Semiempirical Methods of Electronic Structure Calculation

If one reflects upon the range of chemical problems accessible to the current quantum theoretical methods for calculations on the electronic structure of molecules, one is immediately struck by the rather narrow limits imposed by economic and numerical feasibility. Most of the systems with which experimental photochemists actually work are beyond the grasp of ab initio methods due to the presence of a few reasonably large aromatic ring systems. Potential energy surfaces for all but the smallest molecules are extremely expensive to produce, even over a restricted group of the possible degrees of freedom, and molecules containing the higher elements of the periodic table remain virtually untouched due to the large numbers of electrons involved. Almost the entire class of molecules of real biological interest is simply out of the question. In general, the theoretician is reduced to model systems of variable appositeness in most of these fields. The fundamental problem, from a basic computational point of view, is that large molecules require large numbers of basis functions, whether Slater- type orbitals or Gaussian functions suitably contracted, to provide even a modestly accurate description of the molecular electronic environment. This leads to the necessity of dealing with very large matrices and numbers of integrals within the Hartree-Fock approximation and quickly becomes both numerically difficult and uneconomic.

Table of Contents:
1. Ground-State Potential Surfaces and Thermochemistry.- 1. Introduction.- 2. Macroscopic Properties from Molecular Calculations.- 2.1. A Scheme for Thermodynamic Parameters.- 2.2. The Need for Geometry Calculations.- 2.3. Statistical Thermodynamic Formalism.- 2.4. Activation Parameters.- 2.5. The Zero-Point Vibrational Correction.- 2.6. The Partition Function.- 3. Semiempirical Molecular Orbital Theory for Closed Shells.- 3.1. The Nature of Semiempirical Theory.- 3.2. Parametrization.- 3.3. Strengths and Limitations for Potential Surface Calculations.- 4. Exploring Potential Energy Surfaces.- 4.1. The Size and Shape of Potential Surfaces.- 4.2. Geometry Optimization.- 4.3. Force Constants.- 5. Selected Results and Comparisons.- 5.1. Introduction.- 5.2. Molecular Geometries.- 5.3. Energies of Equilibrium States.- 5.4. Activation Parameters.- 5.5. Vibrational Frequencies.- 6. Conclusions and an Opinion.- References.- 2. Electronic Excited States of Organic Molecules.- 1. Introduction.- 2. The Hamiltonian Operator.- 3. The Zeroth-Order Approximation.- 4. The Electronic Wave Function.- 4.1. The All-Valence-Electron Approximation.- 4.2. The SCF Procedure.- 4.3. The Trial Functions.- 4.4. The ZDO Approximation.- 4.5. The Semiempirical Approximations.- 4.6. Comparison of Various Methods.- 5. The Interaction of Matter and Electromagnetic Fields.- 5.1. Transition Moments.- 5.2. Photoelectron Cross Sections.- 6. Spin-Orbit and Spin-Spin Coupling.- 6.1. Spin-Orbit Coupling.- 6.2. Spin-Spin Coupling.- 7. Vibrationally Induced Transitions.- 7.1. Herzberg-Teller Theory.- 7.2. Born-Oppenheimer Breakdown Theory.- 8. Application of ZDO Methods.- 8.1. Simple Organic Compounds.- 8.2. Inorganic Compounds.- 8.3. Interacting Nonplanar 7r-Electron Systems.- 8.4. TripletStates.- 8.5. Free Radicals and Doublet States; Photoelectron Spectra.- 8.6. Rydberg Transitions.- 8.7. Treatment of d Orbitals.- 8.8. Geometry of Excited States.- 8.9. Spin-Orbit, Spin-Spin, and Vibronic Coupling.- 8.10. Ionization Potentials.- 8.11. Dipole Moments and Polarizabilities.- 8.12. Miscellaneous Studies.- 9. Conclusions.- References.- 3. Photochemistry Josef Michl.- 1. Introduction.- 2. Photochemical Processes.- 3. Semiempirical Methods.- 3.1. Model Hamiltonians.- 3.2. Solving the Models.- 4. Examples of Application.- 4.1. Phototautomerism.- 4.2. Electrocyclic Reactions.- 5. Summary and Outlook.- References.- 4. Approximate Methods for the Electronic Structures of Inorganic Complexes.- 1. Inorganic Complexes Contrasted to Organic Molecules.- 2. TheOrbitals.- 3. The Ligand Field and the Crystal Field Methods.- 4. Koopmans' Theorem.- 5. Spin-Orbit Coupling.- 6. NonempiricalCNDO and INDO Methods.- 7. Semiempirical CNDO and INDO Methods.- 8. The Excited States.- 9. The Crystal Field Theory.- 10. Extended Huckel Theory. Angular Overlap Model.- 11. An Example, Ni(CN)4~. Conclusions.- References.- 5. Approximate Molecular Orbital Theory of Nuclear and Electron Magnetic Resonance Parameters.- 1. Introduction.- 2. Magnetic Resonance Parameters.- 3. Molecular Quantum Mechanics.- 3.1. Molecular Orbital Theory.- 3.2. Approximate Molecular Orbital Theory.- 3.3. Perturbation Theory.- 4. NMR Shielding Constants and Chemical Shifts.- 4.1. Quantum Mechanical Development of ?N.- 4.2. Calculation of Shielding Constants.- 5. NMR Nuclear Spin Coupling Constants.- 5.1. Quantum Mechanical Development of KMN.- 5.2. The Fermi Contact Term.- 5.3. The Orbital and Dipolar Terms.- 5.4. Calculations of JMN.- 6. ESRg-Tensors.- 7. ESR Electron-Nuclear Hyperfine Tensors.- 7.1. Quantum Mechanical Development of TN.- 7.2. Isotropic Hyperfine Coupling.- 7.3. Calculations of Isotropic Hyperfine Constants.- 7.4. Anisotropic Hyperfine Coupling.- 7.5. Calculations of Anisotropic Hyperfine Constants.- References.- 6. The Molecular Cluster Approach to Some Solid-State Problems.- 1. Introduction.- 1.1. Perfect Crystalline Solids and the Bloch Theorem.- 1.2. Imperfect Solids and the Breakdown of B loch's Theorem.- 2. Solid-State Theory Approaches to Surface Problems.- 2.1. The Perfect Surface.- 2.2. Surf ace-Adsorbate Interactions.- 3. Molecular Cluster Approach to Surface Problems.- 3.1. Nonmetals.- 3.2. MetalClusters.- 3.3. Metals and Adsorbates.- 4. Summary.- References.- 7. Electron Scattering Donald G. Truhlar.- 1. Introduction.- 2. Explicit Inclusion of Electronic Excitations.- 2.1. Expansions Including Free Waves.- 2.2. L2 Expansions.- 3. Neglect of Electronic Excitation Except for Final State.- 3.1. Strong-Coupling, Static-Exchange, and Distorted-Wave Approximations.- 3.2. High-Energy Approximations.- 4. Inclusion of Effect of Omitted Electronic States by Approximate Polarization Potentials.- References.- Author Index.- Molecule Index.