J. Phys. Chem. B 2009, 113, 15119–15127
15119
Vibrational Modeling of Copper-Histamine Complexes: Metal-Ligand IR Modes Investigation Bertrand Xerri,† Jean-Pierre Flament,‡ Hugo Petitjean,† Catherine Berthomieu,§ and Dorothee Berthomieu*,† Institut Charles Gerhardt, MACS, UMR 5253 CNRS-ENSCM-UM1-UM2, 8, rue de l’Ecole Normale, 34296 Montpellier cedex 5, France, UniVersité Lille1, Sciences et Technologies, Laboratoire de Physique des Lasers, Atomes et Molécules (UMR, CNRS 8523) and CERLA (FR 2416 CNRS), 59655 VilleneuVe d’Ascq Cedex, France, and CEA, DSV, IBEB, Laboratoire des Interactions Prote´ine Me´tal, UMR 6191 CNRS-CEA-UniVersite´ Aix-Marseille, CEA-Cadarache, Saint-Paul-lez-Durance, F-13108, France ReceiVed: June 24, 2009; ReVised Manuscript ReceiVed: August 24, 2009
Recent reports on proteins and related models show that vibrational spectroscopy in the far-infrared domain is a promising technique to characterize metal sphere coordination in proteins. The low-frequency modes are however complex, and there is a need to develop the analysis of metal sites by means of quantum chemical calculations as a support for useful interpretation of the far-IR data. In this study, we determined vibrational properties for systems containing CuII-N(Imidazole) interactions present in many biological complexes by means of quantum chemical calculations and confronted the normal mode description with available experimental data. Analysis of the [Cu(histamine)]2+ complex led us to conclude that the anharmonic contributions are negligible in the far-IR domain. Geometry optimizations and vibrational frequency calculations of [Cu(hm)]2+ and [Cu(hm)2(ClO4)2] complexes were compared using various hybrid DFT functionals and basis sets. These investigations stressed the need of potential energy distribution calculations (PED) to assign the vibrational modes, to obtain an overall description of the vibration modes, and to efficiently compare the methods. Comparison of calculation methods with the B3LYP/6-31+G(d,p) and B3LYP/6-311+G(2d,2p) methods and with available experimental data showed that the B3LYP/6-31G(d,p) level of theory provides accurate predictions of the normal mode frequencies and assignments. These comparisons also enlighten that theoretical investigations of 2H- and 65Cu-labeled [Cu(hm)2(ClO4)2] complexes give with a very good accuracy the band shifts of the labeled copper-histamine derivatives. The theoretical calculations combined with experimental data allowed us to predict and calculate with good accuracy the values and assignments of the low-frequency IR modes, notably those involving metal contribution. Introduction Metals play key roles at active or structural sites in more than one-third of the proteins. Structural knowledge of metalloenzymes is thus of paramount interest to get a better understanding of their activity in biological reactions and to address mechanistic issues related to enzymatic catalysis. Detailed analysis of metal-ligand bond properties by means of vibrational spectroscopy is very useful. In contrast with resonance Raman spectroscopy, infrared spectroscopy applies in principle to all metal sites and redox states. It can provide information on metal-ligand bond properties by the analysis of the far-IR domain. This domain becomes accessible to experimentalists with the development of new setups adapted to the study of biological samples.1-5 The exploitation of farIR data requires reliable assignments of IR bands, to determine contributions from the close environment of the metal and ultimately to correlate IR mode frequencies and structural properties. Quantum mechanics (QM) calculations have shown to be a powerful approach to predict accurately the spectroscopic properties of transition-metal-containing bioinorganic com* Corresponding author. E-mail:
[email protected]. † Institut Charles Gerhardt. ‡ Universite´ Lille1, Sciences et Technologies. § CEA DSV IBEB UMR6191.
plexes, including more recently vibrational spectra.6-10 In addition, computational methods can be followed by a PED (potential energy distribution) calculation which provides an enlightening analysis of the modes, in particular in the far-IR region where many atoms contribute to the modes. The accurate calculation of normal modes of molecular systems such as metalloenzymes needs QM methods accounting for the dynamic correlation of transition metal d electrons. Accurate calculations such as multireference configuration interactions or coupled cluster calculations are currently restricted to relatively small molecules. Calculations approaches based on density functional theory (DFT) are an attractive alternative to treat transition metal complexes of chemically relevant size.11-13 Considering the large number of copper-containing enzymes that involve histidine as metal ligands, the accurate calculation of normal modes involving CuII-N(Imidazole) interactions is of prime importance for the vibrational analysis of these proteins. In the present study, we report on defining the most reliable DFT functional and basis set to predict vibrational modes on small CuII models. This investigation was performed on bioinorganic copper-histamine (hm) derivatives, [Cu(hm)]2+ and [Cu(hm)2(ClO4)2] (Figures 1 and 2), in which CuII is coordinated to the nitrogen atoms of the imidazole ring (im) and to the amine group of the histamine side chain which forms a chelate ring labeled ch (Nπ, C4, CH2, CH2, NH2 from Figure 1). The predicted
10.1021/jp905917z CCC: $40.75 2009 American Chemical Society Published on Web 10/15/2009
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J. Phys. Chem. B, Vol. 113, No. 45, 2009
Figure 1. Structural model of the [Cu(hm)]2+ complex. Atoms are labeled using imidazole ring notation. Gray balls are H atoms; green balls are C atoms; blue balls are N atoms; and the sky blue ball is the Cu atom.
