bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Diffusion Monte Carlo Method For Quantum Systems At Nonzero Temperatures
Authors: Coker D F , Watts R 0. 
Published: November 2023

Abstract
The Schrödinger equation in imaginary time is not the only equation which is isomorphic to the diffusion equation. One important example is the Bloch equation of quantum statistical mechanics, This equation may be solved for F, the Fourier transform of the equilibrium density matrix and, with additional analysis, it gives the probability of finding a quantum system at thermal equilibrium at temperature 1/ /3 in a volume element at a point r in a multidimensional configuration space. With an initial distribution of walkers representing F selected from a classical distribution at high temperature, the diffusion/birth/death procedure for simple diffusion QMC may be followed in time-equivalent /3 to determine distributions at lower temperatures. Many of the devices used for single-state calculations, including importance sampling, may be adopted without modification. Coker and Watts developed these basic algorithms and demonstrated the accuracy of the method for the one-dimensional harmonic oscillator and for the 0-H dimer treated as a Morse oscillator. They went on to generate quantum distributions for a low-density neon gas (two atoms in a periodic box) and the water dimer (confined to prevent dissociation). In each of these four cases, comparisons with results from alternate methods (such as matrix squaring, evaluation of Slater sums, and use of Feynman paths) showed excellent agreement and indicated the “general applicability of the random walk algorithm.”
Variational quantum Monte Carlo nonlocal pseudopotential approach to solids: Cohesive and structural properties of diamond
Authors: Fahy S , Wang X W , Louie S G 
Published: November 2023

Abstract
This paper describes one of the earliest applications of QMC techniques to solids. The calculations are variational calculations for the ground state of diamond, with comparison calculations for the carbon atom. The study introduces nonlocal pseudopotentials originally developed for density functional calculations at the LDA level and makes use of LDA single-particle wavefunctions in constructing the trial function. The trial wavefunction ‘1/JT is of the standard single-determinant Slater-Jastrow type for the valence electrons of the carbon atoms, adapted for a solid structure. The integrals required for evaluating the nonlocal potentials and the associated interactions contributing to the energy were calculated for each configuration using a simple but effective sampling procedure. Metropolis-style variational calculations with sampling based on ‘1/J} were carried out for 16 atoms (64 electrons) and 54 atoms (216 electrons) in diamond-lattice super cells with periodic boundary conditions. Energies were evaluated using Ewald sums. The results, for binding energy and for the lattice constant, gave excellent agreement with experiment. The energy minimum was found for a lattice constant within about 1% of the measured value, and the cohesive energy calculated for that lattice was 7.45(7) eV per atom, which is about one standard deviation from the experimental value of 7.37 eV per atom.
Optimized trial wave functions for quantum Monte Carlo calculations
Authors: Umrigar C J , Wilson K G , Wilkins J W 
Published: November 2023

Abstract
Although many of the diffusion QMC and variational QMC calculations of electronic structure used minimization of the variance in local energies to optimize trial functions in the decades before this paper was published, it provides useful examples of the advantages of the procedure. Even the first electronic structure calculations with importance sampling for molecular systems0 used trial wavefunctions optimized in this way for a fixed set of configurations. The paper reports optimizations of various combinations of determinants with Jastrow and exponential Pade functions for five two-electron systems from H- to Be2+ and for the four-electron Be atom. For the two-electron systems, the standard deviations in local energies could be reduced to a few millihartrees, and the errors in total energies could be reduced to as low as one microhartree. This corresponds to a recovery of more than 99.99% of the correlation energy. In the case of the Be atom, a four-determinant function with an exponential Pade correlation term and a total of 47 free parameters gave a standard deviation in local energy of 0.09 hartrees, a total energy only 1 millihartree above the “exact” energy, and recovery of 99% of the correlation energy. In later work, minimizations of combinations of variance and energy values for optimization have yielded slightly better results in some cases.
Parallel Monte Carlo calculations to determine energy differences among similar molecular structures
Authors: Traynor C A , Anderson J B 
Published: November 2023

