bluuebunny/crossref_metadata_2025_split huggingface dataset:
The differential Green’s function Monte Carlo method. The dipole moment of LiH
Authors: Wells B H 
Published: November 2023

Abstract
Use of correlated random walks in fixed-node diffusion QMC offers the opportunity to calculate differences in energies of similar systems. In this paper wells reports such calculations for LiH in the presence of differing field strengths to determine its dipole moment. Since the local energies for identical electron configuration and importance sampling functions differ only in the potential energy due to the applied electrical field, the local energies are strongly correlated, and the statistical error in the difference in energies can be much lower than that for either of the individual energies. The calculations were started from a ‘l/Jf distribution of walkers with identical moves for each system. Since the multiplication terms were slightly different, variable weights were used for each walker. Although these eventually diverge for the correlated pairs, there is a sufficient period of strong correlation to allow efficient reduction in variance in energy differences. Thus, for an applied field of 0.0001 a. u. versus no field, the energies obtained were -8.0593 ± 0.0030 hartrees and -8.0595 ± 0.0030 hartrees, but the computed energy difference was 0.000227 ± 0.000003 hartrees, corresponding to a dipole moment of 2.27 ± 0.03 au, in good agreement with the value derived from experiments. Since there was no provision for a change in the node structure with applied field, it appears the dipole moment is insensitive to the change if any occurs.
A Green’s function used in diffusion Monte Carlo
Authors: Rothstein S M , Vrbik J 
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.
Alpha particle structure
Authors: Carlson J 
Published: November 2023

Abstract
The time-independent Schrödinger equation for the case of nucleons in light nuclei is more difficult to treat than that of electrons in a light atom because of more complicated interaction terms. Nevertheless, for three-nucleon systems such as the triton, binding energies and structural details have been successfully obtained for realistic nucleon-nucleon interaction models by several different methods, especially by analytic variational methods. For four-nucleon systems such as the alpha particle, realistic models of the interactions are also available, but the added nucleon makes the treatments more difficult and the properties predicted less certain. This paper reports the use of variational QMC calculations to obtain accurate solutions for the alpha particle with several nucleon-nucleon interaction models. For one model, both variational and diffusion QMC calculations provided the opportunity for direct comparisons to assess the accuracy of variational QMC results. The interaction models, chosen to provide a test of the sensitivity of results, included those known as Argonne V14, Nijmegen, Bonn, Reid V8, and Urbana Model 7. Trial wavefunctions previously developed for such problems were constructed of Slater determinants, functions of internucleon distances and spins, as well as correlation terms. Optimizations of parameters were carried out by minimizing the expectation values of the energies, making use of correlated sampling.
Quantum Monte Carlo calculations of three-body corrections in the interaction of three helium atoms
Authors: Mohan V , Anderson J B 
Published: November 2023

Abstract
For inter nuclear distances of about 4 bohr and greater, the potential energy of three helium atoms is very close to pairwise additive. That is, the total interaction energy is very close to the sum of the interaction energies of the three pairs, each in the absence of a third atom. The energy may then be conveniently expressed as where E1 is an atom energy, LlE2 a pairwise interaction energy, and LlEa is a three-body correction term. For pairwise additivity, LlE3 is zero. The correction LlEa is extremely small and is certainly less than 30 microhartrees (about 10 K) for three He atoms in an equilateral triangle configuration of side length 5.6 bohr with a total energy of about 8.7 hartrees. A third-order perturbation analysis by Axilrod and Teller0 and Mutob (ATM) has provided a simple and convenient expression for the three-body correction. Clearly, it must fail at small internuclear distances, but it often has been assumed to be acceptable for distances near the equilibrium dimer distance of 5.6 bohr. The fixed-node diffusion calculations reported were carried out for equilateral triangles with side lengths of 2.5 to 6.5 bohr. The trial function was based on Hylleraas expressions for the atoms in a 36-term antisymmetric sum. The results confirmed that the three-body correction term was less than 10 K for distances greater than about 5.6 bohr, but the uncertainties were about 10 K.
Correlated Monte Carlo wave functions for the atoms He through Ne
Authors: Schmidt K E , Moskowitz J W 
Published: November 2023

