Experimental and Theoretical Polarized Raman Linear Difference

Article pubs.acs.org/ac

Experimental and Theoretical Polarized Raman Linear Difference Spectroscopy of Small Molecules with a New Alignment Method Using Stretched Polyethylene Film Patrycja Kowalska,† James R. Cheeseman,‡ Kasra Razmkhah,† Ben Green,§ Laurence A. Nafie,∥ and Alison Rodger*,† †

Department of Chemistry and Warwick Centre for Analytical Science, University of Warwick, Coventry, CV4 7AL, U.K. Gaussian Inc., 340 Quinnipiac Street, Building 40, Wallingford, Connecticut 06492-4050, United States § Department of Physics, University of Warwick, Coventry, CV4 7AL, U.K. ∥ Department of Chemistry, Syracuse University, Syracuse, New York, 13244, United States ‡

S Supporting Information *

ABSTRACT: This paper reports the development of the new technique of Raman linear difference (RLD) spectroscopy and its application to small molecules: anthracene and nucleotides adenosine-5′-monophosphate, thymidine-5′-monophosphate, guanosine-5′-monophosphate, and cytidine-5′-monophosphate. In this work we also present a new alignment method for Raman spectroscopy where stretched polyethylene films are used as the matrix. Raman spectra using light polarized along the orientation direction and perpendicular to it are reported. The polyethylene (PE) film spectra are consistent with powder samples and films deposited on quartz. RLD spectra determined from the difference of the parallel and perpendicular polarized light Raman spectra are also reported. The equations describing RLD are derived, and RLD spectra of anthracene and thymidine are calculated from these equations using Density Functional Theory and assuming perfect orientation of the samples. Because of the wealth of spectroscopic information in the vibrational spectra of biomolecules together with our ability to calculate spectra as a function of orientation, we conclude that RLD has the potential to provide structural information for biological samples that currently cannot be extracted from any other method.

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(UV)−visible linear dichroism of a range of biomolecular systems including membrane proteins,8 DNA−protein interactions, protein fibers,9,10 and DNA−drug systems11 and have been able to deduce structural information that cannot be obtained by other means.12 However, we have been struggling with the limited information content of the UV−visible region of the spectrum particularly for lipids and sugars (where it is essentially nonexistent), for systems with multiple overlapping transitions, and systems that have matrixes (such as buffers and light scattering particles) with low transmittance in the UV. We see vibrational spectroscopy as a solution to most of these problems. The obvious option of infrared (IR) absorbance spectroscopy and linear dichroism (IRLD) have been used to provided information on the relative orientations of chromophores such as peptides in lipid bilayers.13 However, H2O and D2O absorption bands occur in the same region as many of the most useful biomolecule IR signals making aqueous solution-

aman spectroscopy is a widely used technique in chemistry and physics as well as in art and archeology,1 electronics,2 and material science.3 As instrumentation has improved, Raman spectroscopies of various kinds are seeing increased application to biomolecular systems.4,5 The type of Raman method used depends on the properties and molecular structures of the compounds and samples being investigated.6 Polarized resonance Raman spectroscopy, for example, has been used in a number of elegant applications, such as determining the reorientation of a tryptophan chromophore in bacteriorhodopsin.7 However, resonance Raman spectroscopy effectively uses Raman as a detection method for an electronic transition, and thus it is limited to chromophores with electronic transitions (in the region of available lasers). We wished to explore the possibilities of polarized nonresonance Raman spectroscopy of oriented systems for studying molecules of biological relevance. Our overall goal, of which this paper is the first step, is to establish alignment methods for polarized Raman spectroscopy of molecules that assemble in well-defined ways in biological systems. The underlying motivation in this work is that in our laboratory we have made significant progress with ultraviolet © 2011 American Chemical Society

Received: September 15, 2011 Accepted: November 28, 2011 Published: November 28, 2011 1394

dx.doi.org/10.1021/ac202432e | Anal. Chem. 2012, 84, 1394−1401

Analytical Chemistry

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Figure 1. Structures of investigated compounds: (a) polyaromatic carbohydrates and (b) nucleotides. The approximate orientation axes in PE films deduced from the RLD and UV−LD spectra in this work are indicated by a line on each molecule.

