bluuebunny/crossref_metadata_2025_split huggingface dataset:
Linear scaling for the local energy in quantum Monte Carlo
Authors: Manten S , Lüchow A 
Published: November 2023

Abstract
This paper describes the use of localized orbitals and shortrange correlation functions to achieve near linear scaling in fixednode diffusion QMC calculations. The success of the method is demonstrated with a series of all-electron calculations for linear hydrocarbons in the range of C2H6 to C2sHs2 with 18 to 202 electrons. The procedure used was not very different from that of earlier all-electron calculations for systems of these sizes. Some changes were needed for evaluation of the trial wave functions and their derivatives. The molecular orbitals for the determinantal wavefunction were composed of contracted Gaussian functions decaying rapidly with distance but limited by a cut-off radius. The resulting determinants were sparse and could be evaluated by a standard matrix LU decomposition package. The standard Schmidt Moskowitz correlation function was modified with use of a short-range scaled distance to allow short cut-off radii.
Geometry optimization in quantum Monte Carlo with solution mapping: Application to formaldehyde
Authors: Schuetz C A , Frenklach M , Kollias A C , Lester w. A 
Published: November 2023

Abstract
Since analytic gradients of the energy with respect to nuclear positions are not easily obtained in QMC calculations, determining the locations of critical points, such as energy minima and saddle points, on potential energy surfaces is not straightforward. The statistical uncertainty in QMC energies prevents the direct estimation of these derivatives, and although several techniques for overcoming the problem have been developed their applications have been limited to very small systems. This paper describes a different approach, more readily applicable, in which the number and location of points in the vicinity of a critical point are chosen in such a way as to minimize the computation effort required in predicting the location of the critical point. The method is generally known as “solution mapping” and is often referred to as “factorial design.” The procedure is illustrated with calculations to determine the minimum energy or equilibrium geometry of formaldehyde H2CO, assumed planar and symmetric about the C-0 bond, in terms of the C-0 and C-H bond lengths and the H-C-0 angle. The potential energies calculated at specified points are fit to a polynomial expression of ten terms involving the three variables as l,x1,x2,x3,XI,X ,x ,x1x2,x1x3,x2x3, and ten coeffcients. With 15 points prescribed by the factorial design the determination of the coefficients is simplified by the column orthogonality of the design matrix. Of course, statistical uncertainties in the energies lead to uncertainties in the coefficients, but the method minimizes their effects.
Variational quantum :r-.fonte-Carlo method in surface physics
Authors: Schattke W , Bahnsen R , Redmer R 
Published: November 2023

Abstract
This paper is of interest for its discussions of the QMC treatment of lattice displacements in bulk matter and at solid surfaces with the aim of the prediction of phonon spectra. Earlier calculations had been made with density functional methods. The authors report variational QMC calculations of ground-state energies for gallium arsenide crystals using both local and nonlocal pseudopotentials coupled with trial wave functions of the SlaterJastrow type. Shifting of atomic positions and their corresponding orbitals allowed the simulation of phonon displacements as well as the determination of the bulk modulus and related properties. As an example, the case of the [111] phonon for bulk GaAs was treated in a (2,2,8) simulation cell with arsenic atoms fixed and gallium atoms displaced by up to 10% of the lattice constant. The energies obtained were fit to a quadratic function of the displacement from which the frequency of the mode considered could be calculated. Agreement with experimental values for the frequency was found within the estimated error of a few percent. For the surface the general scheme was the same, but a number of changes were required for a slab geometry. A “confinement potential” was added, the treatment of periodicity was altered, and the Ewald summations were altered. The calculated energies and electron densities revealed several inconsistencies, such that the surface calculations could “only be considered as a first step.” Nevertheless, the calculations demonstrate that QMC treatment of surfaces, including phonon dynamics at surfaces, is feasible.
Efficiency considerations in the construction of interpolated potential energy surfaces for the calculation of quantum observables by diffusion Monte Carlo
Authors: Crittenden D L , Thompson K C , Chebib M , Jordan M J T 
Published: November 2023

Abstract
This paper addresses the problem of choosing configurations of a loosely bound molecular complex for constructing a potential energy surface to be used in calculating quantum observables of the complex. For a tightly bound system, diffusion QMC has been shown to be an efficient sampling method for this purpose.0 A loosely bound complex presents somewhat different problems, and the authors investigated alternative procedures which they found useful in combination with diffusion QMC sampling. The example chosen is the very floppy prototypical water dimer, for which a suitable potential energy surface was available, and this surface took the place of ab initio calculations in providing potential energies for configurations sampled. The data obtained in sampling were not fit to a function representing the surface, but were used in interpolation to obtain the values of potential energies at other points on the surface required in calculations of quantum observables.
Ground state of the electron gas by a stochastic method
Authors: Ceperley D M , Alder B J 
Published: November 2023

