# Optimal intermediates in staged free energy calculations

## Abstract

We examine the precision of free energy perturbation (FEP) methods of molecular simulation. We develop a quantitative model of the calculation in terms of the so-called {ital f} and {ital g} distributions that characterize the energies sampled in a FEP calculation. The model is then re-expressed in terms of the entropy difference between the systems of interest, and the variance of the {ital g} distribution. We apply the model to analyze the optimization of multistage insertion free energy calculations, and reach a quantitative criterion for minimizing the overall variance. The analysis indicates that the appropriate heuristic for optimizing the choice of intermediates is to select them to equalize the {ital entropy} differences among all stages of the overall FEP calculation. A more accurate criterion is specified, but in practice it differs little from this simpler one. We illustrate our conclusions by conducting two-stage FEP calculations using Monte Carlo simulations on Lennard-Jones (LJ) systems at several temperatures and two densities. The LJ systems differ in the presence of a single LJ particle, and the intermediate is defined to have a single hard sphere of diameter that can be used to optimize the two-stage FEP calculation. The model provides an excellent descriptionmore »

- Authors:

- Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, New York 14260-4200 (United States)

- Publication Date:

- OSTI Identifier:
- 362669

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 111; Journal Issue: 10; Other Information: PBD: Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 40 CHEMISTRY; ENTROPY; FREE ENERGY; OPTIMIZATION; MONTE CARLO METHOD; LENNARD-JONES POTENTIAL; SIMULATION; SAMPLING; LIQUIDS

### Citation Formats

```
Lu, N., and Kofke, D.A.
```*Optimal intermediates in staged free energy calculations*. United States: N. p., 1999.
Web. doi:10.1063/1.479206.

```
Lu, N., & Kofke, D.A.
```*Optimal intermediates in staged free energy calculations*. United States. doi:10.1063/1.479206.

```
Lu, N., and Kofke, D.A. Wed .
"Optimal intermediates in staged free energy calculations". United States. doi:10.1063/1.479206.
```

```
@article{osti_362669,
```

title = {Optimal intermediates in staged free energy calculations},

author = {Lu, N. and Kofke, D.A.},

abstractNote = {We examine the precision of free energy perturbation (FEP) methods of molecular simulation. We develop a quantitative model of the calculation in terms of the so-called {ital f} and {ital g} distributions that characterize the energies sampled in a FEP calculation. The model is then re-expressed in terms of the entropy difference between the systems of interest, and the variance of the {ital g} distribution. We apply the model to analyze the optimization of multistage insertion free energy calculations, and reach a quantitative criterion for minimizing the overall variance. The analysis indicates that the appropriate heuristic for optimizing the choice of intermediates is to select them to equalize the {ital entropy} differences among all stages of the overall FEP calculation. A more accurate criterion is specified, but in practice it differs little from this simpler one. We illustrate our conclusions by conducting two-stage FEP calculations using Monte Carlo simulations on Lennard-Jones (LJ) systems at several temperatures and two densities. The LJ systems differ in the presence of a single LJ particle, and the intermediate is defined to have a single hard sphere of diameter that can be used to optimize the two-stage FEP calculation. The model provides an excellent description of the precision of the FEP calculations. {copyright} {ital 1999 American Institute of Physics.}},

doi = {10.1063/1.479206},

journal = {Journal of Chemical Physics},

number = 10,

volume = 111,

place = {United States},

year = {1999},

month = {9}

}