Abstract
This study combines correlated sampling with Green’s function sampling in QMC for highly accurate calculations of potential energy differences among similar molecular structures. The method is exact for nodeless systems. It is illustrated with calculations for the molecular ion Ht to determine the minimum-energy structure and the potential energy surface in that region. The key to Green’s function sampling is the use of geometrically similar structures all related to a primary structure by a single length parameter. The movement of walkers in the secondary system (or systems) is geometrically similar to that in the primary, the electron configurations are geometrically similar, and the sampling of positions is completely correlated. Since the potential energies are not the same for secondary walkers, the multiplication terms V/ E differ, and the weights of secondary walkers diverge from those of the primary walkers as the calculations proceed. Division of secondary walkers with high weights, and elimination of those with low weights, is matched to that of the primary systems. Importance sampling may be incorporated with a single trial function or with scaled trial functions. The results for Ht showed the minimum energy structure for the equilateral triangle to be very close to 1.6500 bohr in side length. The calculations for 12 different structures at the same time required about the same calculation effort as for a single structure when scaled trial functions were used. Energy differences were obtained with high accuracy for structures differing by up to about 10% in size. For those differing more than about 10%, the accuracies in energy differences were much lower.
A quantum Monte Carlo calculation of the ground state energy of the hydrogen molecule
Authors: Traynor C A , Anderson J B , Boghosian B M 
Published: November 2023

Abstract
Since the wavefunction for the ground state of the hydrogen molecule has no nodes, its energy can be determined in QMC without node location error. This paper reports such calculations for the full four-body (two-electron, two-proton) problem to obtain the energy without the use of the Born-Oppenheimer approximation or any other adiabatic approximations. The calculations were carried out with diffusion QMC and with Green’s function QMC. Importance sampling was incorporated into each of the calculations. For the diffusion calculations, extrapolation of energies obtained at several different time-step sizes was required. For the Green’s function calculations there was no time-step error, and sign changes for walkers were avoided by use of a potential energy offset and a minor approximation to eliminate positive potential energies. The energies so determined were not exact but had extremely small systematic errors. 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.
Potential energy surfaces, quasiadiabatic channels, rovibrational spectra, and intramolecular dynamics of (HFh and its isotopomers from quantum Monte Carlo calculations
Authors: Quack M , Suhm M A 
Published: November 2023

Abstract
The hydrogen fluoride dimer (HF)2 is the simplest molecule exhibiting the phenomenon of a hydrogen bond. In this case, the hydrogen fluoride molecules are loosely held together by the relatively weak hydrogen bond to produce a floppy molecule with anharmonic vibrations not easily characterized, but producing an interesting and complex spectroscopy. In this paper, Quack and Suhm report the use of the diffusion QMC method in analyzing the behavior of the dimer and its isotopomers, and the successful prediction and assignment of spectral bands observed in their earlier experiments.a The DQMC calculations were carried out for nuclear motion on two different six-dimensional potential energy surfaces adjusted to reproduce experimentally measured spectra including anharmonic interactions between all vibrational modes. Two new QMC methods for calculating excited rotational and vibrational states were introduced: a clamped-coordinate quasiadiabatic channel and a centrifugal-energy approximation scheme. In general, quantitative agreement with experimental observations was obtained, and the success of DQMC methods in the prediction and analysis of the spectra of hydrogen-bonded systems was clearly demonstrated. 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.
Monte Carlo eigenvalue and variance estimates from several functional optimizations
Authors: Alexander S A , Coldwell R L , Monkhorst H J , Morgan J D 
Published: November 2023

Abstract
Optimization of trial functions by minimization of the variance in local energies began with early variational calculations by Frost,a Conroy/ and later by Coldwell.c Minimizing the variance in local energies clearly leads to VQMC and DQMC energies with a lowered statistical error, but as pointed out in this paper, there may be better choices of functionals to optimize. Ten different functionals, assembled from local energy and weighting terms, all giving emphasis in varying degrees to the variance in local energies and the average of local energies, were investigated, with low-lying states of He, H2, and Hj as example systems. The trial wavefunctions were simple compact functions including explicit r12 terms, with as many as 36 parameters total for He 3 S and 122 for Ht. Optimization for a fixed set of configurations was followed by VQMC calculations for the most promising trial functions generated. Minimizing the variance alone in the optimizations gave the lowest variance in energies for the VQMC results. Minimizing a combination of energy and variance in a form used by Conroyb gave the lowest energies in most but not all cases. The choice of functional was found to have a significant effect on the accuracy of VQMC calculations, and the best choice was found to be system dependent.
Computation of transition dipole moments by Monte Carlo
Authors: Barnett R N , Reynolds P J , Lester W A 
Published: November 2023

