The Raman optical activity of pinane as compared with (-)α- and (-)β-pinene … · 2019. 12....

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Contents lists available at ScienceDirect Vibrational Spectroscopy journal homepage: www.elsevier.com/locate/vibspec The Raman optical activity of pinane as compared with (-)α- and (-)β- pinene: The perspective of intramolecular enantiomerism Hongru Yang a , Peijie Wang a, *, Guozhen Wu b, * a The Beijing Key Laboratory for Nano-Photonics and Nano-Structure, Department of Physics, Capital Normal University, Beijing, 100048, China b State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, China ARTICLE INFO Keywords: Raman optical activity (ROA) Intramolecular enantiomerism Dierential bond polarizability (-)α-pinene (-)β-pinene Pinane ABSTRACT The Raman and Raman optical activity (ROA) spectra of chiral pinane were analyzed by a bond polarizability algorithm. By the dierential bond polarizability, the chirality of pinane is compared with our previous results of (-)α- and (-)β-pinene to show the intramolecular enantiomerism. The intramolecular enantiomerism implies the existence of an approximate mirror symmetry. This symmetry is most destroyed by the on-ring CeC double in (-)α-pinene. This leads to the decrease of ROA from (-)α-pinene, (-)β-pinene to pinane. Variation of dierential bond polarizabilities also follows this trend. This comparison demonstrates the chiral behavior and the roles of the asymmetric centers of (-)α-, (-)β-pinene and pinane from a spectroscopic viewpoint. 1. Introduction Raman optical activity (ROA) [19] can express the couplings among the vibrationally induced electric dipole and magnetic dipole/ electric quadrupole [10,11]. These couplings are not of parity con- servation that for a chiral molecule, its Raman responses to the right and left circularly polarized light are not identical. This leads to its ROA spectrum which is dened as the dierence between these two spectral proles [1217]. Experimentally, to a Raman prole, there corresponds an ROA prole with positive or negative signature at the same spectral position. In the past years, we have tried to elucidate the physical picture behind the ROA spectrum [1820]. Though the method is semi-clas- sical, it does conveniently oer us a lot of information about ROA. The so-called intramolecular enantiomerism is such a result which shows that for a chiral molecule possessing a ring structure, as far as ROA is con- cerned, there may exist an approximate mirror symmetry on the ring such that the pair bonds related by the mirror reection will possess opposite signs for their dierential bond polarizabilities, just like that the right and left handed chiral molecules possess opposite signatures for their ROA spectra. In this work, we will demonstrate this behavior for pinane. But the purpose is not just for demonstration. Through its comparison with our previously obtained results of (-)α- and (-)β-pinene [10,11], we will nd out more their chiral behaviors and the role of the asymmetric centers from a spectroscopic viewpoint in a quantitative way. In the followings, we will rst address the experimental and briey introduce the algorithm for studying Raman/ROA intensities. This is followed by the results and discussion. Then, a conclusion is nalized. 2. Experimental The pinane sample was purchased from Aldrich Chemical Co Ltd. and used without further purication. The sample was held in a micro quartz uorescence sample cell. The ROA spectrum which covers from 700 cm -1 to 1800 cm -1 was taken by Biotool chiral Raman ROA Spectrometer excited by 532 nm laser with a focused power of 400 mW. The scattered circular polarization (SCP) conguration is adopted. The spectral resolution is about 7 cm -1 . In the experiment, depolarized in- cident laser is used and the intensity dierence in the right and left circularly polarized Raman scattered light is measured. The ROA Spectrometer can also generate the Raman spectrum. The experimental details have been published before [10,18]. The structure of pinane is simulated by Gaussian09 DFT B3LYP at the level of 6-311G+. It is shown in Fig.1 together those of (-)α-pinene and (-)β-pinene [11]. The Raman and ROA spectra of pinane together with those of (-)α-pinene and (-)β-pinene [11] are shown in Fig.2. https://doi.org/10.1016/j.vibspec.2019.102988 Received 17 September 2019; Received in revised form 31 October 2019; Accepted 4 November 2019 Corresponding authors. E-mail addresses: [email protected] (P. Wang), [email protected] (G. Wu). Vibrational Spectroscopy 106 (2020) 102988 Available online 15 November 2019 0924-2031/ © 2019 Elsevier B.V. All rights reserved. T

