Similarity in Dissymmetry Factor Spectra: A Quantitative Measure of

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Similarity in Dissymmetry Factor Spectra: A Quantitative Measure of Comparison between Experimental and Predicted Vibrational Circular Dichroism Cody Lance Covington, and Prasad Leela Polavarapu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp401079s • Publication Date (Web): 27 Mar 2013 Downloaded from http://pubs.acs.org on March 28, 2013

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The Journal of Physical Chemistry

1

Similarity in Dissymmetry Factor Spectra: A Quantitative Measure of Comparison between Experimental and Predicted Vibrational Circular Dichroism

Cody L. Covington and Prasad L. Polavarapu* Department of Chemistry Vanderbilt University Nashville, TN 37235 USA

*E-mail address for correspondence: [email protected]

ACS Paragon Plus Environment


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Abstract To quantitatively determine the agreement between experimental and calculated vibrational circular dichroism (VCD) spectra, a new approach, based on the similarity of dissymmetry factor spectra has been developed and implemented. This method, which places emphasis on robust regions both in the experimental and calculated spectra, has been tested with six chiral compounds of known absolute configurations, namely (R)-(+)-3-chloro-1-butyne, (3R)-(+)methylcyclopentanone, (3R)-(+)-methylcyclohexanone, (1S)-(-)-α-pinene, (1R)-(+)-camphor, and (S)-(+)-epichlorohydrin. The criterion of maximum overlap among experimental and calculated dissymmetry factor spectra is shown to have definite advantages over those using maximum overlap among VCD or absorption spectra individually. The new method provides a better assessment of the comparison between experimental observations and quantum chemical VCD predictions and improves the confidence in the assignment of absolute configurations. Keywords: Absolute Configuration, Quantum Chemical Predictions, Infrared, VCD, Ratio Spectra, Spectral Overlap


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Introduction Over the past years vibrational circular dichroism (VCD) spectroscopy has become a reliable tool for elucidation of absolute stereochemistry.1 The richness of vibrational transitions allows for many points of comparison between calculated and experimentally observed spectra. Advances in both VCD instrumentation and theoretical methods, used for predicting VCD spectra, have facilitated the widespread use of VCD spectroscopy. The improvements in the quality of predicted VCD spectra have made it a routine method for determining the absolute configurations and predominant conformers of chiral molecules. VCD is a measure of differential absorption of left and right circularly polarized infrared light resulting from vibrational transitions. VCD differs from the traditional infrared vibrational absorption (VA) in that it can be positive or negative. For a molecular transition, from ground state |𝑖⟩ to excited state |𝑘⟩, the difference in absorption is related to the rotational strength defined as2 Rk = Im[ i μ e k k μ m i ] = Im[μ e,ik • μ m, ki ]

(1)

where 𝝁𝑒 and 𝝁𝑚 are, respectively, the electric and magnetic dipole moment operators. For the vibrational transitions under consideration here, |𝑖⟩ and |𝑘⟩ represent the ground and excited vibrational states, both belonging to the same ground electronic state. The corresponding VA is determined by the dipole strength Dk, given as

Dk = i μ e k k μ e i = i μ e k

2

= μ e2,ik

(2)

VA intensities are also reported as Ak (in Km/mol), which is related to Dk (in 10-40 esu2 cm2) and transition frequency, or band center, ν k0 (in cm-1), as Ak = 25.0967 × 10 −5ν k0 Dk

(3)

Reliability in the predictions of Rk is crucial for making accurate predictions of absolute configurations. As the scalar product of electric and magnetic dipole transition moment vectors, μ e,ik and μ m,ki , rotational strength is written as,

Rk = µ e ,ik µ m ,ki cos ξ

(4)

where 𝜉 is the angle between the two vectors. When 𝜉 is close to 90°, the sign of 𝑅𝑘 can change with only a minimal perturbation of geometry or computational parameters. In light of this issue, the concept of band robustness has been introduced3 by Nicu and Baerends using the angle 𝜉 between transition moment vectors. However Gobi and Magyarfalvi pointed out4 that the angle 𝜉 is an origin dependent quantity and proposed a criterion for band robustness using



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𝜁𝑘 =

�𝝁𝒎,𝒌𝒊 � cos 𝜉 �𝝁𝒆,𝒊𝒌 �

=

|𝑅𝑘 |

(5)

𝐷𝑘

where 𝜁𝑘 , is a number (without units) in the range of 10-3 to 10-5, and for convenience expressed as parts per million (ppm). Gobi and Magyarfalvi suggested4 that the fundamental vibrational transitions with calculated 𝜁𝑘 values above 10 ppm could be considered robust and used in the determination of absolute configuration, while those under 10 ppm should not be considered. The calculated rotational and dipole strengths correspond to the integrated molar absorption coefficients determined experimentally and are given by the relations,5

Rk =

Dk =

0.23 × 10 −38

ν k0 0.92 × 10 −38

ν k0

∫ ∆ε (ν )dν

(6)

