Calculated Vibrational Properties of Ubisemiquinones

Density functional theory has been used to calculate harmonic normal mode vibrational frequencies for unlabeled and isotopelabeled ubisemiquinones in both the gas phase and in several solvents. It is shown that four methoxy group conformations are likely to be present in solution at room temperature. Boltzmann weighted infrared and Raman spectra for the four conformers were calculated, and composite spectra that are the sumof the Boltzmannweighted spectra were produced.ese composite spectra were compared to experimental FTIR and resonance Raman spectra, and it is shown that the calculated band frequencies, relative band intensities, and C and O isotope-induced band shis are in excellent agreement with experiment.e calculations show that the C=O and C=Cmodes of ubisemiquinone strongly mix with methoxy methyl CH bending vibrations, and that the degree of mixing is altered upon isotope labeling, resulting in complicated changes in mode frequencies, intensities, and composition upon isotope labeling. Upon consideration of the calculated potential energy distributions of the normal modes of ubisemiquinone, and how they change upon isotope labeling, an explanation of some puzzling features in previously published Raman spectra is provided.


Introduction
Ubiquinones (UQ : 2,3-dimethoxy-5-methyl-6-polyprenyl-1,4-benzoquinones) play an important role in biological electron and proton transfer processes that occur in both respiration and photosynthesis [1]. In photosynthetic reaction centers from purple bacteria, two UQ molecules, called Q A and Q B , act as terminal electron acceptors [2]. In purple bacterial reaction centers (PBRCs) (see Abbreviations) from Rhodobacter (Rb.) sphaeroides, Q A and Q B are both ubiquinone-10 (UQ 10 ) molecules. Q A and Q B have very different functions; however, Q A is an intermediary cofactor involved in transferring electrons from bacteriopheophytin to Q B , while Q B couples electron and proton transfer processes [3,4]. e very different redox functions of Q A and Q B are testimony to the �exibility of UQs in biological processes. Since Q A and Q B are both UQ 10 molecules, pigment-protein interactions must modulate the functional properties of UQ 10 in PBRCs. Elucidation of these pigment-protein interactions is at the heart of much current research in photosynthesis [5,6].
Fourier transform infrared (FTIR) difference spectroscopy (DS) is a sensitive molecular-level probe of pigmentprotein interactions, and it is widely used to study both the neutral and reduced states of the quinones occupying the Q A and Q B binding sites in PBRCs [7]. Although Q A − /Q A and Q B − /Q B FTIR difference spectra have been obtained under a wide range of conditions for variously treated PBRC's, these spectra continue to be difficult to interpret because many bands not associated with the quinone also contribute to the spectra. Reconstitution of PBRCs with isotopically labeled quinones, however, has allowed some separation of the contributions of the quinones from those of the protein to the spectra [7]. Nonetheless the hypothesized band assignments in the experimental spectra, particularly those assignments associated with the ubiquinone anion radical, are still ambiguous and have not been modeled computationally.
One basis for developing an understanding of bands in Q A − /Q A and Q B − /Q B FTIR DS is to �rst consider spectra of the relevant quinones in solution. Infrared (IR) absorption spectra [8,9] and resonance Raman spectra [10] for ubisemiquinones in solution have been obtained. However, from a computational standpoint, even these simpler solution spectra are poorly understood. e work outlined in this paper is aimed at addressing this problem.
Few computational studies aimed at modeling the vibrational properties of ubisemiquinones (UQ − ) have been undertaken. e work that has been undertaken [11,12] is limited in one way or another; for example, tail-less quinone models in only the gas phase were considered, using relatively low levels of theory. Previously it was claimed that the calculated normal modes and associated isotope-induced frequency shis are in good agreement with experiment [12]. Isotope shis do appear to agree with experiment. However, upon careful examination, it appears that the previously calculated normal modes (frequencies and intensities) are not in agreement with experimental spectra (see below). In the light of this �nding we have used more robust computational methods to investigate the vibrational properties of ubisemiquinones in the gas phase and in solution.
In this paper we describe the simulation of FTIR and Raman spectra associated with labeled and unlabeled tailcontaining ubisemiquinones in both the gas phase and in solvent.

