bluuebunny/crossref_metadata_2025 huggingface dataset:
The Victorious Life
Authors: Marsden George M
Published: November 2023

“Indeed, within the last twenty years,’’ C. I. Scofield observed in 1899, “more has been written and said upon the doctrine of the Holy Spirit than in the preceding eighteen hundred years.” Scofield’s estimate, which appeared in his own work on the Spirit, was not implausible.2 During the preceding decades the movements known in the twentieth century as “Holiness,” “Pentecostal,” and “fundamentalist” had been taking shape and each had a common origin in the resurgence of interest in the Holy Spirit that was sweeping American evangelicalism.
Fundamentalism as an Intellectual Phenomenon
Authors: Marsden George M
Published: November 2023

Clarence Darrow said in Dayton that his intention was to prevent “bigots and ignoramuses” from controlling the schools. This view of the fundamentalist intellect would continue to prevail in the liberal community. Stewart Cole populated his History of Fundamentalism with “religiously disturbed” defenders of “antiquated beliefs,” contending against “open-minded seekers for the truth that makes man free.” According to H. Richard Niebuhr “inadequate development of educational institutions” and “the distrust of reason and the emphasis on emotion” resulted from the isolation, poverty, and hardships of farm life.
Fundamentalism as an American Phenomenon
Authors: Marsden George M
Published: November 2023

In many respects fundamentalist Christianity was not unique to America. It had affinities with revivalist and pietistic movements around the world, and was often successfully propagated overseas by its vigorous missions. Yet almost nowhere outside of America did this particular Protestant response to modernity play such a conspicuous and pervasive role in the culture.
Of Genius, Fire, And Plague
Authors: Christianson Gale E
Published: November 2023

Newton Had No Sooner Graduated From Cambridge Than He was forced to leave the university and return to Woolsthorpe, though not of his own choosing. In London, where the city’s rapidly increasing population had reached half a million by 1660, people were suddenly taken ill. The disease began with a severe headache and dizziness, followed by trembling in the limbs, swelling under the arms and in the groins, raging fever, and, finally, telltale dark splotches on the skin, which the widely read London cleric Thomas Vincent described as “tokens of near approaching death. Within a few hours they must go down into the dust.”
“Kindling Coal”
Authors: Christianson Gale E
Published: November 2023

As Curator Of Experiments For The Royal Socrnty, Robert Hooke was given the considerable task of confirming Newton’s findings with prisms. No portrait of Hooke survives, hut the diary writer Samuel Pepys observed that he “is the most and promises the least of any man in the world I ever saw.” Of medium stature, Hooke suffered from a bent spine; his large head, dominated by bulging gray eyes, seemed too big for his body. A pale complexion and fixed stare created the impression of one detached and unaware of his surroundings. Taking pity on his misshapen friend in print, the biographer John Aubrey felt compelled to add of Hooke, “He haz a delicate head ofhaire, hrowne, and of an excellent moist curle.”
Formulating a Treatment Plan: A Multidimensional Approach
Authors: Lee Mo Yee , Ng Siu-Man , Leung Pamela Pui Yu , Chan Cecilia Lai Wan
Published: November 2023

Integrative Body–Mind–Spirit Social Work uses the metaphor of a “healing wheel” to describe a multidimensional orientation in treatment. The conceptual framework of a multidimensional treatment orientation is based on our clinical experiences as well as assumptions about the multidimensional and interconnected nature of human beings, problem contexts, and reality. We affirm the body–mind–spirit connection within an individual and the person-in-environment perspective in providing treatment. The healing wheel idea is graphically illustrated in Figure 4.1.
From the Body to the Mind and Spirit
Authors: Lee Mo Yee , Ng Siu-Man , Leung Pamela Pui Yu , Chan Cecilia Lai Wan
Published: November 2023

Holistic health is the result of a balanced and integrated body, mind, and spirit. As the body functions as a system, change in one of the components affects the others. Traditional social work and counseling approaches emphasize working through the mind; the body component is less emphasized. This chapter intends to place importance on working on and through the body in order to illustrate how work on the body, mind, and spirit can be linked together.
The Efficacy of the Integrative Body–Mind–Spirit Group and Social Support Group on Female Breast Cancer Patients
Authors: Lee Mo Yee , Ng Siu-Man , Leung Pamela Pui Yu , Chan Cecilia Lai Wan
Published: November 2023

Breast cancer is the most common form of cancer diagnosed among women in Hong Kong (Hong Kong Cancer Registry, Hospital Authority, 2004). Not only is breast cancer a menacing threat to physical health, but it also disrupts the harmony of our physical bodies, our emotions, and our spiritual well-being. Unfortunately, rarely is the disruption confined to just the physical level. Emotional health consequently deteriorates and threatens our spiritual beliefs, values, and meanings of life.
Meditation and Treatment of Female Trauma Survivors
Authors: Lee Mo Yee , Ng Siu-Man , Leung Pamela Pui Yu , Chan Cecilia Lai Wan
Published: November 2023

