We describe a method for computing near-exact energies for correlated systems with large Hilbert spaces. The method efficiently identifies the most important basis states (Slater determinants) and performs a variational calculation in the subspace spanned by these determinants. A semistochastic approach is then used to add a perturbative correction to the variational energy to compute the total energy. The size of the variational space is progressively increased until the total energy converges to within the desired tolerance.

We report that a recent active space model of the nitrogenase FeMo cofactor, proposed in the context of simulations on quantum computers, is not representative of the electronic structure of the FeMo cofactor ground-state. A more representative model does not affect much certain resource estimates for a quantum computer such as the cost of a Trotter step, while strongly affecting others such as the cost of adiabatic state preparation.

This paper presents in detail our fast semistochastic heat-bath configuration interaction (SHCI) method for solving the many-body Schrödinger equation. We identify and eliminate computational bottlenecks in both the variational and perturbative steps of the SHCI algorithm. We also describe the parallelization and the key data structures in our implementation, such as the distributed hash table.

The electronically excited states of methylene (CH2), ethylene (C2H4), butadiene (C4H6), hexatriene (C6H8), and ozone (O3) have long proven challenging due to their complex mixtures of static and dynamic correlations. The semistochastic heat-bath configuration interaction (SHCI) algorithm, which efficiently and systematically approaches the full configuration interaction (FCI) limit, is used to provide close approximations to the FCI energies in these systems.

We present the extension of variational Monte Carlo (VMC) to the calculation of electronic excitation energies and oscillator strengths using time-dependent linear-response theory. By exploiting the analogy existing between the linear method for wave function optimization and the generalized eigenvalue equation of linear-response theory, we formulate the equations of linear-response VMC (LR-VMC). This LR-VMC approach involves the first- and second-order derivatives of the wave function with respect to the parameters.

We extend our recently developed heat-bath configuration interaction (HCI) algorithm, and our semistochastic algorithm for performing multireference perturbation theory, to calculate excited-state wavefunctions and energies. We employ time-reversal symmetry, which reduces the memory requirements by more than a factor of two. An extrapolation technique is introduced to reliably extrapolate HCI energies to the full CI limit.

We extend the recently proposed heat-bath configuration interaction (HCI) method [Holmes, Tubman, Umrigar, J. Chem. Theory Comput. 2016, 12, 3674], by introducing a semistochastic algorithm for performing multireference Epstein-Nesbet perturbation theory, in order to completely eliminate the severe memory bottleneck of the original method. The proposed algorithm has several attractive features. First, there is no sign problem that plagues several quantum Monte Carlo methods.

We introduce a new selected configuration interaction plus perturbation theory algorithm that is based on a deterministic analog of our recent efficient heat-bath sampling algorithm. This Heat-bath Configuration Interaction (HCI) algorithm makes use of two parameters that control the trade-off between speed and accuracy, one which controls the selection of determinants to add to a variational wave function and one which controls the selection of determinants used to compute the perturbative correction to the variational energy.

We introduce an algorithm for sampling many-body quantum states in Fock space. The algorithm efficiently samples states with probability approximately proportional to an arbitrary function of the second-quantized Hamiltonian matrix element connecting the sampled state to the current state. We apply the new sampling algorithm to the recently developed semistochastic full configuration interaction quantum Monte Carlo (S-FCIQMC) method, a semistochastic implementation of the power method for projecting out the ground state energy in a basis of Slater determinants.

We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on the subject, we review in depth the Metropolis-Hastings algorithm used in VMC for sampling the square of an approximate wave function, discussing details important for applications to electronic systems.