Abstract
This paper introduced an expanded form of correlation function to replace the simple Jastrow functions used in trial wavefunctions for both VQMC and DQMC calculations. The result was a significant decrease in the variance in local energies and an increase in recovery of correlation energies for the atoms examined (and for many other atoms and molecules, by subsequent workers using the new functions). The form for the trial functions employed is a single determinant multiplied by a correlation function F proposed by Boys and Handya where the sums are over nuclei I, electrons i and j, and terms for both electron-electron and electron-nucleus interactions. The electron-nucleus terms have the important effect of compensating for electron density changes due to the electron-electron terms, and they give a large improvement over the authors’ previous results. Functions with 7, 9, and 17 terms were optimized for each of the atoms He through Ne and used in variational QMC calculations. Recovery of correlation energy was approximately 100% for He, 97% for Li, and 18% to 85% for Be through Ne. In the case of Ne, the single-determinant with the correlation function recovered 85%, a value higher than the 75% obtained in configuration interaction calculations (with 107 determinants) at the time.
Fixed-node Monte Carlo study of the two-dimensional Hubbard model
Authors: AN G , Leeuwen J M J Van 
Published: November 2023

Abstract
This study extended the fixed-node QMC method to a lattice model for hopping fermions using Green’s function techniques. In general, the modifications of the procedures for continuous systems to adapt them to a lattice system were minor, and there appeared to be no surprises. Applications were made to the two-dimensional Hubbard model with different on-site interactions, lattice dimensions, boundary conditions, node specifications, and trial wavefunctions for importance sampling. Results were compared with those of Hartree-Fock and variational QMC calculations. For the HF calculations with zero interaction, the exact solutions are known, and the Green’s function QMC results agreed with those within statistical error. Trial wavefunctions specifying the nodes were obtained directly as those of HF determinantal solutions for zero interaction, or as variationally optimized determinantal functions with correlation terms. The procedure for fixed nodes was to eliminate walkers crossing the boundaries of a nodal region, a procedure not quite correct, but probably a reasonable approximation. The results in all cases were consistent with the HF and variational QMC calculations, giving lower energies than either for nonzero interaction energies. The existence of a domain-wall phase suggested by the HF and variational QMC results was confirmed by the fixed-node Green’s function results. It was noted that the fixed-node method would be applicable to systems other than the Hubbard model.
Monte Carlo algorithms for expectation values of coordinate operators
Authors: Barnett R N , Reynolds P J , Lester W A 
Published: November 2023

Abstract
In diffusion QMC with importance sampling, walkers provide samples of configurations with probabilities proportional to the product of the true wave function ‘¢ and a trial wavefunction t/Jr. The expectation value of the energy (very fortunately) may be calculated from the local energies of these samples as E = (‘l/JH’l/Jr)/(‘l/Jt/Jr) = (‘l/JE10ct/Jr)/(‘¢’¢r). But for an operator A which does not commute with the Hamiltonian H, the mixed expectation value (‘¢At/Jr) is only an approximation to the “pure” expectation value (‘ljJA’¢). Thus, for most quantities of interest other than the energy, an extension to standard diffusion QMC methods is required. This paper describes two approaches to the problem. Both are based on an earlier development by Liu, Kalos, and Chester0 involving the tracking of descendents of walkers to obtain pure expectation values. The first uses simple DQMC and the second uses VQMC with DQMC “side walkers.” These methods were tested in their application to the model systems H and H2, and both were found effective in yielding accuracies and precisions correct within 0.5% for the quantities (r) for H and (r2) and (z2) for H and H2. The large differences in electron and proton masses led to extensive computation requirements due to the slow equilibration and serial correlation induced by the heavier protons. The calculations were executed on one of the first massively parallel computers, a Thinking Machines CM-2 with 65,536 processors. Frequent communication among the processors was required to balance the number of walkers treated in each.
An accurate quantum Monte Carlo calculation of the barrier height for the reaction H + H2 H2 + H
Authors: Diedrich D L , Anderson J B 
Published: November 2023

Abstract
A lit of fundamental reactions usually begins with the reaction H + H2 -+ H2 + H, the simplest of neutral chemical reactions and the subject of more than 60 years of theoretical studies at the time this paper was published. The potential energy surface and especially the barrier to reaction are essential to any treatment. Earlier theoretical work had led to predictions of a barrier height of9.5 to 9.8 kcal/mol. The QMC calculations reported in this paper reduced the uncertainty by a factor of about ten and specified the barrier height as 9.61 ± 0.01 kcal/mol. The calculations were “exact” QMC calculations based on the Green’s function method with partial cancellations of positive and negative walkers to produce a stable wavefunction with a correct node location. A trial wavefunction was used for importance sampling to aid in determining energies without affecting the node location. Time-step error was avoided with use of the Green’s function approach for the moves of walkers. The complete procedure was exact in that, except for the easily estimated statistical or sampling error, it required no mathematical or physical assumptions beyond those of the Schrodinger equation. No interpolation or extrapolation was required.
Energies, densities, and pair correlation functions of jellium spheres by the variational Monte Carlo method
Authors: Ballone P , Umrigar C J , Delaly p. 
Published: November 2023