∫ ε (ν )dν

(7)

where ε= (εL+εR)/2 and ∆ε= εL-εR, with εL and εR are respectively the decadic molar absorption coefficients for left and right circularly polarized light; for a sample at concentration c, and path length l, decadic molar absorption coefficients are obtained as, εL=AL/cl and εR=AR/cl where A=log10(I0/I) with I0 and I representing respectively the intensity of infrared radiation before and after passing through the sample. In assessing the agreement between experimental and predicted VCD spectra, different approaches have been adapted in the literature. (A). Calculated rotational and dipole strengths are first converted into peak intensities of spectral intensity distributions, in terms of decadic molar absorption coefficients, using assumed band shapes and bandwidths. For Lorentzian spectral intensity distribution,  ∆2k y (ν ) = yk0 Lk (ν ) = yk0   ν − ν 0 2 + ∆2 k k 

(

where y (ν

)

   

(8)

) is the spectral intensity (in terms of molar extinction coefficient) representing y-axis

value at wavenumber ν ;ν k0 is the wavenumber of kth vibrational transition (i.e vibrational band center); yk0 is the peak intensity at ν k0 ; Lk (ν

) is Lorentzian function;

Δk is half-width at half-

th

maximum (HWHM) for k band. For VCD and VA spectra, the peak intensity at the band center of Lorentzian distribution is given (in L mol-1 cm-1 units) as,

∆ε k0 =

ν k0 Rk × 10 −4 22.94 ∆ k π

(9)


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5

0.25 ×ν k0 Dk ε = 22.94∆ k π 0 k

(10)

with Rk expressed in 10-44 esu2 cm2; Dk in 10-40 esu2 cm2; ν k0 and ∆ k in cm-1. The calculated spectral distribution is obtained by multiplying the peak intensities (Eqs. 9, 10) with Lorentzian function, Lk (ν ) (see Eq. 8). Then the calculated and experimental spectra are placed one above the other and correlation between these spectra is visually identified. Since predicted vibrational transition frequencies are often blue shifted from experimentally observed band positions, it is often necessary to scale the calculated vibrational transition frequencies by a frequency scale factor to visualize the correlation between the two spectra. The frequency scale factor depends upon the basis set used in quantum chemical calculations.6 Larger the number of correlated bands that one finds, higher is the confidence in the agreement between experimental and calculated spectra. This has been the most widely used procedure.7 However, there are multiple disadvantages with this approach: i). there is no quantification of agreement between experimental and calculated spectra; ii). personal bias can influence the choice of bands used to identify the correlation; iii). the correlation between calculated and experimental VA spectra is often ignored or not analyzed by many researchers. This is unfortunate because, the electric dipole transition moment, one of the two components on which rotational strength depends, also determines the VA intensity (See Eqs.1, 2). Thus a good correlation among VCD spectra, without a corresponding correlation between VA spectra, could be fortuitous. (B). The integrated intensities of experimentally observed VA and VCD bands are determined (see Eqs. 6, 7) and compared8,9 to the corresponding predicted dipole and rotational strengths (after appropriate frequency scaling). Although a quantitative assessment of comparison between experimental and calculated VCD spectra can be achieved here, the main disadvantages in this approach result from the need to resolve the overlapping experimental bands (using spectral resolution enhancement software or curve fitting software) in the experimental spectra and to manually determine their integrated band intensities. This process can introduce some personal bias, in the case of closely spaced bands, because a priori knowledge of which integrated band intensity corresponds to which of the calculated strengths is not available. Moreover the process of curve fitting and determining integrated band areas from experimental spectra can be very time consuming. (C). Spectral similarity between calculated and experimental spectra is evaluated to determine the agreement between them. There are many ways to compare the similarity between simulated and experimental spectra.10 Two different criteria are used in the case of vibrational spectra. Similarity overlap among VA spectra, SimVA, (also referred to as SimIR) and VCD spectra, SimVCD, developed by Shen et al., 11 and similarity index (SI) and enantiomeric similarity index (ESI) developed by Debie et al12.



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The SimVA and SimVCD are defined as, 𝑆𝑖𝑚𝑉𝐴 =

𝐼𝑐𝑜

𝐼𝑐𝑐 +𝐼𝑜𝑜 −𝐼𝑐𝑜

and 𝑆𝑖𝑚𝑉𝐶𝐷 =

𝐼𝑐𝑜

𝐼𝑐𝑐 +𝐼𝑜𝑜 −|𝐼𝑐𝑜 |

.

