Title: Excited states from quantum Monte Carlo in the basis of Slater determinants

Building on the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm introduced recently by Booth et al. [J. Chem. Phys. 131, 054106 (2009)] to compute the ground state of correlated many-electron systems, an extension to the computation of excited states (exFCIQMC) is presented. The Hilbert space is divided into a large part consisting of pure Slater determinants and a much smaller orthogonal part (the size of which is controlled by a cut-off threshold), from which the lowest eigenstates can be removed efficiently. In this way, the quantum Monte Carlo algorithm is restricted to the orthogonal complement of the lower excited states and projects out the next highest excited state. Starting from the ground state, higher excited states can be found one after the other. The Schrödinger equation in imaginary time is solved by the same population dynamics as in the ground state algorithm with modified probabilities and matrix elements, for which working formulae are provided. As a proof of principle, the method is applied to lithium hydride in the 3-21G basis set and to the helium dimer in the aug-cc-pVDZ basis set. It is shown to give the correct electronic structure for all bond lengths. Much more testing will bemore » required before the applicability of this method to electron correlation problems of interesting size can be assessed.« less

Institut für Physikalische und Theoretische Chemie, Julius-Maximilians Universität Würzburg, Emil-Fischer-Straße 42, 97074 Würzburg (Germany)

Publication Date:

OSTI Identifier:

22415365

Resource Type:

Journal Article

Resource Relation:

Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 19; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:

United States

Language:

English

Subject:

74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; BOND LENGTHS; CONFIGURATION INTERACTION; EIGENSTATES; ELECTRON CORRELATION; ELECTRONIC STRUCTURE; EXCITED STATES; GROUND STATES; HILBERT SPACE; LITHIUM HYDRIDES; MONTE CARLO METHOD; POPULATION DYNAMICS; SCHROEDINGER EQUATION; SLATER METHOD