bluuebunny/crossref_metadata_2025 huggingface dataset:
Quantum Monte Carlo with model potentials for molecules
Authors: Yoshida T , Miyako G
Published: November 2023

Although simple model potentials lack the solid theoretical basis that justifies nonlocal pseudopotentials, they have been used with moderate success in replacing the core electrons in analytic variational calculations and in diffusion QMC calculations. For this paper, a model potential of long standing, proposed by Bonifacic and Huzinagaa in 1974, was investigated in calculations of dissociation energies for the molecules CO, HCl, Na2, and K2, The model potential has an especially simple form for the effective field of the core electrons based on core orbitals. The valence electrons are treated explicitly with Hartree-Fock orbitals used in determinantal trial functions for importance sampling and node location. The numbers of valence electrons treated were: CO, 10; HCl, 8; Na2, 2; K2, 2. In each case, the calculated dissociation energy was found to be accurate to within a few percent of the experimental value and much more accurate than either all-electron or model-potential Hartree-Fock calculations. Despite concerns about its justification, the method appears to be surprisingly successful.
Optimization of quantum Monte Carlo wave functions using analytical energy derivatives
Authors: Lin X , Zhang H , Rappe A M
Published: November 2023

The optimization of parameters in trial wavefunctions by minimizing the variance in local energy was used for some of the earliest variationala and diffusionb QMC calculations, and it has been used ever since by most practitioners of QMC. Perhaps the best known examples are given in the paper by Schmidt and Moskowitzc for optimizing their nine-parameter Jastrow functions for first-row atoms. An alternative method of optimization, leading to lower variational energies for these atoms, is reported in this paper.
Monte Carlo calculation of the Born-Oppenheimer potential between two helium atoms using Hylleraas-type electronic wave functions
Authors: Coldwell R L , Lowther R E
Published: November 2023

Solution of the Schrödinger equation using the Rayleigh-Ritz variational method in combination with numerical integration was introduced as early as 1942 by Frost.a Conroyb added the Monte Carlo aspect with random selection of points in the configuration space of electrons for molecular systems. This paper and a related paperc by the same authors reported calculations similar to those of Conroy using variational QMC to determine the electronic structure of the helium dimer. Along with this Coldwell and Lowther introduced the idea of correlated sampling for such Monte Carlo variational calculations. They used a “biased selection” procedure to select 6400 points from an approximate ψ2 distribution for evaluation of local energies and calculation of the expectation value of the energy for four internuclear distances. The trial functions were anti-symmetrized products of two Hylleraas atomic-helium functions in combination with an exponential term containing dipole-dipole and dipole-quadrupole interaction terms. The energies obtained with reasonably good trial functions gave expectation values of the energy well below the Hartree-Fock limit and in agreement within their fairly large uncertainties with experimentally based estimates of the interaction energies for two helium atoms.
Diffusion Monte Carlo study of circular quantum dots
Authors: Pederiva F , Umrigar C J , Lipparini E
Published: November 2023

Several QMC calculations had earlier treated quantum dots of various shapes and sizes by either variational or diffusion methods. This study extended much farther, with ground and low-lying excited states for circular two-dimensional dots with 2 to 13 electrons. The method was fixed-node diffusion QMC with importance sampling. Comparisons were made with Hartree-Fock and density functional calculations at the LSDA level. The system treated was a standard circular quantum dot with N electrons confined in two dimensions by a parabolic potential V = ½kr2 centered at the origin. The masses, dielectric constants, and the potential energy constants were specified as those for a GaAs crystal. Atomic units were replaced by effective atomic units. Anti-symmetry rules were the same as for atomic systems. Trial functions were expressed for each case as sums of one to five Slater determinants from density functional calculations, along with elaborate generalized Jastrow functions. The coefficients required for satisfying cusp conditions were different from those usually found for three-dimensional problems. A total of 23 cases with different numbers of electrons and L, S eigenstates were treated. The first version of the paper contained a few errors. Corrected results (also with lower uncertainties) were reported in a second version.0 In all cases the diffusion QMC energies were lower than the variational QMC energies, which were in turn lower than the HF energies. Fixed-node error was expected to be small. The differences from LSDA density functional energies were small but not negligible.
Elucidating the role of many-body forces in liquid water. I. Simulations of water clusters on the VRT(ASP-W) potential surfaces
Authors: Goldman N , Saykally R J
Published: November 2023

