Variational and perturbative formulations of quantum mechanical/molecular mechanical free energy with mean-field embedding and its analytical gradients

The Journal of Chemical Physics
Takeshi Yamamoto

Abstract

Conventional quantum chemical solvation theories are based on the mean-field embedding approximation. That is, the electronic wavefunction is calculated in the presence of the mean field of the environment. In this paper a direct quantum mechanical/molecular mechanical (QM/MM) analog of such a mean-field theory is formulated based on variational and perturbative frameworks. In the variational framework, an appropriate QM/MM free energy functional is defined and is minimized in terms of the trial wavefunction that best approximates the true QM wavefunction in a statistically averaged sense. Analytical free energy gradient is obtained, which takes the form of the gradient of effective QM energy calculated in the averaged MM potential. In the perturbative framework, the above variational procedure is shown to be equivalent to the first-order expansion of the QM energy (in the exact free energy expression) about the self-consistent reference field. This helps understand the relation between the variational procedure and the exact QM/MM free energy as well as existing QM/MM theories. Based on this, several ways are discussed for evaluating non-mean-field effects (i.e., statistical fluctuations of the QM wavefunction) that are neglec...Continue Reading

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Citations

Apr 4, 2012·Journal of the American Chemical Society·Takahiro Kosugi, Shigehiko Hayashi
Jun 10, 2010·The Journal of Physical Chemistry. B·Orlando Acevedo, William L Jorgensen
Apr 24, 2013·Physical Chemistry Chemical Physics : PCCP·Hirofumi Sato
Apr 10, 2012·The Journal of Chemical Physics·Hiroshi Nakano, Takeshi Yamamoto
Aug 2, 2013·The Journal of Chemical Physics·Motoyuki Shiga, Marco Masia
Mar 5, 2016·The Journal of Chemical Physics·Yu YamamoriNobuyuki Matubayasi
Jul 21, 2015·Protein Science : a Publication of the Protein Society·Fumitaka KamoNobuyuki Matubayasi
Jun 14, 2014·Journal of Computational Chemistry·Shun Sakuraba, Nobuyuki Matubayasi
Jul 10, 2018·The Journal of Chemical Physics·Naoki YamamotoNobuyuki Matubayasi
Nov 15, 2018·Molecules : a Journal of Synthetic Chemistry and Natural Product Chemistry·Hankyul LeeHyungjun Kim
Apr 2, 2018·The Journal of Chemical Physics·Yoshihiko TokunagaNobuyuki Matubayasi
Nov 23, 2017·The Journal of Chemical Physics·Yu Yamamori, Nobuyuki Matubayasi
Jan 19, 2021·Journal of Chemical Theory and Computation·Cheng Cheng, Shigehiko Hayashi
Jun 24, 2010·The Journal of Physical Chemistry. B·Catalina Soriano-CorreaManuel A Aguilar
Jan 25, 2013·The Journal of Physical Chemistry. B·Samuel Frutos-PuertoIgnacio Fdez Galván
Jan 8, 2013·Journal of Chemical Theory and Computation·Hiroshi Nakano, Takeshi Yamamoto
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Jan 10, 2012·Journal of Chemical Theory and Computation·Takahiro Kosugi, Shigehiko Hayashi
Feb 6, 2019·Journal of Chemical Theory and Computation·Hankyul LeeHyungjun Kim

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