On the evaluation of non-Born–Oppenheimer interactions for Born–Oppenheimer wave functions. V. A body fixed frame approach. Applications to isotope effects on equilibrium geometries and the adiabatic correction for the X 1Σ+ state of LiH

Abstract

The evaluation of the total second derivative nonadiabatic coupling matrix element H(J,I,R)=〈ψJ(r;R)‖∑i(−1/2 Mu)(∂2/∂R2i )ψI(r;R)〉r is considered. Here ψJ(r;R) is the adiabatic Born–Oppenheimer electronic wave function which in this work will be approximated by a large-scale CI wave function developed from an MCSCF reference space. For diatomic and triatomic systems the computational effort associated with the evaluation of H(J,I,R) can be reduced considerably by the use of a body fixed frame approach. In this approach costly evaluation of the derivative wave function with respect to noninternal degrees of freedom in the space fixed frame is replaced by the evaluation of matrix elements of many electron operators including the mass polarization operator (total electronic linear momentum squared) and the L2 operator (total electronic orbital angular momentum squared). The equivalence of the body fixed frame and space fixed frame results leads to valuable diagnostic equations which provide stringent tests of the derivative methodology used to evaluate the remaining second derivatives with respect to internal coordinates. The methods presented here are applied to the benchmark systems BeH+ and LiH. The Born–Oppenheimer diagonal correction or adiabatic correction (AC) is evaluated for the X 1∑+ state of these systems and used to consider the effect of isotopic substitution on equilibrium geometries. For the X 1∑+ state of LiH a troubling discrepancy exists between the AC determined by advanced theoretical and experimental techniques. For R≲Re the AC determined directly with specialized CI wave functions and the experimental value inferred from a detailed spectroscopic analysis of the A→X emission agree. However, for R>Re theory and experiment disagree qualitatively. For R≲Re our results are consistent with the previous work. For R>Re our results are in accord with the experimentally derived AC.