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This work deduces from a series of well defined copper-doped amino acid crystals, relationships between structural features of the copper complexes and ligand-bound proton hyperfine parameters. These were established by combining results from electron paramagnetic resonance (EPR)/electron-nuclear double resonance (ENDOR) studies, crystallography and were further assessed by quantum mechanical (QM) calculations. A detailed evaluation of previous studies on Cu2+-doped into α-glycine, triglycine sulfate, α-glycylglycine and l-alanine crystals reveal correlations between geometric features of the copper sites and proton hyperfine couplings from amino bound and carbon bound hydrogens. Experimental variations in proton isotropic hyperfine coupling values (aiso) could be fit to cosine-square dependences on dihedral angles, namely, for Cα-bound hydrogens, aiso = −1.09 + 8.21cos2θ MHz, and for amino hydrogens, aiso = −6.16 + 4.15cos2 MHz. For the Cα hydrogens, this dependency suggests a hyperconjugative-like mechanism for transfer of spin density into the hydrogen 1s-orbital. In the course of this work, it was also necessary to reanalyze the ENDOR measurements from Cu2+-doped α-glycine since the initial study determined the 14N coupling parameters without holding its nuclear quadrupole tensor traceless. This new treatment of the data was needed to correctly align the 14N hyperfine tensor principal directions in the molecular complex. In order to provide a theoretical basis for the coupling variations, QM calculations performed at the Density Functional Theory (DFT) level were used to compute the proton hyperfine tensors in the four crystal complexes as well as in a geometry-optimized Cu2+(glycine)2 model. These theoretical calculations confirmed systematic changes in couplings with dihedral angles, but greatly overestimated the experimental geometric sensitivity to the amino hydrogen isotropic coupling.
Electron paramagnetic resonance (EPR) spectroscopy has a long history of the study of copper doped crystalline systems1. The primary aim of these were to obtain accurate and unambiguous g and copper hyperfine and quadrupole tensors in order to both define the coordination of the doped metal ion and to understand how the observed spectral characteristics relate to electronic structure. Results from single crystal experiments where doped copper replaced other transition ions in crystalline amino acid models2 have shown that the site can be identified by alignment of the g and copper hyperfine tensor axes with the ligand bond directions in the host. Such tensor alignments were useful in postulating metal coordination in subsequent studies on molecular crystals, where the copper dopes at specific interstitial sites3. The further application of Electron-Nuclear Double Resonance (ENDOR) spectroscopy in measuring ligand 14N and nearby 1H hyperfine couplings became very instrumental in supporting the proposed characteristics of copper-molecular complexes4–10.
Recent advances in pulsed-EPR (Electron Spin Echo Envelope Modulation-ESEEM, pulsed-ENDOR and Hyperfine SubLevel Correlation-HYSCORE) and high-field EPR methods have allowed for the determination of the g and hyperfine tensors in non-oriented copper samples to a precision approaching that found in single crystal studies11. Although still not as unambiguous as the crystal work, these orientation-averaged studies nevertheless provide information on many important biological systems that cannot be investigated in any other way. However, because of the lack of a priori structural information, the usefulness of these methods in understanding the biological role of copper rely heavily on interpreting weak hyperfine coupling interactions from remote nuclei11,12.
The present study aims to proceed further in the analysis of both the amino-bound (Ha) and Cα-bound (HC) hydrogen 1H hyperfine interactions in copper-amino acid complexes by determining possible correlations between the coupling values and coordination geometry. To do this, an analysis was made of results from four previously published examinations of copper-doped single crystal amino acids which had been the subject of combined EPR and ENDOR investigations. These were copper-doped α-glycine4, triglycine sulfate5,6, l-alanine7,8 and α-glycylglycine9. Figure 1 displays13,14 the proposed copper sites in the host crystal structures of α-glycine15, triglycine sulfate16, l-alanine17 and α-glycylglycine18 determined by neutron diffraction experiments. The EPR/ENDOR analyses of these systems were mostly concerned with identifying the copper binding sites, and there has not been any concerted discussion of possible dependences of the ligand couplings on geometric aspects of the copper-amino acid complexes. As mentioned above, knowledge on how molecular geometry influences remote magnetic coupling interactions has useful predictive value in the study of biological systems and gives important insight into the electronic structure of copper coordination.