Figure 2. Film stretcher of this work. A piece of PE film is fixed in place at points A (rubber-lined metal bars). The knob at point B connects to the screw thread (C) that moves the metal bars stretching the film, typically by ∼×3 (it is already stretched during manufacture).

unpolarized detection. These data are equivalent to what would be collected with unpolarized incident radiation and polarized detection. As analytes for this work, we focused our attention on tetracene and anthracene to establish the method and have collected polarized Raman data on nucleotides (Figure 1), which are important components of biological systems. We have also derived the equations required for calculating RLD spectra and undertaken such calculations using using ab initio methods.

phase work a challenge. IR is also in practice restricted in energy range to above 1300 cm−1.14 We have therefore turned to Raman spectroscopy, which in principle can provide similar information to IR but uses UV, visible, or near-IR incident radiation thus avoiding saturation of the signal by water absorption. Also Raman scattering by water can be ignored. As our goal is to deduce orientation information from polarized Raman spectroscopy, we need to establish robust sample orientation methods. There are a number of alignment techniques that have been used for Raman spectroscopy including liquid crystals,15 shear alignment methods with a polymer as a matrix,16,17 and “combing” fibers onto a surface. The methodology we and others use for UV−visible LD spectroscopy first involves characterizing small molecules and chromophores usually using stretched films as the sample matrix followed by flow orientation for macromolecules.12 Following our experience with UV−visible LD,18 we were therefore keen to try stretched PE films as matrixes for polarized Raman spectroscopy. Stretched PE films have been used for many years as the sample support for IR and UV− visible linear dichroism absorbance spectroscopy.12,19−22 However, although PE on its own has been studied extensively using Raman,23−26 it has not been used as a matrix to hold other analytes. In this paper, we report the first use of PE to orient samples for polarized Raman spectroscopy and present the first Raman linear difference (RLD) spectra as the difference in Raman intensity from spectra collected using incident radiation parallel to the PE stretch direction and perpendicular to it with

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EXPERIMENTAL METHODS Materials. All analytes were obtained from Sigma-Aldrich and used without additional purification. Solvents included distilled water (18.2 MΩ cm−1, Millipore Direct-Q machine), chloroform (spectrophotometric grade), dichloromethane, and methycyclohexane. The polyethylene films, used as the sample matrix, were cut from Glad Snap Lock bags. Sample Holders. As sample holders, quartz slides and polyethylene stretched films were used. The film stretcher shown in Figure 2 was custom-built for this work. The quartz slides used were the windows of a suprasil 0.1 mm path length demountable spectroscopy cell (Starna, Hainault, U.K.). Samples and Spectroscopy. Raman spectra of powders, dried films on quartz, and molecules adsorbed to stretched PE films were measured in a backscattering arrangement. The films on quartz were prepared by dissolving each compound in a minimal volume of water or chloroform (as appropriate) and placing a drop of solution on the quartz slide. The solution was dried using a gentle stream of nitrogen or warm air. To prepare 1395



