1798
G. Hilrnes, C. Yeh, and F. S. Richardson
Optical Activity of d-d Transitions in Copper(l1) Complexes of Dipeptides and Dipeptide Amides. Molecular Orbital Model Gary Hilmes,Chin-yah Yeh, and F. S. Rlchardson” Deparfment of Chemistry, University of Virginia, Charlottesville, Virginia 2290 1 (Received January 2 1, 1976) Publication costs assisted by the Petroleum Research Fund
The chiroptical properties associated with the d-d and low-lying charge-transfer transitions in a series of four-coordinate and six-coordinate Cu(I1)-dipeptide and Cu(I1)-dipeptide amide complexes are calculated on a semiempirical molecular orbital model. Electronic rotatory strengths are calculated directly using wave functions of the entire complex generated from the molecular orbital model. Excited states are constructed in the virtual orbital approximation and electric and magnetic dipole transition integrals are computed including all one-, two-, and three-center contributions. The results are compared to those obtained using other theoretical models of molecular optical activity, to semiempirically derived spectra-structure relationships and rules formulated for pseudotetragonal metal complexes, and to empirical data.
I. Introduction Copper(I1) complexes of di-, tri-, and tetrapeptides have been studied extensively because of their importance as models for metalloproteins. Copper(I1) promotes the ionization of amide hydrogens in neutral solutions of simple peptides, yielding chelates containing planar, trans amide bonds with trigonal amide nitrogens as donor atoms. These pseudotetragonal copper(I1)-peptide complexes provide a nearly planar system of chelate rings to which side chains are attached in known dispositions. Because of the relative structural rigidity of these systems they serve as excellent models for examining the origins of optical activity in chiral transition metal complexes. Furthermore, spectra-structure relationships found applicable to these systems are also expected to be at least qualitatively applicable to spectra-structure correlations in metalloenzymes and metal-protein complexes. A considerable number of studies on the chiroptical properties of complexes formed between copper(I1) and amino acid, dipeptide, and tripeptide ligands have been reported in the 1iterature.lJ Several of these studies 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. Of special note is the “hexadecant” sector rule proposed and applied by Martin and co-workers1 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 Mason4r5 and by Ri~hardson.~,’ Although the CD associated with the pure ligand-ligand transitions as well as the ligand-metal charge-transfer (CT) transitions have been studied for many metal complexes, it is generally the CD spectra associated with the metal ion d-d or ligand-field transitions which are used as diagnostic probes of structure or structural changes. These transitions generally fall within an easily accessible region of the spectrum, generally exhibit relatively large dissymmetry factors ( AJt), and are more readily amenable to theoretical analysis than are the less well characterized metal-ligand charge-transfer and ligand-ligand transitions. The Journal of Physical Chernktry, Vol. 80,No. 16?1976
Theoretical treatments of optical activity in chiral transition metal complexes have generally developed along three different lines. In one approach an independent systems representation of the complex is adopted wherein the complex is partitioned into an achiral chromophoric group (which includes the metal ion) and a set of extra-chromophoric groups distributed throughout the ligand environment/-7 Interactions between the chromophoric group and extrachromophoric groups are treated by perturbation techniques and optical activity in the chromophoric transitions is assumed to arise from dissymmetric terms in these interactions. The theoretical bases for most of the sector or regional rules proposed and applied in making spectra-structure correlations in amino and peptide complexes of transition metal ions are found in various forms of the independent systems model. A second approach to examining the origins of optical activity in transition metal complexes focuses on chiral distortions of donor atom orbitals. These distortions reflect the chiral nature of the ligand environment beyond the donor atom set and communicate chirality to the chromophoric electrons of the metal ion via direct bonding (or antibonding) interactions. This approach has been used with varying degrees of success by Liehr,s Karipedes and Piper,g Strickland and Richardson,lo and Schaffer.ll The third approach to studying the chiroptical properties of metal complexes involves direct molecular orbital calculations on the entire complex. That is, the entire metal complex is treated as a single entity and the wave functions obtained from molecular orbital calculations on the complex will have dissymmetry built into them directly (reflecting the symmetry properties of the total molecular Hamiltonian operator). This latter approach has been employed by Schreiner and co-workers,12by Strickland and Richardson,loand by Yeh and Richardson.l3 In the present study we calculate the electronic rotatory strengths associated with the d-d and low-lying chargetransfer transitions in a series of copper(I1)-dipeptide complexes using the molecular orbital model and the direct calculational method. This method is particularly suitable for the Cu(I1)-dipeptide complexes since in these systems one may expect strong d-ir interactions between the metal ion and the peptide and carboxylate (or amide) groups of the ligands, as well as significant electron delocalization over large parts
Optical Activity of d-d Transitions in Cu(l1) Complexes
1799
+
of the complex (metal ion ligands). In these cases it is unlikely that an independent systems model can provide a complete or accurate representation since the basic chromophoric unit for certain of the transitions of interest must be assumed to extend somewhat beyond the metal ion and the donor atoms of the ligands. That is, partitioning the complex into weakly interacting chromophoric and extrachormophoric groups is not easily (or validly) accomplished, and it becomes more appropriate to treat the entire complex as an extended chromophore. The molecular orbital/direct calculational method allows us to do this.