2.1.
Calculations. Molecular geometry optimizations and harmonic vibrational frequency calculations were performed using hybrid density functional theory (DFT) methods, employing the B3LYP functional and the 6-31 + G(d) basis set within Gaussian 03 [13]. 6-31 + G(d) is preferable to 6-31 G(d) for calculations involving semiquinones [14]. For calculations including solvent, the integral equation formalism (IEF) [15][16][17] of the polarizable continuum model (PCM) [18,19] was used. e PCM uses the united atom cavity approach. Cavity parameters used were OFac = 0.89 (overlap index between interlocking spheres) and Min = 0.2 (minimum radius in Angstroms for overlapping spheres). Very similar spectra were calculated when a smaller number of added spheres were considered (OFac = 0.8 and Min = 0.5). e potential energy distribution (PED) (or total energy distribution) of normal modes was calculated using gar2ped [20].
Calculated normal mode vibrational frequencies presented here were scaled by 0.9808. Such a scale factor is standard for calculations using the speci�ed functional and basis set and was derived by comparing the frequencies of bands in experimental and calculated spectra. Such a scaling of the calculated frequencies is undertaken only to facilitate a comparison between calculated and experimental spectra. We are primarily interested in vibrational frequency changes that occur upon isotope labeling, and these frequency differences are accurately calculated without scaling [14,21]. Figure 1 shows a geometry-optimized UQ 1 − model with the atom numbering scheme displayed. UQ has two carbonyl groups (C 1 =O 18 and C 4 =O 15 ), two methoxy groups (C 3 -O 16 -CH 3 and C 2 -O 17 -CH 3 ), a methyl group at C 5 , and an isoprene unit at C 6 . In our calculations we used UQ models with only a single isoprene unit. As outlined previously [21], the calculated vibrational properties of UQ 1 (or UQ 1 − ) are very similar to that found for UQ (with 1). Also shown in Figure 1 are relevant internal coordinates of UQ 1 − . e normal modes will be expressed in terms of contributions from these internal coordinates. Of particular interest in this paper are the coordinates R3, R9, R4, and R10 which are due to C 1 ⋯O, C 4 ⋯O, C 2 ⋯C 3 , and C 5 ⋯C 6 stretching vibrations, respectively. e methoxy methyl CH bending vibrations (coordinates C8 and C9) are also of considerable relevance in this paper, as they strongly couple to the C⋯O vibrations (see below). is was not found to occur for neutral UQ [21].

Calculated Structure of Ubisemiquinone
Previously we showed that neutral UQ 1 can adopt at least eight different methoxy group conformations at room temperature [21]. To establish which conformations may be present for UQ 1 − , single-point energy calculations were undertaken for methoxy group dihedral angles that were stepped in 10 ∘ increments. at is, 36 × 36 structures with �xed methoxy group dihedral angles were geometry optimized.
A contour plot of energy versus the C 2 and C 3 dihedral angles is shown in Figure 2, which indicates that there are four low-energy UQ 1 − conformations, each with C 2 and C 3 dihedral angles close to ±120 ∘ . e four conformers are labeled A, B, E, and F in Figure 2. ese four conformers are similar to the neutral UQ 1 conformers labeled J, L, I, and K, respectively, that were described previously [21].
Following single-point energy calculations, the four UQ 1 − conformations were further geometry optimized (energy minimized) without constraining the dihedral angles. Calculations were undertaken for the four conformations in the gas phase and in several solvents that have dielectric constants spanning a wide range (2.2-78).
Calculated bond lengths, the C 6 -C 10 -C 11 bond angle, and methoxy group dihedral angles for the various UQ 1 − conformers in the gas phase and CCl 4 are listed in Table 1. Similar trends in the listed data are calculated for the conformers in other solvents (data not shown). Data for UQ 10 /UQ 10 − in the Q A /Q B binding site is also listed in Table 1.
e data presented in Table 1 demonstrates that all four conformers in solvent are within 0.45 kcal/mol in energy (kT at 298 K is ∼0.59 kcal/mol), so all four conformers would be expected to be present to some degree in solvent at room temperature. e orientation of the methoxy groups of the four geometry-optimized conformers (in CCl 4 ) as well as the calculated dihedral angles are shown in the insets in Figure 2. e corresponding dihedral angles for the four conformers in different solvents are similar (data not shown).
