Chelate Ring Size and Metal Ion Selection The Basis of Selectivity for Metal Ions in Open-Chain Ligands and Macrocycles Robert D. Hancock Centre for Molecular Design, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa
Chelating ligands and the chelate effect (I)have been known for a long time. The chelate effect is covered in a wide selection of texts (2) on inorganic and general chemistry, as is also the more recent macrocyclic effect (3). In this paper the focus is on the thermodynamic aspects of the chelate and macrocyclic effects. The thermodynamic chelate effect for a n n-dentate chelating ligand refers to the thermodynamics of the reaction where the chelating ligand replaces n unidentate analogues: M(unidentate)*+ chelate 2M(che1ate)+ rammidentate The thermodynamic macrocyclic effect refers to the thermodynamics of the reaction where the open-chain ligand is displaced by its macmcyclic analogue:
Modem texts attempt to cover a vast field of literature. In a n area that may be considered mature by writers of texts, changes in thinking may take some time to diffuse from more specialized research articles to such texts. Thus, the effect of size of chelate ring on complex stability generally (2) is dealt with in terms of the Schwarzenbach (1)model, which requires the decrease in complex stability that occurs on increase of chelate ring size from five membered to six membered to be an entropy effect, when it is (4) in all cases an enthalpy effect. Amore recent interpretation (4,5) of the effect of chelate ring sizeis thus quite different from that which appears in standard texts, and a t the same time much more interesting. In particular, more recent ideas offer (4,5) the opportunity of utilizing chelate
Table 1. Thermodynamics of Complex Formation
(a) For EN (Ive-membered chelate rmgj and TN sx-memberwchelate rmgd
Metal complexb ion Cu(ll)
ML
Cu(ll)
ML2
Ni(ll) Ni(ll) Cd(ll)
ML MLz ML
Cd(ll)
ML2
TN
EN
log K
AH
AS
kg K
AH
AS
10.48 -12.6 19.57 -25.2
6
9.68 -11.4
6
5
16.79 -22.4
2
7.33 -9.0 13.41 -18.3 5.42 -6 9.60 -13.3
3 0
6.30 -7.8 10.48 -15.0 4.47 5
3 -2 4
7.18 -10.0
-1
5 -1
(b) Of EDTA (five-memberedchelate ring involving both Ndonors)
compared with TMDTA (six-membered ring involving both N-donors)' TMDTA
cu2+
0.57
18.70
-8.2
18.82
-7.7
pb2' 1.18 17.88 -13.2 38 13.70 4 . 4 41 'Unitslor H are kcalmor', for S are cabdeg-'mor'. Data from reference 9, at 25 '6.ionic strength 0.1. '~orthecornplexindicated as ML, log Krefersto the euuilibrium M+LZM
and lor the complexes indicated as M b , log Krefen to the equilibrium M + 2L 2 ML2. 'Unitsfor H are kcalmor', for S are cal.deg-'mar'. Data from reference9. %nits are A. from reference 27.
AAAA
NH2 NH NH
NH
NHp
TETREN
"QN'NANf-h2
4 CNH. PENTEN
Figure 1. Ligands discussed in this work Volume 69 Number 8 August 1992
615
chelate ring size, and metal ion radius (10)can be seen in Figure 2. In Figure 2 is shown a plot of Alog K, where Alog K is log K, for the EDTA complex of each metal ion minus log KI for the TMDTA complex, versus metal ion radius. The plot is limited to divalent metal ions to avoid cluttering, and all radii are for octahedral metal ions, except for a few cases such as Cu(I1) where the radius for square planar coordination is used. Figure 2 shows that as the metal ion becomes larger, so thedrop in complex stability becomes larger on increase of chelate ring size. This result is quite general (4-6) in inorganic chemistry. In the next section an explanation for this effect is sought.
