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A New Generation of Doubly Hybrid Density Functionals (DHDFs)

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A New-Generation Density Functional

Part of the book series: SpringerBriefs in Molecular Science ((BRIEFSMOLECULAR))

Abstract

Doubly hybrid density functionals (DHDFs) present a new generation of density functionals, which not only enfold a nonlocal orbital-dependent component (i.e., the Hartree-Fock-like exchange) in the exchange part, but also incorporate the information of unoccupied orbitals (i.e., the second-order perturbative correlation) in the correlation part. Different types of DHDFs have been proposed according to different philosophies. They could be empirical as multicoefficient methods to allow the mixing of wavefunction-based methods with the hybrid density functional methods in order to achieve a good compromise of accuracy, cost, and ease of use for practical calculations, or they have their roots in multideterminant extension of the Kohn-Sham scheme or Görling–Levy’s coupling-constant perturbative theory. In this chapter, we first introduce a classification of the current DHDFs (Sect. 2.1). We then, in Sect. 2.2, discuss the Levy constrained search approach and adiabatic connection formalism, which provide a formal route that the exchange-correlation functional can be pursued. Finally, the underlying physics for the B2PLYP-type DHDFs and the XYG3-type DHDFs is explored in Sects. 2.3 and 2.4, respectively.

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  1. Department of Chemistry, Fudan University, Shanghai, People’s Republic of China

    Igor Ying Zhang & Xin Xu

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Zhang, I.Y., Xu, X. (2014). A New Generation of Doubly Hybrid Density Functionals (DHDFs). In: A New-Generation Density Functional. SpringerBriefs in Molecular Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40421-4_2

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