Posttraumatic stress disorder (PTSD) became a formal diagnosis included in DSM-III only in 1980 on account of the organized efforts of Charles Figley, Chaim Shatan, and other advocate groups for veterans and trauma survivors. Trauma has pervasive and devastating impacts on individuals. Trauma survivors, especially those with prolonged histories of interpersonal abuse, typically suffer from other “co-morbid conditions.” These include, but are not limited to, diagnoses related to substance abuse problems, mood disorders (e.g., depression and manic-depressive disorders), and dissociative identity disorder (Mueser et al., 1998). According to the “self-medication” hypothesis (Khantzian, 1990), people drink to cope with negative emotions and stressors. PTSD clients also have unusually high utilization rates of psychiatric services. Macy (2002) examined records of 384,000 Medicaid recipients in Massachusetts between 1997 and 1998 and reported that PTSD and depression were the most common psychiatric diagnoses among this population. Patients with a PTSD diagnosis spent 10 times as much time in the hospital as patients with a diagnosis of depression only.
Cognitive-Behavioral Therapy With Posttraumatic Stress Disorder An Evidence-Based Approach
Authors: Vonk M Elizabeth , Bordnick Patrick , Graap Ken
Published: November 2023

Posttraumatic stress disorder (PTSD) occurs worldwide among people of all ages who experience traumatic events. The events, in which severe injury or threat of injury and death occur, may be natural disasters, such as earthquakes, or manmade, including war, automobile accidents, and crime. While most people are likely to experience some form of traumatic experience in their lifetimes, not all go on to develop PTSD. In fact, estimates of the lifetime prevalence vary widely, from 9% of the general population to 30% or more of those exposed to particular traumas such as rape, combat, or disaster (Keane & Kaloupek, 2002). In addition, several conditions are often comorbid with PTSD, including depressive and other anxiety disorders and substance abuse. Several risk factors for the development of PTSD have been identified, including female gender, history of prior psychiatric problems or abuse, and unavailability of social support (Brewin, Andrews, & Valentine, 2000). Furthermore, characteristics of the trauma itself— the severity of the trauma, the person’s sense of control over the outcome and extent of injury, and the degree of actual loss—may increase the rate of PTSD development. In general, men are more likely to be exposed to trauma related to war, and women’s exposure is more likely to be related to rape or assault.
Disciplining the Body, Disciplining the Will: Hypocrisy and Asceticism in Cistercian Monasticism
Authors: Newman Martha G
Published: November 2023

In the second decade of the thirteenth century, Goswin, a monk in the Cistercian abbey of Villers in the Brabant, celebrated the holy life and death of the Cistercian lay brother Arnulf by writing Arnulf’s vita. Goswin hardly knew Arnulf. As a lay brother, Arnulf had lived a life distinct from Goswin and the other choir monks: lay brothers did most of the manual labor and estate administration, and, as a result, they performed a shortened liturgy and often resided in granges some distance from the monastery. Goswin’s knowledge of Arnulf derived primarily from information provided by another monk ofVillers, but he nonetheless adopted a narrative stance that implied an intimacy with his subject.1 According to Goswin, Arnulf took advantage of the materials around him­ including bushes with thorns or prickly leaves, metal implements, horse hair, and hedgehog pelts supplied by the monastery’s shepherds-to fashion instruments of self.torture with which he scourged his body.
Crafting “Nearly Self-enforcing” Agreements
Authors: Susskind Lawrence E , Cruikshank Jeffrey L
Published: November 2023

Getting to a plan, and reaching tentative agreement on that plan, is most of the way toward successful consensus building. In many cases, though, it’s not all the way. The consensus-building group still has to worry about challenges during the implementation phase of the process. Briefly stated, the group has to anticipate potential obstacles to implementation, and build into their agreement ways for responding to those obstacles. Otherwise, the agreement may be too brittle to hold up under pressure. Put more positively, the group has to make sure that their agreement is robust, so that when the inevitable pressures come to bear, the agreement is up to the challenge. We use the phrase “nearly selfenforcing” to describe such an agreement. In other words, the package should be structured in such a way that all the constituent groups would rather see it succeed than fail. They don’t need some superior authority rapping their knuckles to make them keep their promises. They are all pulling in the same direction, because they know that’s where their own best interests lie. And since no one can predict the future with any certainty, each agreement has to provide ways for people to get back together and fix the agreement if and when the unexpected happens.
Quantum Monte Carlo
Authors: Anderson James B
Published: November 2023

