bluuebunny/crossref_metadata_2025_split huggingface dataset:
Potential energies for the reaction F + H2 HF + H by the random walk method
Authors: Garmer D R , Garmer D R 
Published: November 2023

Abstract
If the reaction H + H2 H2 + H is number one on the list of interesting chemical reactions, then number two is the reaction F + H2 HF + H. It is very fast, it is highly exothermic, it drives chemical lasers, it can be studied in crossed molecular beams, it can be studied by infrared spectroscopy, and it involves only 11 electrons. This paper, and its companion paper a year earlier, report fixed-node diffusion QMC calculations of the ground-state potential energy surface for the F-H-H systems, with emphasis on the region of the barrier to reaction. At the time this work was completed, it was clear from experiments that the barrier height must be in the range of 1 to 2 kcal/mol. Calculations by a variety of methods gave barrier heights in the range of 1 to 6 kcal/mole for collinear reactions. More recent high-level calculations, QMC and others, place the collinear barrier at about 3 kcal/mol, with a lower height of about 2 kcal/mol for slightly bent configurations. The QMC calculations were fixed-node diffusion calculations with importance sampling, using single-determinant trial functions with orbitals represented by cubic spline functions fit to Gaussian orbitals. Recovery of correlation energy was about 96% for the isolated F atom and for the HF molecule. Total energies for reactions and products were about 40 kcal/mol lower than the lowest energy
Model Hamiltonians for atomic and molecular systems
Authors: Carlson J , Moskowitz J W , Schmidt K E 
Published: November 2023

Abstract
The aim of this study was to reduce the variance in the energies for QMC calculations for atomic and molecular systems by replacing the electron-electron potential energy terms for core electrons by averaged values. The complete Hamiltonian expression was thus altered to become a model Hamiltonian, and while total energies from such calculations may have little meaning, energy differences for similar systems obtained with the same model may give fairly good agreement with those from calculations for the full Hamiltonian. The work reported in this paper indicated that is the case for Li, LiH, and Li2. The average electron-electron potential was expressed as a two-parameter function decreasing with increasing distance from a nucleus. Importance sampling was carried out with a trial function consisting of an unaltered Slater determinant specifying node locations multiplied by a modified Jastrow function. The random walk of configurations was executed with Green’s function sampling for the full set of electrons. Energy differences for LiH versus (Li + H) and Li2 versus (Li + Li) were accurate within about 1 millihartree. The reduction in variance in local energies led to increases in calculation efficiency by a factor of 5 to 7 for these systems. The results indicated such an approach might be successful for larger systems.
H. Sun & R. 0. Watts: Diffusion Monte Carlo simulations of hydrogen fluoride dimers
Authors: Sun H 
Published: November 2023

Abstract
This is one of the earlier QMC papers to describe calculations of molecular vibrational states. As noted by the authors, harmonic oscillator models for vibration are not adequate for treating floppy molecules, and the principal motivation for their study was to “give up the harmonic oscillator assumption and use quantum Monte Carlo to calculate accurate vibrational frequencies for the HF and DF dimers.” Clearly, they were successful in meeting that objective. In doing so they devised several new approaches to the general problem of treating vibrational motion. Diffusion QMC with importance sampling was used with an improved short-time approximation based on an added multiplication term second order in the time-step size. Excited states for which node locations could be specified from consideration of symmetry arguments, as for torsion states, were simulated in fixed-node calculations. For other states an orthogonalization methoda based on cancellation of positive and negative walkers as well as orthogonality with lower states was used. For these it was necessary to simulate the excited states successively, and calculations were limited to four different states. The states involved in tunneling splitting for the dimers were distinguished by an added fixed node. The calculations were carried out for three different potential energy surfaces and results were compared with spectroscopic data. Each one gave reasonable values for low-lying vibrations. Modification of one surface gave still better values.
Wave functions of helium clusters
Authors: Rama M V 
Published: November 2023

Abstract
This paper describes improved trial wavefunctions for helium clusters and their use in variational QMC calculations of their binding energies, structural properties, and breathing mode vibrational excited states, for clusters of 3 to 270 atoms. The wavefunctions developed were similar to those of earlier work but included convenient analytic functions for two- and three-body correlations. All terms were of the Jastrow exponential form, based on sums of one-, two-, and three-body terms t1(ri), t2(rij), and t3(rij, rjk,rki), expressed as functions of interparticle distances. Excited-state wavefunctions for the breathing vibrational mode were obtained with the aid of procedures adapted from treatment of the quantum mechanics of liquid drop models. The interactions of helium atoms were specified as pairwise-additive with an accurate semi-empirical pair potential. Optimizations of parameters in the trial wavefunctions were carried out for individual cluster sizes with an exhaustive search procedure in a series of trial variational calculations, in which the parameters were varied to minimize the energy. A partial correlation of results was obtained by use of identical initial coordinates and random number seeds in these optimization calculations. Once the wavefunctions were optimized, longer calculations were used to determine properties of the clusters. In addition, diffusion QMC calculations were used to obtain more accurate nonvariational energies for comparisons.
Variational quantum Monte Carlo nonlocal pseudopotential approach to solids: Formulation and application to diamond, graphite, and silicon
Authors: Fahy S , Wang X W , Louie S G 
Published: November 2023

