C L A S S I F I C A T I O N OF L I G A N D S ON T H E B A S I S OF R E D O X

P O T E N T I A L S

Y a . D. F r i d m a n UDC541.49

Many r egu la r f ea tu re s of the s tabi l i ty constants of complex compounds in solut ions can be gene ra l - ized on the bas i s of the potent ia ls of the r eac t ions of oxidative d imer iza t ion of the l igands, of the fo rm

_ 2 + 2X~aq) 2e =X2(aq ) o r 2X(aq) - 2e =X 2 (aq) for e l ec t r i ca l l y neut ra l l igands.

The la rge amount of expe r imen ta l data m a k e s it poss ib le to subdivide l igands into g roups which a re cha rac t e r i zed by the fact that the loga r i thms of the stabil i ty constants of compounds of the same type fo rmed by the me ta l with the l igands belonging to a given group genera l ly show a l inear dependence on the potent ia ls of the r eac t ions of oxidat ive d imer iza t ion of the l igands [1-3]. The stabil i ty constants of com- p lexes of the type MX m with l igands of a given group sa t i s fy the equation

0 0 0 log ~ 0 = Cx - - ccxEx' (1)

where E ~ is the potential of the r eac t ion of the ligand, and C~K and ~ a re constants . The change f rom one group to another is accompanied by a b reak on the graph giving the dependence of the stabil i ty constants on the potent ia ls E ~ . At the same t ime. the fo rmat ion of mixed compounds with l igands belonging to di f ferent g roups is poss ib le . The stabi l i ty constants of compounds of this kind with the composi t ion MXjY i a r e de- fined by the equation

�9 0 . 0

log ~I i = C - - ax IEx - - %AE v, (2)

where E ~ and E ~ a re the potent ia ls of the redox r eac t i ons of the l igands X and Y; and C, a X, and ~ y a re coeff ic ients which a r e independent of E%( and E~f. If the l igands X and Y belong to the s ame group, we have

c~ X = C~y.

On the bas i s of expe r imen ta l data, the following groups of l igands have been es tabl i shed [2, 3]: halide �9 , 0 - 2 , i o n s - C1- B r - . I - ; su l fur -conta in ing l igands - g2 ~ SCN-, thiourea; e l ec t r i ca l ly neutra l m o l e c u l e s - a m -

monia , pyr id ine , water ; and bidentate l igands - e thylenediamine, glycinate ions, and oxalate ions. The f i r s t a t t empts to explain the dependence of the stabil i ty constants of complexes on the potent ia ls of the r eac t ions of oxidative d imer i za t ion of the l igands were made by Edwards [4]. who r ega rded these potent ia ls as a m e a - sure of the nucleophil ic nature of the r eagen t s . Variou s re la t ionsh ips between the potent ia ls and the p o l a r - izabi l i ty and has ic s t rength of the l igands were es tab l i shed [5].

In a study of the redox t r a n s f o r m a t i o n s of complex compounds [6] we obtained the following equation giving the dependence of the s tabi l i ty constants of complexes of the type MX on the d i f fe rence in the poten- t ia l s of the redox s y s t e m s of the me ta l ion and the l igands and the d i f ference in the ionization potent ia ls of the valence s ta tes of the s ame spec ies in the i r compound:

R:r In ~,0 = ~ (e~, - - E o - ~0 + ~ ) , C3)

where E~ I and E ~ are the potent ia ls of the redox s y s t e m s of the me ta l ion and the ligand, and q~ M and q ~ a re the ionizat ion potent ia ls of the valence s ta tes of M and X. If in a s e r i e s of compounds of a m e t a l with di f ferent l igands the ionizat ion potent ia ls a re constant or change in p ropor t ion to the potent ia ls E ~ , Eq. (3) r e p r e s e n t s the l inea r dependence of the logar i thms of the s tabi l i ty constants on the potent ia ls of the redox

Inst i tute of Inorganic and Phys ica l Chemis t ry , Academy of Sciences of the Kirgiz SSR, F runze . Trans la ted f rom Teo re t i che s kaya i l gksper imen ta l ' naya Khimiya, Vol. 9, No. 5, pp. 621-626, Sep t ember - October , 1973. Original a r t i c le submit ted March 13, 1972.