Abstract
The interest in QMC for calculating transition dipole moments is driven by the fact that these terms are very sensitive to the quality of the wave functions from which they are calculated. Wavefunctions giving excellent energies may lead to very poor transition moments. In this paper the authors report an investigation of several different approaches within the QMC area that might prove useful in calculating transition moments. The test case for comparisons is the transition dipole moment between the ls and 2px states of the hydrogen atom for which the value is known. The transition moment rmn is given by the expression where the sum is over all electrons, so that sampling must be based on the product of the two wavefunctions &lt;Pm&lt;Pn The authors devised three different ways to do this, with two based on VQMC and the third based on FN-DQMC. The last appears most successful. It requires a Green’s function averaging approach with configurtions for states m and n generated with probabilities proportional to ‘1/JT&lt;P, the product of trial and true wavefunctions, by independent guided walks. For points sampled from one distribution the Green’s function is averaged for points from the other distribution. The combination leads to a distribution with weights proportional to ‘1/Jr&lt;P from which the transition dipole is calculated. As demonstrated this method appears quite reliable and it was deemed to hold promise for larger systems.
Infinitesimal differential diffusion quantum Monte Carlo study of CuH spectroscopic constants
Authors: Belohorec P , Rothstein S M , Vrbik J 
Published: November 2023

Abstract
At the time this paper was written the heaviest atom that had been treated in all-electron QMC calculations was the fluorine atom. This study moved all the way to the copper atom in calculations for the diatomic molecule CuH. The technique used was a differential method introduced earliera by the authors. In this study the vibration-rotation spectroscopic constants for the molecule were determined from the first four derivatives of the total energy with respect to the internuclear distance evaluated at the equilibrium distance. With the aid of the Hellmann-Feynman theorem these were determined from the first four derivatives of the potential energy. The problem of differing time scales for the large-Z atom was solved by using a split-T method in which the electrons of Cu were divided into four groups according to their distances from the nucleus. Those in each group were moved with different time steps in the series 0.016 r, 0.040 r, 0.120 r, and T. The question of how to treat branching in diffusion QMC was avoided by eliminating branching altogether so that the treatment was equivalent to variational QMC. The parameter Twas varied to allow extrapolation to zero time-step size. The trial wavefunction for importance sampling was a minimal SCF function composed of Slater orbitals optimized at the experimental equilibrium internuclear distance to obtain a minimum variance in local energy. The calculations produced the vibration-rotation spectroscopic constants We, WeXe, and O:e and the dipole moment. These were found in reasonable agreement with experimental values, not as good as those of the best CI calculations of the time but quite good for the very simple trial function used. The use of better trial functions and investigation of means for combining branching with the split-T method were suggested.
An exact quantum Monte Carlo calculation of the helium-helium intermolecular potential
Authors: Anderson J B , Traynor C A , Boghosian B M 
Published: November 2023

Abstract
The first theoretical estimate based on quantum mechanics for the minimum in the potential energy of interaction of two helium atoms was published by Slater in 1928, 65 years before this QMC paper. In the intervening years some 50 other papers on the subject were published. None was very successful in predicting the well depth until counterpoise corrections were introduced to reduce the error caused by “basis set superposition,” a term first used for the helium-helium system. By 1991 the best of the counterpoisecorrected CI calculations gave well depths of about 10.93 K. These were obtained from energy differences in calculations for separated and for interacting atoms having errors of about 1200 K in the total energy. The QMC calculations were carried out using the “exact” cancellation methoda applicable to few-electron systems for which the node problem is solved exactly to obtain energies without physical or mathematical approximations beyond those of the Schrodinger equation. The remaining error, the statistical error in the total energy, was only 0.10 K. That was 1/12000 the error in the total energy for the CI calculations.
Introduction To Ancient Scholarship
Authors: Dickey Eleanor 
Published: November 2023

Abstract
For Almost Four Thousand Years, The Peoples Living around the Mediterranean have been attempting to improve their ability to understand ancient texts by systematic study of their language, context, and textual tradition. The Greeks seem to have come to this practice relatively late in comparison with Near Eastern civilizations such as that of the Babylonians, who produced dictionaries of Sumerian in the second millennium bc. The earliest traces of Greek scholarship can be found in the fifth century bc, when philosophers and rhetors began thinking and writing about language in a way that led towards systematic linguistic scholarship and when attempts to explain Homer to schoolchildren resulted in the earliest ancestors of some of our scholia. In the fourth century Plato and Aristotle continued to think systematically about language, while the establishment of an official text of the Athenian tragedies showed a new concern for textual authenticity and the creation of texts like that preserved on the Derveni papyrus showed the development of exegesis. The Stoic philosophers also made important observations about the Greek language that laid much of the foundation for the later grammatical tradition. The real beginning of Greek scholarship in our sense of the term, however, occurred with the foundation of the library and Museum at Alexandria in the early third century bc, and for centuries the librarians and other scholars there were the most important Greek scholars. By the first century bc noted grammarians, lexicographers, and textual critics could be found in many parts of the GrecoRoman world, and scholarship was a flourishing and highly respected profession. These ancient scholars brought to their work a host of advantages that their modern counterparts lack: native-speaker fluency in ancient Greek, access to vast numbers.
Reader
Authors: Dickey Eleanor 
Published: November 2023

