Analytical energy gradient for the two-component normalized elimination of the small component method.

Abstract

The analytical gradient for the two-component Normalized Elimination of the Small Component (2c-NESC) method is presented. The 2c-NESC is a Dirac-exact method that employs the exact two-component one-electron Hamiltonian and thus leads to exact Dirac spin-orbit (SO) splittings for one-electron atoms. For many-electron atoms and molecules, the effect of the two-electron SO interaction is modeled by a screened nucleus potential using effective nuclear charges as proposed by Boettger [Phys. Rev. B 62, 7809 (2000)]. The effect of spin-orbit coupling (SOC) on molecular geometries is analyzed utilizing the properties of the frontier orbitals and calculated SO couplings. It is shown that bond lengths can either be lengthened or shortened under the impact of SOC where in the first case the influence of low lying excited states with occupied antibonding orbitals plays a role and in the second case the jj-coupling between occupied antibonding and unoccupied bonding orbitals dominates. In general, the effect of SOC on bond lengths is relatively small (≤5% of the scalar relativistic changes in the bond length). However, large effects are found for van der Waals complexes Hg2 and Cn2, which are due to the admixture of more bonding character to the highest occupied spinors.