Quantum Mechanics and Modeling II

This course provides a complete description of the structural, electronic, and vibrational properties of molecules, together with the quantum treatment of these properties in computer simulations.

In parallel, the structural and electronic properties of solids are addressed, with an emphasis on the properties of metals and semiconductors.

Hourly volumes:

            CM: 42 hours

            TD: 9 p.m.

1) Understand the peculiarities of the electronic properties of molecules
2) Understand the peculiarities of the vibrational properties of molecules
3) Be able to describe the excited states of molecules
4) Apprehend and be able to determine the electronic properties of a crystal (1D, 2D, 3D)
5) Determine from first principles the transport and thermal properties of solids

Differential calculus. Matrix algebra.

Final exam (1)

7 Molecular Structure: WF methods 9 hours (6 hours lecture, 3 hours tutorial)

7.1 Adiabatic Hypothesis and Born-Oppenheimer Approximation

7.2 SCF MO Treatment of Polyatomic Molecules

7.3 Electron Correlation Methods: CI

7.4 Electron-Correlation Methods: (RS) Perturbation Theory (Mpn)

7.5 Electron Correlation Methods: CC and MR

8 Molecular Structure: Density Functional Theory 4.5 hours (4.5 hours lecture)

8.1 Hohenberg-Kohn Theorems

8.2 The Kohn-Sham Approach

8.3 Exchange-Correlation Functionals

9 Molecular Rotational and Vibrational Motion 9 hours (6 hours of lectures, 3 hours of tutorials)

9.1 Rotation of Molecules

9.2 Vibration of Molecules

9.3 Rotation-vibration spectra of Diatomic Molecules

9.4 Vibrations of Polyatomic Molecules – IR and Raman Selection Rules

9.5 Anharmonicities and Coriolis forces

10 Molecular Electronic Excited States 4.5 hours (4.5 hours lecture)

10.1 Franck-Condon Principle and Vibronic Transitions

10.2 The Electronic Spectra of Molecules

10.3 Spin-Forbidden Transitions

10.4 Decay of Excitations

11 Molecular Electronic Excited States Structure 4.5 hours (4.5 hours of tutorials)

11.1 Linear Response Methods

11.2 MR Methods

12 Electronic Structure of Solids 31.5 hours (21 hours of lectures, 10.5 hours of tutorials)

12.1 Direct and Reciprocal Lattices

12.2 1D - Electronic Structure of the model chain (H)n

12.3 1D - Electronic Structure of the Dimerized Model Chain (H2)n

12.4 First-order Peierls distortions in one-dimensional periodic systems

12.5 2D – Electronic structure of the square lattice (H)n

12.6 Concept of Fermi surface

12.7 Bloch and Crystal Orbitals

12.8 Electronic structure of metals

12.9 Electronic structure of semiconductors

12.10 Transport Properties of Solids

12.11 Thermal properties of solids