of the spectrum at low temperatures. Up to now, Hartree/Hartree-Fock approaches involving their own limitations have been used. It is therefore desirable to implement more accurate ab initio methodologies. Encouraging “full interaction configuration” results, based on a Jacobi-Davidson diagonalization procedure, have been already obtained for small doped fermion clusters [10].

References [1] S. Grebenev,J. P. Toennies, and A. F. Vilesov, Science 279, 2083 (1998) [2] D. López-Durán,M. P. de Lara-Castells, G. Delgado-Barrio, P. Villarreal, Di Paola,F. A. Gianturco, and J. Jellinek, Phys. Rev. Lett. 93,053401 (2004). J. Chem. Phys. 121, 2975 (2004) [3] M. P. de Lara-Castells, D. López-Durán,G. Delgado-Barrio, P. Villarreal, C. Di Paola,F.A.Gianturco,and J. JellinekPhys. Rev. A 71, 033203 (2005) [4] M.P. de Lara-Castells, R. Prosmiti, G. Delgado-Barrio, D. López-Durán, P.Villarreal,F.A.Gianturco, and J. Jellinek, Phys. Rev. A 74, 053201 (2006) [5]M. P. de Lara-Castells, R. Prosmiti, D. López-Durán, G. Delgado-Barrio, P. Villarreal, F. A. Gianturco, and J. Jellinek, Int. J. Quant. Chem.107, 2902 (2007) [6] O.Roncero, R.PérezdeTudela, M.P.deLara-Castells, R.Prosmiti, G. Delgado-Barrio, and P. Villarreal,Int.J.QuantumChem.107(2007)2756. J.Chem. Phys. 128,164313(2008) [7] R. Pérez de Tudela et al., J. Chem. Phys. 132 , 244303 (2010). [8] M. Márquez-Mijares et al., J. Chem. Phys 130 , 154301 (2009). [9] R. Prosmiti et al., J. Phys. Chem. A 113 , 1478 (2009). [10] M.P. De Lara-Castells et al., Few Body Syst. 45,233 (2009)

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P-04


Quantum chemical many-body approach based on QED double Fock-space Coupled Cluster method. Ephraim Eliav School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel The Fock-space coupled cluster (CC) method is a natural framework for development of size-extensive techniques, consistent with the quantum electrodynamics (QED) theory, where the numbers of interacting electrons and photons are not conserved. The main technical problem of merging QED with standard many-body perturbation (MBPT) methods is the energy dependence form of the effective QED potentials. Recently two independent approaches, namely two-time Green functions of Shabaev [1] and the covariant evolution-operator (CEO) method of Lindgren at al. [2] were introduced for calculation of matrix elements of the energy-dependent QED potentials. We have chosen the CEO approach as a basis for development of the multireference double-Fock-space coupled cluster method, based on effective or intermediate Hamiltonians. In addition to the electronic Fock-space sectors, we consider the photonic ones. Matrix elements of the effective Hamiltonian in particular n-electronic and m-photonic Fock-space sector are built by the appropriate CC dressing of the irreducible effective m-photonic electron-electron interactions and the corresponding radiative corrections in the n-valence electronic complete active space. This approach yields a possibility of merging QED in the covariant evolution-operator formulation [2] with the Fock-space CC, one of the most powerful tools of modern quantum chemistry, in a systematic way. With such a technique it might be feasible to substantially increase the accuracy of calculations of heavy atomic and molecular systems and in particular to perform precise QED calculations of highly charged many-electron atoms, which is presently not possible with the techniques available. References: 1. Shabaev, Vladimir. Physics Reports 356, 119 (2002). 2. Lindgren, Ingvar; Salomonson, Sten; Hedendahl, Daniel. 062502/13 (2006)

