A b i n i t i o study of the zero-field splitting parameters of 3B1u benzene

The electron spin dipole–dipole contribution to the zero-field splitting of benzene in its lowest triplet state (3B1u in D6h symmetry) is determined theoretically by ab initio methods. Two hexagonal conformations are considered, distinguished by having carbon–carbon bond lengths appropriate to the 1A1g ground state (1.395 Å) and to the 3B1u state (1.427 Å). In addition, two distorted forms of D2h symmetry are treated, one having a compressed or ’’quinoidal’’ structure and the other having an elongated structure. All calculations are carried out with a double-zeta basis of contracted Gaussian-lobe functions. The correct microscopic spin-dipole Hamiltonian is used and all integrals are evaluated accurately. The hexagonal conformation with 1.427 Å bond lengths gives results in best agreement with experiment. A large configuration-interaction wavefunction leads to D=0.1676 cm−1, to be compared with D=0.1580 cm−1 obtained from the electron resonance spectra of benzene in a C6D6 host crystal. Both the quinoid and elongated forms corresponding to 2% – 3% distortions give zero-field-splitting patterns that are qualitatively different from experiment. Hence, these small deviations from purely hexagonal symmetry are found to have extremely large effects on the unpaired electron spin density in the molecule. The experimentally determined conformation appears to be slightly elongated, but the distortions must be much smaller than those considered in the present study and certainly less than 1%. Electron correlation is also found to have a very large effect on the splitting parameters. For example, the Hartree–Fock value of D for the hexagonal (1.427 Å) form is 0.1087 cm−1 as compared to 0.1676 cm−1 obtained from a large configuration-interaction wavefunction. An extensive analysis of the effect of electron correlation on the splitting parameter shows that excitations of the types σ2→π2 and π2→σ2 have little effect on D. By contrast, excitations of the types π2→π′2 (or π→π′) and σπ→σ′π′ increase D, whereas those of the type σ2→σ′2 (or σ→σ′) decrease D. The sum of the absolute values of the configuration-interaction effects for these classes of excitations is greater than the value of D itself. The implications of these results on previous semiempirical calculations are discussed.