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Magnetic circular dichroism

Magnetic circular dichroism (MCD) is the differential absorption of left and right circularly polarized (LCP and RCP) light, induced in a sample by a strong magnetic field oriented parallel to the direction of light propagation. MCD measurements can detect transitions which are too weak to be seen in conventional optical absorption spectra, and it can be used to distinguish between overlapping transitions. Paramagnetic systems are common analytes, as their near-degenerate magnetic sublevels provide strong MCD intensity that varies with both field strength and sample temperature. The MCD signal also provides insight into the symmetry of the electronic levels of the studied systems, such as metal ion sites.[1]

MCD spectra vary with applied field strength

History edit

It was first shown by Faraday that optical activity (the Faraday effect) could be induced in matter by a longitudinal magnetic field (a field in the direction of light propagation).[2] The development of MCD really began in the 1930s when a quantum mechanical theory of MOR (magnetic optical rotatory dispersion) in regions outside absorption bands was formulated. The expansion of the theory to include MCD and MOR effects in the region of absorptions, which were referred to as "anomalous dispersions" was developed soon thereafter. There was, however, little effort made to refine MCD as a modern spectroscopic technique until the early 1960s. Since that time there have been numerous studies of MCD spectra for a very large variety of samples, including stable molecules in solutions, in isotropic solids, and in the gas phase, as well as unstable molecules entrapped in noble gas matrices. More recently, MCD has found useful application in the study of biologically important systems including metalloenzymes and proteins containing metal centers.[3][4]

Differences between CD and MCD edit

In natural optical activity, the difference between the LCP light and the RCP light is caused by the asymmetry of the molecules (i.e. chiral molecules). Because of the handedness of the molecule, the absorption of the LCP light would be different from the RCP light. However, in MCD in the presence of a magnetic field, LCP and RCP no longer interact equivalently with the absorbing medium. Thus, there is not the same direct relation between magnetic optical activity and molecular stereochemistry which would be expected, because it is found in natural optical activity. So, natural CD is much more rare than MCD which does not strictly require the target molecule to be chiral.[5]

Although there is much overlap in the requirements and use of instruments, ordinary CD instruments are usually optimized for operation in the ultraviolet, approximately 170–300 nm, while MCD instruments are typically required to operate in the visible to near infrared, approximately 300–2000 nm. The physical processes that lead to MCD are substantively different from those of CD. However, like CD, it is dependent on the differential absorption of left and right hand circularly polarized light. MCD will only exist at a given wavelength if the studied sample has an optical absorption at that wavelength.[1] This is distinctly different from the related phenomenon of optical rotatory dispersion (ORD), which can be observed at wavelengths far from any absorption band.

Measurement edit

The MCD signal ΔA is derived via the absorption of the LCP and RCP light as

 

This signal is often presented as a function of wavelength λ, temperature T or magnetic field H.[1] MCD spectrometers can simultaneously measure absorbance and ΔA along the same light path.[6] This eliminates error introduced through multiple measurements or different instruments that previously occurred before this advent. The MCD spectrometer example shown below begins with a light source that emits a monochromatic wave of light. This wave is passed through a Rochon prism linear polarizer, which separates the incident wave into two beams that are linearly polarized by 90 degrees. The two beams follow different paths- one beam (the extraordinary beam) traveling directly to a photomultiplier (PMT), and the other beam (the ordinary beam) passing through a photoelastic modulator (PEM) oriented at 45 degrees to the direction of the ordinary ray polarization. The PMT for the extraordinary beam detects the light intensity of the input beam. The PEM is adjusted to cause an alternating plus and minus 1/4 wavelength shift of one of the two orthogonal components of the ordinary beam. This modulation converts the linearly polarized light into circularly polarized light at the peaks of the modulation cycle. Linearly polarized light can be decomposed into two circular components with intensity represented as  

The PEM will delay one component of linearly polarized light with a time dependence that advances the other component by 1/4 λ (hence, quarter-wave shift). The departing circularly polarized light oscillates between RCP and LCP in a sinusoidal time-dependence as depicted below:

 

The light finally travels through a magnet containing the sample, and the transmittance is recorded by another PMT. The schematic is given below:

 

The intensity of light from the ordinary wave that reaches the PMT is governed by the equation:

 

Here A and A+ are the absorbances of LCP or RCP, respectively; ω is the modulator frequency – usually a high acoustic frequency such as 50 kHz; t is time; and δ0 is the time-dependent wavelength shift.

This intensity of light passing through the sample is converted into a two-component voltage via a current/voltage amplifier. A DC voltage will emerge corresponding to the intensity of light passed through the sample. If there is a ΔA, then a small AC voltage will be present that corresponds to the modulation frequency, ω. This voltage is detected by the lock in amplifier, which receives its reference frequency, ω, directly from the PEM. From such voltage, ΔA and A can be derived using the following relations:

 

 

where Vex is the (DC) voltage measured by the PMT from the extraordinary wave, and Vdc is the DC component of the voltage measured by the PMT for the ordinary wave (measurement path not shown in the diagram).

Some superconducting magnets have a small sample chamber, far too small to contain the entire optical system. Instead, the magnet sample chamber has windows on two opposite sides. Light from the source enters one side, interacts with the sample (usually also temperature controlled) in the magnetic field, and exits through the opposite window to the detector. Optical relay systems that allow the source and detector each to be about a meter from the sample are typically employed. This arrangement avoids many of the difficulties that would be encountered if the optical apparatus had to operate in the high magnetic field, and also allows for a much less expensive magnet.

