# The linear and nonlinear response of infinite periodic systems to static and/or dynamic electric fields. Implementation in CRYSTAL code

## Abstract

An implementation of the vector potential approach (VPA) for treating the response of infinite periodic systems to static and dynamic electric fields has been initiated within the CRYSTAL code. The VPA method is based on the solution of a time-dependent Hartree-Fock or Kohn-Sham equation for the crystal orbitals wherein the usual scalar potential, that describes interaction with the field, is replaced by the vector potential. This equation may be solved either by perturbation theory or by finite field methods. With some modification all the computational procedures of molecular ab initio quantum chemistry can be adapted for periodic systems. Accessible properties include the linear and nonlinear responses of both the nuclei and the electrons. The programming of static field pure electronic (hyper)polarizabilities has been successfully tested. Dynamic electronic (hyper)polarizabilities, as well as infrared and Raman intensities, are in progress while the addition of finite fields for calculation of vibrational (hyper)polarizabilities, through nuclear relaxation procedures, will begin shortly.

- Authors:

- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106 (United States)
- Physical and Theoretical Chemistry, University of Saarland, 66123 Saarbrücken (Germany)
- Equipe de Chimie Physique, IPREM UMR5254, Université de Pau et des Pays de l'Adour, 64000 Pau (France)
- Departimeno di Chimica, IFM, Università di Torino and NIS - Nanostructure Interfaces and Surfaces - Centre of Excellence, Via P. Giuria 7, 10125 Torino (Italy)
- Departimento di Scienze e Tecnologie Avanzati, Università del Piemonte Orientale, Viale T. Michel 11, 15121 Alessandria (Italy)

- Publication Date:

- OSTI Identifier:
- 22390884

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1642; Journal Issue: 1; Conference: ICCMSE-2010: International Conference of Computational Methods in Sciences and Engineering 2010, Kos (Greece), 3-8 Oct 2010; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; C CODES; ELECTRIC FIELDS; HARTREE-FOCK METHOD; MATHEMATICAL SOLUTIONS; MODIFICATIONS; NONLINEAR PROBLEMS; PERTURBATION THEORY; POLARIZABILITY; POTENTIALS; RELAXATION; SCALARS; TIME DEPENDENCE; VECTORS

### Citation Formats

```
Kirtman, Bernard, Springborg, Michael, Rérat, Michel, Ferrero, Mauro, Lacivita, Valentina, Dovesi, Roberto, and Orlando, Roberto.
```*The linear and nonlinear response of infinite periodic systems to static and/or dynamic electric fields. Implementation in CRYSTAL code*. United States: N. p., 2015.
Web. doi:10.1063/1.4906650.

```
Kirtman, Bernard, Springborg, Michael, Rérat, Michel, Ferrero, Mauro, Lacivita, Valentina, Dovesi, Roberto, & Orlando, Roberto.
```*The linear and nonlinear response of infinite periodic systems to static and/or dynamic electric fields. Implementation in CRYSTAL code*. United States. doi:10.1063/1.4906650.

```
Kirtman, Bernard, Springborg, Michael, Rérat, Michel, Ferrero, Mauro, Lacivita, Valentina, Dovesi, Roberto, and Orlando, Roberto. Thu .
"The linear and nonlinear response of infinite periodic systems to static and/or dynamic electric fields. Implementation in CRYSTAL code". United States.
doi:10.1063/1.4906650.
```

```
@article{osti_22390884,
```

title = {The linear and nonlinear response of infinite periodic systems to static and/or dynamic electric fields. Implementation in CRYSTAL code},

author = {Kirtman, Bernard and Springborg, Michael and Rérat, Michel and Ferrero, Mauro and Lacivita, Valentina and Dovesi, Roberto and Orlando, Roberto},

abstractNote = {An implementation of the vector potential approach (VPA) for treating the response of infinite periodic systems to static and dynamic electric fields has been initiated within the CRYSTAL code. The VPA method is based on the solution of a time-dependent Hartree-Fock or Kohn-Sham equation for the crystal orbitals wherein the usual scalar potential, that describes interaction with the field, is replaced by the vector potential. This equation may be solved either by perturbation theory or by finite field methods. With some modification all the computational procedures of molecular ab initio quantum chemistry can be adapted for periodic systems. Accessible properties include the linear and nonlinear responses of both the nuclei and the electrons. The programming of static field pure electronic (hyper)polarizabilities has been successfully tested. Dynamic electronic (hyper)polarizabilities, as well as infrared and Raman intensities, are in progress while the addition of finite fields for calculation of vibrational (hyper)polarizabilities, through nuclear relaxation procedures, will begin shortly.},

doi = {10.1063/1.4906650},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1642,

place = {United States},

year = {Thu Jan 22 00:00:00 EST 2015},

month = {Thu Jan 22 00:00:00 EST 2015}

}