Editing Magnetic circular dichroism (section)

===Origins of A, B, and C Faraday Terms===

[[File:MCD-ABC-terms.svg|thumb|upright=2|<math>\mathcal{A}_1</math>, <math>\mathcal{B}_0</math>, and <math>\mathcal{C}_0</math> term intensity mechanisms for magnetic circular dichroism (MCD) signal]]

The equations in the previous subsection reveal that the <math>\mathcal{A}_1</math>, <math>\mathcal{B}_0</math>, and <math>\mathcal{C}_0</math> terms originate through three distinct mechanisms. 

The <math>\mathcal{A}_1</math> 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 <math>\mathcal{B}_0</math> term is due to the field-induced mixing of states. Energetic proximity of a third state <math>|K\rangle</math> to either the ground state <math>|A\rangle</math> or excited state <math>|J\rangle</math> gives appreciable [[Zeeman effect|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 <math>\mathcal{A}_1</math> term, the <math>\mathcal{B}_0</math> term is generally temperature independent. Temperature dependence of <math>\mathcal{B}_0</math> term intensity can sometimes be observed when <math>|K\rangle</math> is particularly low-lying in energy. 

The <math>\mathcal{C}_0</math> term requires the degeneracy of the ground state, often encountered for paramagnetic samples. This happens due to a change in the [[Boltzmann distribution|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.<ref>{{cite journal|author1=Lehnert, N. |author2=DeBeer George, S. |author3=Solomon, E. I. |author-link3=Edward I. Solomon |journal=Current Opinion in Chemical Biology|date=2001|volume=5|pages=176–187|doi=10.1016/S1367-5931(00)00188-5|pmid=11282345|title=Recent advances in bioinorganic spectroscopy|issue=2}}</ref> Decrease of the temperature and increase of the magnetic field increases the <math>\mathcal{C}_0</math> term intensity until it reaches the maximum (saturation limit). Experimentally, the <math>\mathcal{C}_0</math> 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 <math>\mathcal{A}_1</math> and <math>\mathcal{B}_0</math> terms can be distinguished via their different band shapes.<ref name=solomon/>

The relative contributions of A, B and C terms to the MCD spectrum are proportional to the inverse line width, energy splitting, and temperature:
:<math>A:B:C = \frac{1} {\Delta \Gamma} : \frac {1} {\Delta E} : \frac{1}{kT}</math>
where <math>\Delta \Gamma</math> is line width and <math>\Delta E</math> is the zero-field state separation. For typical values of <math>\Delta \Gamma</math> = 1000&nbsp;cm<sup>−1</sup>, <math>\Delta E</math> = 10,000&nbsp;cm<sup>−1</sup> and <math>kT</math> = 6&nbsp;cm<sup>−1</sup> (at 10&nbsp;K), the three terms make relative contributions 1:0.1:150. So, at low temperature the <math>\mathcal{C}_0</math> term dominates over <math>\mathcal{A}_1</math> and <math>\mathcal{B}_0</math> for paramagnetic samples.<ref>{{cite journal|author1=Neese, F. |author2=Solomon, E. I. |author-link2=Edward I. Solomon |journal=Inorg. Chem.|date=1999|volume=38|pages=1847–1865|doi=10.1021/ic981264d|pmid=11670957|title=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)|issue=8}}</ref>