Variational transcorrelated method

Abstract

We propose a new approach to the use of Jastrow ansatz in the calculation of electron correlations, based on a modification of the transcorrelated method of Boys and Handy [Proc. R. Soc. London, Ser. A 309, 209 (1969)]. In this new method, the original transcorrelated orbital equation is replaced with a general variational equation for the reference wave function, whereas the equation for the correlation factor remains the same. The method can be applied to a single determinant Jastrow ansatz as well as to a multideterminant one. For the single determinant ansatz, we obtain a Hartree-Fock type self-consistent equation for the optimization of orbitals, and for the multideterminant ansatz we have tested a CI type equation. We apply the new method in calculations of the C(2) molecule and compare the results with those of variational quantum Monte Carlo calculations.

Correlated Band Structure of a Transition Metal Oxide ZnO Obtained from a Many-Body Wave Function Theory

“…Moreover, the TC method is deterministic, i.e., free from the statistical error, unlike the QMC methods. Accurate calculations for the Hubbard model [35,36] and molecular systems [37][38][39] were also reported using the TC method or other theories that have a close relationship with the TC method. However, insofar as solid-state calculations are concerned, the TC method has so far been applied only to weakly correlated systems.…”

Iterative diagonalization of the non-Hermitian transcorrelated Hamiltonian using a plane-wave basis set: Application to sp-electron systems with deep core states

“…It is obvious that the purely imaginary Jastrow function u(x i , x j ) that makes the Jastrow factor exp[− i,j( =i) u(x i , x j )] unitary cannot fulfill the cusp condition and the long-range asymptotic behavior mentioned before. Although some previous studies adopted approximations for the effective interaction in the TC Hamiltonian to restore the Hermiticity for molecular systems with a small number of electrons [13,14], it is unclear that such approximation is valid for general molecular and periodic systems. Therefore, in this study, we explicitly handle the non-Hermiticity of the TC Hamiltonian without introducing additional approximations.…”

“…For molecular systems, some * Electronic address: ochi@phys.sci.osaka-u.ac.jp; Present address: Department of Physics, Osaka University, Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan recent works have shown a high potentiality of the TC method [8,10,11]. Optimization of the wave function with a help of Monte Carlo integration [9,12,13] and development of the canonical TC theory [14] are also remarkable recent innovation. For solid-states calculations, the TC method is shown to reproduce accurate band structures [15][16][17] and optical absorption spectra [18].…”

Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems

“…We notice that the DGF method was proposed to deal also with excited vibrational states. 82 Concerning the inclusion of the inter-particle correlation, the transcorrelated Hamiltonian approach 84 seems to be quite attractive. By using a single determinant (permanent) Jastrow ansatz, HF-like equations are obtained and, therefore, this approach seems to be well-suited to interfaces with standard electronic structure codes.…”

“…As a future extension, the trans-correlated Hamiltonian approach 84 can be implemented as it can be formulated to include inter-particle short-range correlation through Hartreelike equations. On the other hand, to describe excited states for the nuclear wave-function, the simple version of the frozen local hole approximation (FLHA) developed by Pahl and Birkenheuer 94 could be used, with electrons replaced by protons.…”