**From:** Mert Gür (*gurmert_at_gmail.com*)

**Date:** Sun Apr 12 2009 - 08:11:21 CDT

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Dear Jeff,

I really appreciate your insightfull comments and references. They were very

helpfull.

But for the sake of discussion I want to add some more points.

The problem with the MD is that you are not at the global minimum which is

assumed by the NMA. In addition to that you have unharmonic behaviour.

The NMA assumes both of these points. As it is explained by the references

you provided to me, the simplicity of the NMA comes from the assumtion that

equilibrium fluctuations are small so that the unharmonic terms in the

series go to the zero.

My understanding is that the PCA mainly gives us the subset of

motions(eigenvectors) which construct the total motion. The eigenvalues

gives us an understanding of the amplitude and hence frequency of the

motion. But I still have not seen anywhere that KE can be defined using

these frequencies the same way in NMA.

If I do simple calculation with my pen as Axel suggested I see that the

velocity does not follow the formula the NMA suggested.

I think that matches with what you were explaining

Best,

Mert

On Sat, Apr 11, 2009 at 11:47 AM, JT <JTibbitt_at_odu.edu> wrote:

*> Mert,Hey, taking a closer look at the derivation of the quasiharmonic
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*> approximation used in PCA, I found that the generated normal modes are, in
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*> fact, harmonic. Altough these modes incorporate anharmonicity, they often
*

*> are inappropriately called 'anharmonic'. Consider the following.
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*>
*

*> In traditional normal mode analysis, the force constant matrix, F, is
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*> related to the harmonic system's covariance matrix, s, by the simple
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*> relation, s = kB*T*F^-1. So the normal modes are obtained by diagonalizing
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*> either the the mass-weighted covariance matrix or the mass-weighted force
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*> constant matrix.
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*>
*

*> Quasiharmonics chooses to use the covariance matrix from a different source
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*> (e.g. an MD trajectory). The potential related (as above) to this other
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*> covariance matrix is called the 'effective harmonic potential'. And then
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*> the normal modes are obtained the same way, by either diagonalizing the
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*> mass-weighted covariance matrix, or by transforming back to the
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*> mass-weighted force-constant matrix (of the effective harmonic potential),
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*> and then diagonalizing it. But as we discussed before, although the modes
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*> are more realistic by incorporating the anharmonicity of the MD trajectory,
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*> the generated eigenvalues (or their related modal frequencies) are not.
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*>
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*> I'm not too familiar with calculating kinetic energies for individual modes
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*> or sets of modes (e.g. the essential ones). It sounds like you already have
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*> an arsenal of things to try. You may want to check out the classic text:
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*> Molecular Vibrations by EB Wilson, JC Decius and PC Cross. It is an
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*> excellent reference and may have other simple methods.
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*>
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*> Also, here is a good paper:
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*> *Harmonic and quasiharmonic descriptions of crambi*n
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*> Teeter MM, Case DA
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*> *J Phys Chem*
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*> 94(21)
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*> pp 8091-8097
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*>
*

*> Jeff Tibbitt
*

*>
*

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