Concluding Remarks
In the application of Kohn-Sham density functional theory (KS-DFT), the exchange-correlation energy must be approximated. A ladder of such approximations has been proposed, none of which is equally good for every problem. There is still a long way to go.
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Concluding Remarks
Abstract In the application of Kohn-Sham density functional theory (KS-DFT), the exchange-correlation energy must be approximated. A ladder of such approximations has been proposed, none of which is equally good for every problem. There is still a long way to go. In this chapter, we first give a brief summary of what we have learned in pursuing an improved functional Sect. 5.1, giving a list of the doubly hybrid density functionals (DHDFs) developed till date in the literature. We then outline, in Sect. 5.2, the limitations and the anticipated future development for the XYG3 type of DHDFs. Finally, a perspective is presented, which highlights some fundamental issues in the ground state KS-DFT. Keywords Density functional theory hybrid density functionals
Exchange-correlation XYG3 Doubly
5.1 Lessons Learned Kohn-Sham density functional theory (KS-DFT) replaces the correlated wavefunction problem by a more tractable problem of non-interacting electron system. Although exact in principle, KS-DFT requires in practice an approximation to the exchange-correlation functional. With increasingly sophisticated approximations, KS-DFT has now become the most widely used method for electronic structure calculations, and has made great contribution to our understanding of molecular science. This book focuses on some recent advances in construction of the so-called doubly hybrid density functionals (DHDFs). It is our opinion that DHDFs currently available shall be classified into three groups according to how they are constructed based on the underlying principles, or technically which orbitals are used to evaluate the second-order perturbative correlations.
I. Y. Zhang and X. Xu, A New-Generation Density Functional, SpringerBriefs in Molecular Science, DOI: 10.1007/978-3-642-40421-4_5, The Author(s) 2014
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5 Concluding Remarks
Table 5.1 Summary of the MC3BB type of DHDFs Name DFT Compounds of wavefunction methods exchange ? correlation
Ref.
MC3BB MC3MPW MC3MPWB MC3TS MCCO-MPW MCCO-MPWB MCCO-TS MCUT-MPW MCUT-MPWB MCUT-TS MCQCISD-MPW MCQCISD-MPWB MCQCISD-TS MCG3-MPW MCG3-MPWB MCG3-TS
[1] [1] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2] [2]
B88 ? B95 mPW ? PW91 mPW ? B95 TPSS ? KCIS mPW ? PW91 mPW ? B95 TPSS ? KCIS mPW ? PW91 mPW ? B95 TPSS ? KCIS mPW ? PW91 mPW ? B95 TPSS ? KCIS mPW ? PW91 mPW ? B95 TPSS ? KCIS
HF/MP2 HF/MP2 HF/MP2 HF/MP2 HF/MP2 HF/MP2 HF/MP2 HF/MP2/MP4(SDQ) HF/MP2/MP4(SDQ) HF/MP2/MP4(SDQ) HF/MP2/QCISD HF/MP2/QCISD HF/MP2/QCISD HF/MP2/MP4(SDQ)/QCISD(T) HF/MP2/MP4(SDQ)/QCISD(T) HF/MP2/MP4(SDQ)/QCISD(T)
Table 5.1 lists the first type of DHDFs, which mix the total energies of a DFT calculation and those of wavefunction methods [1, 2]. The latter are not limited to MP2 (Møller-Plesset perturbation theory at second order) as in MC3BB [1], but updated even to the QCISD(T) level [2] (i.e., quadratic configuration interaction with single and double plus fourth-order and fifth-order quasi-perturbative terms involving triple excitations). They are actually multi-coeffic
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