Efficient two-component self-consistent field procedures and gradients: implementation in TURBOMOLE and application to Au_(20)~-

摘要

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 Au_(147). 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.