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the PE films, the PE was first stretched in the film stretcher and then sample, dissolved in the appropriate solvent, was placed on it and dried. For all PE film samples, UV absorbance (on a Jasco V-630 spectrometer), UV−LD (on a Jasco J-600 spectropolarimeter equipped with a quarter wave plate, Heraeus, Hanau, Germany and avoiding the central screw thread on the holder), and polarized Raman spectra were collected on the same sample. The Raman spectra were recorded using a Renishaw inVia Microscope instrument, equipped with manual sample stage and Renishaw charged coupled device (CCD) detector, which has a detection range from visible to near-infrared. The laser was a 514.5 nm Ar+ laser whose default polarization is denoted parallel (which lies in the horizontal plane along the front of the instrument). By adjusting a half-wave plate, a perpendicular laser beam (which lies in the horizontal plane from front to back of the instrument) was obtained. The laser beam was focused onto the sample by a 20-fold magnifying microscope objective. Data acquisition and baseline corrections were performed using the WiRE 3.1 Renishaw software and Origin Pro 8.1. The film stretcher was oriented so that 0° aligned with the stretch direction. The unpolarized PE spectra are the average of the parallel and perpendicular spectra. Calculations. All calculations were performed using a development version of Gaussian.27 The geometries and force field were computed using the B3LYP28−30/cc-pVTZ31 level of theory. Frequency-dependent polarizability derivatives (Raman tensors) were computed at the B3LYP/aug-cc-pVDZ32 level of theory using an analytical derivative procedure (n + 1 algorithm) as described by Ruud and Thorvaldsen33 at 514.5 nm. The simulated Raman Linear Sum (RLS) and RLD spectra were generated assuming a Lorentzian band shape with a halfwidth of 15 cm−1 and include the appropriate ν4 and Boltzmann factors. Intensities are uniformly scaled to best match the experimental spectra. The polarizability derivatives, with respect to each normal mode, were computed for an initial orientation and then rotated to obtain other orientations. RLD and RLS intensities were computed from the normal mode polarizability derivatives using eqs 1 and 2, respectively.

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RLD(perfect orientation) κ = (αZZ 2(perfect orientation) 2 − αYY 2(perfect orientation)) =

3 κ⎛ 2 1 ⎜α − (αxx 2 + αyy 2) − αxy 2 zz 2⎝ 8 2 ⎞ 1 − αxxαyy⎟ ⎠ 4

(1)

and

RLS(perfect orientation) κ = (αYY 2(perfect orientation) 4 + 2αZY 2(perfect orientation) + αZZ 2(perfect orientation)) =

κ⎛3 1 2 2 2 2 ⎜ (α xx + α yy ) + αzz + αxy 4⎝8 2 ⎞ 1 2 2 + (αxz + αyz ) + αxxαyy⎟ ⎠ 4

(2)

where κ includes all the constants relating to the radiation field and the α are the molecular polarizability tensor components defined in terms of electronic states of the molecule in the Supporting Information. Z is the laboratory-fixed orientation axis. Y is perpendicular to Z and to the incident and scattered light of interest which propagate along X. z is the molecular orientation axis. y is perpendicular to z and the next most oriented direction. x is perpendicular to y and z forming a righthanded axis system. To determine the RLD for a perfectly oriented system computationally, one therefore evaluates the above molecular tensor components and combines them as indicated by eqs 1 and 2. The linear intensity ratio (LIR) = RLD/RLS can also be a useful quantity for analysis. The RLS is not the same as the isotropic Raman spectrum as shown in the Supporting Information. For most real situations, orientation is neither completely random nor perfectly oriented. In contrast to LD (an absorbance phenomenon) and to assumptions made in the literature for polarized resonance Raman spectroscopy,17 the Raman intensity for partially oriented systems cannot be expressed as a weighted sum of perfectly oriented and random molecules. How Samples Are Oriented in Stretched PE Films. The equations given above are only applicable to uniaxial rodlike systems. The equations for the general case are significantly more complex (see the Supporting Information). We therefore wished to determine whether we could assume that our PE films cause long molecules to adopt a uniaxial rodlike orientation. Literature evidence from Michl et al. using thick PE films prepared from pellets of low-density PE was not encouraging.19 However, our previous work with industrially prepared PE films (plastic bags) suggested we should investigate further. We chose to use UV−LD due to its spectral simplicity and chose tetracene as the analyte because it is a planar aromatic molecule that has well-separated long and short axis in-plane transitions. From the data shown in Figure S2 in the Supporting Information, we determined that the two