Figure 2. Structural model of the [Cu(hm)2(ClO4)2] complex. Atoms are labeled using imidazole ring notation. Gray balls are H atoms; green balls are C atoms; blue balls are N atoms; red balls are O atoms; violet balls are Cl atoms; and the sky blue ball is the Cu atom.
low-frequency vibrational modes are compared with available experimental vibrational data. It is important to keep in mind that vibrations are more delocalized over all the structures in the far-IR domain than in the mid-IR domain. The results are thus presented in terms of PED to identify the contributions that emerge from the others in this far-IR domain. Furthermore, the usual harmonic approximation was tested using the smallest [Cu(hm)]2+ complex. This study shows the level of method necessary to model IR with a good accuracy and still be applicable to larger models. Indeed, large models are necessary to study metal centers in proteins using QM or mixed quantum and molecular mechanics (QM/MM) methods. Computational Methods All DFT energies and (anharmonic and harmonic) frequency calculations were carried out using the Gaussian program.14 Geometry optimizations using DFT methods have been considered converged when energy changes were less than 10-5 a.u., and tight SCF convergence criterion was 10-8 a.u. Energy and frequency calculations were performed on fully optimized geometries. IR absorption intensities were calculated from the atomic polar tensors,14,15 and the Raman activity was calculated also as implemented in the Gaussian program.14 Three functionals were used. The B3LYP, BHLYP, and PBE0 hybrid methods were mainly considered since they are known to give reliable results.16-22 We have used all-electron standard 6-31G(d,p), 6-31+G(d,p), and 6-311+G(2d,2p) basis sets for all the atoms. We also used the pseudo potential and SDD basis set that is adapted for transition metal ions and decreases strongly the computation time.23 Normal mode analyses were made using combined approaches: the crude displacement analysis and the PED. For each normal mode, the PED24-26 was calculated,27,28 and contributions larger than 9% are reported. Copper-histamine
Xerri et al. complex Cartesian force constants were transformed into a set of nonredundant internal coordinates: local symmetry coordinates were used for the CH2 and NH2 groups. The coordinates of the imidazole ring (ring deformations, stretches, etc.) were adapted to the D5h symmetry of the regular pentagon.24 The Wilson-Decius stretching, bending, and torsion coordinates of the ch ring (chelate ring) were used, considering that the two CH2 atoms (Figures 1 and 2) of the histamine ch ring are not bound, to avoid redundancies. No scaling factor has been applied to the frequency values. Results and Discussion [Cu(hm)]2+. While vibrational spectra are available for an unlabeled and (2H and 65Cu) labeled histamine complex with +2 valence state copper ([Cu(hm)]2+), allowing a precise comparison of experimental with predicted normal modes,8,29,30 there is no experimental structure for this complex. Thus, theoretical [Cu(hm)]2+ geometrical parameters are compared with X-ray data of [Cu(hm)Cl2] (Table 1).31 In the [Cu(hm)]2+ complex, Cu is coordinated to two nitrogen atoms, the amine group nitrogen NH2 and Nπ of the imidazole ring.32 Relevant geometrical parameters for [Cu(hm)]2+, using three different functionals and four different basis sets, are given in Table 1. The calculated geometry of [Cu(hm)Cl2] was also performed using the B3LYP/6-31G(d,p) and B3LYP/6-31+G(d,p) methods for comparison with the experimental structure. The calculated values using the 6-31G(d,p) basis set (Table 1) for [Cu(hm)Cl2] are close to the experimental ones reported for the first coordination shell, at 1.981 Å for Cu-Nπ and 2.014 Å for Cu-NH2 in the [Cu(hm)Cl2] solid complex31 corresponding to error ranges of 0.003 Å for the Cu-Nπ bond and of 0.024 Å for the Cu-NH2 bond. The geometrical parameters related to the histamine ligand itself differ by no more than 1.4% for the angles and by less than 1.8% for the bond lengths, whatever the basis set used, 6-31G(d,p) or 6-31+G(d,p) basis sets (Table 1). These results indicate that the overall geometrical data are in very good agreement with experimental ones. The optimized geometries obtained for the two complexes, [Cu(hm)Cl2] and [Cu(hm)]2+, showed that the dihedral angle C4-Nπ-Cu-NH2 is never planar but comprised between 4 and 10° for [Cu(hm)Cl2] and between 13 and 16° for [Cu(hm)]2+, depending on the method (Table 1). Whatever the complex, as expected, the calculated Cu-Nπ bond distance is shorter than the Cu-NH2 bond distance. With regard to the [Cu(hm)]2+ structure, the Cu-Nπ bond distance is comprised between 1.837 and 1.959 Å and the Cu-NH2 bond distance between 1.905 and 1.998 Å (Figure 1, Table 1). The basis sets had a larger influence on these bond lengths than the functionals: with the same basis set (6-31G(d,p)), the PBE0 functional led to smaller bond distances than the B3LYP functional by less than 0.02 Å. The increase of the Hartree-Fock exchange from B3LYP to BHLYP induces only small geometrical changes. In contrast, with the same functional (B3LYP), the use of the SDD basis set or the inclusion of a diffuse function (6-31+G(d,p)) or the extended 6-311+G(2d,2p) basis set increased the bond distances by about 0.1 Å with respect to 6-31G(d,p) results (Table 1). The results also indicate that the use of the extended 6-31+G(d,p) and 6-311+G(2d,2p) basis sets, which are expected to improve the results, does not change the structural parameters concerning the histamine unit but leads to larger Cu-N bond distances. Frequency calculations are most generally performed using the harmonic approximation of the potential. Such a simplified approach avoids too large time-consuming calculations and results in general good accuracy. However, low frequency
6-31+g(d,p)