Monte Carlo methods are a class of computational algorithms for simulating the behavior of a wide range of various physical and mathematical systems (with many variables). Their utility has increased with general availability of fast computers, and new applications are continually forthcoming. The basic concepts of Monte Carlo are both simple and straightforward and rooted in statistics and probability theory, their defining characteristic being that the methodology relies on random or pseudo-random sequences of numbers. It is a technique of numerical analysis based on the approximate solution of a problem using repeated sampling experiments and observing the proportion of times a given property is satisfied. The term Monte Carlo was first used to describe calculational methods based on chance in the 1940s, but the methods themselves preceded the term by as much as a century. Quantum Monte Carlo (QMC) first appeared in 1982 and similarly was preceded by development of the related calculational methodology. The success of QMC methods over the past few decades has been remarkable, and this book will clearly demonstrate that success in its discussion of applications. For isolated molecules, the basic material of chemistry, QMC methods have produced exact solutions of the Schroedinger equation for very small systems and the most accurate solutions available for very large systems. The range of applications is impressive: folding of protein molecules, interactions in liquids, structure modeling in crystals and enzymes, quantum dots, designing heat shields and aerodynamic forms, architecture, design, business and economics, and even cinema and video games (3D modeling). This book takes a similar approach to Henry Schaefers classic book Quantum Chemistry (OUP, 1984 now a Dover edition), collecting summaries of some of the most important papers in the quantum Monte Carlo literature, tying everything together with analysis and discussion of applications. Quantum Monte Carlo is a reference book for quantum Monte Carlo applications, belonging near the desk of every quantum chemist, physicist, and a wide range of scientists and engineers across many disciplines, destined to become a classic.
102
Authors: Tuzun R E , Noid D W , Sumpter B G
Published: November 2023

The problem described in this paper is the calculation of the ground-state energy for a 100-atom model polyethylene chain. The chain is represented by 100 mass points, connected in a series and interacting sequentially according to bond stretch terms, one-angle bond terms, and two-angle torsion terms. The lowest-energy configuration is a planar zigzag arrangement. The authors had earlier devised an internal coordinate system to facilitate classical dynamics simulations of such chains, and they used these again to great advantage in diffusion QMC calculations for this problem. In preliminary investigations, it was found that importance sampling was essential. The trial function was expressed as a product of Gaussian terms in each of the internal coordinates. with these the required first and second derivatives, as well as the drift terms, were reduced to very simple, very compact expressions. A series of calculations at different time-step sizes was extrapolated to obtain the ground-state energy. The value of 211 kcal/mol obtained in this way was about 7% below that obtained in a normal coordinate analysis. The application of diffusion QMC to the efficient solution of a long-standing problem is nicely demonstrated in this work.
Nodal hypersurfaces and Anderson’s random-walk simulation of the Schrödinger equation
Authors: Klein D J , Pickett H M
Published: November 2023

Klein and Pickett provided a discussion of the problem of determining the nodes for a fixed-node QMC calculation proposed earlier by Andersona They suggested using the nodes of a Hartree-Fock wavefunction and noted that a Jastrow wavefunctionb consisting of a Hartree-Fock function multiplied by a permutationally symmetric and positive function to correct for electron correlation could be quite accurate. Only later was it realized that the node structures given by Hartree-Fock wavefunctions were surprisingly simple even for large many-electron systems. Combinations of determinantal functions with Jastrow functions were found especially useful as trial functions for importance sampling in diffusion and Green’s function QMC calculations.
Monte Carlo study of core-valence separation schemes
Authors: Staroverov V N , Langfelder p. , Rothstein S M
Published: November 2023

The simplicity of variational QMC and the high accuracies obtained when used with explicitly correlated wavefunctions combine to provide a useful and convenient framework for exploring and testing ideas in quantum chemistry. In this paper, the authors report an investigation of the characteristics of core-valence separation schemes with the aim of providing understanding which might be useful especially for heavy elements. The studies were limited to first-row atomic systems, so that errors introduced by corevalence separation could be determined with sufficient accuracies. The bases for comparisons were all-electron VQMC calculations for Li to Ne and their positive ions using single-determinant/Jastrow wavefunctions. The several core-valence partitioning schemes were investigated with modifications of the original function to provide, after identification of two electrons as core electrons, varying degrees of separation as for ‘l/J = ‘l/Jcore’!/Jval with and without orthogonality and with and without explicit core-valence correlation.
Spin contamination in quantum Monte Carlo wave functions
Authors: Huang C J , Filippi C , Umrigar C J
Published: November 2023