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Phys. Rev. A 73, 062502/1-



P-05 Dimer-covering RVB treatment of single-walled zigzag carbon nanotubes M. A. Garcia-Bach Departament de Física Fonamental, Facultat de Física and Institut de Química Teòrica i computacional, Universitat de Barcelona, Diagonal 647, 08028-Barcelona, Catalonia, Spain. e-mail: [email protected] Single-walled zigzag carbon nanotubes (CNT) with h hexagons around the carbon nanotube, h ranging from 3 to 19, have been investigated from a resonating-valence-bond point of view [1]. These values of h include realistic CNTs with diameters ranging from 0.5 to 1.5 nm, which correspond to h ~ 6 and h ~ 19, respectively. Long-range spin-pairing order (LRSPO) allows to separate the set of VB configurations in h+1 different subsets or phases. The parameter associated with the LRSPO, p, can take the relevant values p = 0, 1, ··· , h. We have obtained the Heisenberg energy per carbon atom, εp(h), in units of J, and also per polyene ring for zigzag single-walled CNTs with h= 3, 4, ··· , 19 and p= 0, 1, ··· , h, witin a dimercovering counting approximation. First, the ground-state energy per carbon atom is obtained when the phase, which we design as p0, is the integer closest to h/3. From the difference in energy per polyene ring, Δ(h), in units of J, between the two lowestlying phases, p0 and p1 it is noted that degeneracy between the two lowest-lying phases occurs when (h+1)/3 is an integer. Therefore, de-confined low-energy topological spin defects would occur. Then, these carbon nanotubes should be conductors, in analogy to polyacethylene. In clear contrast, no such degeneracy is observed for either, h = 3n+1 or h = 3n, so bound pairs of topological spin defects are expected to occur in these cases. [1] M.A. Garcia-Bach, Eur. Phys. J. B 80 (2011) 469.

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P-06 Methyl-Blocked α,γ-Peptide Nanotube Segments. A DFT study. Rebeca García-Fandiño, Luis Castedo, Juan R. Granja, and Saulo A. Vázquez Departamento de Química Orgánica y Centro Singular de Investigación en Química Biológica y Materiales Moleculares. Campus Vida. c/ Jenaro de la Fuente s/n, 15782 Santiago de Compostela, Spain. e-mail: [email protected]

Self-assembling peptide nanotubes (SPNs) have been extensively studied due to their potential applications in chemistry, biology, and material science [1]. One of the advantages of SPNs is the ease with which these materials can be made and modified. In this respect, especially interesting are those derived from α,γ-SPNs, which consist of alternating 3aminocycloalkanecarboxylic acid (γ-Aca), such as (1R,3S)-3-aminocyclohexanecarboxylic acid (Dγ-Ach) or (1R,3S)-3-aminocyclopentanecarboxylic acid (D-γ-Acp) and α-amino acid [2]. While almost all the cyclic peptide nanotubes that have been prepared so far have hydrophilic inner surfaces and can permeate polar molecules only, in the case of the α,γ-SPNs, the C2 methylene group of each cycloalkane moiety is projected into the lumen of the cavity, generating a partially hydrophobic cavity, which can be modulated by simple chemical modification of the β-carbon of the cycloalkane moiety of γ-Acas [3], thus allowing, in principle, the fine control of the transport properties of a very wide range of molecules in the nanotube [4]. The building blocks of this promising class of peptide nanotubes have been explored by computational methods. Specifically, density functional theory (DFT) calculations on monomers and dimers of γ-Ach-based and γ-Acp-based α,γ-cyclo-hexapeptides and cyclo-octapeptides were carried out to investigate the experimentally observed preference for α-α over γ-γ dimerization, associated with the two types of stacking patterns present in these peptide nanotubes, as well as the preference for heterodimerization versus homodimerization. Full geometry optimizations were performed at the B3LYP/6-31G(d) level, and single point calculations were subsequently carried out with the B3LYP and M05-2X functionals and the 6-31+G(d,p) basis set.

[1] D. T. Bong, T. D. Clark, J. R. Granja, M. R. Ghadiri, Angew. Chem., Int. Ed. 40 (2001) 988. [2] (a) M. Amorin, L. Castedo, J. R. Granja, J. Am. Chem. Soc.125 (2003), 2844. (b) R. J. Brea, L. Castedo, J. R. Granja, J. R. Chem. Commun. (2007), 3267. [3] C. Reiriz, M. Amorín, R. García-Fandiño, L. Castedo, J. R. Granja, Org. Biomol. Chem. 7 (2009), 4358. [4] R. García-Fandiño, J. R. Granja, M. A. D´Abramo, M. Orozco, J. Am. Chem. Soc. 131 (2009) 15678.

