The Unitary Group for the Evaluation of Electronic Energy Matrix Elements: Unitary Group Workshop 1979 (Lecture Notes in Chemistry, 22)

During the last thirty years, with the development of high speed electronic computers, methods have evolved, which permit an accurate and quantitative, ab initio determina­ tion of the electronic wavefunctions of atoms and molecules. Thus a detailed elucida­ tion of the electronic energy and structure of molecules has become possible using quantum mechanics directly. Ho\~ever, it is necessary, if such calculations are to yield accurate and reliable results, to include electron correlation explicitely, which requires in general . configuration mixing procedures with an extremely large 5 number of configurations, of the order of 10 configurations. With eigenvalue problems of this size, the limits of even the largest and fastest computers are reached rapidly, and their solution has become possible only, because direct methods have been deve~ loped which permit the determination of eigenvalues and eigenvectors for such large matrices iteratively without constructing the energy matrix explicitely. These direct methods had been limited to the description of closed shell systems, i. e. systems with a single dominant closed shell reference determinant. This limitation arose, because with an open shell reference or with several reference determinants, no procedures were known, which allowed a rapid calculation of the energy matrix elements between configurations with general and widely different spin couplings, which would be necessary. Recently such methods have been developed, based on early work of Gelfand, Biedenharn and Moshinski using a unitary group representation of different spin coupled states; Paldus achieved an extremely compact description. Front Matter....Pages N2-VI Unitary Group Approach to Many-Electron Correlation Problem....Pages 1-50 The Graphical Unitary Group Approach and Its Application to Direct Configuration Interaction Calculations....Pages 51-99 A Harmonic Level Approach to Unitary Group Methods in CI and Perturbation Theory Calculations....Pages 100-107 Many-Body Correlations Using Unitary Groups....Pages 108-118 Factorization of the Direct CI Coupling Coefficients into Internal and External Parts....Pages 119-135 Multiconfiguration Self-Consistent-Field Wavefunction for Excited States....Pages 136-142 Minicomputer Implementation of the Vector Coupling Approach to the Calculation of Unitary Group Generator Matrix Elements....Pages 144-157 New Directions for the Loop-Driven Graphical Unitary Group Approach: Analytic Gradients and an MCSCF Procedure....Pages 158-176 The Occupation-Branching-Number Representation....Pages 177-242 Review of Vector Coupling Methods in the Unitary Group Approach to Many-Electron Problems....Pages 243-259 Symmetric Group Graphical Approach to the Configuration Interaction Method....Pages 260-271 Orbital Description of Unitary Group Basis....Pages 272-285 On the Relation between the Unitary Group Approach and the Conventional Approaches to the Correlation Problem....Pages 286-296 Unitary Bases for X-Ray Photoelectron Spectroscopy....Pages 297-305 Broken Unitary Tableaus, Itinerant Nuclear Spins, and Spontaneous Molecular Symmetry Collapse....Pages 306-331 CI-Energy Expressions in Terms of the Reduced Density Matrix Elements of a General Reference....Pages 332-344 The Unitary Group Formulation of Quantum Chemistry: Generator States....Pages 345-361 The Unitary Group Approach to Bonded Functions....Pages 362-371 Back Matter....Pages 373-375