The Pauli exclusion principle requires that a complete spacespin wavefunction be antisymmetric to the exchange of electrons. This requirement can be met by single-determinant and multi determinant wavefunctions obtained in SCF and CI calculations, which may then be considered acceptable as trial functions for specifying nodal surfaces and for importance sampling in determining energies. If multiplied by a Jastrow correlation function symmetrical to exchange of electrons, the function remains acceptable. However, in QMC, the Jastrow functions most often used have different coefficients for pairs of electrons of the same and opposite spins. These are not symmetric to all exchanges, and in combination with the determinantal function they give a trial function which is not antisymmetric to exchange of electrons and is not an eigenfunction of the spin operator 82 The problem is discussed in detail in this paper. The spin contamination oS2 of a wavefunction may be readily determined by Metropolis integrations as in variational QMC. The calculations reported for Li and Be show the spin contamination to be very small for unsymmetrical Jastrow terms with the usual coefficients of ¼ and ½ for parallel and antiparallel electron pairs. For higher order terms in the Jastrow function, the contamination could be reduced further. \Vith use of symmetric Jastrow factors, the electron-electron cusp conditions are not properly satisfied, so that variance in local energies is higher and computed energies are less accurate, but other properties such as electron densities may be more accurate. An alternative is the use of more complex and computationally expensive functions satisfying both spin and cusp conditions.
Symmetry constraints and variational principles in diffusion quantum Monte Carlo calculations of excited-state energies
Authors: Foulkes W M C , Hood R Q , Needs R J
Published: November 2023

This paper addresses the question of the existence of a variational principle for fixed-node QMC calculations. As pointed out, it has often been assumed that energies obtained with fixed nodes are equal to or greater than the energy for an exact wave function having the symmetry imposed by the nodes. The usual statement that the energy will be too high if the nodes are wrong is not always correct. The case of the 2s excited state of the hydrogen atom illustrates the problem. A trial node located at a fixed radius rt greater than the exact node radius re divides the space in two regions, one with r < rt and the other with r > rt, The solution for this inner region has a lower energy than the outer, and a fixed-node calculation started with walkers in both eventually eliminates those in the outer, and produces an energy lower than the true energy for the complete space with a node of r = re, As shown in the paper, the statement of the variational principle must be restricted to cases in which the trial function of the fixed nodal surface transforms according to a one-dimensional irreducible representation of the symmetry group of the applicable Hamiltonian. Fortunately, this is often the case, as it is for a determinantal wave function which divides the available space into equivalent similar regions. For the ground state of a fermionic system, the variational principle for the full symmetry group does not apply, but for the (fermionic) permutation subgroup the fixednode variational principle does apply. Thus, a single-determinant trial function meets the requirements for applying the variational principle for many-electron fermionic ground states. It is further shown that the variational principle is not limited to the permutation subgroup, but may also be applied to other subgroups with one-dimensional irreducible representations.
On the systematic improvement of fixed-node diffusion quantum Monte Carlo energies using pair natural orbital CI guide functions
Authors: Lüchow A , Fink R F
Published: November 2023

with nodes specified by Hartree-Fock wavefunctions, fixed-node DQivIC calculations recover typically 93 to 95% of the correlation energy for species like N, N2, and H20. Adding a few more determinants to the wavefunction has been found to give little if any improvement, but it is clear that very large CI functions will give improvement. In this paper the authors report the use of PNOs, pseudo-natural orbitals or pair-natural orbitals,a developed in the 1960s for compact multi-determinant wavefunctions in efficient CI calculations with limited computer speeds. With PNOs, transformations are made to produce pairs of orbitals which are either identical or orthogonal, and the CI expansion is much shorter than for the general CI function. With the more compact trial functions, DQMC calculations are much more efficient, and computation requirements are no longer prohibitive. For each of the species N, N2, and H20 calculations were carried out with trial functions containing from one to hundreds of determinants. Configurations making only small contributions to the calculated energy were deleted. In each case, the recovery of correlation energy is improved to 97 to 98% and this compares well with that of analytic MRCI calculations, but the best nonvariational methods for molecules of this size, such as CCSD(T)-R12, give energies closer to the estimated limits for these species. For large systems, the much more favorable N3 scaling observed for DQMC may be expected to favor DQMC.
Quantum Monte Carlo density functional theory characterization of 2-cyclopentenone and 3-cyclopentenone formation from 0(3
P) + cyclopentadiene
Authors: Grossman J C , Lester w. A , Louie S G
Published: November 2023

One of the myriad reactions of interest in the combustion of motor fuels is the addition of an oxygen atom in the 3  P state to cyclopentadiene. The generally accepted mechanism for the reaction begins with addition of the atom to a double bond, and formation of one or the other of two triplet diradicals depending on the point of addition. These can both undergo intersystem crossing to form singlet diradicals which pass through different transition states to the product, 2- or 3-cyclopentenone. In this study possible reaction pathways were investigated using a variety of electronic structure methods to calculate the energetics of critical configurations and intermediate species, along with the reactants and products. Eight different theoretical approaches were employed: HF, G2, QMC, and five variations of density functional theory (LDA, BPW91, BLYP, B3PW91, B3LYP). The QMC calculations were all-electron variational and fixed-node diffusion calculations with single-reference trial functions based on natural orbitals. Molecular structures were optimized for each method, except for diffusion QMC for which B3LYP structures were used.
Torsional diffusion Monte Carlo: A method for quantum simulations of proteins
Authors: Clary D C
Published: November 2023