�9 19 75 Plenum Publishing Corporation, 227 Nest 17th Street, New York, N. Y. 10011. No part o f this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission o f the publisher. A copy o f this article is available from the publisher for $15.00.

489

~, eV

4o ~ " CW

4o!

S~ o; - :

1 , a -

I a,~ a

- 0~- I~

I I I t I a,~ ~a 42 46Es

Fig. 1

0 E X, V ~o y-

z,z

I.~ ct"

-tl le ~x, ev

Fig. 2

Fig. 1. Relat ionship between the e lee t ronega t iv i ty and potent ia ls of the oxidative d imer iza t ion of l igands.

Fig. 2. Dependence of the potent ia ls of the oxidative d imer iza t ion of the ligands on t he i r ha rdness p a r a m - e t e r s .

s y s t e m s of the l igands. F o r a s e r i e s of compounds of nickel and copper L7] it has also been shown that the logar i thms of the s tabi l i ty constants of the complexes a re l inear ly dependent on the potent ia ls of the r e a c - t ions of oxidative d imer iza t ion of the l igands if the p a r a m e t e r s of the splitting of the d - o r b i t a l s of the me ta l ions or the energy of in terconf igura t ional in terac t ion r ema in constant or , in turn, a re l inear functions of the potent ia ls of the r eac t i ons of the l igands.

In [8], the re la t ionship between the potent ia ls of the reac t ions of oxidative d imer iza t ion of the l igands and the i r e lec t ronega t iv i ty and bas ic s t rength was establ ished:

E ~ -- (X x - XH) ~ + 0.059 PKHx, (4)

where X X and X H are the e lec t ronega t iv i t i e s of the ligand X and hydrogen, and PKHx is the exponent of the d issoc ia t ion constant of HX. Compar i son of the potent ia ls of the r eac t ions of oxidative d imer iza t ion of the l igands with the i r e lec t ronega t iv i t i e s showed that the l igands fo rm separa te groups within which l inear r e - la t ionships a re obse rved between these quanti t ies. The dependence of the potent ia ls E% on the e l ec t ronega- tivity of the l igands is shown in Fig. 1. Each group of l igands co r r e sponds to a separa te s t ra ight line. Sep- a ra te groups a re fo rmed by halide ions (CI-, B r - , I-) ; sul fur-conta ining ligands ($2032-, Thio, SCN-); a m - monia , pyr idine, and water ; and the ions SH-, CN-, and OH-. The same groups were es tabl ished in the study of the dependence of the s tabi l i ty constants of the complexes on the potent ia ls E%.

We obtained m o r e genera l conclusions regard ing the c lass i f ica t ion of l igands on the bas i s of the con- cept of hard and soft Lewis acids and bases . According to this concept, complex - fo rming spec ies and l i - gands can be c lass i f ied as hard or soft, depending on the i r polar izabi l i ty , ease of oxidation, and ability to fo rm coordinate bonds of di f ferent types [9]. It was shown in [10] that the ha rdness and sof tness of l igands can be es t imated f rom the magni tude of the change in enthalpy in the reac t ion X(gas ) + ne =xn-(a_) . The heat of the reac t ion is de te rmined as the sum of the e lec t ron affinity of the spemes X and the hydrat ion en- e rgy of the ion X n- . This sum, re la ted to unit charge of the ion X n- , will be r e f e r r e d to as the ha rdnes s p a r a m e t e r of the ligand

E A + A H (5) ( I X - - n

where EA is the e lec t ron affinity of the spec ies X, and AH~ is the hydrat ion energy of the ion X n- .

