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

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 H2 dissociation reveals the surprising stability of the spin-restricted solution at all separations, with a...