Density Functional Investigation of Methoxy...
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J. Phys. Chem. 1996, 100, 14549-14559
14549
Density Functional Investigation of Methoxy-Substituted p-Benzoquinones: Conformational Analysis and Harmonic Force Fields of 2-Methoxy- and 2,3-Dimethoxy-1,4-benzoquinone Marco Nonella* and Christof Bra1 ndli Physikalisch-Chemisches Institut der UniVersita¨ t Zu¨ rich, Winterthurerstrasse 190, CH-8057 Zu¨ rich, Switzerland ReceiVed: April 2, 1996; In Final Form: June 11, 1996X
Structure and harmonic force fields of methoxy-substituted p-benzoquinones have been calculated applying density functional methods. Structural parameters, harmonic force constants, and vibrational frequencies have been shown to depend on the orientation of the methoxy substituents. Stable conformations of the methoxy groups, as predicted by semiempirical or ab initio Hartree-Fock methods, differ qualitatively from those predicted by methods which are considering correlation effects. The agreement of the calculated CdC and CdO modes with experimental data is generally very satisfactory. Due to additional substituents such as methyl or allyl groups, the energetic sequence of CdC and CdO modes is not found to be altered. Calculated frequencies are only slightly affected due to such substituents whereas intensities, mode decompositions, and isotopic shifts are considerably influenced.
1. Introduction Quinones play an important role in the electron transfer processes of photosynthetic bacterial reaction centers. After light excitation of a bacteriochlorophyll dimer, the so-called special pair, an electron is transferred via a bacteriopheophytin molecule to a primary quinone QA and finally to a secondary quinone QB. This secondary quinone accepts two electrons through this pathway, and two protons from the cytoplasmic side of the protein. QBH2 thus formed leaves the reaction center. Detailed reviews of the primary electron-transfer steps of photosynthesis can be found in refs 1-3. The two quinones show considerably different properties inside the protein. QA is a menaquinone in Rhodopseudomonas Viridis and a ubiquinone in Rhodobacter sphaeroides. It is a tightly bound one-electron acceptor whereas QB, which is a ubiquinone in both reaction centers, is loosely bound and can accept two electrons. Although the recent elucidation of the three-dimensional structure of the reaction centers of Rps. Viridis4,5 and Rb. sphaeroides6-9 has provided important information on the amino acid residues which make up the binding pockets of QA and QB, little is known about the electronic structure of these acceptors and the structural modifications of both the protein and the quinones concomitant with the charge stabilization processes. In several reports,10-17 it has been demonstrated that lightinduced Fourier transform infrared (FTIR) difference spectroscopy is a well-suited method for investigations of the binding properties of quinones in reaction centers. This method has the sensitivity to monitor molecular changes that occur at the level of cofactors and of the protein following charge stabilization of quinones. Frequently, in these experiments, absorptions of CdO and CdC vibrations are analyzed. The interpretation of such spectra requires various approaches such as comparison with IR spectra of model compounds,18 investigation of isotope effects on the quinone vibrations,15,17,19,20 and normal-mode calculations.21,22 Various experimental methods have been applied in order to obtain information about the binding properties at the QA binding site. The conclusions from these experiments, however, are not * Corresponding author. X Abstract published in AdVance ACS Abstracts, August 1, 1996.
S0022-3654(96)00974-4 CCC: $12.00
fully consistent. Based on X-ray structural investigations of the reaction centers of Rps. Viridis5 and Rb. sphaeroides,7-9 two hydrogen bonds between QA and the protein have been proposed. While a conserved hydrogen bond between the carbonyl group that is nearest to the isoprenoid chain and the peptide NH groups of Ala M258 and Ala M260, respectively, is proposed in all present structures they differ with regard to the hydrogen bond partner to the CdO bond nearest to the methyl substituent. FTIR studies clearly suggest different interactions of the two carbonyls with the protein. One CdO vibration corresponds to an essentially free CdO vibration whereas the second mode is down-shifted from 1660 to 1601 cm-1.15,18 Different explanations for this large shift have been suggested: First, the IR spectrum is affected by substituents of the quinone. This possibility has been ruled out by reconstitution of reaction centers with chainless symmetrical quinones.18 Second, the orientation of the methoxy groups affects the spectrum. Different conformations for the two methoxy groups have indeed been found in crystal structure studies23 as well as in quantum chemical calculations of 2,6-dimethoxy-1,4-benzoquinone.24 Based on the assumption that in-plane and out-of-plane OCH3 groups could cause two different CdO vibrations, isotope effects on the quinone vibrations measured in Vitro could be explained.19 Third, it has also been suggested that this downshift is caused by a strong hydrogen bond between QA and the imidazole ring of His M219, which is located close to this carbonyl group.19 This contradicts the interpretation of magic angle spinning NMR results of the QA site of Rb. sphaeroides.25,26 In these NMR studies, it was concluded that the two carbonyls are inequivalent but that neither is involved in a strong hydrogen bond. These conclusions have been revised in a more recent 13C NMR investigation27 which is now consistent with a decrease of the bond order of the carbonyl group at C4 most likely due to interactions with the protein. In previous investigations of p-benzoquinone21 and 1,4naphthoquinone28 we have shown that CdC and CdO vibrations can be described very accurately by application of density functional theory methods. In the present study we use the same quantum chemical methods in order to investigate possible conformations of the two methoxy groups and to elucidate the effect of these different conformations on the vibrational © 1996 American Chemical Society
14550 J. Phys. Chem., Vol. 100, No. 34, 1996 spectrum. Such calculations could allow distinct conclusions between possible conformations of ubiquinones in solution or in proteins. Due to the size of the systems, only a few theoretical studies have been carried out on methoxy-substituted quinones in the past. Ab initio Hartree-Fock methods have been applied for conformational analysis of 2,6-dimethoxy-1,4benzoquinone and its radical anion24 and revealed that (i) two conformations of the methoxy groups correspond to minimum energy structures and (ii) rotation of the methoxy groups affects the electron affinity of the molecule. Furthermore, semiempirical calculations of 2,3-dimethoxy-1,4-benzoquinone29,30 have shown that different orientations of the methoxy groups correspond to energy minimum conformations. In the first part (A) of our report we present calculations on the smallest methoxy-substituted 1,4-benzoquinone, namely 2-methoxy-1,4-benzoquinone. In the second part (B) results of calculations of 2,3-dimethoxy-1,4-benzoquinone are discussed, and in the third part (C) we analyze the effects of an additional substituent like a methyl group or an allyl group on the calculated vibrational frequencies and isotopic shifts. Although our calculated force fields provide important information on the complete infrared spectra of the investigated molecules, we confine ourselves in this contribution to the discussion of the experimentally very important CdC and CdO modes. A discussion of other prominent modes found in in ViVo infrared spectra will be given elsewhere.31 2. Methods of Calculation Density functional calculations have been carried out using the program Gaussian 92/DFT.32 The Becke nonlocal exchange functional33 combined with the gradient corrected nonlocal correlation functional of Perdew34 were applied (denoted as BP86). The 6-31G** basis set35 was chosen. Additional calculations using the exchange functional of Becke combined with the correlation functional of Lee, Yang, and Parr36 (BLYP) provided very similar structures and vibrational frequencies. For comparisons, we have also performed density functional calculations with DMol37,38 applying the built-in numerical DNP basis set (double numeric with polarization functions) which is comparable to a 6-31G** basis set. The Janak-MorruziWilliams local correlation functional39,40 (denoted as JMW) was applied in these calculations. Some geometry optimizations at the ab initio Hartree-Fock level have been carried out with Gaussian 92/DFT using the 3-21G basis set.41 Finally, we also performed semiempirical calculations with either the Gaussian 92/DFT program using the MNDO Hamiltonian42 or with AMPAC43 using the AM1 Hamiltonian.44 The dihedral angles of the ring were kept planar during all geometry optimizations. The quantum chemically derived Cartesian force constant matrices were read into the program GAMESS.45 This program was employed to compute normal modes and total energy distributions in order to assign the normal vibrations46,47 and to determine frequencies and total energy distributions of isotopically labeled compounds. Transformation from Cartesian force constants into force constants of internal coordinates was also carried out with GAMESS. The set of internal coordinates chosen for this process is very similar to the one applied in earlier studies with similar compounds.48,49 Valence coordinates and internal coordinates for 2,3-dimethoxy-1,4-benzoquinone are defined in Figure 1 and Table 1. Our calculated force field is a harmonic force field and thus the corresponding frequencies should be compared with harmonic experimental frequencies. Instead, we are comparing our calculated frequencies with observed fundamental frequencies that include anharmonicities. It has, however, been demon-
Nonella and Bra¨ndli
Figure 1. Definition of valence internal coordinates.
