R. N. Barnett

MOLECULES IN HELIUM CLUSTERS : SF6HEN

Variational and diffusion Monte Carlo results are presented for the ground states of several SF6HeN clusters in the range N=1–499. The diffusion Monte Carlo computations are well converged, yielding an expected accuracy in the energy well under 1%. Computations are performed employing both an isotropic and an anisotropic He–SF6 interaction potential. Novel trial wave functions are used to describe both the shell structure of these clusters and the anisotropy arising from the potential. The ground state helium densities show the SF6 located at the cluster center, inducing a large degree of localization and a shell‐like structure in the surrounding helium. Although the full potential causes a large degree of anisotropy in the helium density, general characteristics such as the energy and size are not greatly affected by the potential anisotropy. Finally, we compute spectral shifts for the ν3 SF6 vibration due to the instantaneous dipole–induced dipole mechanism and compare with recent experiments. We find a...

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.

Monte Carlo study of impurities in quantum clusters: H2 4HeN, N=2–19

Variational Monte Carlo techniques are employed in studying 4He clusters, with and without an H2 impurity. We find that a novel, yet simple, analytic nuclear wave‐function form, derived from a numerical H2He wave function, yields high accuracy in computed ground‐state energies of 4HeN. For the clusters studied here, three to twenty atoms, energies range from 94% to 90% of the exact values. Density profiles and distributions of particle separation are also computed. For reasonable computational cost (e.g., <20 Cray/X‐MP14 minutes for the largest cluster), density profiles are determined for the first time to high statistical accuracy to within 0.5 A or less of the cluster center. The density profile of He3 is found to possess a uniquely pronounced peak at the cluster center resulting from contributions of near‐collinear atomic arrangements. We also study the effect of substituting an He by H2, using modified wave functions containing products of pairwise He–H2 terms. For all cluster sizes studied, we find ...

Wave function optimization with a fixed sample in quantum Monte Carlo

The optimization of trial functions consisting of a product of a single determinant and simple correlation functions is studied. The method involves minimizing the variance of the local energy over a finite number of points (sample). The role of optimization parameters, e.g., sample characteristics, initial trial function parameters, and reference energy, is examined for H2, Li2, and H2O. The extent to which cusp conditions are satisfied is also discussed. The resulting variational Monte Carlo energies 〈ΨT‖H‖ΨT〉 recover 46%–95% of the correlation energy for the simple trial function forms studied. When used as importance functions for quantum Monte Carlo calculations, these optimized trial functions recover 90%–100% of the correlation energy. Time‐step bias of the computed quantum Monte Carlo energies is found to be small.

Molecular physics and chemistry applications of quantum Monte Carlo

We discuss recent work with the diffusion quantum Monte Carlo (QMC) method in its application to molecular systems. The formal correspondence of the imaginary-time Schrödinger equation to a diffusion equation allows one to calculate quantum mechanical expectation values as Monte Carlo averages over an ensemble of random walks. We report work on atomic and molecular total energies, as well as properties including electron affinities, binding energies, reaction barriers, and moments of the electronic charge distribution. A brief discussion is given on how standard QMC must be modified for calculating properties. Calculated energies and properties are presented for a number of molecular systems, including He, F, F−, H2, N, and N2. Recent progress in extending the basic QMC approach to the calculation of “analytic” (as opposed to finite-difference) derivatives of the energy is presented, together with an H2 potential-energy curve obtained using analytic derivatives.

Rotational excitations of quantum liquid clusters: He7 and (H2)7

We have studied the quantum clusters, He7 and (H2)7, in their ground (L=0) and rotationally excited states (L=2–8 for He and L=2–12 for H2) by variational Monte Carlo, and selectively by diffusion Monte Carlo. The optimized trial wave functions are eigenfunctions of L2, and, as such, are orthogonal and yield upper bounds to the energy of each state. We report energies and structural results, including density profiles and moments‐of‐inertia distributions. Overall, the He7 cluster is more delocalized than the (H2)7 cluster, but the computed structures show that both He7 and (H2)7 are highly nonclassical and nonrigid, evolving from spherical to toroidal structures as the angular momentum increases. We find that by L=2 for He7 and by L=6 for (H2)7, the clusters become metastable with respect to dissociation, as determined by comparison of excited‐state energies of the N=7 clusters with the ground‐state energies for N=6. The root‐mean‐square bond length fluctuations indicate that both N=7 clusters are liquidl...

Dopant location in SF6He39,40

Recent quantum Monte Carlo studies of doped helium clusters have yielded different results for the location of the SF6 impurity, despite good agreement on helium density profiles, thus raising the question of wave function bias on structural properties. We present here a systematic analysis of the effect of the trial function on variational and diffusion Monte Carlo (VMC and DMC) results for the ground state of SF6HeN (N=39 and 40). Four different sets of wave functions are used, together with isotropic pairwise potentials. Use of a two‐peak term in the He–SF6 wave function to describe the extensive helium structuring induced by the impurity greatly improves the VMC energies and helium densities. For all of the wave functions, the impurity SF6 distribution has its maximum at the cluster center in both VMC and DMC. This result agrees with the conclusion previously presented by Barnett and Whaley, but it contradicts the recent DMC result of Chin and Krotscheck. To explain this discrepancy, we analyze the am...

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...