bluuebunny/crossref_metadata_2025_split huggingface dataset:
Monte Carlo solution of Schrödinger’s equation for the hydrogen atom in a magnetic field
Authors: Tomashima Y , Ozaki J 
Published: November 2023

Abstract
The problem of the hydrogen atom in a magnetic field can be treated satisfactorily by approximate methods which are quite accurate for very low or very high magnetic field strengths. Before this paper the only useful treatments for intermediate field strengths were variational methods giving upper bounds to the energies. As described in the paper the diffusion QMC method was applied in the same way as in earlier solutions for the hydrogen atom, but with additional magnetic terms added to the Hamiltonian expression. These include complex expressions and the required wavefunction includes a corresponding factor. With the magnetic field aligned along one axis, integration over the angle ϕ in (r, θ, ϕ) coordinates reduces the additional terms to real functions of r and z as well as the magnetic quantum number m. In the diffusion/multiplication processes of a random walk procedure these may be simply included with the potential energy term. In this study the energy at each step was determined from the average multiplication factor for the walkers. Importance sampling was not used. Results were obtained for quantum numbers m = 0, 1 at each of three magnetic field strengths. A comparison of results showed good agreement with the lowest values obtained in several of the earlier analytic variational calculations.
Interdimensional degeneracies in van der Waals clusters and quantum Monte Carlo computation of rovibrational states
Authors: Nightingale M P , Moodley M 
Published: November 2023

Abstract
In the course of an investigation of n-body correlations in trial wavefunctions for noble gas clusters the authors varied the spatial dimensionality of some of the clusters and discovered a surprising phenomenon: an interdimensional degeneracy for rotationally invariant states. For Lennard-Jones clusters of N particles in D dimensions they found identical energies for the ground states in dimensions D = N - l and D = N + l. They were able to explain this behavior by considering a D-dimensional Schrodinger equation for all S-states in dimensions D 2’. N - l. The minimum energy was observed and proven to occur for D = N. The calculations were carried out in dimensions D = l to 6 for systems corresponding to clusters of Kr, Ar, Ne, and a hypothetical ½-Ne with half the mass of Ne. The interactions were taken as pairwise-additive L-J 6-12. Very high accuracies were obtained with the aid of trial wavefunctions which were linear combinations of basis functions with nonlinear variational parameters optimized with an iteration procedure.
Quantum Monte Carlo and the Hydride Ion
Authors: Mcdowell K , Doll J D 
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
Muon-Alpha-Particle Sticking Probability In Muon-Catalyzed Fusion
Authors: Ceperley D , Alder B J 
Published: November 2023

Abstract
A negative muon µ has the negative charge of an electron but a mass 207 times that of an electron. Like an electron e binding two protons pin the molecular ion Ht or (epp)+, it can bind two protons in a molecular ion (µpp)+, and because of its higher mass, it binds more strongly. Similarly, a negative muon can bind a deuteron d and a triton t in a molecular ion (µdt)+. With the deuteron and triton held tightly together, they may fuse together, ejecting a neutron, forming an alpha particle, and releasing substantial energy. In about 1% of the events, the muon sticks to the positively charged alpha particle and is lost as a catalyst to additional fusions. This paper describes the use of Green’s function QMC to calculate the wavefunction for the (µdt)+ molecular ion for the purpose of estimating the sticking probability of the muon with the alpha particle. The essential functions are the initial and final wavefunctions at the instant of fusion with the deuteron and triton at the same position (coalescence point), and these functions along with the sudden approximation can be used to estimate the sticking probability. Earlier analytic variational treatments based on the Born-Oppenheimer approximation were not satisfactory. A modified version of Green’s function QMC with the use of a trial density matrix, along with importance sampling, was used to determine energies and sample the wavefunction. Calculations of relative wavefunction values, at the coalescence point relative to others, were made using the evolution procedure described by Liu, Kalos, and Chestera. Determination of normalization factors required special consideration. The calculations were clearly successful and gave a sticking probability of 0.90%, a value about 25% smaller than given by a Born-Oppenheimer wavefunction and closer to estimates derived from experimental measurements.
Quantum Monte Carlo method with the model potential
Authors: Yoshida T , Iguchi K 
Published: November 2023

