Determination of the Absolute Configurations Using Exciton Chirality

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Determination of the Absolute Configurations Using Exciton Chirality Method for Vibrational Circular Dichroism: Right Answers for the Wrong Reasons? Cody Lance Covington, Valentin Paul Nicu, and Prasad Leela Polavarapu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b07940 • Publication Date (Web): 24 Sep 2015 Downloaded from http://pubs.acs.org on September 29, 2015

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The Journal of Physical Chemistry

Determination of the Absolute Configurations Using Exciton Chirality Method for Vibrational Circular Dichroism: Right Answers for the Wrong Reasons? Cody L. Covington1, Valentin P. Nicu2 and Prasad L. Polavarapu1* 1

Department of Chemistry, Vanderbilt University, Nashville, TN 37235 USA. 2

Van 't Hoff Institute for Molecular Sciences, University of Amsterdam,

Science Park 904, 1098 XH Amsterdam, The Netherlands

Title Running Head: Exciton chirality method for vibrational circular dichroism Corresponding Author:Phone/Fax: (615)322-2836/4936; e-mail: [email protected] Notes: The authors declare no competing financial interest.

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Abstract

Quantum chemical (QC) predictions of vibrational circular dichroism (VCD) spectra for the keto form of 3-benzoylcamphor and conformationally flexible diacetates of spiroindicumide A and B are presented. The exciton chirality (EC) model has been briefly reviewed and a procedure to evaluate the relevance of the EC model has been presented. The QC results are compared with literature experimental VCD spectra as well as with those obtained using the EC model for VCD. These comparisons reveal that the EC contributions to bisignate VCD couplets associated with the C=O stretching vibrations of benzoylcamphor, spiroindicumide A diacetate and spiroindicumide B diacetate are only ~30%, ~3% and ~15%, respectively. With such meager EC contributions, the correct absolute configurations (ACs) suggested in the literature for spiroindicumide A diacetate and spiroindicumide B diacetate molecules using the EC concepts can be considered fortuitous. The possibilities for obtaining wrong AC predictions using the EC concepts for VCD are identified and guidelines for the future use of this model are presented.

KEYWORDS Chiroptical Spectroscopy, vibrational circular dichroism, coupled oscillator, exciton, quantum chemical predictions


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1. Introduction The determination of absolute configurations (ACs) of chiral molecules is an important area of current chemical research. This goal is achievable using many different techniques, of which x-ray diffraction and NMR spectroscopy are widely known. The facts that good quality crystals are needed for x-ray diffraction studies and complexation with shift reagents is needed for NMR spectroscopic studies, make these methods not suitable in many situations. These restrictions are not applicable for deducing the ACs using chiroptical spectroscopic methods1, which include electronic circular dichroism (ECD), optical rotatory dispersion (ORD), vibrational circular dichroism (VCD) and vibrational Raman optical activity (VROA), as these studies are undertaken for native samples, generally in the liquid solution phase. However, the main draw back in the use of chiroptical spectroscopic methods is the need for tools that can deduce the ACs from the experimental data. In the early stages of developments of ECD and VCD spectroscopies, conceptual models were the main stay for spectral interpretations. The interpretations of experimental ECD spectra were conducted with the exciton coupling model2,3,4,5, which is also referred to as the exciton chirality model, and both abbreviated here as the EC model. In this model, the dipolar interaction between electric dipole transition moments of chromophores is considered to be the source for generating the ECD features. A large body of literature is available on the utility of the EC-ECD model for ECD spectral interpretations, identifying both successful and unsuccessful applications6,7. During the emergence of VCD spectroscopy, the EC model for CD associated with electronic transitions has been reformulated for CD associated with vibrational transitions and the resulting model was referred to as the coupled oscillator (CO) model8 for VCD. Although the original paper on the CO model8 did not specify the source of coupling between oscillators, subsequent literature papers adopted the dipolar interaction mechanism, as for ECD, for coupling between electric dipole transition moments9,10,11. A different formalism12,13 utilizing the Sayvetz conditions14 was also reported for predicting the absorption and circular dichroism associated with vibrational transitions in A2B2 type segments. 3 Environment ACS Paragon Plus


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Several applications of the CO model for VCD spectral interpretations have appeared in the early stages. But by the time VCD instrumentation was developed to be routinely usable in the laboratories, reliable quantum chemical (QC) theory of VCD15,16,17 and concomitant predictions of VCD spectra have emerged18,19,20,21. These positive developments in the QC predictions of VCD spectra have led many VCD researchers to quickly adopt QC-VCD calculations and the interest in the conceptual CO-VCD model has waned. In recent years, the CO-VCD model has been interchangeably referred to as the EC-VCD model and an increasing number of applications of the EC-VCD model are appearing for the AC determination in the literature22,23,24,25. For bicamphor molecules possessing C2 symmetry, Abbate and coworkers compared the QC-VCD predictions with those of the EC-VCD model and identified some drawbacks of the later26. While the simplicity of the conceptual EC model does provide easy interpretations, non-excitonic contributions such as the intrinsic contributions from individual groups7 and the contribution from interactions with other groups in the molecules are not embedded in the EC model. Moreover, while the dipolar interaction mechanism may be appropriate for electronic transitions, interaction force constants are important for vibrational oscillators. As a result, a simple extension of the EC-ECD concepts to interpret VCD spectra can lead to erroneous predictions. Monde and coworkers22 extracted two natural products spiroindicumides A and B from Chaetomium indicumand and determined their relative configurations using NOEs, as (2’R*,6S*,7S*) and (2’R*,6S*,7R*) respectively. The experimental and QC investigations of VCD spectra did not help in establishing the ACs of spiroindicumides A and B, owing to weak VCD signals associated with these molecules. Upon converting the parent compounds to diacetates, the experimental VCD spectra were claimed to have yielded enhanced VCD signals with a positive VCD couplet in the C=O stretching region. A positive couplet refers to a pair of adjacent bands with positive band appearing at lower energy (wavenumber) and negative band appearing at higher energy (wavenumber). Using the conceptual EC model to interpret this VCD couplet, Monde and coworkers concluded that the AC at 2’ 4 Environment ACS Paragon Plus

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position should be (R) and hence the ACs of spiroindicumide A diacetate and spiroindicumide B diacetate were derived as (2’R,6S,7S) and (2’R,6S,7R) respectively. The structures of (2’R,6S,7S)spiroindicumide A diacetate and (2’R,6S,7R)-spiroindicumide B diacetate are shown in Figures 1 and 2. The four carbonyl groups present in these molecules are labeled as A, B, C and D for convenience in the discussion in a later section. QC-VCD calculations were not undertaken for the diacetates of spiroindicumides A and B, and therefore the reported ACs are subject to further verification. The experimental VCD spectra and QC-VCD calculations were reported23 by Wu and You for (+)-3-benzoylcamphor, which exhibits enol-keto tautomerization with the enol form being the major tautomer and the keto form being the minor tautomer. The enol form contains only one C=O group while the keto form contains two C=O groups. The structure of (1R,3R,4R)-3-benzoylcamphor in the keto form is shown in Figure 3, where the two C=O groups are identified with labels A and B. The experimentally observed positive VCD couplet was reproduced in the QC calculations of Wu and You, with keto form being the sole contributor to the observed positive couplet. The authors interpreted the observed couplet as due to EC phenomenon, despite large (76 cm-1) experimentally observed separation between negative and positive features of the VCD couplet. In establishing the credibility of spectroscopic interpretations, it is important that the right conclusions are obtained for the right reasons. Therefore, the purpose of this manuscript is to demonstrate how to evaluate the relevance of the EC-VCD model and to identify its limitations, so that the tempered applications of EC-VCD model may prevail. The organization of this manuscript is as follows: (a). First, a general theoretical basis for the EC model has been summarized, in a commonly applicable way for both ECD and VCD. (b). Then an automated method to verify the relevance of the EC-VCD model has been presented. (c). QC-VCD predictions for the keto form of 3-benzoylcamphor and two large conformationally flexible molecules, diacetates of spiroindicumide A and B, are presented. These predictions are compared with corresponding literature experimental VCD data, to confirm the ACs of these molecules; (d). For each 5 Environment ACS Paragon Plus