The ha rdnes s of l igands i n c r e a s e s with i nc r ea se in cr X. If we separa te the enthalpy change for the reac t ion X2( a q) + 2e = 2X-(aq) into individual components by m e a n s of the following the rmochemica l cycle:

490

-arts iX~o

Xz(gasW-----~ 2X(ga~) =- 2X(ga.~) ,

a {x--x) 2EA

we can readi ly satisfy ourse lves that the potential of the oxidative d imer iza t ion of the ligands, measured relat ive to the hydrogen electrode, includes the hardness p a r a m e t e r ~X as one of the t e rms:

+11 ] ~ E ~ ~-fi D ( X - - X ) + A H x , + T 6 S - - E H, (6)

where ~X is the hardness pa rame te r of X, D(X-X) is the bond energy in X 2. AHx2 i s the energy of dehydra- tion of X2, AS is the change in entropy, F is F a r a d a y ' s number, and E~ is the potential of the hydrogen electrode.

F igure 2 gives the dependence of the potentials of the oxidative d imer iza t ion of the ligands F - , CI-, Br - . I - , OH-. CN-, and SH- on the p a r a m e t e r s cr X, calculated in [10]. It can be seen from the figure that all the ligands studied can be divided into two groups, each of which is charac te r ized by a l inear dependence of the potentials of the redox reac t ions of the ligands on the pa rame te r ~X" The separate groups are formed by monatomic (F- , CI-, Br - . I-) and diatomic (OH-, CN-, Sit-) ligands. For a given value of the hardness pa rame te r , the diatomic ligands correspond to more negative potentials than the monatomic li- gands, and this can be related to the difference in their polarizabil i t ies.

The enthalpy change in the react ion X(_as ) + e =X-(aN ) cha rac t e r i ze s the ability of X to form ions and g provides a measu re of the hardness of the ligand, whereas the enthalpy change in the react ion 2X(gas ) =X2(aq ) cha rac t e r i ze s the ability of X to form a covalent bond and may serve as a measu re of the softness of X. If we neglect in Eq. (6) the entropy term and regard the quantity (D(X-X) + AHx)/2F as a pa rame te r of the softness of the ligand, we can represen t the potential of the oxidative d imer iza t ion as the sum of the softness and hardness p a r a m e t e r s minus a constant quantity equaI to the potential of the hydrogen e lec- t rode:

E~ = Ox + Sx - - E ~ (7)

where the softness p a r a m e t e r is

D ( X - X) + hHx, (8) Sx = 2F

These l inear re la t ionships between the potentials E~C and the p a r a m e t e r s o- X and electronegat ivi t ies of the ligands are possible if there is a l inear relat ionship between the softness and hardness pa ramete r s :

Sx = ax - - bx%" (9)

Accordingly, the ligands form separate groups within which the relat ionship applies, and the different groups differ in the magnitude of the coefficients of the relationship in Eq. (9). The charac te r i s t i c s of two different groups of ligands are given in Table 1. In each group the softness pa rame te r S X, calculated by means of Eq. (8) f rom the energy of rupture of the bonds in X 2 and the hydration energy [11, 12], in- c reases l inearly with increase in the hardness pa rame te r o- X. The coefficients of Eq. (9) for monatomic ligands are a = 1.6 eV and b = 0.3; for diatomic ligands, a = 1.0 eV and b = 0.14. Drago and Wayland [13] expressed the enthalpy change for the react ion M(aq)+ X~ ~ =MX, ~ as the sum of the products of two ~aqJ ~aqJ pa r ame te r s , charac ter iz ing the softness and hardness of tile reagents . If we neglect the entropy factor , we can de termine the stability constant of MX from the equation

RT ln[~l o = SMSx § (~ M(~ x , (10)

where S M and cr M and S X and o- X are the softness and hardness pa r ame te r s for M and X, respect ively . The

491

TABLE 1.

X--

F- CI-

Br-

I" OH- CN- SH-

Charac t e r i s t i c s of the Ligands, eV

Electro- Hardness Bond enezgy in

Hydration [ Softness energy of ] parara- X2 [12] tetet

2,87 1 , 3 6

1,09 0,62 0,95

--0,18 --0,4

4,0 3,2 2,9 2,4 3.6 3,3 3,2

12,18 9,94 9,22 8,31

10,45 8,78 8,59

--1,61 --2,5 --1,97 - - 1 ,54

--2,16 --4,52 --4,28

--0,25 --0,35 --0,41 --3,85

(0) --0,19

--I ,375 --1,16 --0,975 --2,50 --2,26 --2.23

pK 2~

16

12

8

O

#

12

pA"

$

!

