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

Abstract

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.