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Short- and long-range electron correlation is investigated using new forms of correlated electron trial wave functions in quantum Monte Carlo calculations. The goal of this thesis is to develop new computational methods which enable the determination of the optimal electron correlation factor in a numerical trial wave function such that the expectation value of the system Hamiltonian, i.e., the total energy, is minimized.
The effect of the electron-electron cusp on the convergence of configuration interaction (CI) wave functions is examined. By analogy with the pseudopotential approach for electron-ion interactions, an effective electron-electron interaction is developed which closely reproduces the scattering of the Coulomb interaction but is smooth and finite at zero electron-electron separation. The exact many-electron wave function for this smooth effective interaction has no cusp at zero electron-electron separation. We perform CI and quantum Monte Carlo calculations for He and Be atoms, both with the Coulomb electron-electron interaction and with the smooth effective electron-electron interaction. We find that convergence of the CI expansion of the wave function for the smooth electron-electron interaction is not significantly improved compared with that for the divergent Coulomb interaction for energy differences on the order of 1 mHartree. This shows that, contrary to popular belief, description of the electron-electron cusp is not a limiting factor, to within chemical accuracy, for CI calculations.
A method is presented for the optimization of one-body and inhomogeneous two-body terms in correlated electronic wave functions of Jastrow-Slater type. The most general form of inhomogeneous correlation term which is compatible with crystal symmetry is used and the energy is minimized with respect to all parameters using a rapidly convergent iterative approach, based on Monte Carlo sampling of the energy and fitting of energy fluctuations. The energy minimization is performed exactly within statistical sampling error for the energy derivatives and the resulting one- and two-body terms of the wave function are found to be well-determined. The largest calculations performed require the optimization of over 3000 parameters. The inhomogeneous two-electron correlation terms are calculated for diamond and rhombohedral graphite. The optimal terms in diamond are found to be approximately homogeneous and isotropic over all ranges of electron separation, but exhibit some inhomogeneity at short- and intermediate-range, whereas those in graphite are found to be homogeneous at short-range, but inhomogeneous and anisotropic at intermediate- and long-range electron separation.
Estimates of the van der Waals contribution to the interlayer binding energy of graphite are calculated using a new variational Monte Carlo method, which allows for the explicit removal of interlayer electron correlation. Using a modified many-body Hamiltonian, long-range instantaneous electron interactions are replaced by a static Hartree potential, thereby eliminating van der Waals correlations. This produces an optimal groundstate trial wave function which, in combination with the true fully-interacting Hamiltonian, determines the energy of the system when long-range correlation is removed.
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