Walsh's Rules Applied to Molecules AB2

Fig. 1: Walsh-Diagram for molecules AB2

Figure 1 depicts Walsh's diagram for molecules AB2. With minor changes, it is valid for molecules ABC too. Due to the shown dependencies of the orbital energies to the angle BAB, we expect the following geometry:

Valence electrons Geometry
2 - 16 linear
17 - 20 bent
21 - 24 linear

There is a number of molecules with 12 - 16 valence electrons known to be linear in the ground state. The table below lists some examples. Note that for molecules of point group D∞h and C∞v the same classification is used.
Nv Molecule Ground state
term symbols
12 C3 ...3σg2  2σu2  4σg2  3σu2  1πu4 1Σg+
13 CNC, CCN like C3 in addition 1πg 2Πg
14 NCN, NNC like C3 in addition 1πg2 3Σg, 1Δg, 1Σg+
15 BO2, CO2+, N3, NCO like C3 in addition 1πg3 2Πg
16 CO2, N2O, N3 and many more like C3 in addition 1πg4 1Σg+

Molecules AB2 and ABC with 16 valence electrons have a full shell configuration with with two electrons in all bonding and non-bonding orbitals whereas antibonding orbitals remain empty. These molecules are of remarkable stability. The formally non-bonding orbital 1πg seems to have a weak bonding effect.

Molecules with 17 - 20 valence electrons are less strongly bound because anti-bonding orbitals get occupied. As predicted by Walsh, these molecules are angular.
Nv Molecule Ground state configuration Term symbols
17 NO2, BF2 ... 3a12  2b22  4a12  3b22  1b12  5a12  1a22  4b22  6a1 2A1
18 CF2, O3, NO2 like NO2,   but 6a12 instead of 6a1 1A1
19 NF2 like CF2,   but 2b12  4b2 instead of 4b22 2B2
20 OF2 like CF2,   but 2b12 1A1

In accordance with Walsh's rules, the known molecules AB2 with 22 valence electrons are linear again. For instance, JF2 and XeF2 are linear and have a 1Σg+ ground state.

Quantummechanical calculations on ozone reveal that the hyper potential energy surface of the molecule has a second minimum. This local minimum corresponds to an equilateral triangular structure and an electronic configuration of the same symmetry as the ground state and is situated approximately 70 kJ/mol above the minimum which has been known for a long time. A potential barrier of 140 kJ/mol separates both states. To assume such additional minima for other molecules AB2 to would not be to far off.

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