# [gmx-users] Force Constants and Unit Systems

Lara Bunte lara.bunte at yahoo.de
Thu May 17 18:58:35 CEST 2012

```Hi

>One cannot convert between these units, since kcal/mol is an energy term, and
>kJ/(mol nm^2) is a force constant.

This confuses me, because in the paper where that constants are from is written, I quote:

"Force constant k in kcal / mol calculated by DFT"

In my parametrization I have this values. Could you please explain this?

Greetings and really thanks for your help

Lara

----- Ursprüngliche Message -----
Von: Justin A. Lemkul <jalemkul at vt.edu>
An: Lara Bunte <lara.bunte at yahoo.de>; Discussion list for GROMACS users <gmx-users at gromacs.org>
CC:
Gesendet: 18:52 Donnerstag, 17.Mai 2012
Betreff: Re: [gmx-users] Force Constants and Unit Systems

On 5/17/12 12:25 PM, Lara Bunte wrote:
> Hello
>
> how to transform following units:
>
> 1.) kcal / mol -->  kJ / (mol * nm^2)
>

One cannot convert between these units, since kcal/mol is an energy term, and
kJ/(mol nm^2) is a force constant.

> 2.) kcal / (mol * rad^2) -->  kJ / (mol * rad^2)
>

The transformation between kcal and kJ requires a simple multiplication.

> I have additionally some question to that:  Both should be units of a force
> constant. From Hooke's law F = -kx follows for me, that the unit of a force
> constant is Newton N over distance m, in S.I. units  kg/sec^2 (mass over time
> square).
>
> What is the correspondence between above from Hooke's law and that units of
> force constants in molecular dynamics simulations?

Force is also expressed as kJ/(mol nm) - see Chapter 2 of the Gromacs manual.
Thus, since x is in units of nm (distance), then k has units of kJ/(mol nm^2).

-Justin

--
========================================

Justin A. Lemkul, Ph.D.
Research Scientist
Department of Biochemistry
Virginia Tech
Blacksburg, VA
jalemkul[at]vt.edu | (540) 231-9080
http://www.bevanlab.biochem.vt.edu/Pages/Personal/justin

========================================

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