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of the conformations of the molecules studied, QC-VCD predictions associated with the C=O stretching vibrations are compared with corresponding EC-VCD predictions. (e). Guidelines for the future applications of the EC-VCD model are provided. 2. Theoretical and Computational Methods 2.1. Exciton Coupling, Exciton Chirality, or Coupled Oscillator Model The purpose of this section is to introduce the notation, working relations, identify the main approximations that underline this model, and computational procedures. To provide a general outline applicable to both ECD and VCD, the electronic chromophores, or vibrational oscillators, are referred to as groups. The wavefunctions and associated transitions belong to the electronic states when considering ECD, and to vibrational states when considering VCD. The dipolar interaction is between electric dipole transition moments, in both cases. There is no difference between the EC and CO models, except for the contextual differences mentioned above. For these reasons, the abbreviation EC-CD will represent both EC-ECD and EC-VCD (or CO-VCD) models, although in the discussion relating to VCD spectra we will specifically use the abbreviation, EC-VCD. For a system composed of two groups (labeled A and B), we will designate their individual ground state wavefunctions as  A0 and  B0 and their individual excited state wavefunctions as  A1 and  B1 . The ground state wavefunction for the two-group system is  00   A0 B0 .

The two possible singly excited

states for the two-group system are  10   A1  B0 and  01   A0 B1 . Denoting the energies of ground and excited states of group i as Ei0 and E i1 , respectively, the energies of the above mentioned two excited states are, respectively: E 1A  E B0 and E A0  E B1 . The energy of ground state is E A0  E B0 . In the EC-CD model, while the ground state is assumed to be unperturbed, the excited states are assumed to interact (hence the name exciton coupling). The interaction energy, VAB, is considered to arise from the dipolar interaction between electric dipole transition moments2. The dipolar interaction operator, Vˆ , and resulting interaction energy, VAB, are given by the relations:


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Vˆ 

ˆ A  ˆ B R

3 AB





  3 ˆ A  R AB R AB  ˆ B  5 R AB

V AB   A1  B0 Vˆ  A0 B1 





 01, A   01, B R

3 AB

 

(1)





    3  01, A  R AB R AB   01, B R



(2)

5 AB

 In Eqs (1-2), R AB is the distance vector between center of masses of the two groups; ˆ A and ˆ B are 

electric dipole moment operators for groups 1 and 2, respectively;  01, A   A0 ˆ A  1A   1A ˆ A  A0 and 

 01, B   B0 ˆ B  B1   B1 ˆ B  B0

are, respectively, the electric dipole transition moment vectors for

01 transition in groups A and B. 2.1.1. Degenerate exciton chirality model: When the two groups under consideration are identical (such as those in parent molecules with C2 symmetry), their energies become degenerate. i.e. E A0  E B0  E 0 and E 1A  E B1  E 1 . In this situation, the EC-CD model is referred to as the degenerate EC (DEC) model. The expressions for the DEC-CD model are summarized in this section. In the absence of any interaction, the transitions of both groups appear at the same energy. The dipolar interaction represented by Eqs (1)-(2) causes the excited state wavefunctions of the two groups to mix. The wavefunctions and energies, resulting from dipolar interaction between excited states (see Eq. (2)), become:

 

 10   01

(3)

2

E   E 1  E 0  V AB

(4)

When VAB is positive, + (symmetric vibration in the case of vibrational transitions) has higher energy and - (antisymmetric vibration in the case of vibrational transitions) has lower energy. The opposite occurs when VAB is negative. Using the perturbed wavefunctions represented by Eq (3), the dipole strengths for the two transitions are obtained as: 7 Environment ACS Paragon Plus


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D   00 ˆ  

2



 2   2  2 01, A  01, B cos  01, A

01, B

2

  012 1  cos    D0 1  cos  

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(5)

In Eq. (5) we made use of the fact that for degenerate groups the magnitudes of their electric dipole transition moments will be the same, so  012 , A   012 , B   012  D0 , where Do is the dipole strength of the unperturbed degenerate groups;  is the angle between transition moment vectors. Ignoring the intrinsic magnetic dipole transition moments in individual groups, the rotational strengths, R±, for the two transitions are obtained2, 8 as      0   R   Im  00 ˆ     mˆ  00    R AB   01, A   01, B   2 

(6)

In Eq. (6),  0 represents the unperturbed fundamental vibrational transition frequency of the degenerate groups A and B. This equation can be written2, 5, 26-27 in terms of the angles connecting the geometrical skeleton of the two groups, but that is not necessary when Cartesian coordinates are available for the atoms in the groups, as is the case for molecular structures generated in visualization programs or QC calculations (vide infra). The predictions of absorption and CD spectra in the DEC model, obtained from Eqs (4)-(6), are presented in Figure 4 for visual appreciation. In this figure, the transitions in the absorption spectrum is depicted as unresolved; the two single sided arrows, depicted in Newman projections, represent the electric dipole transition moment vectors. Most literature EC-CD interpretations do not mention, or verify, the sign of VAB, implicitly implying that VAB is always positive, and reference only the two middle traces in Figure 4, assigning positive couplets for P-chirality and negative couplets for Mchirality. However, it is important to note that the energy order of symmetric, +, and anti-symmetric, -, wavefunctions depends on the sign of VAB, while the signs of the associated rotational strengths depend on the handedness of chirality (clockwise vs counter clockwise). 2.1.2. Non-degenerate exciton chirality model When the energies of two groups are non-degenerate ( E A  E B ), the transition frequencies of groups A and B will not be equal to each other. Then the EC model is referred to as the non-degenerate EC 8 Environment ACS Paragon Plus

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(NDEC) model. Although the equations for the NDEC model are available in the literature4-5, here we present a simpler, easily programmable, approach that we are not aware of being reported before. In the NDEC-CD model, the coefficients of wavefunctions 10 and 01 in Eq (3) will not be equal. The general form of the perturbed wavefunctions can be written as,

   c1 10  c 2 01 ,

(7)

   c 2 10  c1 01 ,

(8)

where the coefficients c1 and c 2 are positive and normalized so that, c12  c22  1. The coefficients c1 and

c 2 can be determined by diagonalizing the 2x2 energy matrix with unperturbed transition energies as the diagonal elements and interaction energy as the off-diagonal elements. Using the wavefunctions given by Eqs (7) and (8), the dipole and rotational strengths become: D   00 ˆ  

2

 c12  012 , A  c 22  012 , B  2c1c 2  01, A  01, B cos 

(9a)

D  c 22  012 , A  c12  012 , B  2c1c 2  01, A  01, B cos 

(9b)

   R    0,nd c1c 2 R AB   01, A   01, B 

(10)

In Eq. 10,  0 , nd   A   B  / 2, where  A and  B are unperturbed transition frequencies of nondegenerate groups A and B. For degenerate case, where c1  c2 

1 , Eqs. (9) and (10) reduce to Eqs. 2

(5) and (6). If the unperturbed transition energies of the two groups are significantly different, and the interaction energy is of smaller magnitude, then one coefficient will be much greater than the other; + will have dominating contribution from one unperturbed group wavefunction and - will have dominating contribution from the other. As revealed by Eq (10), the exciton coupling contribution to rotational strengths associated with wavefunctions + and - will be proportional to the product c1c 2 . The EC contribution will be maximum for c1  c2 

1 and for any other set of normalized 2

coefficients, the EC contribution will be reduced. The reduction in the EC contribution can be estimated



