Quantum wave packet ab initio molecular dynamics: An approach to study quantum dynamics in large systems

Abstract

A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.

Quantum Wavepacket Ab Initio Molecular Dynamics: An Approach for Computing Dynamically Averaged Vibrational Spectra Including Critical Nuclear Quantum Effects

“…97,98,137,138 The banded Toeplitz representation of the DAF propagator renders a great deal of efficiency to quantum propagation. 59,97,98,137 The evolution of {R C ,P C } is given by the velocity Verlet integrator, 139 which is also obtained through a third-order Trotter factorization of the classical Liouville form of the AIMD equations. 97 ıp…”

“…59,97,98,137 The evolution of {R C ,P C } is given by the velocity Verlet integrator, 139 which is also obtained through a third-order Trotter factorization of the classical Liouville form of the AIMD equations. 97 ıp…”

“…Both extended Lagrangian 81, 83,84,[107][108][109][110][111] and Born-Oppenheimer treatment 82,85,86 options are available. We have derived and tested a scheme [97][98][99] that allows simultaneous dynamics of all three subsystems coupled through a time-dependent procedure. A few salient features of QWAIMD are: (a) The quantum dynamical propagation is formally exact and computationally efficient, because the quantum propagator is represented as a banded Toeplitz matrix.…”

Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation

“…Practically, discrete inverse Fourier transformation (FT) of the analytically given b(o) [eqn (19)] yields the expansion coefficients b k for the calculation of the new basis functions j i in eqn (20). Derivatives of those interpolating basis functions are analytically available due to the easy derivation of the Gaussian basis functions:…”

“…Also related to moving grids are ''quantum trajectories'', [16][17][18] as modern realizations of Bohmian mechanics. The aspect of non-standard basis functions or grids in quantum wavepacket dynamics, of course, also has been an issue since many years; recently, for example, distributed approximating functionals 19 have been used, as well as sparse grids. 20 Two other central ideas of reducing the size of a basis or grid representation are contraction and pruning.…”