Deuterium Quadrupolar Tensors of l-Histidine Hydrochloride

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J. Phys. Chem. B 2006, 110, 25059-25065

25059

Deuterium Quadrupolar Tensors of L-Histidine Hydrochloride Monohydrate-d7 Xingang Zhao and Gerard S. Harbison* Department of Chemistry, UniVersity of Nebraska at Lincoln, Lincoln, Nebraska 68588-0304 ReceiVed: January 5, 2006; In Final Form: September 21, 2006

A deuterium NMR study at 14 T of a single crystal of L-histidine hydrochloride monohydrate has determined the deuteron quadrupole coupling constants CQ, asymmetry parameters η, and electric field gradient orientation for the imidazolium and primary ammonium groups and for a water of crystallization. The imidazolium deuterons, which have very long relaxation times, have quite different coupling constants, reflecting different hydrogen bonding but nearly identical orientations, with the most distinct principal axis in both cases nearly parallel to the N-D vector. The -ND3 groups undergo 3-fold hops about the C-N bond axis and have typical quadrupole couplings; the D2O undergoes 2-fold hops, leading to a tensor with a large asymmetry parameter. With appropriate corrections for vibrational averaging, density functional cluster calculations give an excellent fit to the imidazolium tensor magnitudes and orientations.

Introduction L-Histidine is a ubiquitous and biologically essential amino acid and, in the crystalline state, has been the focus of many structural1-8 and NMR9-16 studies. Its neutral pK value (ca 6.0) entails that relatively small shifts in pH will change its charge; its heterocyclic imidazole side chain is also an important structural and catalytic element in proteins. For example, histidine plays a key role in both conventional serine proteases, in herpes viral serine proteases (in which they constitute twothirds of the catalytic triad17), and in other hydrolytic proteins.18 Histidyl residues also function in proton transport and cotransport.19 In aqueous solution around neutral pH, L-histidine hydrochloride crystallizes as a monohydrate. The crystal structure of this polymorph has been determined by X-ray1,2 and neutron diffraction.8 As a result of the availability of high-quality structural information, this particular crystal has often been chosen for solid-state NMR studies. and it has an interesting and unusual feature; the hydrogen bonds formed by the two chemically very similar imidazolium nitrogens are, due to lattice packing, quite different. The N(3) or τ nitrogen has a weak and nonlinear N-H‚‚‚O hydrogen bond, with rNO ) 282.9 pm, rNH ) 102.6 pm, and NHO ) 143.1°. In contrast, the N(2) or π nitrogen has a much stronger, linear intramolecular N-H‚‚‚O hydrogen bond (rNO ) 264.2 pm, rNH ) 107.0 pm, ∠NHO ) 170.9°). Harbison et al.10 measured the 15N chemical shift tensors at natural abundance of the two nitrogen atoms in the imidazole ring using single-crystal NMR and found that the hydrogenbonding differences were reflected in the solid-state NMR spectrum: The strongly hydrogen-bonded N(2) nitrogen in the crystal is considerably less shielded than the N(3) nitrogen or either nitrogen in solution. Following measurement of the nuclear quadrupole coupling constants and asymmetry parameters, using double resonance methods, by Edmonds,9 McDowell and co-workers13 determined the full 14N quadrupole coupling tensors in the same material. The quadrupole coupling constants CQ ) eQVzz/h are rather

* Author to whom correspondence should be addressed. E-mail: [email protected].