(11)

where the subscripts ‘c’ and ‘o’ stand for calculated and observed. 𝐼𝑐𝑜 is defined as the overlap of two spectra,

I ij = ∫ Fi (ν )F j (ν )dν

(12)

where Fi (ν ) is the ith spectral distribution and the integral runs over the portion(s) of the spectral

region investigated. SimVA ranges from 0, at zero overlap, to 1 when Fi (ν ) = F j (ν ) . On the other hand, SimVCD ranges from -1 when Fi (ν ) = − F j (ν ) = F j (ν

)

(13)

(note that bar on F indicates the enantiomer VCD spectrum) and 1 when Fi (ν ) = F j (ν ) . A SimVCD value of 0.2 or higher was recommended11 to make a reliable assignment of configuration. SI is a measure of the similarity among VA spectra and is defined as12,

SI = S FG =

∫ F (ν )G(ν ) dν ∫ F (ν ) dν ∫ G (ν ) dν 2

(14)

2

with F (ν ) being the calculated spectrum and G (ν ) being the experimental spectrum. ESI is a measure of the similarity among VCD spectra12 and is more complicated. To obtain ESI, which is adapted from SI to account for the possibility of both positive and negative signs in the VCD spectra, each spectrum is split into positive and negative parts, and similarities calculated −− ++ +− −+ separately as, 𝑆𝐹𝐺 , 𝑆𝐹𝐺 , 𝑆𝐹𝐺 , or 𝑆𝐹𝐺 , where superscripts + and – identify, respectively, the positive and negative parts of the spectra. The positive and negative similarities are weighted by their areas and divided by the total area, and then the contributions from the opposite enantiomer are subtracted out to give ESI value. ESI =

++ ,VCD −− ,VCD −+ ,VCD +− ,VCD Φ + + S FG + Φ − − S FG Φ − + S FG + Φ + − S FG − Φ++ + Φ−− Φ−+ + Φ+−

(15)

where the areas Φ + + , Φ − − , Φ + − and Φ − + are all defined as positive quantities 13 i.e, for example,

Φ++ =

∫

F (ν )> 0

F (ν )dν +

∫ G(ν )dν

G (ν )> 0


(16)

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Φ+− = F

∫ (ν )

F (ν )dν + >0

G

∫(ν )G(ν )dν

(17)

10 −5


(19)


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For calculated VCD, associated with kth transition, Gobi and Magyarfalvi4 suggested 𝜁𝑘 >10-5, as the robustness criterion, which in terms of the dissymmetry factor becomes, g k ,calcd =

4 Rk ,calcd Dk ,calcd

= 4ς k =

∆ε (ν

)k ,calcd ε (ν )k ,calcd

= g (ν

)k ,calcd

> 4 × 10 −5

(20)

Even though the experimental VCD with magnitudes of dissymmetry factors between 10-5 and 4x10-5 could be reliable, the corresponding calculated dissymmetry factors (following Gobi and Magyarfalvi4) would not be reliable enough to compare with the experiment. Thus, the use of g (ν ) > 4 × 10 −5 consistently both for experimental and calculated spectra would satisfy the robustness criteria for both calculations and experiment. To provide some flexibility for individual situations, the limiting value of g (ν ) can be set as a user defined parameter. (2). The frequency scale factor used to maximize the similarity among VA spectra need not be same as the one which maximizes the similarity among VCD spectra and neither of these methods can be optimal individually by themselves. The use of maximum similarity among dissymmetry factors provides a more reliable criterion as will be demonstrated later (vide infra). (3). The correlation between calculated and experimental VA spectra is often ignored or not analyzed by many researchers. This oversight is avoided when similarity among dissymmetry factor spectra is evaluated. (4). In calculating the spectral similarity for VA or VCD spectra separately, one needs to know the concentration of the sample and sample thickness (cell path length for solutions) used. However, concentration is not known in many cases. Also for VA or VCD measurements made on film samples one does not know the concentration or path length. Since dissymmetry factor is independent of concentration and path length, any experimental errors in concentrations and path lengths become immaterial and the similarity of dissymmetry factor method can be used for both solution state and film state measurements. Realization of the above mentioned advantages led us to develop a computer program that calculates the similarity of dissymmetry factor spectra and determines the frequency scale factors that maximize the similarity of dissymmetry factor spectra. Similarity overlap among dissymmetry factor, or ratio, spectra, SimRAT, is defined, in analogy to SimVA and SimVCD11, using dissymmetry factors, g (ν ) , as 𝑆𝑖𝑚RAT =

𝐼𝑐𝑜

𝐼𝑐𝑐 +𝐼𝑜𝑜 −|𝐼𝑐𝑜 |

, where I ij = ∫ g i (ν )g j (ν )dν

(21)

Similarly, enantiomeric similarity index for dissymmetry factor spectra, ESI-RAT, is obtained in analogy to ESI12. For example, Φ + − in ESI (see Eq. 17) is replaced with Φ +−, RAT


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9

g calc (ν )dν +

∫

Φ + − , RAT =

g calc (ν )> 0

∫ g (ν )dν

exp t g exp t (ν )< 0

(22)

and S FG with S gRAT . calc g exp t

∫ g (ν )g (ν ) dν ∫ g (ν ) dν ∫ g (ν ) dν calc

S gRAT = calc g exp t

2 calc

exp t

(23)

