bluuebunny/crossref_metadata_2025_split huggingface dataset:
A quantum Monte Carlo perturbational study of the He-He interaction
Authors: Huiszoon C , Caffarel M 
Published: November 2023

Abstract
The well depth for interaction of two helium atoms at their equilibrium internuclear distance is less than 1/105 the total electronic energy of the pair. Thus, a perturbational approach is a natural way to attack the problem of predictions of the interaction energy, and several such attempts have been made. The work described in this paper is perturbational, but it differs from previous work in that it uses a Q!vIC method, specifically simple diffusion QMC, to determine the values of the perturbation terms required. The interaction energy for the two helium atoms was expressed by a sum of Rayleigh-Schri:idinger (RS) terms and exchange terms as: Caffarel and Hess0 showed earlier that the RS terms could be evaluated in terms of multitime integrals of autocorrelation functions along the trajectories of a diffusion process related to the unperturbed Hamiltonian and that these integrals could be determined by solution of the Fokker-Planck diffusion equation exactly, as in simple diffusion QMC calculations. The exchange terms could be similarly evaluated. The calculations were carried out for several internuclear distances and, within their relatively large statistical errors, gave agreement with “exact” valuesb given by other QMC methods.
Theoretical studies of the structure and dynamics of metal/hydrogen systems: Diffusion and path integral Monte Carlo investigations of nickel and palladium clusters
Authors: Chen B , Gomez M A , Sehl M , Doll J D , Freeman D L 
Published: November 2023

Abstract
In this study, the effect of adsorption of a single hydrogen atom upon the properties of Ni and Pd clusters of up to ten atoms was investigated. The required potential energies for the interactions of the atoms within the clusters were determined with the embeddedatom method, a semi-empirical method with parameters fit to data for bulk systems, giving reasonable agreement in comparisons with experimental observations. with the potential energies then available in convenient form, the properties of the clusters could be investigated to determine minimum-energy structures with and without zero-point energies, preferred hydrogen binding sites, hydrogen vibration frequencies, and related properties as a function of cluster size, using classical and quantum Monte Carlo methods. For the smaller clusters, the lowest-energy structures occur with the hydrogen atom on the outside of the clusters, but for the larger, inclusion of the hydrogen atom within the cluster is favored. Zeropoint vibrations were found to have no significant effects on the favored structures. Classical harmonic vibration analyses for the entire clusters gave about the same zero-point energies as diffusion QMC calculations. For the ground states, the QMC calculations showed the hydrogen atoms to be localized. For some clusters, Pd7H and Pd10H, quantum effects as indicated by diffusion Ql\IC were important in determining the favored structure. The studies were carried further with finite-temperature energy averages determined with the Fourier path integral method. The variation of energy with temperature clearly shows the quantum behavior of the smaller clusters at low temperatures and the shift toward classical behavior with increasing cluster size.
Fixed-sample optimization in quantum Monte Carlo using a probability density function
Authors: Barnett R N , Sun R N , Lester R N 
Published: November 2023

Abstract
The optimization of trial wavefunctions ‘I/Jr for use in QMC calculations can be accomplished with a fixed set of configurations selected with probabilities proportional to ‘1/Jf, often using Metropolis sampling and occasionally using other methods. By varying the coefficients of ‘I/Jr, one can minimize the variance in local energies for the original set of configurations. This is effective except when coefficients affecting the node locations are varied and occasional very high weighting factors ‘I/J}(new)/’1/J}(original) can give large fluctuations in the variance. In this paper, the authors propose the use of probability density functions p to produce nodeless distributions of points replacing the original ‘1/Jf distributions. This has two advantages: it avoids the unbounded weighting problem allowing nodes to be varied, and it facilitates sampling without a Metropolis walk and its associated serial correlation. To be effective, i.e., for high efficiency, p must be carefully selected, it must at least resemble ‘1/Jf, and its distributions must be easily sampled. Tests were performed for the case of CH with optimization of all parameters of a two-determinant-and-Jastrow trial function. These included basis set exponents, MO coefficients, CI coefficient, and SchmidtMoskowitz Jastrow parameters. The resulting variance in local energy was 0.19 h2, versus 0.25 h2 for optimization of the Jastrow coefficients only. More interesting is the improvement in diffusion QMC energy for the complete optimization including node movement. The energy was lowered by 0.004 hartree, or 2.5 kcal/mol, with recovery of correlation energy increased from 92.8 to 94.8%.
Quantum Monte Carlo investigation of exchange and correlation in silicon
Authors: Hood R Q , Chou M Y , Williamson A J , Rajagopal G , Needs R J , Foulkes W M C 
Published: November 2023

