## Abstract

In the size-extensive vibrational self-consistent field (XVSCF) method introduced earlier [M. Keeli and S. Hirata, J. Chem. Phys. 135, 134108 (2011)]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.

Original language | English (US) |
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Article number | 234109 |

Journal | Journal of Chemical Physics |

Volume | 136 |

Issue number | 23 |

DOIs | |

State | Published - Jun 21 2012 |

### Bibliographical note

Funding Information:We thank Dr. Nancy Makri and Dr. Samuel B. Trickey for pointing out the relationship of our methods to the harmonic oscillator bath model and the self-consistent phonon method, respectively. We are indebted to Dr. Kiyoshi Yagi for some of the PES used in this work. This work has been supported by the (U.S.) Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences (DE-FG02-11ER16211). M. R. H. is a C.S. Marvel Fellow of the University of Illinois, M. K. is a University Block Grant Fellow of the University of Illinois, and S. H. is an Alumni Research Scholar of the University of Illinois, a Camille Dreyfus Teacher-Scholar, and a Scialog Fellow of the Research Corporation for Science Advancement.

Copyright:

Copyright 2012 Elsevier B.V., All rights reserved.