It o X, eV

zogp

2 JO

20

c i

70-- i- Br- a" i i i i i i i il |

Fig~ 4 Fig. 3

Fig. 3. Dependence of the exponents of the d issoc ia t ion constants of the acid- base complexes on the ha rdness p a r a m e t e r s of the ligands: 1) HX; 2) HY; 3) CH3HgX; 4) CH3HgY; 5) HgX + ; 6) HgY + ; X = F - , Cl-, B r - , I - ; Y = OH-, CN-, SH-.

Fig. 4. Dependence of the loga r i thms of the stabil i ty constants of m e r c u r y compounds on the ha rdnes s p a r a m e t e r s of the ligands.. 1) HgX2; 2) ttgX2-; 3) HgSCNX; 4} HgCNX. X = CI-, B r - , I - .

f i r s t t e r m in the r ight-hand side of Eq. (10) co r r e sponds to the energy of fo rmat ion of a covalent bond, and the second co r r e sponds to the energy of the e l ec t ros t a t i c in teract ion.

If the l igands fo rm separa te groups within which l inear re la t ionsh ips a re obse rved between the ha rd- ness and sof tness p a r a m e t e r s , it follows that the logar i thms of the s tabi l i ty constants of the compounds MX should show a l inear dependence on the p a r a m e t e r aX:

RT In ~l.o = SMax + ('~M - - S~bx) C~x. (11)

F igure 3 g ives the dependence of the exponents of the d issoc ia t ion constants of HX, HgX + , and CH3HgX for X = CI-, B r - , I - , SH-, OH-, and CN- on the p a r a m e t e r s eX [10]. The d issoc ia t ion constants of HX and CH3HgX are given in [14], and the stabil i ty constants of HgX were de te rmined in [15, 16]. I t follows f rom Fig. 3 that the l igands indicated can be divided into two groups, each of which is cha rac t e r i zed by a l inear re la t ionship between pK and ~X" Separate groups a re fo rmed by mona tomic and d ia tomic l igands. The division of the l igands into groups i s independent of the nature of the complex - fo rming spec ies and r e m a i n s unchanged on going f rom the compounds with the hydrogen ion, which is the ha rdes t acid, to the compounds with Hg 2+ and CH3Hg +, which a r e among the sof test acids. F o r a hard complex - fo rming spec ies the slope of the p K - ~ X s t ra ight l ines is pos i t ive , whe reas for soft complex - fo rming spec ies the slope is negat ive.

F igu re 4 gives the dependence of the l oga r i t hms of the stabil i ty constants of hom'ogeneous and some mixed halogen compounds of m e r c u r y on the p a r a m e t e r o X . In the case where the l igands belong to the same group, the logar i thms of the stabil i ty constants of the complexes with these l igands a re a l inear func- tion of the ha rdnes s p a r a m e t e r , i r r e s p e c t i v e of the type of compound and the number of coordinates spec ies .

492

TABLE 2. Spec ies

~n+

H + Fe3+ Zn2+ Cd2+ pb~+ Ag + CHsHg+ Hg2+

Softness and Hardness Parameters of Complex-Forming

--2,34 --0,74

0,53 0,42 0,75 1,35 1,56 2,58

0,21 0,08 0,054

--0,35 --0,074

0,12 --0,125 --0,224

SM

--!,4 --0,46 --0,33

0,3 0,47 0,84 0,98 1,61

aM

--0,21 --0,18 --0,04 --0,12 --0,21 --0,37 --0,48 --0,58

s M [ lo] sM U4]

2,28 --0,42 3,1 --2,2 3,1 3,5 2,04 4,1 4,2 2,62

4,6 4,64

a M [t5]