In each case shown in Figure 1, the EPR measured g and Cu2+ hyperfine tensors were shown to be consistent with a copper dx2-y2 ground state, with the equatorial xy plane approximately defined by the directly coordinated ligand atoms. It was demonstrated by ENDOR that the coordinated glycine amino nitrogen deprotonates when copper binds, causing the copper complex in glycine to become charge neutral4. Similar evidence showing that ligating amino groups may deprotonate by copper binding to give neutral charged complexes come from early EPR “truth tables” of Peisach and Blumberg19. The postulated glycine, triglycine and glycylglycine sites each have trans 2N2O ligation, while in alanine, a three coordinate N2O complex was proposed8. Here, a distant second amino group is located 2.5Å from copper on the opposite side of the directly coordinated nitrogen. ENDOR results8 indicate that this distant amino group does not deprotonate, and that leaves the copper complex in alanine with a net positive charge. The copper-alanine system is also different than the others because 1H ENDOR measurements of the amino hydrogens indicate a flattening of the amino group from its original tetrahedral geometry8. Additionally, the postulated metal site is one where copper binds the nitrogen at a 90° angle to the N-Cα bond which is unlike the other systems which have angles closer to tetrahedral. In the copper-glycine complex, carboxylate oxygens from two other zwitterionic glycine molecules are positioned on either side, approximately axial to the equatorial plane. In copper-triglycine sulfate, oxygens from two charged sulfate ions are bound axially, leaving the complex with a net −2 charge. In all four systems, ligand 14N hyperfine and quadrupole couplings, as well as amino bound and carbon bound 1H hyperfine tensors, were determined by ENDOR. The relative signs of the Cα-bound and amino proton couplings in triglycine sulfate were established by TRIPLE-ENDOR experiments6. In addition, amino bound 2D hyperfine and quadrupole tensors were obtained in deuterated crystals6. In the copper-doped glycine ENDOR study4, the 14N coupling parameters were computationally refined without the theoretical constraint that the quadrupole tensor remains traceless20. Therefore, published 14N ENDOR frequency data for this system was re-refined in order to conform to treatments of data in the three other crystal complexes.
With the exceptions of a flattening of the alanine amino group, and reorientations of amino hydrogens about the Cα-N bond in triglycine sulfate (and also presumably in glycine), the molecules coordinating to the doped copper ion in the crystal complexes are assumed to maintain the same structure as found in the host crystals. Support for this comes from (1) the measured g, hyperfine and quadrupole tensor directions which have very good correlation with ligand bonds and directions in the native structures, (2) the copper positioned at the inversion center in the α-glycine crystal gives rise to two equivalent pairs of ENDOR coupling tensors, one from each symmetrically equivalent glycine, and (3) the close similarity in the ENDOR measured coupling tensors from the two structurally similar coordinating molecules in triglycine sulfate (molecule II and molecule III). Therefore any adjustments in the molecular positions or geometries when accommodating the copper are not anticipated to be large enough to significantly alter the trends described below.
A careful analysis of the experimental 1H hyperfine couplings in these systems revealed geometrical correlations with certain dihedral angles in the complexes. In order to provide a theoretical basis and comparison with the observed dependencies, QM calculations using Kohn-Sham DFT21,22 were carried out on the crystal complexes in Figure 1 and on a geometry-optimized model of a Cu2+(glycine)2 complex. The QM calculations generated singly occupied molecular orbitals that were consistent with those found in previous QM/DFT treatments of copper-nitrogen and copper-histidine systems24–25. In the present model, the dihedral angle between the Cu-N-Cα and N-Cα-HC planes, and the rotation angle of the amino group hydrogens about the Cα-N bond were varied to determine their influence on proton coupling interactions. The previous DFT computations report disparities between observed 14N and 1H hyperfine coupling values which were attributed to an overestimation of spin transfer and spin contamination22–25. However, these studies also conclude that such deviations are generally systematic for a given atomic basis set, functional and model system, making the prediction of trends in variations of hyperfine couplings in related compounds much more reliable. The results described below may spur further work in improving such theoretical calculations.
