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.     

A new algorithm for the fixed-node quantum Monte Carlo method

A novel algorithm is proposed for the fixed-node quantum Monte Carlo (FNQMC) method.In contrast to previous procedures,its "guiding function" is not optimized prior to diffusion quantum Monte Carlo (DMC) computation but synchronistically in the diffusion process The new algorithm can not only save CPU time,but also make both of the optimization and diffusion carried out according to the same sampling fashion,reaching the goal to improve each other This new optimizing procedure converges super-linearly,and thus can accelerate the particle diffusion During the diffusion process,the node of the "guiding function" changes incessantly,which is conducible to reducing the "fixed-node error" The new algorithm has been used to calculate the total energies of states X3B1 and a1A1 of CH2 as well as π-X2B1 and λ-2A1 of NH2 The singlet-triplet energy splitting (λEsT) in CH2 and π energy splitting in NH2 obtained with this present method are (45 542±1.840) and (141.644±1.589) kJ/mol,respectively The calculated     

A new technique for metropolis Monte Carlo simulation to capture aggregate structures of fine particles: Cluster-moving Monte Carlo algorithm

We present a new Monte Carlo simulation procedure which is capable of capturing aggregate structures in a suspension where fine particles are dispersed. The algorithm we call the “cluster-moving” Monte Carlo algorithm involves moving aggregates (clusters) as unitary particles at every certain Monte Carlo step. We discuss here the theoretical background of the cluster-moving Monte Carlo algorithm and the availability of the algorithm for simulations of systems where fine particles aggregate. The results of simulations for two model systems, magnetic fluids and colloidal dispersions, have shown that the new algorithm produces much more rapid convergence than the conventional one for unstable dispersion systems and reproduces physically reasonable aggregate structures of fine particles.     

Visualizing molecular wavefunctions using Monte Carlo methods

Using explicitly correlated wavefunctions and variational Monte Carlo we calculate the electron density, the electron density difference, the intracule density, the extracule density, two forms of the kinetic energy density, the Laplacian of the electron density, the Laplacian of the intracule density, and the Laplacian of the extracule density on a dense grid of points for the ground state of the hydrogen molecule at three internuclear distances (0.6, 1.4, 8.0). With these values we construct a contour plot of each function and describe how it can be used to visualize the distribution of electrons in this molecule. We also examine the influence of electron correlation on each expectation value by calculating each function with a Hartree–Fock wavefunction and then comparing these values with our explicitly correlated values. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

A new variational Monte Carlo trial wavefunction with directional Jastrow functions

The addition of a directional term to standard Jastrow functions was investigated in variational quantum Monte Carlo calculations for the LiH molecule using wavefunctions composed of Slater determinants combined with Padé and with Schmidt–Moskowitz functions. The recovery of correlation energy was improved significantly by the added term: from 52% to 71% for the Padé function and from 61% to 78% for the Schmidt–Moskowitz function.     

A Monte Carlo method for finding important ligand fragments from receptor data

A simulated annealing method for finding important ligand fragments is described. At a given temperature, ligand fragments are randomly selected and randomly placed within the given receptor cavity, often replacing or forming bonds with existing ligand fragments. For each new ligand fragment combination, the bonded, nonbonded, polarization and solvation energies of the new ligand–receptor system are compared to the previous configuration. Acceptance or rejection of the new system is decided using the Boltzmann distribution , where E is the energy difference between the old and new systems, k is the Boltzmann constant and T is the temperature. Thus, energetically unfavorable fragment switches are sometimes accepted, sacrificing immediate energy gains in the interest of finding a system with minimum energy. By lowering the temperature, the rate of unfavorable switches decreases and energetically favorable combinations become more difficult to change. The process is terminated when the frequency of switches becomes too small. As a test, the method predicted positions and types of important ligand fragments for neuraminidase that were in accord with the known ligand, sialic acid.     

Titration of hydrophobic polyelectrolytes using Monte Carlo simulations

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK(0) values (pK(0) represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree alpha of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK(0) value.     

