108 



P. George, J. Beetlestone and J. S. Griffith 



split in the jfield imposed by six identical ligand groups into a lower set of 

 three orbitals, denoted by t^g, and an upper set of two orbitals, denoted by Cg, 

 as shown in Figs, la and lb. The five cf-orbitals have different spatial 

 orientations (regions of high electron density) characterized as far as their 

 angular variation is concerned, by the subscripts xy, xz, yz, z^-^r^ and x^-y^. 



dx2-y2 



d-orbitals 





dxy <J,i dyi V-y2d,2\^ 



'2g 



'OOO^: 



-o 



fz2 



^xy '-'xz *-'yz 



dxZ dyz 



d. 



•xy 



Fig. 1. Schematic illustration of the splitting of the energy level of the five 

 ^/-orbitals of the free transition metal ion (a), by a regular octahedral field (b), 

 i.e. six identical ligands, and by an irregular octahedral field (c), i.e. four ligands 

 of one kind equidistant on the x- and j-axes, and two other ligands farther 



away on the z-axis. 



For the first three, these regions lie midway between the axes x and 7, x and z, 

 and J and z respectively, and thus point away from the ligand groups situated 

 equidistantly on the x-, y- and z-axes (see Fig. 2). For the remaining two, i.e. 

 z'^—^r^ and x^-y^, these regions lie in the directions of the axes. Hence the 

 energy of an electron in the eg orbitals will be substantially increased by the 

 mutual electrostatic repulsion between electron and ligand, and also by 

 molecular orbital eff'ects associated with the overlap (Griffith, 1956b), whereas 

 the energy of an electron in the ^29 orbitals will be much less affected. 



When transition metal ions with 4, 5, 6 or 7 c^-electrons form regular 

 octahedral complexes, a choice of at least two electronic configurations thus 

 arises. If the electrons distribute themselves between the to,, and e„ orbitals 



