Diffusion Quantum Monte Carlo Simulations Research Articles

Elucidating the role of many-body forces in liquid water. I. Simulations of water clusters on the VRT(ASP-W) potential surfaces.

We test two new potentials for water, fit to vibration-rotation tunneling (VRT) data by employing diffusion quantum Monte Carlo simulations to calculate the vibrational ground-state properties of water clusters. These potentials, VRT(ASP-W)II and VRT(ASP-W)III, are fits of the highly detailed ASP-W (anisotropic site potential with Woermer dispersion) ab initio potential to (D(2)O)(2) microwave and far-infrared data, and along with the SAPT5s (five-site symmetry adapted perturbation theory) potentials, are the most accurate water dimer potential surfaces in the literature. The results from VRT(ASP-W)II and III are compared to those from the original ASP-W potential, the SAPT5s family of potentials, and several bulk water potentials. Only VRT(ASP-W)III and the spectroscopically "tuned" SAPT5st (with N-body induction included) accurately reproduce the vibrational ground-state structures of water clusters up to the hexamer. Finally, the importance of many-body induction and three-body dispersion are examined, and it is shown that the latter can have significant effects on water cluster properties despite its small magnitude.

Solvation of metal atoms in quantum clusters: structural and vibrational properties of Hg(H 2) 12 and Mg(H 2) 12

Diffusion quantum Monte Carlo (DQMC) simulations are used to study the vibrational ground state of the clusters Hg(H 2) 12 and Mg(H 2) 12. In these clusters, the metal atom is located inside, surrounded by a highly delocalized, liquid-like and, for Hg(H 2) 12, also nearly spherical envelope of hydrogens. However, the wavefunctions of the clusters exhibit traces of icosahedral behavior within the delocalized structure, related to the geometry of the corresponding classical systems. A simple model wavefunction is fitted, with excellent agreement to the numerical DQMC data. It provides a convenient interpretation of the vibrational ground state of these clusters.

Excitons in spatially separated electron–hole systems: A quantum Monte Carlo study

Variational and diffusion quantum Monte Carlo simulations of excitons in the type-II semiconductor quantum well system In1−xGaxAs/GaSb1−yAsy are performed for a wide range of composition (0,0)≤(x,y)≤(0.62,0.64) and well width 25 Å ≤L≤200 Å. The exciton binding energy is found to increase with the decrease of the layer thickness and with the increase of the composition. The calculated results suggest that a novel semiconductor–excitonic insulator (Bose condensate)–semimetal transition should be observable in this system.

Biexcitons in quantum wells: A quantum Monte Carlo study

The exact binding energies of biexcitons in GaAs Ga 1−x Al x As quantum wells in the effective mass model are evaluated by diffusion quantum Monte Carlo simulations. The results support the experimental interpretation that biexcitons can exist in quantum confined structures such as the quantum wells of GaAs Ga 1−x Al x As . The electron correlation effects and quantum confinement are shown to enhance the binding of the exciton pairs. The calculated results for various quantum wells provide a guide for further experiments in accurate determination of the binding energies of biexcitons in quantum wells.

Properties of ionic hydrogen clusters: a quantum Monte Carlo study

A diffusion quantum Monte Carlo simulation scheme has been developed to study the electronic structures of ionic hydrogen clusters H + 2 n+1 with n = 1, 2, 3, 4. The molecular energies calculated for H + 5, H + 7, and H + 9 are the best theoretical calculations to date. The equilibrium geometric structures of H + 3 and H + 5 are determined by optimizing their molecular energies and good agreement is found with the best previous configuration interaction calculations. The electronic structure of the H + 2 n+1 clusters is analyzed based on the bonding formation in the systems. An estimate of the dissociation energy for each cluster is made and compared with experimental measurements.

Quantum Monte Carlo studies of small B(H2)n clusters

The structure and stability of clusters of a boron atom with one to eight H2 molecules is investigated. For the simplest BH2 clusters, the lowest ab initio adiabatic potentials for o-H2 and p-H2 interacting with a boron atom are used. For the larger clusters (n=2–8), the p-H2 is treated as a sphere, and the total potential is taken to be the sum of pairwise additive B–H2 and H2–H2 interactions which include, in the former case, an anisotropy due to the orientation of the unpaired B 2p electron. This electronic interaction is considerably more attractive when H2 approaches the B atom in a plane perpendicular to the orientation of the 2p orbital. The local and global minima on these potential surfaces were located and diffusion quantum Monte Carlo simulations were used to determine the energies and properties of the ground state wave functions for these B–(H2)n clusters. For the B(H2) cluster, a comparison is made with the results of variational calculations.

Hydrogen molecule under confinement: Exact results.

The properties of a hydrogen molecule under spatial confinement are studied by diffusion quantum Monte Carlo simulations. The ground-state energy and the bond length of the molecule are evaluated under an equilibrium spheroidal-box condition. Since the calculations of the ground-state properties for this specific system are exact from the diffusion quantum Monte Carlo simulations, the results obtained here can also serve as a criterion to any approximate or variational method applied to highly correlated electronic systems. The possibility of further work to calculate the vibrational frequency and other pressure-dependent physical quantities is discussed.

Static dielectric response of charged bosons.

The dielectric function of a charged Bose gas is determined from the response to an imposed static sinusoidal electric field. Variational and diffusion quantum Monte Carlo simulations are used to calculate the ground-state properties of the system with trial wave functions containing a parameter dependent on the amplitude and wavelength of the perturbation. The induced charge is most efficiently extracted from the difference in ground-state energies at different magnitudes of the external field, rather than directly from the expectation value of the density fluctuation operator. Results are compared to the random-phase approximation for the weakly coupled fluid and to classical lattice values at low densities where the system forms a Wigner crystal. The dielectric function is also calculated at intermediate fluid densities and the transition from positive to negative response is found to occur in the metallic regime.

Estimating the relativistic energy by diffusion quantum Monte Carlo

We report formulas to estimate the relativistic corrections for atoms or molecules (treated as the first order perturbation) by diffusion quantum Monte Carlo (DQMC) simulations. Our formulas involve primarily quantities which are routinely computed in nonrelativistic simulations. Hence our approach entails only minor additional modifications of existing (all electron) DQMC codes. We illustrate our algorithm by estimating various relativistic corrections to the ground state energy of LiH.

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 Schrödinger 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.