## Theory of Solids and Molecular Models

course ID

Lecturer

CFU

8

Length

14 Weeks

Semester DD

First

##### Course details

The Born-Oppenheimer approximation
The Hellmann - Feynman theorem , Epstein theorem.
Band theory in solids Bloch theorem , boundary conditions variational method , tight-binding method and its applications – Ortogonalized Plane Waves, pseudopotentials .
Ab-initio methods : Hartree and Hartree Fock equation , Koopmans theorem , potential for gas exchange electronic homogeneous Fourier Transform Coulomb potential of the homogeneous electron gas with the Hartree Fock. Approximation of Slater, Thomas Fermi approximation. functional derivatives
Density Functional Theory . Theorem of Hohenberg and Kokn , Kohn and Sham equations .
The Local Density Approximation . The problem of the gap in DFT
Examples of applications of DFT
Optical properties
Complex refraction index. The absorption coefficient.
The reflectivity . The dielectric function . Kramers Kroning relations and sum rules
Fermi's golden rule : Calculation of the dielectric function in the dipole approximation
Examples of dielectric function for metals, semiconductors, insulators . Joint density of states ( JDOS ) and it behaviour near the critical points.
Linear response theory and TDDFT .
Boltzman equation for electric and thermal transport
Classical and ab-initio molecular dynamics
Excitonic effects : model hydrogen- Mott – Wannier.
Ab-initio excited state theories Classical Green's functions . Formalism of second quantization . Quantum propagator of a single electron / hole and its representation of Lehmann and relationship with electronic excitations . Dyson equation . Self- energy concept . Quasi-particle Equation. GW method . Bethe- Salpeter equation for the calculation of excitonic effects in the optical response .
Practical lessons at computer of DFT , TDDFT , GW and BSE
which include an introduction to the main commands in linux environment

Co-teaching: Prof.ssa Palummo Maurizia

##### Objectives

LEARNING OUTCOMES:

The course is aimed at completing basic training in the field of quantum physics applied to the study of microscopic and macroscopic properties of materials.
The goal of the course is to provide the main knowledge on theoretical / computational methods for the study of the structural, electronic and optical properties of materials.
The main educational objectives are the understanding of quantum-mechanical semi-empirical and first-principles methods, such as the Density Functional Theory (DFT), the time-dependent Functional density theory and the Green Function theory.
Another objective is the learning and autonomous use of one of the main DFT (quantum-express) calculation codes currently in use in the field of research in material science through the performance of practical exercises by the student.

KNOWLEDGE AND UNDERSTANDING:
The course aims to provide the student with the basic tools needed to understand the structural and opto-electronic properties of materials in terms of a microscopic quantum-mechanical description.
The lessons focus on the mathematical derivation and physical interpretation of the main theoretical investigation tools for the study of the structural, electronic and spectroscopic properties of materials.
Applications relating to materials of current interest in the field of material science research are illustrated during lectures and computer-based simulations in order to broaden the student's knowledge about the state of the art in this field.

APPLYING KNOWLEDGE AND UNDERSTANDING:

The course aims to provide mathematical-physical tools that allow students to understand scientific manuscripts dedicated to the study of materials and to analyze, through their knowledge, various experimental physical observables of interest in materials science.

The student must also be able to identify and understand the theoretical / computational method suitable for the characterization of the chemical-physical properties of the material of interest and tp be able to understand, analysis, discussions and data derioved by these methods.
The student will also be able to tackle new scientific problems and to read scientific texts and articles in English on topics related to the study of electronic structural and optical properties of materials.

MAKING JUDGEMENTS:

Students are required to use the acquired knowledge in a critical manner, specifically to study the structural, electronic and optical properties of materials in order to evaluate their characteristics for an appropriate use in the field of materials science.

COMMUNICATION SKILLS:
Particular attention is paid to the ability to use the knowledge acquired during the lessons appropriately and in a conceptually coherent and rigorous context. The final report related to the computer simulations carried out by the student on a specific material, is foreseen through a seminar-type power-point presentation by the same, and has the purpose of exercising and improving communication skills and transversal skills of the student .

LEARNING SKILLS:

Particular attention is paid to the ability to use the knowledge acquired during the lessons appropriately and in a conceptually coherent and rigorous context.
The final report related to the computer exercise carried out by the student on a specific material, is foreseen through a seminar-type power-point presentation and has the purpose of exercising and improving his/her communication skills and transversal skills .