Elsevier S & T

Computational Quantum Chemistry: An Interactive Introduction to Basis Set Theory

Quinn, Charles M.

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Table of contents
  • Cover
  • Contentsv
  • Prefacevii
  • Chapter 1. Essential atomic orbital theory1
  • 1.1 Atomic orbitals for the hydrogen atom1
  • 1.2 Radial distribution functions for the hydrogen atom7
  • 1.3 Radial wave functions for many-electron atoms11
  • 1.4 Slater-type orbitals17
  • 1.5 Gaussian-type functions„the sto-3g} minimal basis set23
  • 1.6 sto-ng} basis sets28
  • 1.7 Scaling factors37
  • 1.8 The (4s/2s) basis set, polarization and scaling factors for molecular environments49
  • 1.9 Gaussian-lobe and other Gaussian basis sets55
  • Chapter 2. Numerical integration57
  • 2.1 Numerical integration57
  • 2.2 Application of Simpson’s rule to calculate a normalization integral59
  • 2.3 Calculations of normalization constants over the angular coordinates62
  • 2.4 Numerical integration in a cylindrical volume: diatomic and linear molecular geometries63
  • 2.5 Calculation of the overlap integral between 1s orbitals in a Gaussian basis68
  • 2.6 Designing Gaussian basis sets to model Slater orbitals70
  • Chapter 3. Orthonormality79
  • 3.1 Orthonormality in Slater orbital and basis set theory81
  • 3.2 Orthonormality and Slater orbitals82
  • 3.3 Orthonormality and Gaussian orbitals87
  • 3.4 Orthonormality and double-zeta Slater orbitals90
  • 3.5 Orthonormality and split-basis or double-zeta Gaussian basis sets98
  • 3.6 The Jacobi transformation, diagonalization of a symmetric matrix and canonical orthogonalization104
  • 3.7 The S-1/2 ‘trick’111
  • 3.8 Symmetric orthonormalization111
  • Chapter 4. The hydrogen atom „ numerical solutions115
  • 4.1 Eigenvalue calculations for hydrogen based on analytical functions118
  • 4.2 Calculations using Slater orbitals124
  • 4.3 Calculations with Gaussian functions133
  • 4.4 Calculations with split-basis [split-valence] sets148
  • 4.5 Review of results for the 1s and 2s orbital energies in hydrogen154
  • Chapter 5. The helium atom and the self-consistent field159
  • 5.1 Hartree’s analysis of the helium atom problem159
  • 5.2 Calculations with modified hydrogen atom wave functions162
  • 5.3 The Hall–Roothaan equations, the orbital approximation and the modern Hartree–Fock self-cons167
  • 5.4 Calculations using Slater DZ functions172
  • 5.5 Gaussian basis set calculations for the helium atom–two-electron integrals over Gaussian basis175
  • 5.6 A HFS-SCF calculation with split-basis 4-31} for helium181
  • 5.7 Helium, singlet and triplet excited states, electron spin and the role of the Exchange integral186
  • Chapter 6. One- and two-electron diatoms193
  • 6.1 Calculations using hydrogen 1s orbitals195
  • 6.2 ISto-3g} calculations for H2+203
  • 6.3 Calculations using Gaussian basis sets with the exact evaluation of integrals using Fourier tran208
  • 6.4 Calculations involving the two-electron terms; the sto-3g} HF-SCF results for dihydrogen210
  • 6.5 The standard form for the results of HFS-SCF calculations217
  • 6.6 The sto-3g} HFS-SCF calculation for HeH+219
  • 6.7 Polarization functions, Gaussian lobes and higher-order Gaussian basis sets222
  • 6.8 Epilogue228
  • References229
  • Index231
Book details
  • Vendor Elsevier S & T
  • SKU 9780125696821
  • ISBN-13 9780080488530
  • Author Quinn, Charles M.
  • Category Science
  • Subject Physical & Theoretical

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Description eBook delivery & access Reviews
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.