strated repeatedly that density functional calculations in many cases result in harmonic frequencies which are in good agreement with experimental fundamentals50,51 when nonlocal corrections are considered and basis sets of DZP or similar quality are applied. From that agreement one is led to suspect that harmonic force constants are slightly underestimated in these calculations. 3. Results and Discussion A. 2-Methoxy-1,4-benzoquinone. Structure. The potential energy profile for a rotation of the methoxy group is presented in Figure 2. The dihedral angle ϑ(1) is defined as C1-C2O8-C9 (Figure 2). It has been varied in 30° steps. All geometrical parameters except the planarity of the ring and the dihedral angle ϑ(1) have been optimized for the different orientations of the methoxy group. Two conformations which correspond to energy minima have been found with ϑ(1) of 0° and 180°, respectively; the more stable structure corresponds to that with ϑ(1) ) 180° which is in agreement with a recent crystal structure of 2-methoxy-1,4-benzoquinone.52 The energy difference between the two structures is 10.3 kJ/mol, and the torsional barrier for a rotation of the methoxy group from 180° to 0° is 31.0 kJ/mol. Even though this barrier is larger than the one for an essentially free rotation (∼12 kJ/mol for CH3CH353) it is considerably smaller than the one of a rigid double bond. Structural parameters for the more stable conformer are listed in Table 2. The geometries of the two stable conformers are very similar. The most significant difference appears in the angle C2-O8-C9 which is 7° larger in the ϑ(1) ) 0° conformation than in the ϑ(1) ) 180° conformation, most likely due to sterical interactions between methoxy and carbonyl groups in the ϑ(1) ) 180° conformation. We will now compare the structural parameters of the more stable 180° conformation with calculated parameters of pbenzoquinone which are also included in Table 2. Three parameters are considerably affected by addition of the methoxy group. R1 and R2 are longer than in p-benzoquinone whereas R3 is shorter. R1 and R3 differ in their bond lengths by 0.044 Å in 2-methoxy-1,4-benzoquinone whereas they are equivalent in p-benzoquinone. The substituent also slightly influences the bond lengths of the two carbonyl groups: the carbonyl bond in ortho position to the methoxy group is slightly shorter than a CdO bond in p-benzoquinone while the carbonyl bond in meta position is slightly longer. Similar structural trends as they are
Methoxy-Substituted p-Benzoquinones
J. Phys. Chem., Vol. 100, No. 34, 1996 14551
TABLE 1: Numbering and Definition of Internal Coordinatesa
a
number
coordinate
description
2, 5 1, 3, 4, 6 7, 10 8, 9, 13, 14 11, 12, 15, 16, 17, 18, 19, 20 21, 22 23, 24, 25, 26, 27, 28 29, 33 30, 31, 32, 34, 35, 36 37, 40 38, 39 41, 42 43 44 45 46, 49 47, 48 50, 51 52 53 54
R2, R5 R1, R3, R4, R6 R7, R10 R8, R9, R13, R14 R11, R12, R15, R16, R17, R18, R19, R20 R7, R8 R9, R10, R11, R12, R13, R14 τ7, τ10 τ15, τ16, τ17, τ18, τ19, τ20 δ1, δ4 δ2, δ3 δ5, δ6 6-1/2(R1 - R2 + R3 - R4 + R5 - R6) 12-1/2(2R1 - R2 - R3 + 2R4 - R5 - R6) 2-1(R2 - R3 + R5 - R6) 2-1/2(β1 - γ1), 2-1/2(β4 - γ4) 2-1/2(β2 - γ2), 2-1/2(β3 - γ3) 2-1/2(β5 - γ5), 2-1/2(β6 - γ6) 6-1/2(τ1 - τ2 + τ3 - τ4 + τ5 - τ6) 2-1(-τ2 + τ3 - τ5 + τ6) 12-1/2(-τt1 + 2τ2 - τ3 - τ4 + 2τ5 - τ6)
CdC str C-C str CdO str C-O str C-H str C-O-C bend H-C-O bend C-O-C-C tors H-C-O-C tors CdO wag (out-of-plane) C-O wag (out-of-plane) C-H wag (out-of-plane) ring def (in-plane) ring def (in-plane) ring def (in-plane) CdO def (in-plnae) C-O def (in-plane) C-H def (in-plane) ring tors ring tors ring tors
Valence coordinates are defined in Figure 1.
Figure 2. Potential energy profile for rotation of the methoxy group of 2-methoxy-1,4-benzoquinone. No corrections for vibrational zero point energies are included.
predicted by our calculation are also found in the crystal structures of p-benzoquinone54 and 2-methoxy-1,4-benzoquinone52 (Table 2). Can the calculated structural effects be understood with the help of simple chemical concepts? When the methoxy group is oriented in the ring plane, mesomeric structures like those shown in Figure 3 can be constructed when sp2 hybridization is assumed for the oxygen atom. Such mesomeric structures, originally proposed to explain the redox potential of methoxysubstituted quinones,55 can explain the changes of the bonds R2, R3, and R10. But how can the alterations of bonds R1 and R7 be rationalized? We suggest that resonance effects are already present in p-benzoquinone which cause an elongation of the CdO and CdC bonds and a shortening of the C-C bonds. The added methoxy group then weakens or removes the contribution of these original resonances. Compared to “free” CdO, CdC, and C-C bonds which possess bond lengths around 1.21 Å (CdO in formaldehyde), 1.34 Å (CdC bond in ethene), and 1.53 Å (C-C in ethane),56 respectively, the bond lengths of p-benzoquinone exhibit indeed some lengthening of the CdO and CdC double bonds and a shortening of the C-C single bonds (see Table 2). We have found a similar behavior also in the case of BP86/6-31G** calculations which predict bond lengths of 1.22, 1.34, and 1.53 Å, respectively, for these free bonds compared to 1.24, 1.36, and 1.49 Å as we have calculated for p-benzoquinone.21 Vibrational Frequencies and Force Constants. We have also calculated harmonic vibrational frequencies for both stable conformations of 2-methoxy-1,4-benzoquinone. Deviations between the vibrational frequencies of the two conformations in the 1500-1700 cm-1 region are up to 23 cm-1 in the case
of the highest energy mode. In Table 3 we have listed the calculated frequencies of the more stable conformer together with the calculated total energy distribution and the experimental frequencies. The agreement of calculated frequencies and relative intensities with experimental data is very good. Deviations between calculated and measured frequencies are less than 6 cm-1. Thus, the applied density functional method provides results which are of similar quality as those obtained from previous calculations on p-benzoquinone and 1,4-naphthoquinone using the same method.21,28 Based on the total energy distribution listed in Table 3 the mode at 1687 cm-1 can be assigned as an almost pure CdO stretching vibration of the CdO bond located close to the methoxy group (C1dO7). The mode calculated at 1652 cm-1 is assigned as a nearly pure CdO stretching vibration of bond C4dO10. The two other vibrations in this spectral region at 1631 and 1590 cm-1 correspond to the two CdC vibrations which are strongly mixed. The strong coupling between CdO and CdC vibrations which had been found in p-benzoquinone 21 has been removed through the addition of the methoxy substituent. A similar effect has also been found for 1,4naphthoquinone28 where the mixing of the CdO and CdC vibrations had been eliminated due to the addition of the benzene moiety. Calculated force constants of CC and CO bonds of 2-methoxy-1,4-benzoquinone are listed in Table 6. The force constants of bonds R2, R3, and R10 are consistent with the suggested mesomeric resonance structures depicted in Figure 3. Moreover, the force constant of bond R1 is weaker and the one of bond R7 stronger than in p-benzoquinone. As was discussed above, due to the addition of the methoxy group, R1 and R7 have a slightly more pronounced single and double bond character than in p-benzoquinone. The dependence of the force constants of the CdC and CdO bonds on the dihedral angle of the methoxy group is depicted in Figure 4. The behavior of the force constants of the C2dC3 and C4dC10 bonds can also be explained with the concept of resonance structures. The strength of bond C5dC6 is only slightly affected through variation of the dihedral angle whereas bond C1dO7 is clearly becoming weaker during a rotation from 180° to 0°. The difference between the two carbonyl force constants is largest at 180° and becomes relatively small around 90°. The smallest force constants for both CdO bonds are found in the less stable 0° conformation.