Applications edit

MCD can be used as an optical technique for the detection of electronic structure of both the ground states and excited states. It is also a strong addition to the more commonly used absorption spectroscopy, and there are two reasons that explain this. First, a transition buried under a stronger transition can appear in MCD if the first derivative of the absorption is much larger for the weaker transition or it is of the opposite sign. Second, MCD will be found where no absorption is detected at all if ΔA > (ΔAmin) but A < Amin, where (ΔA)min and Amin are the minimum of ΔA and A that are detectable. Typically, (ΔAmin) and Amin are of the magnitudes around 10−5 and 10−3 respectively. So, a transition can only be detected in MCD, not in the absorption spectroscopy, if ΔA/A > 10−2. This happens in paramagnetic systems that are at lower temperature or that have sharp lines in the spectroscopy.[7]

In biology, metalloproteins are the most likely candidates for MCD measurements, as the presence of metals with degenerate energy levels leads to strong MCD signals. In the case of ferric heme proteins,[8] MCD is capable of determining both oxidation and spin state to a remarkably exquisite degree. In regular proteins, MCD is capable of stoichiometrically measuring the tryptophan content of proteins, assuming there are no other competing absorbers in the spectroscopic system. In addition, the application of MCD spectroscopy greatly improved the level of understanding in the ferrous non-heme systems because of the direct observation of the d–d transitions, which generally can not be obtained in optical absorption spectroscopy owing to the weak extinction coefficients and are often electron paramagnetic resonance silent due to relatively large ground-state sublevel splittings and fast relaxation times.[9]

Theory edit

Consider a system of localized, non-interacting absorbing centers. Based on the semi-classical radiation absorption theory within the electric dipole approximation, the electric vector of the circularly polarized waves propagates along the +z direction. In this system,   is the angular frequency, and   = n – ik is the complex refractive index. As the light travels, the attenuation of the beam is expressed as[7]

 

where   is the intensity of light at position  ,   is the absorption coefficient of the medium in the   direction, and   is the speed of light. Circular dichroism (CD) is then defined by the difference between left ( ) and right ( ) circularly polarized light,  , following the sign convention of natural optical activity. In the presence of a static, uniform external magnetic field applied parallel to the direction of propagation of light,[2] the Hamiltonian for the absorbing center takes the form   for   describing the system in the external magnetic field and   describing the applied electromagnetic radiation. The absorption coefficient for a transition between two eigenstates of  ,   and  , can be described using the electric dipole transition operator   as

 
 

The   term is a frequency-independent correction factor allowing for the effect of the medium on the light wave electric field, composed of the permittivity   and the real refractive index  .

Discrete line spectrum edit

In cases of a discrete spectrum, the observed   at a particular frequency   can be treated as a sum of contributions from each transition,

 

where   is the contribution at   from the   transition,   is the absorption coefficient for the   transition, and   is a bandshape function ( ). Because eigenstates   and   depend on the applied external field, the value of   varies with field. It is frequently useful to compare this value to the absorption coefficient in the absence of an applied field, often denoted

 

When the Zeeman effect is small compared to zero-field state separations, line width, and   and when the line shape is independent of the applied external field  , first-order perturbation theory can be applied to separate   into three contributing Faraday terms, called  ,  , and  . The subscript indicates the moment such that   contributes a derivative-shaped signal and   and   contribute regular absorptions. Additionally, a zero-field absorption term   is defined. The relationships between  ,  , and these Faraday terms are

 
 

for external field strength  , Boltzmann constant  , temperature  , and a proportionality constant  . This expression requires assumptions that   is sufficiently high in energy that  , and that the temperature of the sample is high enough that magnetic saturation does not produce nonlinear   term behavior. Though one must pay attention to proportionality constants, there is a proportionality between   and molar extinction coefficient   and absorbance   for concentration   and path length  .

These Faraday terms are the usual language in which MCD spectra are discussed. Their definitions from perturbation theory are[10]

 

where   is the degeneracy of ground state  ,   labels states other than   or  ,   and   and   label the levels within states   and   and   (respectively),   is the energy of unperturbed state  ,   is the   angular momentum operator,   is the   spin operator, and   indicates the real part of the expression.

Origins of A, B, and C Faraday Terms edit

 
 ,  , and   term intensity mechanisms for magnetic circular dichroism (MCD) signal

The equations in the previous subsection reveal that the  ,  , and   terms originate through three distinct mechanisms.

The   term arises from Zeeman splitting of the ground or excited degenerate states. These field-dependent changes in energies of the magnetic sublevels causes small shifts in the bands to higher/lower energy. The slight offsets result in incomplete cancellation of the positive and negative features, giving a net derivative shape in the spectrum. This intensity mechanism is generally independent of sample temperature.

The   term is due to the field-induced mixing of states. Energetic proximity of a third state   to either the ground state   or excited state   gives appreciable Zeeman coupling in the presence of an applied external field. As the strength of the magnetic field increases, the amount of mixing increases to give growth of an absorption band shape. Like the   term, the   term is generally temperature independent. Temperature dependence of   term intensity can sometimes be observed when   is particularly low-lying in energy.