Abstract
A simple way of incorporating sampling into diffusion quantum Monte Carlo calculations was introduced with this paper. Coupled with a nodal relaxation scheme it provided a means for calculating the ground-state energies of a collection of electrons (fermions) over a range of densities. The simulation method may be regarded as a more complex version of the simple diffusion methoda or a less complex version of the Green’s function approach.b With use of a trial function ΨT the diffusion equation may be written in terms of a walker or particle density based on f = ΨΨT the product of the true wavefunction Ψ and the trial wavefunction ΨT, The resulting equation includes a diffusion, a drift, and a multiplication term to take advantage of local energies as described by Grimm and Storer.c The calculations were carried out at first with fixed nodes to establish an upper bound to the exact fermion energy and starting positions for walkers in a released-node calculation. Walkers crossing a node were continued with a sign change to produce an overall distribution proceeding toward the boson ground state but providing at intermediate times an approximation to the fermion ground state. If relaxation to the fermion ground state is fast compared to further relaxation to the boson ground state, the fermion ground-state energy can be determined. For the electron gas at low densities this is the case and useful energies may be obtained. For this paper energies were calculated for a range of densities with systems of 38 to 246 particles and extrapolated to provide results for systems of infinite size.
Solution of the four-nucleon Schrödinger equation
Authors: Zabolitzky J G , Kalos M H 
Published: November 2023

Abstract
An application of the Green’s function QMC method to the problem of four nucleons is reported in this paper. The calculations were carried out for the case of four nucleons interacting according to a pairwise-additive potential given by the sum of the Malfliet-Tjon interaction terms for each pair. The problem was reduced to that of four interacting, spinless bosons and the ground state is nodeless. The calculation was a straightforward application of Green’s function QMC as described by Kalosa with avoidance of sign changes for walkers by a large shift in the zero of potential energy. Energies were evaluated from the growth rate of walkers and with use of importance sampling using a function of the Jastrow form. The energy determined for the case of the a-particle was -31.1 ± 0.2 MeV for a trial function with an expectation value of -28.8 ± 0.01 MeV. Additional calculations were performed for the case of the four-atom helium droplet or cluster He4 with the atoms interacting via pairwise-additive Lennard-Jones potentials. The energy for the cluster was found to be -0.39 ± 0.01 K, a value in agreement with earlier estimates for similar Lennard-Jones potentials. The authors pointed out that the results of QMC calculations such as these could serve as benchmarks for less rigorous methods.
Fixed-node quantum Monte Carlo for molecules
Authors: Reynolds P J , Ceperley D M , Alder B J , Lester W A 
Published: November 2023

Abstract
This paper extends earlier calculations for the molecules H2 and LiH, and it increases the range to six and ten electrons with calculations for Li2 and H2O. The calculations were carried out with importance sampling using trial functions consisting of Slater determinants multiplied by Jastrow factors. For each system the expectation values of the energies for the trial functions were somewhat higher than those of the best configuration interaction calculations available at the time, but the fixed-node diffusion energies were significantly lower. The observed energy obtained for H2 was -1.174 ± 0.001 hartrees, compared to earlier values of -1.1744 hartrees in analytic variational calculations. For H2O it was - 76.377 ± 0.007 hartrees, compared to a value of - 76.3683 hartrees from variational calculations and an estimated true value for H20 of - 76.438 hartrees. The difference between the QMC value and the true value illustrates the problem of inaccurate node locations, in this case corresponding to a node location error of about 38 kcal/mol. Nevertheless, the energy so determined was about 5 kcal/mol lower than that of the lowest energy analytic variational calculation of the time.
Application Of The Green’s-Function Monte Carlo Method To The Compact Abelian Lattice Gauge Theory
Authors: Heys D W , Stump D R 
Published: November 2023

