Analytical State-Average Complete-Active-Space Self-Consistent Field Nonadiabatic Coupling Vectors: Implementation with Density-Fitted Two-Electron Integrals and Application to Conical Intersections.

Ignacio Fdez Galván,Francesco Aquilante,Mickaël G Delcey,Thomas Bondo Pedersen,Roland Lindh

doi:10.1021/acs.jctc.6b00384

Abstract

Analytical state-average complete-active-space self-consistent field derivative (nonadiabatic) coupling vectors are implemented. Existing formulations are modified such that the implementation is compatible with Cholesky-based density fitting of two-electron integrals, which results in efficient calculations especially with large basis sets. Using analytical nonadiabatic coupling vectors, the optimization of conical intersections is implemented within the projected constrained optimization method. The standard description and characterization of conical intersections is reviewed and clarified, and a practical and unambiguous system for their classification and interpretation is put forward. These new tools are subsequently tested and benchmarked for 19 different conical intersections. The accuracy of the derivative coupling vectors is validated, and the information that can be drawn from the proposed characterization is discussed, demonstrating its usefulness.

Highlights

The theoretical study of nonadiabatic processes, those in which the nuclear motion involves more than one Born−Oppenheimer potential energy surface, has seen intense development in the last decades
A key quantity in nonadiabatic processes is the derivative coupling vector. It measures the mixing between the adiabatic (Born−Oppenheimer) electronic states with the nuclear motions and, together with the electronic gradient, defines the first-order shape of the potential energy surfaces close to degeneracy regions
Until now Molcas lacked the ability to compute derivative couplings, analytically or numerically, which limited its potential for use in state-of-the-art applications in the field of nonadiabatic processes. We address this problem by implementing analytical derivative coupling vectors for state-average complete-active-space selfconsistent field (SA-CASSCF) wave functions, the cornerstone of most multiconfigurational calculations with Molcas

Summary

Introduction

The theoretical study of nonadiabatic processes, those in which the nuclear motion involves more than one Born−Oppenheimer potential energy surface, has seen intense development in the last decades. Molecular structures with two or more degenerate electronic states are called conical intersections if the degeneracy is lifted linearly with the nuclear displacements.[7−10] The literature on conical intersections, their significance, optimization, and effects on nonadiabatic processes[11] is profuse, in parallel with the development of nonadiabatic theoretical chemistry studies.[12]. In spite of their significance, derivative coupling vectors are often not available from quantum chemistry software packages, as their implementation is not trivial even if one is willing to allow for numerical differentiation. For the optimization of conical intersections there are algorithms that do not rely on a derivative coupling vector.[14−16] analytical formulations have been published for several electronic structure methods,[17−22] and using analytical derivative couplings is almost always preferable to ad hoc numerical differentiation or approximate methods

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