11. Structures Nineteen Cu(I1)-dipeptide complexes were studied. These are: [Cu(GG)(OH)]-, [Cu(GG)(H20)], [Cu(AG)(OH)]-, [Cu(GA)(OH)l-, [Cu(AG)(H20)1,[Cu(GA)(HzO)l,[Cu(AA)(OH)]-, [Cu(AA)(HzO)l, [CutA’A)(OH)l-, [Cu(AA’)(OH)l-, trans- [Cu(GG)(OH)](OH)23-, trans- [Cu(GA)(OH)](OH)z3-, trans- [Cu(AG)(OH)](OHh3-, trans-[Cu(GG-”)(OH)] (OH)23-, trans- [CU(GA-NH)(OH)](OH)~~-, trans[Cu(AG-NH) (OH)](OH)z3-, trans- [Cu(GG)(HzO)](HzO)z, trans- [Cu(GA)(H20)](H20)2, trans- [Cu(AG)(HzO)j(H20)2, where GA = glycyl-S-alaninato ligand, AG = S-alanylglycinato ligand, GG = glycylglycinato ligand, AA = S-alanyl-Salaninato ligand, A’A = R -alanyl-S-alaninato ligand, AA‘ = S-alanyl-R-alaninato ligand, GA-NH = glycyl-S-alaninamido ligand, AG-NH = S-alanylglycinamido ligand, and GG-NH = glycylglycinamido ligand. The structure parameters for the chelate rings in these systems were adapted from those reported for crystalline glycylglycinatocopper(I1) trihydrate and for crystalline glycylglycinatocopper(I1)dihydrate (obtained from x-ray diffraction data).14J5 The GG, GA, AG, and AA ligands each function as a tridentate chelate system via an amino group donor, a deprotonated peptide nitrogen donor, and a carboxyl group donor. The CuNzO2 (one oxygen atom from either a water molecule or a hydroxyl anion) cluster forms a slightly distorted square. The chelate ring formed by the carboxyl and peptide groups is assumed to be exactly planar in our model structures, whereas the chelate ring formed by the peptide nitrogen and the terminal amino group is very slightly puckered. The GG-NH, GA-NH, AG-NH, and AA-NH ligands each function as a tridentate chelate system via an amino group donor, a deprotonated peptide nitrogen donor, and an amido group donor. The CuN30 cluster forms a slightly distorted square and the chelate rings are each nearly planar. The “in-plane” Cu-OH and Cu-OH2 bond distances were taken to be 1.95 A. The axial Cu-OH and Cu-OH2 bond distances were set at 2.40 A. The GG and GG-NH complexes were constructed to have exact C, symmetry, whereas all the other complexes are entirely lacking in symmetry. 111. Calculations The direct calculational approach was used to compute the electronic rotatory strengths associated with the d-d and lowest-lying charge-transfer transitions of the Cu(I1) systems examined in this study. That is, the rotatory strengths Rij
= Im ($iJPl+j)
($jlfil$i)
(1)
where ii is the electric dipole operator and Ifi is the magnetic dipole operator, are calculated using wave functions obtained directly as approximate eigenfunctions of the complete electronic Schrodinger equation for each complex. The shortcomings of this approach reside in the rather serious approximations one must make in solving the electronic
Schrodinger equation for such large systems as are being studied here, and especially in constructing wave functions for the spectroscopic excited states. Despite these obvious shortcomings, this approach is to be preferred over an independent systems or perturbative model for systems in which electron delocalization beyond the metal ion-donor atom cluster is expected to be significant and in which the chromophoric unit is not localized at a center of high symmetry. In our calculations, ground state electronic wave functions were obtained using a modified Wolfsberg-Helmholz or extended Huckel molecular orbital model. The general procedures employed in carrying out calculations on this model have been described elsewherelOJ3 and will not be discussed further here. The atomic orbital basis set employed in the present calculations included: (1) 3d, 4s, and 4p orbitals on Cu(I1); (2) 2s and 2p orbitals on each carbon, oxygen, and nitrogen atom; and, (3) a 1s orbital on each hydrogen atom. The single-f Slater-type-orbitals (STO) of Clementi and Raimondil6 were chosen for the C, N, and 0 atoms. For the H atoms, we used a Slater type 1s orbital with { = 1.2. The metal ion basis set consisted of single-f4s and 4p orbitals and double-f 3d orbitals.17 Excited state wave functions were constructed in the virtual orbital approximation by promoting an electron from an occupied molecular orbital to an unoccupied (or virtual) orbital. To calculate electronic rotatory strengths (eq 1) both electric and magnetic dipole transition integrals are required. The electric dipole transition integrals were calculated in the dipole velocity representation and then transformed to the dipole length form according to where q = x , y , or z (electron positional coordinate) and m = electron mass. All one-, two-, and three-center terms were included in evaluating the electric dipole velocity and angular momentum integrals required for computing the ($i(b($j)and (klIfil$j)matrix elements. The electric and magnetic dipole transition integrals, dipole strengths (eq 3), rotatory strengths (eq l),oscillator strengths, and dissymmetry factors (eq 4) were calculated using a program (ROTSTR) previously employed in computing chiroptical properties of nonmetal systems18 and extended, recently, to handle 4s,4p, and 3d metal orbitals.13 Dij =