1.959 1.998 105.37 13.18 1.353 1.337 1.369 1.410 1.354 1.487 109.66 107.83 107.37 106.28 123.78 1.952 1.994 105.99 13.24 1.357 1.342 1.373 1.415 1.358 1.492 109.59 107.89 107.36 106.23 123.67 1.901 1.970 107.18 13.78 1.364 1.359 1.401 1.409 1.385 1.501 108.64 108.46 106.95 106.56 123.19
SDD 6-31g(d,p)
1.853 1.917 107.89 15.96 1.339 1.345 1.389 1.379 1.376 1.498 108.64 108.18 107.19 106.50 122.19 1.849 1.919 106.97 15.71 1.334 1.345 1.394 1.370 1.379 1.500 108.48 108.22 107.10 106.59 122.09
6-31g(d,p) 6-31g(d,p)
1.837 1.905 106.25 14.72 1.330 1.340 1.387 1.368 1.372 1.493 108.33 108.34 107.06 106.51 122.15 2.053 2.109 89.13 4.37 1.352 1.325 1.387 1.372 1.383 1.500 109.99 107.29 108.53 105.89 122.60
6-31+g(d,p)
Ref 31. a
histamine
BHLYP PBE0 B3LYP
6-31g(d,p)
1.984 2.038 91.46 9.98 1.350 1.324 1.385 1.371 1.382 1.501 109.93 107.32 108.89 105.99 122.28 1.981 2.014 92.5 14.73 1.327 1.330 1.408 1.352 1.394 1.482 110.7 106.3 108.2 106.4 120.9 d Cu-Nπ d Cu-NH2 R NH2-Cu-Nπ β C4-Nπ-Cu-NH2 d Nτ-C2 d C2-Nπ d Nπ-C4 d C4-C5 d C5-Nτ d C4-CH2 R Nτ-C2-Nπ R C2-Nπ-C4 R Nπ-C4-C5 R C4-C5-Nτ R Nπ-C4-CH2
[Cu(hm)(Cl)2] X-ray
a
metal coordination sphere
B3LYP [Cu(hm)]2+ [Cu(hm)(Cl)2]
TABLE 1: Selected Interatomic d Distances (Å) and r and β Angles (°) from Experimental and Calculated [Cu(hm)]2+ and [Cu(hm)Cl2] Complexes
6-311+g(2d,2p)
Vibrational Modeling of Copper-Histamine Complexes
J. Phys. Chem. B, Vol. 113, No. 45, 2009 15121 modes give rise to Fermi resonance or combination bands that could require anharmonic calculations. The [Cu(hm)]2+ small complex allowed us to calculate anharmonic contributions calculated as implemented in the Gaussian code9-15 and to compare normal-mode frequency values with and without the harmonic approximation (Table 2). Interestingly, for both B3LYP/6-31G(d,p) and B3LYP/6-311+G(2d,2p) methods, the frequency differences are mainly smaller than 3% in the domain below 2000 cm-1, i.e., less than 13 cm-1 in the far-IR region (below 650 cm-1) and less than 10-55 cm-1 in the domain 2000-650 cm-1. In contrast, the anharmonic contribution is 4-5%, i.e., larger than 100 cm-1, for modes with frequencies greater than 3000 cm-1, i.e., in the region involving CH and NH stretching modes (Supporting Information, Table S1). Very similar results were obtained using the BHLYP/6-31G(d,p) and for the B3LYP/6-31G+(d,p) methods. The small contribution of anharmonicity at low frequency (LF) led us to consider frequency values using the harmonic approximation only. The low-frequency IR modes were calculated using different methods and basis sets (Table 3 and Figure 3). The results were compared with the frequency values obtained using the B3LYP/ 6-31+G(d,p) method.33 No significant differences were observed for frequencies calculated with the B3LYP method and SDD or 6-31G(d,p) basis sets and also with increasing Hartree-Fock exchanged from B3LYP/6-31G(d,p) to BHLYP/6-31G(d,p). Larger deviations were obtained using PBE0/6-31G(d,p). As illustrated in Table 3, the largest difference is 66 cm-1, which is quite large and is calculated for the mode ν41 at 414 cm-1 using B3LYP/6-31+G(d,p) and at 480 cm-1 using the PBE0/ 6-31G(d,p) method. In addition to the frequency value, the mode associated to the vibration has to be considered. Indeed, we showed that depending on the methods modes can be ranked in a reversed order: for instance, the modes calculated at 325 cm-1 (ν42) and 307 cm-1 (ν43) using the B3LYP/6-31+G(d,p) method correspond to modes calculated at 335 cm-1 (ν43) and 357 cm-1 (ν42), respectively, using the PBE0/6-31G(d,p) method. Similar inversion is calculated using the extended B3LYP/6311+G(2d,2p) method for the modes at 326 cm-1 (ν42) and 308 cm-1 (ν43). Similar reversed order is observed for the two modes at 322 cm-1 (ν43) and 332 cm-1 (ν42) calculated using the B3LYP/SDD method which are ranked in reversed order as compared to the two modes at 332 cm-1 (ν42) and 344 cm-1 (ν43) calculated using the B3LYP/6-31G(d,p) method or as compared to the two modes at 335 cm-1 (ν42) and 350 cm-1 (ν43) calculated using the BHLYP/6-31G(d,p) method (Table 3). This investigation shows that in contrast with current reported analyses it is necessary to consider the vibration mode associated with the frequency in addition to the energy value of the frequency to validate the theoretical approach. As already mentioned, normal mode calculations allow a useful analysis of the IR spectra since they give a detailed assignment of the normal modes. The normal mode description of the whole IR spectrum in terms of PED of the [Cu(hm)]2+ complex is reported in Table S2a from Supporting Information. As expected,34 modes involving the heavy copper metal are contributing in the low-IR region only (below 1000 cm-1, Supporting Information Table S2a). During vibrations, the copper motions are very small in comparison with those of lighter atoms C, N, O, and H, thus copper contribution in modes does not exceed 5.6% according to the crude displacement analysis. Such a small contribution justifies a PED approach24 which gives a more useful description of the metal contribution in modes. The Cu · · · N coordination leads to characteristic peaks
∆
8 11 9 7 1 1 3 5 1 1 -4 627 610 522 467 349 334 285 208 185 128 66 635 621 530 474 350 335 288 213 186 129 62 12 10 8 13 4 7 8 6 5 2 7 615 572 474 399 322 301 221 191 173 124 74 627 583 482 413 326 308 229 197 178 126 81 11 11 7 11 3 5 7 5 4 2 6 614 568 477 404 322 302 223 195 175 125 75 624 579 484 414 325 307 230 200 179 126 81 625 603 525 463 343 331 281 202 181 129 66 633 614 528 469 344 332 283 205 182 130 67
8 11 3 6 1 1 2 3 1 2 1
(harmonic-anharmonic) (harmonic-anharmonic) (harmonic-anharmonic)
anharmonic harmonic
B3LYP/6-31G(d,p)
∆
harmonic
anharmonic
B3LYP/6-31+G(d,p)
∆
harmonic
anharmonic
B3LYP/6-311+G(2d,2p)
∆
harmonic
anharmonic
BHLYP/6-31G(d,p)
(harmonic-anharmonic)
