Diamagnetic term/operator

A particularity of non-relativistic theory is that the introduction of vector potentials gives rise to second-order magnetic operators as well. These diamagnetic terms contribute as expectation values to second-order properties and are... 

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. 

In order to prove this for all three properties we start by rewriting the operators of the diamagnetic terms as... 

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 ... 

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. 

The total molecular susceptibility has now been expressed as a sum over operators localized on the various atomic nuclei. But they operate on wave functions that extend over the whole molecule. If the average values of these atomic operators are not greatly dependent on parts of the wave function far removed from the nucleus in question and if the relevant properties of the electron distribution around each nucleus are not much different for a given type of atom in different molecules, the terms within each sum over n in Eq. (41) will be independent and constant. They will, in short, be additive atomic susceptibilities that can be evaluated from measured molecules and used to predict the susceptibility of any desired molecule. We have already demonstrated the additivity of the diamagnetic susceptibilities [Eq. (37)]. 

Let us consider a term in Eqn. (1), bilinear with respect to some parameters Ai and A2 (for example, containing IDifferent operators in the Hamiltonian (Eqn. (4)) may contribute to these terms, and those which have a bilinear dependency on Ax and A2 lead to diamagnetic contributions (depending on the ground state wave function only). In the case of the... 

As mentioned above there are four main contributions to the nuclear spin-spin coupling constants the Fermi contact (FC), the paramagnetic spin-orbit (PSO), the spin-dipolar (SD) and the diamagnetic spin-orbit (DSO) contributions. The Fermi contact term is usually the most important of these and also the most sensitive to geometry changes [8]. The Fermi contact contribution arises from the interactions between the terms containing S(riM) and < (riN) in the operators Hon for nuclei N and M (see Eqn. (12)). 

The dominant diamagnetic Hamiltonian term is a simple one-electron operator and its expectation value, when the ground-state determinantal wave function is constructed from the set of occupied molecular spin-orbitals, is... 

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