Calculation Of Non-Adiabatic Coupling Vectors In A Local-Orbital Basis Set

The following article appeared in Journal of Chemical Physics 138.15 (2013): 154106 and may be found at http://scitation.aip.org/content/aip/journal/jcp/138/15/10.1063/1.4801511Most of today's molecular-dynamics simulations of materials are based on the Born-Oppenheimer approximation. There are many cases, however, in which the coupling of the electrons and nuclei is important and it is necessary to go beyond the Born-Oppenheimer approximation. In these methods, the non-adiabatic coupling vectors are fundamental since they represent the link between the classical atomic motion of the nuclei and the time evolution of the quantum electronic state. In this paper we analyze the calculation of non-adiabatic coupling vectors in a basis set of local orbitals and derive an expression to calculate them in a practical and computationally efficient way. Some examples of the application of this expression using a local-orbital density functional theory approach are presented for a few simple molecules: H3, formaldimine, and azobenzene. These results show that the approach presented here, using the Slater transition-state density, is a very promising way for the practical calculation of non-adiabatic coupling vectors for large systems.This work was partially supported by Spanish Ministerio de Economía y Competitividad (Contract No.FIS2010-16046), the Comunidad de Madrid (Contract No.S2009/MAT-1467), the Office of Science, Basic Energy Sciences in the US Department of Energy (Grant No. DEFG02-10ER16164), the Czech Science Foundation (GAČR)(Project No. 204/10/0952), the Grant of the MŠMT of the Czech Republic (Grant No. ME 09048), and COST-CMTS Action CM1002 (CODECS). J.O. gratefully acknowledges support from the Spanish Ministerio de Ciencia e Innovación (PR2008-0027). E.A. gratefully acknowledges financial support by the Consejería de Educación de la Comunidad de Madrid and Fondo Social Europeo