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From: Chris Moth <chris.moth.vanderbilt.edu>

Date: Thu, 22 Feb 2007 17:01:57 -0600

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
*

*> ********************************************
*

*>
*

*> -----------------------------------------------------------------------
*

*> The AMBER Mail Reflector
*

*> To post, send mail to amber.scripps.edu
*

*> To unsubscribe, send "unsubscribe amber" to majordomo.scripps.edu
*

*>
*

*>
*

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Received on Sun Feb 25 2007 - 06:07:25 PST

Date: Thu, 22 Feb 2007 17:01:57 -0600

Kateryna Miroshnychenko wrote in July 2005:

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:

-----------------------------------------------------------------------

The AMBER Mail Reflector

To post, send mail to amber.scripps.edu

To unsubscribe, send "unsubscribe amber" to majordomo.scripps.edu

Received on Sun Feb 25 2007 - 06:07:25 PST

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