### Abstract

The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM, and the closely-related multiple Bennett acceptance ratio method can be improved using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution.

Original language | English (US) |
---|---|

Pages (from-to) | 1079-1089 |

Number of pages | 11 |

Journal | Molecular Simulation |

Volume | 42 |

Issue number | 13 |

DOIs | |

State | Published - Sep 1 2016 |

### Fingerprint

### Keywords

- DIIS
- Free energy
- MBAR
- WHAM

### ASJC Scopus subject areas

- Condensed Matter Physics
- Modeling and Simulation
- Chemistry(all)
- Chemical Engineering(all)
- Materials Science(all)
- Information Systems

### Cite this

*Molecular Simulation*,

*42*(13), 1079-1089. https://doi.org/10.1080/08927022.2015.1110583

**Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace.** / Zhang, Cheng; Lai, Chun Liang; Pettitt, Bernard.

Research output: Contribution to journal › Article

*Molecular Simulation*, vol. 42, no. 13, pp. 1079-1089. https://doi.org/10.1080/08927022.2015.1110583

}

TY - JOUR

T1 - Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace

AU - Zhang, Cheng

AU - Lai, Chun Liang

AU - Pettitt, Bernard

PY - 2016/9/1

Y1 - 2016/9/1

N2 - The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM, and the closely-related multiple Bennett acceptance ratio method can be improved using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution.

AB - The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM, and the closely-related multiple Bennett acceptance ratio method can be improved using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution.

KW - DIIS

KW - Free energy

KW - MBAR

KW - WHAM

UR - http://www.scopus.com/inward/record.url?scp=84977614608&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84977614608&partnerID=8YFLogxK

U2 - 10.1080/08927022.2015.1110583

DO - 10.1080/08927022.2015.1110583

M3 - Article

VL - 42

SP - 1079

EP - 1089

JO - Molecular Simulation

JF - Molecular Simulation

SN - 0892-7022

IS - 13

ER -