Hartree-Fock description, transition-metal

Most of the developments described above occurred before the advent of the electron in chemistry. Then came the golden years of wave mechanics with one-electron wave functions (orbitals), the Pauli principle, the building-up principle (Ai auprinzip) and, even before the end of the 1920s, the idea that chemistry had now become a question of computation was proposed. Not many years later the best conceivable method of describing atomic and molecular systems in terms of fixed orbitals with one or two electrons in each was invented and named the Hartree-Fock description. The s pearance of electronic computers made the method practical for heavy systems, such as atomic 3d transition-metal ions, as early as about 1960. The results for d spectra were enthusiastically received, mainly b use it was wonderful to see that such calculations could actually be done. On second thought and on further development of computational chemistry, the orbitad or one-electron picture of chemistry became... 

This survey of theoretical methods for a qualitative description of homogeneous catalysis would not be complete without a mention to the Hartree-Fock-Slater, or Xot, method [36]. This approach, which can be formulated as a variation of the LDA DFT, was well known before the formal development of density functional theory, and was used as the more accurate alternative to extended Hiickel in the early days of computational transition metal chemistry. 

The quantum-mechanical description of minerals containing transition metals is at a less advanced stage. The accuracy of simple Hartree-Fock-Roothaan methods has not been fully determined for such systems. Local-density-functional methods have been successful for calculating the structural properties of high-symmetry materials, but excitation energies are still poorly reproduced. Local-density-functional cluster calculations have so far been restricted mostly to model potentials (e.g., muffin-tin potentials) so that their full power has not been utilized. We need to determine the accuracy and efficiency of Hartree-Fock-Roothaan (or Har-... 

Transition metals are important materials with intriguing properties and they have been studied with ever improved methods. A major difficulty is posed by the standard one-electron models where the tight-binding model seems appropriate for the narrow, so-called d-bands while near-plane-wave crystal orbitals are adequate for the conduction bands. Canonical Hartree-Fock solutions are awkward starting points for the description of magnetic structures and the use of spin-polarized versions destroys basic symmetry properties. 

F. Fenske. We demonstrate for transition metal complexes that the non-empirical Fenske-Hall (FH) approach provides qualitative results that are quite similar to the more rigorous treatment given by density functional theory (DFT) and are quite different from Hartree-Fock-Roothaan (HFR) calculations which have no electron correlation. For example, the highest occupied molecular orbital of ferrocene is metal based for both DFT and FH while it is ligand (cyclopentadienyl) based for HFR. In the doublet (S = 1/2) cluster, Cp2Ni2(pi-S)2(MnCO)3, the unpaired electron is delocalized over the complex in agreement with the DFT and FH results, but localized on Mn in the HFR calculation. A brief description of the theory of FH calculations is used to rationalize the origin of its similarity to DFT. 

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. 

While most of the focus on and use of localized orbitals has been with regard to closed shell restricted Hartree-Fock (RHF) wavefunctions. the applications of localization criteria are considerably more general. Of particular importance is the fact that complex multi-conligurational wavefunctions can also be localized, as long as the full active space of electrons and orbitals, according to the FORS or CASSCF prescription, is included. MCSCF localized orbitals are particularly useful for the interpretation of bonding. Consider, for example, a typical double bond between a transition metal (M) and a main group element (E). A simple RHF description of such a bond is provided by the wavefunction... 

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