# On the full exploitation of symmetry in periodic (as well as molecular) self-consistent-field ab initio calculations

## Abstract

Use of symmetry can dramatically reduce the computational cost (running time and memory allocation) of self-consistent-field ab initio calculations for molecular and crystalline systems. Crucial for running time is symmetry exploitation in the evaluation of one- and two-electron integrals, diagonalization of the Fock matrix at selected points in reciprocal space, reconstruction of the density matrix. As regards memory allocation, full square matrices (overlap, Fock, and density) in the Atomic Orbital (AO) basis are avoided and a direct transformation from the packed AO to the symmetry adapted crystalline orbital basis is performed, so that the largest matrix to be handled has the size of the largest sub-block in the latter basis. Quantitative examples, referring to the implementation in the CRYSTAL code, are given for high symmetry families of compounds such as carbon fullerenes and nanotubes.

- Authors:

- Dipartimento di Chimica, Università di Torino and NIS, Nanostructured Interfaces and Surfaces, Centre of Excellence, Via P. Giuria 7, 10125 Torino (Italy)
- (Australia)
- Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad, 1001, Col. Chamilpa, 62209 Cuernavaca (Morelos) (Mexico)

- Publication Date:

- OSTI Identifier:
- 22308361

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 141; Journal Issue: 10; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 77 NANOSCIENCE AND NANOTECHNOLOGY; ALLOCATIONS; CRYSTALS; DENSITY; DENSITY MATRIX; ELECTRONS; EVALUATION; FULLERENES; NANOTUBES; SELF-CONSISTENT FIELD; SYMMETRY

### Citation Formats

```
Orlando, Roberto, E-mail: roberto.orlando@unito.it, Erba, Alessandro, Dovesi, Roberto, De La Pierre, Marco, Nanochemistry Research Institute, Department of Chemistry, Curtin University, GPO Box U1987, Perth, WA 6845, and Zicovich-Wilson, Claudio M.
```*On the full exploitation of symmetry in periodic (as well as molecular) self-consistent-field ab initio calculations*. United States: N. p., 2014.
Web. doi:10.1063/1.4895113.

```
Orlando, Roberto, E-mail: roberto.orlando@unito.it, Erba, Alessandro, Dovesi, Roberto, De La Pierre, Marco, Nanochemistry Research Institute, Department of Chemistry, Curtin University, GPO Box U1987, Perth, WA 6845, & Zicovich-Wilson, Claudio M.
```*On the full exploitation of symmetry in periodic (as well as molecular) self-consistent-field ab initio calculations*. United States. doi:10.1063/1.4895113.

```
Orlando, Roberto, E-mail: roberto.orlando@unito.it, Erba, Alessandro, Dovesi, Roberto, De La Pierre, Marco, Nanochemistry Research Institute, Department of Chemistry, Curtin University, GPO Box U1987, Perth, WA 6845, and Zicovich-Wilson, Claudio M. Sun .
"On the full exploitation of symmetry in periodic (as well as molecular) self-consistent-field ab initio calculations". United States. doi:10.1063/1.4895113.
```

```
@article{osti_22308361,
```

title = {On the full exploitation of symmetry in periodic (as well as molecular) self-consistent-field ab initio calculations},

author = {Orlando, Roberto, E-mail: roberto.orlando@unito.it and Erba, Alessandro and Dovesi, Roberto and De La Pierre, Marco and Nanochemistry Research Institute, Department of Chemistry, Curtin University, GPO Box U1987, Perth, WA 6845 and Zicovich-Wilson, Claudio M.},

abstractNote = {Use of symmetry can dramatically reduce the computational cost (running time and memory allocation) of self-consistent-field ab initio calculations for molecular and crystalline systems. Crucial for running time is symmetry exploitation in the evaluation of one- and two-electron integrals, diagonalization of the Fock matrix at selected points in reciprocal space, reconstruction of the density matrix. As regards memory allocation, full square matrices (overlap, Fock, and density) in the Atomic Orbital (AO) basis are avoided and a direct transformation from the packed AO to the symmetry adapted crystalline orbital basis is performed, so that the largest matrix to be handled has the size of the largest sub-block in the latter basis. Quantitative examples, referring to the implementation in the CRYSTAL code, are given for high symmetry families of compounds such as carbon fullerenes and nanotubes.},

doi = {10.1063/1.4895113},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 10,

volume = 141,

place = {United States},

year = {2014},

month = {9}

}