e hydrocarbon chain (isoprene unit) attached at C 6 makes a distinct kink at C 10 . e C 6 -C 10 -C 11 angle is close to 113 ∘ for all four conformers (Table 1). is angle is also R29 R14 X-C 8 -X X-C 9 -X F 1: Structure and atomic numbering scheme for an optimized UQ 1 − model. Various internal coordinates are also outlined. R represents bond stretching, represents a bending of the angle between two bonds, and represents a combination of angle bending centered at a vertex atom. For example, R4 represents a C 2 =C 3 stretching vibration, 1 represents a bending of the angle between the C 1 =C 2 and C 1 =C 6 bonds, and C8 represents a bending vibration of the three C 8 -H groups.
angles. e energy axis was shied so that the lowest energy conformer was set to zero. e insets show the structures of the four optimized methoxy group conformers (obtained for calculations in CCl 4 ). e emphasis is on displaying the methoxy group orientations, so hydrogen atoms have been removed and the tail at C 6 is not shown. Oxygen/carbon atoms are dark/light shade, respectively. C 2 and C 3 dihedral angles are also listed in each of the insets.

4
Computational Biology Journal T 1: Calculated bond lengths (in Å) and bond angles (in degrees) for all UQ 1 − conformers in the gas phase and CCl 4 . Calculated methoxy group dihedral angles and relative energies (in kcal/mol) for all conformers are also listed. e lowest energy conformer is set to zero and the energies of UQ 1 − conformers relative to this zero are listed (kT at 298 K is ∼0.59 kcal/mol). Bond lengths and angles for neutral UQ 10 in the Q A binding site (P�B �le: 1AIJ) and UQ 10 − in the Q B binding site (P�B �le: 1AIG) are also listed.  Figure 3(a) shows calculated IR spectra for the four UQ 1 − conformers in CCl 4 , in the 1530-1425 cm −1 region. is spectral region is chosen because it is the region where the main C⋯O and C⋯C modes of UQ − lie, and it is therefore the region generally focused upon in FTIR studies of UQ − in solution [8][9][10]. e spectra of the conformers in Figure 3(a) have been scaled by the appropriate Boltzmann factors, which were calculated based on the relative energies of the four conformations (Table 1). A composite spectrum which is the sum of the four Boltzmann weighted spectra is also shown in Figure 3(a). e corresponding calculated composite spectra for UQ − in various solvents are presented in Figures 3(b) and 3(c).

Calculated Vibrational Frequencies of UQ
In the composite spectra an intense band is observed at 1500-1478 cm −1 , depending on the solvent. e frequency of this absorption band decreases, and the intensity increases, as the dielectric constant of the solvent increases. e frequency changes as a function of dielectric constant are outlined in the inset in Figure 3(a), which demonstrates that the band frequency is strongly solvent dependant only for solvents with dielectric constant ranging from ∼1 to 20. Similar results have been found for PCM calculations of small neutral ketones in nonprotic solvents [22]. e calculated composite spectrum for UQ 1 − in CCl 4 (Figure 3(a)) displays an intense band at 1493 cm −1 . Lower intensity peaks are observed at 1483 and 1450 cm −1 . Table 2(b) lists the frequencies, IR intensities, Raman activities, and potential energy distributions for the normal modes that contribute to the bands in the spectra of UQ 1F − in CCl 4 . Similar results are calculated for conformers A, B, and E (data not shown), as would be expected given the similarity in the spectra of the conformers in Figure 3(a). For comparison, Table 2(a) also lists data for UQ 1F − in the gas phase.
e 1491 cm −1 normal mode is due predominantly to C 4 ⋯O stretching [R9(56%)] while the 1491 cm −1 normal mode is due predominantly to C 1 ⋯O stretching [R3(46%)]. For all four conformers, the C 1 ⋯O and C 4 ⋯O groups vibrate separately at a similar frequency with similar intensity. is is also observed for UQ 1 − in other solvents (not shown). is behavior is different from that found in calculations for neutral UQ 1 , however, where most of the intensity is in only one of the C=O modes [21].
