Efficient two-component self-consistent field procedures and gradients: implementation in TURBOMOLE and application to

Abstract

The implementation of gradients of two-component density functional (DFT) and hybrid-DFT energies is presented as well as several improvements with respect to our previous version in the self-consistent field (SCF) procedure: Calculation of the Hartree–Fock (HF) exchange with four-centre integrals, use of difference density formalism and partial exploitation of symmetry. Efficiency is demonstrated by comparison to recently reported data and by calculation of energy and gradient of Au147. As an example of use, structure parameters of Au− 20 were optimised and subsequently vibration frequencies were calculated numerically from the analytical gradients at two-component level. For this example, spin–orbit coupling leads to higher degeneracy of vibrational levels by lifting degeneracy of electronic levels, as the latter prevents Jahn–Teller distortion.