The   term requires the degeneracy of the ground state, often encountered for paramagnetic samples. This happens due to a change in the Boltzmann population of the magnetic sublevels, which is dependent on the degree of field-induced splitting of the sublevel energies and on the sample temperature.[11] Decrease of the temperature and increase of the magnetic field increases the   term intensity until it reaches the maximum (saturation limit). Experimentally, the   term spectrum can be obtained from MCD raw data by subtraction of MCD spectra measured in the same applied magnetic field at different temperatures, while   and   terms can be distinguished via their different band shapes.[9]

The relative contributions of A, B and C terms to the MCD spectrum are proportional to the inverse line width, energy splitting, and temperature:

 

where   is line width and   is the zero-field state separation. For typical values of   = 1000 cm−1,   = 10,000 cm−1 and   = 6 cm−1 (at 10 K), the three terms make relative contributions 1:0.1:150. So, at low temperature the   term dominates over   and   for paramagnetic samples.[12]

Example on C terms edit

 
An MCD spectrum and orbital diagram for potassium ferricyanide

In the visible and near-ultraviolet regions, the hexacyanoferrate(III) ion (Fe(CN)63−) exhibits three strong absorptions at 24500, 32700, and 40500 cm−1, which have been ascribed to ligand to metal charge transfer (LMCT) transitions. They all have lower energy than the lowest-energy intense band for the Fe(II) complex Fe(CN)62− found at 46000 cm−1.[13] The red shift with increasing oxidation state of the metal is characteristic of LMCT bands. Additionally, only A terms, which are temperature independent, should be involved in MCD structure for closed-shell species.

These features can be explained as follows. The ground state of the anion is 2T2g, which derives from the electronic configuration (t2g)5. So, there would be an unpaired electron in the d orbital of Fe3+ From that, the three bands can be assigned to the transitions 2t2g2t1u1, 2t2g2t1u2, 2t2g2t2u. Two of the excited states are of the same symmetry, and, based on the group theory, they could mix with each other so that there are no pure σ and π characters in the two t1u states, but for t2u, there would be no intermixing. The A terms are also possible from the degenerate excited states, but the studies of temperature dependence showed that the A terms are not as dependent as the C term.[14]

An MCD study of Fe(CN)63− embedded in a thin polyvinyl alcohol (PVA) film revealed a temperature dependence of the C term. The room-temperature C0/D0 values for the three bands in the Fe(CN)63− spectrum are 1.2, −0.6, and 0.6, respectively, and their signs (positive, negative, and positive) establish the energy ordering as 2t2g2t1u2<2t2g2t2u<2t2g2t1u1

Example on A and B terms edit

To have an A- and B-term in the MCD spectrum, a molecule must contain degenerate excited states (A-term) and excited states close enough in energy to allow mixing (B-term). One case exemplifying these conditions is a square planar, d8 complex such as [(n-C4H9)4N]2Pt(CN)4. In addition to containing A- and B-terms, this example demonstrates the effects of spin-orbit coupling in metal to ligand charge transfer (MLCT) transitions. As shown in figure 1, the molecular orbital diagram of [(n-C4H9)4N]2Pt(CN)4 reveals MLCT into the antibonding π* orbitals of cyanide. The ground state is diamagnetic (thereby eliminating any C-terms) and the LUMO is the a2u. The dipole-allowed MLCT transitions are a1g-a2u and eg-a2u. Another transition, b2u-a2u, is a weak (orbitally forbidden singlet) but can still be observed in MCD.[15]

 
The UV/Vis absorption (top) and MCD (bottom) spectra of tetra-n-butylammonium tetracyanoplatinate in acetonitrile

Because A- and B-terms arise from the properties of states, all singlet and triplet excited states are given in figure 2.

 

 

Mixing of all these singlet and triplet states will occur and is attributed to the spin orbit coupling of platinum 5d orbitals (ζ ~ 3500 cm−1), as shown in figure 3. The black lines on the figure indicate the mixing of 1A2u with 3Eu to give two A2u states. The red lines show the 1Eu, 3Eu, 3A2u, and 3B1u states mixing to give four Eu states. The blue lines indicate remnant orbitals after spin-orbit coupling that are not a result of mixing.