small (-1.29 MHz, 1.47 MHz), and the asymmetry parameters large (η ) 0.95, 0.27); the substantial differences in magnitude and orientation were attributed to differences in hydrogen bonding. Roberts et al.,12 using two-dimensional magic angle spinning separated local field (MAS-SLF) NMR confirmed the orientation of the 15N(2) chemical shielding tensor with respect to the N-H bond axis and found that the unusually long N-H bond reported in the neutron diffraction structures107.0 pms is also quite substantially elongated when measured by NMR dipolar measurements (rNH ) 109.6 ( 2 pm). A remeasurement of the bond length by similar methods by the McDermott group15 gave a short N-H distance of 104.6 pm. Since there are good theoretical reasons why NMR bond distances tend to be longer than neutron distances, this figure has to be counted as anomalous, and later measurements by the Levitt group16 gave a bond length of 109.0 ( 5 pm, in excellent agreement with the earlier method. Using three-dimensional solid-state NMR methods, Ramamoorthy et al.14 studied the magnitude and orientation of the principal elements of the 15N chemical shift, 1H chemical shift, and 1H-15N dipolar coupling in the 15N π histidine nitrogen sites, again confirming the single-crystal results. 15N chemical shift and 14N quadrupole coupling constant calculations of L-histidine hydrochloride monohydrate were performed by Strohmeier et al.20 It was found that cluster calculations were necessary to obtain a reasonable reproduction of experimental parameters and that even so computations tended to overestimate the anisotropy of both chemical shielding and quadrupole coupling tensors; it is likely that neglect of vibrational averaging is responsible for this discrepancy. These differences may mirror differences in proteins, as the two nitrogen atoms may serve very different functions in an enzyme’s active site. For example, in the His48 residue of pancreatic phospholipase A2, the N(2) nitrogen plays a structural role, forming a strong hydrogen bond between His48 and Asp99, while the N(3) nitrogen fixes the catalytic water molecules, being an important factor in catalysis.21,22 Hydrogen-bonding and electrostatic interactions involving these two nitrogen nuclei in histidine therefore provide useful insight into the effect of local structure on biological function.

10.1021/jp0600965 CCC: $33.50 © 2006 American Chemical Society Published on Web 11/15/2006

25060 J. Phys. Chem. B, Vol. 110, No. 49, 2006

Zhao and Harbison

The quadrupole coupling tensor is known to be an excellent probe for local structure and intermolecular interactions because it is very sensitive to the charge distributions on the quadrupole nuclei and small differences in their electrostatic environments. As yet, the quadrupole coupling tensors of the exchangeable deuteron positions in histidine have not been recorded. The development of a new single-crystal NMR method23 has recently made it possible to analyze relatively complex systems such as this one. In this paper we will report the use this method to determine the quadrupole coupling tensors of D(9) (bonded to N(2)), D(10) (bonded to N(3)), -ND3+, and D2O residues in a perdeuterated single crystal of L-histidine hydrochloride monohydrate-d7. Methods L-Histidine hydrochloride monohydrate was purchased from Aldrich Chemical Co., St. Louis, MO, and a single crystal with appropriate dimensions (12 mm × 10 mm × 3 mm) was grown by slow evaporation from a D2O solution at room temperature. 2H NMR spectra were obtained using a Bruker Avance 600 MHz NMR spectrometer, with a home-built singly tuned goniometer probe. All spectra were referenced to the 2H signal from liquid D2O, which was assumed to lie at 4.7 ppm from tetramethylsilane (TMS). The measured 90° pulse was 6 µs; this was rather long, because of the large coil needed to accommodate the single crystal; to achieve a suitable bandwidth, we used a 2 µs pulse. There are four types of chemically nonequivalent deuterons in the molecule, and each unit cell contains four magnetically nonequivalent molecules; therefore 16 quadrupolar-split pairs of NMR signals are expected (with possible further splittings from dipolar couplings). Very usefully, we found that the -ND3+ and D2O deuterons have short longitudinal relaxation times, presumably because of fast water and -ND3+ hopping motions, while D(9) and D(10) have long relaxation times. Through the use of a relaxation delay between NMR acquisitions of 100 ms, only -ND3+ and D2O signals were detected, while waiting 200 s between acquisitions, all four deuteron signals were observed. A spectrum of D(9) and D(10) alone could then be obtained by difference spectroscopy. A typical long relaxation delay spectrum is shown in Figure 2. Data were collected in 6° increments for a full 180° rotation about the goniometer axis; the frequencies of the 2H signals were extracted by a three-point fit to the peaks. Quadrupolar doublet pairs could generally be identified by inspection; differences between the frequencies of these pairs were extracted and plotted. As has been discussed previously, the differences contain contributions from the first-order quadrupole coupling, while the sums of the doublet frequencies contain chemical shifts and second-order quadrupole contributions. The latter are expected to be negligible for deuterium, and the scatter in the data was unfortunately too great to allow reliable extraction of chemical shielding tensors.