Abstract
The purpose of this chapter is to provide practice in reading scholarly Greek. In order to derive maximum benefit from it, readers are advised to work systematically through one or more of the four sections, writing out a translation of each selection and checking it against the key in 5.2 before proceeding to the next selection. Extracts are arranged here by the type of skills required to read them, not by the criteria governing the arrangement of Chapters 2 and 3, and the sections have been arranged in ascending order of difficulty: lexica are on the whole the easiest ancient scholarship to read, while grammatical treatises are the most difficult. Further selections from each group, without key, are provided in 5.3 for use as class assignments or for extra practice. Not all texts discussed in Chapters 2 and 3 are represented here. Owing to space limitations, all that has been attempted is inclusion of some selections from each major type of scholarly material. Some classes of material, however, have been systematically excluded: in addition to fragmentary, lacunose, or corrupt texts, commentary that is primarily philosophical, mathematical, or scientific in nature has been omitted, on the grounds that reading such material requires different skills from the ones it is the purpose of this book to provide. Metrical commentary is likewise omitted, because Hephaestion’s treatise and Van Ophuijsen’s translation of it (1987) already offer a good introduction to reading Greek metrical work. The selections presented here aim to provide a representative view of the type of material found in each category, and therefore some of them contain ancient scholars’ errors. No attempt has been made to select the most important or profound passages from each text; these are rarely self-explanatory enough to be appropriate here and have in any case usually been discussed and translated elsewhere. Examples are presented in exactly the form in which they appear in the editions cited, and there is consequently no consistency in the use of symbols, abbreviations, types of sigma, etc. Any symbols or notations the editors added to the text itself have been included, although those in the margins and apparatus.
Moving From Dis-ease to Disease
Authors: Ford Emily , Liebowitz Michael R , Andrews Linda Wasmer 
Published: November 2023

Abstract
I recall walking through the automatic doors at the super-market as a little girl, feeling a compelling urge to touch the floor before my mother picked me up and propped me in the seat of the shopping cart. I needed a plan, and the one I finally hit upon was fixing my sandal while casually allowing my fingers to brush the floor.
The Anatomy of Normal Sadness
Authors: Horwitz Allan V , Wakefield Jerome C 
Published: November 2023

Abstract
Sadness traditionally has been viewed as humanity’s natural response to deaths of intimates, losses in love, reversals of fortune, and the like. It arises, as Shelley says, because “the world’s wrong!”1 And, when the losses and strains that evoke the sadness are profound, the resulting emotions can also be severe, seeming to defy expression. In Samuel Coleridge’s words: A grief without a pang, void, dark, and drear, A stifled, drowsy, unimpassioned grief, Which finds no natural outlet, no relief, In word, or sigh, or tear.
The Rise of Antidepressant Drug Treatments
Authors: Horwitz Allan V , Wakefield Jerome C 
Published: November 2023

Abstract
The DSM-III’s neutral stance toward the etiology of mental disorders meant that advocates of all treatment orientations were supposed to find equal value in its symptom-based classification system. In practice, how­ ever, pharmaceutical companies were best able to capitalize on the DSM’s focus on symptoms, which allowed them to broadly construe states of intense sadness as depressive disorder and thus to vastly increase the potential market for anti­ depressant medication. Several other developments helped propel an explosive growth in the use of these drugs, including the emergence of the selective serotonin reuptake inhibitors (SSRis) in the late 1980s, the spread of managed care throughout the U.S. health care system in the 1990s, and the approval of direct-to-consumer (DTC) advertisements in 1997. This chapter considers the relationship between the DSM revolution and the roughly contemporaneous exponential growth of drug treatments for depression.
Infatuation: A Madness Most Discreet
Authors: Barusch Amanda Smith 
Published: November 2023

Abstract
At the age of 88, Ted is the picture of health. Tall and slim, he swims regularly and has demonstrated his yoga abilities on television. Located in a quiet residential neighborhood, his home speaks of neglect. There is a sadness about him too—an air of lonely regret, sometimes disguised by a frenzy of thought and movement. When painful topics came up, Ted dashed to his piano to play a tune. We met for two 3-hour sessions, and he never seemed to tire. The story that unfolded was one of repeated infatuations.