Course Outline
Section 1. The Computational Toolbox
1.1 What is computational chemistry?
Areas of application
Examples of combining experimental and computational work
Computational quantities: structure and chemical properties (“single molecule” properties, thermodynamic quantities, and non-observables)
1.2 What are calculations doing?
Potential energy surfaces (PES)
1.3. Chemically interesting stationary points on a PES
Local and global minima
Local and global maxima
Nth-order saddle points
Important stationary points along the PES of a chemical system and a chemical reaction.
Geometry optimizations: The energy gradient
1.4. Main types of calculations
Single-point energy calculations
Geometry optimizations
Frequency calculations
The Hessian of energy
Mathematical definition and characterization of stationary points
Important data to be obtained from the different types of calculations
1.5. Minimum input for calculations
Minimum input for calculations: level of theory, basis sets, charge, multiplicity, molecular geometry
Level of theory
Molecular geometry: Cartesian coordinates and Z-matrices
Internal coordinates
Graphic interfaces
Number of electrons: Charge and multiplicity of a chemical system
Constructing the Z-matrix of any system
Dummy atoms: Applications
Basis sets: Basis functions frequently used in QM – STOs and GTOs
Effects of increasing the size of a basis set
Section 2. Quantum Chemistry for Electronic Structure Methods
2.1. Historic background of quantum mechanics
Differences between classical and quantum mechanics (QM)
Historic background of QM: Wave nature of light; Planck’s theory of quantization; dual wave-particle behavior of microparticles (De Broglie’s equation).
The Heisenberg uncertainty principle
2.2. The wavefunction
Postulate 1: The wavefunction (wf) or state function, Ψ
Characteristics of a well-behaved wf
Physical significance of Ψ
Probability density: Complex conjugates
Normalization condition
2.3. Operators in quantum mechanics
Postulate 2: Observables and QM operators
Operators and some properties (sum, product, commutation)
Evaluation of commutators
Operators in QM: linear momentum operators, the Hamiltonian operator.
2.4. Eigenvalues and eigenvectors
Eigenvalue equations: Eigenvalues and eigenvectors.
Hermitian operators
Postulate 3: Measurement, observable, operator, eigenvalue
Consequence of operators that commute: Simultaneous specification of several exact properties
Postulate 4: Expectation (average) value
2.5. The Schrödinger equation and the Hamiltonian of a molecule
Postulate 5: The Schrödinger equation (time-dependent and time-independent versions)
The Hamiltonian (total energy) operator: expression for several systems (for a particle moving in one and three dimensions, for N particles moving in 3 dimensions)
The Hamiltonian operator of a molecule
The Born-Oppenheimer approximation
2.6. The multielectron wavefunction and the Slater determinant
Postulate 6: The multielectron wf is antisymmetric
Molecular orbital (MO) theory: Molecular orbitals, spin functions and spin orbitals
The Hartree product of spin orbitals
Slater determinants
The LCAO (linear combination of atomic orbitals) approximation
MOs as a linear combination of basis functions
2.7. The Hartree-Fock (HF) theory
The HF approximation: Main features
The correlation energy
The HF equations: identification and understanding of every term
The self-consistent-field (SCF) method
The Roothaan-Hall Equations
Limitations of HF theory
2.7. Other common levels of theory
Electron-correlation methods: CI, CCSD,….
Moller-Plesset Perturbation Theory: MP2, MP4
Density Functional Theory (DFT): Hohenberg-Kohn theorem, Kohn-Sham DFT