A twin question related to the TDDFT method is asked in another post. But any comparisons between both methods in recent developments are welcome.

The time-dependent density functional theory (TDDFT) and the many-body perturbation theory (GW@BSE) methods are considered as the two most popular and successful methods to describe the excited-stated properties of materials. In fact, both methods have been reviewed in this classical paper published in Review of Morden Physics. From that almost twenty years have passed. What are the recent developments of the GW@BSE method? And what are the current challenges to simulate real materials with the GW@BSE method? As far as I know, the BerkeleyGW GROUP and Yambo GROUP have successfully implemented the framework of the GW@BSE method based on plane-wave DFT calculations. Are there any packages to realize this method, especially without dependence on plane-wave DFT?

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    $\begingroup$ I am not an expert on the question, but there are several different implementations both for plane waves and localized basis. The difference I have found were the different approximations implemented: GW is extremely slow and poorly scaling, so all kind of tricks trying to improve those bottlenecks. Sime codes that include GW, generally several different approximations each (I am not sure BSE): VASP, Turbomole, cp2k $\endgroup$
    – Greg
    Jan 10 '21 at 9:45

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