Abstract
QMC calculations can be used to calculate wavefunctions, electron densities, and a wide variety of functions and integrals, all of which may in turn be useful in improving other types of electronic structure calculations. In this variational QMC study of diamond-structure silicon, the quantities of central importance in Kohn-Sham density functional theory were calculated and compared to those from local-density and average-density approximations. In this case, the quantities were the coupling-constantintegrated pair correlation function, the exchange-correlation hole, and the exchange-correlation energy density. All are related to the total exchange-correlation energy. The calculations were carried out for 3 x 3 x 3 fee unit cells containing 54 nuclei with pseudopotentials and 216 valence electrons. The VQMC wave functions were optimized Slater-Jastrow functions giving 85% of the fixed-node correlation energy. Several different techniques were used in sampling to accumulate the diamond quantities, which were illustrated in full-color contour plots showing variations with position in the lattice. Differences between VQMC and local density approximation (LDA) results were similarly illustrated, and the largest errors in the LDA exchangecorrelation energy densities were found in the bonding regions and around the pseudoatoms. As pointed out by the authors, such calculations should aid in developing better functionals by providing much more data than the total energy and the bulk moduli previously available for comparison.
Positronium chemistry by quantum Monte Carlo. I. Positronium-first row atom complexes
Authors: Bressanini D , Mella M , Morosi G 
Published: November 2023

Abstract
Predictions of the energetics of systems containing a positron (e+) present a special challenge to most of the conventional methods of quantum chemistry. The prediction of the binding energy of positronium-atom complexes [A, Ps], where A is an atom and Ps =[e+, e-J, is a good example and one for which different theoretical methods have given widely different results. This paper describes all-electron (or all-electron and one positron) VQMC and DQMC calculations to determine the energies of atoms A, their anions A- or [A, e-J, and their complexes [A, Ps] or [A, e-, e+], where A = Li, B, C, 0, or F. From these energies, the binding energies of complexes relative to dissociation to [A + Ps] could be predicted. The calculations were carried out in fixed-node DQMC with trial functions composed of single determinants for the electrons, a positron-nucleus term, electron-electron correlation terms, and electron-positron correlation terms. The electron affinities of the atoms, given by differences in DQMC-calculated energies for the atoms and their anions, were found in excellent agreement with experimental measurements. The binding energies similarly determined for the atom positronium complexes show the Li, C, 0, and F complexes to be stable and. the B complex to be unstable to dissociation. Other types of electronic structure calculations give a variety of conflicting energetics. Since the DQMC calculations have the ability to recover not only electron-electron correlation energy, but also electron-positron correlation energy, the results “appear superior in accuracy” to previously published values.
Quantum Monte Carlo simulations of the structure in the liquid-vapor interface of BiGa binary alloys
Authors: Zhao M , Chekmarev D , Rice S A 
Published: November 2023

Abstract
The liquid vapor interface of a pure metal has been the subject of a number of simulations by both molecular dynamics and Monte Carlo methods. In this work quantum :t\fonte Carlo calculations for an interface were carried out for electrons and ions in a self-consistent manner, making use of pseudopotentials for the ions, a jellium approximation to determine their densities, and a KohnSham treatment of the electrons. The quantum Monte Carlo aspect appears in the solution of Kohn-Sham equation, which is the same as the one-dimensional Schrodinger equation in this application, which relates the electron wavefunction 1/Jn to the position z normal to the surface and the effective electron potential Veir, which in turn depends on the electron density ne ( z). The solution of this equation for 1/Jn (z) and the energy En may be determined in variational QMC by the Metropolis sampling method. With ne(z) freshly determined and Veir revised, the process may be repeated, a new ne(z) determined, and so forth to achieve self-consistency. For a pure metal, the development of the ionic interactions and the pseudopotential is a rather complex procedure, and it is even more complex for the bismuth-gallium alloy described in this paper. The end results are structures of the interface expressed in terms of longitudinal distributions (normal to the surface) of each of the atomic species, a transverse pair distribution, and the electron densities. Experimental measurements of the structure of alloys such as these are available from grazing incidence x-ray studies. In this case, the measured and predicted longitudinal density profiles are in “rather good” agreement, but differ somewhat in the details.
Selective correlation scheme within diffusion quantum Monte Carlo
Authors: Schautz F , Flad H J 
Published: November 2023