See also edit

References edit

  1. ^ a b c IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "magnetic circular dichroism". doi:10.1351/goldbook.MT06778
  2. ^ a b A. D. Buckingham & P. J. Stephens (1966). "Magnetic Optical Activity". Annu. Rev. Phys. Chem. 17: 399. Bibcode:1966ARPC...17..399B. doi:10.1146/annurev.pc.17.100166.002151.
  3. ^ W. Roy Mason (2007). A practical guide to magnetic circular dichroism spectroscopy. Wiley-Interscience. doi:10.1002/9780470139233. ISBN 978-0-470-06978-3. Retrieved 16 April 2011.
  4. ^ P. N. Schatz; A. J. McCafferyd (1969). "The Faraday effect". Quarterly Reviews, Chemical Society. 23 (4): 552. doi:10.1039/QR9692300552.
  5. ^ Dennis Caldwell; Thorne, J M; Eyring, H (1971). "Magnetic Circular Dichroism". Annu. Rev. Phys. Chem. 22: 259–278. Bibcode:1971ARPC...22..259C. doi:10.1146/annurev.pc.22.100171.001355.
  6. ^ G. A. Osborne (1973). "A Near-Infrared Circular Dichroism and Magnetic Circular Dichroism Instrument". Review of Scientific Instruments. 44 (1): 10–15. Bibcode:1973RScI...44...10O. doi:10.1063/1.1685944.
  7. ^ a b Stephens, P. J. (1974). "Magnetic Circular Dichroism". Annu. Rev. Phys. Chem. 25: 201–232. Bibcode:1974ARPC...25..201S. doi:10.1146/annurev.pc.25.100174.001221.
  8. ^ G. Zoppellaro; et al. (2009). "Review: Studies of ferric heme proteins with highly anisotropic/highly axial low spin (S = 1/2) electron paramagnetic resonance signals with bis-Histidine and histidine-methionine axial iron coordination". Biopolymers. 91 (12): 1064–82. doi:10.1002/bip.21267. PMC 2852197. PMID 19536822.
  9. ^ a b E.I. Solomon; et al. (1995). "Magnetic circular dichroism spectroscopy as a probe of the geometric and electronic structure of non-heme ferrous enzymes". Coordination Chemistry Reviews. 144: 369–460. doi:10.1016/0010-8545(95)01150-N.
  10. ^ Stephens, P. J. (1976). "Magnetic Circular Dichroism". Adv. Chem. Phys. Advances in Chemical Physics. 35: 197–264. doi:10.1002/9780470142547.ch4. ISBN 9780470142547.
  11. ^ Lehnert, N.; DeBeer George, S.; Solomon, E. I. (2001). "Recent advances in bioinorganic spectroscopy". Current Opinion in Chemical Biology. 5 (2): 176–187. doi:10.1016/S1367-5931(00)00188-5. PMID 11282345.
  12. ^ Neese, F.; Solomon, E. I. (1999). "MCD C-Term Signs, Saturation Behavior, and Determination of Band Polarizations in Randomly Oriented Systems with Spin S >/= (1)/(2). Applications to S = (1)/(2) and S = (5)/(2)". Inorg. Chem. 38 (8): 1847–1865. doi:10.1021/ic981264d. PMID 11670957.
  13. ^ Stephens, P. J. (1965). "The Faraday Rotation of Allowed Transitions: Charge-Transfer Transitions in K3Fe(CN)6". Inorg. Chem. 4 (12): 1690–1692. doi:10.1021/ic50034a003.
  14. ^ Upton, A. H. P.; Williamson, B. E. (1994). "Magnetic circular dichroism and absorption spectra of hexacyanoferrate(III) in a poly(vinyl alcohol) film". J. Phys. Chem. 98: 71–76. doi:10.1021/j100052a013.
  15. ^ Isci, H.; Mason, W. R. (1975). "Electronic structure and spectra of square-planar cyano and cyanoamine complexes of platinum(II)". Inorg. Chem. 14 (4): 905. doi:10.1021/ic50146a038.

