Basis expansion leaping: a new method to solve the time-dependent Schrödinger equation for molecular quantum dynamics.

  title={Basis expansion leaping: a new method to solve the time-dependent Schr{\"o}dinger equation for molecular quantum dynamics.},
  author={Werner Koch and Terry J. Frankcombe},
  journal={Physical review letters},
  volume={110 26},
A wide variety of molecular systems that have recently come into the reach of experimental and theoretical investigation is dominated by quantum phenomena. However, even state of the art quantum propagation techniques are either unsuitable for general application to molecular systems with strong interference and tunneling characteristics or are computationally prohibitive for systems with more than a few degrees of freedom. In this Letter, we introduce a novel quantum propagation technique with… 

Figures from this paper

Accurate quantum molecular dynamics for multidimensional systems by the basis expansion leaping multi-configuration Gaussian (BEL MCG) method.
The importance of using basis functions of a width appropriate to the nature of the potential energy surface in the region of configuration space where each basis function is located is highlighted, which has implications for virtually all quantum molecular dynamics methods utilising Gaussian basis functions.
Quantum dynamics simulations using Gaussian wavepackets: the vMCG method
Gaussian wavepacket methods are an attractive way to solve the time-dependent Schrödinger equation (TDSE). They have an underlying trajectory picture that has a natural connection to semi-classical
Apoptosis of moving nonorthogonal basis functions in many-particle quantum dynamics
Due to the exponential increase of the numerical effort with the number of degrees of freedom, moving basis functions have a long history in quantum dynamics. In addition, spawning of new basis
Basis set generation for quantum dynamics simulations using simple trajectory-based methods.
A basis set using trajectories to place time-independent basis functions in the regions of phase space relevant to wave function propagation is suggested, which potentially circumvents many of the problems traditionally associated with global or dynamic basis sets.
Accurate Non-adiabatic Quantum Dynamics from Pseudospectral Sampling of Time-dependent Gaussian Basis Sets
Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic
Non-adiabatic quantum molecular dynamics by the basis expansion leaping multi-configuration Gaussian (BEL MCG) method: Multi-set and single-set formalisms.
This work presents two formalisms for the BEL MCG description of multi-state wave packets, namely, "multi-set" and "single-set," and investigates what is required to yield accurate dynamics.
Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets.
This work proposes and test a modification of their methodology which aims to reduce the size of basis sets generated in their original scheme, and finds that this new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than the original trajectory-guided basis set methodology.
Quantum Dynamics with Gaussian Bases Defined by the Quantum Trajectories.
The time-dependent Gaussian bases are defined through an ensemble of quantum or Bohmian trajectories, known to provide a very compact representation of a wave function due to conservation of the probability density associated with each trajectory.
Pseudospectral Gaussian quantum dynamics: Efficient sampling of potential energy surfaces.
The ability to obtain variational accuracy using only the potential energy at discrete points makes the pseudospectral Gaussian method a promising avenue for on-the-fly dynamics, where electronic structure calculations become computationally significant.


It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.
  • 137, 22A544 (2012). PRL 110, 263202
  • 2013
  • Rev. 35, 1303
  • 1930
Faraday Discuss
  • 1985
Signal Process
  • 41, 3397
  • 1993
Wave Mechanics: Advanced General Theory (Clarendon
  • Oxford, 1934),
  • 1934
  • Rev. Phys. Chem. 50, 167
  • 1999
  • Phys. Lett. 489, 242
  • 2010
  • Phys. Lett. 165, 73
  • 1990
  • 118, 6720
  • 2003