Group-theoretical symbols

The subsets of d orbitals in Fig. 3-4 may also be labelled according to their symmetry properties. The d ildxi y2 pair are labelled and the d yldxMyz trio as t2g. These are group-theoretical symbols describing how these functions transform under various symmetry operations. For our purposes, it is sufficient merely to recognize that the letters a ox b describe orbitally i.e. spatially) singly degenerate species, e refers to an orbital doublet and t to an orbital triplet. Lower case letters are used for one-electron wavefunctions (i.e. orbitals). The g subscript refers to the behaviour of... 

Hie designation of the d-orbltals is that given by Eyring, Walter, and Kimball, Quantum Chemistry (John Wiley and Sons. Inc.. New York, 1944). We have also used throughout the group theoretical symbolism which Is essentially that of these same authors. 

Ao, while the threefold-degenerate d by (2/5)Ao, both relative to a spherical field. The labels Cg and t2g are group-theoretical symbols, which specify the syimnetry properties of the functions (more precisely, they designate irredncible representations of the Oh point gronp). 

If there is more than one symmetry element (symmetry plane, axis etc.), relations similar to Eq. (2.5) hold for every element, and the wave functions can be classified according to group-theoretical symbols (see e.g. ). 

Label each MO with its group theoretical symbol state which orbitals are bonding, nonbonding, and antibonding fill in the electrons and determine the overall bond order and magnetism of the molecule. Also, sketch the predicted shape of each of the MOs. 

Example 16-2. For each of the following coordination compounds, sketch the CF splitting diagram, label the d-orbitals, label each energy level with its group theoretical symbol, fill in the electrons, and predict the magnetism (a) [FeCy , (b) [Co(CNk] -, (c) [Co H20),f+, (d) [IrCI ] -, and (e) [NiCy -. 

For each of the following coordination compounds, sketch the CF splitting diagram, label the d-orbitals, label each energy level with its group theoretical symbol, fill in the electrons, and predict the magnetism. 

Sketch the one-electron MO diagram for the tetrahedral Ni(CO)4 organometallic compound. Label each MO with its proper group theoretical symbol and fill in the correct number of valence electrons. Also, determine the number of v(CO) stretches in the IR spectrum. 

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