IONIC RADIUS
(A)
F gure 2 Plot d change in format~on wnstam, log K. on Increase of chelate nng stze from f ve membered to SIXmemberw, versus lonlc rad us (27) of melal on, (A) fora par of opencha~nlhgands (0).and (€3) for a par of macrocycles (0) The value of log K tor tne opencnam ligands 1s log K, forthe TMDTAcomp exes m nLs log K, for tne EDTA complexes (A), wh~lefor rhe macrocvcles I is 04 K, for tne ICaneN, complex'esminus log K, for the 12-ane~,complexes.The relations hi^ shows that the factor controllino the metal ion size base selectivity bf open-chain ligands and macrocycles is essentially the same, namely the size of the chelate ring. Data from reference 9.
ring size to control ligand selectivity for metal ions on the basis of their size (6). Interest in ligand design has increased in areas ranging from design of imaging agents (7) to detereents (8). . .. so that it should be Dart of a modern course on inorganic chemistry. In this paper are presented recent ideas (4-6) on chelate rine size and com~lexstability, and how chelate ring size c>ntrols the selectivity of both open-chain and macmcyclic ligands. Finally, there is a brief discussion of some other ideas about the chelate and macmcyclic effeds to be found in modern texts.
-
The Effect of Increase of Chelate Ring Size on Complex Stability. Is it an Enthalpy or an Entropy Effect? In Table 1are shown the free energies, enthalpies, and entropies of complex formation of some complexes of EN (see Fig. 1 for key to ligand abbreviations) which forms five-membered chelate rings on complex formation, and of TN,which forms six-membered rings. Also shown are the thermodynamic parameters associated with complex formation for EDTA (five-membered chelate ring involving the nitrocen donor atoms) and TMDTA (six-membered ring invoiving the nitrogen donors) complexes. For these complexes, and all others (9)that the present author has examined, the decrease in complex stability caused by increase of chelate ring size from five to six membered is an enthalpy cffeci. Morcovcr, the decrease in complex stability is stmngly related to metal ion size ( 5 1 ,such that larger metal ions show luwer decreases in comolex stabilitv on increase of chelate ring size. Just how exact the relation is between the decrease in complex stability on increase of
-
616
Journal of Chemical Education
The Geomet of the Chelate Ring, and ~ r e f e r r e y ~ e tIon a l Sizes One can readily understand why change of chelate ring size from five membered to six membered results in an increase in complex stability for small metal ions relative to large metal ions, by reference to the low-strain chair form of cyclohexane (11).Cyclohexane, seen in Figure 3, has in its chair wnformer the minimum strain energy possible for a cycloalkane. All torsional angles are 60', and the C-CC angles are all the ideal value of 109.5'. By comparison, the six-membered chelate ring involving the TN ligand will be similar in geometry to cyclohexane, and also will be of very low steric strain, as long as the metal ion is about the same size as an sp3hybridized carbon atom. The ideal metal ion for coordination to TN thus has a n M-N bond length of 1.6 A, and a N-M-N angle of 109.5'. In wntrast, for the fivechair form of cyclohexane minimum energy
-
d l DOC
A
BlTE SIZE IN FIVEMEMBERED RINGS
cyclohexane
BITE SUE IN SIXMEMBERED RINGS
ideal geometry for ideal geometry for six-membered ring five-membered r i n ~ Figure 3. The low strain chair form wnformer of cyclohexane (A), and how this relates to minimum strain energy forms of the chelate ring with respect to the M-N bond length and N-MN bond angle, for (€3) a five-memberedchelate ring involving EN, and (B) a six-membered
Table 2. me Relationship between Chelate Ring Size, Metal Ion Size, and Complex Stability, for Complexes with ~ i v e - a n dsix-Membered chelate Flings ionic radius
ox
ma1
5
6
trop
acac TIRON CTA
(4"
chelate ring size:
5
6
5
6
log f i forb; Be(li): 0.27
4.96 6.18 7.40 7.90 14.6 16.3 6.23 5.80 9.23 8.25 15.6 15.9 Pb(ll): 4.20 3.98 7.54 4.71 14.8 13.0 "Ionic Radii (A) fmm reference 27. b~ormationmnstants from referenca 9,at 25 OC and ionic strength = 0.
