bluuebunny/crossref_metadata_2025_split huggingface dataset:
Quantum Monte Carlo simulation of intermolecular excited vibrational states in the cage water hexamer
Authors: Severson M W , Buch V 
Published: November 2023

Abstract
The general problem discussed in this paper is that of predicting vibrational excitation in large hydrogen-bonded clusters, and, as the authors point out, “It should be realized that the problem is very difficult.” In this case, the cluster is the cage form of the water hexamer, simplified somewhat by use of rigid-body water molecules. The key to the solution is a new procedure for locating the nodes in the wavefunctions for the excited vibrational states. The method begins with an approximately correct candidate nodal surface, obtained as a zero for a normal coordinate in the harmonic approximation, followed by adjustments to meet the essential criteria for a truly correct nodal surface. These criteria are: (1) energies calculated for either side of a node must be the same, (2) the first derivative of the wavefunction must be continuous across the node, and (3) the wavefunction must be orthogonal to the groundstate wave function. It would seem hopeless to make adjustments to satisfy these criteria, but it was discovered they could be met successfully with nodes constructed from normal coordinates, singly in some cases and in linear combinations of up to three coordinates, subject to trial-and-error adjustments of the coefficients. In testing nodal surfaces, the required diffusion QMC calculations were carried out without importance sampling, so that fluxes into the nodal surface from opposite sides could be determined and mismatches eliminated. Despite the complexity of the systems, the energies for ten different low-lying vibrational states were determined. One of these was assigned to the vibration-rotation tunneling band observed in infrared absorption experimentsa.
Combined diffusion quantum Monte Carlo-vibrational self-consistent field (DQMC-VSCF) method for excited vibrational states of large polyatomic systems
Authors: Broude S , Jung J 0. , Gerber R B 
Published: November 2023

Abstract
Self-consistent field (SCF) solutions of the Schrodinger equation can provide approximate, often very accurate, nodes for DQMC calculations of electronic structure. As shown in this paper, SCF calculations can do the same in specifying nodes for vibrational states of polyatomic systems as large as Ar13. The vibrational selfconsistent field (VSCF) methoda is approximate but quite accurate in itself, and it has been used previously for prediction of low-level excitations of protein molecules, water clusters, and other complex systems. In the calculations described in this paper for Ar3 and Ar13, the SCF function was specified as a product of functions for each of the normal modes, and solutions were obtained with a sixth-order expansion reducing the required integrals to one dimension. For the argon clusters, the potential energy was specified as additive pair potentials. The DQMC calculations were performed using the VSCF nodes as absorbing boundaries without the use of the wave function for importance sampling. In the case of Ar3, the DQMC-VSCF results could be compared with nearly exact results from other methods, and they were found better than those of VSCF alone but with errors as high as 8%. In the case of Ar13, the excitation energies for DQMC-VSCF and VSCF were found quite close to each other for the 33 fundamental excited states, thus exhibiting small “correlation” effects. It was noted that the combined method is better than the VSCF method and that improving on VSCF as with a vibrational M ller Plesset theory might provide even better results.
Quantum Monte Carlo: Direct calculation of corrections to trial wave functions and their energies
Authors: Anderson J B 
Published: November 2023

Abstract
This paper describes a much improved method for reducing the statistical error in fixed-node diffusion QMC calculations. The calculations are designed to determine (1) the difference between the true (fixed-node) wavefunction and a trial wavefunction, and (2) the difference between the fixed-node energy and the expectation value of the energy for the trial wavefunction. When the trial function is a good approximation to the fixed-node result, these differences are small and the statistical errors are smaller still. The nodes of the trial function are not corrected. The general method was described previously.a The basic diffusion equation is altered to allow calculation of the difference between the true and trial functions expressed as g = (‘1/J-’l/Jo)’I/Jo, and this results in additional distributed feed terms for positive and negative walkers. In the new procedure these walkers are generated in Metropolis variational calculations and subsequently used as starting walkers in diffusion calculations with drift. These are continued for a time sufficient to approach equilibrium distributions. In effect, a cancellation of positive and negative walkers in equivalent distributions leaves the correction term g and allows the energy difference to be determined. The method is most useful when the trial function is reasonably accurate. In the case of the ground state of He a trial wave function with an energy expectation value of -2.903 724 376 18 hartrees led to a correction of -0.000 000 000 86(2) h to give an energy within 0.000 000 000 02 h of the (separately known) true value. In the case of H2O with a trial function expectation energy of - 75.560 h, the corrected energy value was -76.16(1) h compared to the independently determined fixed-node energy of -76.17(1) h. It remains to be seen whether this can be extended to determining very accurate energy differences in correlated sampling for similar molecules.
Constraint dynamics for quantum Monte Carlo calculations
Authors: Sarsa A , Schmidt K E , Moskowitz J W 
Published: November 2023

