Calculation of transition matrix elements by nonsingular orbital transformations

Abstract

A general strategy is described for the evaluation of transition matrix elements between pairs of full class CI wave functions built up from mutually nonorthogonal molecular orbitals. A new method is proposed for the counter-transformation of the linear expansion coefficients of a full CI wave function under a nonsingular transformation of the molecular-orbital basis. The method, which consists in a straightforward application of the Cauchy-Binet formula to the definition of a Slater determinant, is shown to be simple and suitable for efficient implementation on current high-performance computers. The new method appears mainly beneficial to the calculation of miscellaneous transition matrix elements among individually optimized CASSCF states and to the re-evaluation of the CASCI expansion coefficients in Slater-determinant bases formed from arbitrarily rotated (e.g., localized or, conversely, delocalized) active molecular orbitals.

Photophysics of BODIPY-Based Photosensitizer for Photodynamic Therapy: Surface Hopping and Classical Molecular Dynamics

“…In a nutshell, if φ ≠ ω and/or φ ≠ τ , the pair of bases of the molecular orbitals φ and η (either ω or τ ) is, through the LU decomposition of the transition overlap matrix S = ⟨ φ | η ⟩ l ii = 1, i = 1, ..., m , transformed to the new pair of bases, say and which are mutually biorthonormal This is the necessary first step toward the efficient evaluation of the matrix elements between eigenfunctions of the nonrelativistic Hamiltonian of different spin multiplicities (unless the molecular orbitals are not allowed to relax in the course of the HF or KS SCF calculations). The second step is the countertransformation of the CI expansion coefficients of the singlet and triplet, whose effect is to compensate for the orbital alterations so as to keep the multielectron wave functions unchanged. − …”