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P-07 Derivatized carbon nanotubes - interactions with membranes, water, and ions. A computational study. 1

Rebeca García-Fandiño, Mark S. P. Sansom Dept. de Química Orgánica y Centro Singular de Investigación en Química Biológica y Materiales Moleculares. Campus Vida. c/ Jenaro de la Fuente s/n, 15782 Santiago de Compostela, Spain. 2 Structural Bioinformatics and Computational Biochemistry Unit, Dept. of Biochemistry, University of Oxford , South Parks Road, Oxford , OX13QU, U.K. e-mail: [email protected]

Carbon nanotubes (CNTs) are considered as unique materials, with very promising future applications, especially in the field of nanotechnology, nanoelectronics, and composite materials.[1] The main difficulties encountered in the application of such materials in biological systems are derived from their poor solubility in aqueous or organic solutions. One of the most efficient ways of improving CNTs’ solubility has been their functionalization by covalently attaching polar or charged groups to CNT surfaces.[2] These modifications can alter the inherent properties of the tube,[3] which opens the possibility to explore new materials with latent and new characteristics that can be very different from those corresponding to the non functionalized CNTs, facilitating the development of novel biotechnology, biomedicine, and bioengineering. The present work aims to gain insight into how the functionalization of the inner wall of CNTs affects the inherent properties of the tube and how it changes their dynamical behaviour and transport properties, studying their interaction with water, ions and a lipid bilayer through Molecular Dynamics simulations, Potential of Mean Force and Adaptive Poisson-Boltzmann Solver (APBS) calculations.

[1] W. R. Yang, P. Thordarson, J. J. Gooding, S. P. Ringer, F. Braet, F. Nanotechnology 18 (2007) 412001. [2] (a) J. G. Yu, K. L. Huang, S. Q. Liu, Chin. J. Inorg. Chem. 24 (2008) 293 (b) J. G. Yu, K. L. Huang, S. Q. Liu, Phys. E 40 (2008) 689. [3] (a) J. Chen, M. A. Hamon, H. Hu, Y. S. Chen, A. M. Rao, P. C. Eklund, R. C. Haddon, Science 282 (1998) 95. (b) J. L. Bahr, J. P. Yang, D. V. Kosynkin, M. J. Bronikowski, R. E. Smalley, J. M. Tour, J. J. Am. Chem. Soc. 123 (2001) 6536. (c) For a review about recent advances on the soluble carbon nanotubes, see: B. I. Kharisov, O. V. Kharissova, O. V.; H. Leija-Gutierrez, O. Ortiz-Méndez, Ind. Eng. Chem. Res. 48 (2009) 572.

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P-08 Mesomeric description, ab initio & Hückel derived approaches Yannick Carissan1, Denis Hagebaum-Reignier2, Nicolas Goudard1 , Stéphane Humbel1 1 iSm2 Institut des Sciences Moléculaires de Marseille, 2 LCP Laboratoire de Chimie Provence, 1&2 Campus St Jérôme, Aix-Marseille Université, 13013 Marseille, France e-mail: [email protected].

Senior chemists (and hopefully students) can get some hints about the delocalized nature of electronic systems with the simple, yet efficient, tool of resonance theory. Electronic delocalization in usual π systems such as the amide, benzene or butadiene is indeed taught via the resonance approach between Lewis structures (so-called “contributing structures”). O !– H

