Ammonia symmetry properties. 64-5

Table 6-6. The Atomic Orbitals of Ammonia Sorted According to their Symmetry Properties...

Before we apply the formalism developed in Section 3 to the vibration—inversion-rotation spectra of ammonia, we shall discuss in this section certain group theoretical problems concerning the classification of the states of ammonia, the construction of the symmetry coordinates, the symmetry properties of the molecular parameters, and the GF matrix problem for the ammonia molecule. 

Moreover, all the symmetry elements intersect at a single point (e.g. the oxygen atom in dimethylether (6-1), the nitrogen atom in ammonia (6-7), the middle of the carbon-carbon bond in ethylene (6-5)). The expression paint-group symmetry is therefore used. For each molecule, there is a corresponding point group that completely characterizes its symmetry properties. 

If ammonia, NH3, were somehow squashed into a triangular planar shape, the molecule would gain in symmetry and become less polar. Of course, the ammonia would no longer be identifiable as ammonia because its physical and chemical properties would become vastly different. 

There is partial localization of the valence density in methane. The condensation into four partially localized pairs of electrons arranged along four tetrahedral axes is a result of the combined effects of the ligand field and the Pauli exclusion principle described above. Most important is that this partial localization of the pair density is reflected in the properties of the VSCC of the carbon atom which undergoes a corresponding condensation into four local concentrations of electronic charge. These properties of the pair density are not just the result of the tetrahedral symmetry of the ligand field in methane because, as we will now see, the Fermi hole exhibits the same behaviour in the ammonia molecule. 

In this section we present the nuclear relaxation (NR) contributions to the vibrational (hyper)polarizabilities of Li C6o and [Li C6o]. As previously stated our treatment requires a geometry optimization in the presence of a finite field. A problem can arise when there are multiple minima on the PES separated by low energy barriers. The finite field method works satisfactorily in that event as long as the field-dependent optimized structure corresponds to the same minimum as the field-free optimized structure. This was the case in previous work on ammonia [42], which has a double minimum potential. However, it is sometimes not the case for the endohedral fullerenes considered here, especially Li C6o- In fact, we were unable to determine the NR contribution in the x direction, i.e. perpendicular to the symmetry plane, for that molecule. It was possible to obtain based on the alternative analytical formulation [32-34], utilizing field-free dipole (first) derivatives and the Hessian. The analytical polarizability components in the other two directions were, then, used to confirm the values of the corresponding finite field method for those properties. 

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