Jastrow-Slater Wave Functions Research Articles

Optimization of configuration interaction coefficients in multideterminant Jastrow–Slater wave functions

A quantum Monte Carlo method for obtaining multideterminant Jastrow–Slater wave functions for which the energy is stationary with respect to variations of CI coefficients is presented. It is a generalization of a recently developed approach to the optimization of single particle functions [C. Filippi and S. Fahy, J. Chem. Phys. 112, 3523 (2000)]. Using ground state calculations of the atoms Be, C, and Ne and the dimer Si2 as illustrative examples, the method is shown to converge rapidly and to significantly lower the energy in most cases.

Quantum Monte Carlo calculations of the one-body density matrix and excitation energies of silicon

Quantum Monte Carlo (QMC) techniques are used to calculate the one-body density matrix and excitation energies for the valence electrons of bulk silicon. The one-body density matrix and energies are obtained from a Slater-Jastrow wave function with a determinant of local density approximation (LDA) orbitals. The QMC density matrix evaluated in a basis of LDA orbitals is strongly diagonally dominant. The natural orbitals obtained by diagonalizing the QMC density matrix resemble the LDA orbitals very closely. Replacing the determinant of LDA orbitals in the wave function by a determinant of natural orbitals makes no significant difference to the quality of the wave function's nodal surface, leaving the diffusion Monte Carlo energy unchanged. The Extended Koopmans' Theorem for correlated wave functions is used to calculate excitation energies for silicon, which are in reasonable agreement with the available experimental data. A diagonal approximation to the theorem, evaluated in the basis of LDA orbitals, works quite well for both the quasihole and quasielectron states. We have found that this approximation has an advantageous scaling with system size, allowing more efficient studies of larger systems.

Variational Quantum Monte Carlo Approach to the Electronic Structure of NiO

The electronic structure of NiO solid with the fcc type-II antiferromagnetic structure has been studied using a variational quantum Monte Carlo approach. The Jastrow-Slater many-body wave function has been used for valence electrons, and the pseudopotentials have been evaluated with the aid of a local approximation. The calculated results for the binding energy and the structural properties are in good agreement with experiment. Reasonable evaluations have also been made for the charge and spin density distributions and the electron-electron radial distribution functions. Although the results for the one-particle energy distribution and the charge-transfer excitation energy gap are encouraging, further increase in Monte Carlo steps and improvements in computational methods would be required for the detailed comparison with experiments and the most dependable density-functional band calculations.

Binding energy of one4He impurity in liquid3He

A variational microscopic calculation of the binding energy of a4He impurity (μi) in homogeneous liquid3He at zero temperature is presented. Starting on an extended Jastrow-Slater wave function including three-body correlations, the expression for μI is derived and the appropriated FHNC formalism for this problem is reviewed. In the framework of the Average Correlation Approximation (ACA), it is proved that it is possible to obtain the chemical potential of the impurity only from liquid3He magnitudes with a good accuracy. Our results are consistent with both a recent experimental determination of μI at zero pressure and the non-solubility of4He in3He. However, numerical uncertainties preclude a firm conclusion about the latter property.

Variational Monte Carlo study of the partially polarized electron gas.

The variational Monte Carlo (VMC) method, using Jastrow-Slater (JS) wave functions, is used to study the partially polarized interacting electron gas for densities spanning the range encountered in bulk metals. We concentrate on a spin polarization \ensuremath{\zeta}=0.42 which allows direct comparison of polarized and unpolarized states for a fixed total number of electrons in the simulation supercell. The radial distribution functions ${\mathit{g}}_{++}$(r), ${\mathit{g}}_{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{-}}}$(r), and ${\mathit{g}}_{+\mathrm{\ensuremath{-}}}$(r) are given particular attention and compared with a model developed by Perdew and Wang (PW) that satisfies known constraints. At high density the agreement with the PW model is good. At the lower densities (electron-gas parameter ${\mathit{r}}_{\mathit{s}}$=4--8) there are differences that can be roughly characterized as the PW model giving a somewhat more extended exchange-correlation hole than the VMC calculations. These discrepancies could be due to limitations either of the PW model or of the JS wave functions used here. Both the VMC and PW results are contrasted with the Hartree-Fock result for parallel spins.