Abstract
In diffusion QMC calculations for clusters of water molecules, it has been found useful in some cases to eliminate the internal motions of the molecules by treating them as rigid rotors.a This has greatly simplified the prediction of intermolecular properties of clusters. A similar situation exists for the internal motions of molecules themselves, in which it may be useful to constrain some of the internal motions. Thus, for large molecules one might wish to fix some bond distances or angles which are already tightly, but not completely, restrained. In this paper a convenient method for applying constraints in diffusion QMC is described and demonstrated. The method is adapted from a procedureb used in molecular dynamics simulations in which similar constraints are used. The constraints are applied as distance constraints between specified pairs of atoms by imposing forces to counter the motions which would otherwise alter their separations. Specifying these forces requires a careful consideration of problems of multiplication of time-step errors, but these are successfully eliminated to yield a relatively simple algorithm incorporating importance sampling. At each step, walkers are first moved in the usual way of drift and diffusion without constraint. This is followed by an iterative procedure in which each pair of atoms is adjusted until all constraints are satisfied. The method is demonstrated to give satisfactory results for the rigid-body treatment of a water molecule and for the ground states of methanol with a floppy dihedral-angle rotation involving one of the H-C-0-H strings of atoms. The method is clearly applicable to many different types of molecules, large and small.
Optimal orbitals from energy fluctuations in correlated wave functions
Authors: Filippi C , Fahy S 
Published: November 2023

Abstract
In conventional Hartree-Fock calculations for molecular systems the optimization of a trial wavefunction by energy minimization with respect to the orbitals of a determinantal wavefunction is relatively easy. When Jastrow factors are included with a determinant as for typical QMC trial functions the task becomes more difficult. Optimization by minimizing the variance in local energies has been one alternative. This paper describes another approach which is, in fact, an analog of the Hartree-Fock method and provides an exact solution to the problem of optimizing the orbitals when a Jastrow function is present.
Linear-scaling quantum Monte Carlo calculations
Authors: Williamson A J , Hood R Q , Grossman J C 
Published: November 2023

Abstract
This study demonstrates linear scaling with system size in fixednode diffusion QMC calculations with pseudopotentials for carbon fullerenes and for hydrogenated silicon clusters with nearly 1000 valence electrons. The range covered is C20 to C18o and SiH4 to Si211H140, The calculations were carried out with standard pseudopotentials (leaving four electrons per C or Si atom) and Slater Jastrow trial functions with orbitals from LDA density functional calculations. The key elements leading to linear scaling were constructions of sparse determinants and simplification of orbital functions. The LDA orbitals were obtained with a plane-wave basis set which was transformed to yield Wannier functions with maximum localization. These functions were then fitted to cubic spline expressions with a limited number of grid points and cut-off distances matching those of the plane-wave orbitals. The computational effort for evaluating trial functions of this type was clearly seen to behave in a linear fashion. Exploration of the effects of variation of cut-off radius revealed that energies, sensitive only to node structures, increased rapidly for cut-offs less than 7 bohr but were unaffected for cutoffs greater than 7 bohr. The accuracies of the calculations were checked in other ways. These included comparison calculations for SiH3 and Si5H12 using Gaussian, original plane-wave, and Wannier function basis sets which gave close agreement for energies.
Ab initio computation of molecular singlet-triplet energy differences using auxiliary field Monte Carlo
Authors: Baer R 
Published: November 2023

Abstract
About 15 years before this paper was published, all-electron fixed-node diffusion QMC calculations by Reynolds, Dupuis, and Lester0 had successfully duplicated the 9 kcal/mol seen in direct experimental measurements ofthe classic problem of singlet-triplet splitting for the methylene molecule CH2. This second QMC paper on the subject was designed less to investigate the CH2 system and more to investigate the method, in this case the shiftedcontour auxiliary field Monte Carlo (SC-AFMC) method,b which overcomes some of the stability problems of the original AFMC method.c The paper describes the application of SC-AFMC to the simplest singlet-triplet problem of linear H-He-H as well as that of methylene, this time with pseudopotentials. The applications were far from straightforward and required investigation of the various approximations needed to obtain the energy differences. Nonlocal B-LYP pseudopotentials were used, along with combinations of restricted and unrestricted HartreeFock determinantal wavefunctions. Correlated sampling was successful in reducing statistical error in energy differences but convergence was slow. Near degeneracies led to problems for H-He-H. Results were sensitive to cell size and grid spacing and especially sensitive to the type of pseudopotential used. Nevertheless, suitable choices produced singlet-triplet splittings in agreement with accepted values when pseudopotentials of the generalized gradient type were used. However, this agreement might have been fortuitous. Further studies of alternative approaches were indicated.
Quantum Monte Carlo for electronic excitations of free-base porphyrin
Authors: Aspuru-guzik A , Akramine O El , Grossman J C , Lester W A 
Published: November 2023