2 exp t

The current implementation of similarity methods differs from the earlier methods in the following points also: (a). a single frequency scale factor is used for the entire wavenumber region investigated and we do not favor using different frequency scale factors for different bands11; (b). The triangular weighting function used12 to modify the experimental spectrum for including neighborhood contributions is avoided, as such weighting will influence the criteria used for dissymmetry factor spectra (vide infra). Unique features of dissymmetry factor spectra The division of two related spectra gives rise to interesting properties for the ratio spectrum, and can be seen in the use of chosen band shapes and relative conformer populations. (A). Band shapes: For illustrative purposes, consider the case of a single vibrational transition. Vibrational spectral simulations normally use Lorentzian intensity distributions (Eq. 8). It is a common practice to use the same band shape and band width for VA and VCD spectral simulations, although band shapes of VA and VCD may differ (due to auto correlation of electric dipole transition moment in the former and cross correlation of electric magnetic dipole transition moments in the later). If the same band shape and band width are used for VA and VCD spectral simulation, it becomes apparent that the dissymmetry factor spectrum becomes independent of band shape for an isolated transition and is a constant that is independent of wavenumber,ν . g (ν

)k ,calcd

=

∆ε (ν

)k ,calcd ε (ν )k ,calcd

∆ε ko,calcd Lk (ν ) ∆ε ko,calcd = o = o ε k ,calcd Lk (ν ) ε k ,calcd

(24)

However, dissymmetry factor associated with a given transition should not contribute at a wavenumber where VA spectral intensity distribution of the transition under consideration is insignificant. This dilemma can be resolved, by imposing the condition that g (ν

)k ,calcd

=

∆ε (ν

)k ,calcd ∆ε ko,calcd × D(ν ) = o × D(ν ) ε (ν )k ,calcd ε k ,calcd


(25)


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where D(ν ) is a box car function that depends on VA intensity tolerance value, τ , such that, D(ν ) = 1, when ε (ν

)k ,calcd

>τ

(26)

)k ,calcd

τ  =  ε (ν )exp t  0 , when ε (ν )exp t < τ 

(32)

Naturally we must treat the calculated spectrum in the same way, so the same tolerance 𝜏 is applied to both calculated and experimental spectra. Since the absorption intensity tolerance, τ can cut off bands in the ratio spectra, care should be taken in selecting the value of τ. We can require robustness in a similar manner by requiring that the similarity is evaluated for dissymmetry factors greater than 4x10-5. It should be noted that the VA spectral intensity tolerance may also be handled by shifting the baseline of the VA spectrum to higher values. Although this “baseline shift”


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approach prevents the denominator of the ratio approaching zero, it also skews the values in the dissymmetry factor spectrum, by causing a disproportionate shift in the spectrum favoring intense VA bands. Therefore the baseline shift method is not preferred to eliminate noise. Two criteria for selecting tolerance level have been considered: (a). visual inspection of VA intensity; (b). maximization of overlap between experimental and calculated dissymmetry factor spectra. These selection methods are applied only to the experimental spectrum, because there is no noise in the calculated spectrum. The final tolerance found is applied to both. Selection of tolerance level through visual inspection is the simplest procedure. The experimental dissymmetry factor spectrum is viewed while adjusting the tolerance to find an optimum level. This will include the entire region of experimental spectrum being analyzed, but minimize the areas with sharp changes due to noise. Selection of tolerance level through maximization of similarity will yield the most similar calculated and experimental dissymmetry factor spectra. However, maximizing similarity via adjusting tolerance level without visual inspection can be problematic because this process can include areas of noise that contribute to the similarity. This can be prevented by a visual inspection afterwards to ensure that all areas of noise are excluded. This is the method that is used to select tolerance parameters for the remainder of this work. An example of VA spectral intensity tolerance applied to (R)-(+)-3-chloro-1-butyne is shown in Figure 4, without applying any frequency scale factor to the calculated spectra (vide infra). Analysis of the chosen molecules was carried out in a stepwise fashion. Any known or suspected artifacts were removed, and a baseline shift was applied, if necessary, to remove negative values in the absorbance spectra. The maximum overlap in SimVA and SimVCD was determined separately by sweeping the frequency scale factor values for calculated spectra and intensity scale (y-scale) factor values for experimental (ε or ∆ε) spectra. The optimal y-scale factors found for VA and VCD were then applied to corresponding experimental spectra and their ratio (experimental dissymmetry factor) spectra calculated. The scaling of experimental intensities will take care of issues such as possible deficiencies in the predicted intensities in addition to errors in sample concentrations, incorrect calibration of VCD spectrometers etc. A ratio of 1 for VA and VCD intensity scale factors is the ideal situation and an indiscriminate use of y-scale factors can affect the magnitude of dissymmetry factor spectra. The y-scale factor procedure can be substituted with spectral normalization12 for VA and VCD spectra. In the case of dissymmetry factor spectra, however, normalization should be done after the absorption intensity tolerance and robustness criterion are applied in obtaining the ratio spectra. We have performed SimVA, SimVCD, and SimRAT calculations for all trial molecules both by finding the optimum y-scale factors and spectral normalization, but the differences noted in the results obtained in these two procedures are minor. The calculated VA and VCD spectra, respectively as ε and ∆ε, for a given frequency scale factor, are ratioed to obtain calculated dissymmetry factor spectrum. The overlap between experimental and calculated dissymmetry factor spectra was calculated using SimRAT. Then