Abstract
This paper describes the use of nonlocal pseudopotentials with variational QMC to calculate the binding energies of the solids diamond, graphite, and silicon. While nonlocal pseudopotentials have the advantage of elimination of core electrons and the large fluctuations of local energies associated with core electrons, they produce several types of difficulties in diffusion and Green’s function QMC. As shown in this paper, the use of variational QMC avoids many of these. The calculations used pseudopotentials of the standard form developed for use in density functional calculations. The trial functions were based on mixtures of short-range Gaussian orbitals and long-range plane-wave functions in single determinants multiplied by Jastrow functions. Metropolis sampling was carried out for movement of one electron at a time, along with its images, in order to take advantage of the efficiencies associated with changing one row of the determinant for a single electron. The solids were treated as cells of up to 54 atoms (216 valence electrons) with periodic boundary conditions. For each of the three systems - diamond, graphite, and silicon - the VQMC structural properties were found in excellent agreement with experiment. Density functional calculations at the LDA level were similarly successful. More important, the VQMC binding energies and energy differences were found in excellent agreement with experiment. For these quantities density functional calculations at the LDA level were far less successful.
Magnetic structure and equation of state of bee solid hydrogen: A variational quantum Monte Carlo study
Authors: Wang X W , Zhu J , Louie S G , Fahy S 
Published: November 2023

Abstract
Solid hydrogen in its atomic bee structure provides an interesting testing ground for various theoretical methods in predicting the properties of its several electronic states. These include three possible magnetic phases: paramagnetic (PM), ferromagnetic (FM), and antiferromagnetic (AFM). The system is simple enough to permit reliable calculations for all three phases to determine their energies as functions of the density and to predict the transitions between phases. The calculations reported in this paper were variational QMC calculations performed primarily on a 54-atom cluster in the bee structure with periodic boundary conditions. The protons were fixed in position. The trial wavefunction was constructed from a product of spin-up and spin-down determinants based on single particle wave functions from density-functional calculations for the system, multiplied by a symmetric Jastrow factor. The specification of magnetic phase was made through modifications of the single-particle orbitals within the determinants and localization of orbitals to one or the other of the cubic sublattices. The calculations for all three phases were performed for a range of densities in which earlier calculations had predicted magnetic and metalinsulator transitions. At the lowest densities, the FM and AFM energies approached the value for free hydrogen atoms, with AFM lower than FM. With increasing density the PM phase drops below the AFM and becomes the ground state. Across the range, the ferromagnetic phase was never the lowest-energy phase.
Nonlocal pseudo potentials and diffusion Monte Carlo
Authors: Mitáš L , Shirley E L , Ceperley D M 
Published: November 2023

Abstract
This paper reports improvements which overcome some of the problems encountered in the use of nonlocal pseudopotentials in QMC. These increase the reliability of the method by reducing or eliminating several approximations of earlier treatments, reduce the variance in local energies, and increase the recovery of correlation energy. Calculations for Si, Sc, and Cu neutrals and ions in several states and the dimer Si2 were used to test the revised method. One key improvement was the use of correlated trial wavefunctions making use of Schmidt-Moskowitz expressions for two- and three-body terms. Additional exponential terms were added in some cases. Atomic orbitals for the determinants were obtained in density functional calculations. Another key improvement was in the procedure for integrating the trial function over a sphere in determining the electron-pseudopotential energetics. For the complete correlated trial function the integrals were determined with numerical quadrature, settling on 18-point quadrature with random orientation on the sphere. Except for these changes, the calculations were similar to those of the earlier studies. Both variational and fixed-node diffusion calculations were made. The recovery of valence conelation energy for atoms and ions was 80%-90% in the variational calculations and estimated to be greater than 95% in the diffusion calculations. Comparison of ionization potentials and electron affinities with experimental values showed agreement within 1% for Si, a few percent for Sc, and about 20% for Cu. The general conclusion was that the method was stable and feasible even for the difficult case of Cu.
Quantum Monte Carlo perturbation calculations of interaction energies
Authors: Caffarel M , HESS O 
Published: November 2023

