Nagao Kobayashi is in the Department of Chemistry, at the Graduate School of Science, Tohoku University, Sendai, Japan. He received his D.Sc. on the magnetic circular dichroism (MCD) of catalase and peroxidase in 1978 and a second Dr. of Pharmacy degree on the electrocatalytic reduction of oxygen using water-soluble porphyrins and phthalocyanines in 1986 from Tohoku University. He has written papers for the journals – JACS, Angew. Chem. and the Chem. Eur. J. and has had a large number of papers published in other high impact factor journals such as Inorg. Chem.,J. Phys. Chem. and Chem. Commun. Overall he has authored about 300 original research papers and has written more than 20 book chapters and reviews on the synthesis and spectroscopy of porphyrins, phthalocyanines, and cyclodextrins. In 2006, he received a Chemical Society of Japan Award for Creative Work in the Field for research involving CD and MCD spectroscopy. The core focus of his research has been the use of electronic absorption, CD and MCD spectroscopy and electrochemical methods to study metal porphyrinoid complexes. Atsuya Muranaka is at the Institute of Physical and Chemical Research (Riken), Wako-shi, Saitama, Japan. He received his B.Sc. degree from Tohoku University in 1999 and received a Ph.D. degree on the CD and MCD studies of oligomeric porphyrins and phthalocyanines from the same university in 2006. Since June 2004, he has been an assistant professor initially working with Prof. N. Kobayashi at Tohoku University and then, since August 2007, with Prof. Masanobu Uchiyama at RIKEN. He was awarded poster prizes during the International Conferences on Circular Dichroism in 2003 and 2007. In 2003-2004, he spent a year as a visiting researcher in the laboratory of Prof. Arnout Ceulemans at the Katholieke Universiteit Leuven in Belgium after receiving funding from the university as a distinguished PhD course student. His current research interests lie in the synthesis, spectroscopy and theoretical studies of porphyrinoids and various element-containing aromatic molecules. He has published many original research papers in high impact journals such as J. Am. Chem. Soc., Chem. Commun., Inorg. Chem., J. Phys. Chem., J. Org. Chem and Chem. Eur. J.

Circular Dichroism and Magnetic Circular Dichroism Spectroscopy for Organic Chemists

By Nagao Kobayashi, Atsuya Muranaka, John Mack

The Royal Society of Chemistry

Copyright © 2012 Royal Society of Chemistry
All rights reserved.
ISBN: 978-1-84755-869-5

Contents

Abbreviations, xv,
Chapter 1 Theory of Optical Spectroscopy, 1,
Chapter 2 Empirical Rules in CD Spectra and Absolute Configuration of Molecules, 42,
Chapter 3 Representative Systems Analysed by the Exciton Coupling Method, 53,
Chapter 4 Cyclodextrin Inclusion Compounds, 93,
Chapter 5 Metal Complexes, 104,
Chapter 6 Circular Dichroism Induced by Optically Active Binaphthyl, 116,
Chapter 7 Analysis of Chiral Systems by Theoretical Calculations, 130,
Chapter 8 Circular Dichroism of Biomolecules, 142,
Chapter 9 Analysis of MCD Spectra, 150,
Chapter 10 Michl’s Perimeter Model in MCD Spectroscopy, 172,
Subject Index, 192,

CHAPTER 1

Theory of Optical Spectroscopy

1.1 Electronic Absorption Spectroscopy

Optical spectroscopy is based ultimately on the interaction between atoms or molecules and incident electromagnetic radiation. In the 1860s, a Scottish physicist called James Clerk Maxwell first postulated that an oscillating electric field generates an oscillating magnetic field and vice versa. A propagating sinusoidal electromagnetic wave can be formed on this basis, with electric and magnetic fields oscillating perpendicular to one another and to the direction of propagation. Electromagnetic radiation exhibits both wave properties and particle properties and was described successfully by Albert Einstein in quantum mechanical terms as a particle, referred to as a photon (hv), which has no mass or charge. At longer wavelengths in the IR region (> 1000 nm) the interaction between the atomic nuclei and the oscillating electric and magnetic fields typically results in molecular vibrations, which can be studied by infrared spectroscopy. At shorter wavelengths the heavier nuclei can no longer oscillate significantly, but the surrounding cloud of electron density can still be polarised in the direction of the oscillating electron field, resulting in an electronic transition from a groundstate electron configuration to an excited state. UV-visible absorption spectroscopy can be used to derive key information about the electronic structures of molecules on this basis, while techniques such as fluorescence spectroscopy can be used to derive information from the manner in which the molecule returns to its groundstate configuration.

