Number Of Slater Determinants Research Articles

Extension of selected configuration interaction for transcorrelated methods.

In this work, we present an extension of popular selected configuration interaction (SCI) algorithms to the Transcorrelated (TC) framework. Although we used in this work the recently introduced one-parameter correlation factor [E. Giner, J. Chem. Phys. 154, 084119 (2021)], the theory presented here is valid for any correlation factor. Thanks to the formalization of the non-Hermitian TC eigenvalue problem as a search of stationary points for a specific functional depending on both left- and right-functions, we obtain a general framework, allowing for different choices for both the selection criterion in SCI and the second order perturbative correction to the energy. After numerical investigations on different second-row atomic and molecular systems in increasingly large basis sets, we found that taking into account the non-Hermitian character of the TC Hamiltonian in the selection criterion is mandatory to obtain a fast convergence of the TC energy. In addition, selection criteria based on either the first order coefficient or the second order energy lead to significantly different convergence rates, which is typically not the case in the usual Hermitian SCI. Regarding the convergence of the total second order perturbation energy, we find that the quality of the left-function used in the equations strongly affects the quality of the results. Within the near-optimal algorithm proposed here, we find that the SCI expansion in the TC framework converges faster than the usual SCI in terms of both the basis set and the number of Slater determinants.

Electron–electron correlation energy calculations by superposition of nonorthogonal Slater determinants

A tractable calculation algorithm to calculate essentially exact electron–electron correlation energies of few-electron systems by the superposition of nonorthogonal Slater determinants (SDs) is presented. The key to the proposed procedure for updating nonorthogonal one-electron wavefunctions to ground states is that linearly independent multiple correction functions are employed and optimized on the basis of a variational principle. The accuracy and applicability of the present scheme are demonstrated through calculations of the ground-state energies for atoms and molecules. The convergence performance to the ground state is improved by multiplying the correction functions. A drastic reduction of the number of SDs required to determine the ground-state energies and a modest increase with increasing system size compared with the full configuration interaction (CI) method are also demonstrated.

Precise correlation energies in small parabolic quantum dots from configuration interaction

We calculate precise correlation energies of ground and low-lying excited states in circular parabolic quantum dots containing $N=2\char21{}20$ electrons by means of a configuration interaction (CI) method with a numerical, mean-field basis set. All excitations are allowed for $2\ensuremath{\le}N\ensuremath{\le}7$ (full CI), while up to hextuple excitations are included for $N=8,9$, and up to pentuple excitations for $10\ensuremath{\le}N\ensuremath{\le}20$. The energies are extrapolated to the limit of basis-set completeness and the truncation error due to restricting the number of Slater determinants is monitored. For high electron densities (Wigner-Seitz radius ${r}_{s}\ensuremath{\approx}1.7{a}_{0}^{\ensuremath{\ast}}$), the approach achieves errors of order $0.3\text{ }{\text{mHa}}^{\ensuremath{\ast}}$ for $N=3$, a few ${\text{mHa}}^{\ensuremath{\ast}}$ for $N=6\char21{}9$, rising to about $100\text{ }{\text{mHa}}^{\ensuremath{\ast}}$ for $N=20$. A comparison is made with recent quantum Monte Carlo calculations.

Monte Carlo simulation of a many-fermion study

The Metropolis Monte Carlo method is used to sample the square of an antisymmetric wave function composed of a product of a Jastrow wave function and a number of Slater determinants. We calculate variational energies for $^{3}\mathrm{He}$ and several models of neutron matter. The first-order Wu-Feenberg expansion is shown always to underestimate the energy, sometimes seriously. The phase diagram for ground-state Yukawa matter is determined. There is a class of Yukawa potentials which do not lead to a crystal phase at any density.