Efficient update of determinants for many-electron wave function overlaps

Abstract

The calculation of overlaps between many-electron wave functions at different nuclear geometries during nonadiabatic dynamics simulations requires the evaluation of a large number of determinants of matrices that differ only in a few rows/columns. While this calculation is fast for small systems, its cost grows faster than the alternative electronic structure calculation used to obtain the wave functions. For wave functions that can be written as a CIS expansion, all determinants can be computed using the set of level-2 minors of the reference matrix. However, this is still a costly computation for large systems. In this paper, we provide an algorithm for efficiently calculating all level-2 minors of a matrix by reutilizing and updating the LU factorization for the determinants of the minors. This approach results in a parallel version of the algorithm that is up to an order of magnitude faster then the current best parallel implementation. The algorithm thus allows the computation of exact wave function overlaps for relatively large systems, with a high density of states, at virtually no cost compared with the electronic structure calculations. Furthermore, the new algorithm opens the path to further investigations in efficient computing of the exact wave function overlaps for complex wave functions such as MR-CIS and MR-CISD.

Ground-to-excited derivative couplings for the density functional based tight-binding method: Semi-local and long-range corrected formulations

“…This does not impede SH simulations, as most implementations require only scalar time-derivative couplings σ(t) = Ψ I |∂/∂t|Ψ J = d IJ • ξ, which can be computed by numerical differentiation without explicit recourse to d IJ . Such an approach can be quite efficient [31,32] so that the coupling evaluation is at least for small molecules not the computational bottleneck in a NAMD simulation. Questions remain about the validity of numerical couplings in the context of TD-DFT, since the theory does not provide many-body wave functions and one is forced to apply ad-hoc approximation to this quantity [20,33].…”