Is there any way to get dynamic structure factor from GROMACS ? The static structure factor S(k) can be calculated by taking a Fourier Transform of radial distribution function g(r), but I couldn't find anything for the dynamic one. If there is a way to do this, please help me out.
thanks
Consult the paper by Van Hove (Phys. Rev. 95, 249 (1954)) - link attached below, as well as Appendix N of the book Solid State Physics, by Ashcroft and Mermin.
While preparing to write this response, I found an interesting relevant talk by Kai Helbig at TU Dresden, the link to which I attach below.
http://journals.aps.org/pr/abstract/10.1103/PhysRev.95.249
https://iktp.tu-dresden.de/IKTP/Seminare/IS2010/Kai_Helbig.pdf
Thank you a lot for your help. I shall surely go through the materials you attached with your answer.
Thanks again
I came to know about another paper where they discussed how to calculate S(k,w) from trajectory.
Interested persons may refer to the following link
http://ac.els-cdn.com/S0006349509002082/1-s2.0-S0006349509002082-main.pdf?_tid=ef648926-5f87-11e6-9676-00000aab0f02&acdnat=1470894992_f953b7b2eeeb661f552c4e3eeb36ef8a
Dear Sayantan, thank you for the reference.
As you notice, the basic formalism underlying the calculations reported in the paper by Brandt and Edholm is that of Van Hove, however instead of explicitly dealing with the vibrational modes of the ions, they extract the dynamics of the ions from their molecular-dynamics simulations. This is a well-known approach, which is used for extracting the phonon frequencies from the molecular-dynamics trajectories of the ions (see for instance Sec. VIII.G of the review article by Payne, Teter, Allan, and Joannopoulos, Rev. Mod. Phys. 64, 1045 (1992)). The approach has its advantages and disadvantages. Disadvantage of the approach is that in a physical system one in general has both low-frequency and high-frequency phonon modes, rendering molecular-dynamics simulations very difficult: to capture the low-frequency modes, one has to integrate the underlying equation-of-motion (see the next paragraph) over a long period of time, and to capture the high-frequency modes, one has to slice this long time interval into very small short intervals, leading to very long and time-consuming calculations. Advantage of the method is that one is not restricted to the harmonic approximation of the dynamics of the phonon modes (see the following paragraph)
To appreciate the formalism underlying molecular-dynamics simulations, consider the expression for rj(t) in the equation following Eq. (8) of the paper by Van Hove. This shows rj(t) to be in the Heisenberg picture, thus satisfying the Heisenberg equation-of-motion, which is a first-order differential equation with respect to time. Molecular-dynamics simulations amount to integration of this equation-of-motion, which is obtained by determining the commutator of the Hamiltonian operator with the operator for rj. For this, one represents both the latter operator and the coordinates and momenta of atoms in the Hamiltonian in terms of bosonic creation and annihilation operators, a procedure that one encounters in Appendix N of the book by Ashcroft and Mermin. See Appendix L of the latter book, where the dynamics of the phonons is assumed to be harmonic (including anharmonic effects amounts to considering a system of interacting phonons).
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