As shown in Figure 1.1, molecular orbital theory can be used to describe this electronic excitation on the basis of the transfer of an electron from an occupied molecular orbital to an unoccupied molecular orbital. The energy difference between the ground and excited states (ΔE) is proportional to the frequency of the absorbed electromagnetic radiation (v):

ΔE = hv = hc/λ (1.1)

where h is the Planck constant (h = 6.626 × 1034 J s), and c and λ denote the velocity of light (c = 2.998 × 108 m s-1) and the wavelength, respectively. Especially in the context of organic molecules, absorption in a particular region of the spectrum is often characteristic of a transition that is associated primarily with a particular type of bond or structural unit within a molecule. These structural units are usually referred to as chromophores. In the context of saturated organic molecules, wavelengths much shorter than 200 nm are required to cause electronic transitions. Since the conventional use of UV-visible absorption spectrometers under an air atmosphere tends to be limited to 200 nm, owing to strong absorption by oxygen and ozone formation at shorter wavelengths, electronic absorption spectroscopy is applied primarily to the π-systems of organic molecules and inorganic metal complexes, which absorb strongly at wavelengths > 200 nm, with a particularly strong focus on aromatic and heteroaromatic cyclic compounds.

The interaction of UV or visible region light (typically 200–750 nm) with a molecule or complex can result in an electronic excitation from one molecular orbital to another, resulting in a transition from the groundstate electronic configuration to an excited state, Figure 1.1. This inherently results in a rearrangement of the electron density of a molecule. Since the size of molecules and complexes will typically be a few orders of magnitude smaller than the wavelength of UV-visible light, the electric field induces an oscillating electric dipole moment upon absorption of a photon. An electric dipole transition moment (edtm), µ, can be defined for each transition, which describes the net linear displacement of charge during a transition. The initial point of this vector is set to the centre of gravity of the molecule, and the square of the transition dipole moment is proportional to the intensity of the electronic transition. If a transition is dipole forbidden, µ = 0, while a transition is said to be allowed if µ > 0. The direction in which l is aligned determines the polarisation of the associated spectral band with respect to the x-, y– and z-axes. It should be noted that edtms are different from static electric dipole moments (also known as permanent dipole moments), which describe the polarisation of charge in a molecule in the groundstate, Figure 1.2. The direction of a static dipole moment can be determined definitively on the basis of the molecular structure. In contrast, since a transition dipole has an oscillating property, the choice of the sense of a transition dipole moment is arbitrary and depends on the phase of the wavefunctions. A magnetic dipole transition moment (mdtm), m, can also be defined for each electronic transition, which describes the net circulation of charge during a transition, Figure 1.3. The edtms are usually the dominant factor in coupling the groundstate with excited states within UV-visible absorption spectroscopy, since they tend to be ca. five orders of magnitude stronger than magnetic dipole moments. It should be noted that this is not the case during the quantitative analysis of CD spectral data, since the intensity mechanism is based on an interaction between electric and magnetic dipole transition moments. Sections 2.2 and 5.2 describe the analyses of carbonyl n -> π* transitions in organic molecules and the d -> d transitions of transition metal complexes, which are magnetic dipole allowed but electric dipole forbidden.

Group theory can be used to determine whether transitions are electric dipole and magnetic dipole allowed or forbidden and the polarisation of the spectral bands, which arise in the UV-visible absorption spectrum based on the value of the transition moment integral:

[MATHEMATICAL EXPRESSION OMITTED] (1.2)

where ψ1 and ψ2 are the wavefunctions of the ground and excited states, respectively, and µ is the transition moment operator, which transforms in different ways along the x-, y– and z-axes depending on the point group. The symmetry characteristics of each component can be obtained from standard character tables based on the point group to which the molecule or complex belongs. If the value of this integral is zero, the transition is forbidden. The integral itself does not need to be calculated, since character tables can be used to determine the symmetry of the transition moment function, ψ1 µ ψ2. If the symmetry of this function spans the totally symmetric representation of the relevant point group, the value of the integral is nonzero and the transition is electronically allowed. If not, although the transition is electronically forbidden it may still gain significant intensity under certain circumstances based on vibronic interactions with close-lying allowed transitions.