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SimRAT is calculated with tolerance selected visually and applied. Calculated vibrational band positions were adjusted, by scaling the calculated transition frequencies. This was done by sweeping through a range of frequency scale factors, each time calculating the SimRAT from experimental and calculated spectra. The absorption intensity tolerance is then optimized at frequency scale factor that gives the highest SimRAT. The tolerance optimization is also performed by sweeping through many numbers and the optimum tolerance applied to the spectra. Another cycle of frequency and tolerance optimizations are then performed with a finer step size. The second cycle is needed because optimum frequency scale factors may have changed slightly. A graphical representation of this process is shown in Figure 5. With the optimum absorption intensity tolerance value identified, a final calculation is made for comparison purposes. A full range of frequency scale factors is swept through again, but this time SimVA, SimVCD, SimRAT, SI, ESI, and ESI-RAT are all calculated. The data points are plotted in a graph of overlap vs. frequency scale factor and used for overall comparison and prediction of absolute stereochemistry. These graphs allow for rapid comparison of different methods. The overlap vs frequency scale factor plot for (R)-(+)-3-chloro-1-butyne, and the spectra with optimal frequency scale factor that yielded maximum dissymmetry factor overlap, are shown in Figure 6. These plots show good agreement between calculated and experimental spectra of (R)(+)-3-chloro-1-butyne. The overlap value in SimRAT is higher than that in SimVCD. The same is true for ESI-RAT (see Fig.S3 in supporting information). This shows that the dissymmetry factor spectrum can provide a better assessment of agreement between calculated and experimental spectra. The overlap vs frequency scale factor plots show that the maximum overlap values in VA, VCD, and ratio spectra all occur at different scale factors. Theoretically, the ratio method aligns the most robust regions in the experimental and calculated spectra. Therefore the frequency scale factor that yields the highest overlap in the ratio method may be considered most reliable. As a precautionary note it should be added that in some cases it is possible that the robustness condition may eliminate all but a few bands, and lead to coincidentally high overlap. The conclusions derived in such cases may not have the desired reliability. As the calculations of SI, ESI, and ESI-RAT yielded results similar to those of SimVA, SimVCD and SimRAT for the molecules investigated here, the summary of results from the former methods are presented in the supporting information. One noticeable feature in the overlap plot (Figure 6, top) is that the points in the SimRAT trace are not smoothly curving. This effect is due to the absorption intensity tolerance and robustness criterion applied in obtaining the dissymmetry factor spectrum, which enforces the dissymmetry factor spectrum to be zero at some positions. When it is not zero, only the absolute values greater than 40 ppm (as defined by Eqs. 20 and 32) are included in the overlap calculation. These conditions can lead to abrupt changes in the overlap when moving from one wavenumber to another (due to the nature of collected spectra, intensity is not as a continuous


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function of wavenumber but rather a discrete function only defined at certain wavenumber intervals). Thus upon integration of the scaled spectra, the integral values will change. This effect will be most prominent when the dissymmetry factor spectrum has sharp block like changes due to the cutoff, as seen in Figures 4 and 6 for 3-chloro-1-butyne. The overlap vs frequency scale factor plots for SimRAT and ESI-RAT can be smoothed out if a different approach is used. Instead of a fixed tolerance value, the intensity below the tolerance can be forced to decay continuously to zero. This makes the frequency scale factor plots smooth, but it creates another issue as the functional form of this decay must be chosen. Therefore in the present work only fixed tolerances have been used. The similarity overlap vs frequency scale factor graph for the dissymmetry factor spectrum can be dramatically different from that for the VA and VCD spectra. The most notable difference can be seen in the analysis of (3R)-(+)-methylcyclopentanone, displayed in Figure 7. This molecule is a good example of the usefulness of the dissymmetry factor spectrum. It has one vibrational band at ~1155 cm-1 which has good intensity in both VA and VCD spectra, so VA and VCD methods will maximize the overlap with this band (as shown in Figure 7b). However, the dissymmetry factor for this mode is small compared to other more robust modes. As a result SimRAT and ESI-RAT methods will not emphasize on this band in maximizing the overlap of dissymmetry factors and instead (as shown in Fig. 7c) maximize the overlap of regions with larger dissymmetry factors (see also Fig.S4 in supporting information). The maximum value of the overlap determines the confidence with which the configuration can be assigned. In this case, the SimRAT and ESI-RAT yield a greater maximum than the corresponding VCD spectral overlap. Comparisons of experimental and predicted VCD spectra for (1S)-(-)-α-pinene, (3R)-(+)methylcyclohexanone, (1R)-(+)-camphor, and (S)-(+)-epichlorohydrin were performed in a similar fashion, with results shown in Figure 8 (and Figs. S5-S8 in supporting information). These molecules do not show a significant difference in the maximum overlap locations for VCD and ratio methods. α-pinene, 3-methylcyclohexanone, and camphor have similar overlaps in VCD and dissymmetry factor spectra. In the case of (S)-(+)-epichlorohydrin, dissymmetry factor spectra yield slightly less overlap than VCD spectra. Again since dissymmetry factor method emphasizes on robust regions, the overlap obtained with this method is expected to be more reliable. As a final comparison, the similarity among spectra of different molecules was evaluated. The similarity between the experimental spectra of α-pinene and the calculated spectra of 3methylcyclopentanone is shown in Figure 9 (and Figure S9 in supporting information). Ideally one should get a zero overlap here, but the nature of vibrational spectra is such that there will be some regions of similarity for different molecules. However such similarity should be small. Accordingly the dissymmetry factor methods show poor overlap (less than 0.2 in the case of SimRAT as well as ESI-RAT).



