One way to alleviate the problem with strongly correlated systems is to develop density functional methods that employ a multiconfigurational reference function; a promising approach of this type is multiconfiguration pair DFT (MC-PDFT) This approach shows great promise and is typically much less computationally demanding than wave function methods of comparable accuracy, but it does raise the cost compared with KS-DFT. Please explain why the energy Why in KS-DFT is not calculated by adding more CSFs but rather by using an exchange-correlation?
In principle you gave parts of the answer yourself: it raises the costs. If you use DFT with exact HF exchange as it's done with hybrids like B3LYP, you get an N4 scaling behaviour (lower for non-hybrid or when you use resolution of identity approximations).
As soon as you go multi-reference, you will immediately get a higher scaling behaviour and can easily let your time, CPU/GPU and RAM requirements deteriorate and therefore get pretty expensive.
Since you can get quite acceptable results with hybrids or meta-GGA functionals (or in some cases already GGA) for many questions, most people will go down that route.
It gives an easy approximation in obtaining a better and accurate results
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