The previous EPR/ENDOR study of copper-doped glycine crystals possibly used a left-handed coordinate system26. This was experimentally confirmed by EPR (Varian E109) X-band spectral measurements at 77K on copper-doped α-glycine single crystals. The doped crystals were grown using published methods4 and the beta angle was identified by microscopic examination of the crystal morphology. Spectra were recorded along the crystalline a, b, and c’ axis (where c’= a × b) and match those reported earlier4 and, as anticipated for monoclinic crystals, rotation about the b-axis displayed no site-splitting. g-value measurements in the ac’ plane showed that the previous EPR/ENDOR analysis was indeed conducted using a left-handed system. The right-handed g-tensor for copper-doped glycine is listed in Table 1. The right-handed tensors are related to those previously published by a sign change in each of the last three direction cosines20.
where AN, QN and gnN are the 14N hyperfine tensor, traceless nuclear quadrupole tensor and nuclear g-value, respectively, and the other quantities have their usual definition. 14N ENDOR line assignments were made following a method applied by McDowell and Naito8 to determine the relative signs of the 14N hyperfine and quadrupole interactions. The refinement procedure has been described in previous work27. The angular dependencies of the 14N ENDOR frequencies were correlated with those of the free proton frequency variations and also therefore with the g-tensor listed in Table 1. The newly refined 14N hyperfine and quadrupole tensors reported in Table 1 are consistent with the 14N coupling parameters found in the three other copper-amino acid crystal systems.
Quantum mechanical calculations were carried out using the Gaussian-0328 (G03) program. As mentioned above, the molecular structures and hyperfine couplings were calculated using DFT with the Becke 3-parameter exchange29 and Lee-Yang-Parr correlation30 functional. DFT computations using this functional have had relative success in estimating 14N, 13C and 1H hyperfine couplings in various copper model complexes23–25. The 3 by 3 hyperfine coupling tensor (A) for a particular nucleus (n) consists of the Fermi contact term (aiso) and a electron spin-nuclear spin dipolar contribution (Ai,j), where A = aiso + Ai,j, with i,j= x,y,z, and were computed as implemented in G03 using the following relations31:
where the spin density at the position of nucleus δ(rn) is given by are elements of the spin density matrix and the ϕκ’s are the atomic basis which span the molecular orbitals, and
where other terms have their usual meaning. Spin-orbit coupling and higher order effects to the hyperfine couplings are neglected in the G03 compilations. Previous work has shown such effects to contribute only small corrections to calculated ligand couplings in copper systems24,25. Triple-ξ atomic basis plus polarization sets32 (TZVP) supplied in G03, were used for all atoms in the QM computations that yielded the hyperfine couplings. Atomic basis of at least triple-ξ quality was recommended to be used for nitrogen and copper atoms in similar DFT calculations on copper-amino complexes24. Single point energy QM computations of the systems in Figure 1 were performed using atomic coordinates from the most recent neutron diffraction results. Copper coordinates were determined according to descriptions in the EPR/ENDOR studies with the exception of alanine where Cu2+ was placed at the midpoint of the two coordinating oxygens. This only slightly repositioned the copper from the proposed site8 and did not significantly alter the results. Also, the amino-bound hydrogens for triglycine sulfate and glycine were positioned according to single crystal 2D ENDOR results as discussed below.
The present study focuses on 1H couplings from hydrogens bound to the amino and adjacent carbon in copper-glycine systems. QM geometry optimizations of the crystalline copper-triglycine sulfate and copper-glycine complexes resulted in the axial ligand molecules to significantly shift towards the complex equatorial plane, forming strong hydrogen bonding interactions with the amino ligands. Since these optimized complexes had far different axial-equatorial interactions than those in the crystal structures, a simpler Cu2+(glycine)2 complex was deemed more suitable to theoretically model the ligand proton couplings. Geometric optimization of this gas phase Cu2+-glycine model was accomplished using the Berny algorithm33, employing a double-ξ plus polarization basis34 (DGDZP) for all atoms. Previous application of similar double-ξ basis yielded acceptable geometries in similar compounds24,25. Atomic coordinates used to initiate the optimization procedure came from the neutron diffraction study of α-glycine. The final geometry of the Cu2+(glycine)2 model was similar to that shown in Figure 1 for the copper-glycine complex, excluding the two axial glycines. All G03 calculations of hyperfine couplings were performed using the NMR keyword and were done without symmetry constraints.
