# Motif based Hessian matrixfor ab initio geometry optimization ofnanostructures

## Abstract

A simple method to estimate the atomic degree Hessian matrixof a nanosystem is presented. The estimated Hessian matrix, based on themotif decomposition of the nanosystem, can be used to accelerate abinitio atomic relaxations with speedups of 2 to 4 depending on the sizeof the system. In addition, the programing implementation for using thismethod in a standard ab initio package is trivial.

- Authors:

- Publication Date:

- Research Org.:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)

- Sponsoring Org.:
- USDOE Director. Office of Science. Advanced ScientificComputing Research

- OSTI Identifier:
- 926286

- Report Number(s):
- LBNL-59974

R&D Project: K11116; BnR: KJ0101030; TRN: US200807%%623

- DOE Contract Number:
- DE-AC02-05CH11231

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review B; Journal Volume: 73; Journal Issue: 19; Related Information: Journal Publication Date: 05/2006

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36; GEOMETRY; IMPLEMENTATION; NANOSTRUCTURES; OPTIMIZATION; geometry optimization motif Hessian matrix preconditioned CGnanostructures convergence acceleration atomic relaxation

### Citation Formats

```
Zhao, Zhengji, Wang, Lin-Wang, and Meza, Juan.
```*Motif based Hessian matrixfor ab initio geometry optimization ofnanostructures*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevB.73.193309.

```
Zhao, Zhengji, Wang, Lin-Wang, & Meza, Juan.
```*Motif based Hessian matrixfor ab initio geometry optimization ofnanostructures*. United States. doi:10.1103/PhysRevB.73.193309.

```
Zhao, Zhengji, Wang, Lin-Wang, and Meza, Juan. Wed .
"Motif based Hessian matrixfor ab initio geometry optimization ofnanostructures". United States.
doi:10.1103/PhysRevB.73.193309. https://www.osti.gov/servlets/purl/926286.
```

```
@article{osti_926286,
```

title = {Motif based Hessian matrixfor ab initio geometry optimization ofnanostructures},

author = {Zhao, Zhengji and Wang, Lin-Wang and Meza, Juan},

abstractNote = {A simple method to estimate the atomic degree Hessian matrixof a nanosystem is presented. The estimated Hessian matrix, based on themotif decomposition of the nanosystem, can be used to accelerate abinitio atomic relaxations with speedups of 2 to 4 depending on the sizeof the system. In addition, the programing implementation for using thismethod in a standard ab initio package is trivial.},

doi = {10.1103/PhysRevB.73.193309},

journal = {Physical Review B},

number = 19,

volume = 73,

place = {United States},

year = {Wed Apr 05 00:00:00 EDT 2006},

month = {Wed Apr 05 00:00:00 EDT 2006}

}

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