An enhanced Monte Carlo outlier detection method

Outlier detection is crucial in building a highly predictive model. In this study, we proposed an enhanced Monte Carlo outlier detection method by establishing cross‐prediction models based on determinate normal samples and analyzing the distribution of prediction errors individually for dubious samples. One simulated and three real datasets were used to illustrate and validate the performance of our method, and the results indicated that this method outperformed Monte Carlo outlier detection in outlier diagnosis. After these outliers were removed, the value of validation by Kovats retention indices and the root mean square error of prediction decreased from 3.195 to 1.655, and the average cross‐validation prediction error decreased from 2.0341 to 1.2780. This method helps establish a good model by eliminating outliers. © 2015 Wiley Periodicals, Inc.     

Two-dimensional Monte Carlo studies of lipid molecules in a bilayer membrane

We present a new model to study in-plane liquid properties of lipid membranes. The different conformations of lipids are represented by a seven-state system of hard triatomic particles, or triples, of varying lengths which correspond to the different cross-sectional areas of the lipids in the plane of the membrane. Two-dimensional Monte Carlo simulations are performed in both the constant NVT and NPT ensembles. The distribution of states has a strong density dependence and a small temperature dependence over the biologically relevant range. There is no long range orientational order in the systems before freezing. The short range orientational order increases with density. Widom's particle insertion method is used to obtain the excess chemical potential of the system for the seven states. These values, along with the pressure, are in excellent agreement with estimates from scaled particle theory.     

Monte Carlo method based QSAR modelling of natural lipase inhibitors using hybrid optimal descriptors

Obesity is one of the most provoking health burdens in the developed countries. One of the strategies to prevent obesity is the inhibition of pancreatic lipase enzyme. The aim of this study was to build QSAR models for natural lipase inhibitors by using the Monte Carlo method. The molecular structures were represented by the simplified molecular input line entry system (SMILES) notation and molecular graphs. Three sets – training, calibration and test set of three splits – were examined and validated. Statistical quality of all the described models was very good. The best QSAR model showed the following statistical parameters: r² = 0.864 and Q² = 0.836 for the test set and r² = 0.824 and Q² = 0.819 for the validation set. Structural attributes for increasing and decreasing the activity (expressed as pIC₅₀) were also defined. Using defined structural attributes, the design of new potential lipase inhibitors is also presented. Additionally, a molecular docking study was performed for the determination of binding modes of designed molecules.     

A new method for generating volume changes in isobaric-isothermal Monte Carlo simulations of flexible molecules

A novel method has been developed to generate volume fluctuations as required in isobaric-isothermal Monte Carlo simulations of flexible (or semi-flexible) chain molecules. While conventional global volume moves entail symmetric changes of the simulation box size, in the new method proposed here, volume changes consist of one-dimensional fluctuations of one of two sections of the system. One of the two sections is a thin slab where all molecular rearrangements are restrained to occur. A deterministric method has been implemented to reposition the molecular segments contained within the slab after a volume change is proposed. The performance of the new method is examined by studying the evolution towards equilibrium of homopolymer hard-core systems upon application of a step increase in the pressure. The new method is shown to be an order of magnitude faster than conventional methods in attaining the equilibrium density of our test systems.     

Monte Carlo study of electron correlation functions for small molecules

A study is made of electron-electron correlation functions for use in trial wave functions for small molecules. New forms are proposed that have only a few variational parameters, and these parameters have physical meanings that are easily discerned. Total energies for H₂, LiH and Li₂ computed using these correlation functions are presented, and comparison is made with previous forms, including the Jastrow-Pade form often used in Monte Carlo studies. We further treat the possibility that correlation depends not only on the separation of a pair of electrons but also on the location of the electron pair relative to the nuclei — indicative of a density-dependent or many body correlation effect. Our results indicate that such a many-body correlation effect is weakly present.This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098     

Monte Carlo studies of tethered chains

Monte Carlo computer simulations of end-tethered chains grafted onto a hard wall have been performed. The chains were modeled as self-avoiding chains on a cubic lattice at athermal solvent conditions. The simulations spanned a wide range of chain lengths, N (100–1000, i.e., up to molecular weights of a few hundred thousands), and anchoring densities, σ (2 × 10⁻⁴ to 0.4), to properly chart the relevant parameter space. It is shown that the reduced surface coverage σ* = σπR is the most appropriate variable that quantitatively determines the mushroom, overlapping mushroom and brush regimes, where R_g is the radius of gyration of a free chain in solution. The simulation data are analyzed to determine the conformational characteristics and shape of the anchored chains and to compare them with the predictions of the analytical self consistent field theory. The strong stretching limit of the theoretical predictions is obtained only for σ* > 8. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47:2449–2461, 2009     

An efficient Monte Carlo method to calculate nuclear spin relaxation times in complex molecules

An efficient Monte Carlo method to calculate nuclear spin relaxation times and nuclear Overhauser enhancements in complex molecules based on the convolution of power spectra for independent processes is proposed and applied to analyze the ¹³C T₁ distribution in poly(N-hexy-4-vinylpyridinium) bromide.     