To the left in Figure 2 is displayed a molecular fragment of Cu-bound glycine. The Cu-N distance and Cu-N-Cα angle are designated as r and η, respectively. The protons of interest are Ha for the amino-bound and HC for Cα-bound hydrogens. The right side of Figure 2 is a scheme that defines θ, , δ and ψ, the dihedral angles between the planes AN,max-N-Cα and N-Cα-HC, AN,max-N-Cα and Ha-N-Cα, AN,max-N-Cα and Cu-N-Cα, and Ha-N-Cα and N-Cα-Cβ, respectively, where AN,max indicates the direction of the largest 14N hyperfine tensor component. For the Cu2+(glycine)2 model, QM calculations were performed at different rotational orientations of the amino group about the Cα-N bond and at different dihedral angles between the Cu-N-Cα and N-Cα-Cβ planes. The former causes changes in the angles for the two amino hydrogens. The latter introduces different θ’s for the Cα–bound hydrogens, and in addition, since the glycine structure beyond Cα is also displaced, geometric optimization of the model complex was again conducted at each dihedral angle setting. Hyperfine couplings were then determined for each newly optimized model geometry.
Figure 3 illustrates plots of the copper binding to the amino group in the four crystal systems and in the Cu2+(glycine)2 model looking down the Cα-N bond. The projections of bonds and principal directions of the maximum 14N hyperfine tensor component (AEXP or ACAL) form the dihedral angles between various planes in the complexes. When copper binds, the amino groups lose a proton. Depending on the initial orientation of the leaving proton, the remaining protons may reorient about the Cα-N bond. In Figure 3, original amino Ha orientations are designated by the dashed bonds and the solid bonds are the proposed Ha (or 2D) orientations. Previous nuclear quadrupole resonance studies have established a correlation between the direction of maximum quadrupole coupling in N-2D and the bond direction35. Quadrupole coupling tensors from the 2D ENDOR study of copper-triglycine sulfate were therefore used to locate the amino group 2D atoms. Assuming hydrogens would undergo a reorientation similar to the deuterons, the amino hydrogens in the copper-triglycine complex were likewise positioned. Here the N-Ha bond lengths were set to 1Å. Comparing their rotational positions before and after copper binding, the triglycine sulfate amino hydrogens (denoted at Da1 and Da2) rotated between 20–30° about the Cα-N from their original positions (Ha2o and Ha3o). These values are consistent with the 30° rotations reported in the 2D ENDOR study6. Moreover, the close similarity between the original amino group orientations of triglycine sulfate and glycine suggest a similar rotation for the glycine amino hydrogens. This similarity prompted an assumption in the present analysis that the original Ha hydrogens of glycine (denoted Ha1o, Ha2o and Ha2o) rotate 20° about the Cα-N rotation when copper binds (Ha1r, Ha2r and Ha2r in the site plot). This rotation causes a better alignment of the Ha3 hydrogen (signified by the dashed bond) for its replacement by the copper ion. In glycylglycine and alanine, the relative closer correspondence between N-Cu and N-Ha3 directions averts a significant rotation of the remaining two amino protons. However, for the alanine crystal complex, both the orientation of copper with respect to the N-Cα bond and the two nearly equivalent amino proton hyperfine couplings suggested a flattened amino group upon copper binding. The placements of the amino hydrogens in the flattened alanine were therefore estimated using the proton hyperfine tensor principal directions reported in the ENDOR study and are denoted Ha1/flat and Ha2/flat, in the site plot.
The experimental 14N maximum hyperfine direction (AEXP) is generally in close alignment with the N-Cu bond direction for all the complexes, and is a good indicator of the projected orientation of the unpaired nitrogen p-orbital. In the corresponding QM calculations, the calculated nitrogen hyperfine maximum (ACAL) directions have small but significant angular deviations (Δδ) from the AEXP directions and in all cases lies close to, but not exactly, the opposite bisector of the Ha1-N-Ha2 projected directions.