For UQ 1 − in the gas phase the most intense band is calculated at 1500 cm −1 . In gas phase calculations, however, this band is due to the out-of-phase vibration of both C⋯O groups [R3(29%)-R9(27%)] (Table 2(a)). In gas phase calculations, the in-phase vibration of both C⋯O groups is found at 1495 cm −1 , and it is approximately a factor of seven lower in intensity than the out-of-phase C⋯O vibration (Table 2(a)). In gas phase calculations the in-phase C⋯O vibration is very strongly Raman active while the out-ofphase C⋯O vibration is not. In contrast, for calculations in CCl 4 , both the C 1 ⋯O and C 4 ⋯O vibrations are strongly Raman active. In all spectra in Figure 3 a weak band is found at 1522 cm −1 . is band is due to an out-of-phase vibration of the C⋯C groups of the quinone ring (R4-R10). Given the antisymmetric nature of the vibration it is very weakly Raman active. e in-phase vibration of the C⋯C groups of the quinone ring occurs at 1607 cm −1 and is IR silent but very strongly Raman active ( Table 2).
A relatively intense band is found at 1450-1456 cm −1 in all of the spectra in Figure 3. is band is due predominantly to CH bending vibrations of both methoxy methyl groups ( C8 and C9) (Table 2(b)). Given that the mode is due to CH bending vibrations of the methoxy methyl groups it is not surprising that the precise frequency of this normal mode can vary by as much as 5 cm −1 among the four conformers (Figure 3(a)).
e calculated spectra of the four UQ 1 − conformers are similar (Figure 3(a)). �e also �nd that the spectra are very similar for isotope-labeled versions of the conformers (not  shown). For this reason we will consider only the Boltzmann weighted composite spectra below. In addition, we will consider spectra for UQ 1 − in CCl 4 , noting that similar results and conclusions hold for UQ 1 − in other solvents. Figure 4 shows calculated IR (le) and Raman (right) spectra for unlabeled, 13 C, and 18 O isotope-labeled UQ 1 − in the gas phase (a) and CCl 4 (b). e normal modes (frequencies, intensities, Raman activities, and PEDs) that give rise to the bands in the spectra in Figure 4 are also listed in Table 2.
As discussed above, for unlabeled UQ 1 − in CCl 4 the 1493 cm −1 band (IR spectrum) is due to separate C 4 ⋯O and C 1 ⋯O vibrations. Upon 13 C labeling the 1493 cm −1 band appears to downshi 39 cm −1 to 1454 cm −1 (Figure 4(b)). Such a downshi is expected for a band that is due to C⋯O groups. Table 2(b) indicates that the 1454 cm −1 band in the spectrum of 13 C labeled UQ 1 − in CCl 4 is due to a C 4 ⋯O stretching vibration mixed with CH methyl bending vibrations (associated with both methoxy methyl groups). A very low-intensity normal mode at 1458 cm −1 also contributes to the 1454 cm −1 band in the IR spectrum of 13 C-labeled UQ 1 − in CCl 4 . is 1458 cm −1 mode is due to a C 1 ⋯O stretching vibration mixed with CH methoxy methyl bending vibrations (Table 2(b)). So both C⋯O groups give rise to intense normal modes for unlabeled UQ 1 − in CCl 4 . However, upon 13 C labeling, only one intense C⋯O mode is found while the other is considerably weaker. Similar 13 C isotope-induced changes are found for calculations of UQ 1 − in the gas phase (Table 2(a)).
Other than the normal modes just discussed, C⋯O stretching vibrations (R9 and R3) contribute to at least 6 other modes in the 1500-1400 cm −1 region for 13 C-labeled UQ 1 − .
Similar results are found for 13 C-labeled UQ 1 − in the gas phase.
In the IR spectrum of unlabeled UQ 1 − in CCl 4 the weak band at 1523 cm −1 is due predominantly to an out-of-phase C⋯C vibration (R4-R10). e in-phase C⋯C vibration (R4 + R10) occurs at 1607 cm −1 , with negligible IR intensity but high Raman activity (Figure 4(b)). e in-phase C⋯C mode downshis 57 cm −1 to 1550 cm −1 upon 13 C labeling with little change in the mode composition (Table 2(b)).

