Substituent effect in theoretical ROA spectra

Abstract

The substituent effect in ROA spectra is reported for the first time. The ROA spectra of substituted indenes and isoindolinones reveal significant correlations with σ_p and pEDA(I) substituent effect descriptors. The correlations are found only when αG′ and β(G′)² ROA invariants are mutually proportional.

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The market of chiral chemicals is estimated at upwards of hundreds of billions of US dollars annually.^1–3 The expenses and sales of the pharmaceutical industry account for the largest part of it. On the one hand, many top selling drugs are chiral and on the other hand there is a tendency to develop single-enantiomer formulations. This drives the development of chiral technologies that enable efficient and reliable synthesis, purification and characterisation of chiral chemicals.⁴ In the latter, chiroptical methods exploiting the phenomenon of Vibrational Optical Activity (VOA) are gaining more and more importance for the assignment of absolute configuration,⁵ determination of enantiomeric purity⁶ or monitoring of chiral reactions.⁷ VOA methods include Vibrational Circular Dichroism (VCD) and Raman Optical Activity (ROA). VCD measures the difference in the absorbance of a sample for left and right circularly polarized light (in the infrared region), and ROA analogously measures the difference in intensity of Raman scattered right and left circularly polarized light.⁸ Despite a long and successful development history that started in the sixties, both VOA techniques still require careful studies on basic spectroscopic issues. This is partly because VOA effects are weak and measurements are still challenging, and partly due to the nature of transition moments involved, which mix electric and magnetic properties. While there is some intuition about the electric transition moments, little is known about the magnetic ones.

Recently, for the first time, we showed the presence of the substituent effect in the theoretical VCD spectra of indenes.⁹ Several correlations of selected VCD intensities with pEDA(I)¹⁰ and Hammett σ_p substituent constants¹¹ were observed. Such relationships were also found for the value of the magnetic-dipole transition moment. In the present study, we complement those findings by demonstrating for the first time substituent effects in theoretical Raman Optical Activity (ROA) spectra.

The calculations were performed using the Gaussian 09 suite of programs¹² on two sets of model 5-substituted: 1-cyano-1H-indenes (IND) and 1-cyanoisoindolinones (IIN) (Scheme 1). We examined a comprehensive group of 28 substituent covering evenly whole range of Hammett σ_p¹¹ and pEDA(I)¹⁰ substituent effect scales (Table S1 in ESI†). The molecules were optimized (to true minima, ascertained by no imaginary frequencies) at the B3LYP/aug-cc-pvDZ level. The ROA spectra were simulated at the same level.‡ For conformationally flexible substituents, the most populated conformers were taken into account by conformational analysis, calculation of Boltzmann population factors, and population-averaged spectroscopic parameters. The chosen theoretical level is a reasonable compromise between computational cost and quality as shown in previous studies.^13,14 Nevertheless, in order to check the dependence of the results on the theoretical method used, six indenes and six isoindolinones were recalculated with 53 other combinations of functionals and basis sets (details in ESI, page ESI-78†). Additionally, the whole set of substituents was also considered at the BLYP/aug-cc-pvTZ and B3LYP/aug-cc-pvTZ levels.

Scheme 1 Model compounds chosen for the study.

Correlational analysis of vibrational spectra parameters must be restricted to well isolated and recognizable modes. Here, we focus on several stretching vibrations of both IND and IIN. Methine stretching in the chiral centre ν(C*H) is inspected first. The ν(C*H) mode in IND and IIN is located in the range of 3015–3005 cm⁻¹ (Tables S2 and S8 in ESI†). In both systems the ν(C*H) frequencies and IR intensities are significantly correlated with σ_p (Fig. S1 and S4†). For this very mode in IND, a strong non-linear correlation of the VCD intensities with pEDA(I) was reported by us previously.⁹ Here, for the same mode in IND and IIN, similar correlations between the ROA intensities and pEDA(I) descriptor are presented (Fig. 1a and b, respectively).§

Fig. 1 Correlations of ν(C*H) ROA intensities in (a) IND and (b) IIN with pEDA(I). (a) ROA = 34 784.33 (±5847.35) pEDA(I)² + 3751.05 (±563.05) pEDA(I) − 1666.40 (±51.02), n = 28, r = 0.93, (b) ROA = 16 424.58 (±3192.88) pEDA(I)² + 2088.05 (±307.45) pEDA(I) − 716.75 (±27.86), n = 28, r = 0.93.

The ν(CN) stretching frequencies in IND and IIN span in the region of 2345–2330 cm⁻¹ (Tables S3 and S9,† respectively). Again, the frequencies and IR intensities of ν(CN) correlate in an almost linear manner to σ_p values (Fig. S7 and S11†). For the ν(CN) in IND, the ROA (and VCD⁹) intensities are correlated with σ_p as well (r = 0.89, Fig. 2, four outliers excluded). However, for the ROA intensities of the ν(CN) mode in IIN no analogous correlation is found (Fig. S12†).¶

Fig. 2 Correlation of ν(CN) ROA intensities in IND with σ_p. ROA = (a + b × σ_p)/(c + σ_p), a = 1237.71 (±219.16), b = 800.73 (±48.44), c = 1.33 (±0.23), n = 24, r = 0.89.