Differential diffusion quantum Monte Carlo method: determination of potential energy surfaces of molecules

A differential approach for self-optimizing diffusion Monte Carlo calculation was proposed in this paper, which is a new algorithm combining three techniques such as optimizing, diffusion and correlation sampling. This method can be used to directly compute the energy differential between two systems in the diffusion process, making the statistical error of calculation be reduced to order of 10-5 hartree, and recover about more than 80% of the correlation energy. We employed this approach to set up a potential energy surface of a molecule, used a "rigid move" model, and utilized Jacobi transformation to make energy calculation for two configurations of a molecule having good positive correlation. So, an accurate energy differential could be obtained, and the potential energy surface with good quality can be depicted. In calculation, a technique called "post-equilibrium remaining sample was set up firstly, which can save about 50% of computation expense. This novel algorithm was used to study the potenti     

Monte Carlo simulation studies of polymer systems

Polymers molecules in solution or melt are more or less flexible and continuously change their shape and size. Thus, characteristic properties of the system fluctuate around statistical mean values which are dependent on the concentration of the solution, on the quality of the solvent used, and on the specific structure of the molecules, e.g. linear or star-branched. The most direct approach to these quantities on a molecular level are computer simulations. Due to restrictions of computer power fully atomistic simulations of macromolecules are presently still at the beginning but several arguments justify the use of simplified models. The most efficient way dealing with polymer systems are Monte Carlo simulations based on lattice chains, at least as long as static properties are of interest only. In the present paper a short introduction to the field is given and selected examples are presented in order to demonstrate the usefulness of these methods.     

Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules

While lattice kinetic Monte Carlo (KMC) methods provide insight into numerous complex physical systems governed by interatomic interactions, they are limited to relatively short length and time scales. Recently introduced coarse-grained Monte Carlo (CGMC) simulations can reach much larger length and time scales at considerably lower computational cost. In this paper we extend the CGMC methods to spatially adaptive meshes for the case of surface diffusion (canonical ensemble). We introduce a systematic methodology to derive the transition probabilities for the coarse-grained diffusion process that ensure the correct dynamics and noise, give the correct continuum mesoscopic equations, and satisfy detailed balance. Substantial savings in CPU time are demonstrated compared to microscopic KMC while retaining high accuracy.     

A general and efficient Monte Carlo method for sampling intramolecular degrees of freedom of branched and cyclic molecules

A simple and easily implemented Monte Carlo algorithm is described which enables configurational-bias sampling of molecules containing branch points and rings with endocyclic and exocyclic atoms. The method overcomes well-known problems associated with sequential configurational-bias sampling methods. A "reservoir" or "library" of fragments are generated with known probability distributions dependent on stiff intramolecular degrees of freedom. Configurational-bias moves assemble the fragments into whole molecules using the energy associated with the remaining degrees of freedom. The methods for generating the fragments are validated on models of propane, isobutane, neopentane, cyclohexane, and methylcyclohexane. It is shown how the sampling method is implemented in the Gibbs ensemble, and validation studies are performed in which the liquid coexistence curves of propane, isobutane, and 2,2-dimethylhexane are computed and shown to agree with accepted values. The method is general and can be used to sample conformational space for molecules of arbitrary complexity in both open and closed statistical mechanical ensembles.     

Path integral Monte Carlo method for ab initio calculation

The Feynman path integral method is applied to the many-electron problem. We first give new closure relations in terms of ordinary complex and real numbers, which could be derived from an arbitrary complete set of state vectors. Then, in the path integral form, the partition function of the system and the ensemble average of energy are explicitly expressed in terms of these closure relations. It is impossible to evaluate the path integral by direct numerical integrations because of its huge amount of integration variables. Therefore, we develop an algorithm by the Monte Carlo method with constraints corresponding to the normalization condition of states to calculate the required integral. Finally, the ensemble average of energy for the hydrogen molecule is explicitly evaluated by the quantum Monte Carlo method and results are compared with the result obtained by the ordinary full configuration interaction (CI) method. © 1996 John Wiley & Sons, Inc.