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Circular Dichroism (CD) is a technique used to determine the differential absorption of left and right circularly polarized light. . This phenomenon is exhibited in the region of electronic absorption between 10-700 nm for an optically active molecule. CD is used to decipher the structure of macromolecules in different disciplines of Chemistry. The French physicist Aime Cotton first discovered the phenomenon of CD in 1896 with his research on transition metals.

Circular Polarized Light
Linearly polarized light consists of two circularly polarized components of equal magnitude. In both components the electric or magnetic vector rotates about the direction of propagation. If the tip of the electric field vector could be viewed as it propagates it would be in the form of a helix. Circularly polarized light is termed as right-handed when the observer is looking at the light source and the electric or magnetic vector rotates clockwise. It is termed as left-handed when the observer is looking at the light source and the electric or magnetic vector rotates counterclockwise.

Interaction of Circularly Polarized Light with Matter
When circularly polarized light passes through an absorbing optically active matter, the speed of the right and left circularly polarized rays are different ( cL≠ cR). Because the two rays travel at different speeds this lead to the wavelengths of the rays also being different (λL≠ λR). The two circularly polarized rays are therefore absorbed to a different extent (εL≠ εR). The difference between the two absorptions (Δε = εL - εR) is called circular dichroism.

Since polarized light itself is "chiral", it interacts differently with chiral molecules. That is, the two types of circularly polarized light are absorbed to different extents. In a CD experiment, equal amounts of left and right circularly polarized light of a selected wavelength are alternately radiated into a (chiral) sample. One of two polarizations is absorbed more than the other one, and this wavelength-dependent difference of absorption is measured, yielding the CD spectrum of the sample. Due to the interaction with the molecule, the electric field vector of the light traces out an elliptical path after passing through the sample.

Molar Circular Dichroism
Molar circular dichroism (Δε) is defined as the difference between the two molar absorption coefficients for left-circularly polarized light (LCPL) and right-circularly polarized light (RCPL).

Δε = εl - εr

The molar absoption coefficient for unpolarized light is the average of εL and εR.

Δε=(εl + εr)/2

This value is used to determine the anisotropy factor or dissymmetry factor.

g = Δε/ε = 2(εl - εr)/(εl + εr)

This value is used to measure how difficult it is to measure the CD in the region of a given absorption band. This is due to the fact that Δε/ε is proportional to the signal to noise ratio. The anisotropy factor is usually around 10-4 and is rarely larger than 10-2.

Absorption
The absorption of unpolarized light is defined by the following equation

A = log(Io/I)

where Io is the intensity of the incident light and I is the intensity after the light has traveled distance l. According to the Beer's law, if the absorbing species has a molar concentration c and the sample has a thickness l, then the absorption is:

A = εcl

All commercially available CD instruments measure ΔA = Al - Ar. This is then converted to Δε by Δε = (Al - Ar)/cl.

Molar Ellipticity
Many CD instruments are calibrated in terms of molar ellipticity. Molar ellipticity is an angular measurement which is related to ΔA by θ = 32.98 ΔA it is defined as [θ] =(100θ)/(lc) = 3,298 Δε

The units are in degrees cm2/dmol.

Interpretation
The interpretation of a CD spectrum is similar to that of an electronic absorption spectrum because they are exciting in the spectral region. Since CD is absorbing left and right polarized light the bands can be either positive or negative. The simplified spectra to the right offers a visual of this phenomenon.

Band Analysis in Coordination Compounds
Ligand-metal-charge-transfer (LMCT) transitions are often observed at low energies if the metal is in a relative high oxidation state, CoIII, FeIII, NiIV, and CuII with oxo or halide ligands or in CrVI or MnVII in complexes such as CrO42- or MnO4-.

Metal-ligand-charge-transfer (MLCT) transitions are often observed at low energies if the metal is reducing and the ligand offering a low lying empty orbital. Organometallics with metals in a low oxidation state and π-accepting ligands such as Pt-olefin complexes or iron-η4-diene complexes. Other MLCT transitions are occurring in CuI, AgI, RhII, and PtII complexes with conjugated ligands such as bpy or phen.