Discussion
e calculated changes in frequency, intensity, and mode composition upon isotope labeling of ubisemiquinone are considerably more complex than those found for the neutral species [21]. In spite of this, however, the calculated data allow a clear and detailed interpretation of bands in experimental Raman and FTIR spectra of ubisemiquinone. e calculated IR and Raman spectra presented in Figure 4(b) correspond very well to experimental spectra [8-10].

Modeling Isotope-Induced Bandshis Observed in Reso-
nance Raman Spectra. Resonance Raman spectra of unlabeled and 13 C-labeled UQ 10 − in the Q A and Q B binding sites in purple bacterial reaction centers have been obtained [10]. For comparison, resonance Raman spectra of unlabeled UQ 10 − in solution were also obtained [10]. For both in vivo and in vitro cases an intense Raman band was observed near 1608 cm −1 , with weaker bands observed near 1523 and 1488 cm −1 . We note that the calculated Raman spectrum for unlabeled UQ 1 − (Figure 4(b)) looks very similar to the experimental spectrum.
e ∼1608 cm −1 band was assigned to a C⋯C mode, weakly coupled to a C⋯O mode, because it downshied to 49-58 cm −1 upon 13 C labeling [10] (Table 3). e ∼ 1488 cm −1 band was assigned to a C⋯O mode because it downshied to ∼28 cm −1 upon 13 C labeling [10] (Table 3). e ∼1523 cm −1 band apparently disappears upon 13 C labeling. Although not suggested in the original manuscript, it is possible that the 1523 cm −1 band (of UQ 10 − in the Q A e out-of-phase C⋯C vibrational mode at 1523 cm −1 mixes with other modes upon 13 C labeling and is not easily identi�able. A strongly Raman active mode of 13 C-labeled UQ − is calculated at 1458 cm −1 (Table 2(b)). e out-of-phase C⋯C vibration contributes 17% to the PED of this mode [R10(6%)-R4(11%)]. e in-phase-coupled vibration of both C⋯O groups [R3(15%) + R9(7%)] also contributes to this mode.
Clearly, the calculated out-of-phase C⋯C vibrational mode at 1523 cm −1 can be associated with the band observed at ∼1521 cm −1 in resonance Raman spectra of UQ − in solution [10]. We suggest that the mode calculated at 1523 cm −1 forms part of a new mode that appears at 1458 cm −1 upon 13 C labeling (Table 3). In phase 13 C⋯O vibrations also contribute to the 1458 cm −1 mode. Our calculated data therefore provides an explanation as to why the ∼1521 cm −1 resonance Raman band that is observed experimentally is not identi�ed in spectra of 13 C-labeled UQ − [10]. Upon 13 C labeling the C⋯C mode mixes with C⋯O modes (and methyl bending modes) to become a new mode that is not distinctly identi�able as a 13 C⋯ 13 C mode.
Bands at 1486/1489 cm −1 in resonance Raman spectra of UQ − in the Q A /Q B binding site downshi 30/27 cm −1 upon 13 C labeling of UQ − (Table 3), respectively. ey were therefore associated with C⋯O modes coupled to C⋯C modes. Computationally, we �nd two C⋯O modes at 1495 and 1491 cm −1 . Both modes are Raman active with the 1491 cm −1 mode displaying the greater activity (Table 2(b)). ese modes give rise to the 1492 cm −1 band in the calculated Raman spectrum (Figure 3(b)), which appears to down-shi 19/35 cm −1 to 1473/1457 cm −1 upon 13 C-labeling. e 1473/1457 cm −1 band in the calculated Raman spectrum for 13 C labeled UQ 1 − is dominated by a mode at 1474/1458 cm −1 , respectively. e 1474 cm −1 mode and to a lesser degree the 1458 cm −1 mode are due predominantly to methyl CH bending vibrations of both methoxy groups coupled to a C 1 ⋯O vibration. Notice that the coupling of the C 1 ⋯O vibration is to methoxy methyl CH bending vibrations, not C⋯C ring vibrations, as was originally proposed based on the experimental spectra.

