Bond dissocation and conformational energetics of tetrasulfur: a quantum Monte Carlo study

Variational Monte Carlo (VMC) and fixed-node diffusion Monte Carlo (DMC) calculations are performed for S4. The effect of single- and multireference trial functions, as well as choice of orbitals, is investigated for its effect on the quality of the Monte Carlo estimates. Estimates of symmetric (two S2 molecules) and asymmetric (S atom and S3 molecule) bond dissociation are reported. The conformational change of S4 from C2v to D2h defines a double-well potential and is also estimated. Multireference DMC with natural orbitals (DMC/NO) estimates the energy of the conformational change as 1.20(20) kcal/mol; the dissociation of the long S-S single bond is estimated at 21.1(1.3) kcal/mol, and the asymmetric bond energy is estimated as 53.2(2.4) kcal/mol. An estimate of the total atomization energy using multireference DMC/NO gives a value of 219.5(2.2) kcal/mol. The relative quality of result and implications for simplified trial function design are discussed.     

Monte Carlo methods for small molecule high-throughput experimentation

By analogy with Monte Carlo algorithms, we propose new strategies for design and redesign of small molecule libraries in high-throughput experimentation, or combinatorial chemistry. Several Monte Carlo methods are examined, including Metropolis, three types of biased schemes, and composite moves that include swapping or parallel tempering. Among them, the biased Monte Carlo schemes exhibit particularly high efficiency in locating optimal compounds. The Monte Carlo strategies are compared to a genetic algorithm approach. Although the best compounds identified by the genetic algorithm are comparable to those from the better Monte Carlo schemes, the diversity of favorable compounds identified is reduced by roughly 60%.     

Scheme for adding electron-nucleus cusps to Gaussian orbitals

A simple scheme is described for introducing the correct cusps at nuclei into orbitals obtained from Gaussian basis set electronic structure calculations. The scheme is tested with all-electron variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods for the Ne atom, the H2 molecule, and 55 molecules from a standard benchmark set. It greatly reduces the variance of the local energy in all cases and slightly improves the variational energy. This scheme yields a general improvement in the efficiency of all-electron VMC and DMC calculations using Gaussian basis sets.     

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with It? calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Ito; calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.     

Assessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters

We present a detailed study of the energetics of water clusters (H(2)O)(n) with n ≤ 6, comparing diffusion Monte Carlo (DMC) and approximate density functional theory (DFT) with well converged coupled-cluster benchmarks. We use the many-body decomposition of the total energy to classify the errors of DMC and DFT into 1-body, 2-body and beyond-2-body components. Using both equilibrium cluster configurations and thermal ensembles of configurations, we find DMC to be uniformly much more accurate than DFT, partly because some of the approximate functionals give poor 1-body distortion energies. Even when these are corrected, DFT remains considerably less accurate than DMC. When both 1- and 2-body errors of DFT are corrected, some functionals compete in accuracy with DMC; however, other functionals remain worse, showing that they suffer from significant beyond-2-body errors. Combining the evidence presented here with the recently demonstrated high accuracy of DMC for ice structures, we suggest how DMC can now be used to provide benchmarks for larger clusters and for bulk liquid water.     

A version of diffusion Monte Carlo method based on random grids of coherent states. II. Six-dimensional simulation of electronic states of H2

We report a new version of the diffusion Monte Carlo (DMC) method, based on coherent-state quantum mechanics. Randomly selected grids of coherent states in phase space are used to obtain numerical imaginary time solutions of the Schrodinger equation, with an iterative refinement technique to improve the quality of the Monte Carlo grid. Accurate results were obtained, for the appropriately symmetrized two lowest states of the hydrogen molecule, by Monte Carlo sampling and six-dimensional propagation in the full phase space.     

