From anisotropy of dielectric tensors to birefringence: a quantum mechanics approach
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PHYSICOCHEMICAL PROPERTIES OF MATTER
From anisotropy of dielectric tensors to birefringence: a quantum mechanics approach Michel Rérat1 · Philippe D’Arco2 · Valentina Lacivita3,4 · Fabien Pascale5 · Roberto Dovesi6 Received: 11 February 2020 / Accepted: 3 July 2020 © Accademia Nazionale dei Lincei 2020
Abstract The way quantum mechanical ab initio computer codes allow to compute, through perturbation theory (the so-called SC-CP, self-consistent coupled-perturbed scheme), many properties resulting from the interaction of the electric field with a crystalline system is illustrated. The polarizability, which leads to the dielectric tensors as well as to the refractive indices and to the birefringence of materials, is the simplest on this list. Higher order tensors, like the first and second hyperpolarizabilities, can be obtained as well with the CRYSTAL code here used. These properties, resulting from the Taylor expansion of the total energy of the solid as a function of the electric field, belong to a large family of phenomena generated by combining in different ways the frequencies of the fields. Second-harmonic generation (SHG), Pockels effect, intensity-dependent refractive index (IDRI), and other quantities now accessible to experiment can be computed at a relatively low cost and with high accuracy. Keywords Refractive index · Birefringence · (Non)linear electric susceptibility tensor · Anisotropy · Quantum mechanical simulation · CRYSTAL code · Gaussian-type basis set
1 Introduction
This paper is the peer-reviewed version of a contribution presented at the Conference on Anisotropic Properties of Matter, organized by Giovanni Ferraris and held at Accademia Nazionale dei Lincei in Rome, October 16–17, 2019. * Michel Rérat michel.rerat@univ‑pau.fr 1
Université de Pau et des Pays de l’Adour, E2S UPPA, CNRS, IPREM, 2 av. président P. Angot, 64053 Pau, France
2
Sorbonne Université, CNRS-INSU, ISTeP UMR 7193, 75005 Paris, France
3
Advanced Materials Lab, Samsung Research America, 10 Wilson Rd., Cambridges, MA 02138, USA
4
Sorbonne Université, CNRS, IMJ UMR 7586, 75005 Paris, France
5
Université de Lorraine-Nancy, CNRS, Laboratoire de Physique et Chimie Théoriques, UMR 7019, Vandoeuvre‑les‑Nancy, France
6
Dipartimento di Chimica, Nanostructured Interfaces and Surfaces (NIS) Centre of Excellence, Università di Torino, Via P. Giuria 7, 10125 Turin, Italy
In this contribution, we illustrate the way modern quantum mechanical methods allow to compute the (hyper)polarizability tensors and, consequently, optical properties such as the refractive index and birefringence, through which the anisotropy of the physical properties of crystalline compounds manifests itself. The properties mentioned above can be obtained by investigating the interaction of the electromagnetic field with a periodic infinite system (the model implies, without serious consequences, that the crystalline compound is infinite). The equations describing this interaction can be formulated at various levels (for example: relati
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