SPIN-ORBIT-COUPLING PATTERNS INDUCED BY TWIST AND PYRAMIDALIZATION MODES IN C2H4 - A QUANTITATIVE STUDY AND A QUALITATIVE-ANALYSIS

A study of the spin-orbit coupling (SOC) mechanisms which couple the t riplet pi pi state (T-1) to the singlet ground state (S-0) in ethylen e is carried out at a variety of computational levels and basis sets, using the full Breit-Pauli (BP) SOC Hamiltonian, the one-electron mean -field (MF) operator, and the approximate one-electron operator based on an effective nuclear charge, Z. The basis set and wave functions r equirements needed for good quality SOC calculations are elucidated by studying the SOC interaction using single- and multireference CI as w ell as MCSCF wavefunctions, with basis sets ranging from the minimal S TO-3G all the way to an extended one with quadruple zeta and polarizat ion quality. Two archetype distortion modes of ethylene were considere d: a twist mode which changes the symmetry from D-2h to D-2 and then t o D-2d and pyramidalization modes which change the ethylene symmetry t o C-2v (Syn-pyramidalization) or C-2h (anti-pyramidalization), as well as C-s (i.e., a mono-pyramidalization distortion). It is found that b oth the twist and syn-pyramidalization distortions-of ethylene promote a nonzero SOC interaction, which involves an interplay between one-ce nter and two-center SOC terms. In the twist distortion, the interplay is strong because the one-center terms arise from a residual incomplet e cancelation of the two;on-site interactions. In contrast, in the syn -pyramidalization distortion the interplay is weak, because the one-ce nter terms add up. Consequently, the syn-pyramidalization promotes SOC matrix elements which exceed 6 cm(-1), while the twist mode has a wea ker SOC on the order of 2 cm(-1). Zero SOC is obtained for distortion which involve either a 90 degrees twist, or an anti-pyramidalization. The monopyramidalization distortion leads to SOC which is ca. 50% of t hat which is generated by the syn-pyramidalization. A qualitative anal ysis based on symmetry and electronic structure enables to understand these trends. A simple physical model, which enables us to carry out t he Vectorial summation of SOC in a pictorial manner, is constructed an d used to explain the trends in the twist and syn-pyramidalization mod es.