Kohn-Sham perturbation theory: Simple solution to variational instability of second order correlation energy functional

2006 ◽  
Vol 125 (18) ◽  
pp. 184108 ◽  
Author(s):  
Hong Jiang ◽  
Eberhard Engel
Keyword(s):  
Perturbation Theory ◽  
Correlation Energy ◽  
Energy Functional ◽  
Second Order ◽  
Simple Solution

scholarly journals Spin-component-scaled and dispersion-corrected second-order Møller-Plesset perturbation theory: A path toward chemical accuracy

2021 ◽  
Author(s):  
Chandler Greenwell ◽  
Jan Rezac ◽  
Gregory Beran
Keyword(s):  
Perturbation Theory ◽  
Density Functional ◽  
Correlation Energy ◽  
Computational Cost ◽  
Second Order ◽  
Spin Component ◽  
Dispersion Interactions ◽  
Reaction Energies ◽  
Moller Plesset ◽  
Plesset Perturbation Theory

Second-order Møller-Plesset perturbation theory (MP2) provides a valuable alternative to density functional theory for modeing problems in organic and biological chemistry. However, MP2 suffers from known lim- itations in the description of van der Waals dispersion interactions and reaction thermochemistry. Here, a spin-component-scaled, dispersion-corrected MP2 model (SCS-MP2D) is proposed that addresses these weaknesses. The dispersion correction, which is based on Grimme’s D3 formalism, replaces the uncoupled Hartree-Fock dispersion inherent in MP2 with a more robust coupled Kohn-Sham treatment. The spin- component scaling of the residual MP2 correlation energy then reduces the remaining errors in the model. This two-part correction strategy solves the problem found in earlier spin-component-scaled MP2 models where completely different spin-scaling parameters were needed for describing reaction energies versus in- termolecular interactions. Results on 18 benchmark data sets and two challenging potential energy curves demonstrate that SCS-MP2D considerably improves upon the accuracy of MP2 for intermolecular interac- tions, conformational energies, and reaction energies. Its accuracy and computational cost are competitive with state-of-the-art density functionals such as DSD-BLYP-D3(BJ), revDSD-PBEP86-D3(BJ), ωB97X-V, and ωB97M-V for systems with ∼100 atoms.

scholarly journals A Proposal of an Orbital-Dependent Correlation Energy Functional for Energy-Band Calculations

2003 ◽  
Vol 17 (17) ◽  
pp. 3075-3134 ◽  
Author(s):  
Masahiko Higuchi ◽  
Hiroshi Yasuhara
Keyword(s):  
Energy Band ◽  
Correlation Energy ◽  
Effective Interaction ◽  
Pair Correlation ◽  
Energy Functional ◽  
High Accuracy ◽  
Second Order ◽  
Exchange Energy ◽  
Band Theory ◽  
Dependent Correlation

An explicitly orbital-dependent correlation energy functional is proposed, which is to be used in combination with the orbital-dependent exchange energy functional in energy-band calculations. It bears a close resemblance to the second-order direct and exchange perturbation terms calculated with Kohn–Sham orbitals and Kohn–Sham energies except that one of the two Coulomb interactions entering each term is replaced by an effective interaction which contains information about long-, intermediate-, and short-range correlations beyond second-order perturbation theory. Such an effective interaction can rigorously be defined for the correlation energy of the uniform electron liquid and is evaluated with high accuracy in order to apply to the orbital-dependent correlation energy functional. The coupling-constant-averaged spin-parallel and spin-antiparallel pair correlation functions are also evaluated with high accuracy for the electron liquid. The present orbital-dependent correlation energy functional with the effective interaction borrowed from the electron liquid is valid for tightly-binding electrons as well as for nearly-free electrons in marked contrast with the conventional local density approximation. There is a strong possibility that the present orbital-dependent correlation energy functional, if applied to the so-called strongly correlated electron systems, will produce the energy-band structure significantly different from that calculated only with the orbital-dependent exchange energy functional particularly in the neighborhood of the Fermi level or the energy gap. A detailed discussion, accompanied by an accurate calculation of the quasiparticle energy dispersion of the electron liquid, is given about the relationship between Kohn–Sham equations and Dyson equations in order to justify the application of Kohn–Sham equations to the band theory.

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