Ferrihaemoprotein Hydroxides 135 



then electron resonance measurements show that D can hardly be less than 

 4°K (Bennett and Ingram, 1956; Griffith, 1956c). With D in these units, 

 the partition function, Z, is given by the equation, 



IQD 2D 8D 



Z = 2e sr +2e3r + 2e3r (19) 



from which the entropy follows from the formula S = 5(/?nogg Z)ldT. For 

 D/r small we deduce S = 3-56 — (28D-i?/9r^). The second term is inappre- 

 ciable (< 0-01) at room temperature for D < 12°K, i.e., an overall splitting 

 of 48 cm~i. Therefore it seems likely, although not certain, that at room 

 temperature this contribution to S is close to 3-56 e.u. 



In the low-spin form we have a spatial degeneracy of three and a spin 

 degeneracy of two. Here, however, it is probable that the three Kramers 

 doublets have a separation large compared with kT at room temperature 

 (Griffith, 1957) so that the contribution to S from the degeneracy is close to 

 1-38 e.u. This means a contribution to A^ for the conversion of the high-spin 

 to the low-spin form of 1-38 — 3-56 = —2-18 e.u. If our assumptions are 

 incorrect the numerical value of this contribution will almost certainly be 

 lower. 



It is much more difficult to obtain any a priori numerical estimate for the 

 remainder of the entropy change, which, using the value obtained in the last 

 paragraph for the degeneracy contribution, is seen to amount to about 

 —5 e.u.* We should expect it to be negative, however, for the following 

 reason. In the high-spin form the overall distribution of the five ^-electrons 

 about the iron has nearly spherical symmetry, thus producing no orientating 

 effect on the environment. On the other hand, in the low-spin form the five 

 electrons are in the three orbitals away from the bond directions, thus im- 

 posing an extra rigidity on the environment of the iron. This would result 

 partly in a more rigid ferrimyoglobin molecule, and partly in a more rigid 

 arrangement of water molecules around the Fe — OH group. 



Just as A// for the conversion is determined by other energy terms besides 



the electronic stabilization energy arising from the splitting of the ^-orbitals, 



so the values of A// for the formation of complexes with different ligands 



cannot be taken as an accurate indication of the variation in A. From one 



extreme to the other, however, a rough correlation would be expected, with 



the high-spin complexes having the less favourable values of AH. This 



trend, which has also been discussed by Havemann and Haberditzl (1958), is 



illustrated by the data in Table 6. The values of AS° become progressively 



more negative from fluoride to cyanide, but they are not amenable to any 



straightforward correlation because the entropies of the ligands themselves 



vary so much, with S"" for F~, 0H~ and CN~ having the values —2-5, —2-3 



and -|-28 e.u. respectively. Some allowance for this can nevertheless be made 



* The assumed additivity of entropies is equivalent to a factorization of the partition 

 function, which is probably a good approximation here at room temperature or below. 



