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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
Strickland and F. S. Richardson
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
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Optical Activity of d-d Transitions in Cu2+ Complexes
sites in complex biomolecular systems. The spectra-structure relationships discovered for the model metal ionamino acid, -dipeptide, and -tripeptide systems are expected to be at least qualitatively applicable to spectrastructure correlations in metalloenzymes and metal-protein complexes. Several of the studies on the chiroptical properties of metal ion-amino acid and -peptide systems have led to the formulation of empirically based spectra-structure relationships which are remarkably successful in correlating the data obtained on various series of similar systems. Additionally, in a few instances these relationships have been interpreted directly in terms of extant theoretical models of molecular optical activity.l Of special note is the “hexadecant sector rule” proposed and applied by Martin and coworkers1 in interpreting the circular dichroism (CD) spectra of a large number of metal ion-amino acid and -peptide complexes. This sector rule derives directly from the one-electron, static coupling model of molecular optical activity as described by Schellman3 and as elaborated upon by Mason4,jand by Richard~on.~~’ Most of the attention in developing spectra-structure relationships for chiral transition metal complexes has been placed on the CD spectra associated with the metal ion d-d transitions. These transitions generally fall within an easily accessible region of the spectrum, generally exhibit relatively large dissymmetry factors (A€/€), and are more readily amenable to theoretical analysis than are the less well characterized metal-ligand charge-transfer and ligand-ligand transitions. Despite the widely acknowledged utility and the apparent reliability of the spectra-structure relationships proposed for chiral metal ion-amino acid and -peptide complexes, a detailed theoretical examination of the optical activity exhibited by the d-d transitions in these systems has not yet been reported. Such an examination is of interest not only for supplying a theoretical foundation for spectra interpretation but also for investigating and testing the current theories of optical activity in chiral transition metal complexes. The theory of optical activity in transition metal complexes has been studied intensively over the past 15 years, but a fully satisfactory theory or model capable of providing widely applicable and reliable spectrastructure correlations has not yet emerged. The metal ionamino acid and -peptide complexes provide excellent model systems for testing and investigating the current theories. Chirality in transition metal complexes is generally attributed to one or more of the following structural features: (1)chiral distortions within the metal ion-donor atom cluster (“inherent dissymmetry” within the d-d chromophore); (2) chiral distributions of chelate rings about the metal ion (“configurational dissymmetry”); (3) chiral conformations of chelate rings (“conformational dissymmetry”); and (4) asymmetric centers within the ligands (including, in some cases, asymmetric donor atoms). Most theoretical analyses and sector rule applications have focused on the latter three sources of chirality, although the possible importance of inherent dissymmetry within the metal ion-donor atom cluster of six-coordinate Co”+ and Cr3+ complexes has also been examined in several recent studies.b-10 In the present study we are concerned with the optical activity of the d-d transitions in Cu2+-amino acid and -peptide complexes. Crystal structure datalJ1 reveal that the Cu2+-donor atom cluster in these systems is approximately symmetrical (achiral) and that the chelate rings are
not dissymmetrically distributed about the metal ion. The d-d optical activity of these systems must arise, then, from conformational dissymmetry within the chelate rings and (or) from vicinal interactions between the metal ion and asymmetric centers in the ligand environment. In the present study we shall neglect both configurational dissymmetry and inherent dissymmetry (within the metal iondonor atom cluster) as sources of optical activity. It is highly likely that there exists considerable (or, a t least, nonnegligible) inherent dissymmetry within the metal ion-donor ion clusters characteristic of metal binding sites in many biological macromolecules. The influence of this type of chiral distortion upon Cu2+d-d optical activity will be presented in a separate report.l* We employ an independent systems model in this study to calculate the d-d rotatory strengths of various Cu2+amino acid, -dipeptide, and -tripeptide complexes. The application of this type of model in calculating molecular optical activity has been elaborated upon by several workers and the details of the method will not be discussed here.”loJ3-l5 Of special relevance to the calculations reported here are the work of Hohn and Weigang13 and of Mason and c o - w o r k e r ~ .We ~ , ~calculate the purely electronic contributions to the d-d rotatory strengths and ignore possible effects arising from vibronic interactions. Neglect of vibronic interactions precludes quantitative prediction of CD spectra since for many of the systems studied here rather substantial pseudo-Jahn-Teller (PJT) interactions are expected between the nearly degenerate (in some cases) d-d excited states. The possible influence of PJT interactions on the chiroptical spectra of systems with nearly degenerate electronic states has been examined elsewhere.l6-I8 In these previous studies it was concluded that such interactions do not invalidate spectra-structure relationships based on “net” rotatory strengths associated with the interacting states. The role of the Herzberg-Teller (HT) vibronic coupling mechanism in determining CD spectral features has been investigated in some detail by Weigang and co-workers. However, the influence of H T type vibronic interactions on the chiroptical spectra of coordination compounds has not been subjected to thorough study. Neglect of vibronic interactions in the present study should have little effect on the qualitative or semiquantitative aspects of spectra-structure correlation; it does, however, preclude detailed spectra prediction. 11. Theory
A. Basic Model. Within the approximations of the independent systems model we partition the metal complexes into three parts: (A) an idealized ML4Z2 metal ion (M)donor atom (L or Z) cluster (including all metal electrons and u-ligating electrons) with exact D4h symmetry; (B) the r-electron systems of the donor atoms or groups; and (C) the nondonor atoms or groups of the complex. In the metal ion-amino acid and -peptide complexes of interest here the Z donor atoms lie along the C4 symmetry axis of the ML4Z2 cluster, and the (B) subsystems include the amide and/or carboxylate ligand moieties. The electronic Hamiltonian of the overall system is partitioned as follows: where ha, hg, and hc represent zeroth-order electronic Hamiltonian operators for the (A), (B), and (C) subsystems, respectively, VA represents a local distortion potenThe Journal of Physical Chemistry, Vol. 80, No. 2, 1976
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R. W.
