Atomic orbital antibonding states

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.

Fig. 1 A schematic illustration of the in-phase and out-of-phase combinations of the atomic orbitals into the bonding and antibonding molecular orbitals, respectively. The dissociation limit of a H molecule corresponds to a pure diradical with degenerate singlet and triplet states...

The two bonding 7r orbitals represented by these wave functions are degenerate. The wave functions for the antibonding states are identical in form except that negative signs are used in the combination of atomic wave functions and in the normalization constants. 

The orbitals of lower energy fill first. This means that the antibonding orbitals remain empty in the ground state. Molecular orbitals formed by the overlap of two atomic orbitals when the centers of electron density are on the axis common to the two nuclei are called o (sigma) orbitals and the bonds are o bonds. The corresponding anti orbitals are designated o or antibonding orbitals. 

In conclusion, the energies E that sahsfy Eq. (1.19) are associated to molecular electronic states. Since Eq. (1.19) is an equation of Nat order, we obtain Nat energy values E/ (/ = 1,. .., Nat), that is, as many molecular levels as atomic orbitals. In the simple example of H2 discussed in Sechon 1.1, Aat = 2 and both I5 atomic orbitals combine to form bonding ag and antibonding a MOs. In the case of N2 (see Fig. 1.1), neglechng I5 core electrons, the combinahon of two sp and one pz atomic orbitals per N atom leads to six MOs. 

Problem 8.55 (a) Apply the MO theory to the C==C—C=C—C carbocation, considering the signs of the upper lobes of adjacent p atomic orbitals (f>) Indicate the relative energies of the molecular orbitals and state if they are bonding, nonbonding, or antibonding, (c) Show the distribution of the n electrons. ... 

Fig. 7.18 The upper figure illustrates the most bonding state of the valence barfd in which all bond orbitals between neighbouring pairs of atoms are in phase. The lower figure illustrates the most antibonding state of the valence band in which the bond orbitals between neighbouring pairs of atoms are 180° out of the phase. (After Heine (1971).)...

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