Theoretical Chemistry

Fundamentals

• BO Approximation
• The Electron Gas
• Variational Method *
• Perturbation Theory *

Ensemble Simulations

A description of Molecular Dynamics and Monte Carlo techniques will be given, with emphasis on ab-initio simulation techniques based on Density Functional Theory, and focus on nanoscience applications.

• Molecular Dynamics (MD) Simulations
  • Empirical potentials
  • Ensemble averages
• ab initio MD
• Quantum Monte Carlo

Chemical Bonding

When molecules share electrons, they form bonds. Atoms can share one, two, or three electrons, forming single, double, and triple bonds. Although it is impossible to determine the exact position of the electron, it is possible to calculate the probablity that one will find the electron in a point around the nucleus.

Single-Molecule Quantum Mechanical Calculations

Quantum chemistry methods, including Hartree-Fock and correlated methods will be discussed and then electronic structure calculations developed within the condensed matter physics community will be introduced.

• ab inito Calculations *
• Semi-empirical Calculations
• Tight binding
• Nearly-free electron model
• Hartree–Fock
• Modern valence bond
• Generalized valence bond
• Møller–Plesset perturbation theory
• Configuration interaction
• Coupled cluster
• Multi-configurational self-consistent field
• Density functional theory
  • Local density Approximations
  • The Kohn-Sham equations
• Quantum chemistry composite methods
• Quantum Monte Carlo
• k·p perturbation theory
• Muffin-tin approximation
• LCAO method

Statistical Mechanics

Rarely does an experiment study the properties of a single individual molecule or atom or energy level etc. This necessitates the introduction of statistical formalisms into describing matter, and the measurements of matter, whereby means, standard deviations and other properties are of considerable interest. Computers provide a sophisticated and powerful tool for exploring and quantifying such aspects.