Expressions for the interpretation of circular intensity differential scattering of chiral aggregates

The derivation of compact expressions of the circular intensity differential scattering (CIDS) of chiral molecules is presented in the first Born approximation of the fields. The expressions derived are valid for a suspension of scattering chiral particles free to adopt any orientation in solution. The connection is established between the preferential scattering cross section for right‐ vs left‐circularly polarized light for a given scattering angle and the geometrical parameters of the molecule. As observed experimentally, the equations predict that the circular differential scattering patterns must show as a function of the scattering angle a series of lobes of alternating sign. In between these lobes, zeros in the differential scattering cross section occur. For the case of two dipole moments arranged in chiral fashion, an expression is derived that shows how the relative arrangement of the dipoles and their separation relative to the wavelength of light control the number and the position of the zeros. A compact expression predicting the CIDS of a sample for very small angles of scattering is derived for a system of helices whose dimensions are small compared with the wavelength of light. Finally, the presence of CIDS in a sample is related to the appearance of anomalous signals in the CD spectrum of chiral systems. Expressions and computations of the magnitudes and sign of the anomalies are presented. The expressions obtained confirm the main features of the experimental CIDS patterns of chiral molecules previously published.

[1]  I. Tinoco,et al.  Circular intensity differential scattering of light by helical structures. II. Applications , 1980 .

[2]  I. Tinoco,et al.  Circular intensity differential scattering of light. IV. Randomly oriented species , 1982 .

[3]  C. Bustamante.  Contribution of differential scattering of circularly polarized light to the optical rotatory dispersion of a sample. , 1984, Journal of the Optical Society of America. A, Optics and image science.

[4]  N. Holzwarth,et al.  Circular dichroism and rotatory dispersion near absorption bands of cholesteric liquid crystals , 1973 .

[5]  I. Tinoco,et al.  The optical activity of nucleic acids and their aggregates. , 1980, Annual review of biophysics and bioengineering.

[6]  M. Maestre,et al.  Contribution of light scattering to the circular dichroism of deoxyribonucleic acid films, deoxyribonucleic acid-polylysine complexes, and deoxyribonucleic acid particles in ethanolic buffers. , 1980, Biochemistry.

[7]  D. Urry,et al.  Differential scatter of left and right circularly polarized light by optically active particulate systems. , 1970, Proceedings of the National Academy of Sciences of the United States of America.

[8]  I. Tinoco,et al.  Differential scattering (CIDS) of circularly polarized light by dense particles , 1984 .

[9]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[10]  S. Edmondson,et al.  Circular dichroism and fluorescence-detected circular dichroism of deoxyribonucleic acid and poly[d(A-C).d(G-T)] in ethanolic solutions: a new method for estimating circular intensity differential scattering. , 1980, Biochemistry.

[11]  R. Gregory,et al.  The differential scattering of circularly polarized light by chloroplasts and evaluation of their true circular dichroism. , 1974, The Biochemical journal.

[12]  Charles Tanford,et al.  Physical Chemistry of Macromolecules , 1961 .

[13]  M. Diem,et al.  Optical activity in vibrational transitions: vibrational circular dichroism and Raman optical activity , 1979 .

[14]  I. Tinoco,et al.  Circular intensity differential scattering of light by helical structures. I. Theory , 1980 .

[15]  I. Tinoco,et al.  Circular differential scattering can be an important part of the circular dichroism of macromolecules. , 1983, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Ignacio Tinoco,et al.  Differential scattering of circularly polarized light by the helical sperm head from the octopus Eledone cirrhosa , 1982, Nature.

[17]  J. S. Cohen.  Structural molecular biology: edited by David B. Davies, Wolfram Saenger and Steven S. Danyluk, Plenum Press, 1982. $65.00 (USA and Canada) $78.00 (elsewhere) (x + 530 pages) ISBN 0 306 40982 8 , 1983 .

[18]  I. Tinoco,et al.  Circular dichroism in samples which scatter light , 1983 .

[19]  I. Tinoco,et al.  Circular intensity differential scattering of light by helical structures. III. A general polarizability tensor and anomalous scattering , 1981 .

[20]  M. Maestre,et al.  Experimental differential light-scattering correction to the circular dichroism of bacteriophage T2. , 1973, Proceedings of the National Academy of Sciences of the United States of America.

[21]  A. S. Schneider,et al.  Angular scattering analysis of the circular dichroism of biological cells. 2. The red blood cell. , 1976, Biochemistry.

[22]  F. C. Chen,et al.  Dyamics of calf‐thymus DNA by single‐clipped photon correlation , 1977 .

[23]  R. Pecora.  Dynamic Light Scattering , 1985 .