Robust strategies for non-orthogonal multi-configuration self-consistent field wavefunctions : Hessian optimization techniques

The recently developed orbital optimized non-orthogonal multi-configurational self-consistent field (NOMCSCF) approach is one of several different-orbitals-for-different-configurations (DODC) methods. This method allowed the optimization to start from an arbitrary initial states, and finds the best set of orbitals in a DODC framework. Additionally, DODC methods provide an intuitive connection to the diabatic picture that is required for describing nonadiabatic processes such as energy and electron transfer. A nonorthogonal quasi-diabatic basis has advantages compared to using an orthogonal determinant basis because the need for diabatization can be avoided, and the wavefunction is computed directly in a simple and chemically intuitive framework. To improve applicability of the NOMCSCF model, robust and efficient of optimization strategies for NOMCSCF type wavefunctions is necessary. In this work, I present the development of the NOMCSCF analytical Hessian, which accounts for different orthogonality regimes of the generalized Slater Condon rules. I illustrate how the NOMCSCF analytical Hessian can be used for analysis of NOMCSCF wavefunction stability,as well as in developing robust optimization strategies.