B2PLYP double hybrid functional

In [170] the authors obtain a test set of ten molecules of specific atmospheric interest in order to evaluate the performance of various Density Functional Theory (DFT) methods in (hyper)polarizability calculations as well as established ab initio methods. The authors make their choice for these molecules based on the profound change in the physics between isomeric systems, the relation between isomeric forms and the effect of the substitution. In the evaluation analysis the authors use arguments chosen from the information theory, the graph theory and the pattern recognition fields of Mathematics. The authors mentioned the remarkable good performance of the double hybrid functionals (namely B2PLYP and mPW2PLYP) which are for the first time used in calculations of electric response properties. 

The biggest problem in DPT is the choice of the functional approximation. In many cases, computationally cheap (meta-)GGAs (e.g.,BLYP, PBE,orTPSS) can be recommended. Such functionals should not be used when the self-interaction error (e.g., in charged open shell systems) plays a role. Then, hybrid functionals are required which also have less tendency for over-polarization. The currently highest level of approximation in DPT is represented by double-hybrid functionals (e.g., B2PLYP) that also perform very well for non-covalent interactions. 

Grimme extended the double hybrid density functional formalism to be able to compute BCD. For a test suite of six molecules, performance of B2PLYP is notably better than for B3LYP. 

B2PLYP and mPW2PLYP are called double-hybrid density functionals (DHDFs), since they mix in not only some exact exchange but also some correlation calculated by the MP2 method. 

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