J. Phys. Chem. B, Vol. 113, No. 45, 2009 TABLE 2: Comparison of Harmonic and Anharmonic Calculations of [Cu(hm)]2+ Normal Modes (in cm-1) Using B3LYP/6-31G(d,p), B3LYP/6-31+G(d,p), B3LYP/6-311+G(2d,2p), and BHLYP/6-31G(d,p) Methods in the Low-IR Region
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Xerri et al. related to ν(Cu-N) stretching modes. The largest calculated contributions of Cu are associated to these Cu-N stretching modes, with PED larger than 50%, for the ν(Cu-Nπ) and ν(Cu-NH2) modes predicted at 344 and 528 cm-1, respectively, using the B3LYP/6-31G(d,p) method (Table 3). As shown in Table 3, the normal mode description reveals the contribution of copper motions in almost all low-frequency modes for the [Cu(hm)]2+ complex. In this far-IR domain, skeleton vibration modes also occur and result from the coupling between stretching and bending motions of atoms from the branched histamine ligand, increasing the difficulty in the normal mode assignments and justifying a PED analysis. In contrast, at higher frequency values, the normal modes are primarily localized on a small number of connected atoms: between 1600 and 3000 cm-1, the modes mainly involve organic functions of the complex without contributions of the chain. All the atoms participate in the vibrational mode calculated at 67-80 cm-1 (Supporting Information Table S2a). As the frequency increases from 100 to 600 cm-1, contributions from both the imidazole ring (im) skeleton and from the chelate ring (ch) slightly decrease, while the contributions of the bending δ(NH2CuNπ) and stretching ν(Cu-N) modes increase: the δ(NH2CuNπ) modes are predicted at 179-190 and 230-291 cm-1 (Table 3), and the ν(Cu-N) stretching modes are dominant in the domain 307-535 cm-1. The effect of substituting 63Cu by 65Cu was also considered since the use of isotope labeling can be very useful in assigning vibration peaks. According to the present B3LYP/6-31G(d,p) calculation, only five modes at 528, 469, 344, 283, and 205 cm-1 were affected by substituting 63Cu by 65Cu (not shown). These frequencies were downshifted by 1 cm-1 for the [65Cu(hm)]2+ complex. Four of the five modes involve ν(Cu-N) (Table 3). In these relevant modes involving dominant contributions from im ring deformations with a small contribution from copper motion, the Cu isotopic substitution effect (ca. 2/63) is expected to lead to almost negligible frequency shifts. Experimental studies of a [Cu(hm)]2+ derivative, [Cu(hm)Cl2], led to similar frequency downshifts of ≈1 cm-1 upon 63Cu/65Cu substitution for seven bands in the 417-189 cm-1 range.29 These IR bands were tentatively assigned to ν(Cu-N) stretching modes.29 Similar small frequency downshifts have been reported upon Pd isotope substitution (104Pd vs 110Pd): reported experimental and theoretical downshifts for the larger [Pd(hm)2]2+ complex are between 2 and 4.5 cm-1 for modes involving the transition metal ion.6 To establish correlation between calculated normal modes and experimental bands, Raman investigations of [Cu(hm)]2+ precipitate and supernatant have been considered.8 [Cu(hm)]2+ complex calculations lead to a good agreement with the spectra obtained in the supernatant fraction, presenting two signals at 310 and 437 cm-1. The B3LYP/6-31G(d,p) calculated frequency values of ν42 at 344 cm-1 and ν41 at 469 cm-1 fit well with the experimental values at 310 and 437 cm-1, respectively.8 These two experimental weak signals at 310 and 437 cm-1 were assigned to ν(Cu-Nπ) and ν(Cu-NH2), respectively.8 According to our calculations, these two peaks are Raman active, and their IR intensities are weak (Supporting Information Table S2a). A detailed analysis of these modes confirms that vibrational modes from other groups are involved to a lesser extent and that frequenciesmayconsistentlybeassignedtostretchingmetal-ligand vibrations (Table 3). Considering only these two experimental values, the best agreement is obtained using the B3LYP functional with the SDD, the 6-31+G(d,p), and the largest 6-311+G(2d,2p) basis sets. However, considering the overall
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TABLE 3: Calculated and Experimental Frequencies (Expressed in Wavenumbers, cm-1) PED and Proposed Assignments of [Cu(hm)]2+a B3LYP/SDD (vib n°)
B3LYP/ 6-31G(d,p) (vib n°)
BHLYP/ 6-31G(d,p) (vib n°)
B3LYP/ 6-31+G(d,p) (vib n°)
B3LYP/ 6-311+G(2d,2p) (vib n°)
PBE0/ 6-31G(d,p) (vib n°)
505 (ν40) 440 (ν41)
528 (ν40) 469 (ν41)
530 (ν40) 474 (ν41)
484 (ν40) 414 (ν41)
482 (ν40) 413 (ν41)
535 (ν40) 480 (ν41)
322 (ν43) 332 (ν42)
344 (ν42) 332 (ν43)
350 (ν42) 335 (ν43)
307 (ν43) 325 (ν42)
308 (ν43) 326 (ν42)
357 (ν42) 335 (ν43)
262 (ν44)
283 (ν44)
288 (ν44)
230 (ν44)
229 (ν44)
291 (ν44)
213 (ν45)
205 (ν45)
213 (ν45)
200 (ν45)
197 (ν45)
219 (ν45)
188 (ν46)
182 (ν46)
186 (ν46)
179 (ν46)
178 (ν46)
190 (ν46)
137 (ν47)
130 (ν47)
129 (ν47)
126 (ν47)
126 (ν47)
128 (ν47)
PEDB3LYP/6-31G(d,p)b 53% ν(Cu-NH2) 21% δ(CH2NH2Cu) 41% ν(Cu-NH2), 17% δ(NπC4CH2) (ch) 11% τ(e′′1(2))d (im) 53% ν(Cu-Nπ) 24% δ(CuNπC4) (ch) 20% butterfly at the ring junction 17% τ(e′′1(2))d (im) 17% δ(NπC4CH2) (ch) 14% δ(NH2CuNπ) 30% δ(NH2CuNπ) 28% δ(CuNπC4) (ch) 17% ν(Cu-Nπ) 14% δ(e′2(1))d (im) 29% τ(NH2-Cu) (ch) 27% δ(CuNπC4) (ch) 24% δ(CH2NH2Cu) 17% τ(Nπ-Cu) (ch) 14% butterfly at the ring junction 56% δ(NH2CuNπ) 33% butterfly at the ring junction 13% τ(NH2-Cu) (ch) 44% τ(Nπ-Cu) (ch) 39% τ at the ring junction 15% butterfly at the ring junction
IR exptl values and proposed assignmentc
437 ν(Cu-NH2) 310 ν(Cu-N)
a im ) imidazole ring and ch ) chelate ring. ν(XY) is the stretching vibration of the bond between atoms X and Y; δ(XYZ) is the vibration of the angles between atoms XYZ; τ(XYZW) is the torsion vibration. Normal modes ranked in reverse order using B3LYP/SDD, B3LYP/ 6-31+G(d,p), and B3LYP/6-311+G(2d,2p) are reported in italics. b Notation according to Figure 1 and internal coordinates defined in Supporting Information Table S2b. c IR data and assignments from ref 8 for [Cu(hm)]2+ supernatant. d D5h symmetry (see § computational method).
