Computational Chemistry

5.

Quantum Mechanical Methods

5.1.

Electronic Structure Theory

5.1.1.

Many-Electron Problem

5.1.2.

Electron-Electron Interactions

5.1.3.

Electron-Nuclear Interactions

5.1.4.

Spin and Antisymmetry

5.2.

Hartree-Fock Theory

5.2.1.

Variational Principle

5.2.2.

Slater Determinants

5.2.3.

Hartree-Fock Equations

5.2.4.

Self-Consistent Field Procedure

5.2.5.

Orbital Energies and Koopman's Theorem

5.2.6.

Limitations and Electron Correlation

5.3.

Post-Hartree-Fock Methods

5.3.1.

Electron Correlation Problem

5.3.2.

Configuration Interaction

5.3.2.1.

Singles Excitations

5.3.2.2.

Doubles Excitations

5.3.2.3.

Higher Excitations

5.3.2.4.

5.3.2.5.

Truncated CI Methods

5.3.3.

Møller-Plesset Perturbation Theory

5.3.3.1.

Second-Order MP2

5.3.3.2.

Higher-Order Corrections

5.3.3.3.

Convergence Issues

5.3.4.

Coupled Cluster Theory

5.3.4.1.

Exponential Ansatz

5.3.4.2.

5.3.4.3.

5.3.4.4.

Size Extensivity

5.3.4.5.

Computational Scaling

5.4.

Density Functional Theory

5.4.1.

Hohenberg-Kohn Theorems

5.4.1.1.

5.4.1.2.

5.4.1.3.

Implications for DFT

5.4.2.

Kohn-Sham Approach

5.4.2.1.

Kohn-Sham Equations

5.4.2.2.

Kohn-Sham Orbitals

5.4.2.3.

Self-Consistent Procedure

5.4.3.

Exchange-Correlation Functionals

5.4.3.1.

Local Density Approximation

5.4.3.2.

Generalized Gradient Approximation

5.4.3.3.

Meta-GGA Functionals

5.4.3.4.

Hybrid Functionals

5.4.3.5.

Double-Hybrid Functionals

5.4.3.6.

Range-Separated Functionals

5.4.4.

DFT Strengths and Weaknesses

5.4.4.1.

Computational Efficiency

5.4.4.2.

Accuracy for Different Properties

5.4.4.3.

Dispersion Interactions

5.4.4.4.

Strong Correlation Problems

5.4.4.5.

Self-Interaction Error

5.5.

Semi-Empirical Methods

5.5.1.

Approximations and Parameterization

5.5.2.

Neglect of Diatomic Differential Overlap

5.5.3.

5.5.4.

5.5.5.

5.5.6.

PM6 and PM7 Methods

5.5.7.

Applications to Large Systems

5.6.

5.6.1.

Linear Combination of Atomic Orbitals

5.6.2.

Slater-Type Orbitals

5.6.3.

Gaussian-Type Orbitals

5.6.4.

Basis Set Classification

5.6.4.1.

Minimal Basis Sets

5.6.4.2.

Split-Valence Basis Sets

5.6.4.3.

Double-Zeta Basis Sets

5.6.4.4.

Triple-Zeta Basis Sets

5.6.5.

Polarization Functions

5.6.5.1.

d Functions on Heavy Atoms

5.6.5.2.

p Functions on Hydrogen

5.6.5.3.

5.6.6.

Diffuse Functions

5.6.6.1.

Augmented Basis Sets

5.6.6.2.

Anions and Excited States

5.6.7.

Correlation-Consistent Basis Sets

5.6.7.1.

5.6.7.2.

5.6.7.3.

5.6.8.

Basis Set Superposition Error

5.6.8.1.

Counterpoise Correction

5.6.8.2.

Boys-Bernardi Method

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