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Myers–Saito and Schmittel cyclization of hepta-1,2,4-triene-6-yne : A theoretical REKS study Sam P. de Visser,a Michael Filatovb and Sason Shaik*a a T he Institute of Chemistry and the L ise Meitner-Minerva Center for Computational Quantum Chemistry, T he Hebrew University, 91904 Jerusalem, Israel b Department of T heoretical Chemistry, GoŽ teborg University, Reutersgatan 2, S-41320 GoŽ teborg, Sweden Received 13th December 2000, Accepted 30th January 2001 First published as an Advance Article on the web 6th March 2001

Spin-restricted ensemble-referenced KohnÈSham (REKS) calculations have been performed on the cyclization process of hepta-1,2,4-triene-6-yne leading to a Ðve-membered ring (Schmittel cyclization) or a six-membered ring (MyersÈSaito process), both products being biradicals. Geometries compare well with density functional as well as ab initio calculations and experimental measurements from the literature. Relative energies and singletÈtriplet gaps were studied and compared with BCCSD(T) calculations.

Introduction Highly unsaturated compounds can undergo cyclization leading to a cyclic biradical. For example, cyclization of cishex-3-ene-1,5-diyne leads to para-benzyne biradicals. This type of process is called the Bergman cyclization1 and is of considerable interest due to the biological activity of the biradicals as anti-tumor antibiotics. As a consequence many theoretical studies have been devoted to the Bergman cyclization processes.2h7 Furthermore, computational e†orts in these systems have led to the prediction of new anticancer drugs.8 Novel types of cyclization mechanisms, which involve biradical systems, are the MyersÈSaito9h12 and Schmittel13h17 reactions, Scheme 1. Both reactions in this Scheme start from cis-hepta-1,2,4-triene-6-yne reactant, 1, and lead to ringclosure into a 5-ring, 2, (Schmittel) or a 6-ring, 3, (MyersÈ Saito). Both product species are biradicals, but in contrast to the Bergman cyclization a r,p-biradical is obtained rather than a r,r-biradical. Schreiner and Prall18 calculated both the Schmittel and MyersÈSaito reactions at the CCSD(T)/ccpVDZ level of theory, and used CCSD(T) in combination with Bruekner-type orbitals in order to eliminate the contributions from single-excitations which lead to instabilities of the CCSD(T) wavefunction. Earlier studies of Engels and Hanrath used CASSCF and MR-CI ] Q to investigate these

reactions.19 Since theoretical calculations8 have already proved a useful means for the design of new antibiotics of the Bergman type, we deemed it necessary to study the new processes in Scheme 1 using density functional theory (DFT). Recently, a new DFT method has been developed in our group which has been found to be particularly suitable for the studies of biradical systems.20 The spin-restricted ensemblereferenced KohnÈSham (REKS) method has been shown, at least so far to reproduce reaction enthalpies and singletÈtriplet energy gaps on a par with high level quantum chemical methods like CCSD(T).21h24 However, to qualify as a low cost alternative to these sophisticated ab initio methods, REKS must Ðrst be tested on a whole reaction pathway. This is done in the present paper using the MyersÈSaito and Schmittel reactions as target processes. As shall be seen, the REKS data compare well with experimental and theoretical results from the literature.

Methods The molecular structures of singlet species were optimized using the spin-restricted ensemble-referenced KohnÈSham method20 which is implemented in the CADPAC5 program package.25 To understand the basic idea of REKS, consider two electrons sharing two degenerate or nearly degenerate orbitals, / r and / . Occupation in / and / can be expressed in terms of s r s the weighted sum of the mixture of the following quasidegenerate states :

7

W \ o / /6 T 1 r r W \ o / /6 T 2 s s (1) W \o/ / T 3 r s W \ o / /6 T, o /6 / T r s 4 r s The density for such a strongly correlated system is represented in terms of KohnÈSham orbitals with fractional occupations n and n of the active orbitals / and / , eqn. (2). r s r s The doubly occupied core orbitals are / . k o(r) \ ; 2 o / (r) o2 ] n o / (r) o2 ] n o / (r) o2 (2) k r r s s

Scheme 1

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Phys. Chem. Chem. Phys., 2001 3, 1242È1245 This journal is ( The Owner Societies 2001