Abstract
This third paper on the subject of effective potentials in 1987 and 1988 reports a somewhat simpler approach to combining effective core potentials with QMC than other papers of the same era. In this work the effective potential is based on an improved version of one introduced by Bonifacic and Huzinaga,a but it is simplified by elimination of core-valence exchange interaction and by use of an approximate core-valence orthogonality. All that remains of the original Hamiltonian are the kinetic energy terms for valence electrons, the potential energy terms for valence electrons interacting with each other and a reduced-charge nucleus, and a simpler radius-dependent potential energy term for each valence electron. FixeD nodes are introduced with a Slater-determinant trial function also used for importance sampling. Tests were made in calculations of the valence energies of the atoms Mg, Ca, and Sr, along with their cations, so that ionization potentials for these atoms could be calculated and compared with experimental values. The statistical uncertainties in the energies were about 0.03 eV, and the deviations in ionization potentials from experiment were about 0.1 eV. The results were significantly better than those of SCF calculations exhibited for comparison. Additional calculations were reported in a later paper.b
Damped-core quantum Monte Carlo method: Effective treatment for large-Z systems
Authors: Haimmond B L , Reynolds P J , Lester W A 
Published: November 2023

Abstract
Heavy atoms are problematic in QMC calculations for several reasons. Their energies are large, they have many electrons, and the time scales for core and valence electron motions are widely different. Larger local energy fluctuations are associated with higher energies. More electrons require longer computational efforts. Different time scales require short steps in one region and long equilibration times in others. The result is an estimated scaling of computational effort with zB-7, the sixth to seventh power of the nuclear charge Z. The Z-dependence can be reduced with the use of pseudopotentials, and this approach has been pursued with success, but not without introducing uncertainties. This paper describes an entirely different method which retains all the electrons, but treats core and valence electrons in different ways. The basic idea is that of treating core electrons by Metropolis sampling and valence electrons by diffusion with drift. Separate trial functions t/JT,core and were chosen orthogonal such that the valence electrons were prevented from collapsing into the core. For the core electrons the Metropolis walks were taken without branching and produced a distribution of walkers. For the valence electrons normal diffusion walks with drift produced a distribution. A smooth transition between regions was obtained with a damping function to eliminate branching as valence electrons approached the core.
Simulation of the electronic structure of an atom dissolved in a hard-sphere liquid
Authors: Dobrosavljević V , Henebry C W , Stratt R M 
Published: November 2023

Abstract
For this paper the authors used diffusion Monte Carlo methods to obtain a first solution to the problem of electronic structure of an atom in a structured liquid. Although models of several types using the assumption of no spatial variation of solvent effects have had some success, they miss essential features which are included naturally in a QMC calculation. The authors treated the problem of a hydrogenic atom in a hard-sphere liquid, specifically a proton and an electron in the presence of a hard-sphere helium-atom solvent. A separate classical simulation of 31 helium atoms and 1 hydrogen atom was used to generate equilibrium configurations of the solvent for 300 K. These were followed by diffusion QMC calculations for the electron in the field of the fixed proton, along with the boundary conditions of a zero wavefunction at the surfaces of helium spheres. A highly effective importance sampling function, incorporating factors of the Jastrow form, reduced the uncertainties in calculated energies and simplified the analysis to determine the characteristics of the electronic structure. Results were obtained for thousands of configurations for each of a number of conditions for liquid structures as well as for bee structures. The major observations were a smooth increase in ground-state energy with liquid density and a solvent-induced hybridization of the p orbital into the ground state at intermediate densities.
Cohesive energy of silicon by the Green’s-function :Monte Carlo method
Authors: Li X -p. , Ceperley D M , Martin R M 
Published: November 2023

