HCN a - Washington State University

JOURNAL OF CHEMICAL PHYSICS

VOLUME 116, NUMBER 8

22 FEBRUARY 2002

Electron binding energies of dipole-bound anions at the coupled cluster level with single, double, and triple excitations: HCNÀ and HNCÀ Kirk A. Peterson Pacific Northwest National Laboratory, Environmental Molecular Sciences Laboratory, Theory, Modeling & Simulations, Richland, Washington 99352 and Department of Chemistry, Washington State University, Richland, Washington 99352

Maciej Gutowskia) Pacific Northwest National Laboratory, Environmental Molecular Sciences Laboratory, Theory, Modeling & Simulations, Richland, Washington 99352, and Department of Chemistry, University of Gdan´sk 80-952 Gdan´sk, Poland

共Received 30 November 2001; accepted 3 December 2001兲 The electron binding energies for the weak dipole-bound anions HCN⫺ and HNC⫺ were found to be 13.2 and 35.7 cm⫺1, respectively, at the coupled cluster level of theory with single, double, and triple excitations 关CCSDT兴. A more approximate approach, in which the triples contribution is treated perturbatively 关CCSD共T兲兴, provides an electron binding energy which is underestimated for HCN⫺ by 25% and overestimated for HNC⫺ by 19%. The new results provide benchmarks for model potentials aiming to reproduce dynamical correlation effects in electron–molecule interactions. © 2002 American Institute of Physics. 关DOI: 10.1063/1.1445743兴

electron correlation effects to D was found to be the largest for systems with small electron binding energies at the KT level, which leads to a large dynamic polarizability of the excess electron and therefore a large dispersion stabilization, and positive correlation corrections to the dipole moment of the neutral.7 The dynamic correlation effects between the excess electron and the neutral molecule were neglected in model potentials designed to describe an excess electron interacting with clusters of polar molecules.15–18 Only recently, the first generation of one-electron model potentials was proposed that includes the dispersion interaction by means of a Drude model.19 The electron binding energies obtained within this model were benchmarked against ab initio calculated electron binding energies. A discrepancy was reported for HNC⫺ , for which the model potential provided an electron binding energy smaller by 12 cm⫺1 than the coupled cluster method with single, double, and non-iterative triple excitations 关CCSD共T兲兴. The discrepancy was assigned to the slow convergence of electron correlation methods rather than to deficiencies of the model potential. HCN and HNC are undoubtedly two of the more challenging systems for describing the binding of an excess electron.7,9,19,20 HCN is challenging because of its very small 共ca. 10 cm⫺1兲 electron binding energy and because of the near-cancellation between the stabilizing electron–molecule dispersion interaction and destabilizing correlation correction to the static Coulomb electron–molecule interaction. Indeed, the HF dipole moment of HCN of 3.29 D is reduced to 3.05 D upon inclusion of electron correlation effects21 and an ab initio treatment of the –CwN triple bond is notoriously difficult. A different kind of challenge is encountered with HNC. The values of D KT and D SCF are only 3.15 and 3.22 cm⫺1, respectively, but electron correlation effects provide an extra stabilization of ca. 40 cm⫺1.7,20 Hence, the HF

It is well established that a polar molecule with a dipole moment exceeding 1.625 D can bind an excess electron in the context of the Born–Oppenheimer approximation.1– 4 However, the value of the dipole moment alone is not sufficient to determine the value of the electron binding energy 共D兲. First, occupied orbital exclusion effects, higher-thandipole multipoles, and electrostatic penetration effects need to be taken into account. This is accomplished at the Koopmans’ theorem 共KT兲 level of theory for the electron binding energy (D KT), in which the charge distribution of the neutral molecule is approximated at the Hartree–Fock 共HF兲 level.5,6 This approach neglects orbital relaxation and electron correlation effects. Orbital relaxation effects, which describe the effects of polarization of the neutral molecule by the excess electron as well as back-polarization, are reproduced when HF energies are obtained for the anion and the neutral and the electron binding energy (D HF) is calculated as a difference thereof. The orbital relaxation effects have been found to be very small for weak dipole-bound anions.7 On the other hand, electron correlation effects were found to provide a large part of electron binding energy.7–14 This contribution is frequently larger in magnitude than the D KT term. The electron correlation contribution to the excess electron binding energy in dipole-bound anions encompasses two effects.14 First, there is a stabilizing dynamical correlation between the excess electron and the electrons of the neutral molecule, analogous to the dispersion interaction in van der Waals complexes. Second, electron correlation effects improve description of the charge distribution of the neutral relative to the HF description, which in turn modifies the magnitude of the static Coulomb interaction between the excess electron and the neutral. The relative contribution of Author to whom correspondence should be addressed 共PNNL兲. Electronic mail: [email protected]

a兲

0021-9606/2002/116(8)/3297/3/$19.00

3297

© 2002 American Institute of Physics

Downloaded 20 Sep 2002 to 134.121.44.19. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

