Molecular orbitals illustrations

Cyclopropane, C.H, is a hydrocarbon composed of a three-membered ring of carbon atoms, (a) Determine the hybridization of the carbon atoms, (b) Predict the CCC and HCH bond angles at each carbon atom on the basis of your answer to part (a), (c) What must the real CCC bond angles in cyclopropane be (d) What is the defining characteristic of a cr-bond compared with a ir-bond, for example (e) How do the C—C cr-bonds in cyclopropane extend the definition of conventional o-bonds (f) Draw a picture depicting the molecular orbitals to illustrate your answer. 

The molecular orbital energy stacking diagram for free acetylene is shown in Fig. 12. It can be seen that all the available bonding molecular orbitals are filled and that the free ligand has formal triple bond character. Upon coordination to a metal atom, the C-C vector lies perpendicular to the er-bonding orbital on the metal and donates electron density from a filled 7i-bonding orbital, as illustrated in Fig. 13. 

The bonding in monometal alkyne complexes is usually interpreted in terms of the Dewar-Chatt-Duncanson model (293), since the alkyne molecule has a pair of n and n molecular orbitals which lie in the plane of the metal and the two carbon atoms. These two orbitals are denoted n and n, and are analogous to those in jr-bonded alkene complexes (394). There is also a pair of n and n molecular orbitals which lie perpendicular to the metal-carbon plane, denoted nL and n . These orbitals are illustrated in Fig. 14. Both sets of n and n orbitals have the correct symmetry to interact with metal d orbitals. The interaction... 

In multi-orbit molecular structures, the need can arise to identify several FCAO-MOs of the same symmetry, over the structure vertices and this requirement provides a second useful example of the general utility of the orbit by orbit approach to the formation of group orbitals. In this section, the calculation of the electronic structure of the moiety Cso as an exercise in Hiickel theory, illustrates the benefits, which arise, when the LCAO-MOs are constructed from group orbitals formed on the vertices of the two structure orbits O20 and Oeo. 

The discussion summarized in Eigure 6.4 explained how, at large internuclear separations, the Icr molecular orbital for Fiz approaches the sum of two hydrogen atomic orbitals, and the Icr molecular orbital approaches the difference of two hydrogen atomic orbitals. As illustrated in Figure 6.5, the Itt molecular orbitals behave differently ... 

The naive application of the picture of Fig. 1 to Ni(C0)4, for example, is totally misleading. It is assumed that the metal can present each CO with one empty pure metal-carbon bonds. This is legitimate for the octahedral case, but not for tetrahedra. The defect is readily removed by a qualitative molecular orbital approach, illustrated in Fig. 3. 

In the case of organic molecules, for instance dyes, several oxidation states generally exist. Each electron transfer step can be correlated qualitatively with the energy of molecular orbitals as illustrated in Fig. 10.2 (triplets are neglected here). A reduction of a molecule M can only occur by electron transfer from an electron donor to an unoccupied level of M. On the other hand, an oxidation of M is only possible by an electron transfer from the lower lying occupied state to a suitable acceptor molecule. These two processes must be described by two different redox potentials, which cannot be... 

We noted in Section 4 that by introducing non-bonded interactions into the molecular orbital scheme we would also lose the non-bonding character of the non-bonding orbitals involved in the p orbital manifold in a similar sort of way to introduction of a central atom s orbital. We illustrate some cases in Fig. 22. 

Thus the backward shift in the CH3 reaction may be partly a mass effect. Qualitative molecular orbital theory is able to account102 for a similarity in the potential surfaces of H + XY and CH3 + XY and their contrast to the halogen atom plus halogen molecule, Z + XY, potential surface. The molecular orbitals are illustrated for the linear reaction complexes in Fig. 22. 

Fig-1 Schematic molecular orbital diagram illustrating d8-d8 and n-n interactions in binuclear platinum(II) polypyridine complexes [5e]... 

In Figures 11 and 12, are depicted some examples of molecular orbital formation from separate atomic orbitals. The illustrations are of surfaces like those of the atomic orbitals we drew in chapter 3 they are of greater physical significance than the actual orbitals themselves. Again we will stress the point that the boundary surfaces are functions of whereas the... 

The relative energies of the lowest 18 molecular orbitals are illustrated in Fig. 14. These are only approximate since configurational interaction has been ignored. The electron densities and mobile bond orders are shown in Fig. 15, assuming different coulombic integrals for the carbon and nitro-... 

As an illustration, picture a magnesium metal crystal, which has an hep structure. Since each magnesium atom has one 35 and three 3p valence atomic orbitals, a crystal with n magnesium atoms has available n is) and 3n 3p) orbitals to form the molecular orbitals, as illustrated in Fig. 10.20. Note that the core electrons are localized, as shown by their presence in the energy "well" around each magnesium atom. Flowever, the valence electrons occupy closely spaced molecular orbitals, which are only partially filled. 

The formal analysis of the mathematics required incorporating the linear combination of atomic orbitals molecular orbital approximation into the self-consistent field method was a major step in the development of modem Hartree-Fock-Slater theory. Independently, Hall (57) and Roothaan (58) worked out the appropriate equations in 1951. Then, Clement (8,9,63) applied the procedure to calculate the electronic structures of many of the atoms in the Periodic Table using linear combinations of Slater orbitals. Nowadays linear combinations of Gaussian functions are the standard approximations in modem LCAO-MO theory, but the Clement atomic calculations for helium are recognized to be very instructive examples to illustrate the fundamentals of this theory (67-69). 

Fig. 42. Molecular orbital interaction diagram between an Fe atom and the (Gdslijle) octahedral fragment to form (Gd Iis Fe) only the cluster-centered orbitals are illustrated orbital occupation is appropriate for RyXijFe.

Figure 30 Qualitative molecular orbital diagram illustrating the bonding in a linear metal nitrosyl species focusing on interactions with the d orbitals. The HOMO of NO is a singly occupied doubly degenerate orbital and its involvement in the bonding requires the metal to contribute three electrons to the derived molecular orbitals. Thus, a d metal center becomes d upon coordination of NO, as illustrated for the case in which n = 3. The interaction may, therefore, be represented via the triply bonded resonance structure M=N-0.

The strong bonds are classified as covalent, ionic, or metallic. Figure 1.5 illustrates the covalent bonds for fluorine, Fj, and methane, CH4. The bonds involve sharing of electrons between the bonding partners. Important in the description of a covalent bond is its directiveness, governed by the molecular oibital that contains the electron pair. Most of the bonds of interest in polymer science involve hybrid bonds of s and p orbitals (molecular orbitals are described by combinations of atomic orbitals, see also Fig. 1.3). Because of the close approach of the atoms in a covalent bond and the frequent involvement of only s and p orbitals in bonding, coordination numbers, CN, of one to four are most frequent. 

The Is and Ipz orbitals combine to give cr molecular orbitals, as illustrated in Fig. 2-11. The normalized wave functions are ... 

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