Abstract
After variational QMC calculations with pseudopotentials for diamond-structure carbon and silicon, the next step higher is fixednode diffusion QMC for these materials. This paper reports that step for silicon with use of a pseudo Hamiltonian° to eliminate core electrons. In this case, the pseudo-Hamiltonian was tested and found accurate in fixed-node diffusion calculations for atomic and diatomic silicon. The trial wavefunction specifying the node locations for valence electrons was a Slater Jastrow combination based on a plane-wave basis set with constants determined in LDA density functional calculations. Both VQMC and fixed-node diffusion QMC calculations were performed for supercells of 64 atoms (216 electrons) with a range of lattice constants. Corrections of results to infinite systems were made with the assumption of size dependence the same as for LDA calculations. The predicted minimumenergy structures for VQMC and FN-DQMC were approximately the same, with lattice constants within 1% of the experimental value. The cohesive energy for FN-DQMC was approximately 0.4 e flower than for VQMC and, at 4.51(3) eV per atom, was within the uncertainties in agreement with experimental values of 4.63(8) eV per atom. Questions regarding the transferability of the LDA-based pseudo-Hamiltonian led the authors to recommend the use of pseudo-Hamiltonians or pseudopotentials based on many body theory in future calculations. As noted by the authors, this work demonstrated that QMC calculations of solids can provide high accuracies.
Quantum chemistry by random walk: Higher accuracy for Ht
Authors: Anderson J B 
Published: November 2023

Abstract
Although the ground-state Born-Oppenheimer wavefunction of the molecular ion Ht is nodeless and cancellation of positive and negative walkers is not required to treat a node structure, the larger step sizes of “exact” cancellation calculationsa in Green’s function QMC made it the choice for the calculations reported in this paper. In this case the higher efficiencies allowed, for the first time ever, the determination of potential energies for a polyatomic system with microhartree accuracy. The calculations were essentially identical to those described earliera for H2 1 E;t” and linear symmetric H-H-H. The calculated energy for Ht in its equilibrium equilateral triangle configuration of side length 1.6500 bohr was found to be -1.343 835 ± 0.000 001 hartrees.
Quantum :Monte Carlo calculation of the Fe atom
Authors: S L Mitáš 
Published: November 2023

Abstract
A variety of earlier calculations for the third-row transition element iron using argon-core pseudopotentials had failed to give good agreement with experimental measurements of the ionization potential, the electron affinity, and excitation energies. This paper reports QMC calculations which give excellent agreement and which are likely to be the most accurate of any type of calculation for the Fe atom in the 1990s. For these the author used neon-core pseudopotentials (leaving 16 electrons, including 3s and 3p electrons, in the valence space) for both variational and fixednode diffusion QMC calculations. The pseudopotential used was an ab initio pseudopotential tested against all-electron results in limited configuration interaction calculations. Relativistic effects were included. The complete Hamiltonian was modified slightly to facilitate treatment of the nonlocal part of the pseudopotential expression. The trial functions for importance sampling and specifying nodes were linear combinations of Slater determinants along with Jastrow functions. Six low-lying neutral states were examined in addition to the ground states of the anion and cation. Recovery of valence correlation energies was 0.6 to 0.8 hartrees for all of these, typically 0.1 to 0.2 hartrees greater that of coupled cluster and configuration interaction calculations. Most impressive is the agreement with experimental measurements: ionization potential, DQMC 7.67(6) eV vs. expt. 7.87 eV; 5 D 3 F transition, DQMC 4.24(9) eV vs. expt. 4.07 eV; 5 D 5 F transition, DQMC 0.84(6) eV vs. expt.
Quantum Monte Carlo of nitrogen: Atom, dimer, atomic and molecular solids
Authors: Mitáš L , Martin R M 
Published: November 2023

