Paramagnetic terms/operator

The expression for the contribution to the spin-orbit induced MCD intensity from perturbation of the ground state is somewhat reminiscent of an expression for the Ag quantity of EPR spectroscopy. The similarity lies in the paramagnetic term, Agp. This term is composed of integrals of a spin-orbit operator over molecular orbitals similar to the expression for the perturbation of the ground state in the presence of spin-orbit coupling (Eqs. 52-56). The paramagnetic contribution to Ag dominates for blue copper proteins and it was suspected that the MCD parameters and Amay have some sort of relationship. It was found that many of the terms that make large contributions to AgP do play a role in the MCD intensity but no simple relationship was found (160). 

Matrix elements of p also enter the paramagnetic term. These are conveniently written in terms of the dimensionless oscillator strength/p, defined in Eq. (4-8) but with the bonding state replaced here by an atomic s state and the antibonding state replaced by a p state oriented parallel to the momentum operator. These terms in p have the same proportionality to a., and are found to have the effect of... 

In SOS-PT a magnetic parameter can be expressed as the sum of two contributions the diamagnetic term involving only the ground-state wave function, and the paramagnetic term containing the resolvant operator... 

The operator quadratic in the vector potential, /2meC, is often called the diamagnetic term and the remaining magnetic-potential operators linear in B (or A, respectively) are called paramagnetic terms. 

Combined with the paramagnetic term in Eq. (6.53) this reformulated diamagnetic contribution replaces in the paramagnetic term the dependence of the orbital angular momentum operator on the nuclear centre of mass Rcm by a dependence on the position of nucleus K. An alternative expression for the spin-rotation tensor is thus... 

These two terms are known as the paramagnetic and diamagnetic terms, respectively and / is a molecular orbital in the presence of the magnetic field, p is the classical linear momentum operator and A the vector potential. In the so-called CSGT or CTOCD-DZ or ipsocentric methods [79-82], the second term is effectively put to zero via the special choice of gauge. What ranains eventually, is the paramagnetic term ... 

There are electron spin-independent and spin-dependent paramagnetic terms (linear in the vector potential), and a diamagnetic spin-independent term that (quadratic in the vector potential). By substituting (12.12a) or (12.12b) in the spin-free linear terms, one obtains the ZORA form of the Orbital Zeeman (OZ) operator... 

The second-order terms give the magnetizability. The first term is known as the diamagnetic part and it is particularly easy to calculate since it is just the expectation value of the second moment operators. The second term is called the paramagnetic part. 

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