Efficient quantum monte carlo energies for molecular dynamics simulations

A method is presented to treat electrons within the many-body quantum Monte Carlo (QMC) approach "on-the-fly" throughout a molecular dynamics (MD) simulation. Our approach leverages the large (10-100) ratio of the QMC electron to MD ion motion to couple the stochastic, imaginary-time electronic and real-time ionic trajectories. This continuous evolution of the QMC electrons results in highly accurate total energies for the full dynamical trajectory at a fraction of the cost of conventional, discrete sampling. We show that this can be achieved efficiently for both ground and excited states with only a modest overhead to an ab initio MD method. The accuracy of this dynamical QMC approach is demonstrated for a variety of systems, phases, and properties, including optical gaps of hot silicon quantum dots, dissociation energy of a single water molecule, and heat of vaporization of liquid water.     

Quantum Monte Carlo study of small hydrocarbon atomization energies

A benchmark study of atomization energies is reported for 22 hydrocarbons using single determinant trial functions in the diffusion Monte Carlo (DMC) variant of the quantum Monte Carlo (QMC) method. The DMC atomization energies are compared to experiment, a complete basis set approach (CBS-Q), density functional theory with the B3LYP functional, and coupled-cluster singles, doubles and perturbative triples, CCSD(T), methods. Comparison of the DMC results to experiment yields a mean absolute deviation of 1.9kcalmol^?1, which is comparable to that of the B3LYP/cc-pVQZ (1.7kcalmol^?1) level of theory, but less accurate than that of CBS-Q (1.1kcalmol^?1). DMC performs similarly for both closed-shell and open-shell molecules with mean absolute deviations of 2.1kcalmol^?1 for the former and 1.7kcalmol^?1 for the latter systems. The use of experimental zero-point energies (ZPEs), rather than scaled B3LYP ZPEs, is found to have negligible effect on DMC atomization energies. The latter reported here provide a baseline from which further improvement in the calculation of DMC atomization energies, including the use of multi-determinant and other trial function improvements, can be measured.     

A new approach to electron-electron interactions in strongly correlated systems at arbitrary spin-polarization and temperature

The uniform electron fluid is the reference model for density functional calculations. Even for this system, many-body perturbation theory, and related methods become questionable when the density parameter r_s exceeds unity. Hence, quantum Monte Carlo (QMC) simulation has been almost the only applicable method. We review a new approach, which uses a mapping of the quantum fluid to a classical Coulomb fluid, based on density-functional concepts. It is applicable at finite temperatures and arbitrary spin polarizations as well, and correctly recovers even the logarithmic terms in the exchange and correlations energies close to T=0. We show by detailed comparison with available QMC data that the method yields accurate pair-distribution functions, spin-dependent energies, static local-field factors, Landau parameter-based quantities like m∗ and g∗, for strongly coupled electron fluids.     

EQUATION OF STATE OF FLUID He+H2 MIXTURES UNDER HIGH PRESSURE

A statistical mechanical variational theory and an improved van der Waals one-fluid model have been used to compute the equation of state of fluid He+H₂ mixtures with different H₂:He compositions under high pressure. The first-order quantum correction is included. Comparing the present results with Monte Carlo simulations indicates that the quantum corrections for calculating the thermodynamic properties become increasingly important at lower temperatures.     

Convergence behaviour of Green's function quantum Monte Carlo simulations of pi electron systems

Green's function quantum Monte Carlo (GF QMC) simulations of fermionic ensembles require the definition of a so-called spectral parameter W to yield trustworthy estimates of the fully correlated ground state energy E. In the present work we discuss the influence of the shift parameter, W, on the convergence behaviour of GF QMC simulations. As model systems we have considered some π molecules which are studied in the framework of the Pariser–Parr–Pople (PPP) Hamiltonian. The influence of the W parameter on the convergence of the GF QMC simulations in many-electron systems with an odd number of electronic permutations within one spin direction exceeds the influence observed in systems without such odd permutations. They do not occur in polyenes and Huckel annulenes with an electron count of (4n + 2) (n = 0, 1, 2…). The GF QMC technique adopted as a computational tool has been developed to study π molecules with fermionic sign problems owing to odd electronic interchanges within one spin direction.     

