Anharmonicity Effects in the Vibrational CD Spectra of Propylene

Letter pubs.acs.org/JPCL

Anharmonicity Effects in the Vibrational CD Spectra of Propylene Oxide Christian Merten,†,∥ Julien Bloino,‡,§ Vincenzo Barone,§ and Yunjie Xu*,† †

Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada, T6G 2G2 Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti OrganoMetallici (ICCOM-CNR), UOS di Pisa, Area della Ricerca CNR, Via G. Moruzzi 1, I-56124 Pisa, Italy § Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy ‡

S Supporting Information *

ABSTRACT: This study reports the first vibrational circular dichroism (VCD) spectra of propylene oxide isolated in an argon matrix. The narrow bandwidth achieved, in addition to the rich VCD features, allows a thorough analysis of the spectra and detailed comparison with the calculated harmonic and anharmonic IR and VCD spectra. Several bands in the fingerprint region are identified as nonfundamental modes based on the harmonic calculation, and three of them feature significant VCD intensity. Anharmonic VCD intensity calculations were carried out using a newly developed methodology based on the second-order level of vibrational perturbation theory. All new bands observed can be undoubtedly assigned to combination or overtone modes except the band at 1486.4 cm−1, which is tentatively identified to contain contributions from an overtone and a combination mode. The study also reveals that the current theoretical approach for anharmonic contributions to VCD spectra needs to be further improved when there is an accidental resonance involved. SECTION: Spectroscopy, Photochemistry, and Excited States

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in the 1960s,10−12 followed by Raman studies.13 Also rotational spectroscopic studies of PO, PO dimer, and PO−water clusters were reported.14−18 The chiroptical properties of PO in liquid and in the gas phase have been probed by VCD spectroscopy19−22 as well as Raman Optical Activity (ROA).23,24 Being such an important prototype molecule, it is not surprising that PO was among the first chiral molecules whose anharmonic VCD calculations were carried out.9 At the time, the obtained anharmonic spectra could only be compared with lowerresolution solution data. The aim of this study is to evaluate this new theoretical approach by comparison of calculated anharmonic spectra with experimental MI-IR and MI-VCD spectra of PO. The advantage of using the MI technique in this case lies in the narrow bandwidth, which allows for more thorough band assignments, and the possibility to observe even very weak VCD signatures of overtones and combinations. Figure 1 shows the experimental matrix-isolation IR and VCD spectra of PO in the fingerprint region measured in an argon matrix at 10 K, together with those obtained in CCl4 solution. The band positions obtained in the matrix are summarized in Table S1, Supporting Information (SI).20,25 The calculated scaled harmonic IR and VCD frequencies (scaling factor 0.986), intensities and signs at the B3LYP/6-311+

ibrational circular dichroism (VCD) spectroscopy has become a valuable tool for the structure elucidation and determination of absolute configurations of chiral molecules in solution. It has been used to study chiral species ranging from biomolecules, such as peptides and carbohydrates, to natural products and other synthetic chiral organic molecules, and to polymers and metal complexes. Recently, matrix-isolation (MI) VCD spectroscopy has been shown to be capable of providing even more insights into the conformational preferences of chiral molecules1 and chirality transfer phenomena.2 This is mainly due to the much narrower bandwidth achieved with the low-temperature matrices than that obtained in solution. Generally speaking, the analysis of VCD spectra relies heavily on the comparison of the experimental and theoretical spectra.3 While the anharmonicity contribution to fundamentals has been shown to be crucial in achieving reliable IR assignments,4 the ability to account for the anharmonicity contribution to combinations and overtones, and to the sign and magnitude of VCD features is important for VCD interpretation. Following the basic theoretical background and implementation introduced by Stephens for the calculation of VCD spectra,5−8 some of us have recently proposed a general formulation including anharmonic corrections at the second-order level of vibrational perturbation theory (VPT2) based on the Rayleigh− Schrödinger perturbation approach.9 As one of the smallest, rigid chiral molecules, propylene oxide (PO), also called methyl oxirane or epoxypropane, has served as a prototype molecule in many vibrational spectroscopic studies. Infrared spectra of PO were first reported © 2013 American Chemical Society

