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In this dissertation, the diffusion Monte Carlo (DMC) method is applied to study the ground state of anionic hydrogen, neutral para-hydrogen, and Lennard Jones clusters. The nuclear quantum effects in anionic hydrogen and neutral para-hydrogen clusters are investigated based on previous claims related to the existence of “magic numbers”. In anionic hydrogen clusters H−(H2)n, the binding energies are found to be a smooth function of increasing cluster size, and their ground state wavefunctions are highly delocalized and do not resemble the structures of the potential energy surface minima. For their deuterated analogues, the wavefunctions are localized, yet their structures are still characterized as disordered. In the para-hydrogen clusters (pH2)N, the analysis of the ground state wavefunctions for N = 24 − 28 revealed that these clusters are structurally very similar to one another. Thus, no “magic number” clusters exist in this range. This lack of size sensitivity is the result of the strong quantum delocalization in these systems, which further suggests that clusters in a much wider size range are also structurally similar. Lastly, in the Lennard Jones clusters, the degree of delocalization of the ground state wavefunction is investigated by decreasing the de Boer quantum delocalization length from Λ ∼ 0.28 (ΛpH2) to Λ ∼ 0.2 (ΛoD2). As this parameter is gradually decreased, the completely delocalized ground state wavefunction undergoes a transition to the regime of “quantum glass”. In other words, the system gradually becomes localized, but remains disordered.

We develop a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials. In the previous researches, last-passage Monte Carlo algorithms on conducting surfaces with a constant potential have been developed for charge density at a specific point or on a finite region and a hybrid BIE-WOS algorithm for charge density on a conducting surface at non-constant potentials. In the hybrid BIE-WOS algorithm, they used a deterministic method for the contribution from the lower non-constant potential surface. In this paper, we modify the hybrid BIE-WOS algorithm to a last-passage Monte Carlo algorithm on a conducting surface at non-constant potentials, where we can avoid the singularities on the non-constant potential surface very naturally. We demonstrate the last-passage Monte Carlo algorithm for charge densities on a circular disk and the four rectangle plates with a simple voltage distribution, and update the corner singularities on the unit square plate and cube.

We explored the energetics, structural properties, and nuclear quantum effects of molecular and atomic clusters, namely water, halide ion-water, and para-hydrogen along with their corresponding deuterated isotopologues. These systems typically have very complex potential energy landscapes with numerous minima corresponding to various geometric motifs and isomers, thus making numerical simulations challenging. Low energy barriers in combination with nuclear quantum effects may cause the ground state wavefunction to spread and become delocalized over more than one minimum in the configuration space. Moreover, isotope substitution may lead to marked structural changes and isotope effects in these systems involving different types of isomers, or even to quantum melting. Often, the ground state wavefunctions of the most quantum isotopologues have appreciable amplitude in several or in numerous potential energy minima, while those of the more classical isotopologues are primarily localized either to a single minimum (i.e., the global minimum) or to a much smaller subset of competing local minima separated by high potential energy barriers. Essentially, all of the aforementioned studies were carried out using the diffusion Monte Carlo (DMC) method, which, in principle, provides numerically exact results for the ground state energies and wavefunctions of nontrivial, many-body systems.

An approach for evaluating spectra from ground state probability amplitudes (GSPA) obtained from diffusion Monte Carlo (DMC) simulations is extended to improve the description of excited state energies and allow for coupling among vibrational excited states. This approach is applied to studies of the protonated water trimer and tetramer, and their deuterated analogs. These ions provide models for solvated hydronium, and analysis of these spectra provides insights into spectral signatures of proton transfer in aqueous environments. In this approach, we obtain a separable set of internal coordinates from the DMC ground state probability amplitude. A basis is then developed from products of the DMC ground state wave function and low-order polynomials in these internal coordinates. This approach provides a compact basis in which the Hamiltonian and dipole moment matrix are evaluated and used to obtain the spectrum. The resulting spectra are in good agreement with experiment and in many cases provide comparable agreement to the results obtained using much larger basis sets. In addition, the compact basis allows for interpretation of the spectral features and how they evolve with cluster size and deuteration.

