Hartree-Fock approximation transition-metal complexes

Molecular-orbital approaches to edge structures differ for semiconducting and isolating molecular complexes. The latter and transition-metal complexes allow one to minimize solid-state effects and to obtain molecular energy levels at various degrees of approximation (semiempirical, Xa, ab initio). The various MO frameworks, namely, multiple-scattered wave-function calculations (76, 79, 127, 155) and the many-body Hartree-Fock approach (13), describe states very close to threshold (bound levels) and continuum shape resonances. 

Density Functional theory [4] (DFT) has been widely recognized as a powerful alternative computational method to traditional ab initio schemes, particularly in studies of transition metal complexes where large size of basis set and an explicit treatment of electron correlation are required. The local spin density approximation [5] (LDA) is the most frequently applied approach within the families of approximate DFT schemes. It has been used extensively in studies on solids and molecules. Most properties obtained by the LDA scheme are in better agreement with experiments [4a] than data estimated by ab initio calculations at the Hartree-Fock level. However, bond energies are usually overestimated by LDA. Thus, gradient or nonlocal corrections [6] have been introduced to rectify the shortcomings in the LDA. The non-... 

The method is an approximate self-consistent-field (SCF) ab initio method, as it contains no empirical parameters. All of the SCF matrix elements depend entirely on the geometry and basis set, which must be orthonormal atomic orbitals. Originally, the impetus for its development was to mimic Hartree-Fock-Roothaan [5] (HFR) calculations especially for large transition metal complexes where full HFR calculations were still impossible (40 years ago). However, as we will show here, the method may be better described as an approximate Kohn-Sham (KS) density functional theory (DFT)... 

DF theory has the simplicity of an independent-particle model, yet it can be applied successfully to those systems-such as transition metal complexes - where non-dynamical electron correlation is of primary importance. DF-based methods are, in general, very easy to use, no matter how sophisticated the functional employed to describe the electron correlation. Also, more sophisticated functionals do not increase the computational requirements significantly, as opposed to post Hartree-Fock ab initio calculations. The application of approximate density functional theory has been reviewed by Ziegler and others [5]. 

Prior to this, it had already been established that even the simplest forms of DFT, based on the exchange-only Slater or Xa scheme, could give good descriptions of the electronic structure of metal complexes and a number of contemporary applications confirmed this. However, in combination with structure optimization, here at last was a quantum chemical method accurate enough for transition metal (TM) systems and yet still efficient enough to deliver results in a reasonable time. This was in stark contrast to the competition which was either based on the single-determinant Hartree-Fock approximation, which had been discredited as a viable theory for TM systems,or on more sophisticated electron correlation methods (e.g., second order Moller-Plesset theory) which are relatively computationally expensive and thus, for the same computer time, treat much smaller systems that DFT. 

The first and very popular energy decomposition scheme that is used to decompose the total INT into various contributing factors was developed by Kitaura and Moroknma in the late 1970s. This method was mainly developed to decompose the INT of hydrogen-bonded systans within the Hartree-Fock approximation. Since then, it has also been successfully applied to donor-acceptor pairs, % and a interactions in transition metal complex, and decomposition of electron density. A broad outline of the key steps involved in the analysis of various components of the INT is provided in the following section. Before we proceed to the KM analysis in detail, it is important to look at the initial decomposition scheme developed by Morokuma. We start the discussion by taking a dimer AB into consideration. 

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