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TABLE 2: Geometric Parameters of 2-Methoxy-1,4-benzoquinone and 2,3-Dimethoxy-1,4-benzoquinonea 2-methoxy-1,4-benzoquinone R1 R3 R4 R6 R2 R5 R7 R10 R8 R9 R13 R14 R7 R8 C1-C2-O8-C9 C4-C3-O11-C12 a
2,3-dimethoxy-1,4-benzoquinone
p-benzoquinone
expb
A
B
C
calcc
expd
1.515 1.471 1.496 1.485 1.369 1.353 1.233 1.242 1.349
1.494 1.451 1.468 1.467 1.341 1.327 1.219 1.228 1.336
1.500 1.500 1.490 1.490 1.375 1.352 1.237 1.237 1.368 1.368 1.448 1.448 115.2 115.2 120.5 120.5
1.477 1.477 1.477 1.477 1.322 1.322 1.222 1.222
1.444
1.512 1.487 1.492 1.486 1.383 1.349 1.234 1.244 1.348 1.375 1.443 1.449 121.5 117.0 -10.3 60.6
1.490 1.490 1.490 1.490 1.355 1.355 1.239 1.239
1.437
1.482 1.482 1.492 1.492 1.394 1.347 1.245 1.245 1.358 1.358 1.444 1.444 122.6 122.6 0.0 0.0
calc (180°)
116.9 180.0
Bond lengths are given in Å and bond angles in degrees. b Reference 52. c Reference 21. d Reference 54.
Figure 3. Mesomeric resonance structure in 2-methoxy-1,4-benzoquinone.
TABLE 3: Experimental and Calculated Frequencies, Intensities, and Total Energy Distribution (in %) of 2-Methoxy-1,4-benzoquinonea experimental c
calculated
freqb
c
freq
int
1681 1656 1623 1595
1682 1650-1655 1625 1596
s s w s
freq
int
total energy distribution
1687 169 84% C1dO7 1652 145 65% C4dO10 1631 10 44% C5dC6 + 20% C2dC3 1590 201 38% C2dC3 + 30% C5dC6
a Frequencies are given in cm-1 and intensities in km/mol. b Reference 60. c Reference 30. s: strong, w: weak.
B. 2,3-Dimethoxy-1,4-benzoquinone. Structure. Calculated potential energy curves as a function of the two dihedral angles ϑ(1) and ϑ(2) defined as C1-C2-O8-C9 and C4C3-O11-C12 , respectively, are shown in Figure 5 (I). We have applied the following procedures: keeping one dihedral angle fixed in the planar orientation either at ϑ(1) ) 0° or 180° and rotating the second dihedral angle ϑ(2) resulted in curves d (ϑ(1) ) 0°) and b (ϑ(1) ) 180°). In order to obtain curve c, both dihedrals were rotated clockwise, resulting in conformations having C2 symmetry. Clockwise rotation of ϑ(1) combined with a counter-clockwise rotation of ϑ(2) resulted in structures having Cs symmetry represented as curve a. According to the potential curves of Figure 5 (I), four stable conformations of the methoxy groups are expected. However, complete minimization of structures A, B, C, and D resulted in only three stable structures, A, B, and C. Structure D was not stable during the total minimization and converged into structure C. The structures of the remaining three stable conformers are shown in Figure 6. According to our calculations, conformer A, which has both methoxy groups in the ring plane and thus has C2V symmetry, corresponds to the most stable conformer. On the other hand, conformer B, having no symmetry elements, possesses an energy only 2.5 kJ/mol higher than conformer A. The energy of conformer C with C2 symmetry, finally, is 17.2 kJ/mol higher
Figure 4. Force constants of CdO and CdC bonds in 2-methoxy1,4-benzoquinone as a function of the dihedral angle of the methoxy group.
than that of A. According to a Boltzmann distribution, conformer C would not be populated significantly. These energy differences, however, are calculated in vacuum and are expected to depend on the environment. Furthermore, the calculated energy differences have not been corrected for the vibrational zero point energy. According to Figure 5 (I), the energy barriers for a rotation of one methoxy group while keeping the second methoxy group in the ring plane are ∼25 kJ/mol (curve c) and ∼5 kJ/mol (curve b). These barriers are very low and the exact orientation of the methoxy groups is therefore expected to be sensitive to sterical and electrostatic intramolecular interactions. Semiempirical calculations29,30 suggested different effects of the orientation of the methoxy groups on the potential energy. We have repeated such calculations with the results shown in Figure 5 (II). The most striking differences between semiempirical and DFT calculations are the following: (i) semiempirical calculations predict the planar conformation (A) not to correspond to a stable structure and (ii) an energy minimum is predicted on curve a where both methoxy groups are oriented on the same side of the ring plane (denoted as ϑ(1) ) -ϑ(2)). How can these qualitatively different results be explained? To address this question we have carried out ab initio Hartree-
Methoxy-Substituted p-Benzoquinones
Figure 5. Potential energy curves calculated with density functional (I) and semiempirical (II) methods: (a) one dihedral is rotated clockwise and the other counter clockwise; (b) one dihedral angle is rotated clockwise and the other dihedral angle fixed at 180°; (c) both dihedral angles are clockwise rotated; (d) one dihedral angle is rotated clockwise and the other dihedral angle is fixed at 0°.
Figure 6. The three stable conformers of 2,3-dimethoxy-1,4-benzoquinone as determined according to the BP86/6-31G** method.
