[gmx-users] Phonon calculations in periodic crystals

David van der Spoel spoel at xray.bmc.uu.se
Thu Jul 15 08:26:15 CEST 2010

On 2010-07-15 00.44, Anne Kelley wrote:
> I am trying to use GROMACS to calculate the phonons (normal modes) of a bulk crystal, CdSe.  I have found a simple force field, Coulomb + Lennard-Jones, in the literature (Rabani, J. Chem. Phys. 116, 258, 2002) which the author showed reproduced the phonon dispersion curves and other mechanical properties of bulk wurtzite CdSe quite well.  A number of other workers have used this force field in molecular dynamics simulations.  But when I use Rabani's force field with GROMACS I get phonon frequencies that are much too high, up to about 2.2 times the experimental ones.
> I am doing all of my calculations with the double precision version of GROMACS.  I have made a .top file for CdSe using Rabani's Lennard-Jones parameters and ionic charges, and a .gro file containing an integer number of unit cells with the known lattice constants.  I first do an energy minimization until the maximum forces are around 1.e-4, and get the right crystal structure and lattice constants.  I am using periodic boundary conditions with PME.  I then use the "nm" integrator (with the -t option to read in the more precise .trr structure file) to calculate the Hessian, and then the g_nmeig_d program to diagonalize the Hessian and get the normal modes.  This all seems to work fine, but I don't get the literature values for the frequencies (calculated maximum about 450 cm-1, literature and experimental about 215 cm-1).  I have checked that when I enter the correct masses and known harmonic force constant for the H2 molecule, I get back the right vibrational frequency.  I
 have tried changing the size of the system (5, 7, or 9 unit cells in each direction) and it has almost no effect on the frequencies.  I have tried things like changing the Coulomb and Lennard-Jones cutoffs, and even tried regular Ewald rather than PME (which took a very long time), but these had no significant effect on my results.  I also tried calculating the phonon spectrum for a different material, AgBr, using a Coulomb + Buckingham potential from the literature (J. Phys. Chem. 99, 14344, 1995).  This gave me a better result, but still the distribution of frequencies is not correct and the maximum phonon frequency is about 15% higher than what the authors got with the same force field.
> Are you aware of any issues with GROMACS in doing normal mode calculations on periodic systems?  Can you suggest any likely things I'm doing wrong?
It seems you're doing everything according to the book. Did you double 
check the parameter conversions to kJ/mol, nm etc.? Some people write 
sigma and epsilon in strange units.
You might want to tighten the ewald_rtol slightly, since you're running 
DP anyway, but this should not have a large effect.
Another thing you could play with is manually selecting the FFT grid 
spacing to be an integer multiple of the number of unit cells, such that 
all the atoms lie on grid points.

Let us know how it goes.

> Anne Kelley
> Anne Myers Kelley
> Professor of Chemistry, School of Natural Sciences
> Secretary-Treasurer, APS Division of Laser Science
> University of California, Merced
> 5200 North Lake Road, Merced, CA 95343
> Tel. 209-228-4345
> amkelley at ucmerced.edu
> http://faculty.ucmerced.edu/amkelley/

David van der Spoel, Ph.D., Professor of Biology
Dept. of Cell & Molec. Biol., Uppsala University.
Box 596, 75124 Uppsala, Sweden. Phone:	+46184714205.
spoel at xray.bmc.uu.se    http://folding.bmc.uu.se

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