skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Assessment of multireference approaches to explicitly correlated full configuration interaction quantum Monte Carlo

Abstract

The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting “universal” explicitly correlated approaches that fit into the FCIQMC framework: the [2]{sub R12} method of Kong and Valeev [J. Chem. Phys. 135, 214105 (2011)] and the explicitly correlated canonical transcorrelation approach of Yanai and Shiozaki [J. Chem. Phys. 136, 084107 (2012)]. The former is an a posteriori internally contracted perturbative approach, while the latter transforms the Hamiltonian prior to the FCIQMC simulation. These comparisons are made across the 55 molecules of the G1 standard set. We found that both methods consistently reduce the basis set incompleteness, for accurate atomization energies in small basis sets, reducing the errormore » from 28 mE{sub h} to 3-4 mE{sub h}. While many of the conclusions hold in general for any combination of multireference approaches with these methodologies, we also consider FCIQMC-specific advantages of each approach.« less

Authors:
;  [1];  [2];  [3]
  1. University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW (United Kingdom)
  2. (Germany)
  3. Department of Physics, King’s College London, Strand, London WC2R 2LS (United Kingdom)
Publication Date:
OSTI Identifier:
22678967
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 145; Journal Issue: 5; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CONFIGURATION INTERACTION; MONTE CARLO METHOD; SCHROEDINGER EQUATION; SLATER METHOD

Citation Formats

Kersten, J. A. F., E-mail: jennifer.kersten@cantab.net, Alavi, Ali, E-mail: a.alavi@fkf.mpg.de, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, and Booth, George H., E-mail: george.booth@kcl.ac.uk. Assessment of multireference approaches to explicitly correlated full configuration interaction quantum Monte Carlo. United States: N. p., 2016. Web. doi:10.1063/1.4959245.
Kersten, J. A. F., E-mail: jennifer.kersten@cantab.net, Alavi, Ali, E-mail: a.alavi@fkf.mpg.de, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, & Booth, George H., E-mail: george.booth@kcl.ac.uk. Assessment of multireference approaches to explicitly correlated full configuration interaction quantum Monte Carlo. United States. doi:10.1063/1.4959245.
Kersten, J. A. F., E-mail: jennifer.kersten@cantab.net, Alavi, Ali, E-mail: a.alavi@fkf.mpg.de, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, and Booth, George H., E-mail: george.booth@kcl.ac.uk. Sun . "Assessment of multireference approaches to explicitly correlated full configuration interaction quantum Monte Carlo". United States. doi:10.1063/1.4959245.
@article{osti_22678967,
title = {Assessment of multireference approaches to explicitly correlated full configuration interaction quantum Monte Carlo},
author = {Kersten, J. A. F., E-mail: jennifer.kersten@cantab.net and Alavi, Ali, E-mail: a.alavi@fkf.mpg.de and Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart and Booth, George H., E-mail: george.booth@kcl.ac.uk},
abstractNote = {The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting “universal” explicitly correlated approaches that fit into the FCIQMC framework: the [2]{sub R12} method of Kong and Valeev [J. Chem. Phys. 135, 214105 (2011)] and the explicitly correlated canonical transcorrelation approach of Yanai and Shiozaki [J. Chem. Phys. 136, 084107 (2012)]. The former is an a posteriori internally contracted perturbative approach, while the latter transforms the Hamiltonian prior to the FCIQMC simulation. These comparisons are made across the 55 molecules of the G1 standard set. We found that both methods consistently reduce the basis set incompleteness, for accurate atomization energies in small basis sets, reducing the error from 28 mE{sub h} to 3-4 mE{sub h}. While many of the conclusions hold in general for any combination of multireference approaches with these methodologies, we also consider FCIQMC-specific advantages of each approach.},
doi = {10.1063/1.4959245},
journal = {Journal of Chemical Physics},
number = 5,
volume = 145,
place = {United States},
year = {Sun Aug 07 00:00:00 EDT 2016},
month = {Sun Aug 07 00:00:00 EDT 2016}
}