Fock calculations using the 3-21G basis set as well as density functional BP86 calculations using the 3-21G basis set. The results from the Hartree-Fock calculations are in good agreement with those of the semiempirical calculations whereas the DFT calculations with the 3-21G basis set gave essentially the same results as those with the larger 6-31G** basis set. These findings exclude an effect of the basis set and strongly suggest that the qualitative differences in the predicted minimum energy structures arise due to correlation effects which are not considered in MNDO or ab initio Hartree-Fock calculations but are to some extent taken into account in density functional calculations. To test this hypothesis we have carried out perturbation theory calculations at the MP2 level with the 3-21G basis set. This calculation paralleled the results of the density functional calculations and clearly shows that the stabilization of the planar geometry is solely an effect of the correlation energy. Calculated structural parameters of all three conformers, together with corresponding calculated and experimental values of p-benzoquinone, are presented in Table 2. We will first compare the structures of the three conformers A, B, and C with the one of p-benzoquinone. Only minor changes are found
J. Phys. Chem., Vol. 100, No. 34, 1996 14553 in the bond lengths R4, R5, and R6 whereas the bonds which are closer to the two methoxy groups are significantly more affected by the substituents. Most strikingly, bond R2 is considerably longer than it has been found in p-benzoquinone. Effects are also evident in the bond lengths R1, R3, R7, and R10. The perturbation due to the addition of the two methoxy groups is predominantly localized on bonds adjacent to the two substituents. We now compare the three conformers A, B, and C. Rotation of a methoxy group out of the ring plane changes the bond angle ring-O-CH3 from ∼120° to ∼115°. Conformer A, with both substituents in the ring plane, has a very long bond R2 of 1.394 Å and CdO bonds which are slightly longer than in pbenzoquinone. These findings are in agreement with the proposed resonance structures for 2-methoxy-1,4-benzoquinone. Conformer C, on the other hand, shows bond lengths R1 and R3 which are close to those in p-benzoquinone and a bond R2 which is shorter than in conformers A and B. In conformer C, therefore, only smaller effects of such resonance structures are found and its geometrical parameters are in close agreement with the ones of p-benzoquinone. Conformer B, which has the methoxy group connected to C2 in the plane and the other one out of plane, shows structural parameters which are very similar to the ones found in 2-methoxy-1,4-benzoquinone. From our discussion we may derive the following rules: Addition of two methoxy groups at positions C2 and C3 affects the bonds R1, R2, and R3 as well as the two carbonyl bonds. R2 is generally enlongated whereas the other bonds become longer or shorter, depending on the orientation of the methoxy groups. The smallest effect on R2 is found when both methoxy groups are oriented out of plane. For this structure, R1 and R3 become about 0.01 Å longer and R2 becomes about 0.02 Å longer than in p-benzoquinone. When one methoxy group is rotated into the ring plane, resonance effects start to be important. R2 becomes longer, and the C-C and CdO bonds proximate to the out-of-plane methoxy group become shorter and longer, respectively. The C-C bond proximate to the in-plane methoxy group is also elongated due to an effect not yet completely understood. When both methoxy groups are in plane, some of these effects on the bond lengths are even more pronounced such as the elongation of R2. Other effects like the elongation of R1 when the methoxy group at C2 is in the plane disappear since the shortening of R1 due to an in-plane methoxy group at C3 seems to be more effective. Vibrational Frequencies. IR spectra of 2,3-dimethoxy-1,4benzoquinone30 and substituted 2,3-dimethoxy-1,4-benzoquinones like Q3,19 Q6,20 and Q820 have been recorded in solution (Qn ) 2,3-dimethoxy-5-methyl-6-(isoprenyl)n-1,4-benzoquinone). All these spectra exhibit three strong absorptions which can be grouped into two bands at higher energy, separated by less than 15 cm-1, and a third absorption band located between 1610 and 1590 cm-1. In the unsubstituted 2,3-dimethoxy-1,4benzoquinone, the two modes on the high-energy side are ∼10 cm-1 higher in energy than in quinone molecules with an isoprenoid chain. Additionally, a fourth absorption with lower intensity is found around 1640 cm-1 in unsubstituted 2,3dimethoxy-1,4-benzoquinone. On the basis of experiments with selectively 13C- and 18O-labeled ubiquinones, the two vibrations at higher energy could convincingly be assigned as predominant CdO modes.19,20 Calculated frequencies and intensities for the three conformers are listed in Table 4. The table also contains experimental data of 2,3-dimethoxy-1,4-benzoquinone30 and Q3.19 The calculated frequencies of conformer A are clearly lower in energy than the experimental frequencies or than those calculated for the other conformers. The total energy distribution given in Table
14554 J. Phys. Chem., Vol. 100, No. 34, 1996
Nonella and Bra¨ndli
TABLE 4: Calculated and Experimental Frequencies and Intensities of 2,3-Dimethoxy-1,4 benzoquinonea A freq
B int
freq
int
1654 1 1676 167 1632 433 1646 107 1622 2 1635 51 1556 140 1580 234 a
2,3-dimethoxy1,4-benzoquinoneb
C int
freq
intd
1670 292 1663 1 1632 7 1576 169
1674 1661 1639 1593
s s m s
freq
cm-1
Q3c freq intd 1663 1650
s s
1611
s
b
Frequencies are given in and intensities in km/mol. Reference 30. c Reference 29. Q3: 2,3-dimethoxy-5-methyl-6-triisoprenyl1,4-benzoquinone. d s: strong, m: medium, w: weak.
5 predicts the vibration at highest energy (1654 cm-1) to correspond to a CdC mode and the two adjacent vibrations at 1632 and 1622 cm-1 as mostly CdO modes. This result clearly disagrees with experimental data as well as with our previous calculations on p-benzoquinone21 and 1,4-naphthoquinone28 and with the presented calculations on 2-methoxy-1,4-benzoquinone. In all these cases the mode at highest energy could be unambiguously assigned to a carbonyl stretching vibration. Furthermore, the IR spectrum of conformer A shows only two strong absorptions whereas the experimental spectrum exhibits three absorptions of comparable intensities. We can finally conclude that neither the frequencies nor the intensities calculated for conformer A are in agreement with experimental data. The frequencies calculated for conformer B considerably differ from those of conformer A. The vibration at 1676 cm-1 can be assigned to a CdO mode and is in good agreement with the experiment. The next two modes at 1646 and 1635 cm-1 are mixed modes between CdO and C5dC6 and the frequency at 1580 cm-1 corresponds to the C2dC3 vibration. Three strong absorptions are found in the calculated spectrum of this conformer which is in agreement with experimental data. Overall, a satisfactory agreement of frequencies and intensities with the experimental spectra of ubiquinones is evident for conformer B. There is, however, one disagreement with experimental data: based on experiments with 13C-labeled Q319 and 18O-labeled Q6,20 the two absorptions at higher energy have been both assigned to CdO vibrations20 whereas the total energy distribution predicts the vibration calculated at 1646 cm-1 to have slightly more CdC character (see Table 5). Our calculations on conformer C predict the two high-energy modes at 1670 and 1663 cm-1 to correspond to mixed CdO vibrations (symmetric and antisymmetric combinations) and the two low-energy frequencies at 1632 and 1576 cm-1 to correspond to partially mixed CdC vibrations. Whereas the energy sequence of these vibrations is in agreement with the experiment, conformer C shows only two strong IR absorptions. As in case of conformer B, the calculated frequencies are in good agreement with experimental data on ubiquinones. The relative order of the calculated normal vibrations for all three conformers in the 1500-1700 cm-1 region is also shown in Figure 7. The question arises, why no evidence for conformer A, which according to our calculations corresponds to the most stable conformer, can be found in experimental spectra. First, our calculations have been carried out in vacuum. Relative energies could significantly depend on different environments. Second, the calculation of accurate relative energies is generally difficult and the small energy difference between conformers A and B might suggest an incorrect energetical order. Third, we can assume that the planar conformation is stabilized through formation of weak intramolecular hydrogen bonds. As soon as energetically more favorable intermolecular hydrogen bonds can be formed, these intramolecular bonds will be broken and the planar geometry will be lost. Some justification for such proposed intramolecular hydrogen bonds can be drawn
from the Mulliken overlap population. In the case of the planar conformation, a small overlap population which is, however, significantly larger than in nonplanar conformations, can be found between the methoxy hydrogens and the carbonyl oxygen. On the basis of our calculations, can we predict the conformation of the methoxy groups of 2,3-dimethoxy-1,4benzoquinone in solution? In the case of p-benzoquinone we have shown that the calculated frequencies of the CdC and CdO modes are in good agreement with the experiment. The largest deviation found in the previous calculations was 13 cm-1 for the CdC mode of ag symmetry. An excellent agreement of calculated and experimental frequencies and intensities was also found in the case of 2-methoxy-1,4-benzoquinone. In the case of 2,3-dimethoxy-1,4-benzoquinone, however, the agreement with experimental data seems to be less favorable than in the previous calculations. On the one hand, with respect to the vibrational frequencies and the assignment of the calculated modes, a better agreement with experimental data is evident for conformer C. On the other hand, when intensities are considered, the agreement with conformer B would be better. Conformations similar to B have been found in investigations of crystal structures.23 The following points, however, have to be taken into account: First, we have carried out calculations on a model molecule which lacks the isoprene unit at C4 and the methyl group at C3. How far such substituents will affect calculated infrared spectra will be investigated in part C. Second, the frequencies of the CdC and CdO vibrations of conformer B at 1646 and 1635 cm-1, respectively, differ by only 11 cm-1. The calculation could simply not be accurate enough to predict the correct energetic order of the two modes. Third, intensities as well as force constants could be affected through intramolecular interactions. Fourth, due to the relatively flat torsional potential of the methoxy groups, the orientation of these groups might be affected through the environment which would modify frequencies as well as intensities. Fifth, intensities could also be affected through resonances with combination or overtones. Our calculations reveal that vibrational frequencies and mode decompositions of the vibrations between 1500 and 1700 cm-1 distinctly depend on the dihedral angles of the two methoxy groups. In contrast to semiempirical calculations,30 our density functional calculations do not predict the two carbonyl modes to be found at higher energy than the CdC modes in all conformations. Force Constants. Calculated force constants of CdC and CdO bonds together with calculated force constants of pbenzoquinone are presented in Table 6. The most prominent deviations, up to 15% from the values calculated for pbenzoquinone, are found in the force constants of the carboncarbon bonds R1, R2, and R3 and of the carbonyl bonds R7 and R10. The larger values for the force constant of R1 and R2, combined with a smaller force constant for R2 and for the carbonyl bonds, which has been found for conformer A, is consistent with the discussed concept of mesomeric structures in the case of methoxy groups which are oriented in the ring plane. The reduction of the CdO force constants is essentially responsible for the energetically low lying CdO modes of this conformer. Differences found in bond lengths and force constants of the C-O bonds between the ring and the methoxy groups can also be explained with the resonance structures. In the case of a planar conformation, the force constant of such a C-O bond is around 6.6 mdyn/Å whereas for a nonplanar conformation, the force constant is only ∼6 mdyn/Å. In conformer B one methoxy group is oriented in plane and the
Methoxy-Substituted p-Benzoquinones
J. Phys. Chem., Vol. 100, No. 34, 1996 14555
TABLE 5: Total Energy Distribution (in %) of 2,3-Dimethoxy-1,4-benzoquinonea A C1dO7 C4dO10 C5dC6 C2dC3 C2-O8 C3-O11 a
B
1654
1632
1622
6 6 56
44 44
39 39 16
1556
1676
C
1646
1635
29 42
56 20 11
1580
85 9 57 7 7
1670
1663
1632
45 45
40 40
6 6 57 14
16 49 12 5
1577
18 54 7 7
Frequencies are given in cm-1.
