### Abstract

The dimer method and its variants have been shown to be efficient in finding saddle points on potential surfaces. In the dimer method, the most unstable direction is approximately obtained by minimizing the total potential energy of the dimer. Then, the force in this direction is reversed to move the dimer toward saddle points. When the finite-temperature effect is important for a high-dimensional system, one usually needs to describe the dynamics in a low-dimensional space of reaction coordinates. In this case, transition states are collected as saddle points on the free energy surface. The traditional dimer method cannot be directly employed to find saddle points on a free energy surface since the surface is not known a priori. Here, we develop a finite-temperature dimer method for searching saddle points on the free energy surface. In this method, a constrained rotation dynamics of the dimer system is used to sample dimer directions and an efficient average method is used to obtain a good approximation of the most unstable direction. This approximated direction is then used in reversing the force component and evolving the dimer toward saddle points. Our numerical results suggest that the new method is efficient in finding saddle points on free energy surfaces.

Original language | English (US) |
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Journal | Journal of Computational Chemistry |

DOIs | |

State | Published - Jan 1 2019 |

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### Keywords

- dimer method
- free energy surface
- rare event
- saddle point
- transition path

### ASJC Scopus subject areas

- Chemistry(all)
- Computational Mathematics

### Cite this

**Finite-Temperature Dimer Method for Finding Saddle Points on Free Energy Surfaces.** / Zhang, Huan; Qiu, Lili; Hu, Dan.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Finite-Temperature Dimer Method for Finding Saddle Points on Free Energy Surfaces

AU - Zhang, Huan

AU - Qiu, Lili

AU - Hu, Dan

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The dimer method and its variants have been shown to be efficient in finding saddle points on potential surfaces. In the dimer method, the most unstable direction is approximately obtained by minimizing the total potential energy of the dimer. Then, the force in this direction is reversed to move the dimer toward saddle points. When the finite-temperature effect is important for a high-dimensional system, one usually needs to describe the dynamics in a low-dimensional space of reaction coordinates. In this case, transition states are collected as saddle points on the free energy surface. The traditional dimer method cannot be directly employed to find saddle points on a free energy surface since the surface is not known a priori. Here, we develop a finite-temperature dimer method for searching saddle points on the free energy surface. In this method, a constrained rotation dynamics of the dimer system is used to sample dimer directions and an efficient average method is used to obtain a good approximation of the most unstable direction. This approximated direction is then used in reversing the force component and evolving the dimer toward saddle points. Our numerical results suggest that the new method is efficient in finding saddle points on free energy surfaces.

AB - The dimer method and its variants have been shown to be efficient in finding saddle points on potential surfaces. In the dimer method, the most unstable direction is approximately obtained by minimizing the total potential energy of the dimer. Then, the force in this direction is reversed to move the dimer toward saddle points. When the finite-temperature effect is important for a high-dimensional system, one usually needs to describe the dynamics in a low-dimensional space of reaction coordinates. In this case, transition states are collected as saddle points on the free energy surface. The traditional dimer method cannot be directly employed to find saddle points on a free energy surface since the surface is not known a priori. Here, we develop a finite-temperature dimer method for searching saddle points on the free energy surface. In this method, a constrained rotation dynamics of the dimer system is used to sample dimer directions and an efficient average method is used to obtain a good approximation of the most unstable direction. This approximated direction is then used in reversing the force component and evolving the dimer toward saddle points. Our numerical results suggest that the new method is efficient in finding saddle points on free energy surfaces.

KW - dimer method

KW - free energy surface

KW - rare event

KW - saddle point

KW - transition path

UR - http://www.scopus.com/inward/record.url?scp=85063130218&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063130218&partnerID=8YFLogxK

U2 - 10.1002/jcc.25824

DO - 10.1002/jcc.25824

M3 - Article

C2 - 30895645

AN - SCOPUS:85063130218

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

SN - 0192-8651

ER -