Computations The neutron diffraction coordinates8 contain an evident typographical error; the z-coordinates for C(5) and H(9) are in serious conflict with the X-ray structure and with published bond lengths in the diffraction structure. The neutron coordinates for C(5) can easily be replaced with the X-ray coordinates,2 since these are of comparable accuracy; however, X-ray structures do not give accurate hydrogen positions, and so coordinates for H(9) had to be generated by density functional theory (DFT) calculations (see below).

Figure 1. Environment of the histidinium cation in L-histidine hydrochloride monohydrate, showing the atoms included in the cluster calculations. Hydrogens are white, carbons black, oxygens red, nitrogens blue, and chlorines green.

Figure 2. Deuterium single-crystal NMR spectrum of L-histidine hydrochloride monohydrate, obtained as described in the text.

In a hydrogen-bonded crystal structure such as that of hydrochloride monohydrate, accurate computations of NMR parameters need to include hydrogen bonds and must therefore include more than the single molecule in the asymmetric unit. In such circumstances, one of two options is usually chosen; either a full unit cell with periodic boundary conditions can be used in a plane-wave DFT calculation, or a “cluster”type calculation can be performed, including the molecule of interest and the residues to which it is hydrogen-bonded. Because of the large size of the orthorhombic unit cell, the latter strategy was chosen. Computations therefore included the L-histidinium cation, two waters of hydration, one hydrogenbonded to the carboxyl and one to the ammonium group, two carboxylates (R-COO-) hydrogen-bonded to the histidinium nitrogens, two ammonium ions (R-NH3+) hydrogen-bonded to the water and to the carboxyl, and three chloride ions, one hydrogen-bonded to the carboxyl water of hydration and two to the protonated amine, all at the crystallographic positions. Two more ammonium ions were then added to ensure charge neutrality of the cluster and facilitate convergence of the electronic wave function. The carboxyl R groups of the extrinsic hydrogen-bonded residues were in both cases replaced by a hydrogen at 107 pm along the C-R bond axis, while the ammonium R groups were replaced by a proton at 103 pm. Once this cluster had been constructed, the positions of all the added hydrogens as well H(9) of the L-histidinium itself were L-histidine

2H

NMR of L-Histidine Hydrochloride Monohydrate

optimized. The basis set used was 6-31G(d) in conjunction with the B3LYP density functional, using the program GAMESS.24 The optimized N(2)-H(9) bond length was 108.8 pm (from the neutron structure, 107.0 pm), and the C(5)N(2)H(9) angle was 120.9°. The full cluster is depicted in Figure 1, and its coordinates are given as Table 4 in the Supporting Information. Upon completion of the restricted optimization, electric field gradient tensor elements Vmn were computed for each exchangeable hydrogen, at various levels of theory up to 6-311++G(2d,p). The most distinct principal value of the second-rank electric field gradient tensor is related25 to the quadrupole coupling constant CQ, by

CQ (Hz) )

eQV33 (Hz) ) -V33 (a.u.) × KQ × Q (fm2) h

with the value of the constant KQ taken as 2 349 647.8 Hz hartree-1 bohr2 fm-2 and the quadrupole moment Q for deuterium as 0.2859 fm2, corresponding to CQ (kHz) ) 671.8V33 (a.u.).26 The sign convention is chosen to make the electric field gradient (EFG) computed by GAMESS for the C-D group in methane and other alkanes yield a positive value for the deuterium quadrupole coupling constant, as is invariably observed in those molecules.27 The computed values given in this paper were obtained using the program Gaussian 0328 at the 6-311++G(2d,p) level; deuterium quadrupole coupling constants and asymmetry parameters computed for other basis sets are compared in the Supporting Information (Table 5). First-order corrections for vibrational averaging were performed by displacing the D(9) and D(10) deuterons along the N-D axis by increments of (5 and (10 pm, fitting the resulting anharmonic potential to a cubic function, and then displacing it by approximately 0.09 rad in either direction along both the in-plane and the out-of-plane torsional coordinates, fitting the energy along each coordinate to a quadratic. The Schro¨dinger equation was then solved variationally using the resulting threedimensional potential function and a 4 × 3 × 3 basis set of harmonic wave functions. At each displaced point electric field gradients were computed, and each element of the EFG tensor was fitted to a quadratic in each of the three dimensions. The expectation value of the three-dimensional EFG tensor was then calculated over the vibrational ground state; none of the vibrationally excited states were sufficiently low in energy to contribute significantly to the thermal average. Where it was necessary to evaluate the vibrational average at nonequilibrium bond lengths, the equilibrium bond length was perturbed by adding a small linear term to the longitudinal potential to effect the required equilibrium bond length change. Experimentally, a single chemically and magnetically distinct deuterium shows an NMR doublet whose frequency splitting to first order in perturbation theory is given by