Another two stretchings of the five-membered rings of the model systems: symmetrical CH ν_s(HC=CH) in IND (Table S4†) and ν(NH) in IIN (Table S10†) are present in the ranges of 3242–3235 cm⁻¹ and 3641–3634 cm⁻¹, respectively. In both cases, while there are very good frequency and IR intensity correlations with the σ_p parameter, no significant correlation between the ROA intensity and either σ_p or pEDA(I) descriptors could be found (Fig. S16, S17, S21, and S22†).||

In several coupled ν(C=C) vibrations of the ring skeletons, in both systems positioned between 1670 and 1590 cm⁻¹ (Tables S5–S7† for IND, Tables S11 and S12† for IIN), manifested were some notable non-linear relationships of IR intensities with pEDA(I). At the same time, the frequencies do not correlate with any of the electronic parameters (Fig. S26, S31, S36, S41 and S46†), nor do the ROA intensities (Fig. S27, S32, S37, S42 and S47†).**

Thus, the electronic substituent effect indeed occurs for the ROA intensities of some vibrations of the studied systems. As it is also the case for frequencies, IR, and VCD intensities, the ROA intensities may correlate with both σ_p and pEDA(I) descriptors. Since σ_p seems to describe the change in electron density at the reaction centre located in the para-position to the substituent,¹⁵ while pEDA(I) depicts the donation or withdrawal of electrons to or from the π-electron system of the transmitting moiety,¹⁰ the ROA intensities of some vibrations are sensitive to such effects in a quantitative manner. Relationships of this kind are intuitively expectable, because ROA intensity (or Raman in general) is related to the polarizability and the polarizability is related to the freedom of movement of the electrons.¹⁶ Electron-withdrawing or electron-donating substituents influence this freedom by altering charge distribution in the manner quantitatively described by substituent effect scales/parameters such as σ_p or pEDA(I).

Interestingly, in the molecules studied here, Raman intensities do not correlate with substituent effect scales, even when considering additional normalization for the conjugation length that had been proposed in the past.^17–19

The IR and VCD intensities are associated with the transition moments described by the electric dipole moments and the scalar product of electric and magnetic dipole moments, respectively. On the other hand, the ROA intensities in the far-from-resonance approximation are described by transition moments related to a linear combination of three invariants of three molecular property tensors:^8,20 the electric dipole–electric dipole polarizability α_αβ, the electric dipole–magnetic dipole optical activity G′_αβ, and the electric dipole–electric quadrupole optical activity A_α,βγ. Averaging over all possible molecular orientations with respect to the incident laser beam and the scattered radiation yields one isotropic (αG′) and two anisotropic (β(G′)² and β(A)²) invariants:

The ROA intensity is then given by the following expression:

where the a₁, a₂ and a₃ coefficients depend on the geometry and polarizations of the experimental setup. Here, we restrict our discussion to the ICPu/SCPu(180) setup (given in Gaussian 09 output as ROA1), †† for which the equation reads:

It is important to add that the contribution of β(A)² to the ROA value is, in most cases, of the order of a few percent.²¹ Thus, the correlations of the electronic substituent effect descriptors with ROA simply stem from the correlations with β(G′)² (Fig. S2, S5 and S8†). In the analysed modes exhibiting dependence on electronic parameters, the more electron withdrawing is the substituent, the larger is the module of β(G′)² and the ROA intensity. For the most electron-donating substituents, note, the sign-change of the ROA intensities of the ν(C*H) vibrations. Thus, the appropriate elements of the electric dipole–electric dipole polarizability, α_αβ, and the electric dipole–magnetic dipole optical activity, G′_αβ, tensors change in the way reflecting quantitatively the electron density changes in the series of molecules.

For our molecules studied at the B3LYP/aug-cc-pvDZ level, the correlations of ROA intensities with substituent effect constants are found only for those modes for which αG′ and β(G′)² invariants are proportional to each other (Fig. 3). As these invariants are, respectively, isotropic and anisotropic invariants related to α_αβ and G′_αβ tensors, it seems that the revelation of an electronic substituent effect may occur only when off-diagonal elements of these tensors become less important or their changes follow somehow the changes in the diagonal elements. This should be possible in the case of vibrations where atom motions associated with a vibration symmetrically affect electric and magnetic polarizabilities in all directions. Unfortunately, not in all cases the method dependence tests performed on six selected substituents with 53 other levels of theory did confirm the co-presence of electronic substituent effects and proportionality of the ROA invariants (Tables S27 and S30†). It is not clear whether this is due to (a) lack of such general regularity (b) scarcity of included data points or (c) inadequacy of some of the tested combinations of functionals and basis sets. This issue will require further investigation. Nevertheless, possibility of such a relation seems to be interesting in that, if confirmed, it would provide important intuition for predicting the change of ROA with electron donor–acceptor properties of substituents.

