From: JT (JTibbitt_at_odu.edu)
Date: Sat Apr 11 2009 - 03:47:57 CDT
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
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