∆V ) Qzz,L )

3eqVzz,L 2h

where Qzz,L and Vzz,L are the laboratory-frame quadrupolar and EFG tensors, respectively. Clearly, therefore, the maximum splitting is obtained with the most distinct principal axis parallel to the field and is equal to three-halves of the quadrupolar coupling constant. Results The quadrupole splittings for each of the four chemically distinct deuteron species are plotted versus rotation angle as the data points in Figure 3. The three OSCULANT transits,

J. Phys. Chem. B, Vol. 110, No. 49, 2006 25061 TABLE 1: Direction Cosines of the Local Molecular Frame Used in This Work, Relative to the Crystallographic abc-Axis System a

b

c

a

b

c

D(9) x -0.4690 0.6927 -0.5479 y 0.8633 0.4905 -0.1189 z 0.1864 -0.5288 -0.8280

D(10) x -0.1852 0.1405 -0.9726 y -0.8441 -0.5295 0.0842 z -0.5032 0.8366 0.2167

-ND3+ x -0.6635 0.3258 y 0.1592 -0.8182 z 0.7311 0.4738

D2O x -0.3371 -0.6316 0.6982 y -0.8477 -0.1191 -0.5170 z 0.4097 -0.7661 -0.4952

0.6736 0.5525 0.4910

where the crystallographic axes cross the plane perpendicular to the field, are evident, at (θ1, θ2, θ3) ) (6°, 26°, 111°). These transit angles directly lead to the Euler angles that relate the crystallographic to the goniometer frame (RG, βG, γG) ) (158°, 87°, -31°). Through the use of these angles, a five-parameter fit was conducted for each deuteron using grid-search methods, optimizing Q33, η, and the three Euler angles, RX, βX, and γX, relating the quadrupolar principal axis frame (PAF) to the crystallographic frame. Once good fits were achieved, the leastsquares error for the entire data set was minimized, using the 20 parameters that determine the crystallographic quadrupolar tensor for the four deuterons and the three angles defining the crystallographic frame in the goniometer frame. Final values for these angles (RG, βG, γG ) from the fit were (157.8°, 86.3°, -30.7°). The best fits are shown by the solid lines in Figure 3. To orient the principal axis frame relative to the molecule, local molecular frames were constructed for each deuteron (Table 1), using the neutron structure coordinates, except for C(5), in which the X-ray coordinates2 were chosen, and D(9), where we used coordinates from the restricted DFT optimization. Molecular frames were chosen as follows: For D(9), the z-axis lies parallel to the N(2)-D(9) bond; the y-axis lies in the D(9)N(2)C(5) plane, and the x-axis is orthogonal to these two; for N(3)-D(10), the z-axis lies parallel to the N(3)-D(10) bond; the x-axis lies in the D(10)N(3)C(5) plane; and the y-axis is orthogonal to x and z. Deuterons in D2O at room temperature usually undergo rapid 2-fold hops about the C2V z-axis, and so we assigned the local molecular frame according to the three approximate C2V axes, the normal to the water plane, the bisector of the D(11)O(3)D(12) angle, and an axis perpendicular to these two. For -ND3+, which was expected to undergo 3-fold hops about the C-N bond, the z-axis was chosen parallel to the N(1)-C(2) vector, the y-axis orthogonal to it in the D(7)N(1)C(2) plane, and the x-axis is orthogonal to z and y. All the quadrupole tensor elements, Euler angles, and direction cosines comparing the local molecular frame to the PAF are listed in Table 2, and the orientations of the quadrupolar tensors are depicted in Figure 4. Discussion 2H Quadrupole Couplings of D(9) and D(10). The two protonated or deuterated imidazolium nitrogens, while formally chemically similar, are quite different in their hydrogen bonding, and this difference has previously been noted to affect the 15N chemical shielding10 and the N-H bond distance measured by both NMR12 and neutron diffraction.8 These hydrogen-bonding differences are observed a fortiori in the deuteron quadrupole coupling constants. The N(2)-D(9)‚‚‚O hydrogen bond distance is 158.0 pm, and the bond angle is 171°, indicating a strong and orthodox hydrogen bond; this is reflected in a relatively