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from Eqs (6) and (10), as

0.5 0 D0  c1c 2 0,nd D A DB 0.5 0 D0



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0.5  c1c 2 where 0.5 is the value of c1c 2 in the 0.5

DEC model; DA and DB are the dipole strengths of unperturbed transitions in non-degenerate groups A and B. As a general guideline, the EC contribution decreases as the separation between the transition energies of the unperturbed groups increases. In actual practice, the NDEC model is rarely used because one needs to know the unperturbed non-degenerate transition energies and their relative ordering for individual groups. This information can be derived from QC calculations, as demonstrated in the examples discussed in later sections for vibrational transitions. 2.2. Verification of the relevance of EC-VCD model predictions:

Here we present a general automated method for evaluating the relevance of EC-VCD phenomenon. From the QC predictions of VCD spectra for molecules containing carbonyl groups, one can identify the two C=O stretching vibrations which are composed of coupled C=O stretching coordinates in a given molecule. The electric dipole transition moment vector for C=O stretching vibration is chosen to point along the C=O bond. In the DEC model, the unperturbed energy of C=O stretching vibration is approximated as the average (see Eq. 4) of the energies of two C=O stretching vibrations in the QC calculations. Similarly, Do is approximated as the average of dipole strengths predicted for those two coupled C=O stretching vibrations in the QC calculations. This is because if the two identical C=O groups are governed by exciton coupling, then Eq. (5) indicates that Do is indeed the average of the dipole strengths of coupled transitions. That is, D0 = (D+ + D-)/2. Then the dipolar interaction energy, VAB, is determined from the equation: V AB







       u A  u B 3 u A  R AB R AB  u B   D0    3 5 R AB  R AB 

(11)

  where u A and u B are the unit vectors associated with the two C=O bonds. The unit vectors point from C to O atoms and the distance vector is calculated from the center of mass of one C=O to another C=O group. 10 Environment ACS Paragon Plus

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Note that in the NDEC model, D0 in Eq. (11) will be replaced with (DADB)1/2 (where DA and DB are dipole strengths of non-degenerate coupled oscillators) so the predicted sign of VAB will be the same  D  DB  in both the DEC and NDEC models. Moreover, since D A D B  D0   A  , the magnitude of 2  

VAB will also not change significantly among the DEC and NDEC models. Using VAB resulting from Eq (11), the vibrational energies in the DEC-VCD model are calculated from Eq (4). The dipole and rotational strengths are calculated, respectively, from Eqs (5) and (12).      0 Do   R    R12  u A  u B  2  

(12)

In the NDEC model,  0 Do / 2 in Eq (12) will be replaced with c1c 2 0,nd D A DB  c1c 2 0 D0 , where

c1 , c 2 are coefficients for the unperturbed group wavefunctions in Eqs. (7) and (8). All these calculations were carried out with an in-house written C++ computer program that directly extracts all the needed information from Gaussian 0928 output files. The user input is limited to specifying the atom numbers for the selected C=O groups involved in the vibrations and their vibrational mode numbers (as specified in the Gaussian 09 output file). The results are verified with a programmed Excel spreadsheet, which requires as input the Cartesian coordinates of four atoms involved in the two groups, the atomic masses and dipole strengths of the two transitions. The C++ program and/or the spreadsheet can be obtained from the authors on request. The frequency order of symmetric and antisymmetric transitions in the EC-CD model is determined by the sign of VAB. However, for vibrational transitions, in the Wilson’s GF matrix method14 for solving the vibrational secular equation for two identical C=O stretching internal coordinates that do not share common atoms, it can be shown that the symmetric and anti-symmetric C=O

stretching

s 

1 2c

vibrational  a frequencies,  s and , respectively are given by the relations29,

f AA  f AB M

(13) 11 Environment ACS Paragon Plus


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a 

1 2c

f AA  f AB M

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(14)

where f AA  f BB are the diagonal force constants (which are always positive) for the two identical C=O stretching coordinates, f AB is the off-diagonal interaction force constant, M is the reduced mass of the C=O group and c is the speed of light. When f AB is positive, symmetric stretching vibrational frequency appears at higher wavenumber and anti-symmetric stretching vibrational frequency appears at lower wavenumber. The reverse is true when f AB is negative. This frequency order will also appear in the QC-VCD calculations in the absence of dominating interactions with other groups. The vibrational frequency separation of the two coupled C=O stretching vibrations predicted by the DEC-VCD model would be 2VAB (see Eq. 4). The comparison of this 2VAB with experimentally observed frequency separation between the two C=O stretching vibrational transitions will reveal if the dipolar coupling between electric dipole transition moments is adequate for explaining the observed energy separation. The comparison of the sign of VAB with that of f AB predicted in the QC calculations will reveal if dipolar interaction between electric dipole transition moments provides the correct energy order for the two transitions. In most literature EC-CD interpretations, the sign of VAB is never mentioned, implicitly implying positive sign for it. Such casual interpretations can be inadequate, because VAB can change  sign around =900. Let us consider a special case where the angle of vector R AB with either one, or   both, of the vectors  01, A and  01, B is 90o. In such cases, Eq (2) simplifies in the DEC model to

V AB 

D0 cos , 3 R AB

(15)

which indicates that the sign of VAB changes when  changes from 0    90 o range to 90 o    180 o range. VAB is a symmetric function of  and does not depend on the handedness (or chirality). This is illustrated, for the case of two O-H groups of H2O2 molecule behaving as two coupled degenerate 12 Environment ACS Paragon Plus

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groups, in the electronic supplementary information (ESI), where a plot of VAB as a function of the dihedral angle in H2O2 molecule is shown (see Figure S1 in the ESI). In general cases, where the angle    of vector R AB with both vectors  01, A and  01, B is not 90o, the sign associated with the second term in Eq

(2) can change sign depending on these angles. The sign of VAB then depends on the two terms in Eq (2) (see Tables S2 and S3 for spiroindicumide A and B diacetates in the ESI). For vibrational transitions, however, it is the sign of interaction force constant, fAB, that is important. The dependence of the sign of interaction force constant on  is not known a priori and reliable QC calculations are needed to obtain this information.

3. Results and Discussion 3.1. Keto form of (+)-3-benzoylcamphor

During enol-keto tautomerization process, the configuration at 3 position can be either (R) or (S). Thus two diastereomers are possible for the keto form. Conformational analysis for (1R,3R,4R) and (1R,3S,4R) diastereomers of 3-benzoylcamphor in the keto form indicated two possible conformers for each. The geometries of these conformers were optimized both in vacuum and in chloroform solvent environment using B3LYP functional and TZVP basis set, using the polarizable continuum model (PCM)30,31 for representing the solvent environment. The second conformer of (1R,3S,4R) diastereomer has negligible population (~0.3% at B3LYP/TZVP level using electronic energies) and will not be considered further. The populations of diastereomers and their major conformers are listed in Table 1. In vacuum calculations, (1R,3S,4R) diastereomer has lower energy than (1R,3R,4R) diastereomer. The electronic energies resulted in 73% population for the (1R,3S,4R) diastereomer. With Gibbs energies this population changed to 58%. In chloroform solvent environment using PCM, however, the relative energies of the diastereomers are reversed. For the (1R,3R,4R) diastereomer, the electronic energies resulted in 59% population, whereas Gibbs energies resulted in ~79% population. Among the two conformers of (1R,3R,4R), the major conformer has 72% population and the second conformer has ~7% population. The individual spectra of diastereomers prepared with in-house 13 Environment ACS Paragon Plus


