Gerade orbital

Section 4-3-3 g for gerade, orbitals symmetric to inversion, and u for ungerade, orbitals antisymmetric to inversion (those whose signs change on inversion). The g or m notation describes the symmetry of the orbitals without a judgment as to their relative eneigies. 

Within the space spanned by the minimal basis set, the exact wave functions will be linear combinations of these six determinants. The Hartree-Fock ground state has two electrons in a gerade orbital and is of g symmetry (plus times plus equals plus). The doubly excited determinant has two electrons in an ungerade orbital and hence is also of g symmetry (minus times minus equals plus). The singly excited determinants, on the other hand, have one electron in a gerade orbital and one electron in an ungerade orbital and, therefore, are of u symmetry (plus times minus equals minus). The exact groimd state wave function of minimal basis H2, Oo)> Hartree-Fock... 

Here, the ungerade orbital is bonding and the gerade orbital is antibonding. 

Fig. 2. Simplified molecular orbital diagram for a low spia octahedral complex, such as [Co(NH3 )g, where A = energy difference a, e, and t may be antisymmetric (subscript ungerade) or centrosymmetric (subscript, gerade) symmetry orbitals. See text.

Figure B A qualitative molecular orbital diagram for ferrocene. The subscripts g and u refer to the parity of the orbitals g (German gerade, even) indicates that the orbital (or orbital combination) is symmetric with respect to inversion, whereas the subscript u (ungerade, odd) indicates that it is antisymmetric with respect to inversion. Only orbitals with the same parity can combine.

A core of two MOs was kept doubly occupied, namely, the lag,lbiu orbitals corresponding to carbon K shells (g and u denote gerade and ungerade, respectively). The remaining 12 electrons were left available for fractional occupation of the 24 MOs. 

Fig. 2.9 Angular wave functions of s, p, d, and / orbitals illustrating gerade and ungerode symmetry (a] s orbital, gerade, (b) p orbital, ungeradai (c) pictorial representation of symmetry of p orbital (d) dx> orbital, gerade (c) pictorial representation of symmetry of d orbital (f) d.i orbital, gerade (g) /,i orbital, ungerode.

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