Metal-metal-charge-transfer (MMCT) transitions occur only in the absorption of polynuclear complexes or metal clusters. Only rare cases of enantiomerically pure complexes are known to display MMCT.

Coordination compounds with two or more very similar strong ligand chromophores arranged in a chiral configuration will have a CD spectra with electric dipole transition moments coupling with each other by a dipole-dipole interaction. Examples of this exciton theory can be seen with tris complexes Co(en)33+ and Co(ox)33-. The CD spectrum will have two bands with opposite sign separated by an energy of the order V12.

V12 = (1/4πε0)(μ2/r12)(sin2α(cosγ - 2) + 2)

Transition Metals
The use of CD with transition metal complexes can provide information on both the origin of the optical activity, the electronic, and geometric structure of chiral molecules. Two bands that are not resolved in the ordinary electronic absorption spectrum can often be separate in a CD spectrum. This characteristic is sometimes due to the difference in selection rules, magnetic-dipole-allowed transitions appear strongly in CD spectra, or because the sign of CD peaks depend on the handedness of the molecule. For the spectra shown here, the electronic coupling element, J, and an energy shift, ΔED, cannot be calculated from the absorption spectrum. The one-exciton model should consist of two absorption bands corresponding with the excited state coupling, and these two bands should be split by an amount of ΔΕ = 2|J|. No clear double band structure can be seen, but with the CD spectrum the double band pattern is seen. The coupling element can also be deduced with the CD spectrum.

Theoretical Approaches
Using theory to help interpret the CD spectra of chiral metal complexes has become a popular strategy as of recently. A preliminary calculated DFT-based CD spectrum of [Ru(bipy)3]2+ has been previously published, but most other first-principles studies are focused on organic molecules because of the best preforming ab initio methods out of range for large molecules. Time-dependent density functional theory (TD-DFT) has been used by Autschbach et al. to compute CD spectra of various Co(III) complexes as well as [Rh(en)3]3+. The same authors have also extended the analysis of the optical activity in the d-d and LMCT transition regions to a larger series of chiral metal complexes. . In most TD-DFT studies the agreement with experimental values was found to differ by a factor of 2 for weak CD intensities, and for more intense charge transfer transitions the calculated values have been even more accurate. The experimental and simulated CD spectrum for this osmium structure have been fully interpreted by Le Guennic et al.. Starting at the low energy section of the CD spectrum the α, β, and γ bands are mainly due to the metal-ligand-charge-transfer (MLCT) from the Os d-orbitals to the phenanthroline π* orbitals. The δ band is less specific, with many contributions of varying character. The ε, ζ, and θ bands are dominated be the phenanthroline's π to π* transition. The very intense circular dichroism of the E/F pair due to the exciton coupling mechanism. The rest of the bands that are higher lying in energy again have MLCT character.

Biological
In general, circular dichroism will be exhibited in absorption bands of any optically active molecule. Therefore it is exhibited by biological molecules because of their dextrorotary and levorotary components. Even more important is that a secondary structure will also impart a distinct CD to its respective molecules. Therefore, the alpha helix of proteins and the double helix of nucleic acids have CD spectral signatures representative of their structures. In most biological studies the CD signals are very small. The ellipticities are usually in the range 10 mdeg which corresponds to an absorbance difference in the order of 3x10-4. Because of the small signals it is important to pay attention to experimental conditions in order to ensure that meaningful data is obtained.

Proteins
There is a growing realization of the need to perform structural studies under the conditions in which proteins actually operate (i.e., generally in solution), as well as under other conditions and to provide measures of the rates of structural changes of proteins, which are often essential to their biological function. Circular dichroism (CD) has become increasingly recognized as a valuable structural technique for addressing these issues.