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developed CdSpecTech program32 are presented in Figure S2 of the ESI. The (1R,3R,4R) diastereomer is predicted, at the B3LYP/TZVP/PCM level, to have opposite VCD signs in the C=O region compared to those of (1R,3S,4R) diastereomer and therefore overall magnitudes of VCD in the C=O region will be reduced when both diastereomers are included in the spectral simulation. In the C=O stretching region, the B3LYP/TZVP/PCM calculations for (1R,3R,4R) diastereomer predicted positive VCD band at 1715 cm-1 with larger magnitude than that of negative VCD band at 1800 cm-1 (See Figure 5). For the mixture of diastereomers, the B3LYP/TZVP/PCM predicted VCD spectrum shows these VCD bands with nearly equal magnitudes (See Figure 6), a pattern that is in close agreement with that seen in the experimental spectrum23 (compare Figs. 5 and 6). In their analysis, Wu and You did not consider the (1R,3S,4R) diastereomer, even though they mentioned23 that two stereoisomers are possible for the keto form. The current results indicate that it is important to consider both diastereomers and their conformers in assessing the agreement between calculated and observed VCD spectra of 3-benzoylcamphor. More importantly, we wish to address the relevance of the EC phenomenon for VCD bands in C=O region of 3-benzoylcamphor in the keto form. As the EC phenomenon is not relevant for the enol form (because it has only one C=O group), we will focus only on the keto form in this manuscript. Table 2 summarizes the B3LYP/TZVP/PCM predicted interaction force constant between groups A and B (labeled fAB; see Figure 3 for group labels A and B), vibrational frequencies, dissymmetry factors for the two C=O stretching modes for (1R,3R,4R) and (1R,3S,4R) diastereomers of 3-benzoylcamphor in the keto form. For information on the DEC-VCD model predictions, we summarize in the same table, VAB, vibrational frequencies and dissymmetry factors. The information on individual dipole and rotational strengths is provided in Table S1 of the ESI. For the C=O stretching vibrations, the B3LYP/TZVP/PCM calculations predict a positive VCD couplet for both conformers of (1R,3R,4R) diastereomer and a negative VCD couplet for (1R,3S,4R) diastereomer. The same signed couplets are predicted by the DEC-VCD model. The interaction force constant between the two carbonyl groups predicted in the B3LYP/TZVP/PCM calculations is positive, 14 Environment ACS Paragon Plus

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so these calculations predict symmetric stretching vibration to appear at higher energy than antisymmetric stretching vibration. The same order is also predicted by the DEC-VCD model because VAB predicted therein is also positive. Despite these similarities in the B3LYP/TZVP/PCM and DEC-VCD calculations, quantitative discrepancies can be found in the predicted band separation and dissymmetry factors. The dipolar interaction energy between degenerate electric dipole transition moments for the major conformer of (1R,3R,4R) diastereomer is predicted to be 9.3 cm-1, which implies that the two transitions associated with positive VCD couplet of C=O stretching vibrations should be separated by ~19 cm-1. The experimentally observed23 separation is ~75 cm-1, so the dipolar interaction mechanism is inadequate for explaining this separation. The force constants associated with individual C=O bonds and their interaction force constant, obtained in the B3LYP/TZVP/PCM calculations, are presented in Table 3, where rA and rB represents the stretching internal coordinates of groups A and B (see Figure 3). From this table, the diagonal force constants can be seen to be different. Using the harmonic oscillator equation,

 k  2c 1 f kk / M , the two diagonal force constants yield unperturbed vibrational frequencies of 1786 and 1729 cm-1, which leads to a difference of 57 cm-1 in their unperturbed vibrational frequencies. In addition, the interaction force constant between the two C=O oscillators contributes to an additional separation of ~14 cm-1, which is obtained as two times the difference between

2c 1  f 0  f AB  / M

and

2c 1

f 0 / M , where f 0   f AA  f BB  / 2. B3LYP/TZVP/PCM

calculations, incorporating these and other interactions with remaining oscillators in the molecule, predict higher and lower frequency C=O stretching vibrational modes to be separated by ~ 80 cm-1 in both diastereomers. This separation faithfully represents the corresponding separation of ~75 cm-1 in the experimental VCD couplet. This information indicates that the two C=O groups in the keto form of 3-benzoylcamphor cannot be treated as degenerate oscillators.



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In the NDEC model, the above mentioned unperturbed vibrational energies, 1786 and 1729 cm-1, can be combined with interaction energy to determine the perturbed wavefunctions. If the interaction energy

2c 1

is

derived

from

the

interaction

( f 0  f AB ) / M and 2c 

1

force

constant,

then

the

difference

between

f 0 / M yields 7.2 cm-1. Solving the 2x2 determinant with

1786 and 1729 cm-1 as the diagonal elements and 7.2 cm-1 as the off diagonal elements, the perturbed wavefunctions (see Eqs (7) and (8)) will be obtained with coefficients: c1 ~0.992 and c 2 ~ 0.123. Based on these coefficients, there will be ~75% reduction of the EC contribution in the NDEC model. If the dipolar interaction energy, instead of the contribution from fAB, is selected then dipolar interaction energy in the NDEC model can be obtained by replacing D0 with

D A DB in Eq (11),

which yields a value of 8.7 cm-1 (see Table S1 in the ESI for DA and DB). Solving the 2x2 determinant with 1786 and 1729 cm-1 as the diagonal elements and 8.7 cm-1 as the off diagonal elements, the perturbed wavefunctions will be obtained with coefficients: c1 ~0.989 and c 2 ~ 0.147. Based on these coefficients, there will be ~70% reduction of the EC contribution in the NDEC model. The use of either set of the abovementioned coefficients indicates that the C=O stretching VCD couplet in (1R,3R,4R) diastereomer has a limited EC contribution (of only 25-30%). The rotational strengths predicted in the DEC model (see Table S1 in the ESI) for the major conformer of (1R,3R,4R) diastereomer are ±442. Those in the NDEC model are obtained by multiplying the DEC model rotational strengths with 2c1c 2 D A DB / D0 (see Eqs (6) and (10)) which yields ±120 (with coefficients obtained using V12). The rotational strengths obtained in the B3LYP/TZVP/PCM calculations (see Table S1 in the ESI) are 197 and -134, which indicates that the NDEC model accounts for ~61% of the positive VCD band intensity and 90% of the negative VCD band intensity in the B3LYP/TZVP/PCM-VCD prediction. Then non-EC contributions (such as the intrinsic individual group contributions and the contributions from interactions with other parts of the molecule.) that are not embedded in the EC-VCD model become significant for explaining the positive VCD band intensity. 16 Environment ACS Paragon Plus

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The DEC-VCD model predicted dissymmetry factors (see Table 2) for the lowest energy conformer are larger than those predicted in the B3LYP/TZVP/PCM calculation, which means that the magnitudes of rotational and dipole strengths obtained in the DEC-VCD model are not commensurate with B3LYP/TZVP/PCM-VCD predictions. Summarizing the results for the keto form of (+)-3-benzoylcamphor, the dipolar interaction between two electric dipole transition moments is not adequate for explaining the observed frequency separation. The frequency separation for the two carbonyl stretching vibrations in the keto form of 3benzoylcamphor arises primarily from the differences in the force constants of individual groups themselves. The use of the NDEC-VCD model indicates the presence of only ~30% EC contribution and accounts for only ~60 % of the positive VCD band intensity predicted in the B3LYP/TZVP/PCM calculations. The experimentally observed23 positive VCD couplet with equal magnitudes for positive and negative components is reproduced in the B3LYP/TZVP/PCM calculations when a contribution from the second diastereomer is also included. These observations suggest that the EC model alone is not sufficient for explaining the observed VCD couplet in the keto form of 3-benzoylcamphor. 3.2. Spiroindicumide A and B diacetates