The bond and nitrogen hyperfine tensor directions in the site plots suggest the possibility for hyperconjugation as a means for the unpaired electron to transfer into the s-orbital of β-hydrogens. The amount of hyperconjugation in carbon free radicals having form p-CH2-CR2-H, where p refers to the carbon unpaired pπ-orbital, follows the amount of orbital overlap of the carbon pπ and hydrogen 1s and therefore depends on the cosine-square of dihedral angle θ between the p-C–C and C-C-H planes36–38. This causes a systematic variation in 1H isotropic hyperfine coupling according to the Heller-McConnell relation36
where ρπ is a measure of the spin density present in the 2pπ-orbital of the carbon, and Bo and B2 are empirical constants36–38. A simplified representation of the copper-amino group complex is where the unpaired spin in the nitrogen 2p-orbital is mostly responsible for the ligand proton isotropic couplings. This would result in a similar type of aiso dependence of the Cα hydrogen in the p-N-Cα-HC moiety. For the p-N-Ha fragment on the other hand, it is not clear whether the Ha couplings would exhibit any such systematic variation. To assess these possibilities, the relative dispositions of the Cα-HC and N-Ha bonds and unpaired nitrogen p-orbital directions with respect to the Cα-N bond, as well as the flattening of the amino group, were analyzed for their affect on the ligand 1H aiso values. The contribution of the copper unpaired orbital to the ligand nitrogen hyperfine couplings has been estimated to be less than 10%.24 And since the amino and Cα hydrogens are in a near eclipsed arrangement on the other side of the amino moiety (Figure 2), the copper orbital contributions to the proton isotropic hyperfine couplings were assumed to be small in the present analysis.
Table 2 lists the experimental and QM calculated 14N hyperfine coupling parameters derived from the tensor quantities. These are A+ = Amax - aiso and A− = Amin - aiso, where Amax and Amin are the maximum and minimum 14N hyperfine couplings, respectively. Also listed are the Cu-N distance (r) and Cu-N-Cα angle (η) for each complex. The experimental distance r varies from a short value of 1.768 Å found in glycine to 2.181Å in glyclglycine, and although none conform to the optimized copper-glycine model value of 2.042Å, these are still within the range of bond lengths found for crystals39. The η for the proposed flattened alanine is near 90°, glycylglycine has a value of 98° and both glycine systems are close to the 108° found for the gas phase optimized copper-glycine model. The anisotropies of the experimental 14N hyperfine tensors are similar and are close to axial, having an average total anisotropy (A+ - A−) of 13.23 MHz, except for the alanine complex, which has a higher value of 14.85 MHz. The isotropic coupling for copper-alanine is also larger (32.13 MHz) than the average found in the other systems (24.95 MHz). Overall, the QM computed anisotropic tensor components have general agreement with the corresponding experimental values, whereas the isotropic couplings have somewhat larger deviations. Calculations also show that a flattening of the alanine amino group significantly decreases the 14N isotropic coupling while increasing its anisotropy, which is inconsistent with the observation. Figure 4 is a plot of the dependence of the anisotropic parameters A+ and A− as a function of aiso for both experimental and calculated 14N tensors, including results for the geometric-optimized Cu2+(glycine)2 model. Besides a smaller overall anisotropy of 11.56 MHz calculated for molecule III of triglycine sulfate, and higher value of 15.63 MHz for alanine and slightly higher (14.08 MHz) for the copper-glycine model, the 14N hyperfine anisotropy remains relatively constant with an overall average of 12.33 MHz and an experimental average value of 13.23 MHz, indicating a nearly equivalent nitrogen p-orbital spin density in the crystal complexes and optimized model.
Table 3 reports the experimental and QM computed (in parentheses) proton hyperfine coupling parameters; A+ = Amax - aiso and A− = Amin - aiso (where Amax, Amin and aiso are the maximum, minimum and isotropic 1H hyperfine couplings, respectively), for both the amino and Cα-bound hydrogens. Also listed are the dihedral angles between the hydrogens and the nitrogen AEXP or ACAL directions. The Cα-N-AEXP and Cα-N-ACAL planes are both found to slightly deviate from Cu-N-Cα with δ ranging from a low of 1° for alanine to a high of 15° for molecule III of trigylcine sulfate. However, there is no apparent correlation between the magnitude of δ and how well the calculated proton couplings agree with the observed values. The agreement is far better for some protons than for others. Figure 5 plots the proton anisotropic parameters A+ and A− versus isotropic coupling aiso for the copper complexes as well as for the optimized copper-glycine model taken from Table 3. Similar plots have been useful in the past to categorize proton couplings in free radicals40. Figure 5 shows that when aiso becomes more positive, the total hyperfine anisotropy decreases by ~20%, from 6.8 MHz to 5.2 MHz for the Cα-bound hydrogens (Figure 5a) and from 21 MHz to 16 MHz for the amino hydrogens (Figure 5b), signifying only a small increase in effective distance between unpaired spin and proton occurs. The large total anisotropy of 11.84 MHz observed for the HC1 of glycylglycine in Figure 5a is anomalous and could be a consequence of its closer proximity to the copper than the other hydrogens. Also, for both the Cα-bound and amino hydrogens, the anisotropic hyperfine parameters calculated for the flattened alanine (open triangles) are smaller than for the general trend of the data.