magnetic, circular, dichroism, differential, absorption, left, right, circularly, polarized, light, induced, sample, strong, magnetic, field, oriented, parallel, direction, light, propagation, measurements, detect, transitions, which, weak, seen, conventional,. Magnetic circular dichroism MCD is the differential absorption of left and right circularly polarized LCP and RCP light induced in a sample by a strong magnetic field oriented parallel to the direction of light propagation MCD measurements can detect transitions which are too weak to be seen in conventional optical absorption spectra and it can be used to distinguish between overlapping transitions Paramagnetic systems are common analytes as their near degenerate magnetic sublevels provide strong MCD intensity that varies with both field strength and sample temperature The MCD signal also provides insight into the symmetry of the electronic levels of the studied systems such as metal ion sites 1 MCD spectra vary with applied field strength Contents 1 History 2 Differences between CD and MCD 3 Measurement 4 Applications 5 Theory 5 1 Discrete line spectrum 5 2 Origins of A B and C Faraday Terms 6 Example on C terms 7 Example on A and B terms 8 See also 9 ReferencesHistory editIt was first shown by Faraday that optical activity the Faraday effect could be induced in matter by a longitudinal magnetic field a field in the direction of light propagation 2 The development of MCD really began in the 1930s when a quantum mechanical theory of MOR magnetic optical rotatory dispersion in regions outside absorption bands was formulated The expansion of the theory to include MCD and MOR effects in the region of absorptions which were referred to as anomalous dispersions was developed soon thereafter There was however little effort made to refine MCD as a modern spectroscopic technique until the early 1960s Since that time there have been numerous studies of MCD spectra for a very large variety of samples including stable molecules in solutions in isotropic solids and in the gas phase as well as unstable molecules entrapped in noble gas matrices More recently MCD has found useful application in the study of biologically important systems including metalloenzymes and proteins containing metal centers 3 4 Differences between CD and MCD editIn natural optical activity the difference between the LCP light and the RCP light is caused by the asymmetry of the molecules i e chiral molecules Because of the handedness of the molecule the absorption of the LCP light would be different from the RCP light However in MCD in the presence of a magnetic field LCP and RCP no longer interact equivalently with the absorbing medium Thus there is not the same direct relation between magnetic optical activity and molecular stereochemistry which would be expected because it is found in natural optical activity So natural CD is much more rare than MCD which does not strictly require the target molecule to be chiral 5 Although there is much overlap in the requirements and use of instruments ordinary CD instruments are usually optimized for operation in the ultraviolet approximately 170 300 nm while MCD instruments are typically required to operate in the visible to near infrared approximately 300 2000 nm The physical processes that lead to MCD are substantively different from those of CD However like CD it is dependent on the differential absorption of left and right hand circularly polarized light MCD will only exist at a given wavelength if the studied sample has an optical absorption at that wavelength 1 This is distinctly different from the related phenomenon of optical rotatory dispersion ORD which can be observed at wavelengths far from any absorption band Measurement editThe MCD signal DA is derived via the absorption of the LCP and RCP light as D A A A A A displaystyle Delta A frac A A A A nbsp This signal is often presented as a function of wavelength l temperature T or magnetic field H 1 MCD spectrometers can simultaneously measure absorbance and DA along the same light path 6 This eliminates error introduced through multiple measurements or different instruments that previously occurred before this advent The MCD spectrometer example shown below begins with a light source that emits a monochromatic wave of light This wave is passed through a Rochon prism linear polarizer which separates the incident wave into two beams that are linearly polarized by 90 degrees The two beams follow different paths one beam the extraordinary beam traveling directly to a photomultiplier PMT and the other beam the ordinary beam passing through a photoelastic modulator PEM oriented at 45 degrees to the direction of the ordinary ray polarization The PMT for the extraordinary beam detects the light intensity of the input beam The PEM is adjusted to cause an alternating plus and minus 1 4 wavelength shift of one of the two orthogonal components of the ordinary beam This modulation converts the linearly polarized light into circularly polarized light at the peaks of the modulation cycle Linearly polarized light can be decomposed into two circular components with intensity represented as I 0 1 2 I I displaystyle I 0 frac 1 2 I I nbsp The PEM will delay one component of linearly polarized light with a time dependence that advances the other component by 1 4 l hence quarter wave shift The departing circularly polarized light oscillates between RCP and LCP in a sinusoidal time dependence as depicted below nbsp The light finally travels through a magnet containing the sample and the transmittance is recorded by another PMT The schematic is given below nbsp The intensity of light from the ordinary wave that reaches the PMT is governed by the equation I D I 0 2 1 sin d 0 sin w t 10 A 1 sin d 0 sin w t 10 A displaystyle I Delta frac I 0 2 left left 1 sin left delta 0 sin omega t right right 10 A left 1 sin left delta 0 sin omega t right right 10 A right nbsp Here A and A are the absorbances of LCP or RCP respectively w is the modulator frequency usually a high acoustic frequency such as 50 kHz t is time and d0 is the time dependent wavelength shift This intensity of light passing through the sample is converted into a two component voltage via a current voltage amplifier A DC voltage will emerge corresponding to the intensity of light passed through the sample If there is a DA then a small AC voltage will be present that corresponds to the modulation frequency w This voltage is detected by the lock in amplifier which receives its reference frequency w directly from the PEM From such voltage DA and A can be derived using the following relations D A V a c 1 1515 V d c d 0 sin w t