Correlation of stability constants of metal complexes with hammett's σ-factor

J. Inorg.Nucl.Chem.,1966,VoL28.pp. 125to 138. PergamonPremLtd. Printedin Northernheland

CORRELATION OF STABILITY CONSTANTS OF METAL COMPLEXES WITH HAMMETT'S e-FACTOR J. J. R. FRAt~STO DA SILVA and J. CrON~ALVES CALADO Centre de Estudos de Quimica Nuclear (LA.C.), Institute Superior Trcnico, Lisboa 1, Portugal (Received I April 1965)

Almmct--A parameter is derived on thermodynamical grounds, which measures the variations in the stability of the metal complexes formed with a series of aromatic ligands, when the basicity of these ligands is altered by changes in substituents. This parameter is shown to be a linear function of Hammett's a-factor for the substituents, using several examples available in the literature. The straight lines obtained have positive slopes, indicating that the complexing reactions are favoured by electron withdrawal from the reaction center. This is taken to imply that the stabilisation is caused by dative metal-to-ligand ~r-bonding. THE correlation between the stability constants of metal complexes formed by a series of related ligands with their respective base strength has always been a focus of interest in the field of solution chemistry. The existence of such a correlation is, of course, a desirable feature for quantitative prediction of unknown constants and may also be a convenient starting point for the elaboration of more general and precise theories concerning complex-formation. Most of the correlations obtained have been shown to obey the equation log K~L = a log Kin, + b

(1)

which was first used by BJERRUMix) and more recently derived on thermodynamic grounds by DUNCAN(2) and IRVING and RoSSeTTI.(3) The latter authors discussed the conditions under which the correlation was to be expected and attributed major deviations to steric effects. Other possible sources of deviations were considered, such as differences in the strength of the metal-ligand bonds relatively to different donor atoms in the chelating agents, when structural changes in L changed the affinity of the donors for the metal, not necessarily to the same extent or even in the same direction. WILLIAMS et al. (4) imposed, however, stricter conditions, pointing out that an equation of the form of (1) should not be of universal validity, since it requires that the dependence of the partial molar free energy of the metal complex GuL° upon the ligand must be similar to that of G~L°. This cannot be expected to be generally true, particularly when substituents in the ligand influence their ability to accept electrons from the metal to form ~r-bonds. Thus, irregularities in plots of the kind expressed by Equation (1) can also be attributed to the formation of such bonds and then have indeed been postulated when was theoretically possible. (~'6) ~1) j. BmltRuM, Chem. Rev., 46, 381 (1950). (s) j. F. DUNCAN,Analyst 77, 830 (1952). ~8~H. I R v ~ o and H. Rosstn~, Acta Chem. Scand. 10, 72 (1956). c,) j. Jot~s, J. PeeLe, J. TOMSm~'aO~and 1%.J. P. Wn.uuu~ Y. Chem. $o¢. 2001 (1958). (5~ R. J. P. Wn.x.lAm, Disc. J~araday See. No. 26, 123 (1958).

125

126

J.J.R.

FRA~rSTO DA SILVA and J. GONqALVES CALADO

Other types of deviations from "normal" values of the stability constants have also been attributed by several authors to the formation of ~r-bonds from metal to ligand. Thus ASmLAr,rD e t aL ~°~ used the ratio of the stability constants of the first and second complexes of certain donors, when this ratio was very different from the expected statistical value, and MURMA~r and BASOLO(TJ noticed that for a series of silver-substituted pyridine complexes the order of stabilities was of an inverse sort. Few attempts have been made to treat this problem on quantitative grounds; GOLDBERGand F~RI,Z~LIUS~s~devised a method in which the stabilities of the complexes of several aliphatic amines were compared with the stabilities of the complexes formed by structurally analogous ligands with heterocyclic nitrogen instead of the amine group. It was recognized that the variation in constitution of the ligand could alter its basic strength and, consequently, its tendency for giving and accepting electrons. To overcome this difficulty these authors suggested that the values to be compared should be "stabilities of the metal-ligand bonds p e r unit of base strength of all the donor atoms in the ligand", i.e. r values in the equation for dibasic ligands, where r = AG,/{(AGr~)I +