Received: August 30, 2013 Accepted: September 26, 2013 Published: September 26, 2013 3424

dx.doi.org/10.1021/jz401854y | J. Phys. Chem. Lett. 2013, 4, 3424−3428

The Journal of Physical Chemistry Letters

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faint indications of some of these VCD bands in the solution spectrum, although they are very weak, not easily distinguishable from the background, and were probably regarded as noise before (cf. Figure S1, SI). The calculated anharmonic IR and VCD spectra obtained at the same level of theory are shown in Figure 2 in comparison

Figure 1. Experimental IR and VCD spectra of PO in the fingerprint region measured in an argon matrix and in CCl4 (7 M, 15 μm path length, intensities scaled by 0.5) and the corresponding scaled harmonic spectra at the B3LYP/6-311++G(3df,3pd) level. The numbers correspond to the fundamental modes and the asterisks mark previously unassigned bands.

Figure 2. Fingerprint region of the experimental MI-IR and MI-VCD spectra of PO measured at 2 cm−1 and 0.5 cm−1 resolution (black and gray experimental spectra, respectively) compared with the calculated anharmonic spectra (B3LYP/6-311++G(3df,3pd)). The asterisks mark previously unassigned bands.

+G(3df,3pd) level are displayed in Figure 1 as the simulated spectra for the (R)-enantiomer and as line spectra for the (S)enantiomer. Details on the experimental and computational procedures can be found in the SI. As already shown in several previous publications, the comparison between the solution IR spectra and the calculated harmonic spectra is very satisfactory. All calculated fundamental modes can be clearly identified in the experimental spectra. Regarding the relative VCD intensities and signs, i.e., the calculated rotational strengths, the harmonic calculations also yield very good results. Therefore the solution data do not provide any critical evaluation of the newly implemented anharmonic calculation approach. The well-resolved MI spectra, on the other hand, reveal several additional bands that are not predicted by the harmonic calculations. These additional bands are either invisible or appear only as shoulders in the related solution IR spectra. While one can fairly straightforwardly correlate the strong and medium strength IR bands to the solution bands and to the harmonic fundamental bands predicted in the lower than 1350 cm−1 region, the situation is somewhat more complex in the region above 1350 cm−1. These new bands are marked in all figures by asterisks. Some of these new bands have obvious corresponding VCD features. In retrospect, one could see the

with the experimental spectra. In order to highlight weaker IR bands, the experimental spectra of the (R)-enantiomer obtained at a resolution of 0.5 cm−1 are included as well. In the line spectra, contributions from overtones and combination modes are highlighted in different colors, while modes with a dipole strength D below 0.1 × 10−40 esu2 cm2 are not shown. In the range below 1350 cm−1, since there are essentially no accidental near resonances between the calculated modes, the anharmonic corrections to the frequencies and intensities can generally reproduce the experimental spectra very well. Guided by the calculations, the overtones of the fundamental modes ν3 and ν2 can be identified in the experimental spectra as very weak bands at 818.5 and 749.4 cm−1 (these bands are only clearly visible when looking at the 0.5 cm−1 resolution spectra). Division of these band positions by a factor of 2 leads to the estimated wavenumbers of the fundamental modes of 409.2 and 374.7 cm−1, which are very similar to those reported for the N2 matrix (409 and 371 cm−1).25 Figure 3 shows an enlarged view of the interesting region between 1550 and 1350 cm −1 where overtones and 3425