Conformational distribution of heptaalanine: Analysis using a new Monte Carlo chain growth method

A distribution of conformations of heptaalanine is obtained using a new Monte Carlo (MC) method that grows the chain atom by atom. Resulting configurations are energy minimized and a detailed analysis is performed of the minimum-energy conformers using a method of classification that partitions ?ψ space. The MC-generated configurations are compared with those generated from high-temperature molecular dynamics (MD) simulations. It is found that the new method generates a wide distribution of low-energy conformers at least 10 times more quickly than the MD. An analysis of the generated energy minima demonstrates that they can be divided into clusters in the space defined by the five pairs of ?—ψ angles of the inner residues. The space occupied by the minima populating each cluster is restricted. © 1992 by John Wiley & Sons, Inc.     

Oscillator strengths of helium computed using Monte Carlo methods

We have optimized trial wave functions for the three lowest states of the helium atom with symmetry 1S, 1P, 1D, 3S, 3P, and 3D using variational Monte Carlo methods. With these wave functions we then computed dipole oscillator strengths for the 1S-1P, 1P-1D, 3S-3P, and 3P-3D transitions using the length, velocity, and acceleration forms. Our values are in good agreement with the best results found in the literature.     

Optimization of 89Zr production using Monte Carlo simulations

Zirconium-89 (⁸⁹Zr) can be produced in a cyclotron by focusing the proton beam on an yttrium-89 (⁸⁹Y) foil target. Optimal combination of beam energy and target assembly configuration enables maximum production of ⁸⁹Zr while minimizing the formation of contaminant nuclides such as ⁸⁸Zr and ⁸⁸Y to allow efficient and effective radiopharmaceutical labeling. Accurate modeling of the proton beam and the target is therefore an essential step to assure the best beam and target specification. We used the radiation transport code MCNPX to simulate the transport of protons through the irradiation assembly and the nuclear reaction code TALYS to obtain the production cross sections of various nuclides from proton-⁸⁹Y reactions. Results from simulating the irradiation of 14 mm diameter targets with aluminum (Al) degrader at 19.8 mA for 1 h suggested that the 0.15 mm thick one would produce 227 MBq while the 0.3 mm thick one would produce 413 MBq of ⁸⁹Zr with less than 1 % uncertainty. These results show excellent agreement with experimental work in literature. This work provides the basis for further experimental and theoretical assessments of the use of ⁸⁹Zr as radiopharmaceutical labels.     

Properties of selected diatomics using variational Monte Carlo methods

Using variational Monte Carlo and highly accurate trial wave functions optimized by Filippi and Umrigar, we calculate a number of molecular properties for the ground state of Li2, Be2, B2, C2, N2, O2, and F2. This is the first time that many of these properties have been computed.     

A rare event sampling method for diffusion Monte Carlo using smart darting

We identify a set of multidimensional potential energy surfaces sufficiently complex to cause both the classical parallel tempering and the guided or unguided diffusion Monte Carlo methods to converge too inefficiently for practical applications. The mathematical model is constructed as a linear combination of decoupled Double Wells [(DDW)(n)]. We show that the set (DDW)(n) provides a serious test for new methods aimed at addressing rare event sampling in stochastic simulations. Unlike the typical numerical tests used in these cases, the thermodynamics and the quantum dynamics for (DDW)(n) can be solved deterministically. We use the potential energy set (DDW)(n) to explore and identify methods that can enhance the diffusion Monte Carlo algorithm. We demonstrate that the smart darting method succeeds at reducing quasiergodicity for n ? 100 using just 1 × 10(6) moves in classical simulations (DDW)(n). Finally, we prove that smart darting, when incorporated into the regular or the guided diffusion Monte Carlo algorithm, drastically improves its convergence. The new method promises to significantly extend the range of systems computationally tractable by the diffusion Monte Carlo algorithm.     