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Page 1: The Raman optical activity of pinane as compared with (-)α- and (-)β-pinene … · 2019. 12. 31. · (-)α-pinene. This leads to the decrease of ROA from (-)α-pinene, (-)β-pinene

Contents lists available at ScienceDirect

Vibrational Spectroscopy

journal homepage: www.elsevier.com/locate/vibspec

The Raman optical activity of pinane as compared with (-)α- and (-)β-pinene: The perspective of intramolecular enantiomerism

Hongru Yanga, Peijie Wanga,*, Guozhen Wub,*a The Beijing Key Laboratory for Nano-Photonics and Nano-Structure, Department of Physics, Capital Normal University, Beijing, 100048, Chinab State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, China

A R T I C L E I N F O

Keywords:Raman optical activity (ROA)Intramolecular enantiomerismDifferential bond polarizability(-)α-pinene(-)β-pinenePinane

A B S T R A C T

The Raman and Raman optical activity (ROA) spectra of chiral pinane were analyzed by a bond polarizabilityalgorithm. By the differential bond polarizability, the chirality of pinane is compared with our previous results of(-)α- and (-)β-pinene to show the intramolecular enantiomerism. The intramolecular enantiomerism implies theexistence of an approximate mirror symmetry. This symmetry is most destroyed by the on-ring CeC double in(-)α-pinene. This leads to the decrease of ROA from (-)α-pinene, (-)β-pinene to pinane. Variation of differentialbond polarizabilities also follows this trend. This comparison demonstrates the chiral behavior and the roles ofthe asymmetric centers of (-)α-, (-)β-pinene and pinane from a spectroscopic viewpoint.

1. Introduction

Raman optical activity (ROA) [1–9] can express the couplingsamong the vibrationally induced electric dipole and magnetic dipole/electric quadrupole [10,11]. These couplings are not of parity con-servation that for a chiral molecule, its Raman responses to the rightand left circularly polarized light are not identical. This leads to its ROAspectrum which is defined as the difference between these two spectralprofiles [12–17]. Experimentally, to a Raman profile, there correspondsan ROA profile with positive or negative signature at the same spectralposition.

In the past years, we have tried to elucidate the physical picturebehind the ROA spectrum [18–20]. Though the method is semi-clas-sical, it does conveniently offer us a lot of information about ROA. Theso-called intramolecular enantiomerism is such a result which shows thatfor a chiral molecule possessing a ring structure, as far as ROA is con-cerned, there may exist an approximate mirror symmetry on the ringsuch that the pair bonds related by the mirror reflection will possessopposite signs for their differential bond polarizabilities, just like that theright and left handed chiral molecules possess opposite signatures fortheir ROA spectra.

In this work, we will demonstrate this behavior for pinane. But thepurpose is not just for demonstration. Through its comparison with ourpreviously obtained results of (-)α- and (-)β-pinene [10,11], we willfind out more their chiral behaviors and the role of the asymmetriccenters from a spectroscopic viewpoint in a quantitative way. In the

followings, we will first address the experimental and briefly introducethe algorithm for studying Raman/ROA intensities. This is followed bythe results and discussion. Then, a conclusion is finalized.

2. Experimental

The pinane sample was purchased from Aldrich Chemical Co Ltd.and used without further purification. The sample was held in a microquartz fluorescence sample cell. The ROA spectrum which covers from700 cm−1 to 1800 cm-1 was taken by Biotool chiral Raman ROASpectrometer excited by 532 nm laser with a focused power of 400 mW.The scattered circular polarization (SCP) configuration is adopted. Thespectral resolution is about 7 cm-1. In the experiment, depolarized in-cident laser is used and the intensity difference in the right and leftcircularly polarized Raman scattered light is measured. The ROASpectrometer can also generate the Raman spectrum. The experimentaldetails have been published before [10,18].

The structure of pinane is simulated by Gaussian09 DFT B3LYP atthe level of 6-311G+. It is shown in Fig.1 together those of (-)α-pineneand (-)β-pinene [11]. The Raman and ROA spectra of pinane togetherwith those of (-)α-pinene and (-)β-pinene [11] are shown in Fig.2.

https://doi.org/10.1016/j.vibspec.2019.102988Received 17 September 2019; Received in revised form 31 October 2019; Accepted 4 November 2019

⁎ Corresponding authors.E-mail addresses: [email protected] (P. Wang), [email protected] (G. Wu).