Abstract
This paper reports the first electronic structure calculations of any type to treat nitrogen solids with very high accuracies accuracies similar to those obtained for atomic and molecular nitrogen. It also reports the first estimate of a band gap for a solid using QMC methods. The calculations were carried out as valence-only calculations with abinitio nonlocal pseudopotentials using diffusion QMC with importance sampling. For the atomic and molecular solids, compressed /213 and Pa3 crystals, cubic structures with eight atoms in a simulation cell and periodic boundary conditions were used. The trial functions for importance sampling were composed of Slater determinants from Gaussian92, Garness, and Crystal92 calculations along with correlation terms optimized in variational QMC calculations. For the atom three different forms for the pseudopotential were found to give identical correlation energies. The pseudopotential of Stevens, Basch, and Kraussa was subsequently used for all systems. For the dimer the DQMC calculations gave a binding energy within 2% of the experimental binding energy . . . a result “comparable with the accuracy of the most extensive quantum chemistry calculations.” For the two compressed solids the binding energies were found to be 3.3(1) and 3.4(1) eV, values much higher than those of Hartree-Fock calculations, 0.01 and 0.25 eV, and lower than those of LDA density functional calculations at 4.45 and 4.75 eV. No experimental energies were available.
Improved quantum Monte Carlo calculation of the ground-state energy of the hydrogen molecule
Authors: Chen B , Anderson J B 
Published: November 2023

Abstract
Since the ground state of the hydrogen molecule is nodeless, it is easily treated by “exact” QMC cancellation methods in a full 12-dimensional, four-particle coordinate space to yield the groundstate energy without the use of the Born-Oppenheimer approximation. Following the discovery of quantum mechanics, the hydrogen molecule has been the frequent target of theoretical predictions of increasing accuracy, in parallel with experimental measurements of its ionization potential and its dissociation energy, also with increasing accuracy. The calculations reported in this paper took advantage of importance sampling and efficient cancellation to yield an accuracy of better than 1 microhartree in the total energy, with the result of -1.164 0237 ± 0.000 0009 hartrees, a value slightly less accurate than analytic variational calculations at the time. Expressed as the dissociation energy and corrected for relativistic and radiative effects, the QMC result in 36117.84 ± 0.20 cm-1, which may be compared with the experimental valuea of 36118.11 cm-1 determined in 1992.
Introduction
Authors: Gilmore Robert , Letellier Christophe 
Published: November 2023

Abstract
The subject of this work is the description of physical systems that possess symmetry exhibit chaotic behavior These systems are described by sets of nonlinear ordinary differential equations. The existence of a symmetry has a profound and far-reaching impact on the properties of the solutions of such equations. The presence of symmetry sometimes complicates and sometimes simplifies our understanding of the physical processes that generate chaotic behavior. In the following sections we describe a number of physical systems with symmetry and present a number of mathematical reasons for studying the relation between symmetries and dynamical systems. We also outline the structure and contents of this book.
Image Dynamical Systems
Authors: Gilmore Robert , Letellier Christophe 
Published: November 2023

Abstract
Dynamical systems with symmetry can be mapped to closely related systems without symmetry by introducing transformations that are diffeomorphisms almost everywhere. For such mappings the Jacobian of the transformation is nonsingular almost everywhere. It vanishes on a set of measure zero. In this chapter and the next we introduce the relation between equivariant dynam­ical systems and their images, invariant dynamical systems. The coordinates for the equivariant dynamical system are capitalized, those for the invariant dynamical sys­tem are in lowercase letters.
Three-Fold and Four-Fold Covers
Authors: Gilmore Robert , Letellier Christophe 
Published: November 2023