A Monte Carlo model for determination of binary diffusion coefficients in gases

A Monte Carlo method has been developed for the calculation of binary diffusion coefficients in gas mixtures. The method is based on the stochastic solution of the linear Boltzmann equation obtained for the transport of one component in a thermal bath of the second one. Anisotropic scattering is included by calculating the classical deflection angle in binary collisions under isotropic potential. Model results are compared to accurate solutions of the Chapman–Enskog equation in the first and higher orders. We have selected two different cases, H₂ in H₂ and O in O₂, assuming rigid spheres or using a model phenomenological potential. Diffusion coefficients, calculated in the proposed approach, are found in close agreement with Chapman–Enskog results in all the cases considered, the deviations being reduced using higher order approximations.     

Quantum Monte Carlo studies on small molecules

The Variational Monte Carlo (VMC) and Fixed-Node Diffusion Monte Carlo (FNDMC) methods have been examined, through studies on small molecules. New programs have been written which implement the (by now) standard algorithms for VMC and FNDMC. We have employed and investigated throughout our studies the accuracy of the common Slater–Jastrow trial wave function. Firstly, we have studied a range of sizes of the Jastrow correlation function of the Boys–Handy form, obtained using our optimization program with analytical derivatives of the central moments in the local energy. Secondly, we have studied the effects of Slater-type orbitals (STOs) that display the exact cusp behaviour at nuclei. The orbitals make up the all important trial determinant, which determines the fixed nodal surface. We report all-electron calculations for the ground state energies of Li₂, Be₂, H₂O, NH₃, CH₄ and H₂CO, in all cases but one with accuracy in excess of 95%. Finally, we report an investigation of the ground state energies, dissociation energies and ionization potentials of NH and NH⁺. Recent focus paid in the literature to these species allow for an extensive comparison with other ab initio methods. We obtain accurate properties for the species and reveal a favourable tendency for fixed-node and other systematic errors to cancel. As a result of our accurate predictions, we are able to obtain a value for the heat of formation of NH, which agrees to within less than 1 kcal mol^?1 to other ab initio techniques and 0.2 kcal mol^?1 of the experimental value.     

Asymmetry in the nuclear magnetic shielding tensor

The applicability of Green's function (GF) and Feynman path-integral quantum Monte Carlo (QMC) methods for the simulation of cyclic networks with (4n + 2) and 4n (n = 1, 2, 3, …) electrons is analysed. Both QMC techniques are employed in simulations on the basis of the simple Hückel Hamiltonian which is exclusively defined by nearest-neighbour hopping elements. In addition we have used the Pariser-Parr-Pople (PPP) Hamiltonian to perform GF QMC simulations. The electronic energies E derived by the QMC methods are compared either with Hückel molecular orbital (HMO) results or exact configuration interaction data where (π) electronic correlations are fully taken into account. A sign problem occurs in QMC simulations of 4n annulenes. This leads to an error in the total energy in the standard formulations of the employed QMC techniques, which is enhanced with decreasing ring size. A simple modification in the QMC formalisms is suggested to avoid the numerical uncertainties caused by the sign problem in 4n annulenes. Renormalization of the kinetic hopping integrals t by t cos (π/M) with M abbreviating the number of atomic sites leads to ground state energies as well as any other quantity close to the values derived by conventional diagonalization techniques. Substitution of t against t cos (π/M) conserves a common sign of all matrix elements containing the hopping. The occurrence of negative probabilities, which lead to numerical problems in the QMC simulations, is thereby prevented. The transformation suggested in 4n rings has a formal connection to so-called Möbius rings.     

Caged H atom and H2 molecule in relation to Monte Carlo study of molecular dissociation at constant volume

Summary Analytic results for electronic kinetic energy are first presented for a hydrogen atom in a spherical cage for two radii near to the corresponding densities employed in the path-integral Monte Carlo study of isochoric molecular dissociation in dense hydrogen by Magroet al. (Magro W. R., Ceperley D. M., Pierleoni C. andBernu B.,Phys. Rev. Lett.,76 (1996) 1240). The relevance of the ?cage? results to the behaviour of dense atomic hydrogen is pointed out. Attention is then shifted to the molecular regime, and the variation with density of electronic kinetic energy for a H₂ molecule in a rigid spheroidal cage is compared and contrasted with the Monte Carlo findings. The rigid-cage model mimics this, as well as bond length contraction, under compression.     