In the quest for a quantitative simulation of liquid water it appears the potential energy of the interaction of water molecules converges very rapidly and may be described adequately by only two- and three-body terms. Measurements of vibration-rotation tunneling (VRT) splittings for water dimers have provided data for fitting an anisotropic site potential with Woermer dispersion (ASPW) to provide a series of highly detailed potential energy surfaces. The expressions for these surfaces include terms corresponding to electrostatic interaction, two-body exchange repulsion, two-body dispersion, and many-body induction. In this paper the authors report an investigation of the suitability of these surfaces and several others for predicting the vibrational ground-state properties of water clusters ranging from the trimer to the hexamer. The calculations were carried out with diffusion Q:tvIC to determine cluster properties, the structures and, in particular, the vibrational average rotational constants for direct comparison with experimentally measured values. The ground-state properties were determined in runs for 1000 walkers with 15,000-20,000 time steps after equilibration. Histograms of configurations were used for calculating the internal tensors leading to the rotational constants.
A ground state potential energy surface for H2 using Monte Carlo methods
Authors: Alexander S A , Coldwell R L
Published: November 2023

Although more accurate values of ground-state electronic energies of the clamped-nucleus H2 molecule have been obtained in analytic variational calculations with explicitly correlated wavefunctions, the Monte Carlo variational calculations reported in this paper provide a useful alternative to analytic calculations. Aside from confirming energies, they may be used in straightforward and simple independent calculations of the quantities needed for nonadiabatic diagonal corrections, relativistic corrections, and radiative corrections to the Born-Oppenheimer potential energy curve. The trial functions used were symmetric exponential functions of products of electron-electron and electron-nucleus distances with integer exponents and up to 128 adjustable parameters optimized to minimize a combination of the energy and its variance. The calculations were carried out for 24 internuclear distances in the range of 0.2 to 10.0 bohr, and they gave energies typically 1-3 microhartrees above analytic variational values with uncertainties typically less than 1 microhartree. Most interesting are the correction terms, which are not variational and were found to confirm earlier values within 1 microhartree. Binding energies calculated for several vibration-rotation levels of H2 using the calculated potential energy curve were found in excellent agreement with those determined from spectroscopic measurements. The authors proposed that the Monte Carlo techniques used be generalized to larger systems for which analytic integrations are much more difficult.
Scheme for adding electron-nucleus cusps to Gaussian orbitals
Authors: Ma A , Towler M D , Drummond N D , Needs R J
Published: November 2023

The trial wavefunction for importance sampling in a diffusion QMC calculation for an atom or molecule has most often been assembled from a Slater determinant or a sum of determinants multiplied by a Jastrow function. The determinantal part is readily obtained from easy-to-use quantum chemistry programs which make use of Gaussian basis sets. The programs take advantage of the analytic integrals available for Gaussian exponentials, but these functions fail to give a good fit to realistic one-electron orbitals and produce large fluctuations in the local energy near the electron-nucleus cusps. One solution to the problem has been to fit the Gaussian functions to simple exponentials, adjust them to satisfy the cusp condition, and use them in the determinantsa. In this paper a new scheme, having the advantages of an automatic procedure and avoiding some of the earlier problems is reported. In this scheme a part of each s-type Gaussian function </J(r) is replaced by a new function ¢ (r) which depends on exp[p(r)] in which p(r) = Do+ a1r + D2r2 + D3r3 + D4r4. Theconstants Di and others are adjusted to fit first and second derivatives to </J(r), to satisfy the cusp condition, and to optimize the behavior of the local energy. This is accomplished analytically. The scheme was investigated in detail with VQMC and fixednode DQMC for the atom Ne and the molecule H2. Calculations were also made for the 55 molecules of a standard test set. Improvement in the standard deviation in local energy, relative to that for no cusp correction, was dramatic. In the VQMC calculations for the test set the standard deviation in individual local energy was reduced by a factor of 2 to 5 for most molecules. This corresponds to a reduction by a factor of 4 to 25 in calculation effort for a fixed statistical error. Total energies were found to be slightly reduced.
Quantum chemistry by random walk: Linear HS
Authors: Mentch F , Anderson J B
Published: November 2023