The (2’R,6S,7S) structure of spiroindicumide A diacetate and (2’R,6S,7R) structure of spiroindicumide B diacetate were built in Chemdraw and exported to Conflex program33 for conformational analysis. This program generated 732 conformations for spiroindicumide A diacetate and 663 conformations for spiroindicumide B diacetate within 20 Kcal/mol. These conformations were reoptimized at PM6 level ( as implemented in the Gaussian 09 program28) which led to the identification of 199 conformations for spiroindicumide A diacetate and 191 conformations for spiroindicumide B diacetate. Further optimization of these conformers at B3LYP/6-31G(d) level, using the PCM for representing the influence of CHCl3 solvent, reduced the number of conformers to 43 for spiroindicumide A diacetate and 20 for spiroindicumide B diacetate. Finally, when optimized at B3LYP/TZVP level with tight optimization option and the PCM, 22 conformers for spiroindicumide A diacetate and 12 for spiroindicumide B diacetate were identified. The distribution of populations depends on the energies 17 Environment ACS Paragon Plus


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(electronic vs Gibbs) utilized for calculating them. The population, based on Gibbs energies, of the two lowest energy conformers of spiroindicumide A diacetate are 51% and 19%, while those based on electronic energies are 25% and 12%, so there are several other conformers with smaller populations. Fortunately, however, population weighted spectra appeared similar regardless of the energies used for calculating the populations (see Figures S5 and S6 in the ESI). In the case of spiroindicumide B diacetate three conformers each with 43%, 34% and 20% populations, based on Gibbs energies, accounted for most of the populations. The corresponding populations derived from electronic energies are 28%, 28% and 9%. The populations for 22 conformers of spiroindicumide A diacetate and 12 conformers of spiroindicumide B diacetate are presented in Table 4. All of the conformations identified in Table 4 at the B3LYP/TZVP/PCM level were used for VCD calculations, with PCM representing the CHCl3 solvent, and population weighted VCD spectra generated. The individual conformer spectra are presented in Figures S3 and S4 of the ESI. The population weighted spectra show a positive couplet in the C=O stretching region, for both spiroindicumide A diacetate and spiroindicumide B diacetate (see Fig. 7 and 8), as also observed in their experimental spectra (see Figs 7 and 8) indicating that the AC used for calculations may be assigned to the sample used for obtaining the experimental spectra. Thus the ACs concluded by Monde and coworkers22 for diacetates of spiroindicumide A and B are supported by the current QC-VCD calculations. However, the main question that we wish to address is the relevance of the EC phenomenon for the VCD couplet in the C=O stretching region (vide infra). There are four C=O groups in these molecules, so in principle one should expect to see four C=O stretching vibrational absorption bands. For the lowest energy conformer of spiroindicumide A diacetate, the four modes associated with C=O stretching motions are predicted, at the B3LYP/TZVP/PCM level, to appear at 1825, 1786, 1779 and 1725 cm-1. In Gaussian 09 output these are associated with vibrations #142, 143, 144 and 146 respectively. There is another mode (#145) at 1728 cm-1 in the same region which is associated with C=C stretching of dimethyl allyl, [(CH3)2C=CHCH2-], side chain. Among the above mentioned C=O stretching modes, the 1825 cm-1 18 Environment ACS Paragon Plus

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vibration originates from C=O stretching coordinate of group A (see Figure 1 for group labels, A-D) coupled to that of group B; 1786 cm-1 vibration originates from C=O stretching coordinate of group D; 1779 cm-1 vibration originates from C=O stretching coordinate of group B coupled to that of group A; 1725 cm-1 vibration originates from C=O stretching coordinate of group C coupled to that of group D. The 1825 and 1779 cm-1 modes are responsible for the positive VCD couplet in the predicted spectrum in most of the conformers. Therefore we selected these two modes (#142 and 144 in Gaussian 09 output) for the EC analysis in spiroindicumide A diacetate. For the lowest energy conformer of spiroindicumide B diacetate, the four C=O stretching modes are at 1823, 1793, 1782 and 1706 at cm-1 (with another mode at 1727 cm-1 in the same region coming from C=C stretching of dimethyl allyl [(CH3)2C=CHCH2-] side chain). These four C=O modes have similar group contributions as in the case of spiroindicumide A diacetate. The 1823 and 1782 cm-1 modes are responsible for the positive VCD couplet in the predicted VCD spectrum of spiroindicumide B diacetate. Therefore we selected these two modes (#142 and 144 in Gaussian output) for the EC analysis in spiroindicumide B diacetate. Table 5 summarizes the B3LYP/TZVP/PCM predicted interaction force constants, vibrational frequencies and dissymmetry factors for the above mentioned two C=O stretching modes of all low energy conformers of spiroindicumide A diacetate. For information on the DEC-VCD model predictions, we summarize in the same table, VAB, vibrational frequencies and dissymmetry factors. Table 6 summarizes the same for spiroindicumide B diacetate. The first observation is that, VAB predicted in the DEC model is not always positive, a point also noted by Abbate and coworkers26. Conformers 213, 209, 154, 181, 113, 215, 126 and 200 of spiroindicumide A diacetate and conformers 32, 49, 60, 54 and 31 of spiroindicumide B diacetate are predicted to have negative VAB. As a result, the DEC-VCD model places the symmetric stretching vibration at lower frequency than antisymmetric stretching vibration for these conformers. On the contrary, the interaction force constant fAB obtained in the B3LYP/TZVP/PCM predictions is positive for all conformations. Therefore the symmetric stretching vibration is at higher frequency and the anti19 Environment ACS Paragon Plus


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symmetric stretching vibration is at lower frequency in the B3LYP/TZVP/PCM calculations for all conformers. Second, the DEC-VCD model predicts positive couplet for all conformers even though VAB has changed sign for some, because chiral handedness of the involved C=O groups also changed for those conformers (see Tables S2 and S3 in the ESI). On the contrary, the B3LYP/TZVP/PCM predictions indicate positive couplet for some conformers and negative couplet for others. Fortunately, wherever B3LYP/TZVP/PCM and DEC calculations are in disagreement, the corresponding conformers have higher energies with low populations (at the B3LYP/TZVP/PCM level).

For the lowest energy

conformers, the DEC model predicted VCD sign pattern is in agreement with that predicted in the B3LYP/TZVP/PCM calculations. The third observation is that the dipolar interaction energy obtained for the three lowest energy conformers of both diacetates is less than 2 cm-1. That means, the maximum separation of the transitions associated with positive and negative VCD bands of the positive couplet should be less than ~4 cm-1. The experimentally observed separation in VCD couplets is deduced from the reported spectra22 to be ~35 cm-1. These observations suggest that dipolar interaction between electric dipole transition moments cannot explain the separation for observed VCD couplets. The observed larger frequency separation between positive and negative parts of the positive VCD couplet can be attributed, in both diacetates, to significant differences among the force constants associated with the individual C=O groups. These force constants obtained at the B3LYP/TZVP/PCM level are displayed in Tables 7 and 8 for the lowest energy conformer of both diacetates. In these tables, rA through rD represent the stretching internal coordinates for groups A through D (see Figures 1 and 2). The diagonal force constant associated with stretching internal coordinate of group A has the largest magnitude. It is followed by diagonal force constant associated with stretching internal coordinate of groups D, B and C, in that order. The decreasing frequency order of four C=O stretching vibrational modes predicted at the B3LYP/TZVP/PCM level is in fact associated respectively with groups A, D, B and C (vide supra). The force constants of C=O groups A and B can be seen to yield unperturbed 20 Environment ACS Paragon Plus

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vibrational frequencies of 1812 and 1782 cm-1, with 30 cm-1 separation between them in spiroindicumide A diacetate and ~25 cm-1 separation in spiroindicumide B diacetate. The interaction force constants between these two carbonyl stretching coordinates contributes to a separation of ~ 2 cm1

in spiroindicumide A diacetate and ~ 4 cm-1 in spiroindicumide B diacetate. These contributions, in

combination with contributions from the interactions with other oscillators (see Tables 7 and 8 for interaction force constants with other C=O stretching coordinates), result in the B3LYP/TZVP/PCM predicted separation of ~ 46 cm-1 for the lowest energy conformer of spiroindicumide A diacetate and ~ 41 cm-1 for the lowest energy conformer of spiroindicumide B diacetate. These predicted separations compare well with a separation of ~35 cm-1 deduced from the reported experimental spectra22. Larger differences among diagonal force constants of four C=O groups in the diacetates of spiroindicumide A and B suggest that C=O groups in these molecules are significantly different and that they cannot be treated as degenerate groups.

