We live in a molecular world, almost closed shell in nature, and for this reason Chemistry has been a science dealing with closed shell mol ecules. However, the high degree of experimental sophistication reached in the past decade has made more apparent the role of open shell structures in chemical research. A parallel phenomenon can be observed in the development of SCF theory, where closed shell molecular calculations at any level of complexity compose the main body of references which can be obtained in Quantum Chemistry today. Besides the linkage between experimental and theoretical behaviour, there are, obviously, other reasons which can be attached to a lack of molecular open shell calculations. Among others, there was no connec tionbetween closed or open shell theoretical treatments. In this manner, many computational features used by closed shell connoisseurs have not been extended to other computational areas. Since the work of Roothaan in 1960, the open shell molecular landscape has been, the oretically, a very closed one. Further development of SCF theory, which has led to an outburst of multiconfigurational procedures, has paid no, or very faint, attention to the interconnection between these SCF theory advanced features, the open shell framework and closed shell common practice. A good theoretical goal, generally speaking, and in particular inside SCF theory, may consist of a procedure which can be used to solve a given chemical problem, within the physical and approx imate limits of the theory.

I. Historical Review

1. The Open Shell Development
2. The Multiconfigurational Scheme
II. Electronic Energy, Fock Operators and Coupling Operators
1. Introduction
2. General Energy Expression
3. General Coulomb and Exchange Operators
4. Energy and Lagrangian Variation: Fock Operators and Euler Equations
5. Coupling Operator
6. Null Gradient Coupling Operator Part
7. Lagrange multipliers Hermitean Condition Coupling Operator Part
8. LCAO Form of Coupling Operator
9. Simplified Energy Forms. Monoconfigurational Open Shell
10. Closed Shell
11. Corollary
III. Eigenspace Manipulations
1. Introduction
2. General Formalism
3. Unconditional Convergence in SCF Procedures: Level Shift Techniques
IV. Multiconfigurational Structure of Monoconfigurational SCF Procedures
1. Monoconfigurational Energy and Euler Equations
2. Results
3. Final Remarks
V. Paired Excitation Multiconfigurational SCF
1. Closed Shell MCPESCF Theory
2. Complete MCPE Energy Expression
3. Two Electron Systems
4. MCPESCF Theory with an Invariant Closed Shell
5. Open Shell PEMCSCF
6. Special Cases
VI. SCF Perturbation Theory
1. Perturbation Theory
2. Open Shell SCF Theory
3. Interaction of Two Molecules as an Application Example
VII. General Theory for Two and Three Electron Systems
1. Two Electron Systems
2. Three Electron Systems
VIII. Approximate SCF Theories
1. Atomic Orbital Representation
2. Decomposition of the Electronic Repulsion Matrix
3. Empirical Approximate Methods
4. Model Potentials: Huzinaga's Approach
IX. Miscellaneous Remarks
1. A Synthetic Approach
2. The Concept of Shell
3. Symmetry
4. Optimization of Non-Linear Parameters
5. Generalized Brillouin's Theorem and Off-Diagonal Hermitean Conditions onLagrange Multipliers
6. Error Analysis
7. Mathematical Structure of SCF
X. The Problem of the Helium Atom First Excited Singlet State
1. A Possible Solution
2. The "Triplet Catastrophe"
3. Further Analysis of the "The Triplet Catastrophe"
4. Some Results on Monoconfigurational He SCF
XI. Applications
1. Introduction
2. SCF Study of Water: Ground and Excited States
3. Paired Excitation Calculation on Water
4. Formaldehyde
5. Magnesium Oxyde
6. Nitrogen Dioxyde
7. Methanol
8. Diimine
9. Methylenimine
10. Glycine
11. Excited States of Some Molecules with C=O and C=N Bonds: INDO Procedure
Appendix A: Monoconfigurational State Parameters
Appendix B: Slater Rules
Appendix C: Multiconfigurational Fock Operators
Suggested Reading
Bibliographical Survey
A. Open Shell SCF Theory
B. Multiconfigurational SCF Theory.