# Improving the efficiency of configurational-bias Monte Carlo: A density-guided method for generating bending angle trials for linear and branched molecules

## Abstract

A new method has been developed to generate bending angle trials to improve the acceptance rate and the speed of configurational-bias Monte Carlo. Whereas traditionally the trial geometries are generated from a uniform distribution, in this method we attempt to use the exact probability density function so that each geometry generated is likely to be accepted. In actual practice, due to the complexity of this probability density function, a numerical representation of this distribution function would be required. This numerical table can be generated a priori from the distribution function. This method has been tested on a united-atom model of alkanes including propane, 2-methylpropane, and 2,2-dimethylpropane, that are good representatives of both linear and branched molecules. It has been shown from these test cases that reasonable approximations can be made especially for the highly branched molecules to reduce drastically the dimensionality and correspondingly the amount of the tabulated data that is needed to be stored. Despite these approximations, the dependencies between the various geometrical variables can be still well considered, as evident from a nearly perfect acceptance rate achieved. For all cases, the bending angles were shown to be sampled correctly by this method with an acceptance rate of atmore »

- Authors:

- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803-1804 (United States)

- Publication Date:

- OSTI Identifier:
- 22420044

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 7; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 2-2-DIMETHYLPROPANE; 2-METHYLPROPANE; ALGORITHMS; APPROXIMATIONS; ATOMS; COMPUTERIZED SIMULATION; DISTRIBUTION FUNCTIONS; EFFICIENCY; MOLECULES; MONTE CARLO METHOD; PROBABILITY DENSITY FUNCTIONS; PROPANE

### Citation Formats

```
Sepehri, Aliasghar, Loeffler, Troy D., and Chen, Bin, E-mail: binchen@lsu.edu.
```*Improving the efficiency of configurational-bias Monte Carlo: A density-guided method for generating bending angle trials for linear and branched molecules*. United States: N. p., 2014.
Web. doi:10.1063/1.4892640.

```
Sepehri, Aliasghar, Loeffler, Troy D., & Chen, Bin, E-mail: binchen@lsu.edu.
```*Improving the efficiency of configurational-bias Monte Carlo: A density-guided method for generating bending angle trials for linear and branched molecules*. United States. doi:10.1063/1.4892640.

```
Sepehri, Aliasghar, Loeffler, Troy D., and Chen, Bin, E-mail: binchen@lsu.edu. Thu .
"Improving the efficiency of configurational-bias Monte Carlo: A density-guided method for generating bending angle trials for linear and branched molecules". United States.
doi:10.1063/1.4892640.
```

```
@article{osti_22420044,
```

title = {Improving the efficiency of configurational-bias Monte Carlo: A density-guided method for generating bending angle trials for linear and branched molecules},

author = {Sepehri, Aliasghar and Loeffler, Troy D. and Chen, Bin, E-mail: binchen@lsu.edu},

abstractNote = {A new method has been developed to generate bending angle trials to improve the acceptance rate and the speed of configurational-bias Monte Carlo. Whereas traditionally the trial geometries are generated from a uniform distribution, in this method we attempt to use the exact probability density function so that each geometry generated is likely to be accepted. In actual practice, due to the complexity of this probability density function, a numerical representation of this distribution function would be required. This numerical table can be generated a priori from the distribution function. This method has been tested on a united-atom model of alkanes including propane, 2-methylpropane, and 2,2-dimethylpropane, that are good representatives of both linear and branched molecules. It has been shown from these test cases that reasonable approximations can be made especially for the highly branched molecules to reduce drastically the dimensionality and correspondingly the amount of the tabulated data that is needed to be stored. Despite these approximations, the dependencies between the various geometrical variables can be still well considered, as evident from a nearly perfect acceptance rate achieved. For all cases, the bending angles were shown to be sampled correctly by this method with an acceptance rate of at least 96% for 2,2-dimethylpropane to more than 99% for propane. Since only one trial is required to be generated for each bending angle (instead of thousands of trials required by the conventional algorithm), this method can dramatically reduce the simulation time. The profiling results of our Monte Carlo simulation code show that trial generation, which used to be the most time consuming process, is no longer the time dominating component of the simulation.},

doi = {10.1063/1.4892640},

journal = {Journal of Chemical Physics},

number = 7,

volume = 141,

place = {United States},

year = {Thu Aug 21 00:00:00 EDT 2014},

month = {Thu Aug 21 00:00:00 EDT 2014}

}