Dissociation energy of the water dimer from quantum Monte Carlo calculations

We report a study of the electronic dissociation energy of the water dimer using quantum Monte Carlo techniques. We have performed variational quantum Monte Carlo and diffusion quantum Monte Carlo (DMC) calculations of the electronic ground state of the water monomer and dimer using all-electron and pseudopotential approaches. We have used Slater-Jastrow trial wave functions with B3LYP type single-particle orbitals, into which we have incorporated backflow correlations. When backflow correlations are introduced, the total energy of the water monomer decreases by about 4-5 mhartree, yielding a DMC energy of -76.428 30(5) hartree, which is only 10 mhartree above the experimental value. In our pseudopotential DMC calculations, we have compared the total energies of the water monomer and dimer obtained using the locality approximation with those from the variational scheme recently proposed by Casula [Phys. Rev. B 74, 161102(R) (2006)]. The time step errors in the Casula scheme are larger, and the extrapolation of the energy to zero time step always lies above the result obtained with the locality approximation. However, the errors cancel when energy differences are taken, yielding electronic dissociation energies within error bars of each other. The dissociation energies obtained in our various all-electron and pseudopotential calculations range between 5.03(7) and 5.47(9) kcalmol and are in good agreement with experiment. Our calculations give monomer dipole moments which range between 1.897(2) and 1.909(4) D and dimer dipole moments which range between 2.628(6) and 2.672(5) D.     

Barrier heights of hydrogen‐transfer reactions with diffusion quantum monte carlo method

Hydrogen‐transfer reactions are an important class of reactions in many chemical and biological processes. Barrier heights of H‐transfer reactions are underestimated significantly by popular exchange–correlation functional with density functional theory (DFT), while coupled‐cluster (CC) method is quite expensive and can be applied only to rather small systems. Quantum Monte‐Carlo method can usually provide reliable results for large systems. Performance of fixed‐node diffusion quantum Monte‐Carlo method (FN‐DMC) on barrier heights of the 19 H‐transfer reactions in the HTBH38/08 database is investigated in this study with the trial wavefunctions of the single‐Slater–Jastrow form and orbitals from DFT using local density approximation. Our results show that barrier heights of these reactions can be calculated rather accurately using FN‐DMC and the mean absolute error is 1.0 kcal/mol in all‐electron calculations. Introduction of pseudopotentials (PP) in FN‐DMC calculations improves efficiency pronouncedly. According to our results, error of the employed PPs is smaller than that of the present CCSD(T) and FN‐DMC calculations. FN‐DMC using PPs can thus be applied to investigate H‐transfer reactions involving larger molecules reliably. In addition, bond dissociation energies of the involved molecules using FN‐DMC are in excellent agreement with reference values and they are even better than results of the employed CCSD(T) calculations using the aug‐cc‐pVQZ basis set. © 2017 Wiley Periodicals, Inc.     

Quantum Monte Carlo study of the Ne atom and the Ne+ ion

We report all-electron and pseudopotential calculations of the ground-state energies of the neutral Ne atom and the Ne(+) ion using the variational and diffusion quantum Monte Carlo (DMC) methods. We investigate different levels of Slater-Jastrow trial wave function: (i) using Hartree-Fock orbitals, (ii) using orbitals optimized within a Monte Carlo procedure in the presence of a Jastrow factor, and (iii) including backflow correlations in the wave function. Small reductions in the total energy are obtained by optimizing the orbitals, while more significant reductions are obtained by incorporating backflow correlations. We study the finite-time-step and fixed-node biases in the DMC energy and show that there is a strong tendency for these errors to cancel when the first ionization potential (IP) is calculated. DMC gives highly accurate values for the IP of Ne at all the levels of trial wave function that we have considered.     

Simulation of steady-state diffusion: Driving force ensured by dual control volumes or local equilibrium Monte Carlo

We provide a systematic comparative analysis of various simulation methods for studying steady-state diffusive transport of molecular systems. The methods differ in two respects: (1) the actual method with which the dynamics of the system is handled can be a direct simulation technique [molecular dynamics (MD) and dynamic Monte Carlo (DMC)] or can be an indirect transport equation [the Nernst-Planck (NP) equation], while (2) the driving force of the steady-state transport can be maintained with control cells on the two sides of the transport region [dual control volume (DCV) technique] or it can be maintained in the whole simulation domain with the local equilibrium Monte Carlo (LEMC) technique, where the space is divided into small subvolumes, different chemical potentials are assigned to each, and grand canonical Monte Carlo simulations are performed for them separately. The various combinations of the transport-methods with the driving-force methods have advantages and disadvantages. The MD+DCV and DMC+DCV methods are widely used to study membrane transport. The LEMC method has been introduced with the NP+LEMC technique, which was proved to be a fast, but somewhat empirical method to study diffusion [D. Boda and D. Gillespie, J. Chem. Theor. Comput. 8, 824 (2012)]. In this paper, we introduce the DMC+LEMC method and show that the resulting DMC+LEMC technique has the advantage over the DMC+DCV method that it provides better sampling for the flux, while it has the advantage over the NP+LEMC method that it simulates dynamics directly instead of hiding it in an external adjustable parameter, the diffusion coefficient. The information gained from the DMC+LEMC simulation can be used to construct diffusion coefficient profiles for the NP+LEMC calculations, so a simultaneous application of the two methods is advantageous.     

