[MMTK] RMSF from Normal Modes

Kamilla Kopec ozero22 at yahoo.co.uk
Fri Oct 16 11:52:39 UTC 2009

Dear All, 

I have been going through the EMBO MMTK normal modes tutorial and have a question about the calculation of RMSF from the results of normal mode analysis.  

The formula given is: 

F(i) = SUM{j} [ KbT/m(i)omega(j)^2] * |ui(j)|^2

Where Kb is the Boltzmann constant. 
Omega(j) is the frequency of normal mode (j) 
Ui(j) is the displacement of atom i in mode (j) 
m(i) is the mass of the atom 

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??  
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? 

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.  

Best Regards   


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