TABLE 7: Calculated Isotopic Shifts of 2,3-Dimethoxy-1,4-benzoquinone (in cm-1)a A 13
18
58 41 44 53
2 31 31 0
C
1654 1632 1622 1556
C5dC6 CdO CdO C2dC3
13
O
18O
C1
2 5 32 1
7
1 4 26 0
B 13
18
42 64 36 54
23 13 27 3
C
Figure 7. Calculated relative energies of CdC and CdO modes for the three conformers A, B, and C of 2,3-dimethoxy-1,4-benzoquinone.
TABLE 6: Force Constants of 2-Methoxy-1,4-benzoquinone and 2,3-Dimethoxy-1,4-benzoquinonea 2-methoxy-1,4parameter benzoquinone R1 R2 R3 R4 R5 R6 R7 R10 R8 R9 R13 R14 a
4.029 7.978 4.675 4.197 8.758 4.396 11.725 11.174 6.794 4.787
A
B
C
4.551 4.132 4.170 7.426 7.626 7.764 4.551 4.428 4.170 4.330 4.310 4.312 9.047 8.959 8.826 4.330 4.425 4.312 10.931 11.631 11.478 10.931 11.024 11.478 6.574 6.764 6.122 6.574 5.959 6.122 4.618 4.649 4.619 4.618 4.564 4.619
1676 1646 1635 1580
C1dO7 C5dC6 C4dO10 C2dC3
Values are given in mdyn/Å for stretching parameters. b Reference
11.
other one out of plane. This inequality clearly shows up in the force constants: the force constant of the carbonyl bond which is closer to the methoxy group oriented in the plane has a force constant which is 0.6 mdyn/Å greater than the one of the other carbonyl group. This difference causes the large splitting of ∼40 cm-1 found for the two CdO modes of conformer B. The smallest deviations from p-benzoquinone are found for conformer C. Only the force constant of the bond C2dC3 exhibits a deviation greater than 0.5 mdyn/Å. The force constants of the two carbonyl bonds essentially correspond to that calculated for p-benzoquinone. This shows up in very similar frequencies of the CdO modes as we have calculated for p-benzoquinone.21 Isotopic Shifts. Isotopic shifts are an important source of information for the correct assignment of experimentally detected infrared absorptions. A theoretically reliable prediction of such isotopic shifts can strongly support a correct assignment of vibrational modes. We have shown for p-benzoquinone and 1,4-naphthoquinone that theoretical force fields determined at the BP86/6-31G** level of theory allow us to accurately predict isotopic shifts. We have calculated isotopic shifts of 13C- and 18O-labeled 2,3-dimethoxy-1,4-benzoquinone. Unfortunately, no experimental data on isotopic shifts of this molecule is available. Therefore, we compare our results to FTIR spectra of 13C- or 18O-labeled ubiquinones which have been investigated in photosynthetic reaction centers as well as in Vitro.15,19,20 We
13
C1
29 6 5 0
13C
18O 7
4
0 4 31 5
24 4 7 0
18O
10
0 3 27 2
C
pbenzoquinoneb 4.309 8.687 4.309 4.309 8.687 4.309 11.400 11.400
O
1670 1663 1632 1576
CdO CdO C5dC6 C2dC3
13C
18O
13C 1
18O
41 42 59 58
26 27 16 1
3 28 8 1
3 21 10 0
7
a 13C: all ring carbons are labeled. 18O: both carbonyl oxygens are labeled. Frequencies and shifts are given cm-1.
will address the question in how far spectroscopic properties are affected by additional substituents in part C. Upon 18O labeling, shifts of 34 and 28 cm-1 have been measured for the two CdO vibrations and a shift of 5 cm-1 for the CdC mode in the case of Q6.20 Upon uniform 13C labeling, shifts of 43 and 41 cm-1 have been found for the CdO modes of Q8.20 The CdC mode in Q8 exhibits a shift of 57 cm-1.20 All these shifts have been measured in Vitro. In recent studies, site-specific labeling of single atoms became also possible in various ubiquinones.15,19 Calculated isotopic shifts of the vibrations in the 1500-1700 cm-1 region of the spectrum for all three conformers of 2,3-dimethoxy-1,4-benzoquinone are listed in Table 7. Due to occasionally strong mixing between CdO and CdC modes the assignment of shifted vibrations is not always straightforward. In most of the cases an assignment based on the total energy distribution results in isotopic shifts which qualitatively agree with experimental or theoretical data on similar molecules. In cases of strong CdC/CdO mixing, however, it is not always clear if a mode can be unambiguously assigned as either a CdC or a CdO mode. For conformer A, labeling all ring carbons results in shifts of 53 and 58 cm-1 for the CdC vibrations and of 41 and 44 cm-1 for the CdO vibrations, respectively. These shifts are in acceptable agreement with experimental data on ubiquinone Q8.20 Labeling the two carbonyl oxygens shifts both CdO modes by 31 cm-1. When only one carbon or oxygen atom of a carbonyl bond is labeled, the corresponding carbonyl mode is most prominently affected and is shifted by 32 cm-1 for a labeled carbon atom and by 26 cm-1 for a labeled oxygen atom. For conformer C, labeling all ring carbons results in vibrations with frequencies at 1629, 1621, 1573, and 1519 cm-1. Based
14556 J. Phys. Chem., Vol. 100, No. 34, 1996 on the total energy distribution, shifts for CdO and CdC modes have been calculated to 41 and 42 cm-1 and 59 and 58 cm-1, respectively. These shifts agree with the experiment as well as with the ones calculated for conformer A or p-benzoquinone. Labeling the two carbonyl oxygen atoms results in vibrations with frequencies at 1644, 1637, 1616, and 1575 cm-1. The total energy distribution would suggest downshifts of 33 and 47 cm-1 for the two carbonyl vibrations and an upshift of 12 cm-1 for mode C5dC6. Compared to conformer A or to p-benzoquinone the shifts of the two carbonyl modes seem to be overestimated. Moreover, the upshift of the C5dC6 mode by 12 cm-1 seems very large. A tentative reassignment of the modes calculated at 1644 and 1616 cm-1 leads to shifts of 26 and 27 cm-1 for the carbonyl modes and of 16 and 1 cm-1 for the CdC vibrations. These latter shifts agree better with the ones of conformer A and p-benzoquinone. As we have found in conformer A, labeling of a single carbonyl carbon or oxygen atom causes mainly a shift of the corresponding carbonyl vibration. These shifts are 28 cm-1 in the case of a 13C substitution and 21 cm-1 when 18O is labeled. Both shifts are slightly smaller than in conformer A. After site-specific 13C or 18O labeling at one carbonyl group we have found an additional shift around 10 cm-1 of the C5dC6 mode which is absent or smaller in conformers A and B. Because of the strong mixing of the CdO and CdC modes, similar problems for an unambiguous assignment of vibrations arise also for conformer B. 13C labeling of all ring carbons leads to frequencies at 1634, 1599, 1582, and 1526 cm-1, respectively. According to the total energy distribution, the modes at 1634 and 1599 cm-1 are predominantly CdO vibrations. On the basis of this analysis we calculate shifts of 42 and 36 cm-1 for the two CdO modes and shifts of 54 and 64 cm-1 for the CdC modes. As in the other conformers and as in p-benzoquinone, CdC modes exhibit larger shifts than CdO modes. 