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overtone of ν4 and the combination mode ν2+ν11. At the same time, the experimental band at 1486.4 cm−1 would be assigned to the fundamental mode ν18. This interesting phenomenon related to the ν18 assignment was noted in the initial comparison of anharmonic calculations with solution phase data.9 However, the lower resolution solution VCD spectra do not offer VCD intensities of overtones and combination bands for a thorough and detailed comparison with the anharmonic VCD calculations. The MIVCD spectra allow further comparison of the experimental VCD signs of the related bands with those predicted by anharmonic VCD calculations. The assignment of the band at 1475.8 cm−1 to the combination mode ν2+ν9 is favored over ν1+ν13, both by the better frequency proximity and the correct negative VCD sign predicted although with very low intensity. The assignment of the experimental band at 1513.6 cm−1 to 2ν4 and ν2+ν11 modes appears to be consistent in terms of the experimental and predicted VCD sign. The assignment of the experimental band at 1486.4 cm−1 to ν18, however, is not supported by the VCD data since the experimental negative VCD sign is opposite of the positive sign predicted for the (R)enantiomer. In addition, the enormous red-shift of the fundamental ν18 due to Fermi resonance seems suspicious given the very good agreement of the (scaled) harmonic spectra with the experimental solution data. At this point, it is worthwhile to investigate the basis set dependence of the calculated frequencies and intensities as well as VCD signs. The employed 6-311++G(3df,3pd) basis set is already very large, so that an improvement of the results with other Pople basis sets is less likely. Therefore, the popular Dunning basis set aug-cc-pVTZ was chosen as a representative for other types of basis sets frequently used. Not surprisingly, the scaled harmonic spectra calculated with this basis were almost identical with the harmonic spectra shown in Figure 1 (cf. Table S2, SI). In the anharmonic spectra, some small changes are noted with the Dunning basis set. For example, while the spacing between the overtone of ν4 and the combination mode ν2+ν11 is slightly increased and the order is switched, the related IR and VCD intensities and VCD signs were not affected. An additional combination mode (ν2+ν10) with medium IR and VCD intensity appears between 2ν4 and ν18 (cf. Figure S2, SI). Overall, the frequency order and the relative IR and VCD intensities and VCD signs of ν18 and other lower-lying fundamentals and combination modes also did not change. Hence, the agreement between the experimental calculated spectra could not be improved by choosing a different family of basis sets. The quality of the calculated anharmonic frequencies depends on the parent harmonic frequencies. Therefore, higher level harmonic frequencies were calculated using the B2PLYP functional,26 a double-hybrid functional with second-order perturbation (PT2) theoretical treatment of the correlation energy. Besides accurate excited electronic states and CD spectra,27,28 this functional has also been shown to provide very good harmonic and anharmonic frequencies.29 In this study, the combination B2PLYP/aug-cc-pVTZ was the only one that yielded ν18 at higher wavenumbers than the overtone of ν4. On the other hand, some other modes got shifted too much (e.g., ν17) so that the overall agreement with the experimental band positions got worse. For B2PLYP/6-311++G(3df,3pd), the anharmonic IR spectrum computed is very similar to that with B3LYP (cf. Figure S4, SI).

Figure 3. Enlarged view of the spectral region 1550−1350 cm−1 of Figure 2. In the line spectra, fundamental modes are indicated in red, overtones in green, and combination modes in blue. The asterisks mark previously unassigned bands, and the “x” marks a known background artifact.

combination modes with relatively strong IR and VCD intensities are observed. The new experimental bands at 1362.5 cm−1 can be assigned to the combination modes ν3+ν7 and ν1+ν12 where the first mode is about 5 times more intense than the second. The combination mode ν2+ν8 is assigned to the experimental band at 1396.7 cm−1 based on the frequency proximity. For both bands, the assignments are further confirmed by summation of the experimental wavenumbers of the corresponding fundamental modes. The anharmonic calculations do not predict significant VCD intensity for these combination modes. This is also consistent with the experiment. The new band between the fundamentals ν16 and ν15 at 1433.3 cm −1 can be unambiguously assigned to the combination mode ν3+ν8. This assignment is again supported by the experimental band positions of the corresponding fundamentals. Furthermore, the positive experimental VCD sign for this band for the (R)-enantiomer is correctly captured by the calculated anharmonic VCD intensity. The band assignments for the three remaining experimental bands between 1520 and 1470 cm−1, however, are less straightforward. The calculation predicts in total five modes (with D greater than 0.1 × 10−40 esu2 cm2): the fundamental mode ν18, an overtone of the low-lying ν4, and three combination modes. The band at 1475.8 cm−1 might originate either from the combination mode ν2+ν9 or ν1+ν13. It is noted that the fundamental ν18 and the overtone of ν4 are found to be in a Fermi resonance. This causes a significant red shift of the fundamental mode ν18 compared to its harmonic frequency. Consequently, if one bases the band assignment on the predicted frequency ordering, the experimental band at 1513.6 cm−1 would no longer be assigned to ν18 but to the 3426



