Analog of the Hellmann-Feynman theorem in multichannel quantum-defect theory - art. no. 052510

A multichannel quantum-defect theory (MQDT) is employed to obtain expressio ns for nonadiabatic coupling matrix elements without recourse to knowledge of the electronic wave functions. Diagonal and nondiagonal analogs of the H ellmann-Feynman theorem are derived by a differentiation of the MQDT quanti zation equations with respect to internuclear distance R. Closed relations for both the adiabatic correction terms and the nonadiabatic matrix element s are given in terms of nuclear derivatives of the reactance matrix. The th eory is tested by calculating the adiabatic correction and nonadiabatic rad ial and angular coupling matrix elements for the g,h(3)Sigma (+)(g) and 4s, 4d(3)Sigma (+)(g) states, corresponding to the first members (n = 3 and 4) of the s,d(3)Sigma (+)(g) Rydberg complex of the H-2 molecule. The derived estimates agree well with available ab initio results.