P. J. Reynolds

Valence quantum Monte Carlo with ab initio effective core potentials

Effective‐core potentials (ECP’s) obtained from ab initio methods are implemented in molecular quantum Monte Carlo (QMC). The theory is presented, and applied to the calculation of electron affinities (EA) of Li and Na, the ionization potential (IP) of Mg, the binding energies (De) of NaH and Na2, and the potential energy curve of Na2. In all cases ECP–QMC results are found to be as accurate as previous all‐electron results. In particular, the calculated quantities (vs experimental values) are (in eV): EA(Li)=0.611±0.020 (0.620), EA(Na)=0.555±0.021 (0.546), IP(Mg)=7.637±0.026 (7.646), De (NaH) =1.954±0.073 (1.971), and De (Na2)=0.746±0.020 (0.747). In addition, the statistical precision obtained surpasses that which can be readily achieved in all‐electron QMC calculations on these systems.

Monte Carlo algorithms for expectation values of coordinate operators

Abstract Two Monte Carlo algorithms for computing quantum mechanical expectation values of coordinate operators, i.e., multiplicative operators that do not commute with the Hamiltonian, are presented and compared. The first employs a single quantum Monte Carlo (QMC) random walk, while the second involves a variational Monte Carlo (VMC) random walk with auxiliary QMC “side walks.” The tagging algorithm used for efficiently tracking descendants of a walker is described in detail for each approach. For the single-walk algorithm it is found that carrying weights together with branching significantly improves efficiency. Exploitation of the correlation between VMC and QMC expectation values is also considered. Large increases in efficiency in the second approach are found when such correlations are incorporated. It is found that both approaches readily yield accuracies and precisions of better than 0.5% for the model systems treated here, namely, H and H 2 . The second method, involving a VMC walk with auxiliary QMC walks, is the more efficient for these systems.

H + H2 reaction barrier: A fixed‐node quantum Monte Carlo study

The classical barrier height for the H+H2 exchange reaction, as well as the energies at two other points along the reaction path, are calculated using fixed‐node quantum Monte Carlo (FNQMC). Several single‐determinant importance functions are used at the saddle point in order to relate the quality of the importance function to the accuracy and precision of the final result. The computed barrier is an upper bound since the energy of H and of H2 is obtained exactly by FNQMC. Our best upper bound (9.70±0.13 kcal/mol) has a mean within 0.1 kcal/mol of the presumed exact value. This best bound is obtained with a single determinant, double‐zeta basis importance function. Contrary to experience with expansion methods, it is found that an importance function with a basis set of near Hartree–Fock quality, as well as one derived from a spin‐unrestricted SCF calculation, are among the least efficient and least accurate of the importance functions used. Specifically, a nodal surface appearing in the lowest energy mol...

Electron affinity of fluorine: A quantum Monte Carlo study

The total nonrelativistic energies of the fluorine atom and its negative ion are calculated using the fixed‐node quantum Monte Carlo (QMC) method. Over 90% of the correlation energy is obtained for both the neutral and the anion. Subtracting these energies yields an electron affinity of 3.45±0.11 eV, in excellent agreement with the recommended experimental value of 3.40 eV. The observed dependence of our Monte Carlo energies on the time step is discussed within the short‐time QMC formalism. As in previous QMC studies in this series, only a single determinant, constructed with a small (double‐zeta) basis set, multiplied by simple functions of electron–electron and electron–nuclear separation, is required as an importance function.

Quantum Monte Carlo approach to electronically excited molecules

Quantum Monte Carlo (QMC) is used to compute the electronic energies of H2(B 1Σ+u) and H2(E 1Σ+g). The E state calculation represents the first application of QMC to a molecular excited state with the same symmetry as a lower state. In this QMC approach a trial function specifies the nodes of the QMC distribution. The role of these nodes in excited state calculations is discussed. QMC energies that contain over 95% of the correlation energy are computed using MCSCF wave functions as trial functions.

Computation of transition dipole moments by Monte Carlo

Three Monte Carlo methods for computing transition dipole moments are presented. Two of these approaches are based on the use of multiple Monte Carlo ‘‘random walks’’ to sample different probability distributions. The remaining technique employs a single Monte Carlo walk and averages an analytic approximation to the Green’s function to sample other distributions. The accuracy and efficiency of each method is investigated by computing the transition dipole moment between the 1s and 2px states of the hydrogen atom. Monte Carlo parameters, such as the time step size and the convergence time, are varied in order to study their effect on computed results. It is found that the approach based on a guided Metropolis walk with quantum Monte Carlo ‘‘side walks’’ and also the approach based on Green’s function averages yield accurate transition dipole moments efficiently. These two methods also yield accurate energies and expectation values for the individual eigenstates. The approach based on two equivalent quantum...

Monte Carlo study of electron correlation functions for small molecules

A study is made of electron-electron correlation functions for use in trial wave functions for small molecules. New forms are proposed that have only a few variational parameters, and these parameters have physical meanings that are easily discerned. Total energies for H2, LiH and Li2 computed using these correlation functions are presented, and comparison is made with previous forms, including the Jastrow-Pade form often used in Monte Carlo studies. We further treat the possibility that correlation depends not only on the separation of a pair of electrons but also on the location of the electron pair relative to the nuclei — indicative of a density-dependent or many body correlation effect. Our results indicate that such a many-body correlation effect is weakly present.

Is there a zeroth order time‐step error in diffusion quantum Monte Carlo?

It is demonstrated that the short‐time Green’s function often used in diffusion quantum Monte Carlo simulations of the Schrodinger equation generates an unbiased probability distribution in the limit of vanishing time step τ. For finite τ, an error is introduced into the potential which is of O(τ). An expression for this term is derived.