Circular dichroism (CD) is dichroism involving circularly polarized light, i.e., the differential absorption of left- and right-handed light.^[1][2] Left-hand circular (LHC) and right-hand circular (RHC) polarized light represent two possible spin angular momentum states for a photon, and so circular dichroism is also referred to as dichroism for spin angular momentum.^[3] This phenomenon was discovered by Jean-Baptiste Biot, Augustin Fresnel, and Aimé Cotton in the first half of the 19th century.^[4] Circular dichroism and circular birefringence are manifestations of optical activity. It is exhibited in the absorption bands of optically active chiral molecules. CD spectroscopy has a wide range of applications in many different fields. Most notably, UV CD is used to investigate the secondary structure of proteins.^[5] UV/Vis CD is used to investigate charge-transfer transitions.^[6] Near-infrared CD is used to investigate geometric and electronic structure by probing metal d→d transitions.^[2] Vibrational circular dichroism, which uses light from the infrared energy region, is used for structural studies of small organic molecules, and most recently proteins and DNA.^[5]

Physical principles

Circular polarization of light

Electromagnetic radiation consists of an electric ${\displaystyle {\boldsymbol {E}}}$ and magnetic ${\displaystyle {\boldsymbol {B}}}$ field that oscillate perpendicular to one another and to the propagating direction,^[7] a transverse wave. While linearly polarized light occurs when the electric field vector oscillates only in one plane, circularly polarized light occurs when the direction of the electric field vector rotates about its propagation direction while the vector retains constant magnitude. At a single point in space, the circularly polarized-vector will trace out a circle over one period of the wave frequency, hence the name. The two diagrams below show the electric field vectors of linearly and circularly polarized light, at one moment of time, for a range of positions; the plot of the circularly polarized electric vector forms a helix along the direction of propagation ${\displaystyle {\boldsymbol {k}}}$. For left circularly polarized light (LCP) with propagation towards the observer, the electric vector rotates counterclockwise.^[2] For right circularly polarized light (RCP), the electric vector rotates clockwise.

Interaction of circularly polarized light with matter

When circularly polarized light passes through an absorbing optically active medium, the speeds between right and left polarizations differ (${\displaystyle c_{\mathrm {L} }\neq c_{\mathrm {R} }}$) as well as their wavelength(${\displaystyle \lambda _{\mathrm {L} }\neq \lambda _{\mathrm {R} }}$) and the extent to which they are absorbed (${\displaystyle \varepsilon _{\mathrm {L} }\neq \varepsilon _{\mathrm {R} }}$). Circular dichroism is the difference ${\displaystyle \Delta \varepsilon \equiv \varepsilon _{\mathrm {L} }-\varepsilon _{\mathrm {R} }}$.^[5] The electric field of a light beam causes a linear displacement of charge when interacting with a molecule (electric dipole), whereas its magnetic field causes a circulation of charge (magnetic dipole). These two motions combined cause an excitation of an electron in a helical motion, which includes translation and rotation and their associated operators. The experimentally determined relationship between the rotational strength ${\displaystyle R}$ of a sample and the ${\displaystyle \Delta \varepsilon }$ is given by

${\displaystyle R_{\mathrm {exp} }={\frac {3hc10^{3}\ln(10)}{32\pi ^{3}N_{\mathrm {A} }}}\int {\frac {\Delta \varepsilon }{\nu }}\mathrm {d} {\nu }}$

The rotational strength has also been determined theoretically,

${\displaystyle R_{\mathrm {theo} }={\frac {1}{2mc}}\mathrm {Im} \int \Psi _{g}{\widehat {M}}_{\mathrm {(elec.dipole)} }\Psi _{e}\mathrm {d} \tau \bullet \int \Psi _{g}{\widehat {M}}_{\mathrm {(mag.dipole)} }\Psi _{e}\mathrm {d} \tau }$

We see from these two equations that in order to have non-zero ${\displaystyle \Delta \varepsilon }$, the electric and magnetic dipole moment operators (${\displaystyle {\widehat {M}}_{\mathrm {(elec.dipole)} }}$ and ${\displaystyle {\widehat {M}}_{\mathrm {(mag.dipole)} }}$) must transform as the same irreducible representation. ${\displaystyle \mathrm {C} _{n}}$ and ${\displaystyle \mathrm {D} _{n}}$ are the only point groups where this can occur, making only chiral molecules CD active.

Simply put, since circularly 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 the 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.

It is important that the chirality of the molecule can be conformational rather than structural. That is, for instance, a protein molecule with a helical secondary structure can have a CD that changes with changes in the conformation.

Delta absorbance

By definition,

${\displaystyle \Delta A=A_{\mathrm {L} }-A_{\mathrm {R} }\,}$

where ${\displaystyle \Delta A}$ (Delta Absorbance) is the difference between absorbance of left circularly polarized (LCP) and right circularly polarized (RCP) light (this is what is usually measured). ${\displaystyle \Delta A}$ is a function of wavelength, so for a measurement to be meaningful the wavelength at which it was performed must be known.

Molar circular dichroism

It can also be expressed, by applying Beer's law, as:

${\displaystyle \Delta A=(\varepsilon _{\mathrm {L} }-\varepsilon _{\mathrm {R} })Cl\,}$

where

${\displaystyle \varepsilon _{\mathrm {L} }}$ and ${\displaystyle \varepsilon _{\mathrm {R} }}$ are the molar extinction coefficients for LCP and RCP light,

${\displaystyle C}$ is the molar concentration,

${\displaystyle l}$ is the path length in centimeters (cm).

Then

${\displaystyle \Delta \varepsilon =\varepsilon _{\mathrm {L} }-\varepsilon _{\mathrm {R} }\,}$

is the molar circular dichroism. This intrinsic property is what is usually meant by the circular dichroism of the substance. Since ${\displaystyle \Delta \varepsilon }$ is a function of wavelength, a molar circular dichroism value (${\displaystyle \Delta \varepsilon }$) must specify the wavelength at which it is valid.

Extrinsic effects on circular dichroism

In many practical applications of circular dichroism (CD), as discussed below, the measured CD is not simply an intrinsic property of the molecule, but rather depends on the molecular conformation. In such a case the CD may also be a function of temperature, concentration, and the chemical environment, including solvents. In this case the reported CD value must also specify these other relevant factors in order to be meaningful.

In ordered structures lacking two-fold rotational symmetry, optical activity,^[8][9] including differential transmission^[10] (and reflection^[11]) of circularly polarized waves also depends on the propagation direction through the material. In this case, so-called extrinsic 3d chirality is associated with the mutual orientation of light beam and structure.

Molar ellipticity

Although ${\displaystyle \Delta A}$ is usually measured, for historical reasons most measurements are reported in degrees of ellipticity. Molar ellipticity is circular dichroism corrected for concentration. Molar circular dichroism and molar ellipticity, ${\displaystyle }$, are readily interconverted by the equation:

${\displaystyle =3298.2\,\Delta \varepsilon .\,}$

This relationship is derived by defining the ellipticity of the polarization as:

${\displaystyle \tan <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}=\frac{E_{\mathrm{R}}-<!--\; -\; -->E_{\mathrm{L}}}{}}$Zdroj:https://en.wikipedia.org?pojem=Circular_dichroism
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