Violations of Hund's rule in molecules — where to look for them and how to identify them

Abstract

Violations of Hund's rule are predicted to be found in D 4 h cyclobutadiene (CBD), D 8 h cyclooctatetraene (COT), and in non-Kekulé hydrocarbon diradicals that have disjoint NBMOs. In D 4 h CBD the singlet is calculated to lie below the triplet by − ΔE ST = 6.3 kcal mol −1 at the CAS-SDCI + (Q)/6-31G ∗ level of theory. This value is bracketed by the CASSCF and CASPT2N values of, respectively, − ΔE ST = 10.6 and 4.0 kcal mol −1. For D 8 h COT CASSCF, CASPT2N and MR-(π-SD, σ-S)CI + (Q)/6-31G ∗ calculations give, respectively, − ΔE ST = 15.8, 6.7 and 8.5 kcal mol −1. In both [4 n]annulenes the geometry of highest symmetry is the equilibrium geometry of the triplet but the transition state for bond shifting in the singlet. Consequently, the “bond-alternation” vibration, which shortens half the CC bonds and lengthens the other half, has a relatively high frequency in the triplet but an imaginary frequency in the singlet. As a result, zero-point vibrational energy corrections increase − ΔE ST by ca. 2 kcal mol −1 in both antiaromatic annulenes. The role of calculations in assigning the electron photodetachment spectrum of COT − and thereby confirming experimentally that D 8 h COT really does violate Hund's rule is discussed. CASPT2N calculations of UV spectra are shown to be useful for deciding whether the singlet or triplet state is responsible for the UV-Vis spectrum of non-Kekulé hydrocarbon diradicals. Comparison of the spectra calculated for the singlet and the triplet states of 1,2,4,5-tetramethylenebenzene (TMB), 4,5-dimethylenecyclopentane-1,3-diyl (DMCPD) and 2,3-dimethylenecyclohexane1,3-diyl (DMCHD) with those observed indicates that TMB has a singlet ground state but that DMCPD and DMCHD both have triplet ground states.