Abstract
The first application of diffusion or Green’s function QMC in treating lattice gauge theories was reported in this paper on the compact U(l) gauge theory, one of the simplest of the lattice gauge theories. Earlier investigations of the U(l) and other Abelian gauge theories had been made by a variety of other methods, including perturbation expansions, variational calculations, and most successfully path integral treatments using Monte Carlo integrations. Aside from investigation of QMC methods for the U(l) theory, one object of this study was to verify results for the path integral approach in the Hamiltonian formulation. The Hamiltonian itself was expressed as a summation of terms involving electric and magnetic fields at each site, link, or plaquette, for which the authors developed the usual Green’s function expression in a discrete form to be applied to an n(p)-space wavefunction X[n(p)], a function of integer-valued plaquette variables. Except for discrete spatial positions, the Green’s function calculations were very nearly the same as those for electronic structure studies. The systems treated were small lattices, 5 x 5 and 3 x 3 x 3, in two and three dimensions with a variable coupling constant A. Variational calculations with different trial functions suitable for strong and weak coupling were found to reproduce known behavior for strong and weak limits. The Green’s function calculations were facilitated with importance sampling and produced similar results, thus indicating the high quality of the trial wavefunctions. The results provide evidence for the existence of a phase transition in the three-dimensional case and for the nonexistence of a phase transition in the two-dimensional case.
Calculations of ground-state properties of liquid 4He droplets
Authors: Pandharipande V R , Zabolitzky J G , Pieper S C , Wiringa R B , Helmbrecht U 
Published: November 2023

Abstract
Earlier calculationsa of the binding energy and compressibility of liquid helium in bulk were successful in reproducing experimental measurements within a few percent. These indicated a pairwise-additive empirical potential to be entirely adequate. In this paper the same potential was used in similar variational and Green’s function QMC calculations to predict the properties of the ground states of liquid 4He droplets, or more recently “clusters,” containing 4 to 728 atoms. The calculation procedure was identical to that of the earlier worka except that boundaries were eliminated. Trial wavefunctions for both types of calculations were expressed as products of functions of interatomic distances similar to those used for the infinite liquid. A comparison of energies for the two types of calculations over the range of 4 to 112 atoms, showing the Green’s function energies only 2-3% lower than the variational energies, indicates a high accuracy for the variational functions by themselves. Density distributions obtained as long-term averages by both methods were somewhat noisy at the droplet centers, but smooth and in good agreement away from the centers. These were fitted by quadratic and higher order functions from which surface tension could be estimated. For the larger droplets, the density was constant across the central region and approached the density of the bulk liquid. The authors noted that the success of these calculations gives confidence in the use of liquid drop formulas in predicting properties of nuclear matter.
Relativistic effective potentials in quantum Monte Carlo calculations
Authors: Hurley M M , Christiansen P A 
Published: November 2023

Abstract
This is the first of three papers,0 each from a different group, to report the use of effective potentials, model potentials, or pseudopotentials in QMC calculations in 1987 and 1988. The authors point out the advantages of eliminating core electrons in order to simplify the calculations, reduce the number of singularities in the wavefunction, and thereby reduce the variance in local energies. They note the primary difficulty in using relativistic effective potentials is the nonlocal character of most potentials and their dependence on angular projection operators rather than on mere electron configurations. In this study, the authors defined a simple local potential V in terms of the nonlocal effective potentials operating on a trial wavefunction. The extent of the error introduced was unknown but possibly small. The effective potentials were taken directly from earlier analytic studies for the species considered. The trial wavefunctions were single determinants of Gaussian orbitals together with Jastrow correlation terms. Calculations were carried out for Li/Li- and K/K- so that electron affinities could be obtained. The values so determined were 0.56 and 0.52 eV, respectively, compared to 0.618 and 0.502 eV determined in experiments. It was noted that corresponding all-electron calculations for the F /F- pair required a vastly greater computation effort, perhaps more than a factor of 1000 greater.
Is there a zeroth order time-step error in diffusion quantum Monte Carlo?
Authors: Reynolds P J , Owen R K , Lester W A 
Published: November 2023

Abstract
These three notes each offer evidence against an earlier claim, added as an appendix to a paper by Moskowitz and Schmidt,a that the discretization of the imaginary-time Schrödinger equation was in error even for infinitesimal time-step sizes and that all results with this short-time approximation were incorrect. As acknowledged by Moskowitz and Schmidt, there was an error in their analysis and they agreed that the short-time approximation was correct after all.
Time step error in diffusion Monte Carlo simulations: An empirical study
Authors: Rothstein S M , Patil N , Vrbik J 
Published: November 2023