This is first of three papers published in 1984 which report calculations for the system H-H-H in a symmetric linear configuration matching the expected saddle point for one of the most basic chemical reactions, the exchange reaction H + H2 -+ H2 + H. In this case, the calculations were fixed-node diffusion calculations, with importance sampling made with four different types of trial functions specifying the nodal structure. Each included simple electronelectron correlation terms. The functions were optimized by minimizing the variance in the local energy H’¢T / ‘¢T using a simplex routine. The lowest energy result obtained for the minimum in the barrier to reaction was -1.6582 ± 0.0003 hartrees, corresponding to a barrier height of 10.2 ± 0.2 kcal/mol relative to the exact minimum for separated H + H2, This value was slightly below the upper bound of 10.28 kcal/mol established in analytic variational calculations and about 0.6 kcal/mol above the expected value. The difference was attributed to node location error.
Quantum Monte Carlo study of the classical barrier height for the H + H2 exchange reaction: Restricted versus unrestricted trial functions
Authors: Reynolds P J
Published: November 2023

In this fixed-node calculation with importance sampling for the H-H-H system, the authors investigated the use of several single determinant SCF trial functions and the effects of restricting the orbital coefficients. The true wavefunction must have identical coefficients for a and (3 electrons, but in variational calculations, the use of unrestricted spin-orbitals (allowing different coefficients) leads to energies lower than (or at least as low as) those for restricted spin-orbitals (requiring identical coefficients). This has been observed in variational QMC calculations for H-H-H. However, in fixed-node diffusion calculations, in which the energies depend only on node locations, the authors found a lower energy for restricted trial functions. For the barrier they obtained an energy of -1.6590 ± 0.0004 hartrees, a value lower than the lowest CI energy at the time, and only 9.69 ± 0.25 kcal/mol above that for separated reactants. This value is an upper bound to the barrier height, but within its uncertainty it overlaps the best recent valuea of 9.608 ± 0.001 kcal/mol.
Quantum chemistry by random walk: A faster algorithm
Authors: Anderson J B
Published: November 2023

This little paper describes two procedures for achieving higher speeds in fixed-node diffusion QMC calculations with importance sampling. The first is an iterative procedure for reducing timestep error, thereby allowing larger and fewer time steps to obtain a given accuracy. The movement of a walker is divided into two parts: a diffusion step selected at random from an appropriate distribution and a drift step calculated from the drift velocity at the initial location. These give a temporary step to a new location for which the drift velocity is again determined. The average of the two velocities together with the original diffusion step is used to determine a permanent step. In tests, the procedure was found to reduce time-step error by a factor of 5 to 10. The second procedure makes use of two trial functions for importance sampling, the first a simple function for walker motion and the second a more complex and more accurate function for determining energies. These allow the more computationally expensive function to be used at large intervals for samples having a lower serial correlation.
Quantum simulation of systems with nodal surfaces
Authors: Coker D F , Watts R 0.
Published: November 2023

Coker and Watts reported modifications of the simple diffusion QMC algorithm to treat the problem of node location in small systems. This enabled the calculation of low-lying states for a vibrating diatomic molecule as well as electronic structures for H 2p, He 3S, and Li 1S. The general method makes use of cancellation of positive and negative walkers occupying the same volume elements of a grid in the coordinate space of the walkers, together with appropriate constraints to prevent decay to a lower-energy solution. In the case of molecular vibration, orthogonality to lower states was enforced by maintaining equal weights of positive and negative walkers in equivalent regions of coordinate space for lower states. For the case of fermion ground states for He 3  S and Li 1  S, equal weights of positive and negative walkers were required for all coordinate space. For the higher dimensionality of the Li case, cancellation was based on proximity of walkers of opposite signs. Results in terms of energy were accurate to about three digits and within their uncertainties overlapped accepted values for each of the systems investigated. These provided a hint of more accurate results to be obtained later for small systems.
Quantum chemistry by quantum Monte Carlo: Beyond ground-state energy calculations
Authors: Reynolds P J , Barnett R N , Hammond B L , Grimes R M , Lester W A
Published: November 2023

