**From:** JT (*JTibbitt_at_odu.edu*)

**Date:** Sat Apr 11 2009 - 03:47:57 CDT

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Mert,

Hey, taking a closer look at the derivation of the quasiharmonic

approximation used in PCA, I found that the generated normal modes

are, in fact, harmonic. Altough these modes incorporate

anharmonicity, they often are inappropriately called 'anharmonic'.

Consider the following.

In traditional normal mode analysis, the force constant matrix, F, is

related to the harmonic system's covariance matrix, s, by the simple

relation, s = kB*T*F^-1. So the normal modes are obtained by

diagonalizing either the the mass-weighted covariance matrix or the

mass-weighted force constant matrix.

Quasiharmonics chooses to use the covariance matrix from a different

source (e.g. an MD trajectory). The potential related (as above) to

this other covariance matrix is called the 'effective harmonic

potential'. And then the normal modes are obtained the same way, by

either diagonalizing the mass-weighted covariance matrix, or by

transforming back to the mass-weighted force-constant matrix (of the

effective harmonic potential), and then diagonalizing it. But as we

discussed before, although the modes are more realistic by

incorporating the anharmonicity of the MD trajectory, the generated

eigenvalues (or their related modal frequencies) are not.

I'm not too familiar with calculating kinetic energies for individual

modes or sets of modes (e.g. the essential ones). It sounds like you

already have an arsenal of things to try. You may want to check out

the classic text: Molecular Vibrations by EB Wilson, JC Decius and PC

Cross. It is an excellent reference and may have other simple methods.

Also, here is a good paper:

Harmonic and quasiharmonic descriptions of crambin

Teeter MM, Case DA

J Phys Chem

94(21)

pp 8091-8097

Jeff Tibbitt

**Next message:**Chris Harrison: "Re: Error : DIDN'T FIND vdW PARAMETER FOR ATOM TYPE C11"**Previous message:**Goutham: "Error : DIDN'T FIND vdW PARAMETER FOR ATOM TYPE C11"**Maybe in reply to:**Tibbitt, Jeffrey A.: "RE: Evaluating kinetic energy from a modified DCD file"**Next in thread:**Mert Gür: "Re: Evaluating kinetic energy from a modified DCD file"**Reply:**Mert Gür: "Re: Evaluating kinetic energy from a modified DCD file"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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