We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in density functional theory (TC-DFT). An effective Hamiltonian, HTC, is introduced by a similarity transformation of a many-body Hamiltonian, H, with respect to a complex function F: HTC = 1/F H F. It is proved that an expectation value of HTC for a normalized single Slater determinant, Dn, corresponds to the total energy:E[n]=<Ψn|H|Ψn>/<Ψn|Ψn>=<Dn|HTC|Dn> under the two assumptions: (1) The electron density n(r) associated with a trial wave function Ψn = DnF is v-representable and (2) Ψn and Dn give rise to the same electron density n (r). This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-) local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.
*Present affiliation：Semiconductor R&D Center, Samsung Electronics, Korea
References: N. Umezawa, "Extended screened exchange functional derived from transcorrelated density functional theory" J. Chem. Phys. 147, 104104 (2017)