Abstract
With 216 Electrons, The Free-Base Porphyrin C20n4h14 Presents A Challenge To Ab Initio Electronic structure calculations. Since it is at the center of the mechanism of photosynthesis, as well as several other biological processes, there has been much interest in this molecule and its electronic spectrum, but despite a number of earlier studies, important questions remain open. This paper provides the most accurate calculations to date of energy levels of states involved in several allowed and nonallowed transitions seen in the spectrum.
Quantum Monte Carlo study of helium clusters doped with nitrous oxide: Quantum solvation and rotational dynamics
Authors: Moroni S , Blinov N , Roy P -N 
Published: November 2023

Abstract
The infrared spectra of small molecules embedded in helium nanodroplets display sharp rotational lines suggesting a decoupling of the molecular rotation from the motion of the helium atoms. The spectra observed for several different molecules have been explained in earlier reptation QMC calculationsa giving moments of inertia and thus effective rotational constants B as a function of the number N of helium atoms in a cluster. This paper reports such calculations for the nitrous oxide molecule NNO which has been observed to have a turnaround in the evolution of B with N. The value of B first decreases to a minimum at N = 6 to 7, then increases slightly to a maximum at N = 11, followed by another minimum and a slow increase. The reptation QMC calculations provided ground-state energies, density profiles, and correlation functions for angular momenta. The results gave excellent agreement with the experimentally determined values of B. The variations of B with N were reproduced quantitively, and the behavior was explained completely with the aid of the helium density profiles showing the accumulation of density at various positions surrounding the NNO molecule as N is increased. Additional calculations using finite-temperature path integral Monte Carlo (PIMC) gave excellent agreement with the energetics and structural properties given by the ground-state calculations. The rotational constants, obtained with Boltzmann statistics in the PIMC calculations, showed no turnaround and no oscillations, thereby indicating that the experimentally observed behavior is the result of exchange effects not included in the PIMC calculations.
Interaction effects in the mesoscopic regime: A quantum :rvionte Carlo study of irregular quantum dots
Authors: Ghosal A , Unirigar C J , Jiang H , Ullmo D , Baranger H U 
Published: November 2023

Abstract
The paper reported the extension of earlier QMC calculations for small symmetric quantum dots to large irregular dots, i.e., from the microscopic to the mesoscopic regime. For a large number N of electrons in a sufficiently irregular confining potential the motion of the electrons may be expected to- be chaotic, and mesoscopic fluctuations may result from electron interaction and interference effects. Studies using density functional theory (DFT) and the random phase approximation (RPA) have met with only limited success in treating these systems. This fixed-node diffusion QMC study was much more successful. The systems treated were two-dimensional quantum dots containing 10-30 electrons confined by a potential energy of the type culations were carried out for dots formed by six different sets of constants. Each of these was investigated with each number of electrons N and the total spin S given by S = 0, 1, and 2 for even N and S = 1/2, 3/2, and 5/2 for odd N in order to determine the ground-state energies and spins. Multi-determinant trial wavefunctions with simple Jastrow functions were assembled from Kohn-Sham orbitals, and coefficients for the determinants were optimized. Both VQMC and fixed-node DQMC calculations produced energies with statistical errors small compared to singleelectron energy-level spacings.
Quantum chemistry by random walk: Importance sampling for H+
3
Authors: Mentch F , Anderson J B 
Published: November 2023

Abstract
In this paper the combination of importance sampling° with diffusion QMC was shown to be remarkably effective in improving the accuracy of electonic structure calculations for molecular systems. The key to success was the use of a simple, fairly accurate trial wavefunction ΨT for which the function itself, its derivatives and the local energy Eioc may be easily computed. This, used in combination with the diffusion-with-drift expression for walkers corresponding to the product f = ΨΨT according to allows the energy to be evaluated as an average for all walkers of every step after reaching a fluctuating steady state. Since there is a time-step error associated with the simulation of diffusion, drift, and multiplication, varying the time-step and an extrapolation to zero step size are required. The result for H3 + in its triangular configuration of side length 1.6500 bohr was -1.3439 ± 0.0002 hartrees, a value well below the lowest variational energy levels at the time and having an error bar straddling the best modern value of -1.343 835 hartrees. The use of importance sampling along with higher computer speeds resulted in an uncertainty about a factor of 60 lower than that of the previous calculation.b
Ground state of excitonic molecules by the Green’s-function Monte Carlo method
Authors: Lee M A , Vashishta P , Kalia R K 
Published: November 2023

