First-Principles electronic structure calculation of solids with a similarity-transformed hamiltonian

Shinji Tsuneyuki

The University of Tokyo, Graduate School of Science, Department of Physics, Tokyo, Japan

I review recent progress of first-principles electronic structure calculation of solids based on the transcorrelated (TC) method.
In the TC method [1, 2], an explicitly correlated wave function of Slater-Jastrow-type is adopted. After similarity transformation of the Hamiltonian H with the Jastrow function F, one obtains so-called TC Hamiltonian and a Hatree-Fock-like self-consistent-field equation to determine one-electron orbitals and orbital energies. Since the transformation does not break the crystalline symmetry, one can obtain electronic band structure of solids with taking account of the screening effect. This is an advantage of the TC method against Quantum Monte Carlo methods with explicitly correlated wave functions. We have demonstrated that the density of states of the uniform electron gas is recovered at the Fermi level and that the band gap of semiconductors shows great improvement [3]. Another advantage is that total energy of solids is calculated without Monte Carlo sampling [4].

A serious drawback of the TC method was its large computational cost due to effective three-body interaction in the TC Hamiltonian. Very recently, however, we developed a new computational algorithm for periodic systems to reduce the computational cost to the same order as that of the Hartree-Fock method [5], which opened the way for practical applications of the TC method.

[1] S.F. Boys and N.C. Handy, Proc. R. Soc. London, Ser. A 309, 209 (1969); ibid. 310, 63 (1969); ibid. 311, 309 (1969).
[2] N.C. Handy, Mol. Phys. 21, 817 (1971).
[3] R. Sakuma and S. Tsuneyuki, J. Phys. Soc. Jpn. 75, 103705 (2006).
[4] N. Umezawa and S. Tsuneyuki, Phys. Rev. B 69, 165102 (2004).
[5] M. Ochi, K. Sodeyama, R. Sakuma and S. Tsuneyuki, in preparation.

Back