Approaching chemical accuracy with quantum Monte Carlo

A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.     

Importance sampling for quantum Monte Carlo in manifolds: addressing the time scale problem in simulations of molecular aggregates

Several importance sampling strategies are developed and tested for stereographic projection diffusion Monte Carlo in manifolds. We test a family of one parameter trial wavefunctions for variational Monte Carlo in stereographically projected manifolds which can be used to produce importance sampling. We use the double well potential in one dimensional Euclidean space to study systematically sampling issues for diffusion Monte Carlo. We find that diffusion Monte Carlo with importance sampling in manifolds is orders of magnitude more efficient compared to unguided diffusion Monte Carlo. Additionally, diffusion Monte Carlo with importance sampling in manifolds can overcome problems with nonconfining potentials and can suppress quasiergodicity effectively. We obtain the ground state energy and the wavefunction for the Stokmayer trimer.     

A Monte Carlo simulation study of lipid bilayer formation on hydrophilic substrates from vesicle solutions

A general lattice Monte Carlo model is used for simulating the formation of supported lipid bilayers (SLBs) from vesicle solutions. The model, based on a previously published paper, consists of adsorption, decomposition, and lateral diffusion steps, and is derived from fundamental physical interactions and mass transport principles. The Monte Carlo simulation results are fit to experimental data at different vesicle bulk concentrations. A sensitivity analysis reveals that the process strongly depends on the bulk concentration C(0), adsorption rate constant K, and all vesicle radii parameters. A measure of "quality of coverage" is proposed. By this measure, the quality of the formed bilayers is found to increase with vesicle bulk concentration.     

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.     

Porosity dependence of electron percolation in nanoporous TiO2 layers

The electron diffusion coefficient at varying porosity has been determined in a series of nanostructured TiO(2) films of different initial thicknesses. The porosity was changed by applying different pressures prior to sintering, thereby modifying the internal morphology of the films though not their chemical and surface conditions. A systematic increase of the effective diffusion coefficient was observed as the porosity was decreased, indicating the improvement of the internal connectivity of the network of nanoparticles. The experimental results have been rationalized using percolation theory. First of all, applying a power law dependence, the diffusion coefficient as a function of porosity from different films collapsed in a single master curve. In addition, application of the models of effective medium approximation (EMA) allows us to compare the experimental results with previous data from Monte Carlo simulation. The different data show a similar dependence in agreement with the EMA predictions, indicating that the geometrical effect of electron transport due to variation of porous morphology in TiO(2) nanoparticulate networks is well described by the percolation concept.     

Method for computing protein binding affinity

A Monte Carlo method is given to compute the binding affinity of a ligand to a protein. The method involves extending configuration space by a discrete variable indicating whether the ligand is bound to the protein and a special Monte Carlo move, which allows transitions between the unbound and bound states. Provided that an accurate protein structure is given, that the protein-ligand binding site is known, and that an accurate chemical force field together with a continuum solvation model is used, this method provides a quantitative estimate of the free energy of binding.     

D_4/N-β-氨乙基-γ-氨丙基甲基二甲氧基硅烷本体共聚反应聚合度变化的Monte Carlo模拟

用MonteCarlo方法模拟八甲基环四硅氧烷 (D4 )与N β 氨乙基 γ 氨丙基甲基二甲氧基硅烷(APAEDMS)的本体开环共聚动力学 .模拟过程采用自由体积理论简化处理扩散效应并与本征反应动力学耦合 .本征动力学常数通过模拟主要共聚基元反应得到 ,基于优化的动力学常数通过模拟从分子水平揭示D4 APAEDMS本体开环共聚反应过程主要表现为活性阴离子聚合行为 ,同时又伴有部分逐步聚合特征 .     

Multiple scattering of light from polymer dispersed liquid crystal material

Light scattering from polymer dispersed liquid crystal (PDLC) material has been studied experimentally and by Monte Carlo simulation. Light scattering was measured as a function of both scattering angle and cell thickness. The cell thicknesses of practical interest are in an intermediate regime where neither single scattering nor light diffusion applies. Both the angular and the thickness dependence of the scattering intensity can be described accurately by a Monte Carlo simulation of multiple scattering from a homogeneous distribution of independent scatterers. The model smoothly interpolates between the single scattering limit for thin cells and the diffusion limit for thick cells. It can easily be extended to include any specific feature of a scattering display system.     

