Comparison of approximate methods for computation of the concerted adiabatic electronic and nuclear fluxes in aligned H2+(2Σg+)

Approximate methods of computing the concerted electronic and nuclear fluxes associated with electronically adiabatic processes are developed and applied to the prototypal system, namely aligned H-2(+) vibrating in its electronic ground state ((2)Sigma(+)(g)), the only realistic system for which highly accurate (exact) electronic (EPD) and nuclear (NPD) probability densities, electronic (EFD) and nuclear (NFD) flux densities, as well as corresponding fluxes, are available. Alternative formulas for the electronic flux, F-e,F-EPD and F-e,F-EFD, based on either the EPD or the EFD, are derived from the continuity equateion. The results of Born-Oppenheimer approximation (BOA) and of an ordered sequence of Born-Huang expansions (BHE) are presented. The BOA and first-order BHE are in excellent agreement with the exact for both the NPD and NFD, as well as for the EPD andF(e,EPD) up to about 1 ps. Higherorder BHE are necessary to achieve similar accuracy at longer times. In contrast, the BOA and first-order BHE yield zero EFD and therefore also zero F-e,F-EFD. Although the higher-order BHE give non-zero values for these properties, they disagree flagrantly with their exact correlates. The error is traceable to numerical ill-conditioning of the working expression for the EFD. In summary, the BOA is adequate to compute accurate NPD, NFD, EPD and F-e,F-EPD for times corresponding to several dozens of vibrational periods; the higher-order BHE is required for longer times. But neither the BOA nor the BHE can provide reliable estimates of the EFD and F-e,F-EFD.