Properties of cationic pnicogen-bonded complexes F4-nHnP+:N-base with H–P···N linear and n = 1–4

Ab initio MP2/aug'-cc-pVTZ calculations have been carried out to investigate the pnicogen-bonded complexes F_4-nH_nP⁺:N-base, for n = 1–4, each with a linear or nearly linear H_ax–P···N alignment. The sp³-hybridised nitrogen bases include NH₃, NClH₂, NFH₂, NCl₂H, NCl₃, NFCl₂, NF₂H, NF₂Cl, and NF_3, and the sp bases are NCNH₂, NCCH₃, NP, NCOH, NCCl, NCH, NCF, NCCN, and N₂. Binding energies increase as the P–N distance decreases, with an exponential curve showing this relationship when complexes with sp³ and sp hybridised bases are treated separately. However, the correlations are not as good as they are for the complexes F_4-nH_nP⁺:N-base for n = 0–3 with F–P···N linear. Different patterns are observed for the change in the binding energies of complexes with a particular base as the number of F atoms in the acid changes. Thus, the particular acid–base pair is a factor in determining the binding energies of these complexes.

Three different charge-transfer interactions stabilise these complexes, namely N_lp→σ*P–H_ax, N_lp→σ*P–F_eq, and N_lp→σ*P–H_eq. Unlike the corresponding complexes with F–P···N linear, N_lp→σ*P–H_ax is not always the dominant charge-transfer interaction, since N_lp→σ*P–F_eq is greater in some complexes. N_lp→σ*P–H_eq makes the smallest contribution to the total charge-transfer energy. The total charge-transfer energies of all complexes increase exponentially as the P–N distance decreases in a manner very similar to that observed for the series of complexes with F–P···N linear.

Equation-of-motion coupled cluster singles and doubles (EOM-CCSD) spin–spin coupling constants ^1pJ(P–N) across the pnicogen bond vary with the P–N distance, but different patterns are observed which depend on the nature of the acid, and for some acids, on the hybridisation of the nitrogen base. ^1pJ(P–N) values for complexes of F₃HP⁺ initially increase as the P–N distance decreases, reach a maximum, and then decrease with decreasing P–N distance as the P···N bond acquires increased covalent character. ^1pJ(P–N) for complexes with H–P···N linear and those with F–P···N linear exhibit similar distance dependencies depending on the number of F atoms in equatorial positions and the hybridisation of the base. Complexation may increase, decrease, or leave the P–H_ax distance unchanged, but ¹J(P–H_ax) always decreases relative to the corresponding isolated ion. Decreasing ¹J(P–H_ax) can be related to decreasing intermolecular P–N distance.     

Plan for nuclear symmetry energy experiments using the LAMPS system at the RIB facility RAON in Korea

We review the calculation of the equation of state of pure neutron matter using quantum Monte Carlo (QMC) methods. QMC algorithms permit the study of many-body nuclear systems using realistic two- and three-body forces in a non-perturbative framework. We present the results for the equation of state of neutron matter, and focus on the role of three-neutron forces at supranuclear density. We discuss the correlation between the symmetry energy, the neutron star radius and the symmetry energy. We also combine QMC and theoretical models of the three-nucleon interactions, and recent neutron star observations to constrain the value of the symmetry energy and its density dependence.     

Electron emission from diamondoids: a diffusion quantum Monte Carlo study

We present density-functional theory (DFT) and quantum Monte Carlo (QMC) calculations designed to resolve experimental and theoretical controversies over the optical properties of H-terminated C nanoparticles (diamondoids). The QMC results follow the trends of well-converged plane-wave DFT calculations for the size dependence of the optical gap, but they predict gaps that are 1-2 eV higher. They confirm that quantum confinement effects disappear in diamondoids larger than 1 nm, which have gaps below that of bulk diamond. Our QMC calculations predict a small exciton binding energy and a negative electron affinity (NEA) for diamondoids up to 1 nm, resulting from the delocalized nature of the lowest unoccupied molecular orbital. The NEA suggests a range of possible applications of diamondoids as low-voltage electron emitters.     

