Molecular magnetizability

The calculation of molecular magnetizabilities Comparison with experiment... 

Among the molecular properties introduced above are the permanent electric dipole moment /xa and traceless electric quadrupole moment a(8, the electric dipole polarizability aajg(—w to) [aiso(to) = aaa(—or, o>)], the magnetizability a(8, the dc Kerr first electric dipole hyperpolarizability jBapy(—(o a>, 0) and the dc Kerr second electric-dipole hyperpolarizability yapys(— ( >, 0,0). The more exotic mixed hypersusceptibilities are defined, with the formalism of modern response theory [9]... 

Birefringences are mostly observed in condensed phases, especially pure liquids or solutions, since the strong enhancement of the effects allows for reduced dimensions (much shorter optical paths) of the experimental apparatus. Nowadays measurements of linear birefringences can be carried out on liquid samples with desktop-size instruments. Such measurements may yield information on the molecular properties, molecular multipoles and their polarizabilities. In some instances, for example KE, CME and BE, measurements (in particular of their temperature dependence) have been carried out simultaneously on some systems. From the combination of data, information on electric dipole polarizabilities, dipole and quadrupole moments, magnetizabilities and higher order properties were then obtained. 

Terms of higher order in the field amplitudes or in the multipole expansion are indicated by. . . The other two tensors in (1) are the electric polarizability ax and the magnetizability The linear response tensors in (1) are molecular properties, amenable to ab initio computations, and the tensor elements are functions of the frequency m of the applied fields. Because of the time derivatives of the fields involved with the mixed electric-magnetic polarizabilities, chiroptical effects vanish as a> goes to zero (however, f has a nonzero static limit). Away from resonances, the OR parameter is given by [32]... 

We do not here attempt to review the developments of methods for calculating molecular polarizabilities and magnetizabilities, nor will we attempt any review of theoretical results obtained for these properties. We will instead outline the approach for calculating molecular properties in general, and the polarizability and the magnetizability of closed-shell systems in particular, using ab-initio methods. We will also devote some time to discuss... 

The response equations are usually solved in some iterative manner, in which the explicit construction of Q is avoided, being replaced by the repeated construction of matrix-vector products of the form Q where v is some trial vector . In general, the solution of one set of response equations is considerably cheaper than the optimization of the wave function itself. Moreover, since the properties considered in this chapter involves at most three independent perturbations (corresponding to the three Cartesian components of the external field), the solution of the full set of equations needed for the evaluation of the molecular dipole-polarizability and magnetizability tensors is about as expensive as the calculation of the wave function in the first place. 

London orbitals were introduced by Fritz London, who in 1937 used Hiickel theory to calculate the contribution to the magnetizability from the ring currents in the 7r-orbital backbone of some aromatic molecules [13]. The great virtue of London s approach is that each individual AO—the building blocks of molecular wave functions—has been harnessed to respond correctly (to first order at least) to the application of an external magnetic field, irrespective of the choice of the external gauge origin. Moreover, since, in London s approach, only the atomic orbitals are modified, this method is fully transparent to the treatment of the electronic structure otherwise. 

The additivity of the molecular dipole polarizability was established already in the 1920s. However, whereas the magnetizability could easily be ratio-... 

In the present paper, we have discussed the ab-initio evaluation of the static polarizabilities and magnetizabilities of molecular systems, with emphasis on the principles underlying such calculations. With the recent widespread availability of powerful computers, these second-order molecular properties may nowadays be calculated a priori for large molecular systems, allowing us to explore, for instance, the relationship between the properties and molecular structure. Such calculations complement the experimental work in the area and may help in reassessing and improving on the empirical schemes... 

Table 16-1. Energies, electric dipolar moments, net atomic populations, vibrational polarizabilities and mean vibrational molecular polarization, magnetizability and contributions thereto, isotropic g tensor and nuclear and electronic paramagnetic and diamagnetic contributions thereto, principal moments of inertia and rotational parameters calculated for H2 C N2 in seven structural isomers... 

The response function magnetizability x of 8 molecular solute can be expressed as second derivatives of the free energy functional ... 

The definition of corresponding molecular tensors arrived at by continuous transformation of the origin of the current density, which formally sets its diamagnetic term to zero (abbreviated as CTOCD-DZ), is discussed in Section 3. Section 4 deals with the problem of origin dependence of magnetizability polarizabilities of a molecule in the presence of uniform EFG. 

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