TY - JOUR
T1 - Spin-orbit coupling patterns induced by twist and pyramidalization modes in C2H4
T2 - A quantitative study and a qualitative analysis
AU - Danovich, David
AU - Marian, Christel M.
AU - Neuheuser, Thomas
AU - Peyerimhoff, Sigrid D.
AU - Shaik, Sason
PY - 1998/7/16
Y1 - 1998/7/16
N2 - A study of the spin-orbit coupling (SOC) mechanisms which couple the triplet ππ* state (T1) to the singlet ground state (S0) in ethylene 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 requirements needed for good quality SOC calculations are elucidated by studying the SOC interaction using single- and multireference CI as well as MCSCF wavefunctions, with basis sets ranging from the minimal STO-3G all the way to an extended one with quadruple ζ and polarization quality. Two archetype distortion modes of ethylene were considered: a twist mode which changes the symmetry from D2h, to D2 and then to D2d and pyramidalization modes which change the ethylene symmetry to C2v, (syn-pyramidalization) or C2h (anti-pyramidalization), as well as Cs (i.e., a mono-pyramidalization distortion). It is found that both the twist and syn-pyramidalization distortions of ethylene promote a nonzero SOC interaction, which involves an interplay between one-center and two-center SOC terms. In the twist distortion, the interplay is strong because the one-center terms arise from a residual incomplete cancelation of the two on-site interactions. In contrast, in the syn-pyramidalization distortion the interplay is weak, because the one-center terms add up. Consequently, the syn-pyramidalization promotes SOC matrix elements which exceed 6 cm-1, while the twist mode has a weaker SOC on the order of 2 cm-1. Zero SOC is obtained for distortion which involve either a 90° twist, or an anti-pyramidalization. The monopyramidalization distortion leads to SOC which is ca. 50% of that which is generated by the syn-pyramidalization. A qualitative analysis based on symmetry and electronic structure enables to understand these trends. A simple physical model, which enables us to carry out the vectorial summation of SOC in a pictorial manner, is constructed and used to explain the trends in the twist and syn-pyramidalization modes.
AB - A study of the spin-orbit coupling (SOC) mechanisms which couple the triplet ππ* state (T1) to the singlet ground state (S0) in ethylene 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 requirements needed for good quality SOC calculations are elucidated by studying the SOC interaction using single- and multireference CI as well as MCSCF wavefunctions, with basis sets ranging from the minimal STO-3G all the way to an extended one with quadruple ζ and polarization quality. Two archetype distortion modes of ethylene were considered: a twist mode which changes the symmetry from D2h, to D2 and then to D2d and pyramidalization modes which change the ethylene symmetry to C2v, (syn-pyramidalization) or C2h (anti-pyramidalization), as well as Cs (i.e., a mono-pyramidalization distortion). It is found that both the twist and syn-pyramidalization distortions of ethylene promote a nonzero SOC interaction, which involves an interplay between one-center and two-center SOC terms. In the twist distortion, the interplay is strong because the one-center terms arise from a residual incomplete cancelation of the two on-site interactions. In contrast, in the syn-pyramidalization distortion the interplay is weak, because the one-center terms add up. Consequently, the syn-pyramidalization promotes SOC matrix elements which exceed 6 cm-1, while the twist mode has a weaker SOC on the order of 2 cm-1. Zero SOC is obtained for distortion which involve either a 90° twist, or an anti-pyramidalization. The monopyramidalization distortion leads to SOC which is ca. 50% of that which is generated by the syn-pyramidalization. A qualitative analysis based on symmetry and electronic structure enables to understand these trends. A simple physical model, which enables us to carry out the vectorial summation of SOC in a pictorial manner, is constructed and used to explain the trends in the twist and syn-pyramidalization modes.
UR - http://www.scopus.com/inward/record.url?scp=0001212273&partnerID=8YFLogxK
U2 - 10.1021/jp980391s
DO - 10.1021/jp980391s
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0001212273
SN - 1089-5639
VL - 102
SP - 5923
EP - 5936
JO - Journal of Physical Chemistry A
JF - Journal of Physical Chemistry A
IS - 29
ER -