(AGa)~}

(2)

This treatment sets out a desirable quantitative basis for discussion; however, the function r has no physical meaning, in the sense that it cannot be directly correlated with the strength of the ~r-bonds. For this reason IRVaNGand DA SILVA(a'10) suggested a new parameter--St-which measures the additional stabilization caused by the formation of such bonds, and obtained a more fundamental relationship demonstrating that this parameter was a linear function of Hammett's tr- factor for a series of substituted pyridines. The slope of the straight line obtained had a sign opposite to that usually found in A p K u r . - - a relationships, demonstrating that the reaction was favoured by electron withdrawal from the aromatic ring. This means that the effect causing the stabilisation was indeed the donation of electrons from the metal to anti-bonding orbitals of the ligand. In general, no direct correlation of the stability constants of metal complexes with Hammett's a- factor has been found feasible. The only known case of such a direct relationship was reported soon afterwards by MAX"and Jo~_.sm) for seventeen copper (II) complexes of substituted benzoic acids. The same authors were however unable to obtain a similar correlation for a series of substituted pyridine adducts of copper (II)acetylacetonates as reported in a later paper, c12) The same has happened before with the sulphonate complexes of cadmium (ls) and in several other cases; the absence of a correlation seems generally agreed. In the present paper we intend to demonstrate that it is possible to obtain good fundamental correlations with Hammett's a- factor if our parameter S I is used, and we show that this parameter appears logically in the thermodynamical derivation of the general equation for the formation of complexes of a series of related ligands. (6) A. ~ A N D , J. CHATr, N. DAVmS and A. WiLtaArcd, J. Chem. Soc. 264, 277 and 1403 0958). ~7~R. K. MOP.MANNand F. BAsot~, J. Amer. Chem. Soc. 77, 3484 (1955). ts~ D. GOLDB~O and W. C. F ~ . ~ . r t r s , J. Phys. Chem. 27, 1248 (1959). tD~j. j. R. F. DA SILVA, D. Phil. Thesis, Oxford (1962). ~o~ H. IRxaNo and L J. R. F. DA SILVA, Proc. Chem. Soc. 250 (1962). ~xx~W. MAY and M. JONES, J. Inorg'. Nucl. Chem. 24, 511 (1962). ~m W. MAY and M. JONES, J. Inorff. Nucl. Chem. 25, 507 (1963). txa~ j. F. TAa~ and M. JoNv.s, J. Amer. Chem. Soe. 83, 3024 (1961).

Stability constants of metal complexes with Hammett's a-factor

127

D E R I V A T I O N OF T H E E Q U A T I O N S

For the derivation of the necessary expressions we follow a line similar to GLASSTONE et al. (m and used in the excellent review on linear free energy relationships by W~LLS.(15) Let us consider two series of reactions, denoted by superscripts A and B, and suppose that within each series the mechanisms involved are the same for all reactions. This is the current case when we deal with a series of reagents differing only in the nature and position of a substituent group. In general, the changes in the standard Gibbs free energy AGO of the reactions are functions of many variables, xx, x2, Xz. . . . and the corresponding variations can be expressed as follows

a aoo =

\

/ax,

(3)

In the particular case considered in which we assume that the processes involved are fundamentally the same for all the reactions of the series, such changes are functions of a single variable x, namely the relative charge density at the reaction center, and accordingly we may write ( ~ AGO~ d AG O = \ ~ / dx

(4)

It will be understood that all the variables such as reaction medium, temperature, ionic strength, etc., are held constant. Assuming that the partial derivative \----~--x ] is constant in the range of variation of x, we can integrate Equation (4) and obtain AGO - AGo0 = (~ AGO] ( x , - :co) \

(5)

Ox /

Since the standard Gibbs free energy changes are proportional to the logarithms of the equilibrium constants of the reactions, A G O = - - R T In K

(6)

relation (5) can be written in the form RT(ln K, -- In leo) = (~ \ ~ }AGO~ (Xo -- x~)

(7)

or

K,

R T l n Ko = g~(xo -- x,)

(8)

Ix*)S. G ~ O N E , K. J. LAIDLERand H. EYmNG, The Theory of Rate Processes. McGraw-Hill, New York (1941). cxs~p. R. WELLS, Chem. Rev. 63, 171 (1963).

