Fighting the curse of dimensionality in first-principles semiclassical calculations: Non-local reference states for large number of dimensions
- 6 December 2011
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 135 (21), 214108
- https://doi.org/10.1063/1.3664731
Abstract
Semiclassical methods face numerical challenges as the dimensionality of the system increases. In the general context of the theory of differential equations, this is known as the “curse of dimensionality.” In the present manuscript, we apply the recently-introduced multi-coherent states semiclassical initial value representation (MC-SC-IVR) approach to extend the applicability of first-principles semiclassical calculations. The proposed strategy involves the use of non-local coherent states with the goal of increasing accuracy in the Fourier transforms, and on the other hand, allows for the selection of peaks of different frequencies. The ability to filter desired peaks is important for analyzing the power spectra of complex systems. The MC-SC-IVR approach allows us to solve a 19-dimensional test system and to resolve on-the-fly the power spectra of the formaldehyde molecule with very few classical trajectories.Keywords
This publication has 91 references indexed in Scilit:
- Multiple coherent states for first-principles semiclassical initial value representation molecular dynamicsThe Journal of Chemical Physics, 2009
- Polynomial-time quantum algorithm for the simulation of chemical dynamicsProceedings of the National Academy of Sciences of the United States of America, 2008
- Using the thermal Gaussian approximation for the Boltzmann operator in semiclassical initial value time correlation functionsThe Journal of Chemical Physics, 2006
- SEMICLASSICAL INITIAL VALUE TREATMENTS OF ATOMS AND MOLECULESAnnual Review of Physical Chemistry, 2005
- SEMICLASSICAL DESCRIPTION OF MOLECULAR DYNAMICS BASED ON INITIAL-VALUE REPRESENTATION METHODSAnnual Review of Physical Chemistry, 2004
- Monte Carlo Method for Evaluating the Quantum Real Time PropagatorPhysical Review Letters, 2003
- Time averaging the semiclassical initial value representation for the calculation of vibrational energy levels. II. Application to H2CO, NH3, CH4, CH2D2The Journal of Chemical Physics, 2003
- Time averaging the semiclassical initial value representation for the calculation of vibrational energy levelsThe Journal of Chemical Physics, 2003
- Semiclassical Calculation of Chemical Reaction Dynamics via Wavepacket Correlation FunctionsAnnual Review of Physical Chemistry, 2000
- A Log-Derivative Formulation of the Prefactor for the Semiclassical Herman-Kluk PropagatorThe Journal of Physical Chemistry A, 2000