Abstract
The discretization of the differential equations describing the transient behavior of a system usually introduces a time-step error. The problem occurs in diffusion QMC and may, in principle, be overcome by varying the time-step size and extrapolating results to a step size of zero. This paper shows that such extrapolations are not so simple, and it provides explanations for some of the surprises encountered in using several different procedures. Following the importance sampling procedure of Grimm and Storer,a the Green’s function and similarly discretization may be separated into individual functions or terms for drift, diffusion, and branching (or weight change). Rothstein et al. combined these in varied orders of full and half steps and examined their behavior in calculations for H2 and LiH with different time step sizes. Both linear observed, and even these depended on the system. Further analysis gave insights into the causes for the trends observed and some practical advice for selecting the best procedures. The problem treated in this paper is that of understanding xenon cluster ions at the microscopic level. Some properties of cluster anions had been measured, but these revealed no detailed information on structure and energetics. In the study reported here, diffusion QMC was used to investigate electron binding to small clusters of up to 19 atoms in fixed minimum-energy configurations. This was followed by path integral calculations to determine equilibrium distributions of cluster structures at temperatures of 10-100 K for several cluster sizes.
Structure and energetics of Xe
Authors: Martyna G J , Berne B J 
Published: November 2023

Abstract
The problem treated in this paper is that of understanding xenon cluster ions at the microscopic level. Some properties of cluster anions had been measured, but these revealed no detailed information on structure and energetics. In the study reported here, diffusion QMC was used to investigate electron binding to small clusters of up to 19 atoms in fixed minimum-energy configurations. This was followed by path integral calculations to determine equilibrium distributions of cluster structures at temperatures of 10-100 K for several cluster sizes. Diffusion QMC calculations for frozen clusters were carried out for an additive electron-xenon pseudopotential: first, using a trial wavefunction given by the product of s-wave solutions for single electron-xenon pairs with the pseudopotential interaction, and second, with an improved function based on the results of the first and minimization of the energies. Variational energies could be determined by numerical quadrature for this three-dimensional problem. For clusters of five and fewer atoms, the binding energy of the electron could not be determined, although an upper bound was found to be 12 K. For 6-19 atoms the binding energy increased in monotonic fashion from 12 K to 1100 K. The change in binding energy with number of atoms exhibited variations which could be explained in terms of the cluster structures. For the smaller clusters, the electron probability distribution was found diffuse and extended outside the cluster. The path integral calculations gave good agreement with the diffusion QMC calculations for the smaller clusters. For larger clusters of 50 and 100 atoms, the electron distribution was localized within the cluster.
Quantum Monte Carlo method for some model and realistic coupled anharmonic oscillators
Authors: Caffarel M , Claverie P , Mijoule M , Andzelm J , Salahub D R 
Published: November 2023

Abstract
This paper reports a first attack on the node location problem for excited states of two-dimensional systems corresponding to coupled one-dimensional oscillators. The zero-point energy of such systems may be readily evaluated using diffusion with or without importance sampling, but as for electronic states, the problem of node locations prevents such easy solutions for excited vibrational states unless the nodes can be specified from symmetry considerations. The authors present a modified fixed-node approach which is a good approximation when the nodes of a reference function are close to the exact nodes. The method is based on variations in node locations to minimize the energies in the regions separated by nodes, subject to the constraint that the energies must be equal. This is accomplished with a complete wavefunction made up of a variable combination of wavefunctions corresponding to those for uncoupled oscillators. Applications for several two-dimensional systems including a realistic model for adsorbed CO on a surface gave essentially exact agreement with the results of analytic variational solutions with large basis sets. The authors concluded that their method avoided many of the problems encountered with other methods and appeared well adapted for systems of strongly coupled oscillators and multiple-well potentials.
Effect of crystallite shape on exciton energy: Quantum Monte Carlo calculations
Authors: Mohan V , Anderson J B 
Published: November 2023

Abstract
About the time that small semiconductor crystallites were first called “quantum dots”, quantum Monte Carlo calculations were first applied in studies of these systems. Small crystallites have spectroscopic properties like those of molecules with molecular orbitals, and they shift to the behavior of electrons and holes in continuous bands as their size is increased. This paper reports a study of the effect of size and shape of crystallites on ground-state energies for an electron-hole pair (or vVannier exciton) confined to the crystallite. The system was investigated using a model by Brusa with the electron-hole pair similar to a hydrogen atom having effective masses for each, unit charges for each, and a coulombic interaction governed by a bulk dielectric constant. The electron and hole were confined to the crystallite by setting the charge densities to zero at the boundaries. Estimates of the energies for several sizes of spherical CdS and ZnO crystallites had been made earlier in variational calculations by Brusa and by others. The calculations of this later paper were carried out for spheres, cubes, and rectangular parallelopipeds of CdS and ZnO crystallites using diffusion QMC with importance sampling. The trial function was a product of three dimensional particle-in-a-box (or sphere) functions for electron and hole, multiplied by a hydrogen-like function of the electron-hole distance.