Figure 3. Comparison of the calculated IR spectra of [Cu(hm)]2+ between 0 and 900 cm-1, obtained using the 6-31G(d,p) basis sets and the B3LYP and PBE0 functionals.
experimental values,8 the best agreement between calculated mode frequencies and experimental bands is obtained using the B3LYP/6-31G(d,p) method. Since the largest basis sets 6-31+G(d,p) and 6-311+G(2d,2p) do not significantly impact the accuracy of the normal-mode frequency values, we have chosen to perform frequency calculations with the 6-31G(d,p) and SDD basis sets for larger copper-histamine complexes. [Cu(hm)2(ClO4)2]. We have considered the [Cu(hm)2(ClO4)2] complex (Figure 2) for which IR spectra29 as well as an experimental structure35 are available. As for the [Cu(hm)]2+ complex, copper is coordinated to the histamines by the NH2 group and the Nπ from the imidazole group. The most stable calculated structure for [Cu(hm)2(ClO4)2] is a hexacoordinated CuII with the two histamines in equatorial position and two
ClO4- anions in axial positions (Figure 2). Most of the present calculations lead to structures with an equatorial plane not fully planar in agreement with other bioinorganic copper complexes36 but as will be detailed below in contrast with X-ray data.35 The Cu-O axial bond lengths are significantly larger than the Cu-N equatorial bond lengths (Table 4), due to the 3d9 copper electronic configuration, as a result of the well-known Jahn-Teller effect. Using the B3LYP/SDD method, a second structure containing a strictly planar equatorial plane has also been obtained (Table 4). The two structures obtained with the SDD basis set are two minima of comparable energies, the planar structure being more stable by 1.1 kcal/mol. The structure parameters calculated using different functionals and basis sets are collected in Table 4. The main differences between experimentally determined and calculated structures concern the β Nπ-NH2-N′π-NH2 dihedral angle and the Cu-O bond distances. As shown in Table 4, the calculated β Nπ-NH2-N′π-N′H2 angles for the distorted structures are around 10°, while it is 0° from X-ray data.35 The structure derived from X-ray data has large and equivalent Cu-O bond lengths, while calculations exhibit shorter and uniquivalent Cu-O bond lengths (Table 4). In contrast with [Cu(hm)]2+, in the [Cu(hm)2(ClO4)2] complex, the experimental and calculated Cu-NH2 bond lengths are not significantly larger than the Cu-Νπ ones. Whatever the method used, the calculated Cu-N bond lengths are generally slightly larger than those reported from X-ray analysis.35 As a general behavior, the PBE0 functional leads to smaller bond distances for the equatorial ligands than the other methods. However, the largest differences are obtained with the SDD basis. On the basis of the results reported in Table 4, the closest agreement with crystallographic studies is obtained with the B3LYP/6-31G(d,p) method. The calculated normal modes in the low-frequency domain are reported in Table 5. From the IR intensities reported in the
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TABLE 4: Selected Interatomic d Distances (Å) and r and β Angles (°) from Experimental and Calculated [Cu(hm)2(ClO4)2] Complexa [Cu(hm)2(ClO4)2] X-rayb d Cu-Nπ d Cu-N′π d Cu-NH2 d Cu-N′H2 d Cu-O d Cu-O′ R Nπ-Cu-NH2 R N′π-Cu-N′H2 R Cu-Nπ-C2 R Cu-N′π-C′2 R Cu-Nπ-C4 R Cu-N′π-C′4 R Nπ-Cu-O R N′π-Cu-O′ R NH2-Cu-O R N′H2-Cu-O′ β Nπ-NH2-N′π-N′H2
B3LYP/SDD , planar .
1.985
2.065 (∆ ) 0.08)
2.05
2.065 (∆ ) 0.015)
2.617
2.306 (∆ ) 0.311)
91.3
91.56 (∆ ) 0.26)
127.9
129.67 (∆ ) 1.77)
126.3
123.32 (∆ ) 2.98)
86.6
83.81 (∆ ) 2.79)
91.0
91.71 (∆ ) 0.71)
0.0
0.012 (∆ ) -0.01)
PBE0/6-31g(d,p) 2.016 (∆ ) 0.031) 2.024 (∆ ) 0.039) 2.031 (∆ ) 0.019) 2.015 (∆ ) 0.035) 2.470 (∆ ) 0.147) 2.370 (∆ ) 0.247) 92.26 (∆ ) 0.7) 90.58 (∆ ) -0.98) 128.46 (∆ ) 1.21) 129.71 (∆ ) -0.04) 124.62 (∆ ) -1.68) 123.80 (∆ ) -2.5) 87.35 (∆ ) 0.75) 81.74 (∆ ) -4.86) 84.64 (∆ ) -6.36) 88.01 (∆ ) -2.99) 11.33 (∆ ) -11.33)
B3LYP/6-31g(d,p) 2.035 (∆ ) 0.05) 2.043 (∆ ) 0.058) 2.049 (∆ ) 0.01) 2.034 (∆ ) 0.016) 2.549 (∆ ) 0.068) 2.391 (∆ ) 0.226) 92.03 (∆ ) 0.73) 90.51 (∆ ) -0.79) 128.31 (∆ ) 0.41) 129.62 (∆ ) 1.72) 124.79 (∆ ) -1.51) 123.92 (∆ ) -2.38) 87.03 (∆ ) 0.43) 81.97 (∆ ) -4.63) 83.87 (∆ ) -7.13) 89.58 (∆ ) -1.42) 12.23 (∆ ) -12.23)
B3LYP/SDD 2.035 (∆ ) 0.05) 2.043 (∆ ) 0.058) 2.049 (∆ ) 0.001) 2.032 (∆ ) 0.018) 2.472 (∆ ) 0.145) 2.280 (∆ ) 0.337) 90.51 (∆ ) 0.79) 92.03 (∆ ) 0.73) 128.08 (∆ ) 0.18) 129.59 (∆ ) 1.69) 124.83 (∆ ) -1.47) 123.62 (∆ ) -2.68) 86.18 (∆ ) -0.42) 80.77 (∆ ) -5.83) 86.15 (∆ ) -4.85) 96.94 (∆ ) 5.94) 12.04 (∆ ) -12.04)
