Orbitals, antibonding atomic

Molecular orbitals are formed by combining atomic orbitals when atomic orbitals interfere constructively, they give rise to bonding orbitals when they interfere destructively, they give rise to antibonding orbitals. N atomic orbitals combine to give N molecular orbitals. 

As to the first, we note the interaction of the s orbital of atom A with the s orbital of B, the with the and the, pair of A with the p y pair of B. In principle, of course, we could have considered the possibility of an interaction between, say, the s orbital on A with a p orbital on B as shown in Fig. 6-2. The sketch shows that net overlap between these orbitals is zero and so no bonding or antibonding molecular orbitals are formed in this way. Now the labels s and p here... 

All lone pair orbitals have a node between the two atoms and, hence, have a slightly antibonding character. This destabilizing effect of the lone pair localized molecular orbitals corresponds to the nonbonded repulsions between lone pair atomic orbitals in the valence bond theory. In the MO theory all bonding and antibonding resonance effects can be described as sums of contributions from orthogonal molecular orbitals. Hence, the nonbonded repulsions appear here as intra-orbital antibonding effects in contrast to the valence-bond description. 

The LUMO on the Si skeleton interacts not with the LUMO on pendant groups but with Si-C antibonding a orbitals. The atomic orbital of the LUMO, (3py — 3s)/-v/2, is divided into two sp a orbitals with the symmetry axes pointed toward two Si-C bonds, as... 

For the n bonds in both the reactant and the product monoolefins, the bonding orbitals are of A symmetry and the antibonding orbitals are of B symmetry. Finally, the symmetries of the new a orbitals, between atom pairs 1, 6 and 4, 5, and their relative energies are as follows ... 

The molecular orbitals are filled with electrons according to the same rules that were used to put electrons in the atomic orbitals of atoms. In this case there are two electrons. These fill the bonding MO. The stability of the molecule is determined by the total energy of the electrons. In the case of H2 the molecule is more stable than the separated atoms by 2(AE). In other words, it would be necessary to add 2(AE) of energy to the H2 molecule to break the covalent bond. As is the case here, the antibonding MOs usually do not have any electrons in them, and they do not affect the energy of the molecule. But they are real and can be occupied by electrons in some situations, such as certain types of spectroscopy and some chemical reactions. 

The MO basis for this effect is seen quite simply in Fig. 3. Here it is seen that electron promotion is from MO 2 which is antibonding (having a negative bond order) between the orbitals at atoms 2 and 3 and, this promotion is to MO 3 which is bonding (i.e. with a positive and large bond order) between atoms 2 and 3. The net effect of excitation then is enhancement of the 2,3-bond order upon electronic excitation. 

These diagrams of molecular energy levels combining to form new bonding and antibonding orbitals are almost identical to those we used in Chapter 4 to make molecular orbitals from atomic orbitals. 

A basic assumption made earlier in the discussion of diatomic molecules and crystalline CsCl is that electronic states can be written as linear combinations of atomic orbitals. We do not need to depart from that assumption now as we begin to describe electronic states in solids as linear combinations of bond orbitals, since bond orbitals can be written as linear combinations of atomic orbitals, and vice versa. Bond orbitals and atomic orbitals arc equivalent representations, but thinking in terms of bond and antibonding orbitals, which can be made to correspond with occupied and empty states of the covalent solid (as was shown in Fig. 2-3), is essential in making approximations. 

The tetracobalt cubanes [ Co(/Li3-S)Cp 4] (67) (M = Co, E = S) have not been studied as extensively as the iron analogues (Section IV,B), but it is to be expected that electrochemical studies will reveal an extensive electron-transfer series. A comparison of the structures of [ Co(/i3-S)Cp 4] (2 = 0 and 1) showed that the nonbonded tetrahedron of metal atoms in the neutral molecule (Co—Coave = 329.5 pm) undergoes a tetragonal distortion. The shortening of four of the cobalt-cobalt distances (317.2 pm) is due to the removal of an electron from an orbital antibonding with respect to the four metal atoms 190). 

FIGURE 6.13 Formation of (a) cr 2p, bonding and (b) a- 2p, antibonding molecular orbitals from 2p orbitals on atoms A and B. Regions with positive amplitude are shown in red, and those with negative amplitude are shown in blue. 

Some of the possible combinations of atomic orbitals are shown in Fig. 5.11. Those orbitals which are cylindrically symmetrical about the internuclear axis are called cr orbitals, analogous to an s orbital, the atomic orbital of highest symmetry. If the internuclear axis lies in a nodal plane, a n bond results. In S bonds (Chapter 16) the internuclear axis lies in two mutually perpendicular nodal planes. All antibonding orbitals (identified with an ) possess an additional nodal plane perpendicular to the internuclear axis and lying between the nuclei. In addition, the molecular orbitals may or may not have a center of symmetry. Of particular interest in this regard are orbitals, which are ungerade, and tt orbitals, which are gerade. 

Electrons Behave as Waves Standing Waves in One and Two Dimensions Standing Waves in Three Dimensions Atomic Orbitals Mixing Atomic Orbitals into Molecular Orbitals Bonding and Antibonding MOs of Hydrogen... 

Bonding molecular orbitals increase electron density between the nuclei and are lower in energy than individual atomic orbitals. Antibonding molecular orbitals have a region of zero electron density between the nuclei, and an energy level higher than that of the individual atomic orbitals. 

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