Abstract
The perturbation approach to predicting interaction energies between molecules avoids many of the problems associated with accurate calculations of total energies for subtraction to obtain energy differences, but it has many problems of its own. This paper reports a slightly successful first attempt to combine the perturbation approach with QMC methods for such calculations. The basis for the development is the nth-order Rayleigh Schri:idinger perturb bation theory, which in principle can be formulated to give a series of energy corrections !}.E(n) that can be expressed as integrals involving the perturbing potential and the unperturbed wavefunctions. In practice this is difficult for interactions of molecules, but the authors succeeded in reformulating the problem so that the required quantities could be determined in diffusion QMC calculations. The interaction energy was split into Rayleigh Schri:idinger and exchange parts which could be separately evaluated. The QMC aspects were carried out in diffusion QMC with importance sampling using Jastrow like trial functions and conditional acceptance of moves to enforce detailed balance. This produced the expectation values required in the expressions for the interaction energy.
Binding energies of positronium fluoride and positronium bromide by the model potential quantum Monte Carlo method
Authors: Schrader D M , Yoshida T , Iguchi K 
Published: November 2023

Abstract
This paper and a companion paper0 describe three pseudopotential QMC calculations for the positronium halides PsF, PsCl, and PsBr with accuracies and reliabilities not previously available. These three compounds have a fleeting lifetime sufficiently long that time-independent nonrelativistic quantum mechanics should give good estimates of their energies but too short to allow direct measurements of those energies. Earlier estimates of several types and calculations at the Hartree-Fock level had given a wide spread in predictions of the binding energies of positronium to the halide ions, mostly in the range of 1 to 3 eV for the three molecules. The calculations were fixed-node diffusion QMC calculations for the eight valence electrons and the positron with a model potential expression replacing the core electrons and halide nucleus. The model or pseudopotential used was a simplified version without valence-core correlation and with several lesser terms eliminated in order to make it a local pseudopotential. This modelb had been used previously in successful predictions of the electron affinity of the Cl atom. An importance sampling trial wavefunction was constructed of Hartree-Fock orbitals for the halide ion and a 2s orbital for the positron, along with an electron-positron term but no electron-electron correlation terms. Checks of the consistency of the calculations with independent estimates of the correlation energies were entirely satisfactory. The results, in terms of binding energies, were obtained in the range of 1-2 eV (with uncertainties of 0.1-0.2 eV) in an order consistent with competitive formation experiments.
Quantum annealing: A new method for minimizing multidimensional functions
Authors: Finnila A B , Gomez M A , Sebenik C , Stenson C , Doll J D 
Published: November 2023

Abstract
Quantum Monte Carlo has found a new application far afield from the solution of the Schrodinger equation for many-body problems. In this paper the authors report a method for solving multidimensional optimization problems that is superior, in many cases, to other methods such as conjugate gradient methods, the simplex method, direction-set methods, genetic methods, and classical simulated annealing. The new approach, aptly titled “quantum annealing,” is closely related to classical annealing, in which a physical system such as a metal cluster is slowly cooled and finds its lowest-energy configuration as the temperature drops to zero. In classical annealing the system follows classical-mechanical dynamics as the temperature drops. In quantum annealing a collection of configurations evolves in the the same way as walkers undergoing diffusion and multiplication in diffusion QMC with the added feature of a slowly dropping value for Planck’s constant h. Classical annealing allows the escape from local minima with the aid of thermal fluctuations. Quantum annealing allows such escape by delocalization and tunneling. Since a QMC walker can multiply in number on entering a low-energy region, a single walker can populate an entire region.
Quantum Monte Carlo simulation of molecular vibrations: Application to formaldehyde
Authors: Lewerenz M , Watts R O 
Published: November 2023

Abstract
The formaldehyde molecule is an often used test system for methods of predicting vibrational levels of polyatomic molecules. It was the first four-atom molecule to be treated in analytic variational calculations and it was the subject of early QMC variational calculations by Bernu et al.a It has also been the subject of several perturbational studies. The study reported in this paper has taken advantage of a preexisting accurate global potential energy surface, providing good descriptions of the several local minima, for fully QMC calculations using the fixed-node diffusion method. The fixed nodes for several of the excited states treated could be specified exactly from symmetry considerations. For the others approximate node locations were used. Importance-sampling trial wavefunctions were assembled from diatomic and triatomic subunits in “modular” constructions. Calculations for a total of eight different vibrational states gave lower energies than variational calculations for the same surface but good agreement in frequencies except for two combination states. Agreement with experiment in terms of vibrational frequencies was good, especially for the lowest states of a given symmetry.
Driven Two-Dimensional Dynamical Systems
Authors: Gilmore Robert , Letellier Christophe 
Published: November 2023