Potential energy curves for the low-lying electronic states of the title molecules in their neutral and anionic forms have been calculated by means of the diffusion Monte Carlo method. The effect of different trial functionals has been investigated using single determinants constructed from density functional theory (DFT) orbitals with B3LYP, B3PW91, and M06-2X functions. Bond length, vibrational frequency, and electron affinity have also been numerically derived for the selected species and the ground state has been assigned. Spectroscopic parameters obtained are interpreted and compared to their isovalents, shedding some light on further investigations on the selected dimers.

Supervisor:前園 涼, 先端科学技術研究科, 博士

We present a paradigmatic example of a strong effect of Jastrow cutoff radii setup on the accuracy of noncovalent interaction energy differences within one-determinant Slater-Jastrow fixed-node diffusion Monte Carlo (1FNDMC) simulations using isotropic Jastrow terms and effective-core potentials. Analysis of total energies, absolute and relative errors, and local energy variance of energy differences vs the reference results suggests a simple procedure to marginalize the related biases. The presented data showcase improvements in dispersion-bounded systems within such a 1FNDMC method.

The spin susceptibility in pure neutron matter is computed from auxiliary field diffusion Monte Carlo calculations over a wide range of densities. The calculations are performed for different spin asymmetries, while using twist-averaged boundary conditions to reduce finite-size effects. The employed nuclear interactions include both the phenomenological Argonne AV8$^\prime$+UIX potential and local interactions that are derived from chiral effective field theory up to next-to-next-to-leading order., 15 pages, 10 figures

Diffusion Monte Carlo provides an effective and efficient approach for calculating ground state properties of molecular systems based on potential energy surfaces. The approach has been shown to require increasingly large ensembles when intra- and intermolecular vibrations are weakly coupled. We recently proposed a guided variant of diffusion Monte Carlo to address these challenges for water clusters [Lee, V. G. M.; McCoy, A. B. J. Phys. Chem. A 2019, 123, 8063-8070]. In the present study, we extend this approach and apply it to more strongly bound molecular ions, specifically CH5+ and H+(H2O)n=1-4. For the protonated water systems, we show that the guided DMC approach that was developed for studies of (H2O)n can be used to describe the OH stretches and HOH bends in the solvating water molecules, as well as the free OH stretches in the hydronium core. For the hydrogen bonded OH stretches in the H3O+ core of H+(H2O)n and the CH stretches in CH5+, we develop adaptive guiding functions based on the instantaneous structure of the ion of interest. Using these guiding functions, we demonstrate that we are able to obtain converged zero-point energies and ground state wave functions using ensemble sizes that are as small as 10% the size that is needed to obtain similar accuracy from unguided calculations.

para-Hydrogen (pH2)N clusters have been the focus of numerous computational studies. Originally motivated by the possibility of observing superfluidity, these studies also revealed rich and complex structural properties of (pH2)N. However, their structural analysis was typically limited to attempts to identify "magic number clusters" by computing their ground state energies EN and the chemical potential μN = EN-EN-1 as a function of N. This was followed by structural analysis based on an ill-defined radial density profile. Surprisingly, however, there were remarkable discrepancies between the results reported in the literature for cluster sizes beyond approximately N = 25, and this ambiguity remained unsettled until now. In the present paper, we apply the diffusion Monte Carlo method to resolve inconsistencies in cluster sizes within the range (N = 24-28). Here, we try to avoid speculations based on the highly demanding energy calculations whose numerical accuracy harbors ambiguity. Instead, we focus on the direct and unambiguous structural analysis of the ground state wavefunctions, which supports the conclusion that the clusters are structurally the same in the size range considered. That is, there are no magic number clusters at least in the range N = 24-28, contrary to what some of the previous publications have suggested. This lack of size sensitivity of para-hydrogen clusters is a direct consequence of the strong quantum delocalization in these systems.