The use of the NDEC model for diacetates of

spiroindicumides A and B will not influence the sign of VAB and therefore the disagreement between signs of fAB and VAB noted earlier for some conformers cannot be reconciled. Moreover, since there are four C=O groups in the molecules under consideration, and there is no a priori knowledge (in the absence of QC calculations) of which oscillators are interacting with each other, one needs to consider all four oscillators and assign the unperturbed vibrational energies for each of them to use the NDEC model. But one would not know (in the absence of QC calculations) which oscillator has higher/lower energy to start with. For these reasons the NDEC model is rarely practiced. However, since we know in this work from the B3LYP/TZVP/PCM calculations that groups A and B are responsible for the VCD couplets in the C=O stretching region of diacetates of spiroindicumide A and B, we can consider the NDEC model just for these two groups. In the NDEC model, for the lowest energy conformer of spiroindicumide A diacetate, the unperturbed vibrational energies derived from the force constants in Table 7 are 1812 and 1782 cm-1. The interaction energy derived from the interaction force constant is 0.8 cm-1. Solving the 2x2 determinant with 1812 and 1782 cm-1 as the diagonal elements and 0.8 cm-1 as the off-diagonal 21 Environment ACS Paragon Plus


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elements, yields the coefficients c1 and c 2 in Eqs (7) and (8) as 0.9996 and 0.0266, predicting 97% reduction in the EC contribution. If the dipolar interaction energy is used, then it is obtained by replacing D0 in Eq (8) with

D A DB which yields 0.59 cm-1. Then the coefficients c1 and c 2 in Eqs (7)

and (8) become ~0.9998 and ~0.0196. These coefficients suggest that the percent reduction of EC contribution in the NDEC model is 96%. With either set of coefficients, the EC contribution to C=O stretching VCD couplet in spiroindicumide A diacetate is predicted to be only ~3%. Similarly for the lowest energy conformer of spiroindicumide B diacetate, the interaction energy is either ~2 cm-1 from the interaction force constant (see Table 8) or 1.57 cm-1 from dipolar interaction. With unperturbed vibrational energies of 1810 and 1784 cm-1 and one of these interaction energies, the percent reduction of EC contribution in the NDEC model is ~85%, suggesting that the EC contribution to C=O stretching VCD couplet in spiroindicumide B diacetate is only ~15% . For the lowest energy conformation (#25) of spiroindicumide A diacetate, the DEC model yields rotational strengths of ±975 (see Table S4 in the ESI), which reduce to ±37 in the NDEC model (using coefficients obtained with VAB), while the B3LYP/TZVP/PCM calculations yield values of +108 and 241. These numbers indicate that the exciton contribution in the NDEC model can only account for ~15% of the negative VCD band intensity and 34% of the positive VCD band intensity in the B3LYP/TZVP/PCM prediction. Similarly, for the lowest energy conformation (#107) of spiroindicumide B diacetate, the DEC model predicts rotational strengths as ±1086 (see Table S5 in the ESI), which reduce to ±128 in the NDEC model (using coefficients obtained with VAB), while the B3LYP/TZVP/PCM calculations yield +284 and -289. These numbers indicate that the exciton contribution in the NDEC model can only account for ~45% of the B3LYP/TZVP/PCM prediction. These observations suggest that the EC phenomenon is not at all dominant in these molecules. Instead, the non-EC contributions (such as the intrinsic contributions and contributions from the inter-group interaction in the remaining parts of the molecule) that are not embedded in the EC-VCD model appear to be more important for the diacetates of spiroindicumide A and B.


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The dissymmetry factors (see Tables 5 and 6) predicted by the DEC-VCD model are larger than the corresponding B3LYP/TZVP/PCM predictions by up to 4 times. That means the magnitudes of rotational and dipole strengths predicted by the DEC-VCD model are not commensurate with the B3LYP/TZVP/PCM predictions. Although we have focused in the previous discussions only on the coupling of C=O groups A and B, there are some conformers where coupling with other C=O groups is important. In the conformer #49 of spiroindicumide B diacetate (see Figure S8 in the ESI), the two acetyl groups come closer and the interaction between carbonyl groups B and D become more important than that between groups B and A. Such possibilities for coupling between different carbonyl groups makes any conclusions based on the DEC-CD model dangerous because, in a system with multiple interacting groups, one does not know beforehand how the groups will couple. The B3LYP/TZVP/PCM calculations turned out to yield higher energy for conformer #49 of spiroindicumide B diacetate, so this conformer did not influence the Boltzmann weighted result. Summarizing the situation for diacetates of spiroindicumide A and B, the dipolar interaction between electric dipole transition moments associated with C=O stretching vibrations is not adequate for explaining the observed frequency separation22. The frequency separation between the carbonyl stretching vibrations of groups A and B arises mainly from the differences in force constants of these bonds themselves. The interaction force constants make much smaller contributions to frequency separation. The wavefunctions obtained in the NDEC model suggest that the EC contribution is not significant in these molecules. Then the EC-VCD model is not really appropriate for explaining the experimentally observed VCD couplets in diacetates of spiroindicumide A and B. The ACs assigned by Monde and coworkers22 for diacetates of spiroindicumide A and B using the EC concepts are fortuitously same as those derived from the B3LYP/TZVP/PCM calculations.

4. Guidelines for the future use of EC-VCD model



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The appearance of bisignate VCD couplets does not necessarily entail the presence, or dominance, of exciton coupling phenomenon. Ad hoc interpretations of the experimental VCD spectra using the conceptual EC-VCD model may yield right conclusions, but they could be originating for the wrong reasons. Therefore, one should avoid attributing the experimental VCD couplets to the EC phenomenon without providing a detailed verification. This verification can be carried out as follows: The first impression for the presence, dominance or absence of EC phenomenon can be obtained from analyzing the appearance of couplets. For this purpose, one may consider the molecules with and without symmetry separately. (1). For groups related through symmetry in the parent molecule, if a sharp intense VCD couplet with positive and negative bands of roughly equal magnitudes and an unresolved absorption band are observed, then exciton coupling with a weak interaction force constant between degenerate groups may be anticipated. (2). For groups related through symmetry in the parent molecule, if a resolved intense VCD couplet with positive and negative bands of roughly equal magnitudes and well resolved absorption bands are observed then exciton coupling with a strong interaction force constant between degenerate groups may be anticipated. If that happens, the ratio of intensities of absorption bands (See Eq. 5), can provide useful information on the relative orientation of the groups and Eq. 5 should be verified. (3). For groups not related through symmetry in the parent molecule, if a weak VCD couplet with positive and negative bands of roughly equal magnitudes and an unresolved absorption band are observed then the dominance of exciton coupling phenomenon may not be present. (4). For groups not related through symmetry in the parent molecule, if a resolved weak VCD couplet with positive and negative bands of roughly equal magnitudes, and well resolved absorption bands, are observed then dominant exciton coupling phenomenon may not be present because a strong interaction force constant is required to favor the exciton coupling in this situation. (5). When the magnitudes of positive and negative bands of a VCD couplet are different, exciton coupling phenomenon may not be the dominant phenomenon, because both DEC and NDEC models predict equal magnitudes for the components of bisignate couplet.