J. J. R. FRA0STO DA SILVA and J. GONqALVES CAI,AOO

128

where [~ AG°] g ' - - = \ Ox /

(9)

This equation can be applied to both series A and B, as follows: K, x R T l n ~ x = g ~ (Xo -- x,) A

K, B

R T l n - ~ = g ~ (x o -- x,) B

(lO) (11)

Combining Equations (10) and (11) we have K~ B _ g , ~ ( x , - - x ~ o~ l o

logK

- g7 Cx,

1," A ,*i

• g Ka

(12)

If the two series of reactions are not very different in type, the ratio (x, -- Xo)B/ (x, -- x0)x may be taken as constant and, in many cases, equal to unity. ~m For the same reason, the ratio g~]3/gxA which measures the influence of the variable x on the standard free energy of two reactions A and B is usually a constant characteristic of the two types of reactions but, in general, different from unity; representing this ratio by j xz, relation (12) is now written log K~B K ia Xo~ = s~AB1^us ~-x

(13)

This equation relates the equilibrium constants of reactions A and B and can take the form of a two-parameter equation if reaction series A is taken as a standard and we denote log (KiA/KoA) by Xt K. A

X~ ~ log

'X Ko

(14)

log K'~ ar~~ X, K0---~ =

(15)

These results can now be applied to a series of reactions A, corresponding to the acid dissociation of several ligands H,L, H,L',. H~L ~ HnL' ~

L + nH L' + n H

(A)

and B, corresponding to the complexation of a metal ion M by the same ligands HnL+ M ~ HnL'+M~ .

.

.

.

.

.

.

.

.

.

.

.

• ML+nH "ML'+nH .

. .

Charges are omitted for the sake of simplicity.

.

.

.

.

.

.

.

(B) .

Stability constants of metal complexeswith Hammett's a-factor

129

The expressions derived above are, of course, valid in this case if we assume that the ligands considered are all of the same type and differ only in the nature and position of a substituent group. Moreover it is necessary that the changes in the hydration of the species are the same, or constant, throughout the series/9) The variable x, which was said to represent the electric density at the reaction center, is also a measure of the difference in basicity of the ligands. In Equation (15) the subscript o refers to the unsubstituted ligand, H,L, taken as the reference. In the present case the equilibrium constants of reactions (B), also denoted by KL, are equal to the ratio of the stability constant of the metal complex ML and the association constant of the ligand H~L

flMl~

(16)

log Kr, = log 3n L and so Equation (13) can take the form tim,' firKA log f f ~ --log ~ = j~B log K0iX

(17)

showing the relative influence of a substituent group in the dissociation constants of the ligands and the corresponding stability of the complexes. The logarithm of the ratio of the acid dissociation constants of a substituted ligand and the unsubstituted one can be identified with the product pa of Hammett's equation; a is the substituent parameter defined in relation to the dissociation constants of substituted benzoic acids, and it measures the ability of the substituent to alter the electronic density at the reaction center; p is a proportionality constant, depending upon the response of the given reaction series to substituent effects, relatively to that of the standard series. The left-hand side of Equation (17) is the stabilization factor ISt--introduced in a previous paper by IRVING and DA SILVAc1°) S1 = log KL, -- log KL

(18)

This factor was shown to be a measure of the ,r-stabilization additional to a-bond formation by back donation of d-electrons from the metal to anti-bonding orbitals in the ligand/a'x°) Equation (16) can now take the simpler form $I = j~B pa

(19)

and if p' is defined by

P'

P = g

= gT"

(20)

denoting by the superscript A' the series of benzoic acids with the same substituent groups, it can be written St

= p'a

(21)

showing a direct proportionality between the stabilization factor S1 and the Hammett's a- factor.

130

J.J.R.

