Theoretical Chemistry

Theoretical Chemistry is a branch of chemistry that employs mathematical models and abstractions to understand and predict the properties and behavior of chemical systems. It focuses on developing theories and computational methods to explain phenomena at the molecular and atomic levels, bridging the gap between experimental observations and chemical principles. This discipline encompasses various areas, including quantum chemistry, molecular modeling, and statistical mechanics, and is essential for interpreting complex reactions, understanding molecular interactions, and designing new materials and drugs in chemistry and related fields.

1. Quantum Chemistry
   1. Wave Function Theory
      1. Schrödinger Equation
         1. Time-Independent Schrödinger Equation
         2. Time-Dependent Schrödinger Equation
         3. Solutions for Simple Systems
            1. Particle in a Box
            2. Harmonic Oscillator
            3. Hydrogen Atom
         4. Approximation Methods
            1. Perturbation Theory
            2. Variational Principle
      2. Hartree-Fock Method
         1. Self-Consistent Field (SCF) Approach
         2. Restricted vs. Unrestricted Hartree-Fock
         3. Hartree-Fock Limit
         4. Basis Sets in Hartree-Fock
            1. Minimal Basis Sets
            2. Split-Valence Basis Sets
            3. Polarization Functions
      3. Post-Hartree-Fock Methods
         1. Configuration Interaction
            1. Configuration State Functions
            2. Full CI vs. Truncated CI
            3. Single and Double Excitations
         2. Coupled Cluster Theory
            1. Coupled Cluster Singles and Doubles (CCSD)
            2. CCSD with Perturbative Triples (CCSD(T))
            3. Advantages over CI
         3. Møller-Plesset Perturbation Theory
            1. MP2, MP3, MP4 Levels
            2. Convergence and Limitations
   2. Density Functional Theory (DFT)
      1. Exchange-Correlation Functionals
         1. Local Density Approximation (LDA)
         2. Generalized Gradient Approximation (GGA)
         3. Meta-GGA Functionals
         4. Hybrid Functionals
            1. B3LYP, PBE0
            2. Range-Separated Functionals
         5. Challenges in XC Functionals Development
      2. Practical Implementations
         1. Plane-Wave Basis Sets
         2. Pseudopotentials
         3. All-Electron vs. Frozen-Core Approaches
      3. Time-Dependent DFT (TD-DFT)
         1. Applications to Excited States
         2. Limitations and Computational Costs
   3. Quantum Chemical Methods
      1. Ab Initio Methods
         1. Born-Oppenheimer Approximation
         2. Multi-Reference Methods
            1. CASSCF (Complete Active Space SCF)
            2. Multi-Reference Configuration Interaction (MRCI)
         3. Challenges with Strongly Correlated Systems
      2. Semi-Empirical Methods
         1. Parametrizations and Their Basis
         2. Computational Efficiency vs. Accuracy
         3. Common Models
            1. AM1, PM3, MNDO
      3. Basis Sets and Approximations
         1. Gaussian Type Orbitals (GTO)
         2. Slater Type Orbitals (STO)
         3. Choosing the Right Basis Set for Accuracy and Efficiency
   4. Quantum Mechanics of Chemical Bonding
      1. Molecular Orbital Theory
         1. Linear Combination of Atomic Orbitals (LCAO)
         2. Homo and Lumo in Molecular Orbitals
         3. Molecular Orbital Diagrams
         4. Symmetry and Orbital Interaction
      2. Valence Bond Theory
         1. Heitler-London Approach
         2. Resonance and Hybridization
         3. Comparison with Molecular Orbital Theory
         4. Applications to Complex Molecules