Abstract
This paper describes the development of a new scheme for using an effective model potential to reduce the number of electrons explicitly treated in a QMC calculation for a molecular system. Like other pseudopotential and model-potential approaches it is based on differing treatments of core and valence (or frozen and explicitly correlated) electrons. It differs from the earlier schemes of Yoshida and co-workers0 in that it is adapted to multicenter systems and includes a projectionlike operator to enforce orthogonality between orbitals for the two sets of electrons. The model potential includes Coulomb and exchange terms and the projectionlike operator. The latter two are nonlocal. For these a localization procedure, similar to those used in pseudopotential calculations, was derived. In implementing the scheme the authors had to explore a number of questions, such as those related to nonequivalent nodal domains, and to devise a number of approximations to simplify the calculations. The triple-bonded nitrogen molecule N2, with correlation for the electrons of the bonding orgitals and with the nonbonding orbitals frozen, was used as a test case. A coupled cluster [CCSD(T)] calculation with a large basis set provided a benchmark with a correlation energy of 228 mhartree for the triple bond estimated to be accurate within a few mhartree. The corresponding result for the QMC calculation using the best approximations differed by 2-6 mhartree. Thus, quantitative agreement was obtained within the limits of statistical error. The authors indicated a “good chance” for further development to enable efficient treatment of problems involving solids and surfaces.
Assessing the Quality of a Wavefunction using Quantum Monte Carlo
Authors: Mcdowell K 
Published: November 2023

Abstract
These two papers introduced the term “Quantum Monte Carlo” to the scientific literature. Earlier in the same year McDowell0 and Berneb had used the term in abstracts for an American Chemical Society meeting, and later in the year Gordon, Rothstein, and Proctorc used it in the title of a paper submitted to the Journal of Computational Physics. The papers report investigations of variational QMC methods with Metropolis sampling using the hydride ion H- and the helium atom He as examples. As had been found by earlier workers it is shown that relatively simple trial functions explicitly incorporating the interelectron distance rij can produce a high level of accuracy comparable to those of configuration interaction (CI) calculations based on many-term trial functions without rij
Green’s function Monte Carlo for few fermion problems
Authors: Arnow D M , Kalos M H , Lee M A , Schmidt K E 
Published: November 2023

Abstract
A method for treating the nodes for small systems was described in this paper. The general procedure involves the use of both positive and negative walkers in Green’s function QMC, along with cancellation of walkers of opposite sign in close proximity. The method is illustrated for the first excited state of a particle in a one-dimensional box and for three model problems with three particles in three dimensions, interacting with each other through square-well potentials with repulsive and attractive parts. The calculations were executed with the Green’s function procedure, made convenient by availability of known Green’s functions satisfying the conditions of the sample problems. A partial cancellation of positive and negative walkers was made on the basis of overlapping Green’s functions, and the distributions of steps for the walkers involved were altered accordingly. Without cancellations, the distributions of positive and negative walkers proceed to the boson ground-state distribution. With cancellation and with control of their numbers, the positive and negative walkers tend to accumulate in separate regions and to commingle in the vicinity of a node. The arithmetic sum of the walkers yields the excited or fermion wavefunction with a node separating positive and negative regions. For the model problems the method successfully produced accuracies within a few percent of the exact energies, where known. It was noted that for larger problems, the total number of walkers required to maintain an adequate density for sufficient cancellation might be prohibitive.
Monte Carlo variational study of Be: A survey of correlated wavefunctions
Authors: Moskowitz J W , Schmidt K E 
Published: November 2023

Abstract
This paper reports a successful attempt to construct simple but accurate wavefunctions for an atomic system by taking advantage of explicit electron-electron distances rij which can be incorporated into wavefunctions intended for QMC calculations which do not require analytic integrations. The principal advance reported is success with the use of functional forms more complex than that of earlier “Jastrow” functions such as exp[brij/(l+crij)]. In this case the forms are the “transcorrelated” expressions of Boys and Handy° which include exponential terms involving rm ijrn ik, mixed powers of electron-electron and electron-nucleus distances. The results were not particularly impressive because the coefficients within these terms were not optimized. Multiplying a Slater determinant by a typical Jastrow term tends to favor the overall expansion of the electron cloud as it keeps electrons apart, but it usually fails to give much improvement unless a corresponding adjustment shrinking the cloud is made. The slight improvements for the Be atom seen in this work were soon superceded in the authors’ later work in which such adjustments produced very much improved wavefunctions.b
A new look at correlation energy in atomic and molecular systems. II. The application of the Green’s function Monte Carlo method to LiH
Authors: Moskowitz J W , Schmidt K E 
Published: November 2023

Abstract
This paper describes the use of a combination of importance sampling with fixed-node diffusion QMC for a molecular system. Although the two devices had been used separately for several four-electron systems, a the combination gives the important advantages of low values of multiplication of walkers and nearly complete elimination of node crossing. The authors derive the Green’s function approach to importance sampling and use the short-time approximation to obtain a calculation procedure essentially the same as that for diffusion with drift. The calculations for LiH were carried out with two different trial functions t/JT specifying the node locations: an SCF function of Slater orbitals and a generalized valence bond function, each multiplied by a simple Jastrow function. This allowed a comparison of results for the two node structures, accompanied with the recognition that the energies represented upper bounds to the true energy which would be given for the correct node locations. At the equilibrium internuclear distance, the calculated energies were the same within their statistical uncertainties. A complete potential energy curve was plotted for the generalized valence bond case. At the equilibrium distance of 3.015 bohr, the energy found was -8.0727 ± 0.0006 hartrees, with an additional uncertainty of about ±0.01 hartree due to time-step error. Within the uncertainties this calculated energy agrees with more recent estimatesb of the exact Born-Oppenheimer energy at 3.015 bohr.
Binding Energy Of Positively Charged Acceptors In Germanium - A Green’s Function Monte Carlo Calculation
Authors: Kalia R K , Vashishta P , Lee M A 
Published: November 2023