RESULTS

Theory of RLD Spectroscopy. The general theory of Raman spectroscopy is well established both in classical and quantum electrodynamic formalisms and for resonance and nonresonance Raman. For the proposed technique of Raman linear difference spectroscopy (RLD), we need equations that account for the orientation of the samples. The key challenge in obtaining these arises because the experiments are performed in a laboratory-fixed axis system, but the molecular properties that can be calculated or perhaps measured by another technique are determined with respect to a molecular axis system.12 For the immediate purpose of this work, we need the RLS (the Raman Linear Sum) and RLD equations for perfectly oriented uniaxial rods. The derivation of the required equations and the more general case is given in the Supporting Information. 1396



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Raman and RLD of Anthracene. Anthracene is one of the simplest molecules that can be oriented in a PE film, it is composed only of carbons and hydrogens. The Raman spectra of the powder, the reconstructed unpolarized spectrum (RLS), the parallel and perpendicular polarized PE film spectra, and the difference between them (RLD) are shown for anthracene in Figure 4. The peaks reported for anthracene in36 between 244 and 1632 cm−1 are all present (as are some from PE). In addition, we have clear signals in the CH stretch region just above ∼3000 cm−1. The CC stretch region has predominantly positive RLD signals (with the exception of the 1555 cm−1 band). This is to be expected from eq 1 for a well-oriented sample since the C C bonds are predominantly along the molecular z direction, which means αzz will usually be the largest tensor component. The C−H stretch RLD signals (above 3000 cm−1) are close to zero but slightly negative, qualitatively in accord with the predominant direction of those bonds. The 244−300 cm−1 region, where we expect to see the 244 cm−1 b1g (αxy) and 288 cm−1 b2g (αxz) transitions, unfortunately has noisy baselines so the relative magnitudes of the bands in the polarized spectra are not apparent. From eq 2 we would expect the b1g (αxy) transition to have a negative RLD signal and b2g (αxz) transitions to have zero RLD, but this is not clear in the spectrum. Thus we conclude that it has been possible to collect meaningful RLD spectra of anthracene in a PE film above 300 cm−1. The calculated RLS and RLD spectra are given in Figure 4c,d. The RLS spectra as a function of orientation shows a similar pattern of intensities as the experimental spectrum. The RLD spectrum (denoted 0°) has the anthracene oriented so its

orientation parameters perpendicular to the long axis are identical, indicating that the orientation of tetracene is indeed uniaxial. Since anthracene (and hence tetracene) was one of the least uniaxial molecules investigated by Radziszewski and Michl,19 we may conclude that uniaxial rodlike behavior operates in PE films for all the more-or-less planar molecules of Figure 1. Raman of PE. Before using PE films as sample supports for Raman, it is important to know what background signals it might contribute. The Raman spectrum of PE is shown in Figure 3. These peaks are potentially present in all PE film spectra and are annotated when significant. The RLD is shown in Figure S3 in the Supporting Information.

Figure 3. Raman spectra of stretched PE film with the laser polarized parallel and perpendicular to the stretch direction together with the RLS (i.e., unpolarized) spectrum overlaid.

Figure 4. Raman spectrum of anthracene. (a) Powder spectrum and RLS PE stretched film spectrum (constructed from polarized spectra). (b) Polarized spectra and RLD. (c) Calculated RLS spectra (with arbitrary, but consistent, intensity scale), and (d) calculated RLD spectra (with arbitrary, but consistent, intensity scale) for anthracene oriented with the anthracene long axis at 0° (Figure 1), 45°, and 90° to the orientation direction. 1397



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Figure 5. Raman spectra of (a) adenosine-5′-monophosphate, (b) thymidine-5′-monophosphate, (c) guanosine-5′-monophosphate, and (d) cytidine5′-monophosphate.

