Advances in deterministic, stochastic, and semistochastic quantum chemistry

In this dissertation, I present my original research in the development of algorithms for computing ground-state properties of strongly-correlated electronic systems from first principles. I present three main algorithms. First, I present a 'semistochastic' projection algorithm, dubbed Semistochastic Quantum Monte Carlo, which combines the best qualities of deterministic and stochastic methods for projecting out a ground state wavefunction in a basis of Slater determinants. This new algorithm can treat systems as large as a fully-stochastic algorithm can, while dramatically reducing the statistical uncertainty and bias by treating the most important part of the problem deterministically. Second, I present an efficient algorithm for sampling many-particle states in Fock space with probability proportional to the Hamiltonian matrix element connecting them to a reference state, which I refer to as the heat-bath distribution. This sampling algorithm, referred to as Efficient Heat-bath Sampling in Fock Space, factors and approximates the heat-bath probabilities in such a way that they can be efficiently stored and sampled, without having to enumerate all of the possible excitations. Efficient Heat-bath Sampling dramatically improves the efficiency of stochastic Fock space methods by sampling the more relevant Slater determinants more frequently. Third, I present the deterministic analog of Efficient Heat-bath Sampling, which enables one to generate all Slater determinants that are connected to a reference by Hamiltonian matrix elements larger in magnitude than a cutoff, without wasting any time on those determinants that do not meet the cutoff. This deterministic heat-bath \sampling" algorithm is then incorporated into a highly-efficient quantum chemistry algorithm that I call Heat-bath Configuration Interaction, which rst generates a variational wavefunction and then computes the lowest-order perturbative correction. Both the variational and perturbative stages of Heat-bath Configuration Interaction make use of deterministic heat-bath "sampling" to perform highly efficient calculations using only the most important Slater determinants