Analog of the Hellmann-Feynman theorem in multichannel quantum-defect theory

Abstract

A multichannel quantum-defect theory (MQDT) is employed to obtain expressions for nonadiabatic coupling matrix elements without recourse to knowledge of the electronic wave functions. Diagonal and nondiagonal analogs of the Hellmann-Feynman theorem are derived by a differentiation of the MQDT quantization equations with respect to internuclear distance R. Closed relations for both the adiabatic correction terms and the nonadiabatic matrix elements are given in terms of nuclear derivatives of the reactance matrix. The theory is tested by calculating the adiabatic correction and nonadiabatic radial and angular coupling matrix elements for the ${g,h}^{3}{\ensuremath{\Sigma}}_{g}^{+}$ and ${4s,4d}^{3}{\ensuremath{\Sigma}}_{g}^{+}$ states, corresponding to the first members $(n=3$ and 4) of the ${s,d}^{3}{\ensuremath{\Sigma}}_{g}^{+}$ Rydberg complex of the ${\mathrm{H}}_{2}$ molecule. The derived estimates agree well with available ab initio results.