Monte Carlo criticality calculation is an iterative process which requires a guess fission distribution to start the simulations. It is important to assess when the fission source has converged, so that a sufficient number of the initial batches are discarded prior to beginning of the Monte Carlo (MC) tallies. Shannon entropy has been highly effective in characterizing convergence of the fission distribution in a reactor core. To compute Shannon entropy, transport-based MC code usually requires additional binning of the geometry along with the use of algorithms to get the distribution of fission source in these bins. This binning is done by superimposing a grid kind of structure over and above the geometry defined for transport simulation. The entropy computation in transport-based MC code thus involves additional computational efforts. In this paper, we have used finite-difference (FD) difference based diffusion MC method to calculate Shannon entropy. In this method, problem is divided into regular meshes. Shannon entropy is estimated in these mesh structures without any additional computational efforts. Shannon entropy for 3D PHWR benchmark is estimated by this method and is compared with Transport MC Code PATMOC and 3D Space Time Kinetics Code KINFIN and the results are found to be in good agreement.

Double-hybrid (DH) approximations have entered into the limelight of density functional theory (DFT) computations of different properties; however, little is known regarding their accountability for spin-state energetics in transition metal complexes. In this work, taking high-level all-electron fixed-node diffusion Monte Carlo data as a reference, we present a survey of the applicability of parameterized and parameter-free DHs as well as their dispersion and non-local corrected versions for predicting the spin splitting energies of transition metal complexes collected from the literature and from our own proposals herein. Our proposed parameter-free DH based on the spin-opposite-scaled (SOS) scheme incorporating the Perdew-Burke-Ernzerhof (PBE) exchange and strongly constrained and appropriately normed (SCAN) correlation as well as high balanced fractions of nonlocal exchange and correlation without any additional correction, SOS0-PBESCAN0-2(a), is found to be superior for overall performance. This model not only surpasses other DFT approximations from various rungs of the "Jacob's Ladder" classification and recently reported DHs for the present purpose but also outperforms wave function-based approaches in most cases. Dissecting the roles played by the non-local exchange and correlation contributions as well as their interplay, it is shown that this good performance arises mainly from an appropriate compromise between energy- and density-driven errors. Furthermore, by employing the proposed model and a variety of modified versions thereof, we scrutinize the roles of various factors, such as the ligand field strength and oxidation state of the metal ions, in both qualitative and quantitative descriptions of spin-state energetics in other complexes with different metals and ligands.

In diffusion Monte Carlo methods, depending on the geometry continuous diffusion can be simulated in many ways such as walk-on-spheres (WOS), walk-on-planes (WOP), walk-on-rectangles (WOR) and so on. The diffusion ways are conformally the same satisfying the Laplace equation with the given boundary geometry. In this paper, using the WOP and the conformal map, we sample the WOS diffusion and show that the indirect sampling is more efficient than the direct WOS sampling. This signifies that fast diffusion Monte Carlo sampling via conformal map can be possible.

We study beryllium dihydride (BeH$_2$) and acetylene (C$_2$H$_2$) molecules using real-space diffusion Monte Carlo (DMC) method. The molecules serve as perhaps the simplest prototypes that illustrate the difficulties with biases in the fixed-node DMC calculations that might appear with the use of effective core potentials (ECPs) or other nonlocal operators. This is especially relevant for the recently introduced correlation consistent ECPs (ccECPs) for $2s2p$ elements. Corresponding ccECPs exhibit deeper potential functions due to higher fidelity to all-electron counterparts, which could lead to larger local energy fluctuations. We point out that the difficulties stem from issues that are straightforward to address by upgrades of basis sets, use of T-moves for nonlocal terms, inclusion of a few configurations into the trial function and similar. The resulting accuracy corresponds to the ccECP target (chemical accuracy) and it is in consistent agreement with independent correlated calculations. Further possibilities for upgrading the reliability of the DMC algorithm and considerations for better adapted and more robust Jastrow factors are discussed as well., Comment: 13 pages, 5 figures