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the correct frequency order, then the signs of the related overtone and combination mode are in error. Further theoretical development will include a more accurate treatment of resonances and the extension of the hybrid scheme to properties to ensure the reliability and accuracy of the calculated intensities. The availability of the well-resolved experimental MI-IR and MI-VCD spectra of PO and other chiral molecules studied in the future will allow further refinement of the theoretical anharmonic approach. The CH stretching region (3200−2700 cm −1 ) to which many combination modes and overtones contribute significantly will likely be the focus of these future studies.

Since B2PLYP could not be used for VCD intensities in a stand-alone approach due to the PT2 contributions, a hybrid approach has been applied in order to provide more accurate harmonic frequencies for the calculation of VCD spectra. In this approach, the harmonic frequencies are taken from calculations with the B2PLYP functional while the anharmonic contributions are calculated at a lower level afterward. When combining B2PLYP/aug-cc-pVTZ harmonic frequencies with anharmonic correction computed with B3LYP and with either of the Pople or Dunning type basis sets used before, the reversed order of ν18 and 2ν4 was preserved (cf. Figures S2− S5 and Tables S2−S4, SI). Unfortunately, none of the hybrid calculations afforded a conclusive band assignment in the 1525−1480 cm−1 region. Finally, a note should be made regarding the method used to compute the anharmonic frequencies and transition moments. VPT2 frequencies have been computed at the generalized VPT2 (GVPT2) level, that is Fermi resonances have been identified by applying the Martin test and then removed before being subsequently treated variationally.9 For intensity, resonant terms are removed with no variational treatment while Fermi resonant terms are identified with the same criteria as those used for frequencies. Although not occurring in the present context, we recall that formulas of the fundamental bands also contain additional sources of singularities due to 1− 1 resonances (ωi ∼ ωj). Hence, there is no a posteriori correction for the contributions to intensities by the discarded resonant terms. As mode ν18 is involved in two Fermi resonances (ω18 ≈ 2ω4 and ω18 ≈ ω2 + ω10), the corresponding terms have been removed, and this can have an impact on the resulting IR and VCD intensities. Regarding the harmonic part, the tests described above, as well as additional tests done at higher levels of theory, confirm that convergence is reached for the electric dipole and vibrational energies. However, the lack of highly accurate theoretical data for the magnetic dipole makes it harder to control the reliability of those data. Overall, it appears that the currently implemented anharmonic correction works well in terms of anharmonic frequency, intensity, and VCD signs where there is no resonance involved but still struggles when resonance is involved. Summarizing the present study, MI-IR and MI-VCD spectra of both enantiomers of propylene oxide were measured in the fingerprint region, and the measurements show very good mirror-image quality. Several experimental IR bands could be identified for the first time as not arising from fundamental modes by comparison to the harmonic spectral calculations. With the state-of-the-art anharmonic spectra calculations, it was possible to clearly assign all new bands observed except in the 1525−1480 cm−1 region. Two out of three bands that feature strong VCD intensities are assigned to the combination mode ν3+ν8 and ν2+ν9. The calculated anharmonic spectra, however, fail to produce a consistent VCD assignment in the 1525−1480 cm−1 region where a fundamental mode, an overtone, and at least one combination mode are expected. This disagreement between experiment and theory could not be solved by varying basis sets or functionals used for the calculations. It was further recognized that the mode ν18 is involved in two Fermi resonances (ω18 ≈ 2ω4 and ω18 ≈ ω2 + ω10), and this is likely the cause for the difficulty associated with the aforementioned wavenumber region. If one assumes that the anharmonic frequencies obtained with the large Pople basis set are correct, then the VCD sign of ν18 is computed incorrectly. Should the B2PLYP with the Dunning basis yield