long axis is along z. The 45° spectrum is a rotation of + or −45° from this. 90° is a 90° rotation. As expected from the above qualitative discussion based on the assumption of the long axis aligning with the stretch direction of the film, the 0° spectrum is consistent with the experimental spectrum except for the C− H region, which is positive in the calculation and negative in the experimental spectrum. This is presumably due to the fact that the C−H stretch region is typically very anharmonic and not really described well by the harmonic calculations. Work is in progress to enable computation of corrected Raman tensors. Unpolarized PE Film Raman Nulcleotides. We then measured Raman spectra of powder and dried film nucleotide samples to compare them with the RLS PE spectra. Our aim was to assess PE as a sample support. Data are shown for four nucleotides (Figure 5). In each case, the PE data are consistent with the literature data37 as well as our own powder and quartz film data. In general the PE intensities are comparable to or better than the powder, though differences in relative intensities are sometimes apparent. We suspect these variations are due to crystal versus film environments, perhaps being a consequence of PE films having more monomeric analyte. Examples of differences include the following ones. The adenosine-5′-monophosphate (AMP) film spectra (Figure 5a) have enhanced out-of-plain ring deformations around 300 cm−1 and the bands corresponding to C−NH2 (1250 cm−1), and the C−C and C−N ring (1340 and 1375 cm−1) stretching vibrations are better defined in the film spectra. On the other hand, the band at 1510 cm−1 (one of the stretching CC bands) is a shoulder in film spectra, while in the powder spectrum it is actually a separate band.

The thymidine-5′-monophosphate (TMP) PE spectrum shows more peaks due to the ribose from 1000−1200 cm−1. The 1660 cm−1 band corresponding to C(4)O and CC stretching vibrations is broad and intense in all spectra. Surprisingly, the expected band corresponding to the C(2)O stretching vibration is not present in any of the spectra. PE peaks are obvious in the TMP spectrum (Figure 5b). For guanosine-5′-monophosphate (GMP), the shapes of spectra are the same with the different sample supports, but the relative intensities of the CO stretches at around 1730 cm−1, the phosphate group vibrations at 970 cm−1, and stretching C C and CN vibrations (1480 cm−1, 1580 cm−1) do differ in relative intensity as a function of the support. Cytidine-5′-monophosphate (CMP) PE spectra are similar to the quartz and the literature but in addition show a band at 1275 cm−1 (corresponding to stretching C−N and C−C vibrations in cytosine ring) that is small or not present in powder and film on quartz. Bands corresponding to the phosphate group vibrations (around 980 cm−1) are better resolved in the PE film spectrum. Bands between 800 and 900 cm−1 (CH2 and CH bending vibrations) have different shapes that may be a consequence of the PE films having more monomeric analyte. The 780 cm−1 CMP ring-breathing mode is sharp and well-defined in all spectra. RLD PE Spectra of Nucleotides. UV−visible LD spectra of all PE film samples were collected to determine whether the molecules were oriented upon stretching. These spectra are shown in Figures S3a−d in the Supporting Information. The UV−LD spectra are all positive, which given our best assessments of UV transition polarizations from the literature 1398



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Figure 6. Polarized Raman spectra of (a) adenosine-5′-monophosphate, (b) thymidine-5′-monophosphate, (c) guanosine-5′-monophosphate, and (d) cytidine-5′-monophosphate.

Figure 7. (a) Unpolarized Raman spectrum calculated for four conformers of TMP at the orientations indicated: A curled phosphate tail; B curled phosphate tail opposite direction; C elongated phosphate tail of A; D elongated phosphate tail of B. (b) RLD spectra of the elongated phosphate tail (conformer C) with z in the plane of the aromatic ring at 0°, 45°, 90°, and 135° (as illustrated).

a larger shape change perpendicular to the orientation axis (the molecular z axis) than parallel to it. The 1580 cm−1 CN stretch and 1320 cm−1 C−N and C−C stretches have positive RLD. These assignments, together with the UV LD (Figure S4a in the Supporting Information) and the known UV transition polarizations (Figure S5a in the Supporting Information) lead to the identification of the z axis indicated in Figure 1. TMP. The RLD spectrum of TMP is also predominantly negative which means (eq 1) that the x/y polarizability tensor components are bigger than the z components for most vibrations. The largest positive peaks are due to PE. Thymine itself is disk-shaped and it is far from clear what conformation