Modeling Isotope-Induced Bandshis Observed in FTIR
Spectra. Electrochemically generated FTIR difference spectra of UQ in various solvents have been obtained [8]. For UQ 10 − in acetonitrile, THF, or dichloromethane an intense FTIR absorption band was observed at 1483-1488 cm −1 . e observation of predominantly a single intense band in experimental FTIR spectra of unlabeled UQ 10 − and UQ 1 − in solution is in line with our calculated IR spectra, which are dominated by an intense band at 1478-1493 cm −1 for UQ 1 − in a variety of solvents (Figures 3(b) and 3(c)).
In experimental FTIR difference spectra for UQ 1 − in dichloromethane, a band is observed at 1483 cm −1 , which downshis to 41 cm −1 upon 13 C labeling (Table 3) [8]. From Figure 3(b) it can be seen that upon 13 C labeling the 1493 cm −1 band downshis from 39 cm −1 to 1454 cm −1 . e calculated result therefore agrees very well with the experimental observation.
Experimentally, for UQ 1 − in dichloromethane, it is also observed that the 1483 cm −1 band downshis from 15 cm −1 to 1468 cm −1 upon 18 O labeling. From the calculated IR spectra in Figure 4(b), the most obvious suggestion is that the 1493 cm −1 band (of unlabeled UQ 1 − ) downshis from 18 cm −1 to 1475 cm −1 upon 18 O labeling. e calculated PEDs in Table 2 (Table  3). e former is in excellent agreement with experiment [8]. Upon 18 O labeling modes also appear at 1481 [R3(14%)] and 1483 cm −1 [R3(7%)]. us, the 1495 cm −1 mode in the unlabeled species also appears to split and downshi to 14 and 12 cm −1 upon 18 O labeling (Table 3). Again, these conclusions are in good agreement with experiment [8]. It is the plethora of mixed modes that appear upon 18 O labeling that give rise to the broad band with a peak near 1475 cm −1 in the calculated spectrum (Figure 3(b)). Unfortunately FTIR spectra for 18 O-labeled UQ 1 − have never been presented. Only the observed shis upon labeling were presented.
From electrochemically generated FTIR difference spectra of 13 C-labeled UQ 10 − in various solvents [8] a band was observed at 1412 cm −1 . It was suggested that this band was due to a 13 C⋯ 13 C vibration that was downshied to 71 cm −1 from 1483 cm −1 in the unlabeled species. Neither the calculated data presented here nor the resonance Raman data presented previously support this hypothesis.  [24,25]. On the basis of 18 O, 13 C, 13 C 1 , and 13 C 4 labeling the 1486/1466 cm −1 bands were assigned to C⋯O/C⋯C vibrations, respectively [24]. e modes were suggested to be considerably mixed. e origin of the 1449 cm −1 band was not considered. Another group, which undertook identical labeling experiments [25], assigned the 1485 cm −1 band to a C 1 ⋯O vibration, the 1466 cm −1 band to C 4 =O vibration, and the 1449 cm −1 band to a C⋯C vibration. All modes were suggested to be strongly mixed.

Experimental Q A
Resonance Raman spectra for UQ − in the Q A binding site display a weak band at 1486 cm −1 , but no bands were apparent at 1466 and 1449 cm −1 . Of course it may simply be the case that the 1466 and 1449 cm −1 normal modes are Raman inactive.
Our calculated spectra for UQ 1 − in solution poorly model observed FTIR bands of UQ − in the Q A binding site. For UQ − in the Q A binding site, the C⋯O modes appear to be separated by 19 cm −1 . For calculations in solvent the two C⋯O modes do appear to be distinct, although the separation of the modes is only 4 cm −1 . In gas phase calculations the two C⋯O modes are coupled. e separation of C⋯O modes of UQ − in the Q A binding site is due to asymmetric interactions with the protein environment. Calculations of UQ − in solvent or in the gas phase cannot model these interactions. Calculations including effects of the protein environment are essential. Such calculations are underway in our lab.