Interplay of master regulatory proteins and mRNA in gene expression: 3D Monte Carlo simulations

We present 3D spatio-temporal Monte Carlo simulations of gene expression for a generic model with negative feedback between the mRNA and regulatory-protein production. The attention is focused on the role of mRNA diffusion between the nucleus and cytoplasm. For rapid diffusion, the model predicts that the fluctuations of the mRNA and protein numbers are comparable to those corresponding to the Poissonian distribution. With decreasing diffusion rate, the fluctuations become much larger. Specifically, the time dependence of the mRNA and protein numbers exhibits huge bursts.     

Numerical solution of a partial differential equation system describing chemical kinetics and diffusion in a cell with the aid of compartmentalization

To build a kinetic model of a cell with diffusion one has to solve a coupled nonlinear partial differential equation system consisting of several hundred equations. (Several hundred chemical components undergoing several hundred reactions.) To solve this formidable mathematical problem the division of the model cell into compartments (most biochemical reactions take place in a certain part of the cell) was suggested.¹ Solving the differential equation system in one compartment, the results can be used as input at other compartments until mutually consistent solutions are achieved. To test this suggestion 10 coupled chemical reactions with diffusion were investigated in a model that contains three compartments. The results in the case of pure diffusion are in excellent agreement with and without compartmentalization. After this the full problem was treated by compartmentalization using for the solution of the differential equation system a discretization of the concentrations as functions of space and time and the Newton–Raphson iterative procedure. The results obtained give reasonable space and time dependence for the concentrations of all 10 components.     

Dynamics of Bond‐Fluctuation Model Chains in Good and Theta Solvents

The dynamic Monte Carlo algorithm is employed to explore the dynamics of flexible linear chains. The chains are represented by the bond‐fluctuation model with and without attractions between non‐bonded units placed at close distances. This mimics the behavior of real chains in the good and poorer solvents. We obtain the chain sizes, diffusion coefficients, Rouse modes, and their relaxation times. We also evaluate the time correlation function of the end‐to‐end vector at different concentrations. Subsequently, we compare the dependence of the simulation results on chain length, solvent quality, concentration, and mode order with the corresponding theoretical predictions. We observe a retardation of diffusion for non‐dilute systems close to the theta state. This retardation is too high to be exclusively attributed to the increase of global friction and can be caused by temporary adherence of the chains to transient clusters.     

Coupled ion and network dynamics in polymer electrolytes: Monte Carlo study of a lattice model

Monte Carlo simulations are used to study ion and polymer chain dynamic properties in a simplified lattice model with only one species of mobile ions. The ions interact attractively with specific beads in the host chains, while polymer beads repel each other. Cross linking of chains by the ions reduces chain mobilities which in turn suppresses ionic diffusion. Diffusion constants for ions and chains as a function of temperature follow the Vogel-Tammann-Fulcher (VTF) law with a common VTF temperature at low ion concentration, but both decouple at higher concentrations, in agreement with experimental observations. Our model allows us to introduce pressure as an independent variable through calculations of the equation of state using the quasichemical approximation, and to detect an exponential pressure dependence of the ionic diffusion.     

Structure of interparticle space in great noncrystalline packings of Lennard-Jones atoms and its influence on diffusional mobility of admixture particles

Models of 100,000 atoms interacting with Lennard-Jones potential have been constructed using the Monte Carlo method at different densities and temperatures. In these models, the structure of empty space is investigated in which the test particle with a diameter smaller than the diameter of matrix atoms can move. The percolation thresholds, when “infinite” cavities penetrating all model space arise, are found. A change of density and temperature of matrix preparation leads to a non trivial redistribution of volume between cavities of different type. By the method of molecular dynamics it is found that the usual (Einsteinian) law of diffusion is established rather quickly, on average. However, the laws for test particles moving in cavities of different type are more complex and specific to each kind of cavities. It should result in different course of chemical reaction in different local areas of a matrix.     

A Monte Carlo simulation of diffusion-controlled reactions in inhomogeneous systems

A random-walk model has been developed to treat the kinetics of reactions taking place in spurs at different solute concentrations. The dependence of the molecular yields on solute concentration has been studied using Monte Carlo techniques for simulation of the formation of spurs and of the random movement of the reactive species.     

