We consider the use in quantum Monte Carlo calculations of two types of valence bond wave functions based on strictly localized active orbitals, namely valence bond self-consistent-field and breathing-orbital valence bond wave functions. Complemented by a Jastrow factor, these Jastrow-valence-bond wave functions are tested by computing the equilibrium well depths of the four diatomic molecules C2, N2, O2, and F 2 in both variational Monte Carlo and diffusion Monte Carlo.

A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multiconfigurational self-consistent field calculation supplemented with primitive functions, chosen such that the asymptotics are appropriate for the potential of the system. Primitives are optimized for the homonuclear diatomic molecule to produce a balanced basis set. Two general features that facilitate this basis construction are demonstrated.

Silicon undergoes a phase transition from the semiconducting diamond phase to the metallic β-Sn phase under pressure. We use quantum Monte Carlo calculations to predict the transformation pressure and compare the results to density-functional calculations employing the local-density approximation, the generalized-gradient approximations PBE, PW91, WC, AM05, PBEsol, and the hybrid functional HSE06 for the exchange-correlation functional.

The accuracy of the fundamental properties of the energy landscape of silicon systems obtained from density functional theory with various exchange-correlation functionals, a tight binding scheme, and force fields is studied. Depending on the application, quantum Monte Carlo or density functional theory results serve as quasiexact reference values.

Molecular calculations in quantum Monte Carlo frequently employ a mixed basis consisting of contracted and primitive Gaussian functions. While standard basis sets of varying size and accuracy are available in the literature, we demonstrate that reoptimizing the primitive function exponents within quantum Monte Carlo yields more compact basis sets for a given accuracy. Particularly large gains are achieved for highly excited states.

We describe correlator product states, a class of numerically efficient many-body wave functions to describe strongly correlated wave functions in any dimension. Correlator product states introduce direct correlations between physical degrees of freedom in a simple way, yet provide the flexibility to describe a wide variety of systems. We show that many interesting wave functions can be mapped exactly onto correlator product states, including Laughlin's quantum Hall wave function, Kitaev's toric code states, and Huse and Elser's frustrated spin states.

We study interaction-induced localization of electrons in an inhomogeneous quasi-one-dimensional system-a wire with two regions, one at low density and the other high. Quantum Monte Carlo techniques are used to treat the strong Coulomb interactions in the low-density region, where localization of electrons occurs. The nature of the transition from high to low density depends on the density gradient-if it is steep, a barrier develops between the two regions, causing Coulomb blockade effects. Ferromagnetic spin polarization does not appear for any parameters studied.

The ground and lowest three adiabatic excited states of methylene are computed using the variational Monte Carlo and diffusion Monte Carlo (DMC) methods using progressively larger Jastrow-Slater multideterminant complete active space (CAS) wave functions. The highest of these states has the same symmetry, A1 1, as the first excited state.

Accurate multideterminant ground-state energies of circular quantum dots containing N≤13 electrons as a function of interaction strength have been evaluated by the diffusion quantum Monte Carlo method. Two unique features are found for these confined two-dimensional systems: (1) as the electron density decreases, the quantum dots favor states with zero orbital angular momentum (L=0); and (2) for some values of N, the ground state cannot be fully spin-polarized because of a symmetry constraint. © 2009 The American Physical Society.

Two aspects of quantum Monte Carlo are discussed. First, we review a procedure for obtaining trial wavefunctions for use in quantum Monte Carlo simulations that have both smaller statistical errors and improved expectation values than commonly used functions. Second, we present a correlated sampling approach for calculating energy differences in variational Monte Carlo much more accurately than the values of the energies. This method is used to calculate the potential energy surfaces of H2 and BH.