Cu(ll):
0.57 1.18
membered chelate ring, the loae pairs on the nitrogens of EN focus on a point some 2.5 A away, creating a N-M-N bond angle of 69'. For both five- and six-membered chelate rings, there is (11)a rapid rise in strain energy as the metal ion departs from the ideal size and geometry. This simple analysis indicates that six-membered chelate rings will be of lowest strain with small metal ions of low coordination number, creating a large N-M-N angle. Fivemembered chelate rings will do best with large metal ions, of high coordination number, which creates a small N-MN bond angle. One can, thus, account for Figure 2 quite simply in terms of the ideas in Figure 3. The arguments here about chelate ring size have been couched in terms of the diamines EN and TN, but it is evident that the arguments also apply equally well if the donor atoms are oxygen, for example, or the coordinated ligands are planar as in acetylacetone (Acac) and tropolone (tmp) rather than being nonolanar as in EN and TN. A question might occur to the reader here. It is commonly stated in cxtbooks that six-membered chelate rings lead to less stable complexes than five-membered chelate rings,without any quaiification. Does not the analysis in
Figure 3 require that the complexes of smaller metal ions be more stable with six-membered t h a n with fivemembered chelate rings? The answer to this is that most metal ions commonly studied are not small enough to satisfy the requirements of the six-membered ring. Thus, the Cu-N bond l e n m for the small square planar Cu(I1)ion is (11)about 2.03 A, considerably longer than the 1.6 A required for strain-free coordination in a six-membered chelate ring. However, the small Be(I1) and B(II1) give very short M-L bond lengths, and here one finds a ready explanation for the greater stability of the complexes of these Lewis acids with a variety of six-memberedligands as compared with the five-membered chelate ring analogues, as seen in Table 2. For the very small B(II1) ion the complex with CTA (chromotropic acid) is also considerably more stable than that with TIRON (9). Chelate Rings Larger Than Six-Membered For chelate rings larger in size than six-membered, it does appear (9)that there is a considerable contribution from entropy to the further decreases in complex stability that occur, and, as would be expected for a ligand related entropy effect, the decreases are not dependent on metal ion size. This type of effect is seen for the tetraaza macrocycles in Figure 4 which, starting with 12-aneN4, have one chelate ring increase steadily in size from five membered through to eight membered. Figure 4 would suggest (12) that chelate ring sizes beyond six membered
- .
I 5
6
7
8
Chelate Ring S i m Figure 4. The effect of increase of chelate ring size beyond six membered on thermodynamic complex stability,illustrated by change in log K, for complexes of tetraaza macrocycles as one chelate ring becomes progressively larger. Redrawn after reference 12.
Figure 5. Three commonly found conformers of complexes of tetraaza macrocycles. The open circles are the N-H hydrogens. while the black spheres are other mordinated donor atoms, such as those of salvent molecules. Volume 69 Number 8 August 1992
617
are of little value in generating metal ion size-based selectivity.
rings, where preference for small metal ions should result.
This is what is observed in the followingtwo examples:
The Implications for Macrocyclic Ligands
The idea about selectivity in macrocycles presented in most inorganic texts is that of size-match selectivity. In this idea, the most stable complex will be formed by a metal ion with the member of a series of macrocycles where the match in ionic radius, and the cavity of the metal ion, is closest. A detailed molecular mechanics analysis of selectivity in the tetraaza macrocycles (13) has shown that these ligands are much more flexible than might be imagined. Thus, at least three conformers, the trans-I, trans- 111, and cis-V, shown in Figure 5, are of comparable energy, but favor different size metal ions. Thus, in particular, for larger metal ions, the trans4 conformer favored has the metal ion coordinated in an oubof-plane POsitwn. In this situation, the factors that govern sklecti;ity are very similarto those in open-chain ligands, namely, the size ofthe chelate ring. The formationconstants ofcomplexes of the tetraaza macrocycles with metal ions of different sizes have thus been rationalized (14) in terms of chelate ring size. As an example, the result that complexes of the very large Pb(I1) ion decreased in complex stability as the size of the macrocyclic ring was increased along the series 12-aneN4through 16aneN4was very puzzling (14). However, with the present insights, this can now be understood in terms of the fact that, although the macrocyclic cavity is getting larger, the five-membered chelate rings are being changed to sjx-membered chelate rings, and a large metal ion such as Pb(I1) does not coordinate well in six-membered chelate rings: ligand: 12-aneN4 13-aneNa 14-aneNn 15-aneNd 16-aneN4 best-fit 1.82 1.92 2.07 2.15 2.38 M-N length: (A, ref 15) 15.9 13.5 10.8 10.5 9.3 2pb(ll)j
12-crown-4 based extractant - no selectivity for Lit.
six-membered chelate rings, selectivity Li*>>Na+'>Kt
small Cu(ll) ion shows increase in log KI with sixmembered chelate ring, large Cd(ll) shows a decrease.