(Figure S5 in the Supporting Information), helps us identify the orientation axes. The two polarized Raman spectra, together with their differences, the RLD spectra, are shown in Figure 6 for the nucleotides. Some vibrations for each compound are discussed further below. To aid analysis, a summary of Raman data available from the literature for these molecules is tabulated in the Supporting Information. AMP. The AMP RLD spectrum is predominantly negative in sign, which means that most of its vibrations including the 1480 cm−1 CC stretch and the 725 cm−1 intensity corresponding to C−C and C−N stretches of the adenine and the sugar cause 1399



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calculated the RLD for z at 35°−60° to see how much this affected the spectrum. The small changes observed (not shown) led us to conclude that the 45° orientation gives the closest match between experiment and calculation using the RLD theory derived above. We have therefore identified a reasonable approximation to the correct conformation and orientation of TMP on the stretched PE film. The reality will be a distribution of orientations and probably conformations.

let-a-lone orientation the thymidine adopts in the PE film. Any orientation direction has to be consistent with the ribose bands at 860, 910, and 980 cm−1, and the C−N and C−C stretches around the 1370, 1440, and the 1660 cm−1 band corresponding to CC and C(4)O stretches all being net negative. Further, the thymidine UV−LD (Figure S4b in the Supporting Information) is positive, requiring the sugar/carbonyl axis to be less than 54.7° from the z axis. This situation is similar for the 205 nm band, which is nearly parallel to the other carbonyl band, we return to the thymidine case below. GMP. The GMP RLD spectrum (Figure 6c) is disappointing with comparatively small signals despite reasonable RLS spectra (Figure 5c). The RLD is predominantly negative in sign. The two negative peaks at 1463 and 1564 cm−1 corresponding to C(8)N(7) and C(2)N(3) and CC stretching vibrations, respectively, suggest an orientation axis close to that illustrated in Figure 1. The low RLD intensities may well indicate a distribution of orientations depending on whether the ring structure or the “tail” determines orientation. CMP. The CMP RLD spectrum (Figure 6d) is predominantly positive in contrast to AMP, TMP, and GMP with the exception of the 820, 980, and 1350 cm−1 bands. The positive bands at 1533 and 1610 cm−1, corresponding to CC and C N stretching vibrations in the cytidine ring, respectively, suggest that these bonds are more parallel than perpendicular to the orientation axis of molecule. The negative sign of the phosphate group band at 980 cm−1 and the UV−LD (Figure S4d in the Supporting Information) is consistent with the orientation axis we have postulated in Figure 1. Unfortunately the band corresponding to stretching CO vibrations at around 1650 cm−1 is only a shoulder. Further Analysis of Thymidine RLD. The qualitative analysis of the thymidine RLS, RLD, and UV−LD spectra given above proves not to be particularly informative. In order to extract more information from the spectrum, we calculated the RLS and the RLD. In contrast to the situation with anthracene, we first had to address the question of what conformation the molecule adopted in the stretched film. The similarity of the powder, quartz film and PE film RLS samples indicated that the orientation on the surface of the sample holder was not very significant for the RLS (though will, of course, affect the RLD). To this end the RLS spectra of four representative structures of thymidine were calculated overlaid in Figure 7a. The conformations with their relative gas phase energies are (A) curled phosphate tail (0.0 kcal/mol), (B) curled phosphate tail opposite direction around the C−C bond (3.1 kcal/mol), (C) elongated phosphate tail version of A (1.0 kcal/mol), and (D) elongated phosphate tail version of B (1.0 kcal/mol). Comparison of the spectra in Figures 5b and 7a suggest structure C is closest to that adopted in the experiments, though we can not rule out a distribution of conformers. This deduction is based particularly on the shapes of the thymidine ring breathing mode at 790 cm−1, the 966 and 1375 cm−1 stretches, and the 1442 cm−1 ribose C−H stretches. As the equations we are implementing are symmetric in the molecular x and y directions and we are assuming perfect orientation as a first approximation, to calculate the RLD we need only decide where to orient z. We assumed it is in the plane of the aromatic ring and then calculated RLD spectra for it being at 0°, 45°, 90°, and 135° as illustrated in Figure 7b. Of the four spectra in Figure 7b, apart from the 480 cm−1 band and to some extent the 780 cm−1 band, the 45° spectrum provides a good representation of the experimental RLD. We therefore