Before this paper studies of the molecular dynamics of proteins had heen carried out primarily with classical dynamics. This paper shows that quantum-dynamical effects are important in determining the energies and geometries of typical proteins. The examples in this study are the proteins gelsolin (with 356 atoms and 142 torsions) and gp41-HIV (1101 atoms and 452 torsions), which were treated with all-atom force fields in diffusion QMC with restriction to torsional motions only. These motions have a much lower frequency than other motions for proteins, and they are the essential motions determining the dynamics of protein folding. The authors were able to assemble a general code for torsional diffusion QMC calculations to be carried out automatically for any protein with known connectivity or atom coordinates converted to internal coordinates of fixed-bond angles, fixed bond lengths, and variable torsion angles. All-atom potential energies were obtained from standard force-field programs. The torsional diffusion calculation is essentially identical to one-dimensional translational motion calculations, except that angles replace distances, and the tt2/2m is replaced by n,2 /21 in the diffusion terms. The results obtained from the calculations are the zero point energies and, with use of descendent weighting methods, distributions of structures or simply vibrationally averaged structures. The calculations show structures significantly changed from minimum-energy structures. It is noted that binding energies for drugs that might inhibit functions of such proteins are likely to be affected and that QMC calculations of this type may be important in drug discovery.
Quantum Monte Carlo studies of density functional theory
Authors: Nekovee, M , Foulkes W M C , Needs R J
Published: November 2023

It is difficult to imagine that density functional theory (DFT) could be useful in improving quantum Monte Carlo methods, but it is easy to imagine that QMC could be useful in improving density functional methods. Since QMC can produce accurate wavefunctions and since wavefunctions lead to all other properties one should be able, in principle, to use QMC to predict the exchangecorrelation energy functional Exc[n(r)], the key (unknown) quantity required in DFT. In practice, that is not so easy, but this paper shows how QMC can take steps in that direction by providing insights gained from comparisons of results from QMC and DFT. The authors considered the case of the strongly inhomogeneous electron gas using variational Q:tvIC to obtain wavefunctions 1/J>. and energies E[7/J>.] for the ground state of the Hamiltonian iI>- = T +AVee+V >. associated with the coupling constant A in the range 0 to 1. Optimization of a Slater-Jastrow many-body wavefunction was made by minimizing a penalty function given by a weighted sum of the variance in local energies and a sum of squares of electron density differences. The variational parameters in 7/J>. and v>. were repeatedly varied to reach convergence followed by additional calculations to obtain the local values of the exchange-correlation energies e c and the exchange-correlation holes n c from which Exe and nxc could be determined.
Excitations in photoactive molecules from quantum Monte Carlo
Authors: Schautz F , Buda F , Filippi C
Published: November 2023

Among the several quantum approaches to the accurate description of excitation processes in biological systems, the most promising candidates are: CASPT2, complete active space second-order perturbation theory; TDDFT, time-dependent density functional theory; ROKS, the restricted open-shell Kohn-Sham method; and QMC, quantum Monte Carlo. Each of these has its disadvantages. CASPT2 scales poorly with system size and is limited to smaller molecules. ROKS and TDDFT can be applied to very large systems but they may or may not be adequate for photoactive molecules. QMC scales favorably with system size but is computationally expensive. The authors address these issues in this paper with fixednode diffusion QMC calculations for ground and excited states for protypical photosensitive molecules, and companion calculations by CASPT2, TDDFT, and ROKS methods. The species chosen were formaldimine (CH2NH), formaldehyde (CH2O), and a protonated Schiff base (C5H6NH!) serving as a model for the retinal chromophore. The all-electron calculations were carried out with trial functions made up of linear combinations of Slater determinants, with Jastrow correlation factors optimized to minimize the average of energies for ground and excited states, using a fixed set of orbitals available for both. This was found to be important in obtaining accurate excitation energies. Transitions were examined along isomerization paths for each of the species, and comparisons of results were made for a variety of configurations.
Quantum chemistry by random walk: Method of successive corrections
Authors: Anderson J B , Freihaut B H
Published: November 2023

This work extended the simple diffusion QMC method of solving the Schrödinger equation for a wavefunction ψ; to that of solving for a correction to a trial wavefunction ψo such that ψ= ψo+ . The method may be applied in the manner of successive corrections to obtain very high accuracies. As described, the method is limited to solutions for systems with fixed nodes. The method was illustrated for the cases of the particle-in-a-box and the hydrogen atom. For the latter, successive corrections improved the accuracy in energy by about a factor of ten with each iteration. For higher dimensional systems, difficulties in the fitting procedure may be expected to limit the applicability of the method.
The accuracy of diffusion quantum l\fonte Carlo simulations in the determination of molecular equilibrium structures
Authors: Lu S -I
Published: November 2023