Vibrational Spectroscopy 106 (2020) 102988

Available online 15 November 20190924-2031/ © 2019 Elsevier B.V. All rights reserved.

T

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3. Raman and ROA spectral intensity analysis

3.1. The algorithm to derive bond polarizabilities

The algorithm for deriving the bond polarizabilities from the Ramanintensities was proposed by Wu et al. [19]. It has been applied to sev-eral cases [20–25] and has revealed significant information of theRaman process. The Raman process is parametrized by ∂ ∂α( (t)/ Q )j ,which shows the response of the electronic charge to the nuclear mo-tion. α (t) is the molecular electronic polarizability, which is a measurehow loosely the charges in a molecule are bound to the nuclei and Qj isthe nuclear normal coordinate. α is also proportional to the amount ofcharges. (Of course, electronic polarizability is a tensor. However, atthis level of experiment, it is proper to treat it as a scalar. This treatmentis enough for our physical interpretation.) For retrieving the bondelectronic information of the Raman excited state, we have to derive∂ ∂α S( (t)/ )k for the bond coordinate Sk from ∂ ∂α( (t)/ Q )j if possible. Forbrevity, ∂ ∂α S( / )k is called the bond (stretch/bend) polarizability. Bondpolarizability is an indication of the disturbed charge in a bond co-ordinate during the Raman process.

The Raman intensity Ij of the j-th normal mode with wavenumber vjis related to ∂ ∂α Q( / )j through the formula by Chantry [26] :

∼ − ∂ ∂I I ν ν ν α Q( ) / ( / )j j j0 04 2

Here, I0 is the intensity of the exciting laser with wavenumber v0.Raman intensity Ij can be obtained from the experimental Raman sig-nals in the wavenumber domain.

From Chantry’s formula, we thus have

∑± ∝−

∂ ∂I Iν ν

νL α S

( )( / )j

j

jkj k0

02

by transforming Qj to the bond coordinates Sk’ s through:

∑=S L Qk kj j

which can be obtained from the normal mode analysis.By defining

=−

av v

vL

( )jk

j

jkj

02

we have the following matrix equation, if only relative intensities andbond polarizabilities are concerned:

⎢⎢⎢⎢

⎥⎥⎥⎥

=⎡

⎢⎢⎢

∂ ∂∂ ∂

∂ ∂

⎥⎥⎥

− − −

II

I

aα Sα S

α S

PP...P

[ ]//

.../

N N

jk

N

1 1

2 2

3 6 3 6

1

2

3 6

Here, the phase Pj is + or - which cannot be obtained from the ex-periment and needs determination.

The bond polarizabilities can be figured out if the above matrixequation is inverted and if the phases preceding the intensities can bedetermined. For the phase determination, various sets of { Pj } aretried to obtain ∂ ∂α( (t)/ S )k which are then checked with physical con-siderations to rule out the inadequate { Pj } sets. Often the matrixequation can be reduced to accommodate only those stretching and/orbending coordinates that are more coupled to each other.

3.2. The algorithm to derive the differential bond polarizabilities

For the ROA intensities, we have + =I I IjR

jL

j and − =I I ΔIjR

jL

j (Rand L stand, respectively, for the right and left circularly polarizedscatterings, ΔIj is the ROA spectrum.) or

= + = −I I ΔI I I ΔI( )/2, ( )/2jR

j j jL

j j

Furthermore, we have

Fig. 1. The structures of (-)α-pinene, (-)β-pinene and pinane. The approximatemirror is along C8-C6-C3. + and – are the signs of the differential bond po-larizabilities. See text for details.

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⎢⎢⎢

∂ ∂∂ ∂

∂ ∂

⎥⎥⎥

=

⎢⎢⎢⎢

⎥⎥⎥⎥

Δα SΔα S

Δα S

a

P I I

P I I

P I I

//

.../

[ ]

( )

( )...

( )t

jk

R L

R L

t tR

tL

1

2 1

1 1 1

2 2 2

Here, Δα is defined formally as −α αR L by ∂ ∂ −∂ ∂α S α S/ /Rk

Lk which are

related, respectively, to the intensities by the right and left circularlypolarized scatterings.

