Quantization of the ab initio nonadiabatic coupling matrix: The C2H molecule as a case study

Abstract

AbstractThe observation that, for a given sub‐Hilbert space, diabatic potentials, just like adiabatic potentials, have to be single‐valued in configuration space led to the unavoidable conclusion that the relevant nonadiabatic coupling matrix (i.e., the matrix that contains the vectorial electronic nonadiabatic coupling terms) has to be quantized along any contour in configuration space. In the present article this statement is tested with respect to the three (excited) states of the C2H molecule, i.e., the 22A′, 32A′, and 42A′ states. For this purpose ab initio electronic nonadiabatic coupling matrices were calculated along various contours surrounding the relevant conical intersections (one conical intersection between the 22A′ and 32A′ states and two conical intersections between the 32A′ and 42A′ states). Employing the line‐integral technique it was shown that as long as the contour that surrounds the (2,3) conical intersection is close enough to the CI and avoids the two (3,4) conical intersections, the 2×2 nonadiabatic coupling matrices are quantized. However they fail to be quantized for contours that also surround one or two of the other conical intersections. In this case one is obliged to employ the three‐state nonadiabatic coupling matrix. Doing that, it was shown that it is the 3×3 matrices that satisfy the quantization condition. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001