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All these comparisons point to important general observations. Similarity overlap vs frequency scale factor plot for a good correlation between experimental and calculated spectra appears with a resemblance to that of Gaussian distribution, with occasional bimodal distribution. The peaks in these overlap plots may not occur at the same scale factor in VA, VCD and dissymmetry factor methods, but a similar distribution should appear in all methods. Multiple overlap peaks and a lack of coherence of overlap plots among VA, VCD and ratio methods (see Fig. 9 for SimVA, SimVCD and SimRAT and Fig. S9 in supporting information for SI, ESI and ESI-RAT) suggest unacceptable correlation between experimental and calculated spectra. Since the dissymmetry factor method identifies the similarity among robust regions in both experimental and calculated spectra, the overlap predicted by this method is a better reflection of the reliability of comparison between experimental and calculated VCD spectra over those predicted by VA and VCD spectra individually. Currently efforts are underway to modify the current algorithm for use with electronic circular dichroism and vibrational Raman optical activity. Conclusions A method based on the similarity of dissymmetry factor spectra has been developed and implemented. This new method utilizes information from both VCD and VA spectra to assign the absolute configurations. The overlap of dissymmetry factor spectra gives a more reliable quantitative estimate of the comparison between experimental and calculated VCD spectra. The developed method appears to perform well in all cases considered thus far. However, we emphasize that this method should not be used as a “black box” method and the influence of absorption tolerance and robustness criteria on dissymmetry factor spectra should be carefully analyzed. The benefits of using the dissymmetry factor spectrum should make it a powerful tool in the elucidation of absolute stereochemistry. ACKNOWLEDGMENT Funding from NSF (CHE-0804301) is gratefully acknowledged. This work was conducted in part using the resources of the Advanced Computing Center for Research and Education at Vanderbilt University, Nashville, TN. We thank Dr. P. Bultinck for communications and clarifying some points related to the equations in Ref. 12. Supporting Information Available: Dissymmetry factor spectra for two band systems, and ESI plots for the studied molecules. This information is available free of charge via the Internet at http://pubs.acs.org.


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17

Figure Captions Figure 1: Vibrational absorption (top), VCD (middle) and dissymmetry factor spectra (bottom panel) simulated for one vibrational transition at 1650 cm-1. The thicker black line is the unaltered dissymmetry factor spectrum. The red line with a box-car shape (bottom panel) was obtained with absorption intensity tolerance, τ=1.0 L mol-1cm-1. Units for the x-axes are cm-1. Yaxis units are L/mol.cm (VA), L.10-4/mol.cm (VCD), and ppm (dissymmetry factor spectra). Figure 2: VA, VCD, and dissymmetry factor spectra calculated for two neighboring bands (1000 cm-1 (+) and 1100 cm-1 (-), black traces) with the same dipole and rotational strengths. For comparison, the spectra calculated for a single isolated band at 1000 cm-1 (+) are shown in red. τ = 2 L/mol.cm. Units for the x-axes are cm-1. Y-axis units are L/mol.cm (VA), L.10-4/mol.cm (VCD), and ppm (dissymmetry factor spectra). Figure 3: VA, VCD and dissymmetry factor spectra (calculated spectrum in black simulated at 4 cm-1 HWHM and experimental spectrum in red) for (R)-(+)-3-chloro-1-butyne. VA in L/mol.cm, VCD in L. 10-4/ mol.cm, dissymmetry factor in ppm, and frequency in cm-1. The spectral region from 1241 to 1291 cm-1 has been blanked out due to solvent absorption. Figure 4: VA, VCD, and dissymmetry factor spectra (calculated spectrum in black simulated at 4 cm-1 HWHM and experimental spectrum in red) of (R)-(+)-3-chloro-1-butyne. Absorption intensity tolerance (τ=5.117 L/mol.cm) applied to dissymmetry factor spectra. VA in L/mol.cm, VCD in L.10-4/mol.cm, dissymmetry factor in ppm, frequency in cm-1. Figure 5: Optimization process for spectral similarity Figure 6: The similarity overlap vs frequency scale factor (top) and the VA, VCD, and dissymmetry factor spectra with frequencies multiplied by 0.979 (bottom) for (R)-(+)-3-chloro1-butyne, τ = 5.117 L/mol.cm. Figure 7: (a). Similarity overlap vs frequency scale factor plot for (3R)-(+)methylcyclopentanone; (b). spectra (experimental in red, calculated in black with 4 cm-1 HWHM) for (3R)-(+)-methylcyclopentanone with maximum overlap among experimental and calculated VA (or VCD) spectra (frequency scale factor, 0.9989); and (c). spectra for (3R)-(+)methylcyclopentanone with maximum overlap among experimental and calculated dissymmetry factor spectra (frequency scale factor, 0.9795). VA in L/mol.cm, VCD in L.10-4/mol.cm, dissymmetry factor spectrum in ppm, frequency in cm-1 and τ=1.6 L/mol.cm. Figure 8: Similarity overlap vs frequency scale factor plot for (a) α-pinene, τ=1.4 L/mol.cm (b) 3-methylcyclohexanone. τ=0.4333 L/mol.cm (c) Camphor τ=2.15 L/mol.cm and (d) Epichlorohydrin τ=1.2 L/mol.cm