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ASSOCIATED CONTENT

S Supporting Information *

Experimental and computational details, experimental band positions, enlarged views of spectra, calculated frequencies, dipole and rotational strengths. This information 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]; Fax: 1-780-492-8231. Present Address ∥

(C.M.) Ruhr-Universität Bochum, Fakultät für Chemie and Biochemie, Universitätsstraße 150, 44801 Bochum, Germany. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research was funded by the University of Alberta, the Natural Sciences and Engineering Research Council of Canada, and Canada Research Chairs Program. We thank Dr. J. R. Cheeseman for stimulating discussions. C.M. acknowledges the Alexander von Humboldt foundation for a Feodor Lynen Postdoctoral fellowship.

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REFERENCES

(1) Merten, C.; Xu, Y. Matrix Isolation Vibrational Circular Dichroism Spectroscopy of 3-Butyn-2-ol and Its Binary Aggregates. ChemPhysChem 2013, 14, 213−219. (2) Merten, C.; Xu, Y. Chirality Transfer in a Methyl Lactate− Ammonia Complex Observed by Matrix-Isolation Vibrational Circular Dichroism Spectroscopy. Angew. Chem., Int. Ed. 2013, 52, 2073−2076. (3) Polavarapu, P. L. Renaissance in Chiroptical Spectroscopic Methods for Molecular Structure Determination. Chem. Rec. 2007, 7, 125−136. (4) Cheng, T. C.; Jiang, L.; Asmis, K. R.; Wang, Y.; Bowmans, J. M.; Ricks, A. M.; Duncan, M. A. Mid- and Far-IR Spectra of H5+ and D5+ Compared to the Predictions of Anharmonic Theory. J. Phys. Chem. Lett. 2012, 3, 3160−3166. (5) Devlin, F. J.; Stephens, P. J.; Cheeseman, J. R.; Frisch, M. J. Ab Initio Prediction of Vibrational Absorption and Circular Dichroism Spectra of Chiral Natural Products Using Density Functional Theory: Camphor and Fenchone. J. Phys. Chem. A 1997, 101, 6322−6333. (6) Devlin, F. J.; Stephens, P. J.; Cheeseman, J. R.; Frisch, M. J. Ab Initio Prediction of Vibrational Absorption and Circular Dichroism Spectra of Chiral Natural Products Using Density Functional Theory: α-Pinene. J. Phys. Chem. A 1997, 101, 9912−9924. (7) Devlin, F. J.; Stephens, P. J.; Cheeseman, J. R.; Frisch, M. J. Prediction of Vibrational Circular Dichroism Spectra Using Density Functional Theory: Camphor and Fenchone. J. Am. Chem. Soc. 1996, 118, 6327−6328. 3427