Jastrow-Slater trial wave functions for the fractional quantum Hall effect: Results for few-particle systems.

We report results of a numerical study of the Jastrow-Slater trial wave functions for the fractional quantum Hall effect proposed by one of us. We study systems of up to eight electrons and find that these trial states are an extremely good approximation to the true Coulomb states.

Stochastic solution of the Schrödinger equation for finite Fermi systems

We apply the Green function Monte Carlo method to model ground states for the atomic nucleus 16O and for a droplet of eight 4He atoms assumed to obey Fermi statistics. Ground-state properties of the two systems are obtained by means of projection onto antisymmetric trial functions. The Monte Carlo process is stabilized by allowing the generation size to grow sufficiently fast. The variational method using refined backflow Jastrow-Slater wave functions is shown to be reasonably accurate.

Stochastic solution of the schrödinger equation for finite Fermi systems

We apply the Green function Monte Carlo method to model ground states for the atomic nucleus 16 O and for a droplet of eight 4 He atoms assumed to obey Fermi statistics. Ground-state properties of the two systems are obtained by means of projection onto antisymmetric trial functions. The Monte Carlo process is stabilized by allowing the generation size to grow sufficiently fast. The variational method using refined backflow Jastrow-Slater wave functions is shown to be reasonably accurate.

Surface and polarization effects in large Fermi systems

The FHNC equations are derived for Fermi systems with spin-isospin single-particle states having different populations. The systems are described by a Jastrow-Slater wave function with a state-independent correlation factor. The equations are also modified in order to take into account the effect of a boundary surface on the energy of the system. The technique discussed is well suited to describe the case of purely central interparticle potentials (as, for instance, in the case of liquid3He), but also to semi-phenomenological models of nuclear matter. Numerical results for the symmetry and surface energy coefficients for nuclear matter are given.

GROUND STATE FLUCTUATIONS IN POLARIZED3He

The ariational approach is adopted to describe mass- and spin-density fluctuations in po- Y larized 1 iquid He. The ground state is approximated by a suitable Jastrow-Slater wave function which incorporates the effects of spatial correlations. The newly developed Fermi-hypernetted chain theory is employed to analyse the associated theoretical particle - and spin-dependent structure functions, spin-fl ip functions, momentum distribution and one-body density matrix. Numerical results on these quantities are presented for liquid 3~e in the unpolarized and completely polarized state, The effect of polarization on the structure- and radial distribution function is studied in detail, A preli'mf- nary numerical estimate is presented for the magnetic equatl'on of state,

Variational calculation for model nuclear matter using a new integral equation method

Calculations of the energy for two different nuclear matter models are carried out using Jastrow-Slater wave functions and an integral equation developed previously by Chakravarty and Woo. Even though the same variational parameters are used, our results differ significantly with those of Ceperley, Chester, and Kalos who employed a Monte Carlo technique. The discrepancy, mainly in the potential energy, is traced to short-range behavior of the pair correlation function. No satisfactory explanation can be offered at this time. Our integral equation is then subjected to a formal analysis for a weakly interacting Bose gas. It is shown to perform at least as well for boson systems as the Bogoliubov-Born-Green-Kirkwood-Yvon equation.NUCLEAR STRUCTURE Many-body variational calculation applied to nuclear matter model.

Variational Calculation of the Properties of LiquidHe3-He4Mixtures at 0°K

The properties of liquid ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$ mixtures at 0\ifmmode^\circ\else\textdegree\fi{}K are studied by a variational method using a Jastrow-Slater trial wave function and the Wu-Feenberg expansion of the energy expectation value: The system of mass-3 boson + mass-4 boson shows complete phase separation; the system of mass-3 fermion + mass-4 boson and the system of mass-3 boson + mass-4 fermion mixtures separate incompletely; and the system of mass-3 fermion + mass-4 fermion mixes completely. The limiting solubility of the mass-3 fermion in the mass-4 boson solvent is found to increase with pressure.