L. E. Orgel 



Jj,2_^2 and d^i on the other, but in a subtle and not easily predictable way if 

 the compound is as complicated as a metal-porphyrin. Thus this gap, which 

 is designated A in Figs. 2 and 3, cannot be calculated, but must be considered 

 as an empirically determined quantity. 



If we have several d electrons available it might perhaps be thought that 

 up to six would first fill the d^y, d^^ and dy^ orbitals and only electrons which 

 cannot be accommodated in this way would go into the ^a-^-j/' ^nd d^i orbitals. 



Fig. 4. Double bonding using the d^y orbital. 



This, however, is not necessarily the case, for electrons tend to keep apart 

 as far as possible in order to lower their electrostatic energy and to maintain 

 their spins parallel so as to maximize their exchange stabilization.* If there 

 are less than three d electrons they can all go into the lower orbitals with 

 their spins parallel thus achieving a maximum stability both in terms of 

 orbital (ligand-field) and exchange energy. If, however, there are A-ld 

 electrons present two different distributions of d electrons in the ground state 

 are possible. 



Let us consider the case of the ferrous ion which has six d electrons. If 

 A is very large then the exchange energy cannot compensate for the loss of 

 orbital energy associated with promoting electrons to the d^2__yi and d^i 

 orbitals. Then all six electrons go into and fill up the d^y, d^^ and dy^ orbitals. 

 Thus we must have three pairs of electrons each with their spins antiparallel. 

 The compound therefore is diamagnetic. We say that diamagnetic ferrous 

 complexes are high-field complexes since they occur only if A is large. 



In the free ion we know that five of the d electrons align their spins parallel 

 and the other, of necessity, has its spin antiparallel to the rest. The free ion 

 corresponds to A = in Fig. 2, and so it follows that for sufficiently small 

 values of A we get four unpaired electrons and a correspondingly large 

 magnetic moment. 



We see therefore that there is a critical value of A such that if it is exceeded 



* Exchange stabilization is a purely quantum mechanical phenomenon which tends to 

 line up electrons with their spins parallel. It provides the explanation of Hund's rules 

 concerning atomic states. 