Consider

= + = + ≈ +I I ΔI I ΔI I I ΔI I2 [ (1 / ) ] [1 /2 ]jR

j j j j j j j j

= − = − ≈ −I I ΔI I ΔI I I ΔI I2 [ (1 / ) ] [1 /2 ]jL

j j j j j j j j

with error < ΔI I[ / ] /8j j2

then

− ≈I I ΔI I/jR

jL

j j

and

⎢⎢⎢

∂ ∂∂ ∂

∂ ∂

⎥⎥⎥

=⎡

⎢⎢⎢⎢

⎥⎥⎥⎥

Δα SΔα S

Δα S

a

P ΔI IP ΔI I

P ΔI I

//

.../

[ ]

( / )( / )

...( / )t

jk

t t t

1

2 1

1 1 1

2 2 2

Though Ij is much larger than ΔIj by an order of 103 to 104, therelative magnitudes of Ij 's and ΔIj 's can be treated independently asnot too small numbers. (For instance, they can be scaled to from 1 to100 in most cases.) By this way, ΔI I/j j can be treated as not too smallnumbers.

In summary, once the bond polarizabilities were obtained from ′I sj ,then together with the elucidated ′P sj and ′ΔI sj which are obtainedfrom the ROA experiment, relative ∂ ∂Δα S/ k can be obtained at hand.∂ ∂Δα S/ k can be called the differential bond polarizability, for con-venience. This molecular parameter is important for understanding theROA mechanism. We have to stress that the terminology for differentialbond polarizability is just formal. We note that this parameter is derived

from the experimental ROA intensity (and Raman intensity). Certainly,it will reflect the ROA effect due to the coupling between vibrationallyinduced electric dipole and magnetic dipole/electric quadrupole asgenerally recognized for ROA.

4. Results and discussion

In this bond polarizability analysis, we will neglect the C–H stretchand bending coordinates. (We note that for the moment, the commer-cial ROA spectrometer is unable to cover the spectral region up to 3000cm−1 where C–H stretch appears.) This of course leads to approxima-tion. However, this approximation is enough to serve our purpose asdemonstrated below. For pinane, there are 11 CeC bond stretches.Listed in Table 1 are the experimental and fitted mode wavenumbers(by the normal mode analysis, however, in which full coordinates in-cluding those of C–H stretch and bending are adopted), the Raman andROA intensities of the 11 modes, which are mainly due to the CeCstretching motion and are chosen for the bond polarizability analysis.

By the Raman mode intensities together with [Lkj] via normal modeanalysis, the bond polarizabilities can be obtained. The criterion for

Fig. 2. (A)(B)(C)and (D)(E)(F)are the Raman and ROA spectra of (-)α-pinene, (-)β-pinene and pinane, respectively. The peaks labeled by * are those employed for thebond polarizability and differential bond polarizability analyses. See text for details.

Table 1The experimental and fitted mode wavenumbers, the Raman and ROA modeintensities of pinane that are employed for the analysis. The values are nor-malized by setting those of the peak at 661 cm−1 as 100.

Experimental (cm−1) Fitted (cm−1) Raman intensity ROA intensity

1299 1296 6.3 01268 1272 13.1 01000 999 30.8 −22.8997 994 9.4 −16.6937 942 12.6 23.0917 912 13.3 −31.3873 875 10.9 2.5853 849 49.7 6.0819 815 31.9 −4.5779 774 10.4 0661 659 100 −100

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accepted phase set is that it leads to positive CeC bond (stretch) po-larizabilities. Once phase set is determined, together with Raman andROA intensities, the differential bond polarizabilities of CeC stretchingcoordinates can be obtained at hand. Though there are multiple ac-cepted phase sets, they lead to very consistent results and only the re-presented one is shown in Fig.3. Table 2 shows the differential bondpolarizabilities of (-)α-pinene, (-)β-pinene and pinane.

From these results, we may have the following observations.

(1) (-)α-pinene, (-)β-pinene and pinane share the common structurethat the mirror symmetry along C8-C6-C3 plane would be ratherstrict if there is no CeH moiety attached at C1 atom. So this at-tachment of CeH moiety causes the asymmetry that leads to ROA.The signs of the differential bond polarizabilities of the CeC bondsare shown in Fig.1. The opposition of the signs of the bonds relatedby the mirror reflection is obvious for these three species, demon-strating the intramolecular enantiomerism, so named since it is justlike that the right and left handed chiral molecules possess oppositesignatures for their ROA spectra and hence their correspondingdifferential bond polarizabilities. However, careful scrutiny shows aflaw in (-)α-pinene that the differential bond polarizabilities of itsC1-C7 and C4-C5 bonds are of the same sign. Apparently the doublebond at α position destroys the mirror symmetry so severely thatintramolecular enantiomerism is not obeyed here. The strict in-tramolecular enantiomerism in (-)β-pinene can be attributed to itsoff-ring CeC double bond. This shows that the mirror symmetry is

more broken in (-)α-pinene than (-)β-pinene, leading to more ROAof (-)α-pinene.

