Comparison of approximate methods for computation of the concerted adiabatic electronic and nuclear fluxes in aligned [formula omitted

Abstract

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 H2+ vibrating in its electronic ground state (2Σg+), 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, Fe,EPD and Fe,EFD, based on either the EPD or the EFD, are derived from the continuity equation. 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 and Fe,EPD up to about 1ps. Higher-order 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 Fe,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 Fe,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 Fe,EFD.