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Figure 3. Rotation plots for the four chemically distinct species in this crystal. The black trace corresponds to the molecules whose coordinates are given in the crystal structure, and blue, red, and green molecules are related by 21 screw operations about the crystallographic a-, b-, and c-axes, respectively.

TABLE 2: Quadrupolar Tensor Principal Values and Direction Cosines of the Principal Axes in the Crystallographic and the Local Molecular Frames ν (kHz) Q11 Q22 Q33

a

b

c

x

D(9) (eqV33/h ) 129.7; η ) 0.104) -87.1 -0.2941 0.7050 -0.6454 0.9799 -107.4 0.9245 0.3812 -0.0048 -0.1669 194.5 0.2427 -0.5980 -0.7639 -0.1095

y

ν (kHz)

z

0.1689 0.1068 0.9856 -0.0253 0.0069 0.9940

D(10) (eqV33/h ) 176.4; η ) 0.184) Q11 -108.0 -0.2116 0.2215 -0.9519 0.9962 -0.0189 Q22 -156.6 -0.8520 -0.5191 0.0686 0.0182 0.9998 Q33 264.6 -0.4789 0.8255 0.2985 -0.0857 -0.0077 Q11 Q22 Q33

TABLE 3: Computed Quadrupolar Tensor Principal Values and Direction Cosines of the Principal Axes in the Crystallographic and the Local Molecular Frames

0.0855 0.0093 0.9963

-ND3+ (eqV33/h ) -52.4; η ) 0.271) 32.2 -0.6863 0.6584 0.3090 0.8779 -0.4772 -0.0380 46.4 -0.2142 -0.5890 0.7792 0.4751 0.8783 -0.0531 -78.6 0.6950 0.4686 0.5453 0.0588 0.0285 0.9979

Q11 Q22 Q33

a

b

c

x

y

D(10) (eqV33/h ) 214.4; η ) 0.116) Q11 -142.1 -0.0923 0.2357 -0.9674 0.9911 -0.1284 Q22 -179.6 -0.8333 -0.5501 0.0545 0.1300 0.9901 Q33 321.7 -0.5451 0.8011 0.2472 -0.0269 0.0567 Q11 Q22 Q33

z

D(9) (eqV33/h ) 109.4; η ) 0.215) -64.4 -0.4114 0.7239 -0.5537 0.9978 0.0657 -0.0009 -99.7 0.9046 0.3987 -0.1508 -0.0654 0. 9944 0.0826 164.0 0.1116 -0.5630 -0.8189 0.0064 -0.0824 0.9966 0.0340 0.0528 0.9980

-ND3+ (eqV33/h ) -54.3; η ) 0.155) 34.4 -0.6804 0.6525 0.3335 0.8886 -0.4580 -0.0245 47.0 -0.1847 -0.5931 0.7836 0.4572 0.8888 -0.0313 -81.5 0.7092 0.4716 0.5241 0.0362 0.0166 0.9992

D2O (eqV33/h ) -122.3 kHz; η ) 0.915) Q11 7.9 -0.3587 -0.6997 0.6178 0.9942 0.0679 0.0831 Q22 177.0 -0.8268 -0.0692 -0.5583 -0.0674 0.9977 -0.0093 Q33 -184.9 -0.4334 0.7111 0.5537 -0.0836 0.0036 0.9965