Some Other Aspects of the Chelate Effect
In section A it was shown that changes in complex stability that accompanied the increase in chelate ring size from five membered to six membered were enthalpy controlled, and reflected steric factors. This was in contrast to the Schwarzenbach (I) type of model that predicts that these effects should be entropy effects. In this model the entropy would reflect the lower probability of attachment of the second donor of the chelate ring once the f r s t donor had been coordinated. as the chelate ring became lareer. The evidence (9)ce&inly supports th'idea that thechelate effect is ~redominantlvan entrow effect, and this can be interpreted adequately by the ~awarzenbachmodel. There is, however, a fairly substantial enthalpy wntribution to the chelate effect (41, as seen in the thermodynam-
The SizeSelectiviIy of Crown Ethers
The concept of size-match selectivity is possibly most strongly supported by the formation constants for crown ethers (16), as seen in F i e 6. However, a puzzling feature (17) of crown ether chemistry is that even with the smallest cavities, as in 12-crown-4,the preference, as seen in Figure 6, is still for the large K+ ion. Might this not simply be that the chelate rings formed by virtually all crown ethers are five-membered, and Kt is about the right size and geometry for these rings? One might answer this by looking (6)at ligands which have neutral oxygen donors that are not part of macrocyclic rings. It is found (6) that addition of neutral oxygen donors as 2-hydroxyethyl groups or a s ethereal groups, as shown for EN and THEEN, or EN and HEEN, produces changes in complex stability exactly in accord with this idea. Thus, the relative affinity of ligands for the large Pb(I1) ion relative to the small Cu(I1)ion, increases as successivelymore neutral oxygen donors are added, as seen in Figure 7. As discussed in reference 6, the changes in log K , produced by adding neutral oxygen donors also show linear relationships with ionic radius of the metal ion, exactly like Figure 3, but of opposite slope. Space does not permit a full discussion of this aspect here, but the evidence suggests that a large component of the observed "size-match selectivity" of crown ethers is in reality a selectivity governed by chelate ring size considerations. The test of this idea must come with neutral donors that are part of six-membered chelate 618
Journal of Chemical Education
1.0 1.4 1.8 IONIC RADIUS ( E ) OF METAL ION
Figure 6. The formation constants, log K,, in methanol, of some crown ether complexes of alkali metal ions, plotted against ionic radius (27).The diagram shows that even with the small 12-crown-4 ligand, there is no real shift of selectivity toward the small Lit ion. Data from reference28.
Thus, one must consider that in NH3 complexes there are ics of complex formation for the EN complexes of Cu(I1) zero order nitrogens, while in EN complexes there are priand Ni(II), and their ammine analogues, in Table 3. It is mary nitrogens, which by the inductive effect (19) of the sometimes pointed out (21, without explanation, that ethylene bridge, are stronger bases than ammonia. That Cd(I1) shows no enthalpy contribution to its chelate effect. the enthalpy contribution to the chelate effect is not a There is no mystery in this. In the ammine complex, only property of the free ligand is seen in that it is reflected (4) four ammonias can be coordinated, suggesting that the in a n increase in the ligand field ( L C strength of Cu(I1) complex is tetrahedral; whereas, in the EN complexes, complexes as the number of chelate rings increases: there is a smooth addition of EN ligands until the tris complex is obtained suggesting that the EN complexes of Cd(I1) are octahedral, which is borne out by X-ray studies in solution (18).This unmmth derlines an important point: for meaningful \ comparison, whether in the chelate effect, the macrocyclic effect, or the cryptate effect, the complexes being compared must be of similar structure, and, as discussed later, one complex should not suffer from a considerably greater I" amount of steric strain than another. What is the origin of the enthalpy contribu17000 18300 19000 19900 tion to the chelate effect? It is often suggested u6d(cm-i) (2) that it arises because of electrostatic repulsion bv the donor atoms of unidentate lipands. AH, kcahor': -22.0 -25.5 -27.7 -32.4 whoseunfavorable contribution to compgx for: mation is removed once the donor atoms are Increased LF strength is an indication of greater overlap joined together to form a chelate. This may play a part, in the M-L bond, in accord with the idea that there is an particularly with charged donor atoms, but there is anincrease in donor strength along the series zeroth primary other contribution that is always overlooked. Studies in secondary tertiary for the above amines. The idea of an inthe gas phase show that (19) the order ofbasicity of m i n e s ductive effect contribution to the chelate effect in polyabases containing the saturated oxygen donor and ~~~i~ may be incorporated (21) into a simple equation are ~ J H < N~H ~ R< N H R ~< N& or ~~0< ROH < ~ ~ 0mines . which predicts the formation constants of complexes of t h e polyamines EN, DIEN, TRIEN, TETREN and PENTEN with all metal ions, as seen Table 3. Thermodynamic Contributions to the Chelate Effect in in Table 4. Complexes of Ethylenediamine (EN)with Cu(ll) and Ni(ll)a ",,idenlate complexb
A~
A~
1
chelate
A~
logKd(polyamin4= 1.152 log.(NH,) + (n- 1)log55.5(1)
A~
Analogue
-3 N~(EN)'+ -10.03 Ni(N~s)z'+ 4 . 9 3 -7.8 N ~ ( E N ) ~ ~-18.47 + N ~ ( N H ~ ) ~ " -11.08 -15.6 -15 Ni(NH3)6'+ -12.39 2 4 -39 N ~ ( E N ) ~ ~-24.16 + CU(EN)'+ -14.38 CU(NH~)Z'+ -10.68 -11.1 -1 c ~ ( E N ) ~-26.74 ~+ cu(NH3)4z+ -17,74 -22,0 -14 , in cal.deg-'.mol". 'Data from relerencs 9 G and H are in kcal.mol~'S 'Coordinated watsm lefl off for simplicity.
complexes of lane Pb(ll) ion increase in complex stability
-9.0 -18.3
4 3
-28.0 -13.1 -25.5
-10 6
I n this equation, n is the denticity of the polyamine, 1.152 is t h e inductive effect factor = pKB(CH3NHz)lpK.(NH3), and the (n - 1)log 55.5 term is (21) the entropy contribution to the chelate effect accordina to Adamson's (22) hmothesis regarding the rol;?of choice of standarditate in producing the chelate effect. One should point out that the fact that eqn 1 works so well may be a little fortuitous, since there appears to be (21) some cansuch as steric strain cellation of ~ontributin~effects in the chelating ligands, and some entropic effects in the ammonia complexes. However, the overall contributions to the chelate effect indicated by eqn 1 do appear to be the dominant effects (211, and eqn
-
Table 4. Values for log K1 for Polyamine Ligaands, Observed, and Calculated Using Eq 1 Metal Ion
Fioure 7. The reswnse of the formation constants. ioa K,. of the comsmell Cullll ion. and the laroe ~bfll)iGn. to addition of &xes ~ d - the neutral oxvoen o-f 2-hvd;oxveih;l . ,--donors -- - h'the ~- iorm ,~ ,~, orouos " ~~, or elheral oxygens, to tne EN Igand. The results are typtcal, ana show that small metal ions snow a decrease in complex staoll ry witn sLcn addit ons. wnale large metal Ions show an ncrease. Format on constant aata from reference 9. r~
~
~~
~~
~~
~
~
log Ki
EN DIEN TRIEN TETREN PENTEN Cu(ll) calcd 10.76 15.92 20.20 21.28 obsd 10.48 15.9 20.1 22.8 Ni(li) calcd 7.59 11.33 14.57 17.28 19.16 obsd 7.35 10.7 14.4 17.4 19.1 Fe(ll) calcdb 4.38 6.82 8.67 10.02 10.87 obsd 4.34 6.23 7.76 9.85 11.1 Pb(ll) calcdb 4.92 7.51 9.59 11.18 12.26 obsd 5.04 7.56 10.35 10.5 Observed values of log KI from reference 9. All data at 25 "C and ionic strength 0.1. b ~ o Pb(l1) r and Fe(ll)only log f i for the NHI complexes is known, and higher log BdNH3 constants for use in eqn 1 were estimated as desnibed in reference21.
Volume 69 Number 8 August 1992
619
Table 5. Thermodynamic Contributions to the Macroc~clicEffect in Complexes of Tetraaza ~acrocycles~
Metal Ion:
Cu(ll)
Zn(ll)
Ni(ll)
log KT 14-aneN4 2,3,2-let log NMAC)
26.5 23.2 3.3
19.4 15.9 3.5
15.5 12.6 2.9
2.3,2-tet AS(MAC)
13 0
10 -2
18 3
a Data fmm reference 9, except for log K, for 14-aneN~ with Ni(ll), which is tram reference29.The Ni(1l)data ail refers (4) to high spin Ni(l1).The values of logK(MAC),aH(MAC), and AS(MAC) are the thermodynamics of the macrocyclic effect, and refer to the reaction [M(14- ans~d)]'*+ 2.3.2-tet. [~(2,3.2-let)]~* + leaneN4
Table 6. Thermodynamics of the Cryptate Effect as Illustrated bv Com~arisonof the Ligands BHE-K22 and ~ r ~ p t a n d - 2 , 2 , 2 ~
Metal Ion
Sr(ll)
Ba(ll)
Ag(l)
Pb(ll)
log KI cryptand-2,22 BHE-K22 log K(CRYPT)
8.0 4.0 4.0
9.5 5.3 4.2
9.6 7.27 2.3
12.0 9.2 2.8
This problem is not present in polyamines, for example, where the N-methyl groups of methylamine analogues are replaced by ethylene bridges, which are not sterically hindering to anywhere near the same extent a s N-methyl groups (21). Methylamine is thus from the steric point of view not a suitable unidentate analogue for the polyamines. The Macrocyclic Effect Is It an Enthalpy or an Entropy Effect? One of the first measurements of the enthalpy of complex formation of a tetraaza macrocycle was (23) of Cu(I1) with 12-aneNa. When comparison was made with the openchain 2,2,2-tet, the macrocyclic effect was found to be entirely an entropy effect. This result has suggested that the macrocyclic effect is primarily an entropy effect. The Cu(I1) ion coordinates with very considerable steric strain (11) into 12-aneNc where the trans-I conformer adopted requires that the Cu(I1) lie well out of the plane of the donor atoms, rather than having the preferred planar geometry. One cannot compare a complex of low steric strain, the 2,2,2-let mmplexbf~u(ll,,with onvofhigh steric strain, the 12-aneN~ comoiex, os a hasrs for anoiyzin~ . - the rnacroc.vc/ic, or any oiher &kt, unless such strains are construed as being within the scope of the definition of the macrocyclic effect. Rather (41, complexes of low strain should be sought, and, for the tetraaza macrocycles, the best wmparison appears to he of the Cu(I1) and Ni(I1) complexes of 2,3,2-tet and 14-aneN4,shown in Table 5. This comparison in Table 5 shows the macrocyclic effect to be almost entirely an enthalpy effect, when complexes of equally low steric strain are wmpared. For Zn(I1) there is an entropic contribution to the macrocyclic effect, which may reflect the fact that 14-aneN4is not the best fit for Zn(II), since log KIis higher for smaller tetraaza macrocycles such as 12aneN4. As also seen in Table 5, the cryptate (24) effect is also entirely an enthalpy effect when the best ligands for making this wmparison are selected (25), namely BHEK22 and cryptand-2,2,2. That there are enthalpy wntributions to the chelate effect, and that enthalpy is the major wntributor to the macrocyclic and cryptate effects may he due to inductive effecta as bridging groups are added (5) removal of enforced electrastatic repulsion between adjacent donor atoms once the complex is formed (26) poor solvation of the donor *toms in restricted cavities of the free ligands, particularly of macrocyclic and cryptate ligands
(3).
his in kca mo -1, ASm caldeg-lmoC1 The therrnadynamcq~antttes assoc ated w In tne cryplate effect, log KICRYPT), r\YCRYPT,. an0 AS(CRYPT) refer to the equilibrium [M(BHE-K22)I"+ cryptand-2,2.2 Z [M(cryptand)lo*+ BHE-22. Data for cryptand-2,2,2 from reference 9, for BHE-K22 fmm reference 25. For key to ligand abbreviations,see Figure 1.
1presents a useful simple interpretation of the chelate effect. Afurther point here is that one may ask why it is necessary to correct for the inductive effect factor in eqn 1by use of the pK. of C&NHa. Would i t not be more appropriate to use the formation constants of the C&N& complexes, which would then have the wrrect inductive properties? The answer (21) to this is that the N-methyl group causes a great deal of steric repulsion with adjacent coordinated ligands, particularly other N-methyl groups. 620
Journal of Chemical Education
The inductive effects are evidenced in complexes of nitroZen donor macrocvcles bv the verv hieh (5)LF streneths as compared to the Apen-chin anzoGes, provided t
