[MMTK] RMSF from Normal Modes

[Konrad Hinsen]

On 16.10.2009, at 13:52, Kamilla Kopec wrote:

> 1) What are the correct units for omega(j) and ui(j) ? If
>
> Kb is  in J/K (Kg m^2 s^-2 K^-1),
> m(i) is in Kg
> omega(j) is in s-1
> f(i) is in m^2
>
> It seems that ui(j) should be dimensionless to ensure units of m^2  
> for f(i) ??? What is the correct unit of ui(j), the eigenvector of  
> the mass weighted force constant matrix??

ui(j) is indeed dimensionless. Eigenvectors of a matrix are only  
defined up to an arbitrary prefactor, which is usually chosen to make  
the vector normalized. This implies that the vector elements are  
dimensionless.

> In the tutorial it says 'The atomic displacements are already scaled  
> by the amplitudes of thermal vibrations " so only a factor of 0.5 is  
> required.  How has this been done?

The amplitudes of thermal vibration are calculated according to the  
formula you quoted, except for a factor of two. This factor come from  
the averaging that is required to calculate the fluctuations.  
Averaging cos^2(t) over one period gives 1/2, so the fluctuation  
formula has a factor 1/2 compared to the squared-amplitude formula.

> I am currently trying to compare the RMSF of specific atoms across  
> different modes using a gaussian03 frequency output. I am just  
> trying to understand the MM implementation before tackling the  
> gaussian equivalent.

Note that comparing displacements for a single mode and a single atom  
is reasonable only for small molecules with well-separated vibrational  
frequencies. Otherwise you have many nearly degenerate modes and the  
slightest change in your potential energy surface can change an  
individual mode significantly. For dense vibrational spectra, you  
should always compare sums over several modes in some frequency  
interval.

Konrad.
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Konrad Hinsen
Centre de Biophysique Moléculaire, CNRS Orléans
Synchrotron Soleil - Division Expériences
Saint Aubin - BP 48
91192 Gif sur Yvette Cedex, France
Tel. +33-1 69 35 97 15
E-Mail: research at khinsen dot fastmail dot net
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