Abstract
In the jellium model for clusters of atoms the charge of the nuclei and of appropriate inner-shell electrons is replaced by a net positive uniform charge distribution. This model has been found especially useful for spherical clusters of alkali metal atoms with explicit treatment of electronic structure limited to valence electrons. In this paper the authors have reported studies of clusters of up to 20 atoms, equivalent to spheres with a distributed charge of +20 along with 20 free electrons. The trial function for variational QMC was constructed in the usual way with single determinants of orbitals generated in density functional (LSDA) calculations multiplied by optimized Jastrow functions. The quality of these functions was tested in fixed-node diffusion calculations indicating that 90% of the fixed-node correlation energy was recovered in the variational calculations. Results for a series of neutral and ionized clusters were compared with those of density functional calculations in terms of total, exchange, and correlation energies as well as pair correlation functions and electron densities. In general, total and spin densities were found in excellent agreement for the two types of calculations. Energies were found in fairly good agreement, but exchange and correlation energies differed by as much as 6% and 30%, respectively. The paper clearly shows the several advantages of QMC for a system different from that of the typical atomic or molecular problem.
Exact quantum Monte Carlo calculation of the H-He interaction potential
Authors: Bhattacharya A , Anderson J B 
Published: November 2023

Abstract
This is the third in a series of papers describing “exact” QMC calculations for few-electron systems with nodes in their wavefunctions. The method used is the exact cancellation Green’s function scheme0 which develops the node structure and is “exact” in that it requires no approximations, no interpolations, and no extrapolations. The treatment used is essentially the same as that for earlier calculations for He 3 P, H2 31:;t, H-H-H, and He-He. The trial function for importance sampling was based on a Hylleraas function for the He atom and a Slater function for the H atom. Energies were calculated for internuclear separations within the range of 5.0 to 15.0 bohr. The minimum was found at -3.403 746±0.000 002 hartrees for a separation of 7.0 bohr, corresponding to a well depth of 6.8 ± 0.5 K. Total energies were approximately 12000 K below those of the lowest-energy variational calculations available. The interaction energy was at least 3 K more accurate than prior estimates by any other method. The calculated potential energy curve was consistent with low-energy scattering cross-section measurements for H with He.
The effect of an uneven potential on the few-electron spectrum in a quantum dot
Authors: Bolton F 
Published: November 2023

Abstract
Quantum Monte Carlo methods devised for atomic and molecular systems may be applied without much change to investigate the physics of quantum dots. The simplest of few-electron quantum dots is the idealized case with two electrons confined in a two-dimensional well by a parabolic potential, which is a good approximation to the confining potential of a uniform background of positive charge. With more electrons the node problem appears, and with an applied magnetic field the Hamiltonian gains more terms and the wave function may be treated as complex. In this study, the effects of adding ripples to the parabolic potential, such as might be found in realistic confining potentials, were investigated for one-, two-, and three-electron systems. Diffusion QMC was used with the equivalent of fixed nodes, which were specified as phase factors in the trial functions in what is termed the fixed-phase approximation. These can be specified for low-lying singlet and triplet states. With the magnetic field varied, the ground state may shift to a state of different total spin. The addition spectrum, corresponding to the energy changes on addition of an electron to the system, and its changes with magnetic field were calculated for conditions matching experiments with GaAs. The calculated and observed spectra were nearly the same, but some differences were found. These were explained in part by additional calculations with realistic ripples added to the parabolic potentials.
Covers
Authors: Gilmore Robert , Letellier Christophe 
Published: November 2023

Abstract
Every covering dynamical system has a unique image. The same is not true for images. Every image dynamical system has many different inequivalent equivariant covers. We make these statements more precise. Every dynamical system Xi = Fi(X) equivariant under symmetry group ( has a unique image dynamical system u1 = g1(u ). The image is obtained by introducing invariant coordinates u1 = u1(x ). The two dynamical systems are locally diffeomorphic but not globally diffeomorphic. Conversely, a dynamical system u1 = g1(u ) without symmetry can be “lifted” to a covering dynamical system with symmetry group( by introducing a set of coordinates Xi with suitable transformation properties under
Larger Symmetries
Authors: Gilmore Robert , Letellier Christophe 
Published: November 2023

Abstract
These equations are truncations of nonlinear partial differential equations that support one or more propagating waves. They involve complex time-dependent amplitudes and possibly their complex conjugates. In these systems the complex amplitudes a1 (t) are coupled to waves of the from ei ( k jX-w jt ) . If the partial differential equation has a quadratic nonlinearity, the projected coupled ordinary differential equations (9.1) contain only bilinear nonlinearities. In this section we will outline the general approach to the study of complex ordinary differential equations of type (9.1) when these equations exhibit a continuous symmetry.
Human Factors
Authors: Robertson Leon S 
Published: November 2023