Abstract
In this chapter we will describe three-fold and four-fold covers of image dynamical systems. It is possible to numerically generate strange attractors equivariant under the groups C3 , C4 , and V4 . This is done by lifting image dynamical systems without symmetry. In this section we present three canonical image dynamical systems. One is the Rossler attractor, the other two are images of equivariant dynamical systems. The strange attractors for all three dynamical systems without symmetry are shown in Fig. 6.1.
Covering Dynamical Systems
Authors: Gilmore Robert , Letellier Christophe 
Published: November 2023

Abstract
The image dynamical system is the foundation upon which all its Q-equivariant covers are built. It is therefore useful-even imperative-to understand in detail all the most important properties of the image dynamical system. The variables that describe the image dynamical system are (u1, u2, ... , UN). These represent points in an N -dimensional phase space. The phase space is often taken to be ]RN . However, the phase space is more generally an N-dimensional manifold MN. We have already seen that the phase spaces for typical image dynamical systems are N dimensional algebraic submanifolds of IRK defined by K - N algebraic constraints called syzygies.
Symmetries Due to Symmetry
Authors: Gilmore Robert , Letellier Christophe 
Published: November 2023

Abstract
Schur’s lemmas play a fundamental role in the analysis of the representations of groups and algebras. They are powerful tools for the construction of a complete set of irreducible representations of any group. We exploit the first of Schur ‘s lemmas to detem1ine the most general form that a dynamical system in JR.N can have if it is equivariant under a group g. The structure is determined by the representations rDef (Q) and rRing (Q) . Although only one of the two lemmas of Schur is needed for our purposes, the lemmas are so powerful, so pretty, and so similar, we provide the proofs of both. The proofs are summarized in Figs. 14.1 and 14.2. The essential idea is that groups act on linear vector spaces through linear trans formations. These are determined by matrices. The matrices are the group representations. Definition: A subspace is invariant if it is mapped into itself under all linear transformations associated with the matrix representation of the group.
Ancient Greek Scholarship
Authors: Dickey Eleanor 
Published: November 2023

Abstract
Ancient greek sholarship constitutes a precious resource for classicists, but one that is underutilized because graduate students and even mature scholars lack familiarity with its conventions. The peculiarities of scholarly Greek and the lack of translations or scholarly aids often discourages readers from exploiting the large body of commentaries, scholia, lexica, and grammatical treatises that have been preserved on papyrus and via the manuscript tradition. Now, for the first time, there is an introduction to such scholarship that will enable students and scholars unfamiliar with this material to use it in their work. Ancient Greek Scholarship includes detailed discussion of the individual ancient authors on whose works scholia, commentaries, or single-author lexica exist, together with explanations of the probable sources of that scholarship and the ways it is now used, as well as descriptions of extant grammatical works and general lexica. These discussions, and the annotated bibliography of more than 1200 works, also include evaluations of the different texts of each work and of a variety of electronic resources. This book not only introduces readers to ancient scholarship, but also teaches them how to read it. Here readers will find a detailed, step-by-step introduction to the language, a glossary of over 1500 grammatical terms, and a set of more than 200 passages for translation, each accompanied by commentary. The commentaries offer enough help to enable undergraduates with as little as two years of Greek to translate most passages with confidence; in addition, readers are given aids to handling the ancient numerical systems, understanding the references found in works of ancient scholarship, and using an apparatus criticus (including an extensive key to the abbreviations used in an apparatus). Half the passages are accompanied by a key, so that the book is equally suitable for those studying on their own and for classes with graded homework.
Energy Characteristics and Control Strategies
Authors: Robertson Leon S 
Published: November 2023

Abstract
Injury epidemiologists should have at least a rudimentary understanding of the forms of energy involved in injury and the tolerance of human beings to exposure to energy. Since incidence and severity of injury are usually classified by vehicles or circumstances rather than by agent, the precise numbers attributable to a given agent are not available in many data sets. At the turn of the century in the United States, about 58 percent of fatal injuries and 62 percent of hospitalized injuries were attributed to motor vehicles, falls, and firearms (Finkelstein et al., 2006).