An advantage of circular dichroism in the studies of proteins is that complementary structural information can be obtained from a number of spectral regions. Proteins have a number of groups, which have characteristic absorption bands in areas of the visible and ultraviolet regions. These groups are called chromophores. The chromophores of interest include the peptide bond (absorption below 240 nm), aromatic amino acid side chains (absorption in the range 260 to 320 nm) and disulphide bonds (weak broad absorption bands centered around 260 nm). The secondary structure of proteins have distinctive CD spectra in the far-UV. CD spectra can be readily used to estimate the fraction of a molecule that is in the alpha-helix, beta-sheet, beta-turn, or unordered conformations. The most characteristic spectrum is of the α helix. Spectra of the α helix show two negative bands that have similar magnitudes near 222 and 208 nm. It also shows a positive band near 190 nm. The α helix CD spectrum is nearly independent of the nature of the side chains, except with peptides containing a large fraction of aromatic residues. The CD spectrum of the β-sheet is less intense. It shows two negative bands near 217 and 180 nm. It also shows a positive band around 195 nm. There is a greater variability for the CD spectra for the β-sheet than the α helix. The β-sheet CD spectrum varies depending on the side chains, solvent, and other environmental factors. This is due to the fact that β-sheets can be antiparallel, parallel, or mixed. The CD spectra of the β-turn occurs over a wide range of conformations and does not have a characteristic CD spectrum. The CD spectra of an unordered confirmation show a negative band near 200 nm and a weak band at a longer wavelength, which can be negative or positive. CD does not allow you to determine where the different conformations that are detected are located within the molecule or even completely predict how many there are. Despite this, CD is a valuable tool, especially for showing changes in conformation. It can, for instance, be used to study how the secondary structure of a molecule changes as a function of temperature or of the concentration of denaturing agents, e.g. Guanidinium hydrochloride or urea. In this way it can reveal important thermodynamic information about the molecule (such as the enthalpy and Gibbs free energy of denaturation) that cannot otherwise be easily obtained.

The tertiary structure have distinctive CD spectra in the near-UV. The distinctive bands arise from the aromatic side chains and disulfides. Nearly all proteins have at least one or more aromatic residues (phenylalanine, tyrosine, and tryptophan). The aromatic groups have characteristic absorption bands between 250 and 300 nm. The aromatic side chain CD bands have provided a useful marker for the R to T transition in hemoglobin. The spectra of heme proteins usually show a board intense band at 260 nm. Hemoglobin also shows a sharp bands in the 270-300 nm region, which are due to tyrosine and tryptophan. The disulfide group bands depend on the dihedral angle of the disulfide. When the angle is 90, there is a single band near 260 nm. As the angle gets bigger or smaller, the band shifts to higher or lower energy respectively. Unlike in far-UV CD, the near-UV CD spectrum cannot be assigned to any particular 3D structure. Rather, near-UV CD spectra provide structural information on the nature of the prosthetic groups in proteins, e.g., the heme groups in hemoglobin and cytochrome c.

Visible CD spectroscopy is a very powerful technique to study metal–protein interactions and can resolve individual d-d electronic transitions as separate bands. CD spectra in the visible light region are only produced when a metal ion is in a chiral environment; thus, free metal ions in solution are not detected. This has the advantage of only observing the protein-bound metal, so pH dependence and stoichiometries are readily obtained. Optical activity in transition metal ion complexes have been attributed to configurational, conformational and the vicinal effects. Klewpatinond and Viles (2007) have produced a set of empirical rules for predicting the appearance of visible CD spectra for Cu2+ and Ni2+ square-planar complexes involving histidine and main-chain coordination.

CD gives less specific structural information than X-ray crystallography and protein NMR spectroscopy, for example, both give atomic resolution data. However, CD spectroscopy is a quick method that does not require large amounts of proteins or extensive data processing. Thus CD can be used to survey a large number of solvent conditions, varying temperature, pH, salinity, and the presence of various cofactors.