Abstract
Most people who are injured are doing something at the time-driving, riding in a vehicle, walking, working, or playing. So are people who are infected by micro organisms, but those who study injury place more emphasis on behavior than do those who study most infectious diseases. Notable exceptions are infectious diseases transmitted by sex. Ironically, sexual behavior in moving vehicles has been neglected as a topic for research.
Introduction: Love Stories of Later Life
Authors: Barusch Amanda Smith 
Published: November 2023

Abstract
“Grow old along with me! The best is yet to be, / The last of life for which the first was made.” Robert Browning wrote these familiar words in 1864, when old meant something quite different from what it means today. In nineteenth-century England life expectancy was under 45 years, and some thought the natural life span of mankind was 58 years. The idea that many people would live—and love—into their eighth and ninth decades was un- fathomable.
Supporting Actors: Family, Friends, and Community
Authors: Barusch Amanda Smith 
Published: November 2023

Abstract
Warm, articulate, and emotionally complex, at the age of 83 Barbara is a quintessential people person. Like the rest of her life, Barbara’s romances take place in an unusually rich social context. Consider what she has to say about the man she married in her early 60s: What happened is I got a letter from my third husband’s wife and I went down. She was a good friend of mine. I went down there and I visited them and at that point something was bothering her. Turned out she had ovarian cancer. And I didn’t know it but then somehow I got a letter from Simon that she had died. I couldn’t believe it. I decided to stop in to pay my respects. Well, I knew he was a good catch and I also knew that he had had a crush on me when I worked for him. I loved Simon as a friend but there was something about him that was very feminine. So anyhow, I went down and he said would you consider a relationship? I said, all you have to do is whistle. I wanted him to know I was interested. He was an upstanding man in the community and I loved his kids. I really did. He had three kids. His kids were accepting. They wanted their father to be happy, so happy. It didn’t take him 6 months to propose. We planned the wedding.
Slippery Slope to the Hospital: Diagnosis and Hospitalization
Authors: Kant Jared Douglas , Franklin Martin , Andrews Linda Wasmer 
Published: November 2023

Abstract
The first thing I learned about psychiatrists is that they have candy. At least, that was true of the psychiatrist I saw after returning home from summer camp. He seemed to understand that something sweet was needed to counter the bitter feelings and experiences we were about to explore.
This psychiatrist formally diagnosed my OCD when I was 11. The shock of what that diagnosis meant came in stages. Ironically, my initial reaction was to feel overjoyed. I was happy and grateful to know that there was a name for what I was going through. It wasn’t until later that the gravity of the situation sank in.
Sensing the Dangers: Chronic and Acute Secondary Stress
Authors: Wicks Robert J 
Published: November 2023

Abstract
To tack a boat, to sail a zigzag course, is not to deny our destination or our destiny–despite how it may appear to those who never dare to take the tiller in their hand. Just the opposite: It’s to recognize the obstacles that stand between ourselves and where we want to go, and then to maneuver with patience and fortitude, making the most of each leg of our journey, until we reach our landfall. (1993, p. 49)
Enhancing Resiliency: Strengthening One’s Own Self-Care Protocol
Authors: Wicks Robert J 
Published: November 2023

Abstract
Care must be taken not to be driven in one’s career to the extent that everything else loses value and accordingly does not receive the attention it should. Although being a clinician is a wonderful way to devote oneself to the welfare of others, unless care is taken to ensure that the rest of one’s life is fulfilling and balanced as well, one’s life becomes too narrow, limited, and eventually distorted. This can have negative impact not only on oneself but also on family life and other interpersonal relations, including one’s clients.
Keepin’ It Real
Authors: Carter Prudence L 
Published: November 2023

Abstract
How can we help African American and Latino students perform better in the classroom and on exams? In Keepin’ It Real: School Success Beyond Black and White, Prudence Carter argues that what is needed is a broader recognition of the unique cultural styles and practices that non-white students bring to the classroom. Based on extensive interviews and surveys of students in New York, she demonstrates that the most successful negotiators of our school systems are the multicultural navigators, culturally savvy teens who draw from multiple traditions, whether it be knowledge of hip hop or of classical music, to achieve their high ambitions.
School Success Has No Color
Authors: Carter Prudence L 
Published: November 2023

Abstract
Too often we adults take it for granted that we know what is best for children, and with the development and experience that come with age, we do. However, many of America’s schoolchildren are sending us a loud and clear message about some breakdowns in the mechanisms of schooling, especially when it comes to how culture is infused into the classroom and how culture influences social actions. The empirical analyses provided here probed the multiple connections between culture and identity among a specific group of low-income Black and Latino students and their particular responses to a structural phenomenon—a hierarchy of cultural meanings that they believed inheres in schools.