(9) 2,7 0,2

--i,0 --0,3 --3,5

--4,0

If the experimental data are used to determine the coefficients of Eq. (11) and to find the values of the connecting coefficients a X and b X from the dependence of S X on ~X' it is possible to calculate the soft- ness and hardness p a r a m e t e r s of the complex-forming species. Table 2 gives the resu l t s of these calcu- lations, ca r r ied out f rom data for the halogen compounds of the meta ls . The slopes of the log f i - a straight l ines and the intercepts which they cut off on the axis of ordinates are denoted by the le t ters A an~ 7. The softness and hardness p a r a m e t e r s of complex-forming species according to the data of Ahrland [10], Klop- man [17], and Yats imirski i [18] are given for comparison. According to the resu l t s of our calculations, the softness of the complex-forming species inc reases in the same order as that given by the data of other workers . The change from hard to soft complex-forming species is accompanied by a change in the sign of the softness pa ramete r . In the se r ies of hard complex-forming species, the softness and hardness pa r ame- t e r s change in the same direct ion, whereas in the se r ies of soft complex-forming species they change in opposite direct ions .

If in a ser ies of ligands l inear re lat ionships are observed between the softness and hardness pa r ame- ters , it follows that the logar i thms of the stability constants of the complexes with these ligands should show a l inear dependence on the potentials of their oxidative dimerizat ion. F rom Eqs. (7), (9), and (11) we obtain

~M - - SMbx ~M ~ SMbx E~ R T In ~1.o = SMaM -b bx_l (a x - - E ~ bx_l (12)

If we i n t r o d u c e the fol lowing s y m b o l s for the cons tan t quan t i t i e s :

aM - - SMbx SMax o _ o COx, 2 . 3 R T ( b x _ l ) ~ a ~ 2.-~--~Jc-CZx(ax E H ) ~

we find that Eq. (12) r e d u c e s to Eq. (1). Thus the l i gands can be d iv ided into g roups wi th in which l i n e a r r e l a t i o n s h i p s a r e o b s e r v e d be tween the s o f t n e s s and h a r d n e s s p a r a m e t e r s . The l o g a r i t h m s of the s t ab i l i t y cons t an t s of the complexes with the l i gands of a given group a re l i n e a r l y dependen t on the p o t e n t i a l s of

the oxida t ive d i m e r i z a t i o n of the l igands .

LITERATURE CITED

!. Ya. D. Fridman, Redox Reactions and Stability of Complex Compounds of Metals in Solution [in Rus- sian], Ilim, Frunze (1966).

2. Ya. D. Fridman, Proceedings of the Third Symposium on Coordination Chemistry, Vol. 2, Budapest (1971), p. 77.

3. Ya. D. Fridman (editor), The Stability of Mixed Complex Compounds in Solution [in Russian], Ilim, Frunze (1971).

4. J.A. Edwards, J. Am. Chem. Soc., 766, 1540 (1954). 5. J.A. Edwards, J. Am. Chem. Soe., 7_88. 1819 (1956). 6. Ya. D. Fridman, Zh. Neorgan. Khim., 3, 1865 (1958). 7. A. Ya. Fridman, "Mixed compounds of metals with complexones in solution," Abstract of Candidate's

Dissertation, Moscow (1970). 8. D.H. McDaniel and A. Vugst, J. Am. Chem. SOe., 8_66. 1334 (1964).

493

9. R.W. Pearson, J. Am. Chem. Soc., 8._55, 3533 (1963). 10. S. Ahrland, Chem. Phys. Let ters , 2, 303 (1968). 11. V.N. Kondrat'ev (editor). The Energy of Rupture of Chemical Bonds [in Russian], Izd-vo AN SSSR,

Moscow (1962). 12. K .P . Mishchenko and G. M. Poltoratskii, Problems of the Thermodynamics and Structure of Aqueous

and Nonaqueous Solutions of Electrolytes [in Russian], Khimiya, Leningrad (1968). 13. R.S. Drago and B. V. Wayland, J. Am. Chem. Soc., 8._77, 3571 (1965). 14. F. Bssolo and R. G. Pearson, Mechanisms of Inorganic Reactions, Wiley (1967). 15. Y. Marcus, Acta Chem. Scand., 1_11,329 (1957). 16. L .G . Sillen and A. E. Martell, Stability Constants of Metal Ion Complexes, London (1964). 17. G. Klopman, J. Am. Chem. SOc., 9_00, 223 (1970). 18. K.B. Yatsimirskii, Teor. Eksper. Khim., 6, 462 (1970).

494