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CONCLUSIONS We have illustrated for the first time how polyethylene can be used effectively as a sample support for Raman and RLD (Raman linear difference) spectroscopy, though for some samples PE peaks are observed. In some cases, we observed differences between spectra for crystal versus film environments, making PE preferred if molecule−molecule interactions or crystal packing effects need to be avoided. The orientations imposed on molecules in the PE films made from Snap Lock bags have been shown, using tetracene, to be approximately uniaxial which enables a much simpler theoretical analysis than would otherwise have been possible. Expressions for the RLD in terms of molecular polarizability tensors have been derived and implemented using ab initio methods to enable calculations of RLD spectra. Experimental and calculated PE film anthracene spectra indicate that the combination of approaches could be used to interpret the spectra. We implemented the combined approach for thymidine where qualitative analysis of the experimental spectra did not lead to an understanding of how the molecule was oriented on the PE film. We identified the dominant conformer using the RLS (Raman linear sum) spectra and then determined the orientation of the molecule on the film using the RLD spectrum. Thus this paper shows the potential of Raman linear difference spectroscopy for geometric analysis of molecules of relevance to biology. The information-rich nature of vibrational spectroscopy of molecules such as nucleotides mean that it will be possible to extract both conformation and orientation information from RLS/RLD spectra when experiment is integrated with calculations. We have limited our consideration here to uniaxial systems and for the calculations presented in this paper have assumed perfect orientation in the films. More accurate calculations will require knowledge of the orientation distribution of molecules for the orientation method used and probably also a means of accounting for the environmental effects on molecular vibrations. Or conversely, in the future, by fitting the Raman experimental data with the calculated Raman tensor components, it may be possible to extract the previously unknown orientation distributions of molecular samples. The extremely encouraging aspect of the integrated experimental/computational approach developed in this work is that the RLD spectra vary significantly in sign and structure as a function of molecular orientation. We anticipate iteratively using molecular dynamics to determine orientation distributions and RLD calculations to interpret geometric data in complex molecular systems in a manner that has simply not been possible to date outside the accurate structure determinations from crystallography and NMR.

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ASSOCIATED CONTENT

S Supporting Information *

Full derivation of the RLD and RLS equations as well as isotropic Raman equations; UV−LD spectra of tetracene, 1400