Quantum Monte Carlo study of first-row atoms using transcorrelated variational Monte Carlo trial functions

The effect of using the transcorrelated variational Monte Carlo (TC-VMC) approach to construct a trial function for fixed node diffusion Monte Carlo (DMC) energy calculations has been investigated for the first-row atoms, Li to Ne. The computed energies are compared with fixed node DMC energies obtained using trial functions constructed from Hartree-Fock and density functional levels of theory. Despite major VMC energy improvement with TC-VMC trial functions, no improvement in DMC energy was observed using these trial functions for the first-row atoms studied. The implications of these results on the nodes of the trial wave functions are discussed.     

Quantum Monte Carlo study of the reaction: Cl+CH3OH-->CH2OH+HCl

A theoretical study is reported of the Cl+CH3OH-->CH2OH+HCl reaction based on the diffusion Monte Carlo (DMC) variant of the quantum Monte Carlo method. Using a DMC trial function constructed as a product of Hartree-Fock and correlation functions, we have computed the barrier height, heat of reaction, atomization energies, and heats of formation of reagents and products. The DMC heat of reaction, atomization energies, and heats of formation are found to agree with experiment to within the error bounds of computation and experiment. M?ller-Plesset second order perturbation theory (MP2) and density functional theory, the latter in the B3LYP generalized gradient approximation, are found to overestimate the experimental heat of reaction. Intrinsic reaction coordinate calculations at the MP2 level of theory demonstrate that the reaction is predominantly direct, i.e., proceeds without formation of intermediates, which is consistent with a recent molecular beam experiment. The reaction barrier as determined from MP2 calculations is found to be 2.24 kcal/mol and by DMC it is computed to be 2.39(49) kcal/mol.     

Diffusion Monte Carlo Calculations of Zero-Point Energies of Methanol and Deuterated Methanol

Diffusion Monte Carlo (DMC) simulations have been used to obtain quantum zero-point energies of methanol and all its isotopologs and isotopomers, using a new, accurate semi-global potential energy surface. This potential energy surface is a precise, permutationally invariant fit to 6676 ab initio energies, obtained at the CCSD(T)-F12b/aug-cc-pVDZ level of theory. Quantum zero-point energies of deuterated methanol isotopomers are very close to each other and so a simple statistical argument can be used to estimate the populations of each isotopomer at very low-temperatures. The DMC simulations also indicate that there is virtually zero probability for H/D exchange in the zero-point state. © 2019 Wiley Periodicals, Inc.     

Monte Carlo computation of ground‐state energy derivatives

Monte Carlo is a simple technique, which uses random numbers to compute ground‐state energies of small molecules (and quantum systems in general). The results always have a small statistical error, which poses a major obstacle when estimating properties defined as ground‐state‐energy derivatives (such as the molecule's geometry, its vibrational frequencies, polarizabilities, etc.). In this article, we present and demonstrate an approach that makes an accurate Monte–Carlo estimation of such derivatives possible. This is achieved by realizing that the simulation constitutes an autocorrelated stochastic process, whose proper analysis then enables us to estimate various energy derivatives as a combination of total correlation between readily computable quantities. The resulting procedure is a natural extension of the usual Monte Carlo algorithm for computing the ground‐state energy, with relatively small computational overhead. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Computing the energy of a water molecule using multideterminants: a simple, efficient algorithm

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule.     