The proton aiso’s of the Cα-bound hydrogens in Table 3 are plotted as a function of dihedral angle θ. This angle represents either the angle between the AEXP-N-Cα and N-Cα-HC planes for the experimental couplings or between the ACAL-N-Cα and Ha-N-Cα planes for the QM calculated couplings. The results are displayed in Figure 6. The solid line represents a best fit curve for the observed couplings with aiso = −1.09(40) + 8.21(82)cos2(θ) MHz. The observed alanine coupling values lie near the curve but were not included in the fit because it was not known whether a flattened amino geometry would demonstrate the same cosine-square parameters as a pyramidal one. Previous EPR and ENDOR studies on bent (pyramidal) carbon free radical systems have measured smaller β-proton aiso’s as compared to the flattened radicals, which was attributed to a reduction in ρπB241–44. The open symbols represent calculated couplings and show marked deviations from the experimental values at high dihedral angles. The dashed line traces out the variation in calculated aiso values for the copper-glycine model which was geometry-optimized at each specific dihedral angle. This line is actually a composite of two near identical lines, one from each of the two HC’s. The values calculated for the unrestricted geometry-optimized Cu2+(glycine)2 are shown as X’s and lie on the dashed curve. The calculated nitrogen hyperfine isotropic coupling (37.7 MHz ± 3%) and total anisotropy (14.2 MHz ± 1%) remain roughly constant over the range of dihedral angles. The model aiso variation gives a maximum near 155° and declines at higher dihedral angle. This result is unexpected for a simple hyperconjugation transfer of spin density which should produce maximum isotropic couplings at dihedral angles of 0° and 180°. Similar aiso variations with dihedral angle were obtained from computations employing different atomic basis sets; 6–311G, DGDVP or EPR-III, in G0328. Previous INDO calculations of pyramidal-shaped carbon free radicals indicate asymmetries in their β-proton cos2θ curves having different aiso maximum values occurring at 0° and 180°42–44, owing presumably to the different spin density distributions of the orbital lobes on either side of the carbon42. To assess whether such a pyramidal shaped amino group causes the declining trend in Figure 6, QM calculations were conducted on a series of copper-glycine models at various θ dihedral angles with the Cα-NH2 amino group flattened into a planar geometry. Here too, the aiso variation curve gave a similar pattern. This consistency suggests that the DFT/B3LYP calculations predict a more complicated mechanism for spin transfer onto the Cα hydrogens.
Figure 7 shows the variation of amino proton aiso‘s with dihedral angle , the angle between planes AEXP-N-Cα and Cα-N-Ha for the observed couplings, or between planes ACAL-N-Cα and Ha-N-Cα for the QM calculated couplings. As this angle approaches 180°, the nitrogen unpaired p-orbital should increase its overlap with the Ha s-orbital. This is consistent with the observed couplings. The solid line represents a good fit to the experimental isotropic values with aiso = −6.16(22) + 4.15(53)cos2 MHz. Again, even though the alanine couplings appear to fall on the fit curve, its amino hydrogen aiso’s were not included in the fit. The near equivalence of the alanine amino proton couplings, both observed (filled triangles) and calculated (open triangles), agrees with the nitrogen 2pπ-orbit symmetry in a flattened amino group. In marked contrast, the calculated aiso’s for the other complexes deviate significantly from the observed values. The two slightly different dashed lines in Figure 7 trace the QM calculated aiso for each amino Ha as the Cα-N bond was rotated in the geometry-optimized Cu2+(glycine)2 model. The slightly different lines are due to the asymmetry of the site. The calculated 14N hyperfine isotropic coupling (39.3 MHz ± 5%) and total anisotropy (13.6 MHz ± 5%) have relatively small variations over this range of dihedral angles and cannot therefore account for the steep dependence shown in this curve. The model and experimental 1H aiso variation curves are very different, having only two small common regions near 105° and 120°. One of these falls near the geometrically-optimized model values of = 119 and 121° for aiso = −6.27 and −5.92 MHz, respectively (shown as X’s on the dashed line). The sharpest minimum in the calculated model variation curve happens when Cα-Cβ eclipses ACAL. This configuration also corresponds to a sharp turnaround in the magnitude of the Cβ Mulliken spin density. It is possible that changes in Cβ unpaired spin density could indirectly affect the calculated isotropic couplings of the amino hydrogens by transferring some spin onto Cα. Overall, the theoretical proton aiso’s for the crystal complexes agree much better with the model variation than with the experimental aiso’s. In general, the extreme geometric sensitivity exhibited by the model variation for the amino hydrogen isotropic couplings is incompatible with the experimental findings.
