The character tables contain various information, for instance the number and kind of irreducible representations for a specific point group. Usually these irreducible representations are denoted using a scheme suggested by Robert S. Mulliken (1896-1986, awarded with the Nobel prize in 1966) in the early 1930s. Here, an overview on the meaning of Mulliken's symbols is given.
|1||A and B|
In vibrational spectroscopy, F replaces T. The very common groups Cnv, Dnh and Dnd possess only characters of the dimension 1 and 2.
Though renouncing on an austere mathematical definition of the dimension of a character, we want to mention that there is a direct connection to the dimension of a vector space. With reference to quantum mechanics, there is an analogy with the degree of degeneracy. Thus, states characterized as A or B are not degenerated, whereas E and T show a two- and threefold degeneracy respectively. In other words, there are two or three wavefunctions for one single energy state.
Sometimes in this context, the minuscules a, b, e, t,... are used to describe systems with one electron (atomic orbitals, wave functions) whereas A, B, E, T,... characterize multielectronic systems.
A and B thus indicate whether rotation of a wave function about an axis causes the sign to change (B) or to remain constant (A).
|change of sign||2|
In the character table of point group Oh, the irreducible representations are denoted by the use of Mulliken's symbols.
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