FRA0SrO D^ SmvA and J. GON~*LVeS CAt.ADO

This equation was derived on the assumption that the complexes formed are of the I : 1 type. In the general case of ML, complexes, the series A and B of reactions to be considered are the following p H,,L ~ p H.L' ~

pL + pn H pL' + pn H

and pHiL+ M pH~L'+M. .

. .

°

.

.

.

.

. .

~ML~ + p n H "ML~'+pnH •

°

°

,

.

.

.

.

,

.

•

.

°

.

.

.

.

Relations (16) and (19) are now written as log KL = log (/~H.L)~

(16')

and S I = d~Bppa

(19')

and Equation (21) takes the general form

s , = p p'~

(21')

Our purpose is now to show that Equations (21) and (21') are verified by most examples for which there are published data. RESULTS AND DISCUSSION

In the present paper the equations derived will be applied to several examples available in the literature, even in cases where the relationship with Hammett's ofactor has been denied. The correlations will be given in tabular and graphical form; the symbols used have the following meanings: KHL: dissociation constant of the ligand KHL = [H][L]/[HL] Pm~,: stability constant (overall) of the metal complex//Mr,, ---- [ML~,]/[M][L] ~ KL : ratio of constants Kr, = fl~m~ " (KaL) ~ = /~m~

~aL)"

St: stabilization factor St = log K v -- log Kr. Silver complexes o f substituted pyridines

This example has been given before in a preliminary note by I~VlNG and ox SILVA.~1°~ Table 1 records the steps necessary for the calculation and a values for the substituents. These were obtained in the well-known review by JArr~ ~le~ and in a quite recent work by FlsCrmR et al. ~17~where values for pKnr. are also found. Stability constants of the silver complexes (t = 25°C) are collected in the monograph edited by the Chemical Society. cls~ (m H. H. J A i l , Chem. Rev. 53, 191 (1953).

(17~A. FlSCHIm, W. J. GALLOWAYand J. VAUOHAN,3". Chem. Soc. 3591 (1964). (181The Chemical Society, Special Publication No. 17 (1964).

131

Stability constants of metal complexes with Hamn~tt's ,-factor TABLE I.--SILVER COMPLEXESOF SUBSTITUTEDPYRIDINE$(2:1 COMPLEXES) Substituent

pKHL

ApKHL

log KL

log fl,~.t

$~

a

Nil 3-CHs 4-CH, 3-OCHs 4-OCHs 3-CN 4-CN 3-NHt 4-NHs 3-CONH2 4-CONH,

5.21 5"67 6"03 4"78 6"58 1"35 1"86 6'04 9"12 3"40 3"61

0 +0.46 +0"82 --0"43 +1"37 --3"86 --3"35 +0"83 +3"91 --1"81 -- 1"60

--6.07 --6"99 --7.67 --5.89 --8"72 +0.20 --0"64 --6'87 --12"04 --3"58 --4"21

4"35 4.35 4"39 3'67 4"44 2"90 3"08 5"21 6"20 3"22 3"01

0 --0.92 --1.60 +0"18 --2"65 +6"27 +5"43 --0"80 --5"97 +2"49 + 1"86

0 --0-08 --0"14 +0"07 --0"23 +0"64 +0"55 --0"14 --0"65 +0"28 +0"27

6

o

4

~pK

S~

2

-4

-6

I

i

i

-0"6

I -0"4

I

I

I

I

-0"2

t

0

i

~

02

I 0"4

f

i

I

0"6

O"

F]o. 1.---Correlation of St and ApK with I-Iammett's a-factor for 1 : 2 complexes of silver with pyridine derivatives.

F i g u r e 1 shows the c o r r e l a t i o n s o b t a i n e d b e t w e e n A p K and Sf versus o. T h e g o o d n e s s o f the fit in the l a t t e r case c a n b e j u d g e d b y calculating the c o r r e l a t i o n coefficient r, defined b y X(x

=

-

-

y)

Zxy - X x . Xy/N { ( Z x 2 - - (Xx)S/N) (Xy 2 -- (Xy)S/N)}}

where ~ a n d ~ are the m e a n values o f x a n d y a n d t h e s u m m a t i o n s are e x t e n d e d to all pairs (x, y ) available. T h e c a l c u l a t e d value o f r is r = 0.995 a n d the theoretical one, for N = n - - 2 = 9 degrees o f f r e e d o m , is r = 0.847 a t the

132

J.J.R.