18O labeling of both carbonyl oxygens results in frequencies at 1653, 1633, 1608, and 1578 cm-1, respectively. Based on the total energy distribution, shifts determined for CdO and CdC modes are 43 and 27 cm-1 and -7 and 2 cm-1, respectively. Comparison with the calculated shifts of conformers A and C suggests that this analysis predicts shifts too large for the carbonyl modes and too small for the CdC modes. The normal-coordinate analysis of the 18O-labeled conformer B shows a very strong mixing between C1dO7 and C5dC6 vibrations for the modes at 1653 and 1633 cm-1. A tentative reassignment of the frequency at 1653 cm-1 as a CdO mode and of the frequency at 1633 cm-1 as a CdC mode implies shifts for carbonyl and CdC vibrations of 28 and 24 cm-1 and 12 and 3 cm-1, respectively. These latter shifts are in much better agreement with those determined for conformers A and C and for p-benzoquinone. Labeling of a single carbonyl carbon or oxygen atom leads to shifts which are very similar to the ones found in conformers A and C. We find slightly different shifts for the C1dO7 and C4dO8 groups, respectively. The shifts of the carbonyl group ortho to the out-of-plane methoxy group are generally slightly larger than the ones of the opposite carbonyl group. In our calculation, the methoxy group connected to C3 is oriented out of plane. The shifts predicted after labeling of C4 or O10 are closer to those shifts determined for conformer A, and the ones after labeling of C1 and O7 are closer to the shifts found in conformer C. The differences, however, are small and are not assumed to be accurate enough to be used for the determination of the conformation of a 2,3-methoxy1,4-benzoquinone analogue in a protein environment. Experimentally, the two modes at higher energy have both been assigned as CdO modes exhibiting shifts of 34 and 28 cm-1 after 18O labeling of both carbonyl oxygens in the case
Nonella and Bra¨ndli of Q6.20 None of our calculations predict the carbonyl mode at higher energy to be shifted more than the CdO mode at lower energy upon 18O labeling. In conformer A the two CdO modes exhibit both a shift of 31 cm-1. In conformers B and C, the corresponding shifts are 24 and 28 cm-1 and 26 and 27 cm-1, respectively. While the shift of the CdO mode at lower energy is well predicted for both conformers, both calculations predict a too small shift for the high-energy CdO mode. The experimental spectrum of 18O-labeled Q6 shows a weak shoulder at 1630 cm-1 which was assigned to the shift of a CdO mode of 34 cm-1.49 This shift could, therefore, as well be overestimated by a few wavenumbers which would make the agreement between experiment data and our calculations on conformers B and C slightly better. Calculated 13C shifts are generally in good agreement with experimental data for all three conformers. On the basis of our calculations of vibrational frequencies, intensities, and isotopic shifts of 2,3-dimethoxy-1,4-benzoquinone, we cannot unambiguously decide whether the conformation of ubiquinones found in solution corresponds to conformers B or C. Whereas vibrational energies and mode assignments are in favor of conformer C, intensities are in better agreement with conformer B. Conformer B is also preferred from the energetic point of view. We have, however, to state clearly that our calculations have been performed on the model molecule 2,3-dimethoxy-1,4-benzoquinone for which no experimental data on isotopic shifts is available. On the basis of the results presented in part C we will be able to judge the quality of this model. In any case the presented results are valuable as predictions of isotopic shifts of this molecule. If we assume conformation C for the quinone found in solution, our calculations offer a straightforward explanation at least for a part of the experimentally detected downshift of the CdO mode of the carbonyl group at C4 in photosynthetic reaction centers. Due to the protein environment, the conformation of the methoxy group connected to C2 rotates into the ring plane which shifts the carbonyl mode C4dO10 down to about 1635 cm-1. Additional contributions to this shift of the CdO vibration could arise from electrostatic interactions with charged groups, most likely with the iron ion which is located between the quinones QA and QB. C. 2,3-Dimethoxy-1,4-benzoquinone with an Additional Substituent at Carbon C6. Based on experimental data and results from semiempirical calculations it has been suggested that consideration of additional substituents might be important for the determination of more accurate isotopic shifts.57 In order to investigate molecules which are more similar to ubiquinones, we have added either a methyl or an allyl group at carbon atom C6. We have also carried out calculations with an 2,3dimethoxy-1,4-benzoquinone with two additional methyl groups at carbon atoms C5 and C6 (MQ0). We will focus onto whether calculated vibrational frequencies and isotopic shifts are affected by this additional substituents and whether the calculated vibrational spectrum depends on the nature of the substituents. We have added these substituents to conformers B and C which are most likely to be found in solution or in the protein. The minimized structures of the two 2,3-dimethoxy-6-allyl1,4-benzoquinone conformers are shown in Figure 8. The allyl group is not oriented in the quinone plane. The angle between the planes of the quinone ring and the ethene unit of the allyl group is almost 90°. Very similar structures have been found in the crystal structure of (R)-3,4-dimethoxydalbergione, which in good approximation corresponds to a 2,3-dimethoxy-1,4benzoquinone with a phenyl ring attached to carbon C6.23 The angle between the planes of the quinone ring and the phenyl ring in this molecule is 83°. Similar orientations of an isoprene
Methoxy-Substituted p-Benzoquinones
Figure 8. Optimized structures of conformers B (a) and C (b) with an additional allyl group attached to carbon C6.
