### Abstract

The relationship between structure and property is central to chemistry and enables the understanding of chemical phenomena and processes. Need for an efficient conformational sampling of chemical systems arises from the presence of solvents and the existence of non-zero temperatures. However, conformational sampling of structures to compute molecular quantum mechanical properties is computationally expensive because a large number of electronic structure calculations are required. In this work, the development and implementation of the effective stochastic potential (ESP) method is presented to perform efficient conformational sampling of molecules. The overarching goal of this work is to alleviate the computational bottleneck associated with performing a large number of electronic structure calculations required for conformational sampling. We introduce the concept of a deformation potential and demonstrate its existence by the proof-by-construction approach. A statistical description of the fluctuations in the deformation potential due to non-zero temperature was obtained using infinite-order moment expansion of the distribution. The formal mathematical definition of the ESP was derived using the functional minimization approach to match the infinite-order moment expansion for the deformation potential. Practical implementation of the ESP was obtained using the random-matrix theory method. The developed method was applied to two proof-of-concept calculations of the distribution of HOMO-LUMO gaps in water molecules and solvated CdSe clusters at 300 K. The need for large sample size to obtain statistically meaningful results was demonstrated by performing 10^{5} ESP calculations. The results from these prototype calculations demonstrated the efficacy of the ESP method for performing efficient conformational sampling. We envision that the fundamental nature of this work will not only extend our knowledge of chemical systems at non-zero temperatures but also generate new insights for innovative technological applications.

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

Article number | 014103 |

Journal | Journal of Chemical Physics |

Volume | 149 |

Issue number | 1 |

DOIs | |

State | Published - Jul 7 2018 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*149*(1), [014103]. https://doi.org/10.1063/1.5026027

**Development of effective stochastic potential method using random matrix theory for efficient conformational sampling of semiconductor nanoparticles at non-zero temperatures.** / Scher, Jeremy A.; Bayne, Michael G.; Srihari, Amogh; Nangia, Shikha; Chakraborty, Arindam.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 149, no. 1, 014103. https://doi.org/10.1063/1.5026027

}

TY - JOUR

T1 - Development of effective stochastic potential method using random matrix theory for efficient conformational sampling of semiconductor nanoparticles at non-zero temperatures

AU - Scher, Jeremy A.

AU - Bayne, Michael G.

AU - Srihari, Amogh

AU - Nangia, Shikha

AU - Chakraborty, Arindam

PY - 2018/7/7

Y1 - 2018/7/7

N2 - The relationship between structure and property is central to chemistry and enables the understanding of chemical phenomena and processes. Need for an efficient conformational sampling of chemical systems arises from the presence of solvents and the existence of non-zero temperatures. However, conformational sampling of structures to compute molecular quantum mechanical properties is computationally expensive because a large number of electronic structure calculations are required. In this work, the development and implementation of the effective stochastic potential (ESP) method is presented to perform efficient conformational sampling of molecules. The overarching goal of this work is to alleviate the computational bottleneck associated with performing a large number of electronic structure calculations required for conformational sampling. We introduce the concept of a deformation potential and demonstrate its existence by the proof-by-construction approach. A statistical description of the fluctuations in the deformation potential due to non-zero temperature was obtained using infinite-order moment expansion of the distribution. The formal mathematical definition of the ESP was derived using the functional minimization approach to match the infinite-order moment expansion for the deformation potential. Practical implementation of the ESP was obtained using the random-matrix theory method. The developed method was applied to two proof-of-concept calculations of the distribution of HOMO-LUMO gaps in water molecules and solvated CdSe clusters at 300 K. The need for large sample size to obtain statistically meaningful results was demonstrated by performing 105 ESP calculations. The results from these prototype calculations demonstrated the efficacy of the ESP method for performing efficient conformational sampling. We envision that the fundamental nature of this work will not only extend our knowledge of chemical systems at non-zero temperatures but also generate new insights for innovative technological applications.

AB - The relationship between structure and property is central to chemistry and enables the understanding of chemical phenomena and processes. Need for an efficient conformational sampling of chemical systems arises from the presence of solvents and the existence of non-zero temperatures. However, conformational sampling of structures to compute molecular quantum mechanical properties is computationally expensive because a large number of electronic structure calculations are required. In this work, the development and implementation of the effective stochastic potential (ESP) method is presented to perform efficient conformational sampling of molecules. The overarching goal of this work is to alleviate the computational bottleneck associated with performing a large number of electronic structure calculations required for conformational sampling. We introduce the concept of a deformation potential and demonstrate its existence by the proof-by-construction approach. A statistical description of the fluctuations in the deformation potential due to non-zero temperature was obtained using infinite-order moment expansion of the distribution. The formal mathematical definition of the ESP was derived using the functional minimization approach to match the infinite-order moment expansion for the deformation potential. Practical implementation of the ESP was obtained using the random-matrix theory method. The developed method was applied to two proof-of-concept calculations of the distribution of HOMO-LUMO gaps in water molecules and solvated CdSe clusters at 300 K. The need for large sample size to obtain statistically meaningful results was demonstrated by performing 105 ESP calculations. The results from these prototype calculations demonstrated the efficacy of the ESP method for performing efficient conformational sampling. We envision that the fundamental nature of this work will not only extend our knowledge of chemical systems at non-zero temperatures but also generate new insights for innovative technological applications.

UR - http://www.scopus.com/inward/record.url?scp=85049751256&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049751256&partnerID=8YFLogxK

U2 - 10.1063/1.5026027

DO - 10.1063/1.5026027

M3 - Article

AN - SCOPUS:85049751256

VL - 149

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 1

M1 - 014103

ER -