3298

J. Chem. Phys., Vol. 116, No. 8, 22 February 2002

K. A. Peterson and M. Gutowski

TABLE I. Electron binding energies for HCN⫺ and HNC⫺ 共in cm⫺1兲 determined at different levels of theory. Method X

DX

Method X

DX

HCN⫺ SCF MP2 MP3 MP4共DQ兲 MP4共SDQ兲 MP4共SDQT兲

11.60a 11.88a 11.77a 11.97 13.01 12.98a

SCF MP2 MP3 MP4共DQ兲 MP4共SDQ兲 MP4共SDQT兲

3.22a 13.20a 9.83a 9.98 11.03 12.67a

HNC⫺

a

CCD CCSD CCSDT CCSD共T兲a

11.42 13.25 13.21 9.92

CCD CCSD CCSDT CCSD共T兲a

9.77 28.07 35.68 42.49

References 7,20.

mean-field approximation only accounts for 8% of the excess electron binding energy. Both the enhancement of the dipole moment of HNC by 0.21 D due to electron correlation effects21 and a dispersion-type electron–molecule interaction contribute to a large stabilization of the excess electron relative to the value of D SCF. Non-Born–Oppenheimer coupling between the electronic and rotational degrees of freedom is expected to be secondary for HCN⫺ and HNC⫺ because their rotational constants, 1.48 and 1.51 cm⫺1, respectively, are one order of magnitude smaller than the calculated values of D. Here, we report the electron binding energies for HCN⫺ and HNC⫺ determined at the coupled cluster level of theory with the full iterative treatment of single, double, and triple excitations 关CCSDT兴.22 These calculations were performed using the ACES II program suite.23 The new results are compared with earlier results obtained at the coupled cluster level with single, double, and noniterative triple excitations.7,20 We used the same basis set, i.e., aug-cc-pVTZ24 supplemented with the diffuse sets of s 共8兲, p 共9兲, and d 共4兲 functions, and the same geometries for HCN and HNC as those discussed in Refs. 7 and 20. The value of D for a method X (D X ) was calculated by subtracting the energies of the anion from those of the neutral D X ⫽E NX ⫺E AX , where E NX and E AX stand for the energies of the neutral and the anion, respectively. The CCSDT calculations on the anions were based on restricted open-shell Hartree–Fock orbitals. The core 1s orbitals were not correlated in the CCSDT calculations. The main finding is that the iterative treatment of triple excitations does make a difference when calculating electron binding energies for weak dipole-bound anions. The values of D determined at the CCSD共T兲 and CCSDT levels differ by 25% and 19% for HCN⫺ and HNC⫺ , respectively. 共See Table I兲. Moreover, the CCSD共T兲 method underestimates the value of D for HCN⫺ and overestimates for HNC⫺ when compared to the CCSDT results. An optimistic finding is that

the convergence of D within the hierarchy of coupled cluster methods 共S, SD, SDT兲 is faster than assumed heretofore on the basis of the CCSD共T兲 results. The discrepancy between D CCSD and D CCSDT is only 0.04 cm⫺1 for HCN⫺ . Hence, the CCSDT value of D is apparently converged. A cancellation between electron correlation effects, which decrease the dipole moment of the neutral, and stabilizing dynamical correlation effects between the excess electron and the neutral molecule, clearly favors this fast convergence. No cancellation occurs for HNC⫺ , as the dipole moment of the neutral increases upon inclusion of correlation effects, and the convergence of the coupled cluster methods is much slower than for HCN⫺ . In fact, the values of D CCSD and D CCSDT still differ by 7.61 cm⫺1 for HNC⫺ . It will require an approach such as CCSDTQ25 to demonstrate convergence with respect to the coupled cluster excitation level for this system. The relatively slow convergence of the coupled cluster expansion is also reflected in the magnitude of the largest amplitudes from the CCSDT calculations, which amount to 0.50 and 0.07 for HNC⫺ and HCN⫺ , respectively. On the other hand, the largest amplitudes for the neutrals HNC and HCN do not exceed 0.02. The largest amplitudes in these anionic calculations are related to single excitations from an orbital occupied by the excess electron. The large values of the T1 amplitudes for HNC⫺ may be related to the fact that the charge distribution of the excess electron becomes significantly contracted when the dipole moment of the neutral core increases upon inclusion of correlation effects. As we suggested earlier,9 the physical interpretation of D would benefit if Bruckner orbitals25 were used to construct the single determinantal wave function for the anion and the neutral. This approach would compensate for inaccuracies in the properties of neutral molecules inherited from the HF approximation; see model II in Ref. 19. The new values of electron binding energies for HCN⫺ and HNC⫺ of 13.2 and 35.7 cm⫺1, respectively, can be used to evaluate the performance of a Drude-model approach to the dispersion interaction.19 The model potential performs very well, as D for HCN⫺ is underestimated by only 7%. A larger underestimation of 18% takes place for HNC⫺ . We cannot claim that the CCSDT result is methodologically converged, but an underestimation of 6.4 cm⫺1 is as large as the difference between D CCSD and D CCSDT. The MPn series converges well for D of HCN⫺ and the discrepancy between the MP4 共SDQT兲 and CCSDT result is only 0.23 cm⫺1. A satisfactory value of D obtained at the self-consistent field 共SCF兲共MP1兲 level results from a fortuitous cancellation of errors described above. The convergence of the MPn series for D of HNC⫺ is slow and the MP4 共SDQT兲 value of D recovers only 36% of D CCSDT. Hence, the usefulness of low-order MPn treatments can be problematic for weak dipole-bound anions. In summary, the CCSDT values of electron binding energies in HCN⫺ and HNC⫺ are 13.2 and 35.7 cm⫺1, respectively. The full iterative treatment of triple excitations does matter for weak dipole-bound anions. The CCSD共T兲 approach, in which triple excitations are treated perturbatively, provides an electron binding energy which is underestimated for HCN⫺ by 25% and overestimated for HNC⫺ by 19%.