displaystyle Delta A frac V ac 1 1515V dc delta 0 sin omega t nbsp A log V d c V e x displaystyle A log frac V dc V ex nbsp where Vex is the DC voltage measured by the PMT from the extraordinary wave and Vdc is the DC component of the voltage measured by the PMT for the ordinary wave measurement path not shown in the diagram Some superconducting magnets have a small sample chamber far too small to contain the entire optical system Instead the magnet sample chamber has windows on two opposite sides Light from the source enters one side interacts with the sample usually also temperature controlled in the magnetic field and exits through the opposite window to the detector Optical relay systems that allow the source and detector each to be about a meter from the sample are typically employed This arrangement avoids many of the difficulties that would be encountered if the optical apparatus had to operate in the high magnetic field and also allows for a much less expensive magnet Applications editMCD can be used as an optical technique for the detection of electronic structure of both the ground states and excited states It is also a strong addition to the more commonly used absorption spectroscopy and there are two reasons that explain this First a transition buried under a stronger transition can appear in MCD if the first derivative of the absorption is much larger for the weaker transition or it is of the opposite sign Second MCD will be found where no absorption is detected at all if DA gt DAmin but A lt Amin where DA min and Amin are the minimum of DA and A that are detectable Typically DAmin and Amin are of the magnitudes around 10 5 and 10 3 respectively So a transition can only be detected in MCD not in the absorption spectroscopy if DA A gt 10 2 This happens in paramagnetic systems that are at lower temperature or that have sharp lines in the spectroscopy 7 In biology metalloproteins are the most likely candidates for MCD measurements as the presence of metals with degenerate energy levels leads to strong MCD signals In the case of ferric heme proteins 8 MCD is capable of determining both oxidation and spin state to a remarkably exquisite degree In regular proteins MCD is capable of stoichiometrically measuring the tryptophan content of proteins assuming there are no other competing absorbers in the spectroscopic system In addition the application of MCD spectroscopy greatly improved the level of understanding in the ferrous non heme systems because of the direct observation of the d d transitions which generally can not be obtained in optical absorption spectroscopy owing to the weak extinction coefficients and are often electron paramagnetic resonance silent due to relatively large ground state sublevel splittings and fast relaxation times 9 Theory editConsider a system of localized non interacting absorbing centers Based on the semi classical radiation absorption theory within the electric dipole approximation the electric vector of the circularly polarized waves propagates along the z direction In this system w 2 p n displaystyle omega 2 pi nu nbsp is the angular frequency and n displaystyle tilde n nbsp n ik is the complex refractive index As the light travels the attenuation of the beam is expressed as 7 I z I 0 exp 2 w k z c displaystyle I z I 0 exp 2 omega kz c nbsp where I z displaystyle I z nbsp is the intensity of light at position z displaystyle z nbsp k displaystyle k nbsp is the absorption coefficient of the medium in the z displaystyle z nbsp direction and c displaystyle c nbsp is the speed of light Circular dichroism CD is then defined by the difference between left displaystyle nbsp and right displaystyle nbsp circularly polarized light D k k k displaystyle Delta k k k nbsp following the sign convention of natural optical activity In the presence of a static uniform external magnetic field applied parallel to the direction of propagation of light 2 the Hamiltonian for the absorbing center takes the form H t H 0 H 1 t displaystyle mathcal H t mathcal H 0 mathcal H 1 t nbsp for H 0 displaystyle mathcal H 0 nbsp describing the system in the external magnetic field and H 1 t displaystyle mathcal H 1 t nbsp describing the applied electromagnetic radiation The absorption coefficient for a transition between two eigenstates of H 0 displaystyle mathcal H 0 nbsp a displaystyle a nbsp and j displaystyle j nbsp can be described using the electric dipole transition operator m displaystyle m nbsp as k a j 0 k a j d w p 2 ℏ N a N j a 2 n a m j 2 displaystyle k pm a to j int 0 infty k pm a to j d omega frac pi 2 hbar N a N j left frac alpha 2 n right left langle a m pm j rangle right 2 nbsp D k a j 0 D k a j d w p 2 ℏ N a N j a 2 n a m j 2 a m j 2 displaystyle Delta k a to j int 0 infty Delta k a to j d omega frac pi 2 hbar N a N j left frac alpha 2 n right left left langle a m j rangle right 2 left langle a m j rangle right 2 right nbsp The a 2 n displaystyle alpha 2 n nbsp term is a frequency independent correction factor allowing for the effect of the medium on the light wave electric field composed of the permittivity a displaystyle alpha nbsp and the real refractive index n displaystyle n nbsp Discrete line spectrum edit In cases of a discrete spectrum the observed D k displaystyle Delta k nbsp at a particular frequency w displaystyle omega nbsp can be treated as a sum of contributions from each transition D k o b s w a j D k a j w a j D k a j f j a w displaystyle Delta k mathrm obs omega sum a j Delta k a to j omega sum a j Delta k a to j f ja omega nbsp where D k a j w displaystyle Delta k a to j omega nbsp is the contribution at w displaystyle omega nbsp from the a j displaystyle a to j nbsp transition D k a j displaystyle Delta k a to j nbsp is the absorption coefficient for the a j displaystyle a to j nbsp transition and f j a w displaystyle f ja omega nbsp is a bandshape function 0 f j a w d w 1 displaystyle textstyle int 0 infty f ja omega d omega 1 nbsp Because eigenstates a displaystyle a nbsp and j displaystyle j nbsp depend on the applied external field the value of D k o b s w displaystyle Delta k mathrm obs omega nbsp varies with field It is frequently useful to compare this value to the absorption coefficient in the absence of an applied field often denoted k 0 w a j k a j 0 w a j k a j 0 f j a 0 w displaystyle k 0 omega sum a j k a to j 0 omega sum a j k a to j 0 f ja 0 omega nbsp When the Zeeman effect is small compared to zero field state separations line width and k T displaystyle kT nbsp and when the line shape is independent of the applied external field H displaystyle H nbsp first order perturbation theory can be applied to separate D k displaystyle