Theoretical Chemistry Accounts

, 134:107 | Cite as

Second-order Møller–Plesset perturbation (MP2) theory at finite temperature: relation with Surján’s density matrix MP2 and its application to linear-scaling divide-and-conquer method

  • Masato KobayashiEmail author
  • Tetsuya Taketsugu
Regular Article
Part of the following topical collections:
  1. Festschrift in honour of P. R. Surjan


In 2005, Surján showed two explicit formulas for evaluating the second-order Møller–Plesset perturbation (MP2) energy as a functional of the Hartree–Fock density matrix \(\varvec{D}\) (Chem Phys Lett 406:318, 2005), which are referred to as the \(\Delta E_\text {MP2}[\varvec{D}]\) functionals. In this paper, we present the finite-temperature (FT) MP2 energy functionals of the FT Hartree–Fock density matrix. There are also two formulas for the FT-MP2, namely the conventional and renormalized ones; the latter of which has recently been formulated by Hirata and He (J Chem Phys 138:204112, 2013). We proved that there exists one-to-one correspondence between the formulas of two FT-MP2 and the \(\Delta E_\text {MP2}[\varvec{D}]\) functionals. This fact can explain the different behavior of two \(\Delta E_\text {MP2}[\varvec{D}]\) functionals when an approximate Hartree–Fock density matrix is applied, which was previously investigated by Kobayashi and Nakai (Chem Phys Lett 420:250, 2006). We also applied the FT-MP2 formalisms to the linear-scaling divide-and-conquer method for improving the accuracy with tiny addition of the computational efforts.


Fractional occupation number Many-body perturbation theory Laplace-transformed Møller–Plesset perturbation Linear-scaling electronic structure method 



The authors are grateful to Prof. Hiromi Nakai and Dr. Takeshi Yoshikawa (Waseda University) for their valuable comments. Some of the present calculations were performed using the computer facilities at Research Center for Computational Science, Okazaki, and at Research Institute for Information Technology, Kyushu University, Japan. This work was supported in part by JSPS KAKENHI Grant No. 25810011.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Chemistry, Faculty of ScienceHokkaido UniversitySapporoJapan
  2. 2.Elements Strategy Initiative for Catalysts and Batteries (ESICB)Kyoto UniversityKyotoJapan

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