Some of the drawbacks are the exchange correlation functional, the temperature effects, and the computational cost in terms of the number of atoms.

"What are the other methods that are more efficient in terms of both accuracy and computing time?" All depends on the size and elemental composition of your systems to model. For example, for some nanosystems, DFT is the best you can afford. For others, even DFT turns to be too expensive.

Dear Sinhué López,

Thank you for your response. In many literature, I found that DFT does not correctly treat the exchange interaction. But I could not understand the term "correct treatment". Do you also mean to say that in your answer? Also, what are the methods then that correctly treats exchange interaction?

DFT is a ground state theorem. When you want to calculate the exciting state properties like optical properties, DFT will not be a handy tool. You can read further about the limitations of DFT in the book "DENSITY FUNCTIONAL THEORY : A Practical Introduction" by Sholl and Steckel, page no.-28.

Hi Mridusmita,

By chance I found a reference today which my help answer your question, if you haven't seen it already:

"Machine learning prediction errors better than DFT accuracy"

https://arxiv.org/abs/1702.05532

Sorry for not digging into it more deeply, and maybe you've considered it already, but you might consider various machine learning approaches and how the compare to DFT.

They specifically mention "post-Hartfree Fock" and "quantum Monte Carlo" in the context of quantum chemistry, but there's also cite past work on the more general neural network technique (Page 1). Looks like they then test a bunch of different methods on the same data: random forsest, neural networks, graph convolutions, Bayesian ridge regressor (Page 2).

Good luck!

Dear Aaron,

Thank you very much for sharing the reference. I should read this paper carefully. Though I know some drawbacks, this paper might describe the pros and cons of DFT in detail.