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(8) Stephens, P. J. Theory of Vibrational Circular Dichroism. J. Phys. Chem. 1985, 89, 748−752. (9) Bloino, J.; Barone, V. A Second-Order Perturbation Theory Route to Vibrational Averages and Transition Properties of Molecules: General Formulation and Application to Infrared and Vibrational Circular Dichroism Spectroscopies. J. Chem. Phys. 2012, 136, 124108/ 1−15. (10) Tobin, M. C. The Infrared Spectrum of Propylene Oxide. Spectrochim. Acta 1960, 16, 1108−1110. (11) Fateley, W. G.; Miller, F. A. Torsional Frequencies in the Far InfraredIII: The Form of the Potential Curve for Hindered Internal Rotation of a Methyl Group. Spectrochim. Acta 1963, 19, 611−628. (12) Winther, F.; Hummel, D. O. The Combination Band of the Methyl Group Torsion and Asymmetrical Stretching FrequencyI. Molecules with One Methyl Rotor. Spectrochim. Acta 1969, 25A, 417− 423. (13) Villarreal, J. R.; Laane, J. Raman Spectra and Internal Rotation of Methylcyclopropane and its Analogs. J. Chem. Phys. 1975, 62, 303− 304. (14) Herschbach, D. R.; Swalen, J. D. Internal Barrier of Propylene Oxide from the Microwave Spectrum. II. J. Chem. Phys. 1958, 29, 761− 776. (15) Swalen, J. D.; Herschbach, D. R. Internal Barrier of Propylene Oxide from the Microwave Spectrum. I. J. Chem. Phys. 1957, 27, 100− 108. (16) Su, Z.; Borho, N.; Xu, Y. Chiral Self-Recognition: Direct Spectroscopic Detection of the Homochiral and Heterochiral Dimers of Propylene Oxide in the Gas Phase. J. Am. Chem. Soc. 2006, 128, 17126−17131. (17) Su, Z.; Wen, Q.; Xu, Y. Conformational Stability of the Propylene Oxide−Water Adduct: Direct Spectroscopic Detection of O−H···O Hydrogen Bonded Conformers. J. Am. Chem. Soc. 2006, 128, 6755−6760. (18) Su, Z.; Xu, Y. Hydration of a Chiral Molecule: The Propylene Oxide···(Water)2 Cluster in the Gas Phase. Angew. Chem., Int. Ed. 2007, 46, 6163−6166. (19) Losada, M.; Nguyen, P.; Xu, Y. Solvation of Propylene Oxide in Water: Vibrational Circular Dichroism and Optical Rotation and and Computer Simulation Studies. J. Phys. Chem. A 2008, 112, 5621−5627. (20) Polavarapu, P. L.; Hess, B. A.; Schaad, L. J. Vibrational Spectra of Epoxypropane. J. Chem. Phys. 1985, 82, 1705−1710. (21) Polavarapu, P. L.; Michalska, D. F. Mid Infrared Vibrational Circular Dichroism in (S)-(−)-Epoxypropane. Mol. Phys. 1984, 52, 1225−1235. (22) Kawiecki, R. W.; Devlin, F.; Stephens, P. J.; Amos, R. D.; Handy, N. C. Vibrational Circular Dichroism of Propylene Oxide. Chem. Phys. Lett. 1988, 145, 411−417. (23) Barron, L. D.; Vrbancich, J. Methyl Torsion Raman Optical Activity in (2S,3S)-(−)2,3-Epoxybutane. Mol. Phys. 1983, 48, 833− 845. (24) Šebestík, J.; Bourĭ, P. Raman Optical Activity of Methyloxirane Gas and Liquid. J. Phys. Chem. Lett. 2011, 2, 498−502. (25) Lowe, M. A.; Alper, J. S.; Kawiecki, R.; Stephens, P. J. Scaled Ab Initio Force Fields for Ethylene Oxide and Propylene Oxide. J. Phys. Chem. 1986, 90, 41−50. (26) Grimme, S. Semiempirical Hybrid Density Functional with Perturbative Second-Order Correlation. J. Chem. Phys. 2006, 124, 034108/1−16. (27) Goerigk, L.; Grimme, S. Calculation of Electronic Circular Dichroism Spectra with Time-Dependent Double-Hybrid Density Functional Theory. J. Phys. Chem. A 2008, 113, 767−776. (28) Grimme, S.; Neese, F. Double-Hybrid Density Functional Theory for Excited Electronic States of Molecules. J. Chem. Phys. 2007, 127, 154116/1−18. (29) Biczysko, M.; Panek, P.; Scalmani, G.; Bloino, J.; Barone, V. Harmonic and Anharmonic Vibrational Frequency Calculations with the Double-Hybrid B2PLYP Method: Analytic Second Derivatives and Benchmark Studies. J. Chem. Theory Comput. 2010, 6, 2115−2125.

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Anharmonicity Effects in the Vibrational CD Spectra of Propylene

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