Results of fixed-node diffusion QMC calculations for 17 small molecules made up of atoms H, C, N, 0, and F were compared in this paper to experimental values for atomization energies, bond lengths, and bond angles, as well as corresponding values from coupled cluster calculations. The QMC calculations were of the Ornstein-Uhlenbeck type,a with trial functions for importance sampling and node locations based on linear combinations of determinants with molecular orbitals composed of floating spherical Gaussian orbitals. Initial geometries were taken from density functional calculations and optimized to find the minima given by the QMC calculations. Zero-point energies were calculated using the energy gradients given by the same calculations. The calculated atomization energies for the 14 species for which experimental data were available were in excellent agreement with the experimental values and with values given by CCSD(T) with a cc-pVQZ basis set. The mean absolute deviation from experimental atomization energies was 0.16 kcal/mol for the QMC and 0.21 kcal/mol for the CCSD(T) calculations. Geometric parameters were in agreement with each other and with experimental values within their uncertainties. Overall, the results provide a solid confirmation of the accuracy of fixed-node diffusion QMC calculations.
Efficient quantum Monte Carlo energies for molecular dynamics simulations
Authors: Grossman J C , Mitáš L
Published: November 2023

This paper opened the area of molecular dynamics to “on the fly” trajectory calculations with Q:tvlC accuracies. Using the continuous evolution of fixed-node diffusion QMC electronic structure calculations simultaneously with the motion of nuclei the authors were able to gain more than an order of magnitude in computational speed and make such calculations feasible for a variety of interesting systems. “On the fly” molecular dynamics simulations using QMC energies were thus advanced to compete with those using density functional theorya. In the simulations described the nuclear Hamiltonian and the electronic wave function, represented by QMC walkers, were updated at each molecular dynamics step. This replaced discrete QMC calculations and took advantage of correlated sampling of electron configurations. Relaxation of the electronic wave function to new nuclear positions was required, but as few as three QMC steps per molecular dynamics step were found adequate. Calculations were carried out using nonlocal pseudopotentials with trial wave functions for valence electrons consisting of Slater determinants and Jastrow functions. Variational QMC was used for optimizations. The efficiency and accuracy of the dynamical QMC approach was demonstrated in calculations for silicon hydride species SiH4 to Si14H20 at 1000 K, for the dissociation of a water molecule as H20 HO + H, and for a 32-molecule liquid-water system along with a single molecule for comparisons. The calculations were clearly successful in producing accurate molecular dynamics simulations at a modest cost in computational effort.
Theoretical study of transition state structure and reaction enthalpy of the F + H2 -+ HF + H reaction by a diffusion quantum Monte Carlo approach
Authors: Lu S -I
Published: November 2023

As noted by the author the reaction F + H2 HF + H has played an important role in the development of theories of chemical dynamics. It has played a similarly important role in the development of accurate ab initio methods for treating the electronic structure of molecular systems, and this paper itself continues that development. After early excitements and disappointments in the 1970s and 1980s several types of quantum calculations in the 1990s were quite successful in predicting potential energy surfaces for this reaction which were entirely consistent with experimental observations. A most recent multi reference coupled cluster (MRCC) study by Kallay et al.a provided excellent agreement. The subject paper extends fixed-node QMC calculations to provide a similarly accurate surface also in excellent agreement, solidifying mankind’s understanding of this reaction. The key to Lu’s success is a multireference trial function of floating spherical Gaussian orbitals and spherical Gaussian orbitals (FSGO-SGG) suitably optimized to specify the nodes of the wavefunction. An earlier QMC calculationb with a single-determinant trial function produced a barrier height too high by 2 to 3 kcal/mo!. The value of 1.09(16) kcal/mo! obtained by Lu is in good agreement with the of 1.11 kcal/mo! from the MRCC calculation.
Quantum chemistry by random walk: Higher accuracy
Authors: Anderson J B
Published: November 2023

In an earlier papera a method for the direct calculation of the difference between a true wavefunction and a trial wavefunction was described for simple diffusion calculations. This paper reports further increases in accuracy obtained by a combination of this difference method with importance sampling. The combination allows the calculation of corrections to the product ΨΨT of true and trial wavefunctions, rather than to the wavefunction Ψ itself. Using a new function g = ΨΨT- Ψ2  T, the original diffusion equation with drift and local energies is altered by replacement of ΨΨT with g and by addition of a distributed source term. Since walkers fed by sampling the source term may be positive or negative, cancellation is required, but both sets of walkers proceed to the same distribution and age-based cancellation may be used. Node locations are not changed and remain at their original locations as specified by the trial function. The corrected wavefunction and the energy obtained are the same as for a fixed-node diffusion calculation using the same trial function for importance sampling. The method is useful in reducing statistical error, and because the statistical error occurs only in the difference terms, it is most effective when the trial wavefunction is already reasonably accurate. In test calculations for the hydrogen atom and the helium atom, both nodeless, the statistical error in the QMC calculations was greatly reduced. Thus, for hydrogen a trial function with an expectation value of -0.4998 hartrees led to a QMC energy of -0.499995(4) hartrees.
The Domain Green’s Function Method
Authors: Moskowitz J W , Schmidt K E
Published: November 2023