The paper describes several extensions of fixed-node diffusion in the areas of obtaining analytic derivatives of the energies of molecules, calculating expectation values for quantities other than the energy, and treating excited states. The calculation of energy derivatives is illustrated with a calculation of the first derivative of the energy of the ground state of H2 with respect to the internuclear distance, without using finite differences. With importance sampling the energy is obtained from a weighted average of local energies expressed in analytic form. These may be differentiated to obtain their derivatives with respect to any of several variables, including the internuclear distance, and their weighted averages may be used to determine the desired derivatives. The results for the H2 energy derivatives were in agreement with independent determinations. For calculation of expectation values of the energy, sampling of the (true wavefunction)(trial wavefunction) ‘1/J’l/Jr distribution is sufficient, but other quantities usually require sampling the ‘ljJ2 distribution, which is not so readily available in QMC calculations. Extrapolations of ‘!/Jf and ‘ljJ’l/Jr results, from variational and diffusion calculations, to ‘!jJ2 results are illustrated for various expectation values for the case of ground-state H2.
Quantum chemistry by random walk: Methane
Authors: Garmer D R , Anderson J B
Published: November 2023

The methane molecule has served as a test case for a lengthy series of electronic structure calculations beginning in 1941 with approximate Hartree-Fock calculations and an energy of -39.47 hartrees, reaching in 1973 to 81% of the correlation energy with extended-basis CI calculations at -40.4584 h, and going much further with this paper in 1987 to 97% of the correlation energy with fixed-node diffusion QMC calculations at -40.506 h. The calculations were carried out by the fixed-node diffusion method with drift, making use of importance sampling with a single determinant trial function based on double-zeta Slater-type orbitals, along with a simple Jastrow function. This function was optimized to minimize both the energy and the variance of the local energy. Time-step error was investigated in detail with six different time-step sizes down to 0.0005 h-1, giving nearly straight line behavior. The calculated energy at -40.506(2) hartrees and 97% of the correlation energy was 31 kcal/mol lower than the lowest analytic variational energy at the time and only 5 kcal/mol above the experimental nonrelativistic energy.
The Diffusion Monte Carlo Method For Quantum Systems At Nonzero Temperatures
Authors: Coker D F , Watts R 0.
Published: November 2023

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

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

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

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

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

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

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

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 <Pm<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<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<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

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

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

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

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

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

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

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

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.
Rituals, Routines, and Recovery: Living With OCD
Authors: Kant Jared Douglas , Franklin Martin , Andrews Linda Wasmer
Published: November 2023

It was during my junior year of high school that I experienced the most horrific and terrifying obsessions. These intrusive thoughts included images that superimposed themselves upon the world around me like an acetate overlay. For instance, in the middle of a conversation with my best friend, Corrine, I would suddenly see myself burying a hatchet into her chest. It was the most terrifying thing I could think of, since I loved Corrine (and still do to this day). Yet this sort of image kept coming back at random times, and when it did, it left me shaking.

I also developed a fear that if I didn’t tell my therapist every single thing I had done the entire day, it would turn out that I had omitted the part where I killed someone and left the body in the woods. To my knowledge, I’ve never actually killed anyone, and I’ve certainly never left a dead body in the woods. But the thought kept returning. This was my OCD telling me that I had done something I found morally reprehensible.
A Round Universe
Authors: Burns Jennifer
Published: November 2023

Spotlights crisscrossed the sky as Ayn and Frank drove toward Hollywood for the long-awaited debut of the movie The Fountainhead in June 1949. While it was being shot Rand had been on the set almost daily, making sure the script she wrote was not altered. She paid special attention to Roark’s courtroom speech. When King Vidor, the director, tried to shoot an abridged version of the six-minute speech, the longest in film history, she threatened to denounce the movie. Jack Warner joked later that he was afraid she would blow up his studio, and he told Vidor to shoot it as written. Rand also successfully battled film censors in the conservative Hays Office, who objected as much to her individualistic rhetoric as the movie’s racy sexuality. But even Ayn Rand was no match for the Hollywood hit machine. At the movie’s starstudded premiere she was devastated to discover the film had been cut, eliminating Howard Roark’s climactic declaration, “I wish to come here and say that I am a man who does not exist for others.”
Between A “Soft” and A “Hard” Place
Authors: Carter Prudence L
Published: November 2023