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Conformational analysis and determining the dominant conformers is a prerequisite for any further analysis. If the concept of dipolar interaction between electric dipole transition moments is adopted as the source of exciton coupling, then it is necessary to determine the dipolar interaction energy for the coupled vibrational transitions. If multiple transitions (such as multiple C=O groups) are involved, then it is necessary to determine which transitions are coupled, and such information can be determined from reliable QC calculations. Since dipolar interaction energy can be calculated using a spreadsheet, such calculations are trivial in modern times as the needed atomic Cartesian coordinates can be generated using many freely available molecular visualization programs. From this calculation two verifications should be made: (a). if the sign of VAB is positive, then positive couplet correlates with P-chirality. If it is negative, then positive couplet correlates with M-chirality. However, one should be

skeptical of VAB because one would not know for certain if the frequency order of symmetric and antisymmetric vibrations predicted by VAB is correct. This is because, unlike in the case of electronic transitions, interaction force constants determine the relative order of symmetric and antisymmetric transitions. The sign of VAB can be different from that of interaction force constant as demonstrated here for diacetates of spiroindicumide A and B and also pointed out by Abbate and coworkers26. The linear transit calculations on 6,6′-Dibromo-[1,1′-binaphthalene]-2,2′-diol34 also revealed that geometrical perturbations can interchange the positive and negative bands of a couplet, even in the absence of a change in handedness. This uncertainty makes the conceptual interpretations using the EC-VCD model dangerous. (b). If the experimental separation between resolved absorption band maxima is not approximately equal to 2VAB, then the difference in the energies of uncoupled oscillators could be the source of frequency separation and the use of the NDEC model becomes necessary. In this context it is useful to note that the separation between absorption bands may differ from that between associated VCD bands, because of the mutual cancellation resulting from opposite signs associated with VCD bands. The force constants, as well as the interaction force constants, can be extracted from the outputs of quantum chemical vibrational frequency calculations. The unperturbed vibrational energies and the 25 Environment ACS Paragon Plus


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interaction energy can be determined from these force constants for the oscillators involved. Solution to a 2 x 2 determinant will yield the eigenvectors (i.e coefficients) needed to construct the perturbed wavefunctions (see a web applet for obtaining the eigenvectors at: http://www.akiti.ca/Eig2Solv.html) given by Eqs (7) and (8). From these coefficients the extent of the EC contribution present in a nondegenerate system can be estimated. If a majority of the EC contribution is not retained by the predicted wavefunction then the prevalence of EC-VCD phenomenon cannot be justified. Considerable progress has been made in recent years for predicting the QC-VCD spectra of large molecules35. Despite this progress, for situations where it is not possible to undertake the prediction of QC-VCD spectra and the EC-VCD model appears to be the only reasonable option, it will be pragmatic to state clearly that the EC-VCD model structural predictions have to be verified independently by other structural methods. 5. Conclusions

The experimentally observed VCD couplets associated with C=O stretching vibrations of the keto form of 3-benzoylcamphor, and of the spiroindicumide A and B diacetates, are reproduced in the B3LYP/TZVP/PCM calculations. The dipolar interaction between electric dipole transition moments cannot explain the observed frequency separation between the transitions associated with the VCD couplets. The C=O groups involved in the molecules considered here are non-degenerate with significant differences in their unperturbed vibrational energies. As a consequence, the EC contribution is limited for the carbonyl stretching vibrations in the keto form of 3-benzoylcamphor, and is insignificant for the carbonyl stretching vibrations of spiroindicumide A and B diacetates. The conceptual applications of EC-VCD model, without a detailed scrutiny, may yield right answers but at the expense of wrong reasoning. The future applications of the exciton chirality model for VCD to determine the absolute configurations are recommended to be accompanied by verification for its relevance, as demonstrated in this article.


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Acknowledgments: 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. Supporting Information Available:

The Supporting Information is available free of charge on the ACS Publications website: Individual conformer spectra, comparison of spectra obtained with different Boltzmann weights, comparison of spectra obtained in vacuum with PCM, rotational strengths and dipole strengths of molecules studied, structural parameters of two group segments in diacetates of spiroindicumide A and B, optimized Cartesian coordinates of low energy conformers of diacetates of spiroindicumide A and B.



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Table 1: Populations of conformers of 3‐benzoylcamphor diastereomers in the keto form Conformer B3LYP/TZVP B3LYP/TZVP/PCM From electronic energies 0.16 0.11 0.73

(1R,3R,4R)‐conformer 1 (1R,3R,4R)‐conformer 2 (1R,3S,4R)‐conformer 1

From Gibbs energies 0.26 0.16 0.58

From electronic From Gibbs energies energies 0.59 0.72 0.08 0.07 0.33 0.21

a

Table 2: Comparison of QC‐VCD predictions with DEC‐VCD model predictions for C=O stretching vibrations of 3‐benzoylcamphor in keto form B3LYP/TZVP/PCM EC‐VCD Model Higher frequency Lower frequency Higher frequency Lower frequency ‐1 ‐1 ‐1 ‐1 VAB fAB gi gi gi gi cm cm cm cm Structure (1R,3R,4R)‐conformer 1 (1R,3R,4R)‐conformer 2 (1R,3S,4R)‐conformer 1

0.11 0.13 0.13

1800 1790 1791

‐0.6 ‐0.3 0.7

1714 1710 1714

1.7 0.8 ‐0.9

9.3 6.0 6.0

1767 1756 1758

a

‐1.7 ‐4.3 4.9

1748 1744 1747

4.4 1.0 ‐1.0

definitions of terms involved are as follows: fAB=interaction force constant (mdyn/A); see Figure 3 for group labels A and B; gi=dissymmetry 4

‐1

factor x 10 ; VAB=dipolar interaction energy (cm ) between electric dipole transition moments of A and B

Table 3: Force constants (mdyn/A) in (1R,3R,4R)‐ benzoylcamphora rA

rB

rA

12.9

0.1

rB

0.1

12.1

a

see Fig 3 for group labels A and B


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Table 4: Populations of conformers of diacetates of Spiroindicumide A and B at B3LYP/TZVP/PCM level spiroindicumide A diacetate spiroindicumide B diacetate from from from from conformer electronic Gibbs conformer electronic Gibbs number energies energies energies energies 25 0.246 0.511 107 0.277 0.428 69 0.115 0.192 168 0.285 0.337 259 0.069 0.105 118 0.086 0.203 305 0.038 0.041 105 0.106 0.012 247 0.045 0.033 32 0.054 0.009 141 0.072 0.017 96 0.035 0.003 194 0.050 0.013 49 0.063 0.002 314 0.021 0.011 60 0.028 0.002 132 0.020 0.011 7 0.014 0.001 333 0.017 0.010 59 0.019 0.001 11 0.020 0.009 54 0.023 0.001 213 0.069 0.007 31 0.012 0.001 41 0.027 0.007 209 0.040 0.006 154 0.035 0.006 40 0.017 0.005 181 0.020 0.005 113 0.020 0.003 215 0.019 0.003 289 0.014 0.003 126 0.011 0.002 200 0.016 0.002



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Table 5: Comparison of QC‐VCD predictions with DEC‐VCD model predictions for A and B C=O stretching vibrations of Spiroindicumide A diacetatea B3LYP/TZVP/PCM EC‐VCD Model Higher frequency Lower Higher Lower ‐1

Conformer

fAB

cm

25 69 259 305 247 141 194 314 132 333 11 213 41 209 154 40 181 113 215 289 126 200

0.01 0.01 0.03 0.03 0.03 0.03 0.03 0.04 0.03 0.03 0.02 0.03 0.02 0.04 0.04 0.03 0.04 0.04 0.04 0.03 0.03 0.03