FRAUSTO DA SILVA and J. GON~ALVES CALADO

99.9 per cent level of significance, implying that there is a very high probability of a linear relationship. The really surprising fact about Fig. 1 is, however, the positive sign of the slope p' in the plot S 1 vs. a, contrary to what happens with p for the relation ApK vs. a, which is negative as usual. In this case p' has the value p' = 4.718 as calculated by the least squares method. Since p' measures the susceptibility of the reaction to changes in the substituents, a positive value can only mean that the reaction studied is favoured by electron withdrawal from the nucleus and thus the stabilization measured by the parameter S1 is due to back-donation of d-electrons of the metal to anti-bonding orbitals in the ligand to form ~r-bonds.

6

4

Sf 2

<1 o

o

o

-4

-6

I

I -- 0"2

I

t 0

r

I 02

I

r 0-4

I

I 0"6

I

I 0"8

[

I I'0

I

r 12

1

o"

FIG. 2.--Correlation of St and A p K with Hammett's a-factor for 1:2 complexes of silver with substituted anilines.

This was already predicted by MURMANNand BASOLO(7) on a qualitative basis, but it is now demonstrated as a consequence of the inverse correlation with Hammett's (rfactor.

Silver complexes of substituted anilines Substituted anilines are also expected to behave as weak rr-acceptors, and this may be tested using the data available for silver-substituted aniline complexes. (1~) Table 2 records the steps of the calculation; data presented for pKaL were obtained from ALBERTand SEAR~A~rr's book. (2°) Figure 2 shows again a reasonably good correlation of S t with o. The calculated value of p' is p' = 2-166 t19~ L. A R ~ N U and C. LueA, Z. Phys. Chem. 214, 81 (1960).

cx) A. A[.B~T, E. P. S ~ J ~ ¢ r ,

Ionization Constants o f Acids and Bases. Methuen, London (1962).

Stability constants of metal complexes with Hammett's a-factor

133

(least squares method) and the correlation coefficient r is r = 0.990 which compares favourably with the theoretical value r : 0"925 for N : n -- 2 = 6 degrees of freedom at the 99.9 per cent level of significance. Again the complexes are shown to be stabilized by 7r-bonding from the metal to the ligand, although this effect is less pronnounced than in the previous example. In fact p' is less than half the value found for the silver pyridine complexes, which means that the reaction of silver with substituted anilines is not so severely affected by substitution in the ligand. TABLE2.--SILVER COMPLEXESOF SUBSTITUTEDANILINES Substituent

pKaL

ApKaL

Nil m-CHs /7-CHa m-NO~ /)-NO2 m-C1 p-C1 p-I

4"58 4"69 5.12 2.50 1"02 3"34 3"98 3"78

0 + 0"11 +0"54 --2"08 --3"56 --1"24 --0"60 - 0-80

log flM~,~ 3.07 3"63 3.86 1-88 1 "55 2"13 2"65 2"50

log Kr, --6.09 - 5-75 -6"38 --3.12 --0"49 --4"55 --5"31 - 5"06

$I

a

0 + 0"34 --0"29 +2"97 + 5"60 +1"54 +0"78 + 1 "03

0 --0-07 --0.17 +0"71 + 1"26 +0.37 +0-23 + 0" 18

Copper (11) complexes of substituted benzoic acids This is the only example quoted in the literature when an inverse relationship of Log Km~ with Hammett's a-parameter has been found, cm Tables 3 and 4 summarize the calculations made according to the method now proposed. Figure 3 shows again an excellent correlation between the parameter S I for 1 : 1 and 2:1 complexes and a-values determined by MAY and JONESfor 50 per cent aqueous dioxane medium in which stability constants were measured, ill) The trends obtained are similar to those found before, with P'ML =

1"544

and

P'Mr,2= 1"235 as calculated by the least squares method. The correlation coefficients are respectively rm~, = 0.998 rMT,2 = 0"999 to be compared with the theoretical value r = 0"725 for N = 15 degrees of freedom, at the 99-9 per cent level of significance. These results are of course consistent with the hypothesis of stabilization of the complexes by back donation of electrons from the metal to the ligand, as was also suggested by MAY and JONES.(11) Their alternative explanation, based upon the effect of a possible breakdown of polymeric forms of the earboxylic acids does not seem likely in view of the previous and following examples.