The boundary conditions required in fixed-node QMC are not appropriate for the use of Green’s functions in a simple way. In this paper, Moskowitz and Schmidt describe modifications to allow the direct use of Green’s functions without the short-time approximation, i.e., without the discretization of the diffusion equation. In this modified procedure, walkers are allowed to move only within a domain in which the trial function specifying the nodes is positive. A linear approximation is used to predict the distance to a node, and the step size is revised accordingly. The distance to a region of net positive potential is similarly considered. The method was used in fixed-node calculations for LiH and H20 with SCF trial functions, as well as for Be and Be-H2 with MCSCF trial functions. Recovery of correlation energy was better than 90% for the best trial functions. The method was developed to supplant the fixed-node diffusion method, with an accompanying “proof” that the fixednode diffusion methods of earlier workers (Anderson,a Reynolds et al.,a and presumably Fermi) were incorrect. The proof contained a mistake subsequently reportedb by the authors.
Valence quantum Monte Carlo with ab initio effective core potentials
Authors: Hammond B L , Reynolds P J , Lester W A
Published: November 2023

This paper reports a more elaborate treatment than either of the other papers reporting effective potentials in QMC calculations in 1987 and 1988. Although justified here as a means to avoid the higher computational requirements of heavy (large Z) atoms, the advantages of eliminating core electrons apply equally well for systems of lighter atoms such as carbon, nitrogen, and oxygen. The treatment in this paper begins with a valence-electron Schrödinger equation in which core electrons are missing. The nuclear charges are replaced by reduced effective nuclear charges, and the corevalence electron-electron repulsions are replaced by a nonlocal effective core potential uECP. This term is a relatively complicated expression which incorporates the core-valence orthogonality condition and is a function of valence electron positions. It is obtained in the course of Hartree-Fock calculations for the atoms involved. The implementation in QMC calculations required a number of minor approximations, along with a lengthy set of derivations, finally resulting in an expression for uECP compatible with QMC. Calculations were carried out in fixed-node diffusion QMC for several systems: Li/Li-, Na/Na+, Mg/Mg+, NaH/(Na+H), and Na2/(Na+Na). These produced electron affinities, ionization potentials, and binding energies which could be compared with experimental values. Statistical uncertainties were typically 0.02 eV for these values, and all agreed with experimental values within their uncertainties. Such accuracies would have required much greater computational efforts for all-electron calculations.
Diffusion Monte Carlo simulation of condensed systems
Authors: Coker D F , Watts R O
Published: November 2023

This paper reports diffusion quantum Monte Carlo calculations for condensed systems, in this case for liquid 4He and for solid molecular H2. Calculations for liquid He made earlier by Whitlock et al.a using Green’s function QMC for the same potential energy surface allowed a comparison of results for this system. Coker and Watts used spherical pair potentials derived from scattering experiments for both systems, along with Axilrod-Teller-Muto three body terms. The calculations were performed with importance sampling, using a simple product of pair functions as a trial function for helium. For hydrogen a simple pair function multiplied by a single-particle term for position in the fee lattice was used. Periodic boundary conditions were employed, and calculations were carried out for several particle densities of each species. For helium, good agreement with the prior Green’s function calculations was obtained for thermodynamic and structural properties and for radial distribution functions. For hydrogen, the calculated average energies and pressures gave general agreement with experimental measurement, but they differed up to 10% in energy and 12% in pressure in a manner to be expected for neglect of molecular anisotropy. The problem treated in this paper is that of understanding xenon cluster ions at the microscopic level. Some properties of cluster anions had been measured, but these revealed no detailed information on structure and energetics. In the study reported here, diffusion QMC was used to investigate electron binding to small clusters of up to 19 atoms in fixed minimum-energy configurations. This was followed by path integral calculations to determine equilibrium distributions of cluster structures at temperatures of 10-100 K for several cluster sizes.
Development of a pure diffusion quantum Monte Carlo method using a full generalized Feynman-Kac formula. I and II
Authors: Caffarel M , Claverie P
Published: November 2023