(2) The magnitude variation of the differential bond polarizabilities islargest for (-)α-pinene and least for pinane as shown in Table 2.This is in conformity with the previous assertion that the on-ringand off-ring positions of the double bond makes this variation. Theleast variation of pinane is obviously due to its lack of CeC doublebond. This implies that ROA decreases from (-)α-pinene, (-)β-pinene to pinane.

(3) Table 3 shows the differences of the differential bond polariz-abilities of the pair CeC bonds that are related by the mirror re-flection in (-)α-pinene, (-)β-pinene and pinane. The chiral centersare C5 and C7 atoms. This difference for the pair bonds that arecloser to the centers will be larger, showing more significant ROA.Indeed, the difference for the pair C1-C3 and C3-C4 is the least (orclose to the least in (-)β-pinene) than other pair bonds that areconnected to C5 and C7.

As the mirror symmetry is less destroyed, less ROA and smaller thisdifference for the pair CeC bonds will be. (Recall that as the mirrorsymmetry is strict, the molecule will be achiral and there will be noROA and this difference will be zero.) Indeed, Table 3 shows that from(-)α-pinene, (-)β-pinene to pinane, this difference follows a decreasingtendency. This is in conformity with the decrease of ROA from (-)α-pinene, (-)β-pinene to pinane as was asserted.

5. Concluding remarks

Our intensity analysis offers an interpretation for the ROA spectrum.The differential bond polarizability characterizes well the chirality of(-)α-pinene, (-)β-pinene and pinane. The intramolecular enantiomerismimplies the existence of an approximate mirror symmetry in thesemolecules. This symmetry is most destroyed by the on-ring CeC doublein (-)α-pinene. This leads to the decrease of ROA from (-)α-pinene, (-)β-pinene to pinane. Variation of differential bond polarizabilities alsofollows this trend.

The differential bond polarizability difference for the pair bondsthat are related by the mirror reflection is larger as it is closer to theasymmetric center, leading to larger ROA. This characterizes the role ofthe asymmetric center from a spectroscopic viewpoint in a quantita-tively way. We note, in general, this asymmetry is but mentioned from ageometric viewpoint: the non-superimposability of the mirror imagesaround the asymmetric atom, or equivalently, that the four bondsconnected to the asymmetric carbon atom are different. Differentialbond polarizability puts this on a spectroscopically significant ground.

Declaration of Competing Interest

We have no Conflict of Interest.

Acknowledgements

This project is supported by the National Natural ScienceFoundation of China (No. 21473115; 21872097.) and the ScientificResearch Base Development Program of the Beijing Municipal

Fig. 3. The differential bond polarizabilities of (-)α-pinene, (-)β-pinene andpinane.The values of C5-C8 are normalized to 1. See text for details.

Table 2The differential bond polarizabilities of (-)α-pinene, (-)β-pinene and pinane.The values are normalized by setting those of C5-C8 as 1.

bond (-)α-pinene (-)β-pinene pinane

C1-C2 −15.1 1.25 −2.4C1-C3 0.44 3.5 0.6C1-C7 −25.5 −1 2.2C3-C4 −7.0 −4.2 −1C4-C5 −2.1 2.2 −1.6C5-C6 10.6 3.2 1.4C5-C8 1 1 1C6-C7 −3.2 −3.7 −3C7-C8 −27 −4.5 −1.8C8-C9 −17.8 1.5 −2.4C8-C23 −19.6 −2.5 8.8

Table 3The differences of the differential bond polarizabilities of the pair CeC bondsthat are related by the mirror reflection in (-)α-pinene, (-)β-pinene and pinane.

bonds (-)α-pinene (-)β-pinene pinane

C1-C3 and C3-C4 6.6 0.75 0.4C4-C5 and C1-C7 23.4 1.2 0.6C5-C6 and C6-C7 7.4 0.5 1.6C5-C8 and C7-C8 26 3.5 0.8

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Commission of Education. Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds (No.025185305000/184/205).

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