134

J.J.R.

FRAt~STODA SILVA and J. GONqALVESCALADO

/

2"4

210

1"6

1"2

0"8

~

0.4

-0-4

-0-8

-I-2

-I.6 I

i

-- 0 ' 4

l~t

-- 0 ' 2

r

0

r

r

0'2

i

,

0.4

I

I

'

0.6

[

0.8

I

r

I'0

Flo. 3.--Correlation of N/and ApK with Hammett's ~-factor for 1 : 1 and 1: 2 complexes of copper 0I) with substituted benzoic acids. TABLE 3.---C~PPER ([l) COMPLEXESOF SUesr~xUEt) BENZOICACIDS: 1 : 1 COMPLEX~ Substituent

pKnr.

ApKnz

Nil m-F p-F m-Cl p-Cl m-Br p-Br m-I p-I m-t-C4H9 p-t-C,H9 m-OH p-OH m-NOz p-NOs p-OCI-I, p'CHs

5"79 5.40 5'42 5"48 5"19 5.32 5'59 5"40 5.28 5-67 5.63 5.85 6.03 4.92 4"78 6"12 6"12

0 --0-39 --0.37 --0-31 --0.60 --0.47 --0.20 --0"39 --0.51 --0"12 --0.16 ~- 0"06 +0.24 --0-87 -- 1"01 +0"33 ÷0"33

log KMT. 3'91 4"14 4.15 4"08 4.20 4.11 4-00 4"15 4.23 4-00 4.11 3-88 3.78 4.40 4"43 3"71 3"78

log KT. -- 1"88 --1.26 --1.27 --1.40 -0.99 --1.21 --1.59 --1.25 --1.05 --1.67 --1"52 -- 1.97 --2"25 --0"52 --0"35 --2"41 --2"34

St 0 +0"62 +0"61 -[-0.48 +0"89 +0.67 +0"29 +0"63 +0.83 +0"21 +0"36 --0.09 --0.37 + 1-36 + 1"53 --0"53 --0"46

0 +0"39 +0"37 +0-31 +0-60 +0"47 +0"20 +0"39 +0.51 +0"12 +0.16 --0.06 --0.24 +0-87 + 1"01 --0"33 --0"33

Stability constants of metal complexes with Hammett's a-factor

135

TAnLE 4.---C~PPEa (LI) COMPLF.XF~O1~ SUBSTITUTEDnENZOIC ACIDS" 2:1 CO~,~'LEXES Substitucnt

pKnT.

ApKHz

log K ~

Nil m-F p-F m-Cl p-Cl m-Br p-Br m-I p-I m-t-C4I-I~ p-t-C4H9 m-OH p-OH m-NOs p-NOi p-OCH, p-CHa

5-79 5-40

0 --0.39 --0.37 --0.31 --0.60 --0-47 --0-20 --0.39 --0.51 -0.12 --0.16 +0.06 +0.24 -- 0.87 1"01 +0"33 -0"16

3.65 3.78 3"81 3.76 3.90 3.85 3.70 3.81 3.90 3.65 3.78 3.57 3.48 4.11 4"11 3"42 3"48

5"42

5.48 5.19 5.32 5.59 5.40 5.28 5.67 5.63 5.85 6.03 4.92 4.78 6"12 6"12

-

-

log KL --7.93 --7.02 -- 7"03 --7.20 --6.48 -6-79 --7.48 --6.99 -6.66 -7.69 --7.48 --8"13 --8"58 - 5.73 -- 5"45 -8"82 -8"76