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(18) Patel, K. K.; Plummer, E. A.; Darwish, M.; Rodger, A.; Hannon, M. J. J. Inorg. Biochem. 2002, 91, 220−229. (19) Radziszewski, J. G.; Michl, J. J. Am. Chem. Soc. 1986, 108, 3289− 3297. (20) Yogev, A.; Margulies, L.; Amar, D.; Mazur, Y. J. Am. Chem. Soc. 1969, 91, 4558−4559. (21) Thulstrup, E. W.; Thulstrup, P. W. Acta Chim. Slov 2005, 52, 371−383. (22) Ismail, M. A.; Sanders, K. J.; Fennel, G. C.; Latham, H. C.; Wormell, P.; Rodger, A. Biopolymers 1998, 46, 127−143. (23) Wool, R. P.; Bretzlaff, R. S. J. Polym. Sci., Part B: Polym. Phys. 1986, 24, 1039−1066. (24) Fagnano, C.; Rossi, M.; Porter, R. S.; Ottani, S. Polymer 2001, 42, 5871−5883. (25) Snyder, R. G.; Scherer, J. R.; Peterlin, A. Macromolecules 1981, 14, 77−82. (26) Chao, Y.; Jianming, Z.; Deyan, S.; Shouke, Y. Chin. Sci. Bull. 2006, 51, 2844−2850. (27) Frisch, M. J., Trucks, G. W., Schlegel, H. B., Scuseria, G. E., Robb, M. A., Cheeseman, J. R., Scalmani, G., Barone, V., Mennucci, B., Petersson, G. A., Nakatsuji, H., Caricato, M., Li, X., Hratchian, H. P., Izmaylov, A. F., Bloino, J., Zheng, G., Sonnenberg, J. L., Liang, W., Hada, M., Ehara, M., Toyota, K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., Honda, Y., Kitao, O., Nakai, H., Vreven, T. J., J. A. M., Peralta., J. E., Ogliaro., F., Bear-park., M., Heyd., J. J., Brothers., E., Kudin., K. N., Staroverov., V. N., Keith., T., Kobayashi., R., Normand., J., Raghavachari., K., Rendell., A., Burant., J. C., Lyengar., S. S., Tomasi., J., Cossi., M., Rega., N., Millam., J. M., Klene., M., Knox., J. E., Cross., J. B., Bakken., V., Adamo., C., Jara-millo., J., Gomperts., R., Stratmann., R. E., Yazyev., O., Austin., A. J., Cammi., R., Pomelli., C., Ochterski., J. W., Martin., R. L., Morokuma., K., Zakrzewski., V. G., Voth., G. A., Salvador., P., Dannenberg, J. J., Dapprich, S., Parandekar, P. V., Mayhall, N. J., Daniels, A. D., Farkas, O., Foresman, J. B., Ortiz, J. V., Cioslowski, J., Fox, D. J. Gaussian Development Version, revision H.12+; Gaussian, Inc.: Wallingford, CT, 2011. (28) Becke, A. D. Phys. Rev. A 1988, 38, 3098−3100. (29) Becke, A. D. J. Chem. Phys. 1993, 98, 5648−5652. (30) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785−789. (31) Dunning, T. H. Jr. J. Chem. Phys. 1989, 90, 1007−1023. (32) Kendall, R. A.; Dunning, T. H. Jr.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796−6806. (33) Ruud, K.; Thorvaldsen, A. J. Chirality 2009, 21, E54−E67. (34) Craig, D. P., Thirunamachandran, T. Molecular Quantum Electrodynamics: An Introduction to Radiation-Molecule Interactions; Academic Press: London, 1984. (35) Schipper, P. E.; Rodger, A. Chem. Phys. 1985, 98, 29−40. (36) Bridge, N. J.; Vincent, D. J. Chem. Soc., Faraday Trans. 2 1972, 68, 1522−1535. (37) Lord, R. C.; Thomas, G. J. Spectrochim. Acta 1967, 23A, 2551− 2591.

adenosine-5′-monophosphate, guanosine-5′-monophosphate, cytidine-5′-monophosphate, thymidine-5′-monophosphate; PE RLD spectra, and detailed assignments of Raman signals of nucleotides from the literature. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

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ACKNOWLEDGMENTS The manuscript was written through contributions of all authors, and all authors have given approval to the final version of the manuscript. Helpful discussions with James Mc Lachlan, Laurence Barron, Adam Squires, and Ewan Blanch are gratefully acknowledged. Engineering work of Marcus Grant and Lee Butcher has been appreciated. The authors acknowledge funding from European Commission (Marie Curie fellowship, Grant Agreement Number PIEF-GA-2009237333), the Engineering and Physical Sciences Research Council (Grant GR/T09224), and the Department for Business, Innovation and Skills Travel Grant. The equipment used was obtained through the Science City Advanced Materials project “Creating and Characterizing Next Generation Advanced Materials".

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REFERENCES

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Experimental and Theoretical Polarized Raman Linear Difference

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