bluuebunny/crossref_metadata_2025_split huggingface dataset:
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

Abstract
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 &lt; rt and the other with r &gt; 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

Abstract
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

Abstract
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

Abstract
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

Abstract
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&gt;. and energies E[7/J&gt;.] for the ground state of the Hamiltonian iI&gt;- = T +AVee+V &gt;. 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&gt;. and v&gt;. 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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.