DOI : 10.1039/b009965l

The ground state REKS energy (EREKS) gives then the followgs ing expression : n n EREKS \ r E(/ /6 ) ] s E(/ /6 ) gs r r s s 2 2 ](n n )3@4[E(/ / ) [ 1 E(/ /6 ) [ 1 E(/ /6 )] (3) r s r s 2 r s 2 s r The one-electron orbitals and fractional occupation numbers are obtained by self-consistent minimization of the energy with respect to the density. See ref. 20 and 23 for more details. Triplet states were calculated using the spin-restricted open shell KohnÈSham method (ROKS).26,27 All calculations were performed with a 6-31G(d) basis set using the BLYP exchange functional and full geometry optimization was done. The optimizations were carried out without symmetry constraints. A full numerical frequency analysis was performed and all minimum energy structures discussed here had real frequencies only, whereas the transition states had one imaginary frequency. Optimized geometries are close but not identical to those obtained by Schreiner and Prall18 at the BLYP level of theory with unrestricted broken-spin symmetry wavefunctions (UBS-BLYP).

Results and discussion The triplet state biradicals 2 and 3 (Scheme 1) have two closely lying singly occupied orbitals with a@ and aA symmetry in C symmetry which is maintained in the process. The a@ S orbital is a r-type orbital located in the plane of symmetry (the molecular plane r ), while the aA orbital is a p-type xy orbital. The shape of the orbitals is depicted in Scheme 2. While the r-orbitals are located primarily on one of the carbon atoms, the p-orbitals are delocalized over the whole system. For the singlet state, the optimized REKS orbitals are not pure symmetry a@ and aA orbitals. Rather, the two orbitals involved (/ with a@ symmetry and / with aA symmetry) are 1 2 50 : 50 mixtures ; a \ (/ ] / )/J2 and b \ (/ [ / )/J2. 1 2 1 2 With these orbitals the REKS wavefunction W \ REKS 1/J2 o aa6 T [ 1/J2 o bb6 T belongs to a 1AA state. One can check by direct substitution of the expressions for a and b, that the REKS wavefunction with such orbitals does indeed belong to the AA irrep and not to A@. In short, it is the total wavefunction which should belong to a certain irrep, not necessarily the one-electron orbitals. Our REKS orbitals are delocalized for the 1AA state, and not localized as one can expect from the (2, 2)CASSCF wavefunction. At the same time, the total REKS

Scheme 2

wavefunction is correct, and is precisely the same as would be obtained from (2,2)CASSCF. Optimized geometries in the singlet and triplet state of reactant cis-hepta-1,2,4-triene-6-yne (1), Schmittel product (2) and MyersÈSaito product (3) have been schematically depicted in Fig. 1. Additionally, the transition states leading to the Schmittel product (TS2) and the MyersÈSaito product (TS3) have been located for the singlet spin state. Both transition states were characterized by a frequency calculation and were found to have one imaginary frequency with magnitude i 485 cm~1 (TS2) and i 223 cm~1 (TS3). As expected, the mode of the imaginary frequencies corresponds to a ring-closure bending mode. The vectors of the imaginary modes have been depicted in Fig. 2. The geometries optimized with REKS compare reasonably well with those obtained by Schreiner and Prall18 at the UBSBLYP/6-31G* level of theory. Bond distances of 1 and 3 are reproduced within 0.002 and 0.004 AŽ , respectively. The product molecule 2, however, shows somewhat larger di†erences up to a maximum of 0.015 AŽ . The calculated ringclosure bond length in TS3, though, is appreciably shorter than that of Schreiner and Prall who found 2.114 AŽ , whereas our result is 2.009 AŽ . The spin contamination in the UBSBLYP may be the origin of these di†erences.

Fig. 1 Optimized molecular structures of intermediates leading to Schmittel product (2, top) and MyersÈSaito product (3, bottom). Bond distances are in AŽ and angles are in degrees. Optimized triplet geometries are written in brackets.

Phys. Chem. Chem. Phys., 2001, 3, 1242È1245

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Table 1 Relative energies of 1, TS2, 2, TS3 and 3 obtained at various levels of theory

1 TS2 2 TS3 3

REKS 6-31G(d) (This worka)

CASSCF(10,10) 6-31G(d) (Ref. 19b)

MR-CI ] Q 6-31G(d) (Ref. 19b)

BLYP 6-31G(d) (Ref. 18a)

CCSD(T) cc-pVDZ (Ref. 18a)

BCCSD(T) cc-pVDZ (Ref. 18a)

Experiment (Ref. 10)

0.0 33.4 16.5 20.0 [8.3

0 37 18 29 ]4

0 35 12 25 [21

0 34 19 23 [2

0 35 17 23 [24

0 35 10 23 [12

]22 ^ 1 [15 ^ 3

a Includes zero point energy corrections. b No corrections for zero point energies.