unit have also been found in semiempirical quantum chemical studies.29,30,58 Calculated frequencies and isotopic shifts are summarized in Table 8. Addition of a methyl group to conformer B results in vibrations at 1670, 1660, 1635, and 1588 cm-1. The modes at 1670 and 1635 cm-1 are predominantly CdO modes and the ones at 1660 and 1588 cm-1 are CdC modes. An effect due to the methyl group is mainly calculated for the mode C5dC6 , which is at 1646 cm-1 in 2,3-dimethoxy-1,4benzoquinone and shifts to 1660 cm-1 due to the methyl group and for the CdO mode at higher energy which shifts from 1676 to 1670 cm-1. When an allyl group is added, we calculate frequencies at 1674, 1666, 1653, 1634, and 1584 cm-1 when the methoxy group at C2 is in the plane (which in the following will be denoted as BR) and frequencies at 1673, 1671, 1648, 1633, and 1587 cm-1 when the methoxy group at C3 is in the plane (denoted as Bβ). The mode at highest energy always corresponds to the CdC mode of the allyl group. The modes at 1666 and 1634 cm-1 and 1671 and 1633 cm-1, respectively, correspond to CdO modes and the ones at 1653 and 1584 cm-1 and 1648 and 1587 cm-1, respectively, are predominantly CdC modes. Addition of two methyl groups at C5 and C6 to conformer B, finally, results in absorption lines at 1661 and 1629 cm-1 for CdO modes and at 1646 and 1595 cm-1 for CdC modes. Addition of an allyl group to conformer C yields vibrations at 1674, 1664, 1654, 1642, and 1585 cm-1. Again, the vibration at highest energy corresponds to the CdC mode of the allyl group. The modes at 1664 and 1642 cm-1 both correspond to CdO vibrations. Replacing the allyl group with a methyl group and adding a second methyl group at C5 changes the frequencies to 1656, 1650, 1635, and 1590 cm-1. The two modes at higher energy are again predominantly CdO vibrations. Additional substituents at carbons C5 and C6 cause shifts of up to ≈15 cm-1 of the calculated vibrational frequencies of CdC and CdO modes without changing the energetic sequence of these modes as compared to the unsubstituted 2,3-dimethoxy1,4-benzoquinone. Besides the frequencies, such substituents also affect intensities, mode decompositions, and isotopic shifts of the CdC and CdO modes. In the case of the unsubstituted molecule, conformer B shows strong absorptions at 1676, 1646, and 1580 cm-1, whereas the mixed CdC/CdO mode at 1635 cm-1 has only weak intensity. Addition of one allyl group leads to strong absorptions at 1666, 1634, and 1584 cm-1 for BR, and 1671, 1633, and 1587 cm-1 for Bβ, respectively. The absorptions at 1653 (BR) and 1648 cm-1 (Bβ) are most likely too weak to be detected. For conformer C, only two strong
J. Phys. Chem., Vol. 100, No. 34, 1996 14557 absorptions are found in the case of the unsubstituted molecule at 1670 and 1576 cm-1. Addition of one allyl group weakens the band at 1664 cm-1 and slightly intensifies the absorption at 1654 cm-1. We can compare our results to experimental data of Q1 which corresponds to a 2,3-dimethoxy-1,4-benzoquinone with one methyl group attached to C5 and one isoprene unit attached to C629 and with 5,6-dimethyl-1,4-benzoquinone (MQ0).18 IR absorptions of Q1 have been found at 1664, 1649, and 1611 cm-1. MQ0 has slightly different vibrations at 1666, 1651, and 1614 cm-1. In general, the agreement with experimental data is satisfactory for our calculated modes of the molecules derived both from conformers B and C. The CdC vibration of the isoprene unit is presumably to weak to be detected. The downshift of the CdO vibration from 1674 to 1664 cm-1 due to the substituents at C5 and C6 is predicted correctly by our calculations which reveal shifts from 1676 to 1666 or 1671 cm-1 in the case of conformer B and from 1670 to 1664 cm-1 in the case of conformer C. The shift to higher energy of the mode at 1593 cm-1 to 1611 cm-1 is also predicted correctly by our calculations. The best agreement with experiment in the case of this mode at lower energy is achieved for the molecule having methyl groups attached to carbons C5 and C6. In that case frequency upshifts of 15 cm-1 (conformer B) and 14 cm-1 (conformer C) have been calculated. Substituents at both positions seem to be required for an accurate description of this frequency shift. Calculated isotopic shifts after 18O and 13C labeling are also included in Table 8. Isotopic shifts are found to be more sensitive to additional substituents than absolute frequencies. Particularly in the case of conformer B, we calculate a larger shift for the CdO mode at higher energy than for the second CdO mode after 18O labeling which is in good agreement with experimental data on Q6.20 How do the calculations of substituted 2,3-dimethoxy-1,4benzoquinones affect our discussion on the most likely found conformer in solution and in the protein? In the following we are referring to the calculations on conformers B and C of allyl substituted 2,3-dimethoxy-1,4-benzoquinone. In the case of conformer C we have found that intensities are changed due to an additional allyl group, making a third absorption around 1650 cm-1 more likely to be detectable. The two CdO modes are separated by 6-10 cm-1 which is in good agreement with experimental findings. The shifts of both CdO modes upon 18O labeling are between 33 and 36 cm-1, showing a slightly larger shift for the mode at lower energy. No significant shift for CdC modes are expected according to our calculation on conformer C. Experimentally, shifts of 34 and 28 cm-1 for the CdO modes and an additional shift of 5 cm-1 for a CdC mode have been found upon 18O labeling of Q6.20 For site-specific labeled Q10 and Q3 in solution,15,19 shifts from 1666 to 1620 ccm-1 (1663 to 1618 and 1620 cm-1 in Q3) and from 1611 to 1600 cm-1 (1611 to 1601 cm-1 in Q3) have been observed after labeling of 13C1. Upon 13C1 labeling of conformer C, our calculation predicts only one shift larger than 2 cm-1, namely a shift from 1664 to 1616 cm-1. Labeling of 13C6 causes two larger shifts from 1642 to 1620 cm-1 and from 1585 to 1575 cm-1. Due to the calculated intensities, the calculated mode at 1585 cm-1 most likely corresponds to the absorption detected at 1611 cm-1. In contradiction to the assignment of Brudler et al.,15 we assign this mode to a predominant C2-C3 vibration (Brudler et al. are using a different labeling scheme according to the IUPAC rules. For simplicity we have kept the same labeling as in case of 2,3-dimethoxy-1,4-benzoquinone). The C5-C6 mode, which according to our calculation would be shifted by 22 cm-1, is most likely too weak to be detected. The
14558 J. Phys. Chem., Vol. 100, No. 34, 1996
Nonella and Bra¨ndli
TABLE 8: Calculated Frequencies and Isotopic Shifts of Substituted 2,3-Dimethoxy-1,4-benzoquinones (in cm-1)a 2,3-dimethoxy-6-methyl-1,4-benzoquinone
2,3-dimethoxy-6-allyl-1,4-benzoquinone
BR ∆(18O) CdCiso CdO CdC CdO CdC
1670 1660 1635 1588
37 -2 29 3
BR ∆(13C)
42 60 41 55
CdCiso CdO CdO CdC CdC a
A negative shift denotes a shift to higher energy. shifts are given cm-1. b Reference 18.
∆(18O)
Bβ
∆(13C)
1674 1666 1653 1634 1584
0 33 0 29 2
Conformer B 0 1673 40 1671 58 1648 43 1633 55 1587
1674 1664 1654 1642 1585
0 35 36 -3 1
Conformer C 0 42 40 60 57
13C:
expb
calc
∆(18O)
∆(13C)
0 38 -4 28 5
0 42 55 46 55
all ring carbons are labeled.
calculated isotopic shift of the C2-C3 vibration after 13C6 labeling is smaller than experimentally found. As we have seen in the calculations on the 5,6-dimethyl-substituted quinone, the frequency of this CdC mode rises when substituents at C5 and C6 are present. This effect will increase the mixing between the two CdC modes and most likely cause a larger isotopic shift of the C2dC3 mode. We can conclude that whereas we find good agreement in the case of the two CdO modes and their splitting, intensities and isotopic shifts are not in good agreement with the experimental data. For conformers B, the energy gap between the two CdO modes is larger than has been found experimentally. As our calculations demonstrate, this splitting is sensitive to the orientation of the methoxy groups which we expect to be sensitive to intermolecular interactions. The CdC modes calculated at 1653 and 1648 cm-1 for BR and Bβ, respectively, are most likely too weak to be detected. After 18O labeling, isotopic shifts between 33 and 38 cm-1 and between 24 and 29 cm-1 are calculated for the two CdO modes. For the CdC mode between 1580 and 1590 cm-1, shifts between 2 and 7 cm-1 are calculated. These shifts agree very well with experimental data. Site-specific labeling of 13C1 yields shifts from 1666 to 1626 cm-1 for BR and from 1633 to 1603 cm-1 and from 1587 to 1577 cm-1 for Bβ. Since the energy difference between the two conformations of conformer B is less than 0.3 kJ/mol, a nearly 1:1 mixture of BR and Bβ has to be expected in solution. Labeling of 13C1 would then give rise to three shifts of 40, 30, and 10 cm-1 which is in perfect agreement with the experiment.15,19 Labeling of 13C6 gives rise to shifts of 17, 7, and 7 cm-1 for conformer BR and of 26 and 7 cm-1 for conformer Bβ. Among the two larger shifts, only the mode at 1622 cm-1, caused by the shift of the CdC mode at 1648 cm-1 of conformer Bβ, carries medium intensity and is most likely experimentally detectable. The too small shifts of 7 cm-1 of the C2dC3 modes of both BR and Bβ can be explained with the same arguments we have used for conformer C. We find a good agreement with experimental data for intensities and isotopic shifts for conformers BR and Bβ. Only the splitting of the two CdO modes is overestimated in the calculation. Similar conclusions can be drawn from the comparison of experimental and calculated shifts of MQ0. The determination of the experimental shifts after 18O labeling of both carbonyl oxygens is not completely clear since two modes are most likely shifted into the same energy region.18 Shifts of 43 and 28 cm-1 have been proposed for the CdO modes. The CdC mode at 1614 cm-1 is downshifted by 6 cm-1. The better agreement with this data is achieved for conformer B.
