Raman Optical Activity of Biological Samples
In this Chapter, the fundamentals and instrumentation of vibrational Raman optical activity are briefly presented. Next, we describe selected examples of successful applications of computational approaches to the analysis of ROA spectra of biomolecules sh
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Raman Optical Activity of Biological Samples Katarzyna Chruszcz-Lipska and Ewan W. Blanch
Abstract In this Chapter, the fundamentals and instrumentation of vibrational Raman optical activity are briefly presented. Next, we describe selected examples of successful applications of computational approaches to the analysis of ROA spectra of biomolecules showing that such calculations are an important aspect of this incisive structural technique. Keywords Chirality • Raman optical activity (ROA) • Theoretical calculations • Two-dimentional correlation analysis • Data clustering techniques • Terpenes • Carbohydrates
4.1 Introduction to the Theory of Raman Optical Activity The fundamental scattering mechanism responsible for ROA was discovered in 1969 by Peter W. Atkins and Laurence D. Barron [1]. These researchers found that interference between light waves scattered via the molecular polarizability and optical activity tensors of a molecule leads to a dependence of the scattered light intensity on the degree of circular polarization of the incident light and also to a circular component in the scattered light. Barron along with A.D. Buckingham [1–12] subsequently published a more definitive version of the original theory in which they also introduced as an experimental observable a quantity they called the dimensionless circular intensity difference (CID), which was defined as: (4.1) ∆ (I R I L ) / (I R I L )
K. Chruszcz-Lipska () Jagiellonian Centre for Experimantal Therapeutics, Jagiellonian University, Bobrzyńskiego 14 Str., 30-348, Kraków, Poland e-mail: [email protected] E. W. Blanch Manchester Institute of Biotechnology and Faculty of Life Sciences, The University of Manchester, 131 Princess Street, M1 7DN, Manchester, UK M. Baranska (ed.), Optical Spectroscopy and Computational Methods in Biology and Medicine, Challenges and Advances in Computational Chemistry and Physics 14, DOI 10.1007/978-94-007-7832-0_4, © Springer Science+Business Media Dordrecht 2014
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K. Chruszcz-Lipska and E. W. Blanch
where I R and I L are the scattered Raman intensities in right- and left-circularly polarized incident light, respectively. CID expressions for forward (0°) and backward (180°) scattering geometries from an isotropic sample for incident transparent wavelengths much larger than the molecular dimensions can be expressed in terms of the electric dipole–electric dipole molecular polarizability tensor, α , and the αβ electric dipole–magnetic dipole and electric dipole–electric quadrupole optical activity tensors, G ′ and A , respectively [13, 14], as [13]: αβ
αβγ
∆(0° ) =
4[ 45αG ′ + β(G ′)2 − β( A)2 ] c[ 45α + 7β(α) ] 2
°
∆(180 ) =
2
,
1 β( A)2 3 , c 45α 2 + 7β(α)2
24β(G ′)2 +
(4.2a)
(4.2b)
where the isotropic invariants of these quantities are defined as
α=
1 α , 3 αα
(4.3a)
G′ =
1 G′ , 3 αα
(4.3b)
while the anisotropic invariants are defined as
β(α)2 =
1 (3ααβ ααβ − ααα αββ ), 2
(4.4a)
β(G ′)2 =
1 (3ααβ Gαβ ′ − ααα Gββ ′ ), 2
(4.4b)
1 ωα ε A . 2 αβ αγδ
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