D3h point group

Determine the symmetries of the resultant moleeular orbitals in the D3h point group. Draw a qualitative orbital energy diagram using the HMO energies you have ealeulated. 

Using the hybrid atomie orbitals as labeled above (funetions fi-f/) and the D3h point group symmetry it is easiest to eonstruet three sets of redueible representations ... 

Clearly, Eq. (E.12) shows that to a first approximation the electronic energy varies linearly with displacements in p, increasing for one component state while decreasing for the other. Thus, the potential minimum cannot be at p = 0. This is the statement of the Jahn-Teller theorem for a X3 molecule belonging to the D3h point group. 

The symmetry components of normal coordinates of AX3 in D3h point group... 

The character table for D3h point group and the reduction to irreducible representations of D3h of the (27 + 1) states with a given 7 are presented in Tables 8.35 and 8.36. The JM) basis functions for six irreducible representations of D3h are listed in Table 8.37. 

The 17, M) basis functions for the irreducible representations of D3h point group symmetry. 

BF3 belongs to D3h point group. The maximum number in the column headed by the identity E is the maximum orbital degeneracy possible in a molecule of that symmetry group. The character table of D3h shows that maximum degeneracy is 2, as no character exceeds 2 in the column headed E. This means, the orbitals cannot be triply degenerate. 

The projection formula (6.10) and the character table for the D3h point group (Table 6.24) should be helpful. The complete set of symmetry operations is given in Table 6.25. 

By considering the effect of each symmetry operation of the D3h point group on the symmetric deformation mode shown in Fig. 3.14, confirm that this mode has A2 symmetry. 

In Example 13.3e, we are assuming that resonance structures of NO3 are "averaging" out the symmetry to an overall D3h point group. If resonance weren t assumed, what point group would define the structure of NO3 ... 

The C2 axis is one of a set of three (each passes through a C atom and the centre of the opposite C—C bond). Rotation around any of these axes leaves one C unaffected but swaps around aU the H atoms so, in either basis set, any of the three axes gives the same total character. The three C2 axes form another class within the D3h point group so, in the corresponding character table heading we see 3C2 and would assign gc = 3 when considering this class. 

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