# [gmx-users] Force Constants and Unit Systems

Thu May 17 19:18:33 CEST 2012

```Hi Lara,

On Thu, 2012-05-17 at 17:58 +0100, Lara Bunte wrote:
> 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:
Which paper?
>
> "Force constant k in kcal / mol calculated by DFT"

The unit of Force is  [Mass]*[Length] /[Time]^2 = [Energy]/[Length] in
any unit system.

Therefore either they have a potential of the form 1/[Length] or they
weren't using the term correctly.

A harmonic bond must have a force constant with units [ Energy ]/
[ Length ]^2 In gromacs this is therefore kJ/(mol nm^2)

The conversion from kcal/mol to kJ/mol is easily found by googling:
kcal/mol

Richard
>
>
> 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
>
> ========================================
>

```