Table 2 SingletÈtriplet energy gaps for Schmittel product (2) and MyersÈSaito product (3)a

2 3

REKS 6-31G(d) (This workb)

MCSCF(8,8) cc-pVDZ (Ref. 28)

MR-CI ] Q 6-31G(d) (Ref. 19)

UBS-BLYP cc-pVTZ (Ref. 18b)

CCSD(T) cc-pVDZ (Ref. 18b)

BCCSD(T) cc-pVDZ (Ref. 18b)

Experiment (Ref. 29)

]3.2 ]0.4

È [3.0

]5 0.0

]1.7 [0.8

]8.8 [15.1

]2.9 [1.2

P[5.0

a A negative value implies a singlet ground state. b Includes corrections for zero point energies.

Fig. 2 Vibrational modes of imaginary frequencies for TS2 and TS3.

Energies of the optimized structures have been calculated relative to cis-hepta-1,2,4-triene-6-yne (1) and are collected in Table 1. The barrier (via TS2) leading to the Schmittel product is identical to the theoretical results at the CCSD(T), BCCSD(T) and MR-CI ] Q levels from the literature.18,19 The biradical geometry (2) of the Schmittel process calculated with REKS is energetically within 2 kcal mol~1 of the CCSD(T) and CASSCF(10,10) results from ref. 18 and 19. Somewhat larger discrepancies for the MyersÈSaito process (via TS3) were obtained. Nevertheless, the height of the barrier TS3 is still within 2È3 kcal mol~1 of the CCSD(T), BCCSD(T) and experimental values. Our calculations predict isomer 3 to be 3.7 kcal mol~1 higher in energy than the calculations obtained at the BCCSD(T) level of theory. The experimental value, on the other hand, is 6.7 ^ 3 kcal mol~1 lower than our result. The literature values for this species, though, span a range starting from ]4 kcal mol~1 (CASSCF(10,10)/ 6-31G(D)) to [24 kcal mol~1 (CCSD(T)/cc-pVDZ) with the experimental value almost midway in between this range ([15 kcal mol~1). If the BCCSD(T) result is used as a benchmark then the REKS result is quite good. Although the much less computationally demanding UBS-BLYP method manages to reproduce the relative energies of the transition states (TS2 and TS3) well with respect to the BCCSD(T) and experimental results, the relative energies of the biradicals 2 and 3 are signiÐcantly less accurate. Thus, for biradical systems REKS gives a substantial improvement with respect to UBS-BLYP, both in terms of electronic structure as well 1244

Phys. Chem. Chem. Phys., 2001, 3, 1242È1245

as in energetic terms, and reproduces fairly closely the BCCSD(T) results, see Table 1. The Schmittel (2) and MyersÈSaito (3) product species have been fully optimized in the singlet as well as the triplet spin state and the results are presented in Table 2. SingletÈtriplet gaps for 2 and 3 calculated at a high level of theory are due to Schreiner and Prall,18 Engels and Hanrath19 and Wenthold et al.28 Our value obtained for 2 is in perfect agreement with the BCCSD(T) result of Schreiner and Prall and within 2 kcal mol~1 of the MR-CI ] Q calculations of Engels and Hanrath. The calculated singletÈtriplet energy gap for the Myers product 3 is ]0.4 kcal mol~1 (REKS) pointing to a triplet ground state. Results from the literature, however, indicate a singlet ground state. Experimentally, Logan et al.29 determined the lower limit of the singletÈtriplet gap to be [5.0 kcal mol~1, which is signiÐcantly lower than our result. Nevertheless, the highest level calculations, BCCSD(T)18 and MRCI ] Q19 indicate that the value is extremely small, as predicted also by REKS. Unlike in other cases, here the UBSBLYP results are also good. This, however, reÑects error cancellation. This can be gleaned from Table 1 which shows that the stability of the singlet state of 3 is underestimated signiÐcantly. The same applies to the triplet state.

Conclusions Density functional theory calculations on cyclization processes of hepta-1,2,4-triene-6-yne (1) have been performed using the REKS method. REKS calculations reproduce high level ab initio calculations from the literature reasonably well. For the target system, REKS gives better agreement with experiment for these systems than CCSD(T) with a cc-pVDZ basis set. Relative energies, geometries and singletÈtriplet gaps are close to those obtained with BCCSD(T). Consequently, REKS provides a low-cost alternative for studies of a whole reaction path for biradical systems.

Acknowledgements This work was Ðnancially supported by the Robert Szold Fund and the Niedersachsen Foundation.

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