A Monte Carlo approach for estimating measurement uncertainty using standard spreadsheet software

Despite the importance of stating the measurement uncertainty in chemical analysis, concepts are still not widely applied by the broader scientific community. The Guide to the expression of uncertainty in measurement approves the use of both the partial derivative approach and the Monte Carlo approach. There are two limitations to the partial derivative approach. Firstly, it involves the computation of first-order derivatives of each component of the output quantity. This requires some mathematical skills and can be tedious if the mathematical model is complex. Secondly, it is not able to predict the probability distribution of the output quantity accurately if the input quantities are not normally distributed. Knowledge of the probability distribution is essential to determine the coverage interval. The Monte Carlo approach performs random sampling from probability distributions of the input quantities; hence, there is no need to compute first-order derivatives. In addition, it gives the probability density function of the output quantity as the end result, from which the coverage interval can be determined. Here we demonstrate how the Monte Carlo approach can be easily implemented to estimate measurement uncertainty using a standard spreadsheet software program such as Microsoft Excel. It is our aim to provide the analytical community with a tool to estimate measurement uncertainty using software that is already widely available and that is so simple to apply that it can even be used by students with basic computer skills and minimal mathematical knowledge.     

A Monte Carlo study of liquid benzene

A Monte Carlo study for liquid benzene, where the pair potential is described as a sum of Lennard-Jones (12, 6) interactions acting between six equivalent centres of each molecule, has been carried out. The potential parameters have been chosen in such a way that the internal energy and virial pressure were in agreement with the experimental values. The liquid structure has been examined in detail by computing several distribution functions: the radial, the angular correlations and the radial-angular distribution between molecular planes.     

A Monte Carlo study of water clusters

The free energy, internal energy and entropy for water clusters of 8 and 64 molecules have been calculated using the Monte Carlo method and both the Lie-Clementi (C-XII) and Stillinger (ST2) potential functions. Detailed structural data for a cluster of 64 water molecules was also obtained by averaging over a large number of configurations. Average dipole orientations and radial density distributions indicated that individual water molecules were not particularly restricted to fixed orientations and that general ordering tendencies were small.     

Computing upper and lower bounds using Monte Carlo methods

We computed lower bounds for some ground and excited states of the helium atom using variational Monte Carlo and the Weinstein, Temple, and Stevenson formulas. For these systems, the Temple and Stevenson bounds are approximately the same and have similar standard deviations. The Weinstein bounds are much further from the actual energies and have much larger standard deviations. We also investigated the reliability of these lower bound formulas when nonorthogonal wave functions are used. The Temple formula has been shown to produce an accurate lower bound even under such circumstances, while the Weinstein and Stevenson formulas are shown to yield incorrect results. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Monte Carlo free energy calculations using electronic structure methods

The molecular mechanics-based importance sampling function (MMBIF) algorithm [R. Iftimie, D. Salahub, D. Wei, and J. Schofield, J. Chem. Phys. 113, 4852 (2000)] is extended to incorporate semiempirical electronic structure methods in the secondary Markov chain, creating a fully quantum mechanical Monte Carlo sampling method for simulations of reactive chemical systems which, unlike the MMBIF algorithm, does not require the generation of a system-specific force field. The algorithm is applied to calculating the potential of mean force for the isomerization reaction of HCN using thermodynamic integration. Constraints are implemented in the sampling using a modification of the SHAKE algorithm, including that of a fixed, arbitrary reaction coordinate. Simulation results show that sampling efficiency with the semiempirical secondary potential is often comparable in quality to force fields constructed using the methods suggested in the original MMBIF work. The semiempirical based importance sampling method presented here is a useful alternative to MMBIF sampling as it can be applied to systems for which no suitable MM force field can be constructed.     

Rovibrationally averaged properties of H2 using Monte Carlo methods

Using variational Monte Carlo and a simple explicitly correlated wave function, we have computed 18 molecular properties of the hydrogen molecule (X¹∑) at 24 internuclear distances. These properties have been combined with rapidly convergent rovibrational wave functions to produce rovibrationally averaged properties for several of the lowest rotational and vibrational levels of this system. Our results are in very good agreement with previous values found in the literature. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

A ground state potential energy surface for H2 using Monte Carlo methods

Using variational Monte Carlo and a simple explicitly correlated wave function we have computed the Born-Oppenheimer energy of the H2 ground state (X 1Sigmag+) at 24 internuclear distances. We have also calculated the diagonal correction to the Born-Oppenheimer approximation and the lowest-order relativistic corrections at each distance using variational Monte Carlo techniques. The nonadiabatic values are evaluated from numerical derivatives of the wave function with respect to the nuclear coordinates. With this potential energy surface we have computed several of the lowest vibrational-rotational energies for this system. Our results are in good agreement with the best values found in the literature.