The experimental hyperfine isotropic couplings for the amino hydrogens in the copper-doped crystal complexes depend on the dihedral angle between the nitrogen p-orbital and the N-Ha bond, according to aiso = −6.16 + 4.15cos2 MHz (Figure 7). It must be noted that the angular range over which this fit takes place is quite limited (about 45°) but this may also span the physically relevant geometries for copper coordinated amino acids. Also, the geometric variation of spin density on these hydrogens cannot really be ascribed to hyperconjugation simply because they are bound directly to the central atom (nitrogen) that bears the pπ spin density. On the other hand, the observed trend is consistent with a systematic change in the amount of hydrogen s contribution to the unpaired wavefunction. Similar empirical relationships have been proposed for V=O complexes and are useful predictors of metal coordination geometry45,46. Clearly, for the present systems, the QM calculations do not support the observed trend and instead demonstrate a very large geometric sensitivity of the proton isotropic coupling as the nitrogen p-orbital direction changes relative to the N-Ha bond. As remarked above, some of this sensitivity may arise from indirect effects caused by spin density delocalized on Cβ, and this remains a point for further investigation.
If one of the Ha‘s is oriented in the nodal plane of the nitrogen unpaired p-orbital, i.e., with =90°, the empirical formula in Figure 7 gives an aiso of −6.16 MHz. The structure of the oriented p-N-Ha resembles a planar nitrogen radical, permitting the application of the McConnell relationship47 aiso = Qρπ, where constant Q is proportional to the amount of spin polarization of the hydrogen 1s orbital, to calculate the spin density in the nitrogen 2pπ-orbital. With aiso = −6.16 MHz and using a Q of −81 MHz found for nitrogen free radicals48, one finds ρπ ≈ 0.076 for the amino nitrogen. This is somewhat lower than the spin density ρπ ≈ 0.094 determined using the ratio of the observed nitrogen hyperfine anisotropy (average total value =13.23 MHz) to the anisotropy calculated for the nitrogen valence p-state self consistent wavefunction (141 MHz)38. However, the latter ρπ should be reduced by ~10% to take into account the copper unpaired orbital contribution to the nitrogen hyperfine anisotropy24. Both ρπ values fall within the range of nitrogen spin densities determined by a previous QM/DFT study of ligand hyperfine couplings in similar copper-nitrogen systems24.
The experimental data in Figure 6 fit a Heller-McConnell cosine-square function of the form aiso = −1.09 + 8.21cos2θ MHz, and suggests a hyperconjugative-like mechanism for the direct transfer of spin density from the amino nitrogen to the β-positioned Cα hydrogens. In order to test the derived B0 and B2 quantities, a comparison was made with 1H isotropic couplings measured by ENDOR on Trinitrophenylmethylnitroxide49, a nitroxyl radical which contains a rotating methyl group bound to the nitrogen which carries significant π spin density. If the methyl group rotates rapidly, then an average isotropic hyperfine coupling <aiso> is observed for each β-proton, where <aiso> = ρπ(B0+½B2), and ρπ is the spin in the nitrogen 2pπ-orbital37. Spin density is equally shared between the oxygen and nitrogen 2pπ-orbitals of the nitroxyl. This gives ρπ≈0.5 for the nitrogen p-orbital. The single crystal ENDOR analysis finds <aiso> = 29.5 MHz for the rotating methyl group hydrogens, which in turn gives (B0+½B2) ≈ 59 MHz. Using the fit B0 and B2 parameters in Figure 6 and a nitrogen spin density of 0.076 from above, (B0+½B2) ≈ 40 MHz. for the Cα hydrogens, which is somewhat smaller than for Trinitrophenylmethylnitroxide. However, allowing for the small number of available data and the difference between a nitroxyl radical and a copper coordinated amino group, the parameters in Figures 6 and and77 for the cosine-square relationships are very reasonable.
