Atomic orbitals clusters

Figure 2.29. The bonding energy of lithium clusters calculated with a basis of interstitial atomic orbitals. Clusters of 8, 20, and 30 atoms are relatively stable. This size preference has been observed in mass spectroscopy.

Figure 2.14. The molecular orbitals of gas phase carbon monoxide, (a) Energy diagram indicating how the molecular orbitals arise from the combination of atomic orbitals of carbon (C) and oxygen (O). Conventional arrows are used to indicate the spin orientations of electrons in the occupied orbitals. Asterisks denote antibonding molecular orbitals, (b) Spatial distributions of key orbitals involved in the chemisorption of carbon monoxide. Barring indicates empty orbitals.5 (c) Electronic configurations of CO and NO in vacuum as compared to the density of states of a Pt(lll) cluster.11 Reprinted from ref. 11 with permission from Elsevier Science.

Thus, the calculations show that the outer ns(np) atomic orbitals can play a significant role in the formation of M-M bonds in transition metal acido-clusters. The probability that these atomic orbitals will participate in the formation of M-M bonds is maximal for elements of Group 7, particularly, for technetium, in whose clusters Zeff for technetium atoms is the lowest of those observed in all known acido-clusters. 

For simplicity, one can allocate 3 electron pairs to nonbonding orbitals on each metal atom, which leaves three AO s on each metal atom for cluster skeletal bonding, and 7 electron pairs to be accommodated in the bonding MO s these AO s generate. This description is reminiscent of that outlined above (Fig. 7) for EgHa ". Each Ru(CO)j unit of H2Rue(CO)i8, like each BH unit of can contribute three... 

Self-consistent calculations for actinide clusters have been made using cellular multiple scattering techniques and through linear combinations of atomic orbitals. Band calculations have been made using the self-consistent RKKR and... 

Various theoretical methods and approaches have been used to model properties and reactivities of metalloporphyrins. They range from the early use of qualitative molecular orbital diagrams (24,25), linear combination of atomic orbitals to yield molecular orbitals (LCAO-MO) calculations (26-30), molecular mechanics (31,32) and semi-empirical methods (33-35), and self-consistent field method (SCF) calculations (36-43) to the methods commonly used nowadays (molecular dynamic simulations (31,44,45), density functional theory (DFT) (35,46-49), Moller-Plesset perturbation theory ( ) (50-53), configuration interaction (Cl) (35,42,54-56), coupled cluster (CC) (57,58), and CASSCF/CASPT2 (59-63)). 

Combinations of atomic orbitals that result in bonding molecular orbitals in an octahedral cluster such as... 

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