Even some DFT methods or beyond DFT methods such as MP2 calculations are computationally very expensive today even with clusters. If you compare QMC (quantum monte carlo) calculations with them, are the QMC calculations way too much expensive? Is it worth to invest time in QMC?

  • $\begingroup$ What's the meaning of QMC? $\endgroup$ – Jack Sep 13 at 2:43
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    $\begingroup$ Quantum monte carlo probably? $\endgroup$ – Tristan Maxson Sep 13 at 2:52

Quantum Monte Carlo (QMC) calculations in various forms, for example variational QMC or diffusion QMC have been used to study periodic systems for decades. In most cases, they provide results that are more accurate than DFT, so it is often taken as a reference for solid state calculations. Indeed, the pioneering QMC calculations of the electron gas by Ceperley and Alder (see here) form the basis of common approximations to exchange correlation functionals, so in a sense enable DFT.

So is it worth investing time in QMC? The method is still computationally more expensive than DFT, so the answer depends. If the system/property you are interested in is well-described by DFT (e.g. weak correlations) then there is no point in doing QMC calculations. However, if you need higher accuracy, there is a definite case for using QMC methods. Another point to consider for the longer term is that many QMC methods are trivially parallelizable, so they are capable of making full use of modern computer architectures, which means that they will probably become increasingly pervasive.

The go-to review article of the use of QMC methods to study solids by Matthew Foulkes and co-workers can be found here.

This is a list of codes that implement QMC calculations for solids that are widely used (feel free to add more):

  1. CASINO: https://vallico.net/casinoqmc/
  2. QMCPACK: https://qmcpack.org
  3. QWalk: http://qwalk.github.io/mainline/
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  • $\begingroup$ Thanks for the nice answer. I have a question, how much is expensive than DFT? Is there a ratio or something that you can say? I need it for reference calculations. How many core and memory would make it possible for TMDC's ground state energy calculation $\endgroup$ – Alfred Sep 13 at 16:17
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    $\begingroup$ @Alfred I think it is very difficult to put a number to this. I suspect the answer will strongly depend on the system, and on top of that QMC is a stochastic technique, so the answer will also depend on the size of error bar that you aim for. Another big variable are the computational resources available: QMC scales very well, while standard DFT doesn't, so depending on how many cores you can throw at the problem the answer will again vary. Another issue to consider is that QMC is not as "black-box" as DFT at present, so there will be a steep learning curve... $\endgroup$ – ProfM Sep 13 at 16:50
  • $\begingroup$ Thanks for the answer. Now it's more precise, but I have one short question, and I think it'll give me an idea. Is it computationally expensive than the MP2 and ACFDT/RPA methods? If you would choose between them for reference calculation, which one you would choose? $\endgroup$ – Alfred Sep 13 at 17:01
  • $\begingroup$ @Alfred, unfortunately I have no experience in MP2 or ACDFT/RPA methods, so cannot answer. However, this looks like something that the larger community could help with, so perhaps you could ask it as a new question? $\endgroup$ – ProfM Sep 13 at 18:06

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