Comparison of kinetic Monte Carlo and molecular dynamics simulations of diffusion in a model glass former

We present results from kinetic Monte Carlo (KMC) simulations of diffusion in a model glass former. We find that the diffusion constants obtained from KMC simulations have Arrhenius temperature dependence, while the correct behavior, obtained from molecular dynamics simulations, can be super-Arrhenius. We conclude that the discrepancy is due to undersampling of higher-lying local minima in the KMC runs. We suggest that the relevant connectivity of minima on the potential energy surface is proportional to the energy density of the local minima, which determines the "inherent structure entropy." The changing connectivity with potential energy may produce a correlation between dynamics and thermodynamics.     

Unraveling rotation-vibration mixing in highly fluxional molecules using diffusion Monte Carlo: applications to H3+ and H3O+

A thorough examination of the use of fixed-node diffusion Monte Carlo for the study of rotation-vibration mixing in systems that undergo large amplitude vibrational motions is reported. Using H(3)(+) as a model system, the overall accuracy of the method is tested by comparing the results of these calculations with those from converged variational calculations. The effects of the presence of a large amplitude inversion mode on rotation-vibration mixing are considered by comparing the H(3)(+) results with those for H(3)O(+). Finally, analysis of the results of the fixed-node diffusion Monte Carlo calculations performed in different nodal regions is found to provide clear indications of when some of the methodology's underlying assumptions are breaking down as well as provide physical insights into the form of the rotation-vibration coupling that is most likely responsible.     

New insights into diffusion in 3D crowded media by Monte Carlo simulations: effect of size, mobility and spatial distribution of obstacles

Particle diffusion in crowded media was studied through Monte Carlo simulations in 3D obstructed lattices. Three particular aspects affecting the diffusion, not extensively treated in a three-dimensional geometry, were analysed: the relative particle-obstacle size, the relative particle-obstacle mobility and the way of having the obstacles distributed in the simulation space (randomly or uniformly). The results are interpreted in terms of the parameters that characterize the time dependence of the diffusion coefficient: the anomalous diffusion exponent (α), the crossover time from anomalous to normal diffusion regimes (τ) and the long time diffusion coefficient (D*). Simulation results indicate that there are a more anomalous diffusion (smaller α) and a lower long time diffusion coefficient (D*) when obstacle concentration increases, and that, for a given total excluded volume and immobile obstacles, the anomalous diffusion effect is less important for bigger size obstacles. However, for the case of mobile obstacles, this size effect is inverted yielding values that are in qualitatively good agreement with in vitro experiments of protein diffusion in crowded media. These results underline that the pattern of the spatial partitioning of the obstacle excluded volume is a factor to be considered together with the value of the excluded volume itself.     

Extrapolation of the time-step bias in diffusion quantum Monte Carlo by a differential sampling technique

A new method of eliminating the finite-time-step error inherent in diffusion quantum Monte Carlo is presented, utilizing an improved version of the existing differential techniques. An implementation is described and results of several small but representative calculations are discussed. The pertinent computation requirements on these systems were reduced by up to a factor of five by the new algorithm. It is speculated that this method may be easily applied to other quantum Monte Carlo and discretized path integral Monte Carlo techniques having related finite step-size errors with a possibility of obtaining similar good results.     

HF in clusters of molecular hydrogen: II. Quantum solvation by H2 isotopomers, cluster rigidity, and comparison with CO-doped parahydrogen clusters

We present a comprehensive theoretical study of the quantum solvation of the HF molecule by small clusters of the H2 isotopomers, p-H2, HD, and o-D2, with up to 13 hydrogen solvent molecules. This complements our earlier work on the HF-doped parahydrogen clusters [H. Jiang and Z. Bacic, J. Chem. Phys. 122, 244306 (2005)]. The ground-state properties of the clusters are calculated exactly using the diffusion Monte Carlo method. Detailed information is obtained regarding the size and isotopomer dependences of the energetics, vibrationally averaged structures, and their rigidity. The rigidity of these clusters is investigated further by analyzing the distributions of their principal moments of inertia from the diffusion Monte Carlo simulations. The clusters are found to be rather rigid, especially when compared with the pure parahydrogen clusters of the same size. Extensive comparison is made with the quantum Monte Carlo results for the CO-doped parahydrogen clusters and significant differences are observed in the size evolution of certain properties, notably the chemical potential.