Carbon-atom orbitals

The formaldehyde molecule is planar in its ground state (Figure 7-6). We first construct three strong a bonds involving thje carbon, the two hydrogen, and the oxygen atoms. Since the angles in the plane all are approximately 120°, we construct three equivalent orbitals in the xy plane which are directed from carbon toward Hx, H2, and O. For this purpose we hybridize the three carbon atomic orbitals 2s, 2px, and 2py. From three orbitals we can construct three linearly independent hybrid orbitals. 

Figure 21-13 Calculated molecular-orbital energies of planar cyclic systems made up of N 2p carbon atomic orbitals, in units of a and fi.

As may be seen in figure 4 and as noted above for C60 the fullerene n molecular orbitals are composed of carbon atomic orbitals which contain a substantial amount of 2s orbital character and as the carbon 2s orbital lies so much lower in energy than the 2p orbital the resulting orbitals are expected to exhibit an enhanced electronegativity when compared with their planar counterparts. Furthermore the fullerenes are not only of intermediate hybridization, but probably exhibit variable hybridization as they pass through different states of reduction, for the pyramid-alization of anions is well known. Based on figure 3 it seems that the reduction potential of C60 is lowered by about 0.8V as a result of rehybridization effects. 

The most probable excitations in the valine fi decay correspond to transitions—of an electron from the MO made up of the 2s carbon atom orbitals and the nearly orbitals of the hetero atoms, and of the Is orbitals of helium—into the lower vacant MO, and they have an energy of 40 eV. 

A general interpretation of this phenomenon was given, taking into account the space overlap 2p , 2p ) of carbon atomic orbitals which induces in these molecules a three-dimensional conjugation. 

The a bonds in the backbone of vinyl polymers should not be describable in terms of local states of small model molecules because of overlap of carbon atomic orbitals only 1.5X apart. This concept can be tested in polyethylene where the least bound C-C bond band widths have been calculated to be about 3 eV (.8). The energy loss function, Im(-l/e), for polyethylene is given in Figure 3 where and the real and imaginary parts of the... 

FIGURE 5-20 Symmetry of the Carbon Atomic Orbitals in the D2ft 0 - Oi - "Tgiw 3m ... 

The two most common forms of carbon, diamond and graphite, are typical network solids. In diamond, the hardest naturally occurring substance, each carbon atom is surrounded by a tetrahedral arrangement of other carbon atoms to form a huge molecule [see Fig. 10.22(a)]. This structure is stabilized by covalent bonds, which, in terms of the localized electron model, are formed by the overlap of sp hybridized carbon atomic orbitals. 

Matching Orbitals on the Central Atom To determine which atomic orbitals of carbon are of correct symmetry to interact with the group orbitals, we will consider each group orbital separately. The carbon atomic orbitals are shown in Figure 5.19 with their symmetry labels within the D2h point group. 

FIGURE 5.19 Symmetry ofthe Carbon Atomic Orbitals in the Djf, Point Group. 

In boron and beryllium there are fewer electrons than available orbitals. The outer orbitals can be filled, for example, in dimethyl beryllium, by a mechanism whereby one carbon atom orbital overlaps with an orbital from each of two neighboring beryllium atoms. The resulting high-molecular-weight chain of dimethyl beryllium thus has three center bonds, which leads to an absurd structural formula when valences are represented in the normal way. Boron hydrides and some aluminum compounds have similar structures ... 

Figure 10.8 Electronic structures of CO interacting with a Rul9 cluster. Overlap population densities of states are represented of the carbon atomic orbitals of CO interacting with Ru d-valence electrons as a function of electron orbital energies. Orbital densities are shown for energies of maximum electron...

The orbital combinations for p and Py (hereafter abbreviated as x and y, respectively), the p orbitals perpendicular to the chain propagation axis, are of course of the same energy (or degenerate). We see from 19 that s, x, and y give the most bonding crystal orbital when the unit cell (here a single carbon atom) orbitals are all in-phase, i.e., have the same sign. This is the k = 0 (termed r) Bloch function. 

The first RE is of limited interest, as many molecules cannot absorb an energy of the order of 54 eV in an ionization process. This is probably the case for all hydrocarbons, as they are built up of carbon atomic orbitals with orbital energies of the order of 300, 24, and 13 eV, and hydrogen atomic orbitals at 13 eV. As the third RE is too low for ionization of most molecules, the electron will enter the 2s or 2p orbital of He if partial charge exchange takes place when He meets a molecule. The effective RE will then be somewhat lower than 13.6 eV. 

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