Explanation by Stefan Grimme + solution ansatz

Dear Sonu Keshri, I am not sure why you think DFT is not appropriate for dealing with interactions like the one described by the potential V=-eE (if the field E is constant, did I understand this correctly?). DFT proper indeed does not include some long-range electron-electron interactions, namely those, which are both long-range and also require electron-electron correlation, like in particular the London dispersion forces a.k.a. van der Waals. These can be added to DFT in some approximate way, e.g. the Tkatchenko-Scheffler method, but of course, there may arise questions about suitability of the approximation for your particular case etc. However, the potential V=-eE seems to be an externally imposed one. DFT should have no problem with external potentials at all (another question is of course to what extent the particular computer code you are using an an implementation of DFT allows you to add such an external potential). What can cause some trouble is that many DFT codes assume periodic boundary conditions and the V=-eE potential is obviously non-periodic. So you would have to approximate it somehow, most likely by a saw-tooth shaped potential, which could cause some troubles itself, but that's an issue separate from your original question.

Sorry, I noticed only now that you are particularly interested in optical phenomena. I am not very familiar with these myself. But in such cases, perhaps the trouble is that the potential you need is in fact time-dependent?

@Oliver Pfaff, thanks for your references.

Dear Martin,

Thanks for your comments. I am using Quantum Espresso Package. As you mentioned some extremely worthy ponts, V=-eE is non periodic, and use of saw tooth like approximation. I am not sure how to deal with such approximations. In optical response theory, E is clearly a time dependent field but it's dealings with TDDFT in Quantum Espresso is not given for extended systems. I don't know why? Thanks again.

Unfortunately, I am not using Quantum Espresso myself, and do not know how to solve the problem there, so I can't help here much. But yes, extended systems do not go well with a saw tooth potential. In general, the discontinuity of the potential should be placed in an empty space, but there is no empty space when you deal with something like a bulk crystal. I am sure there must be some way to get optical properties of materials in QE, it is a pretty standard problem, although not one within my expertise. By a brief search, I gathered that people usually use some post-processing tools for this: They calculate eigenvalues and eigenvectors of the system without the external potential and then apply some procedure based on perturbation theory to get e.g. frequency-dependent dielectric tensor based on the unperturbed eigenvectors (wave functions). Is this an option for you?

Sonu Prasad Keshri you should not use a sawtooth field for an extended system, use the Berry phase polarisation method instead. It will only work for systems with a band-gap (otherwise the ground state is a steady-state current), and you will need to be careful with your k-point sampling, if it's too dense your material can undergo dielectric breakdown.