Computational Quantum Chemistry - 1st Edition - ISBN: 9780125696821, 9780080488530

Computational Quantum Chemistry

1st Edition

An Interactive Introduction to Basis Set Theory

Authors: Charles M. Quinn
eBook ISBN: 9780080488530
Imprint: Academic Press
Published Date: 28th February 2002
Page Count: 237
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Computational Quantum Chemistry removes much of the mystery of modern computer programs for molecular orbital calculations by showing how to develop Excel spreadsheets to perform model calculations and investigate the properties of basis sets. Using the book together with the CD-ROM provides a unique interactive learning tool. In addition, because of the integration of theory with working examples on the CD-ROM, the reader can apply advanced features available in the spreadsheet to other applications in chemistry, physics, and a variety of disciplines that require the solution of differential equations.

This book and CD-ROM makes a valuable companion for instructors, course designers, and students. It is suitable for direct applications in practical courses in theoretical chemistry and atomic physics, as well as for teaching advanced features of Excel in IT courses.


Undergraduate and graduate students, lecturers, and professionals in theoretical or physical chemistry, as well as those interested in computational chemistry and its applications with Excel.

Table of Contents


1 Essential Atomic Orbital Theory

1.1 Atomic Orbitals for the Hydrogen Atom

1.2 Radial Distribution Functions for the Hydrogen Atom

1.3 Radial Wave Functions for Many-Electron Atoms

1.4 Slater-Type Orbitals

1.5 Gaussian-Type Functions—the |sto-3g› Minimal Basis Set

1.6 |sto-ng› Basis Sets

1.7 Scaling Factors

1.8 The (4s/2s) Basis Set, Polarization and Scaling Factors for Molecular Environments

1.9 Gaussian-Lobe and Other Gaussian Basis Sets

2 Numerical Integration

2.1 Numerical Integration

2.2 Application of Simpson’s Rule to Calculate a Normalization Integral

2.3 Calculations of Normalization Constants Over the Angular Coordinates

2.4 Numerical Integration in a Cylindrical Volume: Diatomic and Linear Molecular Geometries

2.5 Calculation of the Overlap Integral Between 1s Orbitals in a Gaussian Basis

2.6 Designing Gaussian Basis Sets to Model Slater Orbitals

3 Orthonormality

3.1 Orthonormality in Slater Orbital and Basis Set Theory

3.2 Orthonormality and Slater Orbitals

3.3 Orthonormality and Gaussian Orbitals

3.4 Orthonormality and Double-Zeta Slater Orbitals

3.5 Orthonormality and Split-Basis or Double-Zeta Gaussian Basis Sets

3.6 The Jacobi Transformation, Diagonalization of a Symmetric Matrix and Canonical Orthogonalization

3.7 The S−1/2 ‘Trick’

3.8 Symmetric Orthonormalization

4 The Hydrogen Atom—Numerical Solutions

4.1 Eigenvalue Calculations for Hydrogen Based on Analytical Functions

4.2 Calculations Using Slater Orbitals

4.3 Calculations with Gaussian Functions

4.4 Calculations with Split-Basis [Split-Valence] Sets

4.5 Review of Results for the 1s and 2s Orbital Energies in Hydrogen

5 The Helium Atom and the Self-Consistent Field

5.1 Hartree’s Analysis of the Helium Atom Problem

5.2 Calculations with Modified Hydrogen Atom Wave Functions

5.3 The Hall–Roothaan Equations, the Orbital Approximation and the Modern Hartree–Fock Self-Consistent Field Method

5.4 Calculations Using Slater DZ Functions

5.5 Gaussian Basis Set Calculations for the Helium Atom–Two-Electron Integrals Over Gaussian Basis Functions

5.6 A HFS-SCF Calculation with Split-Basis |4-31› for Helium

5.7 Helium, Singlet and Triplet Excited States, Electron Spin and the Role of the Exchange Integral

6 One- and Two-Electron Diatoms

6.1 Calculations Using Hydrogen 1s Orbitals

6.2 Sto-3g Calculations for H2+

6.3 Calculations Using Gaussian Basis Sets with the Exact Evaluation of Integrals Using Fourier Transforms

6.4 Calculations Involving the Two-Electron Terms; the |sto-3g› HF-SCF Results for Dihydrogen

6.5 The Standard Form for the Results of HFS-SCF Calculations

6.6 The |sto-3g› HFS-SCF Calculation for HeH+

6.7 Polarization Functions, Gaussian Lobes and Higher-Order Gaussian Basis Sets

6.8 Epilogue




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© Academic Press 2002
Academic Press
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About the Author

Charles M. Quinn

Affiliations and Expertise

National University of Ireland, Maynooth, Co. Kildare, Ireland