Chapter 13
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X-ray Natural Circular Dichroism: Theory and Recent Developments Brian Stewart Department of Chemistry and Chemical Engineering, University of Paisley, Paisley PA1 2BE, Scotland, United Kingdom
A theoretical model is described for the origins o f natural circular dichroism (XNCD) in X-ray pre-edge and near-edge ( X A N E S ) photoabsorption. The predominant contribution results from the interference between the electric dipole and electric quadrupole transition moments (E1-E2 mechanism) and gives rise to orientation-dependent C D . For the photoelectron continuum absorption, a chiral multiple¬ scattering approach successfully acounts for the X A N E S C D of rare-earth L edge absorption in enantiomorphic single crystals. The same approach successfully treats gyrotropic single crystal X N C D where individually achiral units are arranged helically. Ab-initio Gaussian orbital calculations have been extended to treat core-valence C D and are able to account for the large pre-K edge C D seen in 2[Co(en) Cl ].NaC1.6H O. 3
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© 2002 American Chemical Society
In Chirality: Physical Chemistry; Hicks, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 2002.
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Introduction Since the days of Pasteur, the importance of mirror image properties of matter have been recognized as playing a key role in the structure of biomolecules and their discriminatory interactions. Physical techniques giving molecular chirality information have been developed using the differential interaction of circularly polarized radiation with chromophores in the visible, near and vacuum ultraviolet, the near infrared and the vibrational infrared spectral regions. Recently these techniques have been extended to the X-ray region (1,2) due to the development of high-brilliance synchrotron sources with insertion devices capable of delivering well-defined and high circular polarization rates. This article describes some of the developments in the theory of natural C D in the X-ray region where, by extending the well-developed analytical tools for X-ray near-edge absorption features, element-specific information about local chirality may be obtained. The extremes of the electromagnetic spectrum have been less accessible for instrumental reasons (see preceeding chapter). Additionally however, there are sum rules and dimensional arguments which suggest that the C D effect is expected to decrease in magnitude for very long or very short wavelengths in comparison to the scale of a chiral molecular structure. More accurately, the characteristic excitation length should be considered. This is especially relevant in the vibrational IR where wavelengths are very large in comparison to the characteristic length of localized vibrational excitations. The Condon-Eyring sum rule for optical activity:
implies that optical rotation vanishes at very low and very high energies relative to the excitation energies of the electronic system. However, this does not mean that circular dichroism is necessarily small at these extremes. In particular, in the X-ray region, the interaction with quadrupole transition moments is enhanced when the dimensions of the electronic displacement are comparable to the wavelength of the radiation (breakdown of the dipole approximation). This allows substantial C D to be derived from the E1-E2 mechanism (see below). This situation pertains to the near-edge absorption ( X A N E S ) where multiple scattering of the photoelectron by near neighbour atoms is largely responsible for the structure of the absorption profile. In the present work, it is also relevant to pre-edge excitations with effectively pure quadrupole character (eg ls-3d in the transition metals and 2p-4f in the lanthanides).
In Chirality: Physical Chemistry; Hicks, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 2002.
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Photon-molecule interactions
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Absorption The quantum mechanical approach to light absorption (3) involves evaluating matrix elements of a radiation-molecule interaction operator between initial and final states, subject to the conservation of energy. The cross section for a photon absorption process in which there is an electronic transition from an initial state Re {