These two papers describe the development of a variant of diffusion QMC with importance sampling and its applications to a few simple systems. The method is based on the generalized FeynmanKac path integral formalisma and is termed the “full generalized Feynman-Kac” or FGFK method. Its major advantage, relative to other diffusion-based methods, is the elimination of branching or multiplication of walkers. Its major disadvantage is a greater complexity. The basic implementation is very nearly the same as that of standard diffusion QMC with importance sampling, and it incorporates diffusion with drift in the same way. The uses of trial functions, fixed nodes, extrapolation to zero time-step size, and other procedures except for branching are identical. However, the evaluation of mean quantities can be carried out in terms of ‘lj;2 sampling to obtain energies and other properties based on the FGFK formula. The applications described include ground and excited states of the harmonic oscillator and the helium atom and the ground state of the hydrogen molecule. For these the energies as well as a dozen other observables such as the averages of interelectron distances were determined. The results were found to be in good agreement with accepted values. A combination of FGFK with the released-node method was investigated for the case of the one-dimensional harmonic oscillator and found to be successful for that case.
Estimating the relativistic energy by diffusion quantum Monte Carlo
Authors: Vrbik J , Depasquale M F , Rothstein S M
Published: November 2023

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

As reported in this paper, both variational and fixed-node diffusion QMC calculations were used to determine electronic properties for bulk lithium. The calculations were carried out for cubic supercells containing lithium nuclei at fixed sites in body-centered cubic and face-centered cubic lattice structures with up to 108 atoms. The trial functions for importance sampling were constructed in two forms: one with Gaussian plane-wave functions and the other with more complex augmented plane-wave functions. Slightly lower energies were obtained in variational QMC for the Gaussian form, and equivalent results were obtained in fixed-node diffusion Q1,1C for the two forms. Simple spherical trial functions gave significantly higher energies for compressed systems. Energies, pair distribution functions, and electron densities were investigated for crystal densities ranging from about 0.25 to 90 times the densities at normal pressures. The variation of cohesive energy with density was found in reasonable agreement with experimental results in calculations using the larger numbers of atoms in the supercell. The lattice constants were also in good agreement for these cases. In general, this paper showed that fixed-node diffusion calculations were feasible for metallic systems and could be competitive with alternative methods.
Quantum chemistry by random walk: Exact treatment of many-electron systems
Authors: Anderson J B , Traynor C A , Boghosian B M
Published: November 2023

This paper reports the first exact quantum treatment of a manyelectron system. The QMC method used is exact in that it requires no mathematical approximations and no physical approximations beyond those of the Schrödinger equation. It requires no interpolations and no extrapolations. As in most Monte Carlo methods, there is a statistical or sampling error which is readily estimated and which may be made arbitrarily small by additional computation. The method is illustrated with applications to the problems of a particle in a two-dimensional box, excited H2 3E;!”, and linear symmetric H-H-H. The “sign problem in fermion Monte Carlo” is solved by a cancellation scheme in which positive and negative walkers in close proximity may cancel each other, a device mentioned in an early paper by Ulama and described later by Arnow et al.b Time-step error is eliminated by use of Green’s function QMC, and cancellation is made on the basis of overlapping Green’s functions for movement of walkers, made efficient by a Monte Carlo procedure to eliminate conditional acceptance of walker moves. Importance sampling is incorporated in order to reduce statistical error in the energies determined. For the case of clamped-nucleus H2 3E;!” at an internuclear distance of 1.4 bohr, the calculated energy was -0.7838 ± 0.0007 hartrees, a value consistent with prior analytic variational calculations. For the H-H-H system at separations of 1.757 bohr, the energy determined was -1.6591 ± 0.0003 hartrees, a value lower than that of any variational
Treatment of rigid bodies by diffusion Monte Carlo: Application to the para-H2-H20 and ortho-H2-H20 clusters
Authors: Buch V
Published: November 2023

This paper describes the application of diffusion QMC to the problem of motions of molecules in small clusters in which some or all of the molecules can be treated as rigid bodies. For the loosely bound ground state of H2-H20 clusters the high-frequency intramolecular vibrations of H atoms in H2 and in H20 are decoupled from the lower-frequency intermolecular vibrations and both H2 and H20 can be considered rigid bodies. A potential energy surface based on rigid bodies was obtained as an approximate fit to data from abinitio calculations. It has three minima for H2 in the plane of the H20 molecule and two out of the plane. The diffusion calculations were carried out in angular coordinates for the rigid rotor motions and cartesian coordinates for the H2-H20 translational motions. In some cases the H20 molecule was completely fixed. For para-H2 and para-H20 the ground state wavefunctions are fully symmetric and without nodes so that no restrictions were necessary. For ortho-H2 and para-H20 a cancelnlation procedure for walkers with opposite H2 rotation vectors was required to impose the antisymmetry condition. In this case the rotational state of free H2 is triply degenerate and the degeneracy was observed to remain in the presence of H20 with distributions