Ab initio spin–orbit coupling SCF calculation of parity-violating energy of chiral molecules

Abstract

The spin–orbit coupling SCF (SOC-SCF) wavefunction was obtained on the basis of Breit–Pauli Hamiltonian and generalized spin-orbitals and was used to calculate the parity-violating energy, E pv, of chiral molecules. For the twisted HOOH molecule, the magnitude of SOC-SCF E pv is comparable with those of RPA, MC-LR, and DHF methods, and 2 or 3 times as large as that calculated by sum-over-state perturbation theory (SOS-PT). Moreover, the SOC-SCF method gave a reliable variation in the E pv value for the conformational change of l-alanine zwitterion ( l-ALAZ), indicating that the SOC was introduced appropriately into the SOC-SCF wavefunction. Calculations for several chiral molecules have suggested that the [5s2p/3s] basis set was acceptable for the SCF–SCF E pv calculation of large molecules. The contribution of one- and two-electron spin–orbit coupling terms to E pv was analyzed by dividing the E pv values in parts. It was confirmed that only one-center terms of the spin–orbit coupling integrals are sufficient in the SOC-SCF E pv calculation, although both one- and two-electron terms should be included. The SOC-SCF method with the [5s2p/3s] basis set was applied to l-ALAZ in aqueous solution, and the E pv map was created as a function of two torsion angles, ϕ for the NH 3 group and θ for the CO 2 group. In the ( ϕ, θ) map of E pv, the positive E pv area is wider than the negative one, and the averaged E pv value was +2.1×10 −20 hartree, indicating that l-ALAZ is more unstable than d-ALAZ in aqueous solution due to the parity-violating weak neutral current interaction.