Electron binding energies of HCN⫺ and HNC⫺

J. Chem. Phys., Vol. 116, No. 8, 22 February 2002

The role of iterative triple excitations for dipole-bound anions and solvated electrons with electron binding energies one order of magnitude larger than those of HCN⫺ and HNC⫺ is currently being investigated. ACKNOWLEDGMENTS

This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division and Polish State Committee for Scientific Research 共KBN兲 Grant No. DS/8371-4-0137-1. This research was performed in the William R. Wiley Environmental Molecular Sciences Laboratory 共EMSL兲 at the Pacific Northwest National Laboratory 共PNNL兲. Operation of the EMSL is funded by the Office of Biological and Environmental Research in the U.S. DOE. PNNL is operated by Battelle for the U.S. DOE under Contract No. DE-AC06-76RLO 1830. E. Fermi and E. Teller, Phys. Rev. 72, 399 共1947兲. J. Simons and K. D. Jordan, Chem. Rev. 87, 535 共1987兲. 3 D. R. Bates, Adv. At., Mol., Opt. Phys. 27, 1 共1991兲. 4 J. Kalcher and A. F. Sax, Chem. Rev. 94, 2219 共1994兲. 5 K. D. Jordan and W. Luken, J. Chem. Phys. 64, 2760 共1976兲. 6 K. D. Jordan and J. J. Wendoloski, Chem. Phys. 21, 145 共1977兲. 7 M. Gutowski and P. Skurski, Recent Res. Devel. Phys. Chem. 3, 245 共1999兲. 8 M. Gutowski, P. Skurski, A. I. Boldyrev, J. Simons, and K. Jordan, Phys. Rev. A 54, 1906 共1996兲. 1 2

3299

9

M. Gutowski, K. D. Jordan, and P. Skurski, J. Phys. Chem. A 102, 2624 共1998兲. 10 P. Skurski and M. Gutowski, J. Chem. Phys. 108, 6303 共1998兲. 11 G. L. Gutsev and R. J. Bartlett, J. Chem. Phys. 105, 8785 共1996兲. 12 D. M. A. Smith, J. Smets, Y. Elkadi, and L. Adamowicz, J. Chem. Phys. 107, 5788 共1997兲. 13 D. M. A. Smith, J. Smets, Y. Elkadi, and L. Adamowicz, J. Chem. Phys. 109, 1238 共1998兲. 14 M. Gutowski and P. Skurski, J. Phys. Chem. B 101, 9143 共1997兲. 15 J. Schnitker and P. J. Rossky, J. Chem. Phys. 86, 3462 共1987兲. 16 R. N. Barnett, U. Landman, C. L. Cleveland, and J. Jortner, J. Chem. Phys. 88, 4421 共1988兲. 17 C. Desfrancois, Phys. Rev. A 51, 3667 共1995兲. 18 A. Wallqvist, D. Thirumalai, and B. J. Berne, J. Chem. Phys. 85, 1583 共1986兲. 19 F. Wang and K. D. Jordan, J. Chem. Phys. 114, 10717 共2001兲. 20 P. Skurski, M. Gutowski, and J. Simons, J. Chem. Phys. 114, 7443 共2001兲. 21 The QCISD/aug-cc-pVTZ results from Refs. 7 and 20. 22 J. Noga and R. J. Bartlett, J. Chem. Phys. 86, 7041 共1987兲. 23 ACES II is a program product of the Quantum Theory Project, University of Florida. Authors: J. F. Stanton, J. Gauss, J. D. Watts, et al. Integral packages included are VMOL 共J. Almlo¨f and P. R. Taylor兲; VPROPS 共P. Taylor兲; ABACUS 共T. Helgaker, H. J. Aa. Jensen, P. Jørgensen, J. Olsen, and P. R. Taylor兲. 24 R. A. Kendall, T. H. Dunning, Jr., and R. J. Harrison, J. Chem. Phys. 96, 6796 共1992兲. 25 R. J. Bartlett and J. F. Stanton, in Reviews in Computational Chemistry, edited by K. B. Lipkowitz and D. B. Boyd 共VCH, New York, 1994兲, Vol. V.