Abstract
There is a general structure theory for dynamical systems-sets of coupled nonlinear ordinary differential equations-that remains to be worked out. This theory takes the form of the structure theory that is well known for algebraic systems-in particular, the structure theory that exists for groups and their representations. Groups may be nonsemisimple, semisimple, or simple [31]. Representations of groups can be reducible, fully reducible, or irreducible. We will adopt the language of representations to describe the structure theory for dynamical systems,on the grounds that such equations form representations of physical processes. We summarize schematically the structure theory for groups, representations, and dynamical systems in Table 8.1.
Group Theory Basics
Authors: Gilmore Robert , Letellier Christophe 
Published: November 2023

Abstract
The parameters c = ( c1, c2, · · · , ck) are called control parameters. They are parameters that typically appear in the dynamical systems equations. For example, for the Lorenz equations (2.1) the three control parameters are c = ( c1 , c2, c3) = (R, u, b) and for the Rossler equations (5.7) they are c = ( c1, c2, c3) = ( a, b, c). The control parameters are points in a k-dimensional manifold whose global topology is less important than that of the phase space. The dynamical systems equations (10.1) are typically coupled nonlinear equations. They are deterministic under mild conditions on the source functions f(x; c). Trajec­tories exist through any point at which a Lipschitz condition is satisfied. Such tra­jectories are locally extendable and unique. Specifically, the theorem is as follows [S].
Equivariant Dynamics in RN
Authors: Gilmore Robert , Letellier Christophe 
Published: November 2023

Abstract
The properties of equivariant dynamical systems X = F(X) are highly constrained by the sylllllletry group Q. The number of fixed points is to some extent determined by Q. The singular set SS(Q) is completely determined by the action of Q on JRN through the defining matrix representation rDe f (Q). Most important, the structure of the forcing functions F(X) is determined by ro e f (Q), the spectrum of irreducible representations of Q, and the ring basis functions R(a ) ( X) that transform under these irreducible representations
All the Covers of the Horseshoe
Authors: Gilmore Robert , Letellier Christophe 
Published: November 2023

Abstract
This book covers them. All of them. As we have progressed through the chapters our understanding and appreciation of covers has become increasingly complex. At first, covers were dynamical systems with some symmetry that could be mapped to a dynamical systems without symmetry in a locally one to one way. Many examples of such symmetric dynamical systems, and their images, were given in Chapter 3. Fig. 16.1 shows two symmetric attractors, the Lorenz attractor and the Burke and Shaw attractor, and their 2 , 1 images, the proto-Lorenz, and the proto-Burke and Shaw attractors. The original attractors are the covers, the proto attractors are the images. As a next step, the cover-image mapping could be inverted. This allows us to lift an attractor without symmetry, and the dynamical equations that generate that attractor, to attractors with symmetry, and the equations that generate the symmetric attractors. At this stage we encountered our first enriching experience.
Five Days that Changed My Life
Authors: Ford Emily , Liebowitz Michael R , Andrews Linda Wasmer 
Published: November 2023

Abstract
The money I was costing my parents had been steadily adding up. By the spring of 2005, I had drained tens of thousands of dollars from their bank accounts by pursuing failed stays in faraway places and start-up businesses that would have allowed me to work completely by myself, but that never seemed to get off the ground. My medical insurance covered none of the cost of monthly visits to the psychiatrist or the medication I was taking, so my parents paid for those, too. They had also financed my undergraduate degree as well as the graduate degree that I hadn’t finished, and they had paid the security deposits and monthly rent for no fewer than five apartments. The cost was straining my relationship not only with my parents, but also with my sisters, who implied that my constant financial demands were extremely selfish.
My Life Today, Your Life Tomorrow
Authors: Ford Emily , Liebowitz Michael R , Andrews Linda Wasmer 
Published: November 2023

Abstract
As a child, Emily was incomparable, unusual, even precocious. At age four she was writing little poems and stories, enjoying music, art, and a myriad of creative pastimes. The breadth of her imagination along with her joie de vivre was a charming combination. Then in her teens, Emily became increasingly self-conscious. Immediate post-college days marked the beginning of her deep depression. I think of it as her dark period. During this time she frequently slept by day and was up all night. Emotional reactions were almost nonexistent. Emily withdrew socially; personal interactions became rare. Anxiety plagued her to the point of refusing to talk on the phone, which, of course, was a detriment to work situations. Her eating habits became bizarre, eating all oatmeal one week, and toast and coffee the next. Remarkably, Emily has abandoned her dark despair and reemerged into the radiance of self-delight and that of the world around her. Of her own accord she found and put herself under the aegis of an anxiety treatment center. Through psychotherapy and medication Emily has become a ‘‘new’’ person, ironically by becoming her ‘‘old’’ self.