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Transition metal complexes perturbation methods

An X-ray atomic orbital (XAO) [77] method has also been adopted to refine electronic states directly. The method is applicable mainly to analyse the electron-density distribution in ionic solids of transition or rare earth metals, given that it is based on an atomic orbital assumption, neglecting molecular orbitals. The expansion coefficients of each atomic orbital are calculated with a perturbation theory and the coefficients of each orbital are refined to fit the observed structure factors keeping the orthonormal relationships among them. This model is somewhat similar to the valence orbital model (VOM), earlier introduced by Figgis et al. [78] to study transition metal complexes, within the Ligand field theory approach. The VOM could be applied in such complexes, within the assumption that the metal and the... [Pg.55]

The results obtained from thermal spin equilibria indicate that AS = 1 transitions are adiabatic. The rates, therefore, depend on the coordination sphere reorganization energy, or the Franck-Condon factors. Radiationless deactivation processes are exothermic. Consequently, they can proceed more rapidly than thermally activated spin-equilibria reactions, that is, in less than nanoseconds in solution at room temperature. Evidence for this includes the observation that few transition metal complexes luminesce under these conditions. Other evidence is the very success of the photoperturbation method for studying thermal spin equilibria intersystem crossing to the ground state of the other spin isomer must be more rapid than the spin equilibrium relaxation in order for the spin equilibrium to be perturbed. [Pg.47]

Some years ago the Wolfsberg-Helmholz method enjoyed some popularity as a means of calculating energy levels in transition metal complexes. Its quantitative success was very limited, however, and in common with many other semi-empirical m.o. methods has been the subject of considerable criticism for its theoretical inconsistencies It is interesting, therefore, that Schaffer subsequently suggested a perturbation formalism for the AOM which does not refer to the Wolfsberg-Helmholz scheme. He sets out three assumptions for his perturbation model ... [Pg.5]

One fundamental aspect in the understanding of the photochemical behaviour of transition metal complexes is the role of the triplet states on the photoreactivity. The calculation of Spin-Orbit Coupling (SOC) effects is mandatory and should be performed in connection with highly correlated methods. The zero-field splitting of triplet molecular states can be calculated by the means of perturbation theory until the spin-orbit effects are not of... [Pg.126]

Figure 17 Comparison of PM3(tm)- and MP2-predioted metal-ligand multiple bond lengths for PM3(tm) semi-empirical Hamiltonian and the MP2 perturbation theory method. Reprinted with permission from Cundari, T. R. Deng, J. PM3(tm) Analysis of Transition Metal Complexes J. Chem. Info. Comput Sci. 1999, 39, 376-381. 1999 American Chemical Society. Figure 17 Comparison of PM3(tm)- and MP2-predioted metal-ligand multiple bond lengths for PM3(tm) semi-empirical Hamiltonian and the MP2 perturbation theory method. Reprinted with permission from Cundari, T. R. Deng, J. PM3(tm) Analysis of Transition Metal Complexes J. Chem. Info. Comput Sci. 1999, 39, 376-381. 1999 American Chemical Society.
The isotopic perturbation method is very useful for studying fractional bonding and hypercoordination in coordinatively unsaturated and electron deficient compounds such as transition metal complexes or carbocations. The 2-norbornyl cation and the bicyclobutonium cation are the most prominent examples of carbocations whose structures have led to much controversial discussion (the so-called classical-nonclassical ion controversy). The application of the isotopic perturbation methed is likely to be the most decisive piece of nmr evidence for the hypercoordinated structure of these two cations in solution. [Pg.81]

The issue of nondynamical correlation not only vexes wavefunction ab initio practitioners, but also bedevUs the presently much larger DFT developer and especially user community as well. While DFT is generally more resilient toward nondynamical correlation than, for example, many-body perturbation theory, it is common knowledge that, for example, pure DFT and hybrid DFT methods may yield very different answers in such multireference systems as early transition metal complexes. [Pg.245]

Because the convenience of the one-electron formalism is retained, DFT methods can easily take into account the scalar relativistic effects and spin-orbit effects, via either perturbation or variational methods. The retention of the one-electron picture provides a convenient means of analyzing the effects of relativity on specific orbitals of a molecule. Spin-unrestricted Hartree-Fock (UHF) calculations usually suffer from spin contamination, particularly in systems that have low-lying excited states (such as metal-containing systems). By contrast, in spin-unrestricted Kohn-Sham (UKS) DFT calculations the spin-contamination problem is generally less significant for many open-shell systems (39). For example, for transition metal methyl complexes, the deviation of the calculated UKS expectation values S (S = spin angular momentum operator) from the contamination-free theoretical values are all less than 5% (32). [Pg.350]


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