D2O (eqV33/h ) -160.2 kHz; η ) 0.831) Q11 20.2 -0.1639 -0.5878 0.7922 0.9796 -0.2006 -0.0091 Q22 220.1 -0.8976 -0.2443 -0.3670 0.2006 0.9797 0.0012 Q33 -240.3 0.4093 -0.7712 -0.4876 0.0087 -0.0030 1.0000

small quadrupole coupling constant of 129.7 kHz. (The sign of the constant is determined by computation, not experiment; see below.) The other deuteron, D(10) with a much longer, nonlinear hydrogen bond (rD‚‚‚O ) 194.1 pm; ∠NDO ) 143°), has, as would be predicted, a significantly larger CQ of 177.4 kHz. The orientations of the tensors are not remarkable; in both cases the most distinct axis (corresponding to Q33) is nearly parallel to the N-D bond: D(9) and D(10) deviate from their respective bond axes by 6° and 5° respectively. The smallest principal value is directed in both cases approximately perpendicular to the imidazolium plane: The respective deviations are 12° and 1°. It is not uncommon for single-crystal studies to produce deviations of a few degrees from symmetry axes, and the

question always arises if these deviations are real or the result of systematic error. It is useful, therefore, to compare the experimental principal axes with those obtained by DFT calculations. The computed tensor principal axes in the local molecular frame are given in Table 3; they show about the same deviation from the local molecular frame as the experimental values, leading one to believe that the deviations of experimental values from the local frame may well be real and not artifactual. In both cases, the computed CQ values are of a similar magnitude to the experimental values, and since the signs of the CQ values cannot easily be experimentally determined, experimental CQ values are assigned negative signs to correspond to computed values. The experimental CQ values are

2H

NMR of L-Histidine Hydrochloride Monohydrate

J. Phys. Chem. B, Vol. 110, No. 49, 2006 25063

Figure 4. Deuterium EFG tensor orientations (red arrows) relative to the local molecular frames (green), defined in the text, for (a) the imidazolium deuterons, (b) the ammonium deuterons, and (c) the water deuterons.

also quite close to the empirical relationship determined by Soda and Chiba,29 modified for nonlinearity

CQ ) A +

B cos R (rO‚‚‚D (Å))3

(1)

which, when parametrized according to Hunt and Mackay30 with A ) 282 kHz and B ) 572 kHz (R is ∠NDO), leads to CQ values of 139 and 219 kHz for D(9) and D(10), respectively. Given the ∼15% deviation between computed and experimental imidazolium CQ values, we decided to determine if a better correspondence with experiment could be obtained by averaging the computed CQ over the vibrational zero-point motion. In view of the complexity of the system, we chose a simple model of three local vibrational modes parallel to and orthogonal to the N-D bond vectors. This model neglects mode couplings and deviation of the system from approximate local C2V symmetry, but in view of the size of the corrections it is probably adequate for the task. After performing the calculations as described in the Computations section, we obtained values of CQ ) 103.2 kHz and η ) 0.215 for D(9) and CQ ) 179.9 kHz and η ) 0.124 for D(10). The CQ of D(10) is now approximately 15% reduced from the computed value at the equilibrium structure, in excellent agreement with experiment; the major part of the decrease results from averaging of the wave function along the longitudinal ND coordinate and specifically from the increased weighting of contributions from long ND distances by the anharmonicity of the wave function. The D(9) values are in poorer agreement. However, in this system (as in others34) the CQ is a strong function of the bond

length. Since the position of D(9) used in our calculations was computed and approximately 1.8 pm longer than the experimental value, we adjusted the DFT potential by adding a small linear term to bring the equilibrium value of the N(2)D(9) distance into agreement with that reported by neutron diffraction.8 This correction gave a vastly improved values for the deuterium tensor (CQ ) 126.3 kHz and η ) 0.190 for D(9)). Vibrational averaging did not substantially affect the orientation of either tensor. The very long T1 relaxation times observed for D(9) and D(10) are evidence that the hydrogen-bonding network involving the imidazolium ring is quite rigid. While it is often assumed in solid-state NMR, as a rule of thumb, that 2H T1 values will be short, in this system, relaxation delays on the order of 3-4 min are required to avoid saturation, even with a 30° excitation pulse. Deuterium, therefore, cannot always be assumed to relax efficiently in biological solids. 2H Quadrupole Coupling of -ND +. The C and η values 3 Q were found to be -52.4 kHz and 0.174 respectively; the considerable reduction in the magnitude of CQ and the short relaxation time are certainly due to motional averaging by 3-fold hops about the C-N bond axis. For comparison, quadrupole coupling constants for rotating -ND3+ groups of other amino acids were CQ ) (51.3 kHz and η ) 0.272 for R-glycine31 and CQ ) (49.2 kHz and η ) 0.176 for L-alanine.32 Those values are very close to ours. Since each deuteron spends an equal amount of time in each of the three static positions, the effective quadrupole tensor is an average of the three static tensors. For an exactly tetrahedral group averaged by 3-fold hops about one of the vertexes, a simple calculation shows that

