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.

1. Hückel Theory and Topology.- 1. Introduction.- 2. Equivalence between Hiickel Theory and the Graph Spectral Theory of Conjugated Molecules.- 3. Two-Color Problem in Hiickel Theory.- 4. Relationship between the Topology of Conjugated Systems and Their Corresponding Characteristic Polynomials.- 5. Topological Formulas for Hiickel Energy and ?-Resonance Energy.- 6. Conclusions.- References.- 2. The Neglect-of-Differential-Overlap Methods of Molecular Orbital Theory.- 1. Background.- 2. The NDO Methods.- References.- 3. The PCILO Method.- 1. Main Features of the PCILO Method.- 2. Derivation of the PCILO-CNDO Energy Contributions.- 3. Efficiency and Limits of the Method; Applications and Extensions.- 4. Concluding Remarks.- References.- 4. The X? Method.- 1. Introduction.- 2. Derivation of the Equations.- 3. Applications of the Method.- 4. Comparison with Other Methods.- References.- 5. The Consistent Force Field and Its Quantum Mechanical Extension.- 1. Introduction.- 2. Empirical Potential Functions.- 3. The Consistent Force Field (CFF) Method.- 4. Quantum Mechanical Extension of the CFF Method to Ground and Excited States of Conjugated Molecules.- 5. Applications.- 6. Concluding Remarks.- References.- 6. Diatomics-in-Molecules.- 1. Introduction.- 2. Formulationof the Method.- 3. Application of the Method.- 4. Assessmentof the Method.- 5. Properties Other Than Energy.- 6. Polyatomics-in-Molecules.- 7. Conclusions.- References.- 7. Theoretical Basis for Semiempirical Theories.- 1. Introduction.- 2. Semiempirical Theories: Background.- 3. The True Effective Valence Shell Hamiltonian.- 4. Extraction of True Parameters.- 5. Approximate Evaluation of True Parameters.- 6. Model Pseudopotentials.- 7. Discussion.- References.- Author Index.- Molecule Index.