Wavefunction stability analysis without analytical electronic Hessians: application to orbital-optimised second-order Moller-Plesset theory and VV10-containing density functionals

作者：Sharada Shaama Mallikarjun; Stueck David; Sundstrom Eric J; Bell Alexis T; Head Gordon Martin^*

来源：Molecular Physics, 2015, 113(13-14): 1802-1808.

DOI：10.1080/00268976.2015.1014442

• density functional theory
• quantum chemistry
• Brueckner orbitals
• orbital optimisation
• stability analysis

Wavefunction stability analysis is commonly applied to converged self-consistent field (SCF) solutions to verify whether the electronic energy is a local minimum with respect to second-order variations in the orbitals. By iterative diagonalisation, the procedure calculates the lowest eigenvalue of the stability matrix or electronic Hessian. However, analytical expressions for the electronic Hessian are unavailable for most advanced post-Hartree-Fock (HF) wave function methods and even some Kohn-Sham (KS) density functionals. To address such cases, we formulate the Hessian-vector product within the iterative diagonalisation procedure as a finite difference of the electronic gradient with respect to orbital perturbations in the direction of the vector. As a model application, following the lowest eigenvalue of the orbital-optimised second-order Moller-Plesset perturbation theory (OOMP2) Hessian during H-2 dissociation reveals the surprising stability of the spin-restricted solution at all separations, with a second independent unrestricted solution. We show that a single stable solution can be recovered by using the regularised OOMP2 method (delta-OOMP2), which contains a level shift. Internal and external stability analyses are also performed for SCF solutions of a recently developed range-separated hybrid density functional, omega B97X-V, for which the analytical Hessian is not yet available due to the complexity of its long-range non-local VV10 correlation functional.

• 出版日期2015-7-18