25064 J. Phys. Chem. B, Vol. 110, No. 49, 2006 the field gradient should be averaged by a factor of 3. Experimentally, solid deuterioammonia has a deuterium CQ of 72.4 kHz.33 -ND3+ groups in amino acids generally rotate rapidly about the N-C bond with local approximate C3 symmetry; in a situation of exact C3 symmetry, η should be zero, and the unique axis of the averaged tensor should lie along the N-C bond. We find experimentally that the Q33 element in L-histidine hydrochloride monohydrate lies 3.9° from that direction. The significant asymmetry parameters in such systems indicate substantial deviation of either the geometry34 or the hydrogen bonding from 3-fold symmetry. In the present case, both conditions are met: The respective ∠CND angles are 110.2°, 113.4°, and 108.9°, while the D(6)‚‚‚Cl hydrogen bond at rDCl ) 217 pm is near linear (∠NDCl ) 169°) and significantly stronger than D(8)‚‚‚Cl (rDCl ) 226 pm; ∠NDCl ) 149.4°). There is no straightforward way to compare the strength of these two D‚‚‚Cl hydrogen bonds to that between D(7) and the oxygen from the water of crystallization. Averaging the computed electric field gradient tensors gives CQ and η values of -48.3 kHz and 0.196 respectively, in fair agreement with experiment (Table 3); the most distinct computed principal axis lies 1.5° from the C-N bond; all three computed axes lie within 1.8° of the experimental values . The unaveraged tensors for the individual deuterons of the -ND3+ group are given as Supporting Information in Table 6. 2H Quadrupole Coupling of D O. The quadrupole coupling 2 of O-D groups also depends strongly on hydrogen bonding and dynamics. In free water molecules25 and LiOD,26 which are not hydrogen-bonded, CQ values of 318.6 and 320 kHz, respectively, were measured, with the Q33 element nearly parallel to the O-D bond. If the dynamics are neglected, in other words for static O-D‚‚‚O systems, then the CQ value can be correlated with the hydrogen bond length,27 using eq 1, with parameters A ) 303 kHz and B ) 521 kHz. Therefore, a static D2O molecule with a weak hydrogen bond will typically have a CQ value of around 200 kHz, as observed in several hydrates.27 However, D2O molecules often flip about their 2-fold axis, resulting in a lower CQ value and a η value of nearly 1.0. In R-RbAl(SO4)2‚12D2O, for example, the static values were CQ ) 186.5 kHz and η ) 0.1234, while the 2-fold hops led to CQ ) -122.1 kHz and η ) 0.8087. For the D2O residue in L-histidine hydrochloride monohydrate-d7, we obtained a CQ value of -122.3 kHz with η ) 0.915. This result immediately indicates that the D2O undergoes rapid reorientations around the local 2-fold axis. The orientation of the quadrupole coupling tensor is almost parallel with the local pseudo-C2V symmetry axes, with the Q33 element 4.7° from the normal to the molecular plane and the Q11 element 6.2° from the bond bisector. D2O forms hydrogen bonds with the carboxyl group and a Cl- ion, probably contributing to the reduced CQ value. In addition, there is evidence for considerable librational motion in the present crystal; the O-H bond lengths given in the neutron structure8 are significantly shorter than those expected for water, particularly a hydrogen-bonded water. The computed CQ value is significantly higher than the experimental value, but if librational motion shortens the apparent O-H bond length, since CQ values increase as rOH decreases, then a larger computed CQ value is not unexpected. The unaveraged tensors for the individual deuterons of the D2O group are also given as Supporting Information in Table 6. General Discussion. While there is an extensive literature charting the dependence of the deuterium quadrupole constant on hydrogen bonding, from the very weakest and most nonlinear hydrogen bonds, to the strongest, there is very little information