C

H

H

100%

O

O

H N !+

C

N

H

H

66%

N

H

H minor

H Major

=

C

+

34%

Fig. 1

Fig. 2

The double arrow in Fig. 1 represents a Configuration Interaction (CI) between localized structures, that is Ψmesomery = C1Ψ1 + C2Ψ2. Due to the non orthogonality of the localized structures, the evaluation of the relative importance of each of them necessitates, in principle, quite a few computational efforts. [1] After a short introduction to most selected ab initio techniques on the subject, we shall present two alternatives based on Hückel hamiltonian and orbitals. One is based on a simulated CI, where the CI hamiltonian is rebuilt from the energy of the delocalized solution relative to that of the localized structures (Hückel-Lewis CI).[2] Drawbacks of this straightforward approach will lead us to the second alternative, based on the wave functions similarity. Because it corresponds to a projection of the delocalized solution onto the localized ones, it is called Huckel-Lewis Projected (HL-P).[3] Both approaches are embedded in a pedagogical java applet (HuLiS : http://www.hulis.free.fr) that initially targets at education for both organic and quantum chemistry (Fig. 2). The validity of the HL-P approach will be discussed as well as the utility of a trust factor defined as τ = . For benzene for instance τ varies from τ=60% (with 2 Kekule's), to τ=70 % (adding Dewar's) and up to τ=94% for larger CI. Current work on the subject will be discussed. [1](a) Y.R. Mo, S.D. Peyerimhoff, J. Chem. Phys. 109 (1998) 1687; (b) E.D. Glendening, F. Weinhold, J. Comp. Chem. 19 (1998) 593 ; (c) M. Linares, S. Humbel, B. Braïda, Faraday Discussions 135 (2007), 273. [2] S. Humbel, J. Chem. Educ. 84 (2007) 1056-1061 [3] Y. Carissan, D. Hagebaum-Reignier, N. Goudard, S. Humbel, J. Chem. Phys. A 118 (2008), 13256.

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P-09 Theoretical and experimental study of the parabanic acid molecule following VUV excitation and photodissociation A. F. Lago,1, J. M. Oliva2, J. Z. Dávalos2 1 Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170, Santo André, SP, Brazil 2 Instituto de Quimica-Fisica “Rocasolano”, CSIC, Serrano 119, 28006, Madrid, Spain. e-mail: [email protected]

We present relevant theoretical and experimental results from the valence level excitation, ionization and photodissociation of the parabanic acid molecule (C3H2N2O3, oxalylurea or imidazolidine-2,4,5-trione) in gas phase, using the photoelectron photoion coincidence technique, and synchrotron radiation in the VUV photon energy range of 11–21 eV provided by the TGM beamline from the LNLS synchrotron facility (Brazil) [1-3]. Parabanic acid is an historic compound, because many famous organic chemists (F. Wöhler, J.v. Liebigs, C.A. Wurtz, etc.) were involved in its synthesis and characterization. Its biological interest is that this compound results from the oxidation of biological fundamental compounds (such as uric acid [4]). Parabanic acid is also important in polymer science (used to prepare Fe complexes and sensors) and astrobiology (it has even been found in the Murchison meteorite [5]). In this work, we used Time-of-Flight Mass Spectrometry in the single (PEPICO) coincidence mode and synchrotron radiation to elucidate the ionic dissociation pathways as a function of the photon energy, covering the VUV valence region. Relative abundances and branching ratios have been determined for the molecular ion and the ionic fragments from the analysis of the corresponding peak shapes in the PEPICO mass spectra. Our present results extend the currently scarce knowledge on the valence photoionization processes of these important imidazol derivative compounds in the VUV, and provide new information on the valence-shell excitation and photodissociation of the parabanic acid molecule. High level DFT calculations have been performed for this molecule in order to obtain additional information on the geometry, electronic structure and energies, which ones were carried out at B3LYP/augcc-pVTZ level of theory. The electronic structure computations for its radical cations were carried out with the unrestrictred implementation UB3LYP/aug-ccpVTZ level of theory. References [1] Lago, A.F.; Coutinho, L.H.; Marinho, R.R.T.; Naves de Brito, A.; de Souza, G.G.B., Chem. Phys., 307 (2004) 9. [2] Lago, A.F.; Santos, A.C.F., de Souza, G.G.B., J. Chem. Phys., 120 (2004) 9547. [3] Pilling, S.; Lago, A.F.; Coutinho L. H.; Castilho, R.B.; de Souza, G.G.B.; Naves de Brito, A. Rapid Comm. Mass Spectr, 21 (2007) 3646. [4] Sanguinetti, S.M.; Batthyány, C.; Trostchansky, A.; Botti, H.; López, G.I.; Wikinski, R.L.W.; Rubbo, H.; Schreier, L.E. Arch. Biochem. Biophys. 423 (2004) 302–308. [5] Cooper, G.W.; Cronin, J.R. Geochim. Cosmochim. Acta 59 (1995) 1003–1005.