Delta k nbsp into three contributing Faraday terms called A 1 displaystyle mathcal A 1 nbsp B 0 displaystyle mathcal B 0 nbsp and C 0 displaystyle mathcal C 0 nbsp The subscript indicates the moment such that A 1 displaystyle mathcal A 1 nbsp contributes a derivative shaped signal and B 0 displaystyle mathcal B 0 nbsp and C 0 displaystyle mathcal C 0 nbsp contribute regular absorptions Additionally a zero field absorption term D 0 displaystyle mathcal D 0 nbsp is defined The relationships between D k displaystyle Delta k nbsp k 0 displaystyle k 0 nbsp and these Faraday terms are D k A J w 4 3 g N A 0 A 1 A J ℏ f j a 0 w w B 0 A J C 0 A J k B T f j a 0 w H displaystyle Delta k A to J omega frac 4 3 gamma N A 0 left frac mathcal A 1 A to J hbar frac partial f ja 0 omega partial omega left mathcal B 0 A to J frac mathcal C 0 A to J k B T right f ja 0 omega right H nbsp k A J 0 w 2 3 g N A 0 D 0 A J f j a 0 w displaystyle k A to J 0 omega frac 2 3 gamma N A 0 mathcal D 0 A to J f ja 0 omega nbsp for external field strength H displaystyle H nbsp Boltzmann constant k B displaystyle k B nbsp temperature T displaystyle T nbsp and a proportionality constant g displaystyle gamma nbsp This expression requires assumptions that j displaystyle j nbsp is sufficiently high in energy that N j 0 displaystyle N j approx 0 nbsp and that the temperature of the sample is high enough that magnetic saturation does not produce nonlinear C displaystyle mathcal C nbsp term behavior Though one must pay attention to proportionality constants there is a proportionality between D k displaystyle Delta k nbsp and molar extinction coefficient ϵ displaystyle epsilon nbsp and absorbance A C l displaystyle A Cl nbsp for concentration C displaystyle C nbsp and path length l displaystyle l nbsp These Faraday terms are the usual language in which MCD spectra are discussed Their definitions from perturbation theory are 10 A 1 1 d A a l J l L z 2 S z J l A a L z 2 S z A a A a m J l 2 A a m J l 2 B 0 2 d A ℜ a l K J k 1 E K E J J l L z 2 S z K k A a m J l K k m A a A a m J l K k m A a K A k 1 E K E A K k L z 2 S z A a A a m J l J l m K k A a m J l J l m K k C 0 1 d A a l A a L z 2 S z A a A a m J l 2 A a m J l 2 D 0 1 2 d A a l A a m J l 2 A a m J l 2 displaystyle begin aligned mathcal A 1 amp frac 1 d A sum alpha lambda left langle J lambda L z 2S z J lambda rangle langle A alpha L z 2S z A alpha rangle right times left langle A alpha m J lambda rangle 2 langle A alpha m J lambda rangle 2 right mathcal B 0 amp frac 2 d A Re sum alpha lambda left sum K neq J kappa frac 1 E K E J langle J lambda L z 2S z K kappa rangle times left langle A alpha m J lambda rangle langle K kappa m A alpha rangle langle A alpha m J lambda rangle langle K kappa m A alpha rangle right right amp qquad left sum K neq A kappa frac 1 E K E A langle K kappa L z 2S z A alpha rangle times left langle A alpha m J lambda rangle langle J lambda m K kappa rangle langle A alpha m J lambda rangle langle J lambda m K kappa rangle right right mathcal C 0 amp frac 1 d A sum alpha lambda langle A alpha L z 2S z A alpha rangle times left langle A alpha m J lambda rangle 2 langle A alpha m J lambda rangle 2 right mathcal D 0 amp frac 1 2d A sum alpha lambda left langle A alpha m J lambda rangle 2 langle A alpha m J lambda rangle 2 right end aligned nbsp where d A displaystyle d A nbsp is the degeneracy of ground state A displaystyle A nbsp K displaystyle K nbsp labels states other than A displaystyle A nbsp or J displaystyle J nbsp a displaystyle alpha nbsp and l displaystyle lambda nbsp and k displaystyle kappa nbsp label the levels within states A displaystyle A nbsp and J displaystyle J nbsp and K displaystyle K nbsp respectively E X displaystyle E X nbsp is the energy of unperturbed state X displaystyle X nbsp L z displaystyle L z nbsp is the z displaystyle z nbsp angular momentum operator S z displaystyle S z nbsp is the z displaystyle z nbsp spin operator and ℜ displaystyle Re nbsp indicates the real part of the expression Origins of A B and C Faraday Terms edit nbsp A 1 displaystyle mathcal A 1 nbsp B 0 displaystyle mathcal B 0 nbsp and C 0 displaystyle mathcal C 0 nbsp term intensity mechanisms for magnetic circular dichroism MCD signal The equations in the previous subsection reveal that the A 1 displaystyle mathcal A 1 nbsp B 0 displaystyle mathcal B 0 nbsp and C 0 displaystyle mathcal C 0 nbsp terms originate through three distinct mechanisms The A 1 displaystyle mathcal A 1 nbsp term arises from Zeeman splitting of the ground or excited degenerate states These field dependent changes in energies of the magnetic sublevels causes small shifts in the bands to higher lower energy The slight offsets result in incomplete cancellation of the positive and negative features giving a net derivative shape in the spectrum This intensity mechanism is generally independent of sample temperature The B 0 displaystyle mathcal B 0 nbsp term is due to the field induced mixing of states Energetic proximity of a third state K displaystyle K rangle nbsp to either the ground state A displaystyle A rangle nbsp or excited state J displaystyle J rangle nbsp gives appreciable Zeeman coupling in the presence of an applied external field As the strength of the magnetic field increases the amount of mixing increases to give growth of an absorption band shape Like the A 1 displaystyle mathcal A 1 nbsp term the B 0 displaystyle mathcal B 0 nbsp term is generally temperature independent Temperature dependence of B 0 displaystyle mathcal B 0 nbsp term intensity can sometimes be observed when K displaystyle K rangle nbsp is particularly low lying in energy The C 0 displaystyle mathcal C 0 nbsp term requires the degeneracy of the ground state often encountered for paramagnetic samples This happens due to a change in the Boltzmann population of the magnetic sublevels which is dependent on the degree of field induced splitting of the sublevel energies and on the sample temperature 11 Decrease of the temperature and increase of the magnetic field increases the C 0 displaystyle mathcal C 0 nbsp term intensity until it reaches the maximum saturation limit Experimentally the C 0 displaystyle mathcal C 0 nbsp term spectrum can be obtained from MCD raw data by subtraction of MCD spectra measured in the same applied magnetic field at different temperatures while A 1 displaystyle mathcal A 1 nbsp and B 0 displaystyle mathcal B 0 nbsp terms can be distinguished via their different band shapes 9 The relative contributions of A B and C terms to the MCD spectrum are proportional to the inverse line width energy splitting and temperature A B C 1 D G 1 D E 1 k T displaystyle A B C frac 1 Delta