In UV-visible absorption spectra, either absorbance (A) or molar absorptivity (ε) are usually used as the y-axis unit for intensity, while either a wavelength (λ) or a wavenumber (cm-1) scale is used to plot the x-axis. A wavelength scale tends to be the norm in the literature. It is important to bear in mind that this is inversely proportional to an energy scale, however. Some authors prefer to use a wavenumber scale for the x-axis, so that the relative energies of the spectral bands can be visualised readily. Absorbance (A) is defined to be the logarithm of the ratio of the incident (I0) and transmitted (I) radiation.

A = log10(I0/I) (1.3)

The relationship between A and ε (mol l-1 cm-1) is described by BeerLambert’s law:

A = εcl (1.4)

where c is the concentration of the molecule, expressed in mol. l-1 and l is the pathlength in cm.

A key question that needs to be addressed in any detailed analysis of not just the UV-visible absorption spectrum, but also the CD and MCD properties, is the extent to which a particular transition will absorb incident radiation, and why. In some instances molar absorptivities can be very large, for example those of the electric dipole allowed π -> π* bands associated with the π-conjugation systems of aromatic compounds (> 10 000), but in others, such as bands arising from the d -> d transitions of metal complexes, which are electric dipole forbidden (ca. 100), they are very small. The overlap of the orbitals involved in the electronic excitation is often a key factor in this regard. A typical absorption spectrum is shown in Figure 1.4. The absorption band with a λmax value of about 300 nm is associated with the HOMO (π) -> LUMO (π*) transition and is polarised parallel to the long axis of the molecule. Since the energy gap between the HOMO and LUMO decreases with increasing π-delocalisation, the electronic spectra of organic molecules often provide an indication of the size of an aromatic or heteroaromatic π-system and its degree of delocalisation. Conjugated systems such as anthocyanins, carotenoids and chlorophylls have relatively small HOMO–LUMO band gaps and are strongly coloured because they absorb in the visible region.

With the recent development of commercially available software packages time-dependent density functional theory (TD-DFT) calculations can now be carried out routinely, so experimental spectral data can usually be compared readily to a calculated spectrum and, at least in the case of smaller molecules, bands can often be assigned to specific electronic transitions on this basis. For larger complexes and molecules, TD-DFT calculations typically only provide a reliable description of absorption bands in the lower energy region of electronic absorption spectra, because there tends to be extensive configuration interaction between the electronic states in the higher energy region. This means that the main focus of quantitative analyses often tends to be the CD and MCD signals associated with the lower energy transitions. It is not possible to calculate εmax values based on TD-DFT, because the spectral bands associated with each transition vary markedly in width in a manner that cannot be readily predicted, owing to the excitation of molecular vibrations and the effect of Heisenberg uncertainty on the lifetime of the excited states. Theoretical approaches, therefore, tend to focus on the integrated intensity of the entire spectral band rather than the ε value at a discrete wavelength. When the absorption spectrum is plotted using wavenumber units, the total absorption under a band can be expressed as an integral based on an energy rather than a wavelength scale:

[Florin] = 4.32 × 109 ∫ εdv (1.5)

Integration (dv) over the entire spectral band results in an oscillator strength value, [Florin], which provides a measure of the probability that a molecule will absorb incident electromagnetic radiation over a certain energy range. The oscillator strength can be approximated by viewing the spectral band as a triangle:

[Florin] ≈= 4.32 × 109 εmax Δv1/2 (1.6)

by multiplying the εmax value at the band centre by the width of the band at half height, Δv1/2. Calculations of the UV-visible absorption spectra based on density functional theory (DFT) typically provide oscillator strength values, [Florin], for each spectral band, since the oscillator strength values are related to the transition dipole moments and hence can be calculated from the wavefunction of the molecule.

A related unit referred to as the dipole strength, D, based on the square of the edtm, is sometimes used instead:

[MATHEMATICAL EXPRESSION OMITTED] (1.7)

where F is a factor that depends on the units used and conventions followed. In the context of MCD spectroscopy, we recommend the use of a definition proposed by Piepho and Schatz, which is denoted as D0, for reasons that will be described in Section 1.3.3:

[MATHEMATICAL EXPRESSION OMITTED] (1.8)

where D0 is expressed in (Debye) units (D2), vmax is the band centre energy in cm-1 and