In QWAIMD, the quantum dynamics, that is solution to time-dependent Schrodinger equation, is performed on Cartesian grids. Hence, the predominant bottleneck is the computation of the grid-based, time-dependent electronic structure potential and gradients generated by the motion of the classical nuclei. This limitation is partially surmounted through the following methodological improvements.

  • A time-dependent deterministic sampling (TDDS) technique was introduced (see references below), which when combined with numerical methods such as an efficient wavelet compression scheme and low-pass filtered Lagrange interpolation, provides computational gains of many orders of magnitude.

  • Multiple diabatic reduced single particle electronic density matrices are propagated simultaneously with the quantum wavepacket and the associated diabatic states are used to construct an adiabatic surface at every instant in time using a non-orthogonal CI formalism. The diabatic approximation allows reuse of the two-electron integrals during the on-the-fly potential energy surface computation stage and leads to substantial reduction in computational costs.