∆: difference between calculated and experimental parameters. See Figure 2 for atom labeling using imidazole ring labeling. The ′ notation is used in the present table to distinguish between the two histamines and the two ClO4 ligands. b Ref 35. a
Supporting Information Table S3a, it is predicted that most of the peaks are weak in this region even if few of them are slightly more intense. Even if the IR intensity requires very accurate calculations, this general tendency is in agreement with experimental data. As previously mentioned, modes involving copper appear in the far-IR domain. For the [Cu(hm)2(ClO4)2] complex, the highest ν(Cu-N) stretching mode appears at 428 cm-1 (mode ν95) using the B3LYP/6-31G(d,p) method. The copper contribution to the modes does not exceed 10% according to the crude displacement analysis, while it can be larger than 60% considering the PED for Cu-N stretching modes (see ν95 assigned to ν(Cu-NH2) for 61% in Table 5 and Supporting Information Tables S3a and S3b). As a general pattern, the ν(Cu-NH2) mode contributions appear at higher energies (309-428 cm-1) than the ν(Cu-Nπ) (152-268 cm-1), and the ν(Cu-O) stretching modes are calculated at the lowest energies (Table 5, B3LYP/6-31G(d,p) calculations). Small differences in frequency values are obtained for normal mode predictions using the B3LYP/6-31G(d,p) and PBE0/6-31G(d,p) methods in the far-IR domain (Supporting Information Table S4). In contrast, large differences are obtained using B3LYP/6-31G(d,p) and B3LYP/SDD methods (Supporting Information Table S4). As previously shown for [Cu(hm)]2+, a detailed PED analysis of the modes shows that they can be ranked in a different order, depending on the basis set and functional. For example, the mode ν101 calculated at 276 cm-1 using SDD is very similar to the mode ν105 at 268 cm-1 using the 6-31G(d,p). According to the PED analysis, these two modes involve ν(Cu-Nπ) and δ(Cu(T1u(2))) (Supporting Information Tables S4 and S3a). The two modes ν89 at 438 cm-1 and ν95 at 428 cm-1 using SDD and 6-31G(d,p), respectively, are also ranked in a different order. They both correspond mainly to the ν(Cu-NH2) stretching mode. Part of these differences most probably results from differences in the structure parameters as shown above (Table 4). Experimental difficulties in the assignment of normal modes in the far-IR domain result from the involvement of a large number of atoms in these modes and calls for the application of QM calculations. The detailed comparison of experimentally determined IR band frequencies and normal mode calculations is of prime interest to evaluate the strengths and limits of calculations in the analysis of experimental data. Therefore, the
experimental and predicted low-frequency modes were compared for the unlabeled, 2H- and 65Cu-labeled [Cu(hm)2(ClO4)2] complexes, using calculations performed with the B3LYP/631G(d,p) method (Table 5). Low-Frequency Modes Involving Metal-Ligand Vibrations. In the IR spectrum of [Cu(hm)2(ClO4)2], a band observed at 420 cm-1 was proposed to correspond to the ν(Cu-NH2) mode, based on the 1 cm-1 downshift observed upon 65Cu/63Cu substitution and the 13 cm-1 downshift observed upon hm deuteration.29 This band clearly corresponds to the ν95 mode calculated at 428 cm-1 using the B3LYP/6-31(d,p) method, for which very similar downshifts of 1 and 12 cm-1 are predicted upon 65Cu/63Cu substitution and hm 2H labeling, respectively (Table 5). The PED analysis shows that this mode indeed corresponds to ν(Cu-NH2) and that it includes a large proportion of bending of the axial ClO4- ligand in the hm 2H-labeled complex. Two other bands observed at 282 and 249 cm-1, and downshifted by 2.5 and 1 cm-1, respectively, upon 65Cu/63Cu substitution were proposed to account for ν(Cu-Nim).29 These frequencies are very close to those of the ν105 and ν106 modes, calculated at 268 and 244 cm-1. Moreover, similar downshifts of 3 and 1 cm-1 upon 65Cu/63Cu substitution were calculated for these modes. The normal mode calculation predicts a significant contribution of the ν(Cu-NH2) at 338 cm-1 (ν103, Table 5) coupled with δ(CuNπC4)(im) bending. Downshifts of 11 and 0 cm-1 are predicted upon hm 2H labeling and 65Cu/63Cu substitution (Table 5). A very comparable downshift of 11 cm-1 was observed for an IR band at 338 cm-1 upon hm 2H labeling.29 This band was tentatively assigned to a δ(NCuNH2) mode. The calculation allows correcting the assignment of this mode with the addition of the ν(Cu-NH2) contribution. These comparisons demonstrate the accuracy of normal-mode frequency predictions using DFT and the interest of predicting isotope shifts for the assignment of experimental modes. The calculations also allow a better description of the normal modes. According to the PED analysis of modes below 200 cm-1, even if the metal cation is involved in the modes, including ν(Cu-N) stretching motions, 63Cu/65Cu labeling does not always induce frequency shifts as mentioned above for the [Cu(hm)]2+ complex. This result suggests a different assignment to the one
