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In the language of symmetry, g (gerade = even (German)) → g and u (ungerade = odd) → u transitions are forbidden. Allowed transitions must involve a change in parity, either g → u or u → g. For atoms s and d orbitals are gerade, and p and f orbitals are ungerade.
An alternative method for determining the symmetry of an MO is to rotate the orbital about the axis joining the two nuclei and then rotate the orbital about a line perpendicular to the axis. If the sign of the lobes remains the same, the orbital is gerade, and if the sign changes, the orbital is ungerade. [3]
In chemistry, molecular symmetry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain many of a molecule's chemical properties , such as whether or not it has a dipole moment , as well ...
Molecular symmetry in physics and chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular symmetry is a fundamental concept in the application of Quantum Mechanics in physics and chemistry, for example it can be used to predict or explain many of a molecule's properties, such as its dipole moment and its allowed ...
A MO with σ symmetry results from the interaction of either two atomic s-orbitals or two atomic p z-orbitals. An MO will have σ-symmetry if the orbital is symmetric with respect to the axis joining the two nuclear centers, the internuclear axis. This means that rotation of the MO about the internuclear axis does not result in a phase change.
Symmetry labels are further defined by whether the atomic orbital maintains its original character after an inversion about its center atom; if the atomic orbital does retain its original character it is defined gerade, g, or if the atomic orbital does not maintain its original character, ungerade, u. The final symmetry-labeled atomic orbital ...
The transitions are therefore forbidden. Likewise, d orbitals have g symmetry (meaning gerade, even), so the triple product g×u×g also has u symmetry and the transition is forbidden. [4] The wave function of a single electron is the product of a space-dependent wave function and a spin wave function.
The rule arises because in a centrosymmetric point group, IR active modes, which must transform according to the same irreducible representation generated by one of the components of the dipole moment vector (x, y or z), must be of ungerade (u) symmetry, i.e. their character under inversion is -1, while Raman active modes, which transform ...