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P-10 Geometries and Adiabatic Excitation Energies of the Low-Lying States of CNC, C2N, N3, and NCO Studied with the Electron-Attached and Ionized Equation-of-Motion Coupled-Cluster Methodologies Jared A. Hansen1, Piotr Piecuch1, Jesse J. Lutz1, and Jeffrey R. Gour2 1Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA 2 Department of Chemistry, Stanford University, Stanford, California 94305, USA email: [email protected] The full and active-space electron-attached equation-of-motion coupled-cluster methods with up to 3-particle-2-hole (3p-2h) excitations in the electron-attaching operator R( N 1) , abbreviated as EA-EOMCCSD(3p-2h), and their ionized counterparts with up to 3h-2p excitations in the electron-removing operator R( N 1) , abbreviated as IP-EOMCCSD(3h-2p), that use the CCSD approach to obtain the ground state of the reference N-electron closed-shell system, introduced in Ref. 1, are used to optimize the geometries of the low-lying states of CNC, C2N, NCO, and N3, and determine the corresponding adiabatic excitation energies. It is shown that the active-space EA-EOMCCSD(3p-2h) and IP-EOMCCSD(3h-2p) approaches using small numbers of active orbitals provide excitation energies and geometries that are in excellent agreement with the results of the significantly more expensive full EA-EOMCCSD(3p-2h) and IP-EOMCCSD(3h-2p) calculations. Although the EA-EOMCCSD(3p-2h) calculations for the CNC and C2N molecules improve the EA-EOMCCSD(2p-1h) excitation energies, some differences with experiment remain in spite of the use of complete basis set extrapolations, indicating that either one needs 4p3h excitations or that the experimental data are uncertain. [1] Gour, J.R.; Piecuch, P.; Włoch, M. J. Chem. Phys. 123 (2005) Art. No. 134113 (14 pages). Gour, J.R.; Piecuch, P.; Włoch, M. Int. J. Quantum Chem. 106 (2006) 2854-2874. Gour, J.R.; Piecuch, P. J. Chem. Phys. 125 (2006), Art. No. 234107 (17 pages). [2] Hansen, J.A.; Piecuch, P.; Lutz, J.J.; Gour, J.R. Phys. Scr., accepted.

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P-11 Pi-bonding and biradical character in the valence iso-electronic series O3, S3, SO2 and OS2 V.A. Glezakou1, S.T. Elbert1, S.S. Xantheas,1 K. Ruedenberg2 1 Pacific Northwest National Laboratory, Richland WA 99352, USA 2 Ames Laboratory and Department of Chemistry, Iowa State University, Ames, IA 50011, USA [email protected] The bonding patterns in the valence isoelectronic series of the molecules O3, S3, SO2 and OS2 have been analyzed on the basis of electronic wave functions that include all strong correlations in the full molecule-optimized valence space, i.e. the MCSCF wave functions in terms of all 12126 determinants that are generated in C2v symmetry by the 18 valence electrons using 12 molecular orbitals. The atomic orbital bases were Dunning’s cc-pVTZ set for oxygen and ccpV(T+d)Z set for sulfur. Intrinsic localization of the optimized orbitals yielded molecular orbitals of quasi-atomic character which, by means of a general unbiased criterion, were transformed into directed bonding and non-bonding quasi-atomic orbitals on each atom. Examination of the first-order density matrix in this representation furnished a quantification of the decrease in the diradical character with the increasing strength of pi-bond formation due to charge donation from the central atom to the end atoms. The biradical character is found to increase from SO2 (0.09) to S3 (0.34) to O3 (0.44) to OS2 (0.63), a systematic trend that is manifestly related to the electro-negativity difference between these two atoms. Thus, while ozone cannot be described as a regular closed shell singlet, such as SO2, it can also not be visualized as having single electrons in non-bonded quasi-atomic π-orbitals at the end atoms, i.e. it is far from the full-blown biradical sometimes inferred from VB structures. Pi-bonding, though partial, is not insubstantial. Figure: Directed quasi-atomic FORS molecular orbitals in ozone