The two empirical formulas found above are also consistent with results reported by pulsed-EPR/ENDOR studies of Cu2+-histidine in frozen solution, which measured and analyzed the proton hyperfine parameters in a bis-histamine coordination complex25,50. This study reports aiso values of −10 and −9 MHz for the two amino hydrogens, and 10.9 MHz for the alpha-carbon hydrogen. Although the magnitudes of these three couplings exceed the maximum values predicted by the empirical formulas above, this can be explained if the complex possessed a larger amino nitrogen pπ spin density than for the present systems. The present results would then suggest that the Ha’s of Cu2+-histidine have similar angles (near 120°) and predicts a AN,max-N-Cα-H dihedral angle of ~160°. The latter supports the authors conclusion, based on the their analysis of the proton anisotropic hyperfine parameters, that the Cα-H bond is directed significantly away from the copper25,50. Unfortunately, this cannot be evaluated since the coordinated nitrogen hyperfine couplings for the Cu2+-histidine complex have yet to be measured and analyzed.
Experimental values of amino-bound and Cα-bound proton isotropic hyperfine couplings in copper-amino acid complexes were found to empirically depend on the cosine-square of dihedral angles containing the nitrogen p-orbital and the hydrogen atoms. The Cα-bound hydrogen couplings varied according to aiso = −1.09 + 8.21cos2θ MHz (Figure 6), and the amino hydrogen couplings varied as aiso = −6.16 + 4.15cos2 MHz (Figure 7). The geometry of the p-N-Cα-H moiety would further suggest a hyperconjugative-like mechanism for transfer of spin density from nitrogen into the Cα-hydrogen s-orbital. For the amino-bound hydrogens, the mechanism for spin transfer is likely to be more complicated.
Results from the DFT quantum mechanical calculations gave mixed agreement with the experimental data. The hyperfine anisotropies calculated for both 14N and 1H couplings had much better correspondence with experimental trends than the isotropic couplings. The angular dependency of the proton isotropic hyperfine coupling computed by DFT only partially modeled the variation observed for the Cα hydrogens and failed to model the amino hydrogens. Although there appears to be some correlation with the amount of spin delocalized on Cβ and the extreme geometric sensitivity of the aiso’s for the amino hydrogens, no simple explanation can be devised. The theoretical findings also failed to match successes found by previous QM/DFT studies on vanadyl–water and vanadyl-imidazole complexes45,46. In these and earlier studies, water hydrogen and imidazole nitrogen couplings were found to experimentally depend on the dihedral angle containing the vanadyl unpaired d-orbital and the O–H bond for the water complex45 or the coordinated nitrogen pπ-orbital direction for the imidazole complex51. These variations were subsequently found to be in very good agreement with those theoretically determined45,46. Apparently for copper-amino acid systems, the subtle balance of unpaired electron spin on Cu, N, Cα and possibly Cβ has significant influence on the theoretically computed proton hyperfine couplings. In addition, the difficulty in being able to accurately model small ligand hyperfine couplings using DFT has been discussed in recent studies23–25. Nevertheless, the deduced empirical spatial-spectral relationships found in the current work will be useful in revealing bonding aspects found from EPR studies of similar complexes, improves our understanding of spin delocalization in copper-amino acid complexes and will help in interpreting proton hyperfine couplings in biological systems.
We thank SUNY/Old Westbury student Ms. Kacey-Ann Thompson for her help in the early stages of the crystallographic analysis. The following grants are acknowledged for financial support: NIGMS 5S06GM008180 (to MJC), NIGMS GM071512 (to JV), and U.S. Public Health Service Grant GM40168 (to JP).
Supplementary Information Available: (Figure S1) Pictorial views of the singly occupied molecular orbital (SOMO) and spin density calculated for the geometry optimized Cu2+(glycine)2 model and for this model with one of the CN bonds rotated by 40°. This material is available fee of charge via the Internet at http://pubs.acs.org.