# Re: Force constant for Umbrella sampling and WHAM

From: Giacomo Fiorin (giacomo.fiorin_at_gmail.com)
Date: Wed Feb 13 2019 - 12:19:47 CST

Hello Udaya, the harmonic potential used in Colvars is defined here:
https://colvars.github.io/colvars-refman-namd/colvars-refman-namd.html#sec:colvarbias_harmonic
and it is misleading to look in other parts of the NAMD documentation.

For example, consider the "harmonic" potential used in e.g. constraints AKA
position restraints, which are discussed in this thread:
https://www.ks.uiuc.edu/Research/namd/mailing_list/namd-l.2017-2018/1016.html

The "harmonic" potential (note the quote) without the 1/2 is a tradition
inherited from CHARMM (both the program and the force field). For obvious
reasons, parts of NAMD that require compatibility with CHARMM must follow
that.

Apart from the scaling by width (which obviously does not affect you with a
width of 1), the standard definition of the harmonic potential is 1/2 k x^2.

Giacomo

On Wed, Feb 13, 2019 at 1:09 PM Udaya Dahal <dahal.udaya_at_gmail.com> wrote:

> Hi,
>
> I am using colvar module for running umbrella sampling (1D) with window
> width of 1A and a force constant (1 kCal/mol). Since, NAMD defines energy
> as (k x^2) to rescale the force constant (as can be seen in log file by
> modifying the width of the window) but in case of WHAM ( by Grossfield) ,
> the energy is defined as 1/2 k x^2. I am wondering if I need to use
> different force-constant to match the exact value used in simulation -- in
> my case 2kCal/mol/A^2 while doing the free energy calculation.
>
> I would like to point out that I am getting exactly double the value of
> the free energy when I doubled the force constant.
>
>
> Best Regards,
> Udaya Dahal
>

```--
Giacomo Fiorin
Associate Professor of Research, Temple University, Philadelphia, PA
Contractor, National Institutes of Health, Bethesda, MD
http://goo.gl/Q3TBQU
https://github.com/giacomofiorin
```

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