Vibrational Modeling of Copper-Histamine Complexes
J. Phys. Chem. B, Vol. 113, No. 45, 2009 15125
TABLE 5: Effect of 2H Labeling and 65Cu/63Cu Substitution on the Predicted Mode Frequencies (In Wavenumbers, cm-1) for the [Cu(hm)2(ClO4)2] Complex and Comparison with Experimental IR Dataa B3LYP/6-31G(d,p) experimentb
[1]
(562) (545) 420(407)[1.0]e
577 554 428
461(459)
363(358) 338(329)[0.5]
[2]
[1]-[2]
[3]
[1]-[3]
(ν85) (ν91) 61% ν(Cu-NH2) (ν95)
447 434 416
130 120 12
577 554 427
0 0 1
411 409
82% δ(ClO4(e)) (ν96) 83% δ(ClO4(e)) (ν97)
408 405
3 3
411 409
0 0
402
32% ν(Cu-NH2) 31% δ(ClO4(e)) 23% δ(Cu(T2g(3)))d (ν98) 95% δ(ClO4(e)) (ν99) 72% δ(ClO4(e)) (ν100), (ν98) 21% butterfly at the ring junction (ν101) 15% δ(NπC4CH2) (ν103) (im)
398
4
402
0
396 382
397 394
0 0
356 327
1 12 20 7 11
362 337
0 0
27% δ(CuNπC4) (im) 25% ν(Cu-NH2) (ν104) 59% δ(CuNπC4) (im) 28% ν(Cu-NH2) (ν105) 37% ν(Cu-Nπ) 14% δ(Cu(T1u(2))) (ν106)
294
15
309
0
264
4
265
3
236
8
243
1
34% ν(Nπ-Cu) 17% δ(CuNπC4) (im) (ν107) 23% δ(CuNπC4) (im) 13% δ(Cu(T1u(2))) (ν108)
218
9
227
0
203
10
213
0
191 178
5 4
196 182
0 0
165
27% butterfly at the ring junction (ν109) 40% δ(Cu(T2g(3))) 14% δ(CuNπC4) (im) (ν110) 33% butterfly at the ring junction (ν111)
162
3
165
0
161
13% δ(Cu(T2g(2))) (ν112)
159
2
161
0
152
48% τ(Cu-Nπ) (ch) 23% δ(Cu(T1u(1))) 16% δ(Cu(T2u(1))) (ν113) 46% ν(Nπ-Cu) (ν114)
148
4
152
0
142
2
144
0
397 394 402 362 338 309
282(280)[2.5]
268
249(246)[1]
244 227 213
181(174)
157 (152)
196 182
144
[1] PED description (vib n°)
126
54% τ(Nπ-Cu) (ch) 12% δ(Cu(T2g(2))) (ν115)
125
1
126
0
120
42% δ(CuOCl) 25% δ(Cu(T1u(3))) 14% τ(Cu-O-Cl-O) 13% τ(Nπ-Cu-O-Cl) (ν116) 44% ν(Cu-O) 31% δ(CuOCl) (ν117)
119
1
120
0
101
2
103
0
103 96
35% δ(Cu(T2u(3))) 21% δ(CuOCl) (ν118)
94
1
96
0
87
18% τ at the ring junction 14% δ(CuOCl) (ν119)
86
2
87
0
[2] PED description (vib n°) 100% φ(NτH) (im) (ν93) 97% φ(NτH) (im) (ν94) 37% δ(ClO4(e))c 32% ν(Cu-NH2) (ν95) 85% δ(ClO4(e))(ν 96) 56% δ(ClO4(e)) 30% ν(Cu-NH2) (ν97) 80% δ(ClO4(e)) (ν98) 85% δ(ClO4(e)) (ν99) 34% δ(Cu(T2g(3)))d 39%ν(Cu-NH2) (ν100) 13% δ(NπC4CH2) (im) (ν101) 29% ν(Cu-NH2) 25% δ(CuNπC4) (im) (ν103) 58% δ(CuNπC4) (im) 33% ν(Cu-NH2) (ν104) 44% ν(Cu-Nπ) 18% δ(Cu(T1u(2))) (ν105) 41% δ(CuNπC4) (im) 18% ν(Nπ-Cu) 13% δ(Cu(T1u(3))) (ν106) 16%δ(Cu(T2g(3))) (ν107) 21% τ (ch) 31% butterfly at the ring junction 15% δ(Cu(T1u(2))) 13% τ(Nπ-Cu) (ch) (ν108) 36%δ(Cu(T2g(3))) (ν109) 31% butterfly at the ring junction (ν110) 29% ν(Nπ-Cu) 13% δ(Cu(T2g(2))) (ν111) 43% τ(Cu-Nπ) (ch) 20% δ(Cu(T1u(1))) 14% δ(Cu(T2u(1))) (ν112) 31% ν(Nπ-Cu) 18% δ(Cu(T2g(2))) 16% τ(Cu-Nπ) (ch) (ν113) 41% τ(Nπ-Cu) (ch) 15% δ(CuOCl) (ν114) 50% δ(CuOCl) 24% δ(Cu(T1u(3)))d 14% τ(Cu-O-Cl-O) (ν115) 47% ν(Cu-O) 26% δ(CuOCl) (ν116) 37% δ(Cu(T2u(3))) 13% ν(Cu-O) 15%δ(CuOCl) (ν117) 16% τ at the ring junction 14% δ(Cu(T2g(2))) 14%δ(CuOCl) (ν118) 31% τ(Cu-O-Cl-O) 26% δ(Cu(T2u(3))) 18% δ(Cu(T1u(2))) 17% τ(Nπ-Cu) (ch) 13% ν(Cu-O) (ν119)
a Data for [Cu(hm)2(ClO4)2] are in column [1], for [Cu(hm-2H3)2(ClO4)2] in column [2], and for [65Cu(hm)2(ClO4)2] in column [3]. The PED analysis is shown for [Cu(hm)2(ClO4)2] [1] and Cu(hm-2H3)2(ClO4)2] [2]. The calculations were performed using the B3LYP/6-31g(d,p) method. Only PED > 12% is reported. νXY is the stretching vibration of the bond between atoms X and Y, δXYZ is the vibration of the angles between atoms XYZ, τXYZW is the torsion vibration, and φYX is the out-of-plane vibration of atom X from a plane YZW. b Ref 29. c Assignment using the conventional copper histamine labeling (see Figure 2) and internal coordinates assignment in Supporting Information Table S3c. d Oh symmetry ν stretching; δ in plane bending or deformation; Fw wagging; Fr rocking; Ft twisting; Fs scissoring; im ) imidazole ring; and ch ) chelate ring. e 2H labeled isotope [2] frequency values are given in parentheses and the [1]-[3] isotope shift is given in brackets.