tial within the ML4Z2 cluster to accommodate deviations from strict D4h symmetry, and VAB, VAC, and VBCare pairwise interaction potentials operative among the three subsystems of the complex. Adopting a perturbation approach we rewrite eq 1as
H = hA 4- hg + hc + v = H o + v
+
+
(2)
+
where the operator, V = V A VAB VAC VBC,is treated as a perturbation on the eigenstates of the operator, H o = hA hg hc. To zeroth order, the electronic states of the system are written as
+
+
+@ : ?
= IAaBoCy)
ond order in the basis (+zoo, +&o, +goy, &). The electric and magnetic dipole transition moments associated with transitions (000) (a00)were expressed to second order (in perturbation coefficients), and the electronic rotatory strengths +
.
(5) ~ o o o , m o o= Im (+ood4+a00) ( + a o d ~ l + o o o ) were also expressed to second order. €3. Interaction Matrix Elements. Assuming exact D4h symmetry for the ML4Z2 cluster and neglecting VA,the following interaction matrix elements appear in our secondorder expressions for the +,OO wave functions:
(+%d VAB+ VAC~ +$oo) Vnp= (+8dVABI+:do) Vu, = (+llod V~cl+80,) VpY = (+&d VBCI+:o,) Va6 = (+:id VABI$40) Vm = (+&d VAIJ+!o)
VaU!=
where A,, Bo, and Cy are eigenfunctions of hA, hg, and hc, respectively. The ground state is designated by +&o, an excited state localized on MLIZP is denoted by +too, an excited ?r state localized on a (B) subsystem is represented by +&o, and an excited state localized on a (C) subsystem is given by $by.To first order in perturbation theory, the electronic wave function for an excited state (a00)is given by +a00
= +:o,
+ a’#, c
cB
(+%o ($860
I vl+:oo)+:~oolm:,,, + I VI +“,o) + & o l ~ : @ +
c
(+80,1
Y
vl+:oo)+&,I~:
(3)
where represents the energy difference between zeroth-order states i and j . Doubly excited configurational states are excluded from the expansion given in eq 3. Equation 3 for the first-order wave functions is correct only if we neglect exchange interactions between the electronic distributions of the three subsystems (A), (B), and (C). This formulation allows for dynamical excitation (energy) exchange interactions and for static Coulombic interactions between the subsystems, but it excludes charge exchange (or charge-transfer) interactions. In the systems of interest in the present study, charge-transfer (CT) between the (B) subsystems and the ML4Z2 cluster may be of significant importance in determining the spectroscopic properties of electronic transitions primarily localized within the ML4Z2 chromophore. To include these specific CT processes we relax the independent systems approximation, include CT states in our basis set of zeroth-order states, introduce an electron-exchange term into VAB,and add an interaction term VCDto V which represents the interaction between subsystems (C) and the CT states of the composite group D = AB. Now, in addition to the excited states IA,,BoCo), IAoB&o), and IAoBoC,), we also have CT states of the type I A ~ B ~ C O = )IDsCo), in which an electron has been transferred out of a configuration on (A) and into one on (B) or vice versa. Equation 3 can now be rewritten as = +%o
+ c m
+ ,C (Y
(+:pod
q+%o)+floolAERc~, +
#