St

a

0 +0.91 +0.90 +0.73 + 1.45 + 1.14 +0.45 +0-94 + 1.27 +0.24 +0.45 --0.20 -0.65 + 2.20 + 2"48 -0"89 -0"83

0 +0.39 + 0"37 +0.31 +0-60 +0.47 +0"20 +0.39 +0.51 +0-12 +0.16 --0.06 -0.24 + 0.87 + 1"01 -0"33 --0"33

Substituted pyridine adducts of copper (II)-acetylacetonates This is one o f the cases w h e n no o b v i o u s c o r r e l a t i o n o f stability c o n s t a n t s with the electron releasing o r w i t h d r a w i n g n a t u r e o f t h e substituents has been f o u n d ;(1~) it differs f r o m t h e previous cases in t h a t t h e r e a c t i o n center is n o t the m e t a l a l o n e b u t

J

-41

-6 [

I ~ -0-6

] -04

I

[ -0.2

I

~1 0

I 0.2

[

i 04

i

I 0-6

I

o"

FIo. 4.---Correlation of S t and ApK with Hammctt's ~-factor for substituted pyridine adducts of Copper (ID acctylacetonates. a definite c o m p o u n d , c o r r e s p o n d i n g to the f o r m u l a Cu(CsH70~) 2. This is a p l a n a r c o m p l e x a n d ff one t a k e s this as the x y p l a n e the f o r m a t i o n o f a d d u c t s with p y r i d i n e bases involves at least a n i n t e r a c t i o n with the d~, o r b i t a l o f the m e t a l to f o r m a ~-bond. T a b l e 5 s u m m a r i z e s the calculations r e q u i r e d b y o u r m e t h o d , a n d Fig. 4 shows

136

J . J . R . FRA0SrO DA SILVAand J. GON~ALWSCALADO

again a very good correlation of the same sort as before, with p' = 5.780 As usual, we have calculated the correlation coefficient r = 0-997 for comparison with the theoretical value r = 0.925, for six degrees of freedom at the 99.9 per cent level of significance. This indicates dative metal-to-ligand rr-bonding, which must involve the d~¢ or the dez orbitals of the metal. The pyridine bases have then a definite orientation relative to the plane of the acetylacetonate complex, a result which may be significant for the interpretation of certain reactions of coordinated ligands. This example is perhaps the best demonstration of the correctness of our treatment which provides a remarkably good correlation, when the usual direct approach is quite inconclusive. TABLE 5.--SUBSTITUTED PYRIDINE ADDUCTS OF CU ( LI) ACETYLACETONATES

Substituent

pKaT,

ApKar,

Nil 3-CHs 4-CHs 4-Cl 3-Br 3-CN 3-CHsCO 4-C6H5CO

5'21 5-67 6"03 3"83 2"85 1'35 3"18 2"68

0 4-0"46 4-0-82 -- 1"38 --2"36 --3"86 --2.03 -2"53

log KK~. 0.94 0.78 1.04 0"75 0-70 0.83 1"01 1"26

log K~.

SI

a

--4.27 --4.89 -- 4"99 --3.08 --2"15 --0.52 --2.17 - 1"42

0 --0"62 -- 0"72 4.1"19 4,2"12 4--3-75 4.2"10 +2'85

0 --0.08 -- 0.14 4"0"23 4-0"39 4-0.64 4-0"38 4-0"46

Substituted pyridine adducts of Fe (II)-mesoporphyrine complexes The results obtained in the previous example suggest that similar behaviour may be found in other planar systems, some of which are of considerable biological significance. Data obtained by Low~ and PmLLIVS for some substituted pyridine adducts of Fe (II)---mesoporphyrine complexes, c21~ easily transformable to stability constants, prompted a comparison in the basis outlined in the present paper--Table 6, Fig. 5. A very definite correlation is again obtained while very little could be concluded by direct examination. The value of p' is p' = 6.560 and that of the correlation coefficient is r :- 0.996 For the 99.9 per cent level of significance and N = 7 -- 2 degrees of freedom, theoretical r is 0.951, showing a quite high probability of a linear relationship. Hence, the formation of such adducts is indeed stabilized by ~r-bonds, and furthermore the reaction is very sensitive to this effect, judging by the high value of p'. tll~ M. B. LowE and J. N. PHILLIPS.Unpublished c.f.J.E. FALKand J. N. P~LtaPs, Co-ordination Chemistry of Pyrrole Pigments, in ChelatingAgents and Metal Chelates, (Edited by F. P. Dw~R and D. P. MELteR)pp. 458, 464. Academic Press, New York (1964).

