[gmx-users] Quasi-Harmonic entropy and g_covar

[Nguyen Hoang Phuong]

>
> ---- Message from Nguyen Hoang Phuong
> <phuong at theochem.uni-frankfurt.de> at 2004-10-28 18:38:13 ------
> >
> >
> >> I tried to calculate the quasi-harmonic entropies from an MD
> simulation
> >> from the covariance matrix, using g_covar as follows:
> >> (1). Using the -nofit flag
> >> (2). After fitting the coordinates to the initial configuration
> >>
> >> When examining the eigenvalues, I got 3N eigenvalues for (1) and
> 3N-6
> >> for (2) - i.e. the last 6 values were several orders of magnitude
> >> smaller than the eigenvalues just prior to them, and some were
> negative
> >> (and still, very close to zero).
> >>
> >> According to Andricioaei and Karplus (J Chem Phys 115: 6289), one
> needs
> >> to use 3N-6 degrees of freedom in order to calculate the entropy
> in a
> >> quasi-harmonic representation. Hence, my questions are:
> >> 1. Should I expect to find the difference in the number (and
> magnitude)
> >> of eigenvalues in (1) and (2), or is there a problem with the
> accuracy
> >> of the simulation?
> >> 2. Which eigenvalues should I use?
> >> 3. If I use the eigenvalues obtained from (2), do I account for all
> >> degrees of freedom or just for the vibrational?
> >>
> >> I'd appreciate any comments,
> >
> >You should expect to find the difference in the number (and
> magnitude)
> >of eigenvalues in (1) and (2).
> >
> >you should use the eigenvalues obtained from (2) for the
> >vibrational entropy. There is the mixing between vibrational motions
> and
> >rotational motion in (1). This mixing is shown in the last 6
> eigenvalues
> >obtained from (1).
> >
>
> I agree with this. It is necessary to remove rotational and
> translational motion by fitting to a structure. You could argue that
> it is better to fit to the average of your equilibrated frames, as
> this is in some way the centre of your quasi-harmonic motion, but I
> don't think this makes a significant difference in most cases. Worth
> trying though.

usually about the first 10 eigenvalues (low frequencies) contribute
significantly to the entropy since entropy is proportional to exp(-hbar*omega/KT). If the
frequency omega is large, i.e small eigenvalue then the value
exp(-hbar*omega/KT) is essentially zero.

The mixing between vibrational motions and overall rotation is large
for low frequency modes.

>From above arguments, I think that the entropy will be different in two
cases, but one should try as you said.

Phuong