Abstract
Spectroscopic measurements of germanium crystals have revealed some of the characteristics of impurity complexes which can be explained in terms of charge acceptors interacting with surrounding holes to form so-called pseudoatoms. With suitable modifications, these complexes can be treated in the same way as real atoms and ions by conventional quantum methods, as described in earlier work, and by QMC methods as described first in this paper. The complexes of interest include double acceptor impurities Be and Zn binding three holes and quadruple acceptors binding four holes, equivalent to negatively charged infinite-mass nuclei (of charge -Z) surrounded by positively charged holes (of charge +1). with use of effective masses for the holes, an effective dielectric constant, and a modification of Fermi statistics to allow four holes in ls orbitals, these systems may be treated as simple atoms and ions in diffusion QMC with importance sampling. The systems treated were equivalent to nodeless H-, He+, He, He-, Li+, Li, and Li-. Both variational and diffusion calculations used the same trial wavefunctions, which were symmetrized ls orbital products with added correlation terms linear in the interelectron distances. For the one- and two-hole systems, the energies could be deduced from the analogous systems. For these the diffusion QMC calculations gave equivalent results. In all cases the diffusion calculations gave slightly lower energies than the variational calculations. In comparisons with experiment, agreement was good for double acceptors and poor for triple acceptors, for which the pseudoatom model was judged to be inadequate.
The infrared predissociation spectra of water clusters
Authors: Coker D F , Miller R E , Watts R O 
Published: November 2023

Abstract
Coker, Miller, and watts carried out experimental measurements of the infrared predissociation spectra of small water clusters in molecular beams formed with free jet expansions of water vapor in helium. The spectra include several O-H stretch absorptions and an H-O-H bend overtone. Theoretical analyses based on empirical intramolecular/intermolecular potential energy surfaces were made using normal mode theory, local mode theory, and a novel extension of the simple random-walk procedure without importance sampling. The normal mode analysis was found inadequate and the local mode analysis not quite satisfactory, but the QMC-based quantum simulation procedure predicted the observed vibrational bands for the dimer and trimer very accurately. The simple QMC method was used to generate a large number of walkers with a distribution corresponding to the ground state wavefunction 7/J0. This many-body function was then projected onto the local vibrational coordinates for each molecule to give single-variable functions, each then fit by a Morse function. A variational calculation including cross terms for low-lying excited states was then made with this reference state. The results gave unambiguous assignments for the observed O-H stretching vibrations in the dimer, good agreement for the bending overtones, and satisfactory agreement for the O-H vibrations in the trimer. Repetition using a different pair interaction potential established that the experiment could provide a sensitive method for testing pair interactions.
Auxiliary field Monte Carlo for quantum many-body ground states
Authors: Sugiya G , Koonin S E 
Published: November 2023

Abstract
This paper describes a different Q11C method for solving the Schrödinger equation, one unlike variational, diffusion, and Green’s function methods. It can be applied to many-body systems to produce solutions for ground states. For systems of fermions, antisymmetrization can be imposed to overcome the problem of node location, but the instability of the method is a serious shortcoming, so that the method as described is limited to treating relatively simple systems. Nevertheless, this auxiliary field quantum 1,fonte Carlo (AFMC) method was demonstrated to be successful for test cases reported in this paper, and in time has been improved to allow treatment of realistic systemsa. The method makes use of the imaginary-time propagation of an initial wavefunction toward the ground-state function. It requires use of a trial wavefunction which is the product of single-particle orbitals for bosons or an antisymmetrized product for fermions. A Hubbard-Stratonovich transformation of the propagator changes the many-body problem to a problem of a collection of single particles interacting with a fluctuating (auxiliary) field which replaces the many-body interactions. The authors developed an integral expression for the energy which, after discretization, could be evaluated by a Metropolis Monte Carlo integration forward in time. The algorithm was tested for one-dimensional systems of particles: 6 to 20 bosons with varied interactions, 2 to 6 neutron-proton pairs, others with repulsive potentials. Importance sampling was found to be critical and computational requirements to be large. For spin systems on a lattice the AFMC method was considered feasible, but for general multidimensional systems the method appeared to be limited by its computation requirements.
Validity of random walk methods in the limit of small time steps
Authors: Anderson J B , Garmer D R 
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.