In the size-extensive vibrational self-consistent field (XVSCF) method introduced earlier [M. Keçeli and S. Hirata, J. Chem. Phys. 135, 134108 (2011)] https://doi.org/10.1063/1.3644895, only a small subset of even-order force constants that can form connected diagrams were used to compute extensive total energies and intensive transition frequencies. The mean-field potentials of XVSCF formed with these force constants have been shown to be effectively harmonic, making basis functions, quadrature, or matrix diagonalization in the conventional VSCF method unnecessary. We introduce two size-consistent VSCF methods, XVSCF(n) and XVSCF[n], for vibrationally averaged geometries in addition to energies and frequencies including anharmonic effects caused by up to the nth-order force constants. The methods are based on our observations that a small number of odd-order force constants of certain types can form open, connected diagrams isomorphic to the diagram of the mean-field potential gradients and that these nonzero gradients shift the potential minima by intensive amounts, which are interpreted as anharmonic geometry corrections. XVSCF(n) evaluates these mean-field gradients and force constants at the equilibrium geometry and estimates this shift accurately, but approximately, neglecting the coupling between these two quantities. XVSCF[n] solves the coupled equations for geometry corrections and frequencies with an iterative algorithm, giving results that should be identical to those of VSCF when applied to an infinite system. We present the diagrammatic and algebraic definitions, algorithms, and initial implementations as well as numerical results of these two methods. The results show that XVSCF(n) and XVSCF[n] reproduce the vibrationally averaged geometries of VSCF for naphthalene and anthracene in their ground and excited vibrational states accurately at fractions of the computational cost.
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21 June 2012
Research Article|
June 20 2012
Size-extensive vibrational self-consistent field methods with anharmonic geometry corrections
Matthew R. Hermes;
Matthew R. Hermes
Department of Chemistry,
University of Illinois at Urbana-Champaign
, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
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Murat Keçeli;
Murat Keçeli
Department of Chemistry,
University of Illinois at Urbana-Champaign
, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
Search for other works by this author on:
a)
Author to whom the correspondence should be addressed. Electronic mail: sohirata@illinois.edu.
J. Chem. Phys. 136, 234109 (2012)
Article history
Received:
March 26 2012
Accepted:
June 01 2012
Citation
Matthew R. Hermes, Murat Keçeli, So Hirata; Size-extensive vibrational self-consistent field methods with anharmonic geometry corrections. J. Chem. Phys. 21 June 2012; 136 (23): 234109. https://doi.org/10.1063/1.4729602
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