Kateryna Miroshnychenko wrote in July 2005:
> Dear All,
>
> I wonder what is the meaning of 108.587 coefficient which is used to
> convert eigenvalues of mass-weighted covariance matrix to sm-1 (see
> below part of the file analyze.c from ptraj). In what units are the
> eigenvalues of mass-weighted covariance matrix before this conversion?
> I suppose they are in A2*amu?
Sorry to take 18 months to think about this. :)
I believe I have the answer finally. Perhaps Thomas Cheatham and Holger
Gohlke might like to update their comments in ptraj's analyze.c code.
I suspect from the ?'s in the current comments, that the ptraj code was
simply pasted in from the quasih.f module.
There are _MANY_ constants and unit conversions folded into 108.587 ( ! )
First, yes, the eigenvalues are in units of A2*g or equivalently A2*mol
(we live in a world of AMBER forces of units kCal mol-1)
Frequency = sqrt(Energy/(mass * mean square fluctuation)) =
sqrt(Energy/eigval[i]) (see any book on mechanics, Hayward. Kitao, Go
in Protein Science 1994 3: 936-943)
.6 is kT at 300K in units of kCal/mol
so sqrt(.6/eigval[i]) in the C code gives you a frequency in the
delightful :) units of:
sqrt(kCal/mol or g)/(A * sqrt(mol or g))
The 108.597 converts this value to a wavenumber energy in cm-1
This is how:
Useful Unit Conversions
------------------------
1 kJ = 1000 m2 kg s-2
1 kCal = 4.184 kJ = 4.184 * 1000 * m2 * 1000g * s-2
Pulling out squared units, sqrt(.6/eigval[i]) now simplifies to
m * s-1 * sqrt(.6 * 4.184 * 1000 * 1000g * 4.184 ) / (A sqrt(g))
Converting meters to angstroms, and simplifying gives
10^10A * s-1 * sqrt(.6) * sqrt(g) * 489/(A sqrt g)
Simplifying all this gives frequency in s-1
sqrt(.6) * 2.05 * 1013 * s-1
To convert to cm-1, divide by 2.998 * 1010 cm/s and that gives:
sqrt(.6) * 682.28 cm-1 s
But, of course, we want to convert to wavenumbers. Dividing 682.28 by
2Pi gives
108.59 cm-1 s <<<<<< ***************
Kateryna Miroshnychenko wrote:
> Dear All,
>
> I wonder what is the meaning of 108.587 coefficient which is used to
> convert eigenvalues of mass-weighted covariance matrix to sm-1 (see
> below part of the file analyze.c from ptraj). In what units are the
> eigenvalues of mass-weighted covariance matrix before this conversion?
> I suppose they are in A2*amu?
>
> Thanks,
> Katya
>
> ______________________________________________
> Convert eigenvalues to cm-1
> */
> for(i = 0; i < neval; i++){
> if(eigval[i] > 0.0)
> eigval[i] = 108.587 * sqrt(0.6/eigval[i]); /* "0.6" is
> conversion of kT for 300K into kcal/mol(?) */
> else if (eigval[i] < 0.0)
> eigval[i] = -108.587 * sqrt(-0.6/eigval[i]);
> ______________________________________________
>
>
>
> ******************************************** Kateryna Miroshnychenko
> post-graduate student
> Department of Biological Physics,
> Institute of Radiophysics and Electronics,
> National Academy of Sciences of Ukraine,
> Kharkiv, Ukraine
> E-mail:kateryna_mirosh.ire.kharkov.ua
> ********************************************
>
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Received on Sun Feb 25 2007 - 06:07:25 PST