I ($ilbl$j) l2
Gij = 4Rij/Dij
dipole strength
(3)
dissymmetry factor
(4)
IV. Results The optical properties computed for the d-d transitions in 15 of the Cu(I1)-dipeptide and Cu(I1)-dipeptide amide complexes are listed in Tables 1-111. The optical properties computed for the three lowest energy charge-transfer transitions in six of these complexes are listed in Table IV. In each of the four-coordinate systems studied the energy ordering of the 3d metal orbitals was calculated to be: d,z-yz(t) >d,,(f) >dzz(6) > d , , ( ~ ) >d,,(&Ineachofthesix-coordinate systems the energy ordering of the 3d orbitals was calculated to be: d,z-yz(c) > dzz(6) > dxy(f)> dxz(v)> dyt(f). The coordinate systems employed in our calculations are depicted in Scheme I. The d,, ( 7 ) orbital is directed toward the peptide nitrogen atom and the dyz(E) orbital points toward the amino nitrogen and carboxyl oxygen (or amide nitrogen) atoms. The Journal of Physical Chemistry, Vol. 80, No. 16, 1976
G.Hilmes, C. Yeh, and F. S. Richardson
1800
TABLE I: Computed Optical Properties of Four Lowest Energy Transitions in Four-Coordinate Cu(I1)-Dipeptide Complexes R,
Complex
X,nm D,D2 643 0.43 610 0.26 604 0.27 539 0.02 652 0.24 610 0.23 601 0.27 536 0.03 651 0.49 615 0.11 604 0.23 537 0.02 661 0.25 618 0.43 601. 0.25 534 0.03 654 0.28 621 0.40 603 0.31 538 0.04 654 0.28 621 0.40 603 0.31 538 0.04
esu2 cm2 (GI 0 0 0 0
0 0 0 0
-1.44 2.45 -8.41 0.06 -2.66 4.70 -18.66 -0.26 -3.22 6.55 -22.88 -0.03 0.96 1.46 -7.42 -0.14 -0.96 -1.46 1.42 0.14
Transition
r-
8-6 7-e 6-t
0.0023 { - + e 0.0043 8 - 6 0.0116 7 - e 0.0008
0.0022 0.0171 0.0325 0.0048 0.0047 0.0057 0.0366 0.0004 0.0013 0.0015 0.0095 0.0014 0.0013 0.0015
0.0095 0.0014
[-+e {-e 8-6
7-e
[-+e {+c
8-c 7-e [-+e
{-e 8-e 7-e [-e
.(+e 8-c 7-c
[-e
Scheme I 0
?8Y0
N-CU-o-tY
I
S
+
4
X
X
S =OH- or H,O The four lowest energy transitions calculated for each complex are essentially d-d excitations localized on the metal ion. For all the complexes studied, the three lowest energy charge-transfer transitions involve excitation of an electron out of a predominantly ligand-localized orbital into the halffilled d+.yz(t) metal orbital. The highest occupied ligandlocalized orbital is calculated in each case to be slightly bonding with respect to the dxy([) metal orbital and it has maximum amplitude in the xy plane. This orbital is designated P‘. The second highest occupied ligand-localized orbital is designated ?I and it is found to be entirely nonbonding with respect to the metal orbitals. This orbital has maximum amplitude in the xy plane and is somewhat localized on the carbonyl oxygen atom of the terminal carboxylate or amido moiety. The third highest occupied ligand-localized orbital is an out-of-plane T orbital with maximum amplitude on the nitrogen and oxygen atoms of the central peptide group. We designate this orbital as P. The P” orbital in our calculations closely resembles a carbonyl oxygen nonbonding or “n” orbital, and the P orbital in our calculations closely resembles the “ 0 “nonbonding” orbital found in isolated amide chromophores. (The PO orbital in amide groups is often called “nonbonding” because it has a near nodal plane a t the carbonyl carbon atom of the OCN group.) The orbital occupation numbers calculated for the 4s and The Journal of Physical Chemistry, Vol. SO, No. 16, 1976
4p metal orbitals in the ground state of the various complexes were found to lie in the range 0.45-0.62. The occupation numbers calculated for the dXz+(e) orbital in the ground state of the various complexes fall in the range 0.70-0.74. With the several parameter sets we examined in constructing our semiempirical molecular orbital model, very little mixing between the 4s, 4p, and 3d metal orbitals was found among the occupied and low-lying virtual molecular orbitals. The orbital occupation numbers listed above suggest significant participation of the metal 4s and 4p atomic orbitals in metal-ligand bonding in the ground states of the Cu(I1)-dipeptide complexes. However, our calculations give little evidence for significant sp2d hybridization in the ground states of these systems (although this point cannot be settled by the very approximate types of calculations performed in this study). Axial perturbations by ligands located in the fifth and sixth positions determine the relative ordering of the d,z(6) and dxy({) orbitals as seen by comparing the calculated results for the four-coordinate and six-coordinate complexes. The dipole strengths and rotatory strengths of the 0 t and {- t transitions are also quite sensitive to the presence or absence of axial ligands (see Tables I and 11).