1825 1822 1823 1825 1824 1823 1823 1821 1822 1821 1820 1819 1822 1821 1820 1822 1821 1820 1820 1822 1818 1819

gi ‐0.7 ‐0.6 ‐0.8 ‐1.2 ‐1.0 ‐0.6 ‐0.7 ‐0.9 ‐0.6 ‐1.2 ‐0.5 0.5 ‐1.0 0.6 0.6 ‐0.6 0.5 0.7 0.7 ‐0.9 0.5 0.2

cm

‐1

1779 1779 1783 1781 1781 1777 1779 1781 1777 1780 1779 1768 1778 1768 1769 1776 1774 1770 1768 1778 1768 1768

‐1

gi

VAB

cm

0.5 0.7 1.3 1.5 1.3 1.6 1.2 1.5 1.6 1.6 0.8 ‐0.7 1.2 ‐0.8 ‐0.7 1.6 ‐0.8 ‐0.7 ‐0.8 1.3 ‐0.8 ‐0.6

0.6 0.5 1.7 1.5 1.6 3.0 3.1 2.2 3.0 1.9 2.8 ‐4.6 2.8 ‐4.7 ‐4.6 3.1 ‐4.3 ‐4.6 ‐4.7 3.0 ‐4.5 ‐4.6

1803 1801 1805 1804 1804 1803 1804 1803 1802 1803 1802 1799 1803 1799 1799 1802 1801 1800 1799 1803 1797 1798

gi ‐6.9 ‐7.5 ‐4.1 ‐4.2 ‐4.1 ‐5.3 ‐5.3 ‐3.7 ‐5.3 ‐3.9 ‐5.7 ‐2.7 ‐5.4 ‐2.7 ‐2.7 ‐5.2 ‐2.7 ‐2.7 ‐2.7 ‐5.3 ‐2.7 ‐2.7

cm

‐1

1801 1800 1801 1801 1801 1797 1798 1799 1796 1799 1797 1789 1797 1790 1790 1796 1793 1791 1790 1797 1788 1789

gi 2.3 2.1 3.6 3.5 3.6 2.7 2.7 3.9 2.7 3.7 2.6 3.6 2.7 3.6 3.6 2.8 3.5 3.5 3.6 2.7 3.6 3.4

a

definitions of terms involved are as follows: fAB=interaction force constant (mdyn/A) between

groups A and B ;see figure 1 for group labels A and B; gi=dissymmetry factorx104; VAB=dipolar interaction energy (cm‐1);


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 6: Comparison of QC‐VCD predictions with DEC‐VCD model predictions for A and B C=O stretching vibrations of Spiroindicumide B diacetatea B3LYP/TZVP/PCM EC‐VCD Model Higher frequency Lower Higher Lower ‐1

Conformer

fAB

cm

107 168 118 105 32 96 49 60 7 59 54 31

0.03 0.03 0.03 0.02 0.03 0.03 0.03 0.03 0.02 0.03 0.03 0.04

1823 1824 1824 1823 1821 1823 1819 1821 1825 1823 1819 1820

gi ‐0.9 ‐1.1 ‐1.0 ‐0.8 0.4 ‐0.7 0.1 0.4 ‐0.6 ‐0.9 0.2 0.4

cm

‐1

1782 1782 1782 1779 1774 1779 1768 1774 1778 1779 1768 1774

‐1

gi

VAB

cm

1.2 1.5 1.4 1.2 ‐0.8 1.2 ‐0.7 ‐0.8 3.1 1.2 ‐0.7 ‐0.8

1.6 1.6 1.7 3.2 ‐4.4 3.2 ‐4.7 ‐4.5 2.9 3.1 ‐4.9 ‐4.2

1804 1805 1805 1804 1802 1805 1798 1802 1804 1804 1799 1801

gi ‐4.2 ‐4.2 ‐4.2 ‐5.3 ‐2.7 ‐5.3 ‐2.7 ‐2.7 ‐5.1 ‐5.3 ‐2.7 ‐2.7

a

cm

‐1

1801 1801 1801 1798 1793 1798 1789 1793 1798 1798 1789 1793

definitions of terms involved are as follows: fAB=interaction force constant (mdyn/A) between gropus A and B (see Figure 2 for group labels A and B); gi=dissymmetry factorx104; VAB=dipolar interaction energy (cm‐1)


gi 3.5 3.6 3.5 2.7 3.5 2.7 3.4 3.5 2.9 2.7 3.4 3.5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 7: Force constants (mdyne/A) associated with C=O stretching internal coordinates in lowest energy conformer of spiroindicumide A diacetatea rA rB rC rD rA

13.30

0.01

0.03

0.00

rB

0.01

12.86

0.01

0.00

rC

0.03

0.01

11.99

0.00

rD

0.00

0.00

0.00

12.98

a

see Figure 1 for group labels A‐D

Table 8: Force constants (mdyne/A) associated with C=O stretching internal coordinates in lowest energy conformer of spiroindicumide B diacetatea rA rB rC rD rA

13.27

0.03

0.04

0.01

rB

0.03

12.89

0.01

0.00

rC

0.04

0.01

11.77

0.03

rD

0.01

0.00

0.03

13.10

a

see Figure 2 for group labels A‐D


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Figure Legends Figure 1: The structure of (2’R,6S,7S)-spiroindicumide A diacetate identifying the four carbonyl groups

as A-D. Figure 2: The structure of (2’R,6S,7R)-spiroindicumide B diacetate identifying the four carbonyl groups

as A-D Figure 3: The structure of (1R,3R,4R)-benzoylcamphor identifying the two carbonyl groups as A and B. Figure 4. DEC model predictions of absorption (bottom traces) and CD (middle and top traces) for two

degenerate electric dipole transition moment vectors as a function of their chiral orientation and the sign of their dipolar interaction energy (VAB). Note that only the two middle traces in this figure are generally referenced without identifying the symmetric and antisymmetric wavefunctions. Figure 5: B3LYP/TZVP/PCM predicted VA (bottom) and VCD (top) spectra for (1R,3R,4R)-

benzoylcamphor in the carbonyl stretching vibrational region. The experimental VCD and VA spectra of You et al 23, shown as dashed line traces, are digitized (normalized to the lower frequency band peak intensity in the calculated spectrum) and presented here for comparison. Reproduced from (Ref 23). Copyright (2012, American Chemical Society). Figure 6: B3LYP/TZVP/PCM predicted VA (bottom) and VCD (top) spectra in the carbonyl stretching

vibrational region for the mixture of diastereomers of 3-benzoylcamphor in the keto form. The experimental VCD and VA spectra of You et al

23

, shown as dashed line traces, are digitized

(normalized to the lower frequency band peak intensity in the calculated spectrum) and presented here for comparison. Reproduced from (Ref 23). Copyright (2012, American Chemical Society). Figure 7: The population weighted B3LYP/TZVP/PCM predicted VA (bottom) and VCD (top) spectra

in the carbonyl stretching vibrational region for (2’R,6S,7S)-spiroindicumide A diacetate. The experimental VCD and VA spectra of Monde et al22 shown as dashed line traces, are digitized (normalized to the lower frequency band peak intensity in the calculated spectrum) and presented here for comparison. Reproduced from (Ref 22). Copyright (2013, American Chemical Society). 33 Environment ACS Paragon Plus


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Figure 8: The population weighted B3LYP/TZVP/PCM predicted VA (bottom) and VCD (top) spectra

in the carbonyl stretching vibrational region for (2’R,6S,7R)-spiroindicumide B diacetate. The experimental VCD and VA spectra of Monde et al22 shown as dashed line traces, are digitized (normalized to the lower frequency band peak intensity in the calculated spectrum) and presented here for comparison. Reproduced from (Ref 22). Copyright (2013, American Chemical Society).


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Figure 1



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2


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Figure 3



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 4


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Figure 5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6


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Figure 7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 8


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References

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Exciton Coupling O (EC) ??

C O

Quantum Calculations

C

Non‐Degenerate EC

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Degenerate EC

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