Fig. 3 Relationships between αG′ and β(G′)² invariants for a few studied vibrations.

Considering the involvement of ROA tensors (and their invariants) in substituent effects on ROA intensities, it will be also interesting to look at ROA robustness parameters recently proposed by Tommasini et al.²² In the case of our molecules, we were not able to find any correlations of electronic substituent effect constants with these parameters. Nevertheless, for some vibrations there is a clear relationship of the G-robustness parameter to substituents volume (Fig. S51–S53†). Detailed discussion of this observation requires more exploration.

Conclusions

In conclusion, we report here the first correlational study on the substituent effect in the theoretical Raman Optical Activity spectra. Significant correlations of the ROA intensities of ν(C*H) stretching vibrations in IND and IIN molecules with pEDA(I) descriptor as well as of the ROA intensities of ν(CN) stretching vibrations in IND ones with σ_p constants were found. Some ROA intensities are hence predicted to be sensitive to the overall electronic substituent effect or its resonance component represented here by pEDA(I). For the systems studied here, the correlations were found only for those vibrations for which the αG′ and β(G′)² ROA invariants are mutually proportional. This may suggest that the substituent effect would be visible only when the electric and magnetic polarizabilities of a given mode are affected in some specific way.

Acknowledgements

The study was supported by National Science Centre in Poland (NCN, Grant DEC-2013/09/B/ST5/03664). Computational Grants G19-4 from the Interdisciplinary Centre of Mathematical and Computer Modelling (ICM) at University of Warsaw and “substeff” Grant from PL-Grid Infrastructure are gratefully acknowledged. Generous allotment of computer time within the Grant from Świerk Computing Centre of the National Centre for Nuclear Research is gratefully acknowledged. We are also most thankful for interesting comments made by anonymous reviewers that helped to improve the manuscript. Our appreciation is extended to Professors Petr Bouř, Matteo Tommasini and James Cheeseman who provided us with helpful suggestions.

Notes and references

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Footnotes

† Electronic supplementary information (ESI) available: Substituent constants used in the study, detailed spectral parameters of all considered modes, energetics of examined conformers, correlation plots of minor importance, full Gaussian 09 citation, details of method dependence tests and coordinates of optimized structures. See DOI: 10.1039/c6ra01396a

‡ If not otherwise stated, the presented correlations refer to data obtained at the B3LYP/aug-cc-pvDZ level.

§ Equally good correlations are found for the ν(C*H) ROA intensities in IND in all other 53 combinations of functionals and basis sets (Table S25,† n = 6). At the BLYP/aug-cc-pvTZ level: r = 0.91 (n = 25) and at the B3LYP/aug-cc-pvTZ level: r = 0.94 (n = 21). In the case of IIN model system, the BLYP and B3LYP functionals combined with different basis sets reproduce this correlation, while calculations using CAM-B3LYP and M06-2X yield much weaker relationships (Table S28,† n = 6). At the BLYP/aug-cc-pvTZ level: r = 0.89 (n = 24) and at the B3LYP/aug-cc-pvTZ level: r = 0.92 (n = 21).

¶ The ν(CN) ROA intensities in IND correlate strongly with Hammett σ_p substituent constants in all 53 computational variants used (Table S26,† n = 6). At the BLYP/aug-cc-pvTZ level: r = 0.85 (n = 25) and at B3LYP/aug-cc-pvTZ level: r = 0.84 (n = 21). Consistently, no such correlation is found for the ν(CN) ROA intensities in IIN when using any of the tested theoretical methods (Table S29†).

|| In accordance with these results, no correlations are found for the ν_s(HC=CH) ROA intensities in IND whatever method is used (Tables S25 and S26†). Similarly, no such relationships are found for ν(NH) in IIN with all methods but those including the BLYP functional where modest correlations are observed in the six-substituent set (Tables S28 and S29†). On the other hand, when all substituents are considered, no correlation is found (BLYP/aug-cc-pvTZ, n = 25).

** Here, the method dependence tests on six-substituent sets yield results partially inconsistent with the ones discussed above. In the IND system, some theoretical methods predict the existence of such relationships while others do not, and no clear pattern as to the functional or the basis set is observed (Tables S25 and S26†). Note however that the testing is done on only six substituents. At the BLYP/aug-cc-pvTZ and the BLYP/aug-cc-pvTZ levels, no correlations are found when the whole substituent set is considered, consistently with the results presented above. In the case of IIN system, most methods (including BLYP/aug-cc-pvTZ and BLYP/aug-cc-pvTZ) give no correlations (Tables S28 and S29†).

†† The results from other setups are highly correlated to ROA1 and their analysis leads to the very same conclusions. For the sake of completeness they are provided in Tables S2–S12.†

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