Quantum Monte Carlo calculations of nanostructure optical gaps: application to silicon quantum dots

Quantum Monte Carlo (QMC) calculations of the optical gaps of silicon quantum dots ranging in size from 0 to 1.5 nm are presented. These QMC results are used to examine the accuracy of density functional (DFT) and empirical pseudopotential based calculations. The GW approximation combined with a solution of the Bethe-Salpeter equation performs well but is limited by its scaling with system size. Optical gaps predicted by DFT vary by 1-2 eV depending on choice of functional. Corrections introduced by the time dependent formalism are found to be minimal in these systems.     

van der Waals interactions between thin metallic wires and layers

Quantum Monte Carlo (QMC) methods have been used to obtain accurate binding-energy data for pairs of parallel thin metallic wires and layers modeled by 1D and 2D homogeneous electron gases. We compare our QMC binding energies with results obtained within the random phase approximation, finding significant quantitative differences and disagreement over the asymptotic behavior for bilayers at low densities. We have calculated pair-correlation functions for metallic biwire and bilayer systems. Our QMC data could be used to investigate van der Waals energy functionals.     

Electron correlation in two-dimensional systems: CHNC approach to finite-temperature and spin-polarization effects

Applying the classical-map hypernetted-chain method (CHNC) developed recently by Dharma-wardana and Perrot, we have studied the temperature and spin-polarization effects on electron correlation in the uniform quantum two-dimensional gas (2DEG) over a wide range of temperature T and spin-polarization ζ. The quantum fluid at the temperature T is mapped to a classical fluid at the temperature T_cf given by T_cf²=T²+T_q², where the quantum temperature T_q is determined by comparing the calculated correlation energy to that of Monte Carlo results for the fully spin-polarized quantum system at zero temperature. By the iterative solution of the modified HNC equation and the Ornstein-Zernike equation, we have obtained the pair distribution function (PDF) and correlation energy for the two-component classical 2DEG with a classical fluid temperature T_cf. The anti-parallel bridge function B₁₂(r) appearing in the modified HNC equation is determined by using the Monte Carlo correlation energy at T=0 or STLS (Singwi-Tosi-Land-Sjölander) result at T>0 and the numerical solution to the Percus-Yevick (PY) equation for the system of hard disks. By calculating the Pauli potential, the bridge function, PDFs, structure factors and correlation energy, we have shown that in some cases, the properties of the uniform quantum 2DEG depend remarkably on the temperature and spin-polarization.     

Computation of partial molar properties using continuous fractional component Monte Carlo

ABSTRACT

An alternative method for calculating partial molar excess enthalpies and partial molar volumes of components in Monte Carlo (MC) simulations is developed. This method combines the original idea of Frenkel, Ciccotti, and co-workers with the recent continuous fractional component Monte Carlo (CFCMC) technique. The method is tested for a system of Lennard–Jones particles at different densities. As an example of a realistic system, partial molar properties of a [NH₃, N₂, H₂] mixture at chemical equilibrium are computed at different pressures ranging from P = 10 to 80 MPa. Results obtained from MC simulations are compared to those obtained from the PC-SAFT Equation of State (EoS) and the Peng–Robinson EoS. Excellent agreement is found between the results obtained from MC simulations and PC-SAFT EoS, and significant differences were found for PR EoS modelling. We find that the reaction is much more exothermic at higher pressures.     

Thermodynamic test of defect formation energies calculated by simulation techniques for nonstoichiometric oxides. application to CeO2−x, UO2 ± x, TiO2−x, Mn1−xO,Fe1−xO

A relation has been derived between (i) ΔH(O₂), the partial molar enthalpy of mixing of oxygen in a nonstoichiometric oxide, which may be directly measured by high temperature microcalorimetry, and (ii) the defect formation energies which may be calculated by simulation techniques. This relation permits the testing of the consistency between the experimental ΔH(O₂) and the theoretical defect formation energies. This thermodynamic test, though necessary, is not sufficient since it does not take entropy terms into account. As yet this test can be rigorously applied only for small deviations from stoichiometry, but may be however very useful for large deviations. Applications have been developed for the oxides UO_2+x, UO_2?x, TiO_2?x, Mn_1?xO, Fe_1?xO and CeO_2?x. For the first five oxides, it concluded that the theoretical formation energies for the majority defects derived from simulation calculations are not compatible with experimental ΔH(O₂). A good agreement is found for CeO_2?x.     