Abstract
The biexciton bound complex of two electrons and two holes is equivalent to the hydrogen molecule with different masses0 and it can be treated in the same way as the hydrogen molecule by QMC methods. For equal electron and proton masses the complex is equivalent to a positronium molecule. The authors applied simple diffusion QMC with importance sampling to calculate ground-state energies of biexcitons for a range of electron-to-hole mass ratios a= me/mh. The full four-body problem was treated with positive and negative charges of unity interacting with Coulomb potentials. Since the ground state is nodeless, the problem of nodes does not occur, and the importance sampling function was taken as a simple product of electron-electron and hole-hole Jastrow functions with exponential terms. The results gave energies considerably lower than variational estimates and better agreement with experimental measurements for several crystalline materials. The limiting behavior as a -+ 0 was found in excellent agreement with the exact result.
Quantum Monte Carlo For Molecules: Green’s Function And Nodal Release
Authors: Ceperley D M , Alder B J 
Published: November 2023

Abstract
This paper describes the application of the nodal release or “transient estimate” method,0 successfully used earlier for treating the electron gas problem, to several small molecules: H3, LiH, Li2, and H20. This method can, in principle, provide a means for overcoming the node location problem for such systems, but it does require difficult extrapolations for most systems of interest. The basic calculations are carried out as for simple Green’s function QMC without nodes as boundaries. A trial wavefunction ‘I/Jr is used to locate approximate node positions, and a guide function ‘1/Ja, everywhere positive and approximately equal to l’I/Jrl and nonzero but small at the nodes, is used for importance sampling. A released-node calculation is begun with walkers at steady state in a fixed-node calculation. These are then released and permitted to cross fixed-node surfaces. After a number of steps, the distribution of walkers includes walkers inside and outside the starting region. The difference (inside less outside) approaches the fermion ground state distribution, but with increasing number of steps the difference is lost in the noise as the inside and outside approach boson ground state distributions. Nevertheless, useful results were obtained for the systems examined, with energies correct within their statistical uncertainties. For the largest system, H20, the calculated energy was - 76.43 ± 0.02 hartrees, which may be compared with a value of - 76.438 hartrees based on experimental measurements.
Quantum Monte Carlo calculation of the singlet-triplet splitting in methylene
Authors: Reynolds P J , Dupuis M , Lester W A 
Published: November 2023

Abstract
The methylene molecule CH2 is one of those simple species with a long history in the development of quantum chemistry. First observed experimentally in 1959 by Herzberg and Shoosmitha it was the object of an especially important near-SCF study by Foster and Boysb predicting (correctly) the ground state to be the triplet 3 B1 with a bond angle of about 129°. Shortly thereafter, Herzberg concluded the molecule in the 3B1 state was linear, but eventually experiments by others, as well as higher level calculations, showed Foster and Boys to be correct.c The singlet-triplet splitting (singlet energy minus triplet energy), initially thought to be about 2 kcal/mole from experiment and about 30 kcal/mol from theory, is now known to be 9-11 kcal/mole. The fixed-node calculations of Reynolds et al. were carried out for optimum geometries indicated by analytic variational calculations, and they gave energies more than 15 kcal/mole below the lowest energy variational calculations available at the time. The trial functions for node location and importance sampling were single-determinant double-zeta functions with optimized Jastrow terms. The QMC result for singlet-triplet splitting, obtained by subtracting energies, is 9.4 ± 2.2 kcal/mole. With allowance for the zero-point energy and relativistic effects the splitting becomes 8.9 ± 2.2 kcal/mole. These are in very good agreement with very recent theoretical and experimental values. This substantial cancellation of node-location error for these two similar systems occurs in the same way as expected for the somewhat larger errors in analytic variational calculations for similar systems.
Quantum Monte Carlo calculations on Be and LiH
Authors: Harrison R J , Handy N C 
Published: November 2023

Abstract
In their first paper in the quantum Monte Carlo area, Harrison and Handy investigated the use of multi-configuration trial wavefunctions and various forms of Jastrow functions in fixednode QMC. Calculations were repeated for the small molecules He, Be2+, Be, and LiH. For the nodeless ground states of He and Be2+, they used two- to six-term Hylleraas functions and found significant gains in efficiency for the more accurate trial functions despite the additional terms. They reproduced known energies for these species within statistical error. For Be, it was found that the fixed-node results for a five-term multi-configuration SCF function were far superior to those for a single-term SCF trial function. For LiH, the use of one-, two-, and four-term MC-SCF functions was found to produce little improvement in the variance in local energies or the values of the energies obtained. Recovery of correlation energy was about 99% in each case. This paper introduced the use of higher order terms in a Jastrow function similar to those used by Handy and Boysa in their transcorrelated method. Also considered was the use of an additional electron-nucleus term in the Jastrow function. These attempts at improving the Jastrow factor were not very successful, but planted the seeds for later successes by Schmidt and Moskowitz.