Work supported by the Chemical, Geo- and Biosciences Division, Basic Energy Sciences Office, US Department of Energy, at Pacific Northwest National Laboratory and at Iowa State University through the Ames Laboratory.

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P-12 Parametrization of the Extended Hubbard Model for hydrocarbons derived from RASPT2 potential energy curves of stretched ethene T. G. Schmalz1, Luis Serrano-Andrés2, Vicenta Sauri2, Manuela Merchán2, Josep M. Oliva3 1 Texas A&M University at Galveston, P. O. Box 1675, Galveston, TX 77553, USA 2 Instituto de Ciencia Molecular, Universitat de València, P.O. Box 22085, ES-46071 Valencia, Spain 3 Instituto de Química Física "Rocasolano", CSIC, ES-28006, Madrid, Spain e-mail: [email protected]

In this work we derive an Extended Hubbard Model in order to predict excited state energies in conjugated hydrocarbons and polymers where the ab initio computations are difficult or not feasible [1]. An effective electron-electron repulsion term is added to the Hückel Hamiltonian to account for electron correlation resulting in the Hubbard Hamiltonian [2]. According to the strength of this term, the Hubbard model allows to connect Molecular Orbital and Valence Bond theory to describe the chemical bond. In other words, the Hubbard model can treat the transition between conducting and insulating systems, i.e. independent electron and correlated electron systems. The parameters of the model are fit from ab initio computations of two-atom fragments and then transferred to large systems. The MS-RASPT2 method is used to compute the lowest potential energy surfaces of ethene as a function of the carbon-carbon bond length which are employed to parametrize the model for conjugated hydrocarbons [3,4]. This multiconfigurational method deals with bond-breaking properly and an extended basis set with diffuse functions on carbon atoms is required to treat the valence-Rydberg mixing in ethene. The Hubbard model can predict the transition energies of hydrocarbons and a sample of them are computed to be found in agreement with those obtained by MS-RASPT2.

[1] J. Hubbard, Proc. R. Soc. London, Ser. A 276 (1963) 238; 281 (1964) 401. [2] E. Hückel, Z. Physik 70 (1931) 204; 76 (1932) 628. [3] P. A. Malmqvist, K.. Pierloot, A. R. M. Shahi, C. J. Cramer, L. Gagliardi, J. Chem. Phys. 128 (2008) 204109. [4] V. Sauri, L. Serrano-Andres, A. R. M. Shahi, L. Gagliardi, S. Vancoillie, K. Pierloot, J. Chem. Theory Comput. 7 (2011) 153-168.

