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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 ...
The symmetry operations in the molecular symmetry group are so-called 'feasible' permutations of identical nuclei, or inversion with respect to the center of mass (the parity operation), or a combination of the two, so that the group is sometimes called a "permutation-inversion group". [17] [25] Examples of molecular nonrigidity abound.
In 1928 Eugene Wigner and E.E. Witmer proposed rules to determine the possible term symbols for diatomic molecular states formed by the combination of a pair of atomic states with given atomic term symbols. [4] [5] [6] For example, two like atoms in identical 3 S states can form a diatomic molecule in 1 Σ g +, 3 Σ u +, or 5 Σ g + states.
This lists the character tables for the more common molecular point groups used in the study of molecular symmetry. These tables are based on the group-theoretical treatment of the symmetry operations present in common molecules, and are useful in molecular spectroscopy and quantum chemistry. Information regarding the use of the tables, as well ...
The molecular term symbol is a shorthand expression of the angular momenta that characterize the electronic quantum states of a diatomic molecule, which are also eigenstates of the electronic molecular Hamiltonian. It is also convenient, and common, to represent a diatomic molecule as two-point masses connected by a massless spring.
Quantum theory also indicates that molecular orbitals (MO) of identical symmetry actually mix or hybridize. As a practical consequence of this mixing of diatomic molecules, the wavefunctions s+s and p z +p z molecular orbitals become blended. The extent of this mixing (or hybridization or blending) depends on the relative energies of the MOs of ...
For homonuclear diatomic molecules, the index g or u denotes the existence of a center of symmetry (or inversion center) and indicates the symmetry of the vibronic wave function with respect to the point-group inversion operation i.
An example of a molecular species with square prismatic geometry (a slightly flattened cube) is octafluoroprotactinate(V), [PaF 8] 3–, as found in its sodium salt, Na 3 PaF 8. [6] While local cubic 8-coordination is common in ionic lattices (e.g., Ca 2+ in CaF 2 ), and some 8-coordinate actinide complexes are approximately cubic, there are no ...