Gamma frac 1 Delta E frac 1 kT nbsp where D G displaystyle Delta Gamma nbsp is line width and D E displaystyle Delta E nbsp is the zero field state separation For typical values of D G displaystyle Delta Gamma nbsp 1000 cm 1 D E displaystyle Delta E nbsp 10 000 cm 1 and k T displaystyle kT nbsp 6 cm 1 at 10 K the three terms make relative contributions 1 0 1 150 So at low temperature the C 0 displaystyle mathcal C 0 nbsp term dominates over A 1 displaystyle mathcal A 1 nbsp and B 0 displaystyle mathcal B 0 nbsp for paramagnetic samples 12 Example on C terms edit nbsp An MCD spectrum and orbital diagram for potassium ferricyanide In the visible and near ultraviolet regions the hexacyanoferrate III ion Fe CN 63 exhibits three strong absorptions at 24500 32700 and 40500 cm 1 which have been ascribed to ligand to metal charge transfer LMCT transitions They all have lower energy than the lowest energy intense band for the Fe II complex Fe CN 62 found at 46000 cm 1 13 The red shift with increasing oxidation state of the metal is characteristic of LMCT bands Additionally only A terms which are temperature independent should be involved in MCD structure for closed shell species These features can be explained as follows The ground state of the anion is 2T2g which derives from the electronic configuration t2g 5 So there would be an unpaired electron in the d orbital of Fe3 From that the three bands can be assigned to the transitions 2t2g 2t1u1 2t2g 2t1u2 2t2g 2t2u Two of the excited states are of the same symmetry and based on the group theory they could mix with each other so that there are no pure s and p characters in the two t1u states but for t2u there would be no intermixing The A terms are also possible from the degenerate excited states but the studies of temperature dependence showed that the A terms are not as dependent as the C term 14 An MCD study of Fe CN 63 embedded in a thin polyvinyl alcohol PVA film revealed a temperature dependence of the C term The room temperature C0 D0 values for the three bands in the Fe CN 63 spectrum are 1 2 0 6 and 0 6 respectively and their signs positive negative and positive establish the energy ordering as 2t2g 2t1u2 lt 2t2g 2t2u lt 2t2g 2t1u1Example on A and B terms editTo have an A and B term in the MCD spectrum a molecule must contain degenerate excited states A term and excited states close enough in energy to allow mixing B term One case exemplifying these conditions is a square planar d8 complex such as n C4H9 4N 2Pt CN 4 In addition to containing A and B terms this example demonstrates the effects of spin orbit coupling in metal to ligand charge transfer MLCT transitions As shown in figure 1 the molecular orbital diagram of n C4H9 4N 2Pt CN 4 reveals MLCT into the antibonding p orbitals of cyanide The ground state is diamagnetic thereby eliminating any C terms and the LUMO is the a2u The dipole allowed MLCT transitions are a1g a2u and eg a2u Another transition b2u a2u is a weak orbitally forbidden singlet but can still be observed in MCD 15 nbsp The UV Vis absorption top and MCD bottom spectra of tetra n butylammonium tetracyanoplatinate in acetonitrile Because A and B terms arise from the properties of states all singlet and triplet excited states are given in figure 2 nbsp nbsp Mixing of all these singlet and triplet states will occur and is attributed to the spin orbit coupling of platinum 5d orbitals z 3500 cm 1 as shown in figure 3 The black lines on the figure indicate the mixing of 1A2u with 3Eu to give two A2u states The red lines show the 1Eu 3Eu 3A2u and 3B1u states mixing to give four Eu states The blue lines indicate remnant orbitals after spin orbit coupling that are not a result of mixing See also editCircular dichroism Faraday effect X ray magnetic circular dichroismReferences edit a b c IUPAC Compendium of Chemical Terminology 2nd ed the Gold Book 1997 Online corrected version 2006 magnetic circular dichroism doi 10 1351 goldbook MT06778 a b A D Buckingham amp P J Stephens 1966 Magnetic Optical Activity Annu Rev Phys Chem 17 399 Bibcode 1966ARPC 17 399B doi 10 1146 annurev pc 17 100166 002151 W Roy Mason 2007 A practical guide to magnetic circular dichroism spectroscopy Wiley Interscience doi 10 1002 9780470139233 ISBN 978 0 470 06978 3 Retrieved 16 April 2011 P N Schatz A J McCafferyd 1969 The Faraday effect Quarterly Reviews Chemical Society 23 4 552 doi 10 1039 QR9692300552 Dennis Caldwell Thorne J M Eyring H 1971 Magnetic Circular Dichroism Annu Rev Phys Chem 22 259 278 Bibcode 1971ARPC 22 259C doi 10 1146 annurev pc 22 100171 001355 G A Osborne 1973 A Near Infrared Circular Dichroism and Magnetic Circular Dichroism Instrument Review of Scientific Instruments 44 1 10 15 Bibcode 1973RScI 44 10O doi 10 1063 1 1685944 a b Stephens P J 1974 Magnetic Circular Dichroism Annu Rev Phys Chem 25 201 232 Bibcode 1974ARPC 25 201S doi 10 1146 annurev pc 25 100174 001221 G Zoppellaro et al 2009 Review Studies of ferric heme proteins with highly anisotropic highly axial low spin S 1 2 electron paramagnetic resonance signals with bis Histidine and histidine methionine axial iron coordination Biopolymers 91 12 1064 82 doi 10 1002 bip 21267 PMC 2852197 PMID 19536822 a b E I Solomon et al 1995 Magnetic circular dichroism spectroscopy as a probe of the geometric and electronic structure of non heme ferrous enzymes Coordination Chemistry Reviews 144 369 460 doi 10 1016 0010 8545 95 01150 N Stephens P J 1976 Magnetic Circular Dichroism Adv Chem Phys Advances in Chemical Physics 35 197 264 doi 10 1002 9780470142547 ch4 ISBN 9780470142547 Lehnert N DeBeer George S Solomon E I 2001 Recent advances in bioinorganic spectroscopy Current Opinion in Chemical Biology 5 2 176 187 doi 10 1016 S1367 5931 00 00188 5 PMID 11282345 Neese F Solomon E I 1999 MCD C Term Signs Saturation Behavior and Determination of Band Polarizations in Randomly Oriented Systems with Spin S gt 1 2 Applications to S 1 2 and S 5 2 Inorg Chem 38 8 1847 1865 doi 10 1021 ic981264d PMID 11670957 Stephens P J 1965 The Faraday Rotation of Allowed Transitions Charge Transfer Transitions in K3Fe CN 6 Inorg Chem 4 12 1690 1692 doi 10 1021 ic50034a003 Upton A H P Williamson B E 1994 Magnetic circular dichroism and absorption spectra of hexacyanoferrate III in a poly vinyl alcohol film J Phys Chem 98 71 76 doi 10 1021 j100052a013 Isci H Mason W R 1975 Electronic structure and spectra of square planar cyano and cyanoamine complexes of platinum II Inorg Chem 14 4 905 doi 10 1021 ic50146a038 Retrieved from https en wikipedia org w index php title Magnetic circular dichroism amp oldid 1216417793, wikipedia, wiki, book, books, library,

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