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Figure 9: Comparison of similarity among spectra of different molecules using SimVA, SimVCD, and SimRAT methods (experimental spectra of α-pinene vs calculated spectra for 3methylcyclopentanone). τ=2.117 L/mol.cm.


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References (1) Stephens, P.J.; Devlin, F. J.; Pan, J. J. The Determination of the Absolute Configurations of Chiral Molecules Using Vibrational Circular Dichroism (VCD) Spectroscopy. Chirality 2008, 20, 643-663; (b). He, Y.; Wang, B.; Dukor, R. K.; Nafie, L. A. Determination of Absolute Configuration of Chiral Molecules Using Vibrational Optical Activity: A Review. Applied Spectrosc. 2011, 65, 699-723; (2) Eyring, H.; Walter, J.; Kimball, G. E. Quantum Chemistry; John Wiley & sons: New York, 1944. (3) (a). Nicu, V. P.; Baerends, E. J. On the Origin Dependence of the Angle Made by the Electric and Magnetic Vibrational Transition Dipole Moment Vectors. Phys Chem Chem Phys 2011, 13 (36), 16126-16129; (b) Nicu, V. P.; Neugebauer, J.; Baerends, E. J. Effects of Complex Formation on Vibrational Circular Dichroism Spectra. J. Phys. Chem. A 2008, 112, 6978–6991; (c) Nicu, V. P.; Baerends, E. J. Robust Normal Modes in Vibrational Circular Dichroism Spectra. Chem. Chem. Phys. 2009, 11, 6107–6118. (d) Nicu, V. P.; Debie, E.; Herrebout, W.; van der veken, B.; Bultinck, P.; Baerends, E. J.A VCD Robust Mode Analysis of Induced Chirality: The Case of Pulegone in Chloroform. Chirality 2010, 21, E287-E297. (4) Gobi, S.; Magyarfalvi, G. Reliability of Computed Signs and Intensities for Vibrational Circular Dichroism Spectra. Phys Chem Chem Phys 2011, 13 (36), 16130-16133. (5) Faulkner, T. R., Ph. D. Thesis, University of Minnesota, Minneapolis, 1976. (6) Merrick, J. P.; Moran, D.; Radom, L. An Evaluation of Harmonic Frequency Scale Factors. J. Phys. Chem. A. 2007, 111, 11683-11700. (7) Yang, G.; and Xu, Y. Vibrational circular Dichroism Spectroscopy of Chiral Molecules. Topics in Current Chemistry, 2011, 298, 189-236. (8) 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. (9) He, J.; Petrovich, A.; Polavarapu, P. L. Quantitative Determination of Conformer Populations: Assessment of Specific Rotation, Vibrational Absorption, and Vibrational Circular Dichroism in Substituted Butynes. J. Phys. Chem. A 2004, 108, 1671-1680. (10) de Gelder, R.; Wehrens, R.; Hageman, J. A. A Generalized Expression for the Similarity of Spectra: Application to Powder Diffraction Pattern Classification. J. Comp. Chem 2012, 22, 273289.



