Abstract
A new algorithm for the computation of the overlap between many-electron wave functions is described. This algorithm allows for the extensive use of recurring intermediates and thus provides high computational efficiency. Because of the general formalism employed, overlaps can be computed for varying wave function types, molecular orbitals, basis sets, and molecular geometries. This paves the way for efficiently computing nonadiabatic interaction terms for dynamics simulations. In addition, other application areas can be envisaged, such as the comparison of wave functions constructed at different levels of theory. Aside from explaining the algorithm and evaluating the performance, a detailed analysis of the numerical stability of wave function overlaps is carried out, and strategies for overcoming potential severe pitfalls due to displaced atoms and truncated wave functions are presented.
Highlights
The evaluation of matrix elements between many-electron wave functions expanded in different orbital basis sets or over different molecular geometries is a task where the full complexity of these wave functions becomes apparent
Because of the general formalism employed, overlaps can be computed for varying wave function types, molecular orbitals, basis sets, and molecular geometries
A flexible formalism is used allowing for the computation of wave function overlaps for varying wave function expansions, molecular orbitals (MOs), basis sets, and molecular geometries
Summary
The evaluation of matrix elements between many-electron wave functions expanded in different orbital basis sets or over different molecular geometries is a task where the full complexity of these wave functions becomes apparent. We first discuss the general theory of wave function overlaps in the framework of Slater determinant expansions Using this foundation, specific algorithmic improvements are explained, Received: December 4, 2015 Published: February 8, 2016. A path integral over the coupling vector in coordinate space is computed, and the results are compared to standard nonadiabatic theory.[19] In addition, the results are verified against two previous implementations.[12,13] In order to give practical advice for future applications, the numerical stability of the results with respect to wave function truncation and atom displacements is discussed, and we show how orthogonalization of the overlap matrix can significantly improve the results.
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