Single-electron theory

Mi CO). The first metal-metal bond to be characterized (35) is the formally single Mn-Mn bond in Mi CO). This compound has often been used as the model for developing electronic structure theories (1.18.36.37). Extremely efficient photofragmentation is responsible for the structureless electronic spectrum and the lack of emission following excitation of this molecule. This spectroscopic deficiency necessitates photofragmentation studies to obtain data to verify theoretical models. Most of the photochemical experiments in the past explored the reactions of the lowest excited singlet state in the near ultraviolet. 

The wave function for the electronic structure can in principle be any of the constructions employed in electronic structure theory. The preferred choice in this context is a wave functions that can be classified as single and multi-configurational, and for the latter type only complete active space (CAS) wave... 

Establishing a hierarchy of rapidly converging, generally applicable, systematic approximations of exact electronic wave functions is the holy grail of electronic structure theory [1]. The basis of these approximations is the Hartree-Fock (HF) method, which defines a simple noncorrelated reference wave function consisting of a single Slater determinant (an antisymmetrized product of orbitals). To introduce electron correlation into the description, the wave function is expanded as a combination of the reference and excited Slater determinants obtained by promotion of one, two, or more electrons into vacant virtual orbitals. The approximate wave functions thus defined are characterized by the manner of the expansion (linear, nonlinear), the maximum excitation rank, and by the size of one-electron basis used to represent the orbitals. 

In electronic structure theory, the single-configuration picture (e.g., the ls22s22p4 description of the Oxygen atom) forms the mean-field starting point the configuration interaction (Cl) or perturbation theory techniques are then used to systematically improve this level of description. 

Instead, practical methods involve a subset of possible Slater determinants, especially those in which two electrons are moved from the orbitals they occupy in the HF wavefunction into empty orbitals. These doubly excited determinants provide a description of the physical effect missing in HF theory, correlation between the motions of different electrons. Single and triple excitations are also included in some correlated ab initio methods. Different methods use different techniques to decide which determinants to include, and all these methods are computationally more expensive than HF theory, in some cases considerably more. Single-reference correlated methods start from the HF wavefunction and include various excited determinants. Important methods in inorganic chemistry include Mpller-Plesset perturbation theory (MP2), coupled cluster theory with single and double excitations (CCSD), and a modified form of CCSD that also accounts approximately for triple excitations, CCSD(T). 

We now consider some aspects of the theory of electronic spin angular momentum. What follows here is a relatively brief and simple exposition we will return to a comprehensive description of the details of electron spin theory in chapter 3. For a single electron, the spin vector. S is set equal to (1 /2)[Pg.54]

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