Binding of hydrogen on benzene, coronene, and graphene from quantum Monte Carlo calculations

Quantum Monte Carlo calculations with the diffusion Monte Carlo (DMC) method have been used to compute the binding energy curves of hydrogen on benzene, coronene, and graphene. The DMC results on benzene agree with both M?ller-Plessett second order perturbation theory (MP2) and coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] calculations, giving an adsorption energy of ～25 meV. For coronene, DMC agrees well with MP2, giving an adsorption energy of ～40 meV. For physisorbed hydrogen on graphene, DMC predicts a very small adsorption energy of only 5 ± 5 meV. Density functional theory (DFT) calculations with various exchange-correlation functionals, including van der Waals corrected functionals, predict a wide range of binding energies on all three systems. The present DMC results are a step toward filling the gap in accurate benchmark data on weakly bound systems. These results can help us to understand the performance of current DFT based methods, and may aid in the development of improved approaches.     

Quantum monte carlo study of heats of formation and bond dissociation energies of small hydrocarbons

A quantum Monte Carlo (QMC) benchmark study of heats of formation at 298 K and bond dissociation energies (BDEs) of 22 small hydrocarbons is reported. Diffusion Monte Carlo (DMC) results, obtained using a simple product trial wavefunctions consisting of a single determinant and correlation function, are compared to experiment and to other theory including a version of complete basis set theory (CBS‐Q) and density functional theory (DFT) with the B3LYP functional. For heats of formation, the findings are a mean absolute deviation from experiment of 1.2 kcal/mol for CBS‐Q, 2.0 kcal/mol for B3LYP, and 2.2 kcal/mol for DMC. The mean absolute deviation of 31 BDEs is 2.0 kcal/mol for CBS‐Q, 4.2 kcal/mol for B3LYP, and 2.5 kcal/mol for DMC. These findings are for 17 BDEs of closed‐shell molecules that have mean absolute deviations from experiment of 1.7 kcal/mol (CBS‐Q), 4.0 kcal/mol (B3LYP), and 2.2 kcal/mol (DMC). The corresponding results for the 14 BDEs of open‐shell molecules studied are 2.4 kcal/mol (CBS‐Q), 4.3 kcal/mol (B3LYP), and 2.9 kcal/mol (DMC). The DMC results provide a baseline from which improvement using multideterminant trial functions can be measured. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 583–592, 2005     

Efficient global biopolymer sampling with end-transfer configurational bias Monte Carlo

We develop an "end-transfer configurational bias Monte Carlo" method for efficient thermodynamic sampling of complex biopolymers and assess its performance on a mesoscale model of chromatin (oligonucleosome) at different salt conditions compared to other Monte Carlo moves. Our method extends traditional configurational bias by deleting a repeating motif (monomer) from one end of the biopolymer and regrowing it at the opposite end using the standard Rosenbluth scheme. The method's sampling efficiency compared to local moves, pivot rotations, and standard configurational bias is assessed by parameters relating to translational, rotational, and internal degrees of freedom of the oligonucleosome. Our results show that the end-transfer method is superior in sampling every degree of freedom of the oligonucleosomes over other methods at high salt concentrations (weak electrostatics) but worse than the pivot rotations in terms of sampling internal and rotational sampling at low-to-moderate salt concentrations (strong electrostatics). Under all conditions investigated, however, the end-transfer method is several orders of magnitude more efficient than the standard configurational bias approach. This is because the characteristic sampling time of the innermost oligonucleosome motif scales quadratically with the length of the oligonucleosomes for the end-transfer method while it scales exponentially for the traditional configurational-bias method. Thus, the method we propose can significantly improve performance for global biomolecular applications, especially in condensed systems with weak nonbonded interactions and may be combined with local enhancements to improve local sampling.     

Efficiency of nested Markov chain Monte Carlo for polarizable potentials and perturbed Hamiltonians

Nested Markov chain Monte Carlo is a rigorous way to enhance sampling of a given energy landscape using an auxiliary, approximate potential energy surface. Its practical efficiency mainly depends on how cheap and how different are the auxiliary potential with respect to the reference system. In this article, a combined efficiency index is proposed and assessed for two important families of energy surfaces. As illustrated for water clusters, many‐body polarizable potentials can be approximated by simplifying the polarization contribution and keeping only the two‐body terms. In small systems, neglecting polarization entirely is also acceptable. When the reference potential energy is obtained from diagonalization of a quantum mechanical Hamiltonian, a first‐order perturbation scheme can be used to estimate the energy difference occuring on a Monte Carlo move. Our results indicate that this perturbation approximation performs well provided that the number of steps between successive diagonalization is adjusted beforehand. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2342–2346, 2010