Numerically Stable Resonating Hartree-Fock for Computational Photochemists

Nonadiabatic molecular dynamics (NAMD) simulations are powerful tools that provide atomic scale insights into photochemical processes. However, the effectiveness of these NAMD simulations is extremely dependent upon the quality of their underlying electron structure theory (EST) engine. The ideal EST method for NAMD applications will produce correct electronic state crossings and balanced descriptions of states of different character, all without breaking the computational bank. The Parker research group believes state-averaged Resonating Hartree-Fock (SA-ResHF) is a promising candidate for the next generation of NAMD simulations. The ResHF wavefunction is a linear combination of nonorthogonal Slater determinants, which affords it enough flexibility to balance the demands of electronic states of starkly different character but comes at the cost of numeric instability. In this talk, I will demonstrate the strengths of ResHF by showing how it avoids state-averaging errors that commonly plague the CASSCF method. I will then present our numerically stable reformulation of the ResHF equations, which uses singular value decomposition and the matrix adjugate to avoid numeric "blow-ups" resulting from nearly orthogonal Slater determinants.