Introduction to Quantum Chemistry

Contents

     How Are Quantum Chemical Methods Used?

Overview: What will the methods be used for?

     The Molecular Schrodinger Equation

Born - Oppenheimer Approximation

Electronic Schrodinger Equation

Electron Spin

Slater Determinants

Restricted and Unrestricted

• Hartree-Fock Method:

The Fock Operator

Introduction of a Basis Set

The Roothan Matrix Equations-1

The Roothan Matrix Equations-2

Direct Hartree-Fock Algorithm

Hartree-Fock Gradients and 2nd Derivatives

Restricted and Unrestricted Hartree-Fock

UHF Instabilities

• Basis Sets:

Gaussian Type Orbitals

Angular Dependence of Basis Functions

Polarization and Diffuse Basis Functions

Taxonomy of Basis Sets-1: Huzinaga-Dunning

Taxonomy of Basis Sets-2: Pople Basis Sets

Basis Set Superposition Error

Where to Get Basis Sets

          Basis Set Input in Gaussian 9X Format
          Role of HF in Quantum Chemical Protocol

• Accuracy of Hartree Fock Chemical Properties:

HF Predicted Bond Lengths

HF Structural Properties: Open Shells

Structural Properties for Large Molecules

HF Predicted Rotational Barriers

Hartree-Fock Isomerization Reaction Energies

Hartree-Fock Entropies

Caveat Emptor

UHF & RHF Poor at Homolytic Bond Breaking

• Atomic Charges:

Mulliken Populations

Natural Atomic Orbital Populations

Basis Set Dependence of Atomic Charge Methods

Chemical Meaning of Atomic Charges

• Electron Correlation:

Basis Sets and Levels of Theory

Perturbation Theory:

Moller-Plesset Perturbation Theory

Convergence of Moller-Plesset Expansion

Configuration Interaction

Size Consistency

Coupled Cluster Methods

Multiconfigurational SCF

Density Functional Theory (DFT)

Accuracy of Correlated Methods-1

Accuracy of Correlated Methods-2

Accuracy of Correlated Methods-3

Accuracy of Correlated Methods-4

Empirically-Corrected QC Protocols

"Gaussian" Theory

• Semi-Empirical Quantum Chemistry:

MNDO and MINDO Parameter Sets (1985)

Accuracy of Semi-empirical Methods

1. Summary: Ab Initio Quantum Chemistry
2. Summary: Quantum Chemical Wavefunctions (and their acronyms)

          Examples of Quantum Chemistry Study:
Properties Included in Quantum Chemical QSAR
Significant Predictors of Log MP
Relationship of Nitrenium Stability to LUMO Energy
Hydride Shift Energies: 1-4 Hydride Shift
Relationship of Hydride Shift Energy to Nitrenium Charge

• Quantum Chemistry Software

Standard Quantum Chemistry Software (commercial): Gaussian 94 ACES II Spartan Standard Quantum Chemistry Software (free): Gamess Columbus Argus MOPAC

• Anatomy of a QC Input

Specification of Molecular Geometries: Cartesian and Z-Matrix
Example of a Gaussian 94 Input File 

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