Machine generated contents note: 1 Essential atomic orbital theory -- 11 Atomic orbitals for the hydrogen atom -- 12 Radial distribution functions for the hydrogen atom -- 13 Radial wave functions for many-electron atoms -- 14 Slater-type orbitals -- 15 Gaussian-type functions-the Isto-3g) minimal basis set -- 16 isto-ng) basis sets -- 17 Scaling factors -- 18 The (4s/2s) basis set, polarization and scaling factors for molecular -- environments -- 19 Gaussian-lobe and other Gaussian basis sets -- 2 Numerical integration -- 21 Numerical integration -- 22 Application of Simpson's rule to calculate a normalization integral -- 23 Calculations of normalization constants over the angular coordinates -- 24 Numerical integration in a cylindrical volume: diatomic and linear -- molecular geometries -- 25 Calculation of the overlap integral between Is orbitals in a Gaussian -- basis -- 26 Designing Gaussian basis sets to model Slater orbitals -- 3 Orthonormality -- 31 Orthonormality in Slater orbital and basis set theory -- 32 Orthonormality and Slater orbitals -- 33 Orthonormality and Gaussian orbitals -- 34 Orthonormality and double-zeta Slater orbitals -- 35 Orthonormality and split-basis or double-zeta Gaussian basis sets -- 36 The Jacobi transformation, diagonalization of a symmetric matrix and -- canonical orthogonalization -- 37 The S-1/2 'trick' -- 38 Symmetric orthonormalization -- 4 The hydrogen atom -numerical solutions -- 41 Eigenvalue calculations for hydrogen based on analytical functions -- 42 Calculations using Slater orbitals -- 43 Calculations with Gaussian functions -- 44 Calculations with split-basis [split-valence] sets -- 45 Review of results for the ls and 2s orbital energies in hydrogen -- 5 The helium atom and the self-consistent field -- 51 Hartree's analysis of the helium atom problem -- 52 Calculations with modified hydrogen atom wave functions -- 53 The Hall-Roothaan equations, the orbital approximation and -- the modem Hartree-Fock self-consistent field method -- 54 Calculations using Slater DZ functions -- 55 Gaussian basis set calculations for the helium atom-two-electron -- integrals over Gaussian basis functions -- 56 A HFS-SCF calculation with split-basis 14-31) for helium -- 57 Helium, singlet and triplet excited states, electron spin and the role -- of the Exchange integral -- 6 One- and two-electron diatoms -- 61 Calculations using hydrogen Is orbitals -- 62 Sto-3g calculations for H2+ -- 63 Calculations using Gaussian basis sets with the exact evaluation of -- integrals using Fourier transforms -- 64 Calculations involving the two-electron terms; the Isto-3g) -- HF-SCF results for dihydrogen -- 65 The standard form for the results of HFS-SCF calculations -- 66 The Isto-3g) HFS-SCF calculation for HeH+ -- 67 Polarization functions, Gaussian lobes and higher-order Gaussian -- basis sets -- 68 Epilogue.