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J. Phys. Chem. B, Vol. 113, No. 45, 2009
proposed for the experimental signals identified at ∼97, 157, and 181 cm-1 for the [Cu(hm)2(ClO4)2] complex.29 These experimental signals were assigned to the imidazole ligand as concluded from the lack of 63Cu/65Cu frequency shift in the IR data.29 According to the PED analysis, our calculations (Table 5) predict that modes below 200 cm-1 result from contributions of several coordinates such as the coordination sphere deformation of Cu, ring deformations (in-plane and out-of-plane) of the two histamines, essentially the torsion and the “butterfly” vibration” at the C-N junction of the cycles, coupled with a rocking of the O-Cu-O axis, and also ν(Cu-Nπ) and ν(Cu-O). 65Cu labeling does not affect the mode frequencies since the center of mass of the molecule is very close to the copper position. In this far-IR domain, IR contribution from lattice modes in the sample may also induce differences between experimental data and predicted normal mode. A comparison of the present data including the labeled derivative with previous experimental data29 allows us to assign with good accuracy the experimental signals and to give a detailed analysis of the mode contributions, as reported in Table 5. Bending Modes. Larger differences are obtained between experimental and calculated bending modes involving the imidazole side chain and ClO4. This is exemplified by the φ(NτH)(im) modes, predicted at 577 and 554 cm-1 for the unlabeled [Cu(hm-H3)2(ClO4)2] complex (ν85 and ν91 out-ofplane φ(NτH) of the imidazole rings, respectively) (Table 5) and at 447 and 434 cm-1 for the 2H-labeled [Cu(hm2 H3)2(ClO4)2] complex (ν93 and ν94, respectively) (Table 5), corresponding to large downshifts of 130-120 cm-1 upon hm deuteration. The corresponding bands were not observed experimentally for the unlabeled [Cu(hm-H3)2(ClO4)2] complex. For the 2H-labeled [Cu(hm-2H3)2(ClO4)2] complex, however, two intense bands observed at 562 and 545 cm-1 and tentatively assigned to the hm moiety29 most probably correspond to the calculated imidazole φ(NτH) modes. The difference between experimental and predicted frequency values is about 110 cm-1. Given the large downshift predicted upon hm 2H labeling for these modes, for the experimental unlabeled [Cu(hmH3)2(ClO4)2] complex these bands should occur above 600 cm-1, which is the detection limit of the experiment. Interestingly, an intense band was observed at 604 cm-1 in the spectra of the neutral histamine in aqueous solution and assigned to the imidazole φ(NτH) mode.37 Furthermore, this band was observed at 491 cm-1 for histamine in 2H2O,37 and the large downshift of 113 cm-1 corresponds to that predicted for the φ(NτH) modes in the [Cu(hm)2(ClO4)2] complex. Thus, the normal-mode analysis is useful in bands assignment, notably using the prediction of effects induced by isotope labeling, even if large frequency differences are obtained with the experiment. It also shows that the frequency of these modes is very sensitive to the environment of the histamine imidazole and that the differences in mode frequency probably result from intermolecular contacts in the experimental sample that are not taken into account in the calculations. Similarly, δ(ClO4) modes were calculated at 411-397 cm-1. The calculated modes most probably correspond to the band observed at 461 cm-1 experimentally29 (Table 5). Indeed, the calculated and observed downshifts upon hm 2H labeling are similar for the calculated and experimental bands (-3 and -2 cm-1, respectively, Table 5). These differences between experimentally determined and calculated mode frequencies also probably result from intermolecular contacts in the sample, consisting of a Nujol mull,
Xerri et al. which may hinder the bending motion. These intermolecular interactions may also explain the differences in Cu-O(ClO4) distances between experimentally determined and calculated structures (see above). In contrast, a large band observed at 363 cm-1 and downshifted by 8 cm-1 upon hm 2H labeling is predicted with accuracy by the calculations as a butterfly at the ring junction mode at 362 cm-1, with a 7 cm-1 downshift upon hm 2H labeling (Table 5). Normal mode prediction is accurate for vibrations involving the first coordination sphere less influenced by intermolecular interactions. Conclusion Due to the development of new setup and emerging techniques, far-IR studies of metalloproteins will provide a unique view of metal-ligand fingerprints since most of the modes are permitted, and in principle all metal centers can be addressed. We showed that the interest of this analysis is reinforced when it is performed by a combined approach involving both DFTbased calculations and PED analysis. As emerged from the study of the [Cu(hm)]2+ complex, a detailed analysis of the computed normal modes shows that a careful PED analysis of the modes is required to obtain an overall description of the vibration modes and to compare the calculation methods. A thorough investigation of the performances of the vibration predictions shows that at low frequency values the harmonic approximation is completely justified to predict the normal mode values and assignments. We showed that significant differences in the frequency values are obtained depending on the methods for the [Cu(hm)]2+ and [Cu(hm)2(ClO4)2] complexes. We showed also that the pseudopotential triple-ζ basis set SDD leads to results which are close to those obtained with the 6-31G(d,p) method for the [Cu(hm)]2+. While the largest basis sets 6-31+G(d,p) and 6-311+G(2d,2p) significantly increase the computational time, the use of the smaller basis set 6-31G(d,p) did not significantly change the accuracy of the results. Finally, we note that the use of the modeling to simulate the labeled derivatives is of great importance to predict with a very good accuracy the band shifts of the labeled copper-histamine derivatives and to assign the experimental spectra. Acknowledgment. This work was funded in part by the French program Toxicologie Nucle´aire Environnementale and the ANR French Agency (ANR-08-PCVI-0011-01). These calculations were carried out on the IBM SP4 computers of the CINES (Centre Informatique National de l’Enseignement Supe´rieur) in Montpellier (France) and of the IDRIS (Institut des Ressources en Informatique Scientifique) in Orsay (France). Supporting Information Available: Tables S1-S4 and Figures S1 and S2. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Chu, H.-A.; Sackett, H.; Babcock, G. T. Biochemistry 2000, 39, 14371. (2) Visser, H.; Dube, C. E.; Armstrong, W. H.; Sauer, K.; Yachandra, V. K. J. Am. Chem. Soc. 2002, 124, 11008. (3) Kimura, Y.; Mizusawa, N.; Ishii, A.; Yamanari, T.; Ono, T. Biochemistry 2003, 42, 13170. (4) Berthomieu, C.; Marboutin, L.; Dupeyrat, F.; Bouyer, P. Biopolymers 2006, 82, 363. (5) Marboutin, L.; Desbois, A.; Berthomieu, C. J. Phys. Chem. B 2009, 113, 4492. (6) Drozdzewski, P. M.; Kordon, E.; Roszak, S. Int. J. Quantum Chem. 2004, 96, 355.
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