Variational Monte Carlo and various projector Monte Carlo (PMC) methods are presented in a unified manner. Similarities and differences between the methods and choices made in designing the methods are discussed. Both methods where the Monte Carlo walk is performed in a discrete space and methods where it is performed in a continuous space are considered. It is pointed out that the usual prescription for importance sampling may not be advantageous depending on the particular quantum Monte Carlo method used and the observables of interest, so alternate prescriptions are presented.

The computational cost of quantum Monte Carlo (QMC) calculations of realistic periodic systems depends strongly on the method of storing and evaluating the many-particle wave function. Previous work by Williamson et al. (2001) [35] and Alfè and Gillan, (2004) [36] has demonstrated the reduction of the O(N3) cost of evaluating the Slater determinant with planewaves to O(N2) using localized basis functions.

We combine explicit correlation via the canonical transcorrelation approach with the density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods to compute a near-exact beryllium dimer curve, without the use of composite methods. In particular, our direct density matrix renormalization group calculations produce a well-depth of De = 931.2 cm-1 which agrees very well with recent experimentally derived estimates De = 929.7±2 cm-1 [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)] and De= 934.6 cm-1 [K. Patkowski, V.

Time-dependent density-functional methods are used to compute excitation energies and, via the adiabatic-connection fluctuation-dissipation theorem, ground-state correlation energies of atoms, ions, and the H2 molecule at various bond lengths. Various exchange-correlation potentials vxc and exchange-correlation kernels fxc are tested. Accurate exchange-correlation potentials are found to be essential for getting accurate energies.

We study the quantum phase transition of interacting electrons in quantum wires from a one-dimensional (1D) linear configuration to a quasi-1D zigzag arrangement using quantum Monte Carlo methods. As the density increases from its lowest values, first, the electrons form a linear Wigner crystal, then, the symmetry about the axis of the wire is broken as the electrons order in a quasi-1D zigzag phase, and, finally, the electrons form a disordered liquidlike phase.

We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially stochastically with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty.

A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol.

We present a technique for optimizing hundreds of thousands of variational parameters in variational quantum Monte Carlo. By introducing iterative Krylov subspace solvers and by multiplying by the Hamiltonian and overlap matrices as they are sampled, we remove the need to construct and store these matrices and thus bypass the most expensive steps of the stochastic reconfiguration and linear method optimization techniques.

We report state-of-the-art quantum Monte Carlo calculations of the singlet n→π∗ (CO) vertical excitation energy in the acrolein molecule, extending the recent study of Bouabça et al. (J Chem Phys 130:114107, 2009). We investigate the effect of using a Slater basis set instead of a Gaussian basis set, and of using state-average versus state-specific complete-active-space (CAS) wave functions, with or without reoptimization of the coefficients of the configuration state functions (CSFs) and of the orbitals in variational Monte Carlo (VMC).

When using Hartree-Fock (HF) trial wave functions in quantum Monte Carlo calculations, one faces, in case of HF instabilities, the HF symmetry dilemma in choosing between the symmetry-adapted solution of higher HF energy and symmetry-broken solutions of lower HF energies. In this work, we have examined the HF symmetry dilemma in hydrogen rings which present singlet instabilities for sufficiently large rings. We have found that the symmetry-adapted HF wave function gives a lower energy both in variational Monte Carlo and in fixed-node diffusion Monte Carlo.