Heavy Atoms and Transition Metals

What is the simplest singlet diradical hydrocarbon species  

In one-determinant HF (i.e. SCF) theory, each MO has a unique energy (eigenvalue), but this is not so for the active MOs of a CASSCF calculation. Why  

In doubtful cases, the orbitals really needed for a CASSCF calculation can sometimes be ascertained by examining the occupation numbers of the active MOs. Look up this term for a CASSCF orbital. 

Why does an occupation number (see question 3 above) close to 2 or 0 (more than ca. 1.98 and less than ca. 0.02) indicate that an orbital does not belong in the active space  

It has been said that there is no rigorous way to separate static and dynamic electron correlation. Discuss. 

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Some Special Topics Solvation, Singlet Diradicals, A Note on Heavy Atoms and Transition Metals... 

Heavy Atoms and Transition Metals Easier Questions... 

In the review by Kanatzidis et al. (2005), the preparation by the tin-flux method is mentioned also for several ternary phosphides and polyphosphides of rare-earth and transition metals. Typically the components (R metal, T metal, P and Sn in an atomic ratio of about 1 4 20 50) in sealed silica tubes were slowly heated, to avoid violent reactions, up to 800°C, annealed at that temperature for 1 week and slowly (2 K/h) cooled to ambient temperature. The tin-rich matrix was dissolved in diluted hydrochloric acid. The authors described the preparation of compounds corresponding for instance to the formula MeT4P12 (Me = heavy rare-earth metals and Th and U, T = Fe, Ru, etc.) and to the series of phases MeT2P2 (Me is a lanthanide or an actinide and T a late transition metal) having a structure related to the BaAl4 or ThCr2Si2 types. 

Figure 29. AH-TAS plot for chelation of heavy and transition metal ions by soft glymes (containing more than two nitrogen and/or sulfur atoms).

A growing number of applications using post-column derivatization in combination with photometric detection opened the field of heavy and transition metal analysis for ion chromatography, thus providing a powerful extension to conventional atomic spectroscopy methods. 

Ion chromatography provides an alternative to atom spectroscopic methods for the determination of heavy and transition metals. Its main advantage is the simultaneousness of the procedure and the possibility to distinguish between different oxidation states. For example, the determination of iron(III), copper, and zinc in a chromic acid bath (Fig, 8-41) may be performed free of interferences despite the high chro-mium(VI) load. Fig. 8-42 illustrates the determination of heavy and transition metals in a nickel/iron plating bath. Both oxidation states of iron can be clearly distinguished via ion chromatography. 

An even simpler but less well-justified approximation avoids the calculation of the matrix elements of the two-electron part of the operator altogether. Only the matrix elements of the one-electron part of are computed, and in the sum over nuclei a in Equation 3.3, contributions from each atom are not multiplied by Z but by the effective spin-orbit coupling nuclear charge of atom a, which has been optimized empirically to represent the partial compensation of the one-electron part by the two-electron part of the operator. Recommended values of for atoms of main-group and transition metal elements are listed in Table 3.1. This method is generally acceptable in molecules containing heavy atoms but is not very accurate in those composed of light atoms only. 

Relativistic and electron correlation effects play an important role in the electronic structure of molecules containing heavy elements (main group elements, transition metals, lanthanide and actinide complexes). It is therefore mandatory to account for them in quantum mechanical methods used in theoretical chemistry, when investigating for instance the properties of heavy atoms and molecules in their excited electronic states. In this chapter we introduce the present state-of-the-art ab initio spin-orbit configuration interaction methods for relativistic electronic structure calculations. These include the various types of relativistic effective core potentials in the scalar relativistic approximation, and several methods to treat electron correlation effects and spin-orbit coupling. We discuss a selection of recent applications on the spectroscopy of gas-phase molecules and on embedded molecules in a crystal enviromnent to outline the degree of maturity of quantum chemistry methods. This also illustrates the necessity for a strong interplay between theory and experiment. 

Finally, transition metals are heavy atoms and one should consider whether relativistic effects need to be considered [45]. In general, apart from using a relativistic effective core potential, relativity is not included for first and second-row metals but must be treated for third-row species. The relativistic effect can be broken down into three components—the Darwin correction (mass-velocity), the Zitterbewegung and spin-orbit coupling. The former two are more or less straightforward to implement and capture most of the relativistic energy. 

In spite of strong competition from atomic spectrometric techniques, ion chromatography of heavy and transition metal cations is now well established as the relative cheapness, ease of automation, and online capability is particularly attractive in a wide variety of routine trace analysis. 

From theoretical considerations of bond formation in electrosorbates it was concluded that the underpotentially deposited metal ad-atoms can approximately be considered to be covalently bonded and nearly completely discharged if the difference in the Pauling s electronegativities of the substrate and adsorbed metal is I Ax I < 0.5 [6]. That means these systems have electrosorption valency i/z 1. Systems in which the electrosorption valency is equal to the ionic charge are those resulting from the UPD of heavy metal ions on noble and transition metal electrodes. 

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... 

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