Quantum Mechanics and Modeling II

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

At the same time, the structural and electronic properties of solids are examined, with an emphasis on the properties of metals and semiconductors.

Hourly volumes*:

            CM: 42H

            TD: 9:00 p.m.

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

Differential calculus. Matrix algebra.

Final Exam (1)

7 Molecular Structure: WF Methods 9 hours (6 hours lecture, 3 hours lab)

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 of seminar)

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 lecture, 3 hours lab)

9.1 Rotation of Molecules

9.2 Molecular Vibration

9.3 Rotational-Vibrational 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 The 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 tutorial)

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 1D Periodic Systems

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

12.6 Concept of the 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