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Epilogue

Douglas J. Klein Texas A&M University at Galveston, Galveston, Texas, USA

The meeting was small with about 50 participants, from both chemistry & physics, representing a variety of views, but a relaxed & congenial attitude, in a beautiful setting in A Coruña. Surely a sincere thank you goes to the organizers: Josep Oliva, Mª Àngels Garcia-Bach, Moisés Canle, Antonio Chana, Isabel Fernández, Victoria García, & Arturo Santaballa, helped by Daniel Rodríguez and Eduardo Pinheiro. There were a variety of talks, starting with historical comments on classical chemical-bonding ideas & Valence-Bond (VB) theory. Then there were several “first principles” (explicitly) correlatedelectron computations, frequently of especially high accuracy, say by Wei Wu, by Rod Bartlett, and by Klaus Ruedenberg & L. Bytautas. Further, Gerardo Delgado-Barrio reported on the delicate matter of correlation involved in the binding of Hen & Hn+ clusters. Several researchers reported on different spin-coupled computational methods – including B. Braida, I. G. Kaplan, J. Gao, B. J. Duke, C. Valdemoro, and P. Piecuch (who described his coupled-cluster work in a comprehensive lecture, amazingly compressed into his time allotment). The work to obtain an ab-initio Heisenberg model for groupings of open-shell transition metal ions was described by M.-B. Lepetit, by C. J. Calzado & D. Maynau, and by R. Valenti. There were contributions on some qualitative or conceptual aspects, including the extent of unpairing of electrons localized along a boundary or at a set of vacant sites in a conjugated carbon π-network – for instance, it was described that resonating VB theory predicts the extent of such unpairing to be simply related to counts of primary & secondary sites occurring in the “starred” & “unstarred” sets of sites – such was described by P. Ordejón (& colleagues), by J. A. Alonso (& colleagues), and by myself (though but briefly). Joe Paldus reviewed work (by himself & colleagues) on “symmetry breaking”, especially as concerns different unrestrictions in the HartreeFock SCF method. A. Shurki, D. Danovich & especially S. Shaik focused on computations on different bioinorganic enzymes. P. C. Hiberty & colleagues described some interesting aspects of chemical bonding: the nominally covalent bonding of a few representative non-metals to F (or perhaps also O): this bonding was argued to be more properly viewed as a type of coordinate covalent (or dative) bonding. A few researchers (I. Panas, M. A. Garcia-Bach, and Jan Zaanen) addressed the problem of high-Tc superconductivity – in quite different ways, with no general agreement (as evidently is typical in the field), except that electron correlation is crucial, and that there are significant problems to understand not only regarding the superconducting phase but also adjacent phases (in the generic T vs. doping phase diagram). There were a few talks on many-body ideas –

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from V. O. Cheranovskii & E. V. Ezerskaya, from J. P. Coe, & from T. Nishino. J. I. Cirac described a general many-body (“tensor”) mathematical framework for explicitly correlated wave-functions, encompassing superpositions of spin-pairing resonance structures. R. W. A. Havenith described an interesting correlated band-structure approach to solids (reminding me of J. Hubbard’s X-functions and R. McWeeny’s group functions – but Havenith has implemented it in an ab-initio framework). A few of the reports concerned “density-matrix renormalization group” schemes – in particular, the talks by S. Sharma & G. K-L Chan and by R. Valenti – and finally J.-P. Malrieu’s interesting report seemed to be along this same line. Also there were notable further contributions by J. Michl and I. P. R. Moreira, and there was a good selection of posters – including one by J. M. Oliva and friends on carboranes. After Jan Zaanen’s “colorful” presentation, we celebrated Carmela Valdemoro’s birthday (and her fundamental on-going work in dealing with the 2nd-order reduced density matrix Nrepresentability approach in quantum chemistry). A few major contributors to the field were missed: P. W. Anderson, David Cooper, Roy McWeeny, & Ruben Pauncz. Especially in light of all the abinitio VB work reported, a tribute could be imagined to Joe Gerratt – and too I could mention my PhD advisor F. A. Matsen – but in fact there are several leaders (L. Pauling, G. W. Wheland, G. Rumer, W. T. Simpson, O. Kahn, P. O. Lowdin – and more) in the field who have now sadly passed away. Rod Bartlett posed a general question as to how resonating valence-bond descriptions, and presumably other schemes based on localized orbitals, could be fundamentally framed, say as derived from the first-order reduced density matrix. One answer was intimated in numerous talks, in that a simpler better description of a wave-function resulted – simpler perhaps in the sense of having fewer spin-coupled configurations – or simpler perhaps in terms of chemical interpretation. But the question posed really referred to how one would recognize the resonating valence-bond structure from say a complete CI wave-function. One sort of answer is framed in terms of different “long-range orders” (for macroscopic systems), each associated with a macroscopic eigenvalue of a reduced density matrix, generally of second or higher order (a macroscopic eigenvalue being one that scales with a positive power of the system size). Thus an RVB wave-function can give such a macroscopic eigenvalue (to a reduced density matrix), whilst a typical corresponding MO wave-function gives size-independent eigenvalues – and it is unreasonable to expect a perturbative (or related) approach to the base MO wave-function to give a good description. Yet another way to say this is that for large systems “renormalization flows” may be away from an MO description toward a resonating VB description – or some other highly correlated localized-orbital description. It seems, at least to this attendee, that there was a marvelous mix of interesting work described, interesting people to meet, and questions to be addressed – all in a delightfully beautiful congenial setting. I appreciate the discussions I had with several of the attendees, while I regret missing the opportunity to talk one-on-one with a few of the attendees. I hope that such a get together might be again entertained, especially with focus toward future trends and questions.

