# 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:

- Dipartimento di Fisica, Università di Roma, “ Tor Vergata ”, INFN, Sezione di Roma 2, Via della Ricerca Scientifica - 00133 Roma (Italy)
- (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}

}

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