skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A novel proof of the DFT formula for the interatomic force field of Molecular Dynamics

Abstract

We give a novel and simple proof of the DFT expression for the interatomic force field that drives the motion of atoms in classical Molecular Dynamics, based on the observation that the ground state electronic energy, seen as a functional of the external potential, is the Legendre transform of the Hohenberg–Kohn functional, which in turn is a functional of the electronic density. We show in this way that the so-called Hellmann–Feynman analytical formula, currently used in numerical simulations, actually provides the exact expression of the interatomic force.

Authors:
 [1];  [1];  [2]
  1. Dipartimento di Fisica, Università di Roma, “ Tor Vergata ”, INFN, Sezione di Roma 2, Via della Ricerca Scientifica - 00133 Roma (Italy)
  2. (Italy)
Publication Date:
OSTI Identifier:
22617464
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 377; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; GROUND STATES; INTERATOMIC FORCES; MOLECULAR DYNAMICS METHOD

Citation Formats

Morante, S., E-mail: morante@roma2.infn.it, Rossi, G.C., E-mail: rossig@roma2.infn.it, and Centro Fermi-Museo Storico della Fisica e Centro Studi e Ricerche E. Fermi, Compendio del Viminale, Piazza del Viminale 1, I-00184 Rome. A novel proof of the DFT formula for the interatomic force field of Molecular Dynamics. United States: N. p., 2017. Web. doi:10.1016/J.AOP.2016.12.011.
Morante, S., E-mail: morante@roma2.infn.it, Rossi, G.C., E-mail: rossig@roma2.infn.it, & Centro Fermi-Museo Storico della Fisica e Centro Studi e Ricerche E. Fermi, Compendio del Viminale, Piazza del Viminale 1, I-00184 Rome. A novel proof of the DFT formula for the interatomic force field of Molecular Dynamics. United States. doi:10.1016/J.AOP.2016.12.011.
Morante, S., E-mail: morante@roma2.infn.it, Rossi, G.C., E-mail: rossig@roma2.infn.it, and Centro Fermi-Museo Storico della Fisica e Centro Studi e Ricerche E. Fermi, Compendio del Viminale, Piazza del Viminale 1, I-00184 Rome. Wed . "A novel proof of the DFT formula for the interatomic force field of Molecular Dynamics". United States. doi:10.1016/J.AOP.2016.12.011.
@article{osti_22617464,
title = {A novel proof of the DFT formula for the interatomic force field of Molecular Dynamics},
author = {Morante, S., E-mail: morante@roma2.infn.it and Rossi, G.C., E-mail: rossig@roma2.infn.it and Centro Fermi-Museo Storico della Fisica e Centro Studi e Ricerche E. Fermi, Compendio del Viminale, Piazza del Viminale 1, I-00184 Rome},
abstractNote = {We give a novel and simple proof of the DFT expression for the interatomic force field that drives the motion of atoms in classical Molecular Dynamics, based on the observation that the ground state electronic energy, seen as a functional of the external potential, is the Legendre transform of the Hohenberg–Kohn functional, which in turn is a functional of the electronic density. We show in this way that the so-called Hellmann–Feynman analytical formula, currently used in numerical simulations, actually provides the exact expression of the interatomic force.},
doi = {10.1016/J.AOP.2016.12.011},
journal = {Annals of Physics},
number = ,
volume = 377,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2017},
month = {Wed Feb 15 00:00:00 EST 2017}
}
  • We present a hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics study of 18-crown-6 (18c6) in both polar hydrogen bonding and nonpolar solvents. The QM/MM method described here is based on our previous QM/MM study of K{sup +}/18c6 which employed the semiempirical AM1 method for 18c6 and the SPC/e model for H{sub 2}O. We improve our previous QM/MM method by including MM torsion terms to better describe the energetics of OCCO and COCC rotamers. The torsion terms are parametrized against the ab initio calculations of Jaffe et al. for 1,2-dimethoxyethane. The resulting torsion-modified AM1 Hamiltonian is used with our previous QM/MMmore » parameters to describe the conformational energetics of free 18c6 in both H{sub 2}O and CCl{sub 4}. 71 refs., 17 figs., 3 tabs.« less
  • A molecular-level description of the unique properties of hydrogen-bond networks is critical for understanding many fundamental physico-chemical processes in aqueous environments. In this article a novel simulation approach, combining an ab-initio based force field for water with a quantum treatment of the nuclear motion, is applied to investigate hydrogen-bond dynamics in liquid water with a specific focus on the relationship of these dynamics to vibrational spectroscopy. Linear and nonlinear infrared (IR) spectra are calculated for liquid water, HOD in D2O and HOD in H2O and discussed in the context of the results obtained using other approaches that have been employedmore » in studies of water dynamics. A comparison between the calculated spectra and the available experimental data yields an overall good agreement, indicating the accuracy of the present simulation approach in describing the properties of liquid water at ambient conditions. Possible improvements on the representation of the underlying water interactions as well as the treatment of the molecular motion at the quantum-mechanical level are also discussed. This research was supported by the Division of Chemical Sciences, Biosciences and Geosciences, US Department of Energy. Battelle operates the Pacific Northwest National Laboratory for the US Department of Energy.« less
  • The behavior of Liquid N,N-dimethylformamide subjected to a wide range of externally applied electric fields (from 0.001 V/nm to 1 V/nm) has been investigated through molecular dynamics simulation. To approach the objective the AMOEBA polarizable force field was extended to include the interaction of the external electric field with atomic partial charges and the contribution to the atomic polarization. The simulation results were evaluated with quantum mechanical calculations. The results from the present force field for the liquid at normal conditions were compared with the experimental and molecular dynamics results with non-polarizable and other polarizable force fields. The uniform externalmore » electric fields of higher than 0.01 V/nm have a significant effect on the structure of the liquid, which exhibits a variation in numerous properties, including molecular polarization, local cluster structure, rotation, alignment, energetics, and bulk thermodynamic and structural properties.« less
  • A force field model for calculating local field factors, i.e. the linear response of the local electric field for example at a nucleus in a molecule with respect to an applied electric field, is discussed. It is based on a combined charge-transfer and point-dipole interaction model for the polarizability, and thereby it includes two physically distinct terms for describing electronic polarization: changes in atomic charges arising from transfer of charge between the atoms and atomic induced dipole moments. A time dependence is included both for the atomic charges and the atomic dipole moments and if they are assumed to oscillatemore » with the same frequency as the applied electric field, a model for frequency-dependent properties are obtained. Furthermore, if a life-time of excited states are included, a model for the complex frequency-dependent polariability is obtained including also information about excited states and the absorption spectrum. We thus present a model for the frequency-dependent local field factors through the first molecular excitation energy. It is combined with molecular dynamics simulations of liquids where a large set of configurations are sampled and for which local field factors are calculated. We are normally not interested in the average of the local field factor but rather in configurations where it is as high as possible. In electrical insulation, we would like to avoid high local field factors to reduce the risk for electrical breakdown, whereas for example in surface-enhanced Raman spectroscopy, high local field factors are desired to give dramatically increased intensities.« less