-
V. Discussion As was pointed out in the Introduction, metal ion-peptide complexes provide excellent model systems for testing and investigating theoretical methods for calculating and interpreting molecular chiroptical properties. They have relatively rigid structures and well-defined chromophoric units, and their chiroptical properties have been studied extensively by experimental methods. Previously we have investigated the origins of d-d optical activity in these and similar systems using both the static coupling (one-ele~tron)~ and dynamical couplinglg variants of the independent systems model. The spectra-structure relationships and sector rules most commonly applied to these systems have their basis in the static coupling or one-electron theory as formulated by Schellman3 (and elaborated upon in ref 6 and 7). The “hexadecant” sector rule proposed and applied by Martin1,z0 has proved to be especially useful in making spectra-structure correlations. Our previous studies have shown, however, that neither the static coupling model nor the dynamical coupling model (carried to first and second order in perturbation theory) provides a complete or adequate representation for chiroptical properties of the metal ion-peptide systems. This does not diminish the importance or utility of the semiempirically derived spectra-structure relationships and sector rules applied to these systems, for these relationships retain their validity independent of theoretical justification. However, it is of some interest to understand better the electronic structural and stereochemical factors responsible for the chiroptical observables in these important model systems. The direct calculational approach based on a molecular orbital description of the molecular electronic states (as used in the present study) provides yet another representation for examining the chiroptical properties of these systems. Given the approximations in the molecular orbital model employed in the present study, this approach is not expected to yield inherently more accurate results or a superior representation of the optical activity mechanisms; rather, it provides an alternative and supplementary view. In neutral solution, Cu(I1)-(AG), Cu(I1)-(GA), and Cu(I1)-(AA) complexes exhibit a single broad CD band in the region 500-700 nm.20,21This broad band is centered near 650 nm and is generally presumed to span all four d-d transitions.
Optical Activity of d-d Transitions in Cu(l1) Complexes
1801
TABLE 11: Computed Optical Properties of Four Lowest Energy Transitions in Six-Coordinate Cu(I1)-Dipeptide Comdexes Complex
A, nm
D, D2
trans- [Cu(GG)(OH)](OH)z3-
721 641 600 532 662 569 548 492 721 640 604 536 641 556 552 478 725 645 609 536 643 561 556 486
0.09 0.52 0.30 0.02 0.10 0.71 0.44 0.12 0.13 0.47 0.32
trans- [Cu(GG)(HzO)](HzO)z
trans- [Cu(AG)(OH)](OH)23-
trans-[Cu(AG)(HzO)](H2O)z
trans - [Cu(GA)(OH)](OH)z3-
trans - [Cu(GA)(HzO)](H2O)z
0.09
0.18 0.54 0.38 0.08 0.13 0.48 0.33 0.06 0.18 0.51 0.36 0.09
R,
IG I
em2 cm2 0 0 0 0 0 0 0 0
0.88 -0.84 -5.15 -0.72 0.12 -1.21 -4.24 -0.71 0.66 -2.18 -8.44 -0.21 0.41 -2.12 -7.92 -0.40
0 0 0 0 0 0 0 0
Transition 8-€ i--e 7-f [-e
e-€
l-
e
7-6 6-t
0.0025 0.0007 0.0059 0.0032 0.0003 0.0009 0.0045 0.0004 0.0018 0.0017 0.0102 0.0014 0.0009 0.0017 0.0088 0.0018
8-t (-+e 9-e [-+e
8-e
i--
6
7-€ E-c
8-e