2,3-dimethoxy-5,6-dimethyl-1,4-benzoquinone (MQ0)
18O:
∆(18O)
∆(13C)
1661 1646 1629 1595
34 1 24 7
40 54 48 55
1656 1650 1635 1590
33 34 0 0
41 40 62 42
∆(18O)
1666
43
1651 1614
28 6
1666 1651
43 28
1614
6
both carbonyl oxygens are labeled. Frequencies and
Mode decompositions and calculated shifts upon 18O or 13C labeling have shown to be very sensitive to additional substituents at carbon atoms C5 and C6, proving that a molecule like 2,3-dimethoxy-1,4-benzoquinone is only a poor model molecule for ubiquinones. In particular, measured isotopic shifts are now in better agreement with the ones calculated for conformer B. According to the discussion above we consider conformer B as the conformer preferentially found in solution. This conclusion is in agreement with the results from semiempirical calculations.30 The downshift of the C4dO10 vibration found in photosynthetic reaction centers would then have to be explained as entirely due to intermolecular interactions. 4. Conclusions We have carried out density functional calculations of the methoxy-substituted p-benzoquinone molecules 2-methoxy-1,4benzoquinone and 2,3-dimethyl-1,4-benzoquinone. In the case of 2-methoxy-1,4-benzoquinone an excellent agreement of vibrational frequencies and intensities with the experimental spectrum has been obtained in the 1500-1700 cm-1 region where CdC and CdO vibrational frequencies are found. Therefore, the applied density functional method has proven to yield results of similar quality as we have found in previous calculations on p-benzoquinone and 1,4-naphthoquinone. The force constants of both carbonyl bonds and of the CdC bond proximate to the methoxy substituent were found to be sensitive to the orientation of the methoxy group relative to the ring plane. In the case of 2,3-dimethyl-1,4-benzoquinone three stable conformations have been found which differ in the orientation of the methoxy groups. Qualitatively different structures are predicted by semiempirical or ab initio Hartree-Fock methods as compared with methods, which consider correlation effects such as density functional or perturbation theoretical methods. The calculated infrared spectra of the three stable conformers differ in their frequencies, mode decompositions, and intensities. In general, agreement with experimental frequencies is surprisingly good if the size and complexity of the investigated molecules is taken into account. Compared to the expected acurracy of the calculations, the differences between the calculated modes in the 1500-1700 cm-1 region are relatively small. This makes it difficult to clearly determine the conformer most likely found in solution. Since the torsional barriers of the two methoxy groups are relatively small, their orientation and in turn the resulting vibrational spectra can be significantly affected by the solvent or the protein environment. The flexibility of the methoxy groups is a property which distinguishes this molecule from the rigid molecules p-benzoquinone
Methoxy-Substituted p-Benzoquinones and 1,4-naphthoquinone. Based on the calculated frequencies in combination with calculated intensities and isotopic shifts, a better agreement with experimental data in solution is finally found for conformer B. Our systematic investigation of the dependence of force constants and vibrational spectra on the orientation of the methoxy substituents has improved our understanding of the vibrational spectra of ubiquinones. Further investigations focussing onto the effect of the protein environment on the vibrational spectrum are certainly justified as long as quantum chemical methods of similar quality are applied. In the case of p-benzoquinone, very accurate quantum mechanical force fields have also been determined using either a UNO-CAS approach49 or second-order perturbation theory (MP2)59 followed by a scaling procedure for the force constants. Both force fields resulted in an excellent agreement with experimental data. The agreement was of similar quality as the frequencies we have obtained applying an unscaled quantum mechanical force field determined with density functional methods. While we consider UNO-CAS as well as MP2 calculations not feasible for methoxy-substituted benzoquinones, the density functional approach has shown to be a promising method to predict vibrational spectra of molecules of biological relevance. The applied quantum chemical method, however, will not be applicable to much larger systems than those we have investigated in this study. How far cheaper semiempirical methods are useful for the discussion of conformational, vibrational, and electrochemical properties of substituted quinones is an important question and has to be considered.29,30 Acknowledgment. The authors acknowledge Jacques Breton, Eliane Nabedryk, and Jean-Rene´ Burie for many stimulating discussions, for making experimental results available to us prior to publication, and for critically reading the manuscript. Semiempirical calculations of Jean-Rene´ Burie have given first indications on how normal vibrations might depend on the orientation of the methoxy groups and guided us in developing a strategy for our calculations. We are also grateful to J. Robert Huber, Paul Tavan, and Jose´ Dobado for critically reading the manuscript. Support by the Swiss National Foundation (Project 31-39376.93) is gratefully acknowledged. Computing time has been provided by the Rechenzentrum der Universita¨t Zu¨rich. References and Notes (1) Kirmaier, C.; Holten, D. Photosynth. Res. 1987, 13, 225. (2) Parson, W. W. Photosynthesis. In New comprehensiVe biochemistry; Amesz, J., Ed.; Elsevier: Amsterdam, 1987; p 43. (3) Boxer, S. G.; Goldstein, R. A.; Lockhart, D. J.; Middendorf, T. R.; Takiff, L. J. Phys. Chem. 1989, 93, 8280. (4) Deisenhofer, J.; Epp, O.; Miki, K.; Huber, R.; Michel, H. Nature 1985, 318, 618. (5) Deisenhofer, J.; Michel, H. EMBO J. 1989, 8, 2149. (6) Allen, J. P.; Feher, G.; Yeates, T. O.; Rees, D. C.; Deisenhofer, J.; Michel, H.; Huber, R. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 8589. (7) Allen, J. P.; Feher, G.; Yeates, T. O.; Komiya, H.; Rees, D. Proc. Natl. Acad. Sci. U.S.A. 1988, 85, 8487. (8) El-Kabbani, O.; Chang, C.-H.; Tiede, D.; Norris, J.; Schiffer, M. Biochemistry 1991, 30, 5361. (9) Ermler, U.; Fritzsch, G.; Buchanan, S.; Michel, H. In Research in Photosynthesis; Murata, N., Ed.; Kluwer Academic Publishers: Dordrecht, 1992; Vol. I, p 341. (10) Bauscher, M.; Nabedryk, E.; Bagley, K.; Breton, J.; Ma¨ntele, W. FEBS Lett. 1990, 261, 191. (11) Thibodeau, D. L.; Nabedryk, E.; Hienerwadel, R.; Lenz, F.; Ma¨ntele, W.; Breton, J. Biochem. Biophys. Acta 1990, 1020, 253. (12) Nabedryk, E.; Bagley, K.; Thibodeau, D. L.; Bauscher, M.; Ma¨ntele, W.; Breton, J. FEBS Lett. 1990, 266, 59. (13) Breton, J.; Thibodeau, D. L.; Berthomieu, C.; Ma¨ntele, W.; Verme´glio, A.; Nabedryk, E. FEBS Lett. 1991, 278, 257. (14) Breton, J.; Berthomieu, C.; Thibodeau, D. L.; Nabedryk, E. FEBS Lett. 1991, 288, 109.
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