Strategies for solving the excited-state self-consistent-field problem for highly excited and multiply ionized states

Abstract

The dynamics of molecules exposed to intense x-ray radiation involve a large number of multiply ionized and highly excited electronic configurations. To model these dynamics a reliable and efficient electronic structure model is imperative. Employing the Hartree-Fock-Slater electronic structure model in combination with the maximum overlap method, we quantify the associated convergence failures when calculating electronic states of carbon monoxide with multiple vacancies in the core and valence levels. We characterize these cases and describe strategies to overcome the convergence problems. The described techniques not only eliminate all convergence issues for CO but also result in a significant reduction of convergence failures for simulations of the x-rayinduced multiple ionization dynamics of the phenol molecule.

Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States

“…One of the most used is the maximum overlap method (MOM), where at each iteration of the optimization, the orbital occupations are chosen to maximize the overlap with a set of reference orbitals, , typically the orbitals used as an initial guess . However, for charge transfer excitations in organic molecules, MOM does not eliminate the risk of variational collapse completely, as shown recently for the intramolecular charge transfer states of nitrobenzene and twisted N -phenylpyrrole (PP). , Preliminary studies show that the calculations can collapse to lower-energy solutions where the charge is too delocalized, giving an inadequate description of the excited state. , Moreover, even when MOM manages to prevent variational collapse, the convergence can still be problematic when using SCF algorithms based on the eigendecomposition of the Hamiltonian matrix, such as the direct inversion in the iterative subspace (DIIS). ,− …”

Excited State-Specific CASSCF Theory for the Torsion of Ethylene

“…The simplest approximation is self-consistent field (SCF) theory, where each excited state is represented by a single Slater determinant and the optimal orbitals are computed with either Hartree–Fock theory or Kohn–Sham density functional theory. − This approach has proved to be successful for predicting double excitations, charge transfer states, , and core excitations . However, for open-shell states away from the ground state equilibrium geometry, one must resort to symmetry-broken SCF approximations that introduce spin or spatial symmetry contamination. , Furthermore, state-specific SCF solutions often disappear along a potential energy surface, ,,− creating discontinuities that prevent dynamic simulations.…”

“… 21 However, for open-shell states away from the ground state equilibrium geometry, one must resort to symmetry-broken SCF approximations that introduce spin or spatial symmetry contamination. 22 , 23 Furthermore, state-specific SCF solutions often disappear along a potential energy surface, 8 , 17 , 23 − 25 creating discontinuities that prevent dynamic simulations.…”