Configuration-interaction theory introduction

In the section that follows this introduction, the fundamentals of the quantum mechanics of molecules are presented first that is, the localized side of Fig. 1.1 is examined, basing the discussion on that of Levine (1983), a standard quantum-chemistry text. Details of the calculation of molecular wave functions using the standard Hartree-Fock methods are then discussed, drawing upon Schaefer (1972), Szabo and Ostlund (1989), and Hehre et al. (1986), particularly in the discussion of the agreement between calculated versus experimental properties as a function of the size of the expansion basis set. Improvements on the Hartree-Fock wave function using configuration-interaction (Cl) or many-body perturbation theory (MBPT), evaluation of properties from Hartree-Fock wave functions, and approximate Hartree-Fock methods are then discussed. 

In spite of the impressive progress which has been achieved with conventional ab-initio methods as the Configuration-Interaction or Coupled-Cluster schemes in recent years density functional theory (DFT) still represents the method of choice for the study of complex many-electron systems (for an overview of DFT see [1]). Today DFT covers an enormous variety of fields, ranging from atomic [2,3], cluster [4,5] and surface physics [6,7] to the material sciences [8-10]. and theoretical biophysics [11-13]. Moreover, since the introduction of the generalized gradient approximation DFT has become an accepted method also for standard quantum chemical applications [14,15]. Given this tremendous success of nonrelativistic DFT the question for a relativistic extension (RDFT) arises quite naturally in view of the large number of problems in which relativistic effects play an important role (see e.g. Refs.[16,17]). 

Circular Dichroism Electronic Configuration Interaction Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Force Fields A Brief Introduction Force Fields A General Discussion Geometry Optimization I Geometry Optimization 2 Infrared Data Correlations with Chemical Structure Intensities of Infrared and Raman Bands Magnetic Circular Dichroism of it Systems Molecular Magnetic Properties. 

One cannot, of course, develop or even comprehensively review eata-strophe theory in the brief space afforded the subject in this book. The theory has in any event been admirably presented by Poston and Stewart (1978) and the reader desirous of more detail is referred to this text. What we do here is illustrate the principal ideas of the theory and its method of application to obtain useful results in the area of molecular structure. The knowledge of the theory presented here is sufficient to enable the reader to make similar applications and it will serve as a suitable introduction to the subject for an interested novice. To one familiar with the method, the examples given are further evidence of the ability of abstract mathematics to describe and predict the events which occur around us. All readers will observe that the theory applies in a direct and natural manner to the study of changes in chemical structure. There is a behaviour space, the real space occupied by the atoms in a molecule, and there is a control space, nuclear configuration space R , as the interactions between the atoms are altered by the relative motions of their nuclei. 

In crystal field theory, we consider repulsions between (/-electrons and ligand electrons, but ignore interactions between (/-electrons on the metal centre. This is actually an aspect of a more general question about how we describe the interactions between electrons in multi-electron systems. We will now show why simple electron configurations such as Is p or As >d do not uniquely define the arrangement of the electrons. This leads us to an introduction of term... 

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