On the independence of nonadiabatic coupling elements on the choice of origin of the coordinate system

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Abstract
A finite-difference approach is employed to demonstrate the manner in which the values of nonadiabatic radial coupling matrix elements vary with the choice of origin of the nuclear coordinate system. Configuration interaction (CI) calculations for a series of excited states of the HCl molecule verify that such results do not depend on the location of the center of mass XCM as long as it is held fixed during the differentiation process. The reason that radial coupling matrix elements are found to vary with the choice of origin of the coordinate system in standard scattering formulations is that the corresponding motion is not purely internal but rather has a definite translational component, namely a linear dependence of XCM on the bond distance R is assumed. An identity which relates variations of such (mixed internal-translational motion) nonadiabatic coupling elements to the value of the electric dipole transition moment when the latter prescription is employed for choosing the origin of the nuclear coordinate system is also verified by the present CI calculations.