In Q B − /Q B FTIR DS a single IR band is observed near 1479 cm −1 . It was suggested that this band was due to both C⋯O modes of UQ − in the Q B binding site [7,26,27]. It was also suggested that the 1479 cm −1 band downshis 33/52 cm −1 upon 18 O/ 13 C labeling, respectively [7,26,27]. Such shis are difficult to rationalize in view of the shis calculated (15/37 cm −1 ) and observed experimentally (15/27-41 cm −1 ) for UQ in solution (Table 3). Additionally, there appears to be some inequivalence in the C⋯C modes of UQ in the Q B binding site when perturbed speci�cally at the C 1 or C 4 position [7,26,27]. It was suggested that this inequivalence is a result of speci�c protein interactions [7,26,27]. Again, calculations including effects of the protein environment appear to be necessary (essential) in order to accurately simulate the vibrational spectra of UQ in the Q B binding site.

Previous Calculations of Ubisemiquinones.
DFT-based vibrational frequency calculations (using the BP86 functional) have been undertaken for 2,3-dimethoxy-1,4-benzoquinone and 2,3-dimethoxy-5,6-dimethyl-1,4-benzoquinone in the gas phase [12]. Comparison of calculated data for the two models showed that substituents at C 5 and C 6 are required in order to better model the properties of ubiquinones and ubisemiquinones. In the above study isotope shis were calculated. However how the C⋯O and C⋯C modes couple with each other and with CH methoxy methyl bending vibrations was not considered. As we have shown above, the extent of mode mixing can be considerably altered upon labeling, making it difficult to identify how the different bands shi upon labeling. As we show here, the detailed PEDs are a crucial tool in the analysis of how calculated bands shi upon isotope labeling. One problem with previous DFT calculations (in the gas phase) [12] is that for 2,3-dimethoxy-1,4-benzoquinone the C⋯O modes were found at a higher frequency than the C⋯C modes. For 2,3-dimethoxy-5,6-dimethyl-1,4-benzoquinone (in the gas phase) the C⋯O modes were found at slightly lower frequency than the C⋯C modes (3-4 cm −1 ). However, from Raman experiments the out-of-phase C⋯C mode is found to be ∼32 cm −1 higher in frequency than the C⋯O mode [10] (Table 3).
Furthermore, the antisymmetrically coupled C⋯O mode (for 2,3-dimethoxy-5,6-dimethyl-1,4-benzoquinone) was calculated to be more than a factor of 26 times more intense than the C⋯C mode [12]. is calculated result is not in line with experimental IR spectra [8].
Clearly, previous DFT calculations [12] poorly model the experimental Raman and IR spectra. In contrast, in our calculations for UQ 1 − in CCl 4 , the out-of-phase C⋯C modes are 28-32 cm −1 higher in frequency than either of the C⋯O mode (Table 2(b)). In gas phase calculations the out-of-phase C⋯C mode is still 24 cm −1 higher in frequency than the antisymmetrically coupled C⋯O mode (Table 2(a)). In addition, in gas phase calculations and in solvent, the intensity of antisymmetrically coupled C⋯O mode is ∼7.5 times more intense than the out-of-phase C⋯C mode. ese results are in excellent agreement with experimental IR and Raman spectra. e limitations in previous calculations are most likely related to the choice of functional and basis set, and the inadequacy of a UQ structural model that lacks an isoprene unit.

Conclusions
We calculate that four UQ 1 − conformers are likely present in solution at room temperature. Calculated IR spectra for all four UQ 1 − conformers are similar. Calculated IR spectra of unlabeled and isotope-labeled UQ 1 − in the gas phase and in solution show a similar band pattern, although in some cases there are differences in the composition of the modes that contribute to the bands in the spectra.
Calculations show that upon isotope labeling the out-ofphase C⋯C ring modes and C⋯O modes of UQ 1 − strongly couple with methyl C-H bending vibrations of the methoxy groups. is leads to complicated splitting of modes and unusual downshis upon isotope labeling. Nonetheless by consideration of PEDs of the calculated normal modes, sense can be made of the isotope-induced shis and intensity changes, and it is shown that the calculated data provide a rational and detailed interpretation of experimentally observed isotope-induced band shis in experimental FTIR and Raman spectra of UQ 1 − in solution.