A new Monte Carlo power method for the eigenvalue problem of transfer matrices

We propose a new Monte Carlo method for calculating eigenvalues of transfer matrices leading to free energies and to correlation lengths of classical and quantum many-body systems. Generally, this method can be applied to the calculation of the maximum eigenvalue of a nonnegative matrix  such that all the matrix elements of Â^k are strictly positive for an integerk. This method is based on a new representation of the maximum eigenvalue of the matrix  as the thermal average of a certain observable of a many-body system. Therefore one can easily calculate the maximum eigenvalue of a transfer matrix leading to the free energy in the standard Monte Carlo simulations, such as the Metropolis algorithm. As test cases, we calculate the free energies of the square-lattice Ising model and of the spin-1/2XY Heisenberg chain. We also prove two useful theorems on the ergodicity in quantum Monte Carlo algorithms, or more generally, on the ergodicity of Monte Carlo algorithms using our new representation of the maximum eigenvalue of the matrixÂ.     

Diffusion radius of muonic hydrogen atoms in H-D gas

The diffusion radius of the 1S muonic hydrogen atoms in gaseous H₂ targets with various deuterium admixtures has been determined for temperatures T=30 and 300 K. The Monte Carlo calculations have been performed using the partial differential cross sections for pμ and dμ atom scattering from the molecules H₂, HD and D₂. These cross sections include hyperfine transitions in the muonic atoms, the muon exchange between the nuclei p and d, and rotational-vibrational transitions in the target molecules. The Monte Carlo results have been used for preparing the time-projection chamber for the high-precision measurement of the nuclear μ^- capture in the ground-state pμ atom, which is now underway at the Paul Scherrer Institute.     

Thermochemistry,bond energies and internal rotor barriers of methyl sulfinic acid,methyl sulfinic acid ester and their radicals

Sulfur–Oxygen containing hydrocarbons are formed in oxidation of sulfides and thiols in the atmosphere, on aerosols and in combustion processes. Understanding their thermochemical properties is important to evaluate their formation and transformation paths. Structures, thermochemical properties, bond energies, and internal rotor potentials of methyl sulfinic acid CH₃S(?O)OH, its methyl ester CH₃S(?O)OCH₃ and radicals corresponding to loss of a hydrogen atom have been studied. Gas phase standard enthalpies of formation and bond energies were calculated using B3LYP/6‐311G (2d, p) individual and CBS‐QB3 composite methods employing work reactions to further improve accuracy of the ${\Delta} _{{\bf f}} H_{{\bf 298}}^{{\bf o}} $ . Molecular structures, vibration frequencies, and internal rotor potentials were calculated. Enthalpies of the parent molecules CH₃S(?O)OH and CH₃S(?O)OCH₃ are evaluated as ?77.4 and ?72.7 kcal mol^?1 at the CBS? QB3 level; Enthalpies of radicals C^?H₂? S(?O)? OH, CH₃? S^?(?O)₂, C^?H₂? S(?O)? OCH₃ and CH₃? S(?O)? OC^?H₂ (CBS‐QB3) are ?25.7, ?52.3, ?22.8, and ?26.8 kcal mol^?1, respectively. The CH₃C(?O)O—H bond dissociation energy is of 77.1 kcal mol^?1. Two of the intermediate radicals are unstable and rapidly dissociate. The CH₃S(?O)? O. radical obtained from the parent CH₃? S(?O)? OH dissociates into methyl radical (${\bf CH}_{{\bf 3}}^{{\bf .}} $ ) plus SO₂ with endothermicity (ΔH_rxn) of only 16.2 kcal mol^?1. The CH₃? S(?O)? OC^?H₂ radical dissociates into CH₃? S^?=O and CH₂=O with little or no barrier and an exothermicity of ?19.9 kcal mol^?1. DFT and the Complete Basis Set‐QB3 enthalpy values are in close agreement; this accord is attributed to use of isodesmic work reactions for the analysis and suggests this combination of B3LYP/work reaction approach is acceptable for larger molecules. Copyright © 2010 John Wiley & Sons, Ltd.