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(11) (a). Shen, J.; Zhu, C.; Reiling, S.; Vaz, R. A Novel Computational Method for Comparing Vibrational Circular Dichroism Spectra. Spectrochim Acta, 2010, 76, 418–422; (b). Shen, J.; Li, Y.; Vaz, R.; Izumi, H. Revisiting Vibrational Circular Dichroism Spectra of (S)-(+)-carvone and (1S,2R,5S)-(+)-menthol Using SimIR/VCD Method. J. Chem. theory Comput. 2012, 8, 27622768. (12) Debie, E.; De Gussem, E.; Dukor, R. K.; Herrebout, W.; Nafie, L. A.; Bultinck, P. A Confidence Level Algorithm for the Determination of Absolute Configuration Using Vibrational Circular Dichroism or Raman Optical Activity. ChemPhysChem 2011, 12, 1542-1549. (13) Personal communication with Dr. P. Bultinck. (14) Kuhn, W. The Physical Significance of Optical Rotatory Power. Trans. Faraday Soc. 1930, 26, 293-308. (15) Barron, L. D. Molecular Light Scattering and Optical Activity; Cambridge Univ Press: Cambridge, 2004. (16) He, J.; Petrovich, A.; Polavarapu, P. L.. Quantitative Determination of Conformer Populations: Assessment of Specific Rotation, Vibrational Absorption, and Vibrational Circular Dichroism in Substituted Butynes. J. Phys. Chem. A 2004, 108, 1671-1680. (17) He, J.; Petrovic, A. ; Polavarapu, P. L. Determining the Conformer Populations of (R)-(+)3-Methylcyclopentanone Using Vibrational Absorption, Vibrational Circular Dichroism, and Specific Rotation. J. Phys. Chem. B, 2004, 108, 20451-20457. (18) Longhi, G.; Abbate, S.; Gangemi, R.; Giorgio, E.; Rosini, C. Fenchone, Camphor, 2Methylenefenchone and 2-Methylenecamphor: A Vibrational Circular Dichroism Study. J. Phys. Chem. A, 2006, 110, 4958-4968. (19) Wang, F.; Polavarapu, P. L. Conformational Stability of (+)-Epichlorohydrin. J. Phys. Chem. A 2000, 104, 6189-6196. (20) Zhang, P.; Polavarapu, P. L. Spectroscopic Investigation of the Structures of Dialkyl Tartrates and Their Cyclodextrin Complexes. J. Phys. Chem. A 2007, 111, 858-871. (21) 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. et al, Gaussian 09 program, Gaussian, Inc., Wallingford CT, 2009. (22) CONFLEX program, CONFLEX Corporation, AIOS Meguro 6F, 2-15-19, Kami-Osaki, Shinagawa-ku, Tokyo 141-0021, Japan; www.conflex.us.


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21

Table 1: Compounds investigated and the sources for their experimental and theoretical data.

Name

Solvent

Low Energy Conformers Calculation

Source of data He et al.16

(R)-(+)-3-chloro-1-butyne (1S)-(-)-α-pinene

CCl4 Neat

1 1

B3LYP/aug-cc-pVTZ B3LYP/aug-cc-pVDZ

(3R)-(+)-methylcyclopentanone

CCl4

2

B3LYP/aug-cc-pVTZ

current work He et al.17

(3R)-(+)-methylcyclohexanone

CCl4

2

B3LYP/aug-cc-pVDZ

current work

(1R)-(+)-camphor

CCl4

1

B3PW91//TZVP

Longhi et al.18

(S)-(+)-epichlorohydrin

CCl4

3

B3LYP/6-31G*

Wang and Polavarapu

(2S,3S)-dimethyl-D-tartrate

CCl4

2

B3LYP/aug-cc-pVDZ

Zhang and Polavarapu20


19


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With Tolerance

Without tolerance

Figure 1


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Figure 2



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24

Figure 3


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Figure 4



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Raw Expt. Spectra

Comparable Spectra

Raw Calc. Spectra

Align bands

Shifted Spectra Repeat Adjust Tolerance

Optimal Spectra

Overlap Improved

Figure 5


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Behavior due to cut off below tolerance.

Figure 6



28

Overlap

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0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 0.94

SimVA SimVCD SimRAT

0.96 0.98 1 Frequency Scale Factor

(a)

(b)

Figure 7 (c)


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1

SimVCD

0.8

SimRAT

0.4

SimVCD SimRAT

0.4 0.2

0.2

0

0 -0.2

SimVA

0.6 Overlap

0.6 Overlap

1

SimVA

0.8

0.94

0.96

0.98

1

Frequency Scale Factor

-0.2

0.94

0.98

1

(b) 3-methylcyclohexanone

1

1 SimVA

0.8

SimVA

0.8

SimVCD

SimVCD

0.6

0.6 Overlap

SimRAT

0.4

SimRAT

0.4 0.2

0.2

0

0 0.94 -0.2

0.96


(a) α-Pinene

Overlap

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0.96

0.98

Frequency Scale factor

1

0.94 -0.2

(c) Camphor

Figure 8


0.96

0.98

Frequency Scale factor

(d) Epichlorohydrin

1


30

SimVA 0.2

SimVCD

0.15

SimRAT

0.1

Overlap

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0.05 0 -0.05

0.94

0.95

0.96

0.97

0.98

0.99

1

-0.1 -0.15 -0.2


Figure 9


1.01

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For Table of Contents Only


Similarity in Dissymmetry Factor Spectra: A Quantitative Measure of

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