Convergence optimization of restricted open-shell self-consistent field calculations

Abstract

Different self-consistent field SCF iteration schemes for open-shell systems are discussed. After a brief summary of the well-known level shifting and Ž . damping procedure, we describe the quadratically convergent SCF QCSCF approach based on the gradient and the Hessian matrix in a space of orbital rotation parameters. An analytical expression for the latter is derived for the general many-shell case. Starting from the expression for the energy change obtained by the QCSCF method, we then present a simplified direct procedure avoiding matrix diagonalization but also the difficulties of the QCSCF method in handling the Hessian matrix. Numerical calculations on some open-shell systems involving transition-metal complexes show that this method leads to rapid and reliable convergence of the iteration process in cases where the usual SCF procedure of iterative diagonalization tends to diverge.

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. I. General formalism and application to open-shell states

“…where we adopted the conventional ordering, [20][21][22] in which µ = 1 labels the doubly occupied shell, and µ = 2, 3 refer to the singly occupied ones. Notice that we also consider the subspace of unoccupied orbitals as a proper shell (labelled by µ = 0), even though its Fock operator is undefined (this is, however, irrelevant since it is always premultiplied by zero), and therefore this shell is not included in the definition of b given above.…”

“…are numerical coefficients (or state parameters) specific to the particular form of the wavefunction, [20][21][22] which in general is a sum of many Slater determinants. Equation (52) leads to the energy expression…”

“…Most notably, it includes all possible spin-adapted states that can be generated from a given electronic configuration. [20][21][22] To derive the optimal equations of motion for the single-particle orbitals, we now proceed as in the previous sections. Inserting Eq.…”

“…In this way, we are implicitly assuming a minimal description of the electronic wavefunction, such that, for symmetry reasons, the expansion coefficients can be treated as time-independent. We are particularly interested in specialising to the case of general open-shell states, [20][21][22] which are relevant for many physical processes of interest, such as the dynamics of photoexcitations in molecules.…”

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains

“…In Sec. II, the MCTDHF method for general open-shell states [34][35][36] is briefly outlined and combined with Ehrenfest molecular dynamics. In Sec.…”