Journal Article: On the ground state calculation of a many-body system using a self-consistent basis and quasi-Monte Carlo: An application to water hexamer

Title: On the ground state calculation of a many-body system using a self-consistent basis and quasi-Monte Carlo: An application to water hexamer

Given a quantum many-body system, the Self-Consistent Phonons (SCP) method provides an optimal harmonic approximation by minimizing the free energy. In particular, the SCP estimate for the vibrational ground state (zero temperature) appears to be surprisingly accurate. We explore the possibility of going beyond the SCP approximation by considering the system Hamiltonian evaluated in the harmonic eigenbasis of the SCP Hamiltonian. It appears that the SCP ground state is already uncoupled to all singly- and doubly-excited basis functions. So, in order to improve the SCP result at least triply-excited states must be included, which then reduces the error in the ground state estimate substantially. For a multidimensional system two numerical challenges arise, namely, evaluation of the potential energy matrix elements in the harmonic basis, and handling and diagonalizing the resulting Hamiltonian matrix, whose size grows rapidly with the dimensionality of the system. Using the example of water hexamer we demonstrate that such calculation is feasible, i.e., constructing and diagonalizing the Hamiltonian matrix in a triply-excited SCP basis, without any additional assumptions or approximations. Our results indicate particularly that the ground state energy differences between different isomers (e.g., cage and prism) of water hexamer are already quite accurate within the SCPmore » approximation.« less

Chemistry Department, University of California, Irvine, California 92697 (United States)

Department of Mathematics, University of California, Irvine, California 92697 (United States)

Publication Date:

OSTI Identifier:

22251365

Resource Type:

Journal Article

Resource Relation:

Journal Name: Journal of Chemical Physics; Journal Volume: 139; Journal Issue: 20; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:

United States

Language:

English

Subject:

37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; EVALUATION; EXCITED STATES; FREE ENERGY; GROUND STATES; HAMILTONIANS; ISOMERS; MANY-BODY PROBLEM; MONTE CARLO METHOD; POTENTIAL ENERGY; WATER