Stability constants of metal complexeswith Hammett's a-factor

137

Although this is not a system found in living species, its similarity to natural haemoglobin should not be overlooked. Haemoglobin, the oxygen-transporting pigment in the blood of all vertebrates, is the ferrous complex of protoporphyrin (haem) combined with a protein component (globin). The linkage between the two units is believed to be effected by coordination of the iron atoms with donors in the globin component, namely the nitrogen atoms of the iminazole residue of histidine, c~) Since

xo. O

<3

-10

I -0.75

I -050

I -0-25

I 0

I 0.25

I 0.50

I 0.75

FIo. 5.---Correlation of Sl and ApK with Hammett's t~-factorfor substituted pyridine adduets of Fe (II)-mesoporphyrine complexes. TABLE 6.--SUBSTrrUTED PYRIDINE ADDUCTS OF F E (II) MESOPORPHYRINE COMPLEXES

Substituent

pK~L

ApKar.

Nil 3-NH2 4-NH~ 3-CN 4-CN 3-CHs 4-CHa

5-21 6.04 9"12 1"35 1"86 5-67 6"03

0 +0"83 +3"91 --3"86 --3"35 +0.46 +0"82

log flML2 4"6 4"2 4'0 5"1 5"8 5"2 5"5

log K~

S1

tr

--5"8 --7"9 -- 14"2 +2"4 +2.1 --6.1 --6"6

0 --2"1 --8"4 +8'2 +7"9 --0"3 --0"8

0 --0"14 --0"65 +0"64 +0"55 --0"08 --0'14

the iminazole nucleus is also a ,r-acceptor, it is to be expected that these bonds are stabilized mainly by back donation of d-electrons of the ferrous ion to anti-bonding orbitals of the ligand, similarly to the several examples discussed in the present paper. This agrees with the views expressed by LOWE and PHILLIP#zl) and means that the iminazole nucleus must have also a quite definite orientation relative to the plane of the haem unit (xy) since either the d~ or the d,, orbitals will be involved in bonding. The discussion is, of course, outside the scope of the present paper, but it should be emphasised that the results obtained may help to explain the stereochemistry and mechanisms of reactions of other equally important systems of biological significance. t~ cf. E. H. RODD, Chemistryof Carbon Compounds,p. 1130. Elsevier, Amsterdam (1959).

138

J.J.R.

FRA0STO DA SILVA and J . GON(~ALVl~ CALADO

CONCLUSIONS The examples above show the generality of the present approach and its superiority over other methods. Only in one case was it found not to apply: that of Fe (III) complexes of substituted phenols. (~) Since Fe (III) is not a ~r-donor, one wouldn't expect a similar correlation. Some reasons may however be advanced for this fact, because not even for the phenols themselves is a normal correlation possible with the'values quoted, c~) Phenols sometimes behave abnormally a6) and this is probably one of the cases when they do. More data is however necessary to clear up this point. Besides providing a mean of"detecting" the occurrence of ~r-bonds by measurements of stability constants, and consequently allowing a fair prediction of the structure of the complexes, the method now proposed has also another advantage. Indeed, g' is a direct measure of the susceptibility of the reaction to change in substituent. Now if the ligands are kept the same and the metal is varied, the p' obtained for each metal will also measure their tendency to donate d-electrons. This problem, which has so far eluded a convenient solution will be dealt with in a future paper. (N) K. E. JAI)ARI)URVALAand R. M. MILBURN, Proceeding of 8th International Conference Coordination Chemistry, p, 349. Wien (1964).

on