Zhao and Harbison on the orientation changes with hydrogen bond strength. The present work suggests that it does not; D(9), involved in a strong linear hydrogen bond, has essentially the same orientation in the frame of local symmetry as D(10), where the hydrogen bond is much weaker and nonlinear. In this respect, our deuterium results differ from the nitrogen quadrupole tensors measured by McDowell and co-workers.13 The computed magnitudes of these tensors are only in fair agreement with experiment without vibrational correction but in excellent agreement once vibrational effects are added, a salutary lesson on the importance of including zero-point and thermally excited vibrational motion in EFG calculations of hydrogen-bonded deuterons35,36 to accurately reproduce deuterium quadrupole coupling constants. Even with the use of the OSCULANT methods, L-histidine hydrochloride monohydrate probably approaches the feasible size limit for a conventional single-crystal determination; tracing and assigning the 32 rotation plots (and ignoring the additional dipolar splittings evident at certain orientations) was a major undertaking. In larger systems, more sophisticated methods employing angle-flipping or perhaps rapid angle-dependent twodimensional NMR may be necessary to give adequate resolution and to facilitate assignment. Acknowledgment. This research was funded by the National Institutes of Health (Grant No. R01 GM 065252). Supporting Information Available: Coordinates of the cluster used in ab initio calculations, comparison of the computed quadrupolar coupling constant and asymmetry parameters of L-histidine hydrochloride monohydrate-d7 over various basis sets, and computed quadrupolar tensor principal values and direction cosines for the unaveraged -ND3+ and D2O deuterons in L-histidine hydrochloride monohydrate. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Donohue, J.; Lavine, L. R.; Rollett, J. S. Acta Crystallogr. 1956, 9, 665. (2) Donohue, J.; Caron, A. Acta Crystallogr. 1964, 17, 1178. (3) Lehmann, M. S.; Koetzle, T. F.; Hamilton, W. C. Int. J. Pept. Protein Res. 1972, 4, 229. (4) Kistenmacher, T. J.; Hunt, D. J.; Marsh, R. E. Acta Crystallogr., Sect. B 1972, 28, 3352. (5) Madden, J. J.; McGandy, E. L.; Seeman, N. C. Acta Crystallogr., Sect. B 1972, 28, 2377. (6) Madden, J. J.; McGandy, E. L.; Seeman, N. C.; Harding, M. M.; Hoy, A. Acta Crystallogr., Sect. B 1972, 28, 2382. (7) Edington, P.; Harding, M. M. Acta Crystallogr., Sect. B 1974, 30, 204. (8) Fuess, H.; Hohlwein, D.; Mason, S. A. Acta Crystallogr., Sect. B 1977, 33, 654. (9) Edmonds, D. T. Phys. Rep. 1977, 29, 233. (10) Harbison, G. S.; Herzfeld, J.; Griffin, R. G. J. Am. Chem. Soc. 1981, 103, 4752. (11) Munowitz, M.; Bachovchin, W. W.; Herzfeld, J.; Dobson, C. M.; Griffin, R. G. J. Am. Chem. Soc. 1982, 104, 1192. (12) Roberts, J. E.; Harbison, G. S.; Munowitz, M. G.; Herzfeld, J.; Griffin, R. G. J. Am. Chem. Soc. 1987, 109, 4163. (13) McDowell, C. A.; Naito, A.; Sastry, D. L.; Takegoshi, K. J. Magn. Reson. 1986, 69, 283. (14) Ramamoorthy, A.; Wu, C. H.; Opella, S. J. J. Am. Chem. Soc. 1997, 119, 43. (15) Song, X.; Reinstra, C. M.; McDermott, A. E. Magn. Reson. Chem. 2001, 39, S30. (16) Zhao, X.; Sudmeier, J. L.; Bachovchin, W. W.; Levitt, M. H. J. Am. Chem. Soc. 2001, 123, 11097. (17) Khayat, R.; Batra, R.; Massariol, M. J.; Lagace, L.; Tong, L. Biochemistry 2001, 40, 6344. (18) Janssen, M. J. W.; van de Wiel, W. A. E. C.; Beiboer, S. H. W.; van Kampen, M. D.; Verheij, H. M.; Slotboom, A. J.; Egmond, M. R. Protein Eng. 1999, 12, 497.

2H

NMR of L-Histidine Hydrochloride Monohydrate

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