Soon-to-be high-school graduate Maxwell Tucker, speaking rather pointedly and anecdotally as he reflected on his school experiences with me one evening at his home, presented a picture of his high-school world that was consistent with reports from scholars, researchers, and journalists. Girls are outperforming boys in the classroom (Jacobs 1996; Lewin 1998; Mickelson 1989). Whether they are actually smarter remains to be seen; there are no proven differences in intelligence between the sexes. Still, research shows that throughout their scholastic careers, girls perform better in subjects that require verbal competence. Although studies show that boys do better than girls in math and science (Catsambis 1994; Maccoby and Jacklin 1974; Nowell and Hedges 1998; Stevenson and Newman 1986), overall, girls have higher grade point averages and college attainment rates (Jacobs 1996; Mickelson 1989).
Models of Social Work Supervision
Authors: Brittain Charmaine R
Published: November 2023

Child welfare supervision models reflect the nature of social work itself; they come from a blending of models from various disciplines, which result in models compatible with the nature of child welfare supervision. As social work and, more specifically, child welfare has become more professional and standardized rather than ad hoc, so has supervisory practice. This chapter explores models of supervision that may help to guide such practice.

Models help us make sense of our world by providing a framework for explaining behavior, phenomena, or objects. A model makes generalizations about observations of events or behavior and consists of an interrelated, coherent set of ideas and concepts that coalesce to promote understanding of events or behavior and thus offer implications for a course of action. Use of a model provides a broader understanding of supervision so that the practice of supervision can occur more effectively (Kadushin, 1976; Tsui, 2005). A model is distinguished from a philosophy of practice, which is a supervisor’s personal and professional integrated belief system that guides both supervisory and case practice (Munson, 2002). In this chapter, we present brief information about various models that guide social work supervision, to provide grounding for our understanding of supervision in child welfare. A fuller and more thorough analysis can be found in Tsui (2005) or Kadushin and Harkness (2002).
Working In Changing Environments
Authors: Cahn Katharine , Berns David
Published: November 2023

Child welfare services are in a state of constant change. In fact, it might be said that change is the only constant in child welfare. New practices, new programs, and changes in organizational structure and policy, both planned and unplanned, are constant and often overlap. It is this ongoing change that makes the field interesting as it evolves over time to better meet the needs of children and families. Change can be a source of new energy, new resources, and increased effectiveness. But the constant pace of change can also be a source of stress. When poorly managed, change at this pace can be distracting, confusing, and even upsetting to child welfare staff. Managing change processes well is key to effectiveness as a child welfare supervisor.

This chapter explores change in two ways. The first part introduces a basic understanding of the dynamics of change in child welfare organizations. The second part reviews seven aspects of the supervisor’s role in managing change. The reader should finish the chapter with a thorough appreciation of the importance of the child welfare supervisor in understanding and managing change, having reviewed the areas where the supervisor can make a difference and encountered practical suggestions for managing change successfully to the benefit of children and families.
Help of All Kinds
Authors: Silverman Phyllis R , Kelly Madelyn
Published: November 2023

After a death in the family, you and your children find yourselves in a frightening and surreal situation, almost like waking up in an altered universe. Even if the death was anticipated, that element of surprise is still there. The life you were leading has collapsed, and now you have to dig yourselves out of the rubble. Overwhelmed by events, and lacking knowledge and perspective, you will need all the help you can get to feel supported and whole, to cope more effectively, and to deal with your changed and changing world. Help is out there, but too often, you won’t know what you need, or how to get it.
Looking Back, Looking Ahead
Authors: Silverman Phyllis R , Kelly Madelyn
Published: November 2023

In the years after the death of a loved one, you learn to accommodate your pain and loss as you and your children adjust to your new reality. Sometimes it might even be hard to remember what it was like before the death when you were all together. Over time, feelings become clearer and the pain, while still real, is not as intense as before. You have not “recovered,” you have not “gotten over it,” but you are rebuilding a life. Ten years after Dale’s death, his father tries to describe this delicate balance: