161
Limitations of Mn(ll) Selective Broadening in NMR
i e
7
16
-
2o
ties. In this regard the pronounced effect of formamide at low concentrations is a special feature. At high concentrations it is less effective than either methanol or glycol (see Figure 4). All these results adjudicate a complex analysis when aprotic solvents are used. Further experiments are needed for a meaningful dissection.
-
I I
14-
12
-
Acknowledgment. The authors extend their thanks to Professor M. N. Das, Head of the Physical Chemistry Section, for laboratory facilities.
4
g -
10-
I
08
-
06
-
References and Notes
04-
02-
1 0
I 0.01
002
003
004
005
(1)S.P. Moulik, A. K. Chatterjee, and K. K. Sen Gupta, Spectrochim. Acta, Sect. A, 29,365 (1973). (2)S . P. Moulik, A. K. Chatterjee, and K. K. Sen Gupta, Ind. J. Chem., 12, 92 (1974). (3)G. Akerlof, J. Am. Chem. SOC.,54, 4125 (1932). (4)P. Rohdewald and M. Moldner. J. Phys. Chem., 77, 373 (1973). (5)J. Wyman, Jr., J. Am. Chem. SOC.,55, 41 16 (1933). (6)K. K. Kundu and K. Majumdar, J. Chem. SOC., Faraday Trans. 1. 69, 806 (1973). (7)E. H. Lane, S. D. Christian, and J. D. Childs, J. Am. Chem. SOC.,96,38 (1974). (8)J. L. Ernst and J. Manashi. Trans. faraday SOC..59, 230 (1963). (9)J. W. Smith, J. Chim.,Phys.,58, 182 (1964). (lp)R. M. Scott and S. N. Vinogradov, J. Phys. Chem., 73, 1890 (1969). (11) S. N. Vinogradov, R. A. Hudson, and R. M. Scott, Biochim. Biophys. Acta, 214, 6 (1970). (12)G. C. Pimentel and A. L. McClellan, "The Hydrogen Bond", W. H. Freeman, San Francisco. Calif., 1960. (13)E. M. Arnett, E. J. Mitchell, and T. S. S.R. Murty, J. Am. Chem. SOC., 96, 3875 (1974).
Limitations Concerning Use of Manganese(II) Selective Broadening in Nuclear Magnetic Resonance Spectroscopy for Determination of Ligand Binding Sites William G. Espersen and I?.Bruce Martin' Chemistry Department, University of Virginia, Charlotfesville, Virginia 2290 1 (Received July 3 1, 1975) Publication costs assisted by the National Science Foundation
From comparison of proton and carbon-13 spin-lattice and transverse relaxation times in the presence of Mn(II), it is concluded that in many cases the dipolar term is not the dominant contribut'or to line broadening. Hence selective broadening experiments to determine the site of Mn(I1) binding to small ligands based on an r6dependence between Mn(I1) and the affected nucleus are not generally applicable. Binding sites and distances may be estimated from selective TI measurements, but in this case it must be established that the predominant dipolar interaction contributing to relaxation is that between the paramagnetic ion and the affected nucleus and that other, closer interactions from unpaired spin density on the ligand do not contribute importantly.
Sites of Mn(I1) binding to molecules such as nucleic acid bases, nucleosides and their phosphates, histidine and derivatives, and other amino acids and peptides have often been characterized by selective broadening of resonance lines in nuclear magnetic resonance spectroscopy due to
hydrogen and carbon-13 atoms that are near to the presumed metal ion binding site. I t is the purpose of this paper to assess the validity of selective broadening results with Mn(1I) on a variety of small ligands. Previously we have shown that there are severe limitations to use of selecThe Journal of Physical Chemistry, VOI. 80,NO 2, 1976
162
William G. Espersen and R. Bruce Martin
tive broadening with Cu(II);lp2 this paper reports a parallel study with Mn(I1). Implicit in identification of metal ion binding sites by selective broadening experiments are two assumptions. In the first, the paramagnetic ion induced line broadening which is proportional to the inverse transverse relaxation time in , given only by the presence of paramagnetic ion, T ~ p - l is the first term in parentheses in eq 1 so that the fast exchange limit appliesa2-4
+
T2p-l = p q ( T 2 ~ - ' T M A W M ~ )
(1)
In eq 1,p is the ratio of molar concentrations of paramagnetic ion to ligand (typically or less), q is the average number of ligands bound in an identical way, T ~ is Mthe transverse relaxation time of the bound ligand, T M is the mean lifetime of a ligand bound to the metal ion, and AWM is the chemical shift between bound and unbound ligand resonances. When the second term in eq 1 is dominant, the intermediate exchange limit applies and the information required from T ~ M -is' lost. For other restrictions involved in eq 1see ref 2-4. In the second assumption, the inverse transverse relaxation time for a nucleus on the bound ligand is given only by the first or dipolar term in eq 2, while the second or scalar term is negligible.2-4
T ~ M=-7 ~ a ~ , r ' -+~ bA2re
(2)
+
In eq 2, a = yr2g2/32S(S 1)/15, T~ is the correlation time modulating the dipolar interaction, r is the distance between the paramagnetic ion and the measured nucleus, b = S(S 1)/3h2, A is the scalar or hyperfine coupling constant, which is generally different for each ligand nucleus, and is the correlation time modulating the scalar interactions. Only when the first or dipolar term of eq 2 dominates does the r-6 dependence appear and furnish the basis for stating that lines from nuclei nearest to the paramagnetic ion are most broadened. In order for a selective broadening experiment to designate the site of paramagnetic metal ion binding to a ligand, only the first terms of both eq 1 and 2 should be dominant. Not only must the fast exchange limit apply, but the dipolar term should exceed the scalar term. A test for dominance of these two terms is to compare the value of T2p-l determined from line broadening to the spin-lattice relaxation time due to the paramagnetic ion, Tlp-l, obtained from pulsed NMR experiments. There is no intermediate exchange region for Tlp-l, and the scalar term is almost always negligible so that
+
Tp-1 = pqT1M-l = pq6as,r6
(3)
Combination of the first terms of eq 1 and 2 with eq 3 yields
Tlp/TZp = 716 = 1.17
(4)
Equation 4 is valid only for predominance of the dipolar term in the fast exchange limit. Values greater than 716 for the ratio of eq 4 indicate that the fast exchange limit of eq 1 is not attained and/or that the dipolar term of eq 2 is not predominant. In the fast exchange limit, 50% dipolar and 50% scalar contributions to T ~ M -yields ' T I P / T S= P 713 = 2.33. Thus ratios greater than 2.33 indicate that the dipolar term is no longer the dominant contributor to paramagnetic ion induced line broadening.lp2 A 2:l dipolar to scalar contribution yields T1pIT2p = 714 = 1.75. Hence, the ratio The Journal of Physical Chemistry, Vol. BO, No. 2, 1976
need not be much greater than 1.17 for the scalar term in eq 2 to be significant. The main paramagnetic metal ion considered in this paper is Mn(I1). For complexes of Mn(I1) the inverse scalar correlation time is nearly equal to the inverse electron spin - lo8 ~ sec-l. Since the ligands relaxation time, T , - ~ = T ~ = studied were small, the inverse dipolar correlation time is nearly that of the inverse rotational correlation time of the complex T , - ~ N T R - ~= 1O1O sec-l.
Experimental Section High quality commercial ligands were prepared in D2O solvent a t concentrations of 0.1-0.5 M for the proton and 2 M for the carbon-13 experiments. Carboxylic acid ligands were about 75% ionized, amine ligands about half-neutralized, and amino acid ligands had their amine half-neutralized. Magnetic resonance experiments were performed at 23.5 kG on a JEOL PFT-lOOP/EC 100 FT-NMR spectrometer. Relaxation times in presence of paramagnetic ion were calculated from Tip-' = ( T 1 p - l ) ~" (Tip-')o where the terms on the right are the inverse spin-lattice relaxation times with and without Mn(II), respectively, and
T2p-' = X ( Whin - Wo) where W M and ~ WOare the full line width in Hz a t halfheight with and without Mn(II), respectively. T1 values were measured accurately (&lo%)with a 180°-~-900 pulse sequence and calculated by an external least-squares fit program. Linear first-order plots indicated exponential decays. Other details have already been supplied elsewhere.2 When T p / T z p is near 716, the ratio may be difficult to determine accurately due to the lack of significant broadening.
Results Table I lists inverse spin-lattice and transverse relaxation times for hydrogen and carbon-13 nuclei determined for each nucleus on a single solution for a series of ligands in the presence of Mn(I1). Representative [Mn2+]/[ligand] ratios for a single experiment are also presented, but experiments were performed over a range of Mn(I1) concentrations. Ratios of T1p-l or T2p-l to [Mn2+]/[ligand]reveal the sensitivity of the two inverse relaxation times to Mn(I1) concentration. Thus, for a specified amount of Mn(II), lesser broadening (T2p-l) occurs for the unidentate carboxylates than for the other ligands in Table I. Imidazole was studied with four paramagnetic divalent first row transition metal ions and the results are shown in Table 11. In addition to the T1p/T2p ratios for each metal ion for protons and carbon-13, Tlp-l and the scalar coupling constant, A , are tabulated for the ratio of the nucleus at the 2 position to the average of the two nuclei a t the 4 and 5 positions. The scalar coupling constant ratios were evaluated by assuming the fast exchange limit in eq 1 and combining with eq 2 and 3 to obtain T2p-l = 7Tlp-'/6
+ pqbA2Te
from which A ratios may be calculated.
Discussion More than half the ligands of Table I exhibit T ~ T P P values greater than 2.3, indicating that the dipolar term of
163
Limitations of Mn(ll) Selective Broadening in NMR TABLE I: Spin-Lattice and Transverse Relaxation Times in Presence of Mn(I1) lo4[Mn'+]/ Ligand [ligand] TIp-I, sec-' Protons Acetate 15 4.4 Chloroacetate 22 4.9 Malonate 1.5 4.5 24 21 Succinate 7.1 6.0 1,2-Diaminoethane 5.8 27 Glycinate 2.8 5.4 Sarcosinate CH, 5.7 CH, 3.6 13.7 N, N-Dimethylglycinate CH, 15.1 CH, L-Methionine CH 0.8 7.7 SCH, 1.8 0.17 CH, 6.4 1.5 S-Methyl-L-cysteine 1.1 11.5 4.8 CHZ 0.74 CH, 5.1 4.2 Gly cylglycinate CH,COO13.5 CH,NH, 3 .O 6.3 Imidazole H2 3.4 H4. H5 18.2 1.2 H8' 5'-AMP 6.5 3.6 H2
'g:
Gly cinate
CHZ
Imidazole
c2 c4, c 5
Carbon-13 4.5 0.7 0.09
coo -
TABLE 11: Ratios of Relaxation Times for Imidazole in Presence of Metal Ions
Metal ion Mn(I1) Co(11) Ni( 11) Cu( 11)
Mn(11) Cu(11)
TIPlT2P H2 H4, H5
2.6 6.0 4.2 21
4.6 17 9.2 48
TIP-' H2/H4. H5
A H2/H4. H5
1.8 1.9 2.0 1.7
0.88 0.77 0.88 0.85
c2
c4, c 5
c2/c4, c5
c2/c4, c5
106 500
140 460
2.1 1.4
1.25
1.28
eq 2 contributes less than 50%to the broadening of proton lines. Therefore, the use of selective broadening by Mn(I1) to ascertain the site of ligand binding is subject to severe limitations, as the r6term is only a minor contributor to broadening in most cases. In only one-third of the cases in Table I does the dipolar term contribute 213 to broadening. Since the requisite frequency and temperature dependent studies have not been performed, it is uncertain whether the limitation on greater dipolar contributions is due to the intermediate exchange second term of eq 1 or the scalar term of eq 2, but it is more likely to be the latter in most cases. Whatever the reason, the fact that the dipolar term is seldom a predominant contributor to broadening renders suspect arguments of Mn(I1) site binding dependent upon the dipolar r-6 dependence between the paramagnetic ion and the affected nuclei. Compared to the proton TplT2p values found for Cu(II),'v2 those for Mn(I1) are similar for carboxylate ligands and much lower for amine donors. The scalar contribution to broadening is much greater for aliphatic amines
8.9 1.o 0.35 0.16
T2p-I, sec-'
TIPlT2P
I
11.6 16.5 34 39 45 21 33 18.3 34
3.0 2.4 3.7 1.6 6.5 1.7 3.9 5.8 1.3 2.3
7.9
4.4
2.9
1.9
4.3 7.9 21 16.5 15.8 24 9.8
5.8 1.9 1.6 2.6 4.6 1.3 1.5
11.0 4.7 37 22
1.2 4.7 106 140
13.1
bound to Cu(I1) than to Mn(I1). With adenosine monophosphate (AMP) the interaction with Mn(I1) is mainly dipolar while that with Cu(I1) is predominantly scalar. A greater proportion of Mn(I1) than Cu(I1) will be a t the phosphate rather than the adenine, however. Since eq 3 for T1p-l does not contain intermediate exchange or scalar terms, determination of the spin-lattice relaxation time should allow derivation of distance information as r6 TIP. The sixth root of ratios of T I P of two nuclei in the same complex should relate relative distances of these two nuclei to the paramagnetic metal ion in selective T1 experiments. Nearly identical TIP values for the two kinds of protons in both sarcosinate and dimethylglycinate indicate Mn(I1) binding a t the amino group. From the T1p-l values in Table I for L-methionine, the methyl protons are 1.5 and 1.9 times as far from the Mn(I1) as the SCH2 and CH protons, respectively. For S-methyl-L-cysteine the methyl protons are 1.4 and 1.6 times as far from the Mn(I1) as the CH2 and CH protons, respectively. Allowing for conformational mobility in the side chain, these results indicate that, at these high ligand to Mn(I1) ratios, the ligands chelate to the Mn(I1) as substituted glycinates with the ether sulfurs unbound. For the case of Cu(I1) the same conclusion was reached for methionine, but for S-methylcysteine it was suggested that a weak interaction may occur with the ether sulfur while Cu(I1) is chelated at the glycinate locus.2 For C-13, the T1pIT2p ratio of 1.24 for the CH2 carbon of glycinate suggests a nearly wholly dipolar interaction. For imidazole the T1plT~pratios are 1100 for both carbons, suggesting predominant scalar interactions in this system. Selective broadening experiments designed to locate the Mn(I1) binding sites by C-13 NMR in aromatic ligands such as imidazole derivatives and nucleic acids are suspect since the broadening does not depend on r-+. Since the hy-
-
The Journal of Physical Chemistry, Vol. 80, No. 2, 1976
164
R. W. Strickland and F. S. Richardson
perfine constants vary for each carbon, the scalar interactions are apt to vary a t each carbon about the ring. Even larger T ~ p / T z pratios are found for Cu(I1) and the carbons of glycinate and imidazole.2 The T l p / T 2 p ratios for complexes of imidazole with several metal ions reported in Table I1 indicate that the dipolar term is never dominant. It has been established that the main contributor to the high ratio for protons for Cu(I1) is the scalar term of eq 2.2 The ratios of the scalar coupling constants are quite constant for H2/H4, H5 for Mn(II), Ni(II), and Cu(I1). This result suggests that unpaired spin densities are distributed in similar ratios about the imidazole ring for each of the three metal ions. A constant ratio is also obtained for C2/C4, C5 for Mn(II), and Cu(I1). This ratio is different than that found for protons since the scalar coupling constants are generally different for different nuclei. In contrast to the constancy of the scalar coupling constant ratios for imidazole complexes of Mn, Ni, and Cu ions in Table 11, the T 1 p - l ratios are not constant for either the proton or carbon-13 nuclei. Constant nucleus Z/nuclei 4, 5 ratios are expected if the only dipolar interaction is that between the paramagnetic metal ion and the affected nucleus. Small differences in imidazole-metal ion bond lengths5 are unable to account for the discrepancies and it is unlikely that other differences in geometry would do so. Rather, the lack of constancy of the T 1 p - l ratios lends further support to the suggestion that additional dipolar terms are important.2 As was pointed out for Cu(I1) and
imidazole, a small amount of unpaired spin density at C5 is much closer to H5 than is the large unpaired spin density on the Cu(I1) bound at N3. As a result of the strong r-6 dependence, the small amount of unpaired spin density at C 5 is likely to be the major contributor to relaxation a t H5. This kind of occurrence should also apply to other paramagnetic metal ion complexes. Selective broadening is severely compromised because the dipolar term makes only a minority contribution to broadening in many cases. Selective T I experiments according to eq 3 may enable the requisite distance information to be determined. However, if selective TI arguments are employed to estimate distances, it must be established that the predominant dipolar interaction contributing to relaxation is that between the paramagnetic ion and affected nucleus as other more local interactions from unpaired spin density on the ligand may contribute importantly to relaxation and result in significant errors.6 References a n d Notes (1) W. G. Espersen, W. C. Hutton, S. T. Chow, and R. E. Martin, J. Am. Chem. Soc., 96, 8111 (1974). (2) W. G. Espersen and R . B. Martin, J. Am. Chem. SOC., in press. (3) T. J. Swift and R. E. Connick, J. Chem. Phys., 37, 307 (1962); 41, 2553 (1964). (4) R. A. Dwek, R. J. P. Williams, and A. V. Xavier in “Metal Ions in Biological Systems”, Vol. 4, H. Sigel, Ed., Marcel Dekker, New York, N.Y., 1974, Chapter 3. (5) R . J. Sundberg and R. 8. Martin, Chem. Rev., 74, 471 (1974). (6)This research was supported by two grants from the National Science Foundation, one from the molecular biology section and the other from the chemistry section for the purchase of the NMR instrument.
Optical Activity of d-d Transitions in Copper(l1) Complexes of Amino Acids, Dipeptides, and Tripeptides. Dynamical Coupling Model R. W. Strickland and F. S. Richardson. Department of Chemistry, University of Virginia, Charlottesviile. Virginia 2290 1 (Received July 17, 1975) Publication costs assisted by the Petroleum Research Fund
The chiroptical properties associated with the d-d transitions in dissymmetric Cu2+-amino acid, -dipeptide, and -tripeptide complexes are calculated on a theoretical model based on an independent systems representation of the electronic structure in these complexes. The metal ion and fragments within the ligand environment are treated as independent subsystems to zeroth order in the model and interactions between these subsystems are then treated by perturbation techniques. Wave functions for the d-d excited states of the Cu2+ ion are calculated to second order in perturbation theory. Rotatory strength expressions for the d-d transitions are developed to first, second, and third order in perturbation coefficients and these expressions are used in carrying out calculations. In evaluating the interaction energies between subsystems in our model we retain only the dynamical coupling terms resulting from the correlation of electron motion on the interacting groups. Static coupling mechanisms are not admitted into the model. The dynamical coupling terms are assumed to arise from electric quadrupole (metal)-electric dipole (ligand), electric hexadecapole (metal)-electric dipole (ligand), and electric dipole (ligand)-electric dipole (ligand) interactions between transition densities localized on the various subsystems. The rotatory strengths calculated for the Cu2+ d-d transitions are correlated with various structural features of the complexes studied and possible spectra-structure relationships are discussed.
I. Introduction A considerable number of studies on the chiroptical properties of complexes formed between transition metal The Journal of Physical Chemistry, Vol. 80. No. 2, 1976
ions and amino acid, dipeptide, and tripeptide ligands have been reported in the These studies are of special interest for developing chiroptical spectroscopy as a probe of’ the structural characteristics of metal ion binding