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List of Participants Participant J. A. Alonso R. J. Bartlett R. Berger B. Braïda C. J. Calzado M. Canle A. Chana V. O. Cheranovskii I. Cirac J. P. Coe D. Danovich J. Z. Dávalos G. Delgado Barrio B. J. Duke E. Eliav M. I. Fernández J. Gao M. A. García-Bach M. V. García Dopico R. García Fandiño F. J. González Alonso Gu Junjing R. W. A. Havenith P. C. Hiberty S. Humbel I. G. Kaplan D. J. Klein A. Lago M. – B. Lepetit E. Lomba García J. J. Lutz J. - P. Malrieu J. Michl I. P. R. Moreira T. Nishino J. M. Oliva P. Ordejón J. Paldus S. Peifeng P. Piecuch I. Panas Z. Rashid K. Ruedenberg J. A. Santaballa M. V. Sauri Peris S. Shaik S. Sharma A. Shurki C. Valdemoro S. Vázquez R. Valenti W. Wu J. Zaanen

Institution (Country) Universidad de Valladolid (Spain) University of Florida (USA) TU Darmstadt (Germany) Université Pierre et Marie Curie (France) Universidad de Sevilla (Spain) Universidad de A Coruña (Spain) CSIC (Spain) Karazin Kharkov National University (Ukraine) Max-Planck-Institut für Quantenoptik (Germany) Heriot-Watt University (UK) The Hebrew University-Institute of Chemistry (Israel) CSIC (Spain) CSIC (Spain) Monash University (Australia) Tel Aviv University (Israel) Universidad de A Coruña (Spain) University of Minnesota (USA) Universitat de Barcelona (Spain) Universidad de A Coruña (Spain) Universidad de Santiago de Compostela (Spain) CSIC (Spain) Xiamen Univ. (China) University of Groningen (The Netherlands) Université de Paris-Sud (France) Aix-Marseille Université (France) Universidad Nacional Autónoma de México (México) Texas A&M University (USA) Universidade Federal do ABC (Brasil) CNRS-ENSICAEN (France) CSIC (Spain) Michigan State University (USA) Université Toulouse (France) University of Colorado (USA) Universitat de Barcelona (Spain) Kobe University (Japan) CSIC (Spain) CIN2, CSIC-ICN (Spain) University of Waterloo (Canada) Xiamen Universtiy (China) Michigan State University (USA) Chalmers University of Technology (Sweden) Utrecht University (The Netherlands) Iowa State University (USA) Universidad de A Coruña (Spain) Universitat de Valencia (Spain) Hebrew University (Israel) Cornell University (USA) The Hebrew University (Israel) CSIC (Spain) Universidad de Santiago de Compostela (Spain) Goethe Universität Frankfurt (Germany) Xiamen University (China) Leiden University (The Netherlands)

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Workshop e-mail: [email protected] Workshop web page: http://watoc2011satelliteconferencecoruna.webs.com/

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O-10 PL-10 O-03 PL-11 PL-12 PL-03 O-11 O-07 P-02 O-01, P-03 O-12 P-04 O-02 P-05 P-06, P-07 O-09 PL-13 P-08 PL-06 PL-01 P-09 O-06 P-10 PL-20 PL-05 PL-15 PL-08 PL-07 PL-14 PL-16 O-04 P-01 O-05, P-11 P-12 PL-09 PL-02 O-08 PL-17 PL-18 PL-04 PL-19



Sponsors

Vicerreitoría de Investigación

GEFAM

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Sponsors

Vicerreitoría de Investigación

GEFAM