### Abstract

A low-computational-cost algorithm and its parallel implementation for periodic divide-and-conquer density-functional tight-binding (DC-DFTB) calculations are presented. The developed algorithm enables rapid computation of the interaction between atomic partial charges, which is the bottleneck for applications to large systems, by means of multipole- and interpolation-based approaches for long- and short-range contributions. The numerical errors of energy and forces with respect to the conventional Ewald-based technique can be under the control of the multipole expansion order, level of unit cell replication, and interpolation grid size. The parallel performance of four different evaluation schemes combining previous approaches and the proposed one are assessed using test calculations of a cubic water box on the K computer. The largest benchmark system consisted of 3,295,500 atoms. DC-DFTB energy and forces for this system were obtained in only a few minutes when the proposed algorithm was activated and parallelized over 16,000 nodes in the K computer. The high performance using a single node workstation was also confirmed. In addition to liquid water systems, the feasibility of the present method was examined by testing solid systems such as diamond form of carbon, face-centered cubic form of copper, and rock salt form of sodium chloride.

Original language | English |
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Journal | Journal of Computational Chemistry |

DOIs | |

Publication status | Accepted/In press - 2017 |

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### Keywords

- Density-functional tight-binding method
- Divide-and-conquer method
- Massively parallel calculation
- Multipole expansion
- Periodic boundary condition

### ASJC Scopus subject areas

- Chemistry(all)
- Computational Mathematics

### Cite this

**Parallel implementation of efficient charge-charge interaction evaluation scheme in periodic divide-and-conquer density-functional tight-binding calculations.** / Nishimura, Yoshifumi; Nakai, Hiromi.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Parallel implementation of efficient charge-charge interaction evaluation scheme in periodic divide-and-conquer density-functional tight-binding calculations

AU - Nishimura, Yoshifumi

AU - Nakai, Hiromi

PY - 2017

Y1 - 2017

N2 - A low-computational-cost algorithm and its parallel implementation for periodic divide-and-conquer density-functional tight-binding (DC-DFTB) calculations are presented. The developed algorithm enables rapid computation of the interaction between atomic partial charges, which is the bottleneck for applications to large systems, by means of multipole- and interpolation-based approaches for long- and short-range contributions. The numerical errors of energy and forces with respect to the conventional Ewald-based technique can be under the control of the multipole expansion order, level of unit cell replication, and interpolation grid size. The parallel performance of four different evaluation schemes combining previous approaches and the proposed one are assessed using test calculations of a cubic water box on the K computer. The largest benchmark system consisted of 3,295,500 atoms. DC-DFTB energy and forces for this system were obtained in only a few minutes when the proposed algorithm was activated and parallelized over 16,000 nodes in the K computer. The high performance using a single node workstation was also confirmed. In addition to liquid water systems, the feasibility of the present method was examined by testing solid systems such as diamond form of carbon, face-centered cubic form of copper, and rock salt form of sodium chloride.

AB - A low-computational-cost algorithm and its parallel implementation for periodic divide-and-conquer density-functional tight-binding (DC-DFTB) calculations are presented. The developed algorithm enables rapid computation of the interaction between atomic partial charges, which is the bottleneck for applications to large systems, by means of multipole- and interpolation-based approaches for long- and short-range contributions. The numerical errors of energy and forces with respect to the conventional Ewald-based technique can be under the control of the multipole expansion order, level of unit cell replication, and interpolation grid size. The parallel performance of four different evaluation schemes combining previous approaches and the proposed one are assessed using test calculations of a cubic water box on the K computer. The largest benchmark system consisted of 3,295,500 atoms. DC-DFTB energy and forces for this system were obtained in only a few minutes when the proposed algorithm was activated and parallelized over 16,000 nodes in the K computer. The high performance using a single node workstation was also confirmed. In addition to liquid water systems, the feasibility of the present method was examined by testing solid systems such as diamond form of carbon, face-centered cubic form of copper, and rock salt form of sodium chloride.

KW - Density-functional tight-binding method

KW - Divide-and-conquer method

KW - Massively parallel calculation

KW - Multipole expansion

KW - Periodic boundary condition

UR - http://www.scopus.com/inward/record.url?scp=85031499582&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031499582&partnerID=8YFLogxK

U2 - 10.1002/jcc.25086

DO - 10.1002/jcc.25086

M3 - Article

AN - SCOPUS:85031499582

JO - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

SN - 0192-8651

ER -