Induced moment mechanisms

In spherically symmetric systems the induced diamagnetism depends primarily on the mean square radius of the valence electrons as the small contribution from the inner-shell electron core can usually be neglected 1 ). In the case of molecules with symmetry lower than cubic, the quantum mechanical treatment by Van Vleck 23> indicates that another term must be added to the Larmor-Langevin expression in order to calculate correctly diamagnetic susceptibilities. This second term arises because the electrons now suffer a resistance to precession in certain directions due to the deviations of the atomic potential from centric symmetry. The induced moment will now be dependent on the orientation of the molecule in the applied magnetic field and thus in general the diamagnetic susceptibility will not be an isotropic quantity 19-a8>. 

The most important component of the water trimer nonadditive energy is the induction interaction of the second order in V. Its simple mechanism is shown in Fig. 33.3 a permanent multipole moment on monomer A induces multipole moments on monomer B which in turn interact with the permanent multipole moments of monomer C. Higher orders involve interactions between induced moments. The nonadditive induction energy is in general the most important nonadditive component for hydrogen-bonded systems. As already mentioned, it is the only term used—and only in the asymptotic approximation, i.e. neglecting charge-overlap effects—in the polarizable empirical potentials. 

Thus, also a permanent dipole mechanism may be characterized by a transition of the X quantity from a quadratic field strength dependence to a linear one concomitant with the E dependence the temperature variation changes from T to T K Therefore the temperature dependence of equilibrium and rate constants may be used to differentiate between permanent and induced moments. 

FIGURE 1. Principle of the saturatable induced dipole mechanism causing positional changes of side chains in helical membrane proteins. In bacteriorhodopsin helical parts with different net charge may move transversal to the membrane plane in opposite directions when the electric membrane field is increased, (a) - (b). The geometrically limited increase in the distance of the charge centers is equivalent to a saturatable induced dipole moment. The transversal displacement of at least one of the two helical parts can thereby cause a concerted rotational shift of the retinal (=o) and of aromatic amino acid side chains which may sandwich (T. H. Haines) the retinal chromophore. 

Electrical Properties. The piezoelectricity of the technologically important polymer of vinylidene fluoride (PVDF) has been the subject of modeling for several decades (see Piezoelectric Polymers). An early example of the use of molecular mechanics to aid in the calculation of the mechanical and electrical properties of this polymer is found in the work of Tadokoro and co-workers (390,391). Subsequent investigation of PVDF by Karasawa and Goddard (83) focussed on the prediction of alternative crystal structures with use of the shell model to captiu-e polarization effects. The latter phenomenon was further explored by Carbeck and co-workers (84), who used the shell model to show that the induced moment because of neighboring dipoles in the crystal increases the dipole per repeat imit by about 50% over its value in the isolated molecule. 

This formula can be derived either from classical considerations or by using quantum mechanical perturbation theory. In either case it is clear that only linear polarizabilities are included that is, the induced moments described by Eq. (29) are a linear response to the fields and field gradients of the neighbouring molecules. For a complete description we should also allow for contributions to the induced moments that depend on quadratic and higher powers of the electric fields. For a uniform field, we should use, instead of Eq. (24), the form... 

Three basic types of physical phenomenon are responsible for electroopti-cal behavior of a macromolecule in solution dipole moment, diffusion coefficients, and extinction coefficients. Amplitudes and time constants depend on both the properties of the macromolecules and experimental conditions. The sum of relaxation amplitudes is related to the linear dichroism of the solution at saturation, and depends on both the electric and optical properties of the molecule under investigation. The saturating behavior of linear dichroism calculated for a pure permanent moment, a pure induced moment or a mixed orientational mechanism is traditionally used in determining electrical responses and optical anisotropy by fitting the experimental results to a theoretical curve.Pqj. molecules with effective cylindrical symmetry (regarding their orientational behavior), the optical signal observed in the experiment can be represented as a product of orientational factor, < )(j, and a limiting reduced dichroism at infinite field. 

The SOC induced orbital magnetic moments / oib as obtained by the SPR- and SOPR-KKR-CPA for the di.sordered alloy. sy.stem bcc-Fe Coi-a are given in Fig. 2. As for the pure elements one finds an enhancement of / oib by the OP-term by around 60 %. This enhancement brings the total theoretical orbital magnetic moment for the alloy in very satisfying agreement with experimental data derived from magneto mechanical as well as spectroscopic g-factor measurements [15]. 

Ma BY, Lii JH, Allinger NL (2000) Molecular polarizabilities and induced dipole moments in molecular mechanics. J Comput Chem 21(10) 813—825... 

Observe that all the mechanisms—that is, the classical indirect mechanism and the two quantum ones—predict a satisfactory isotope effect when the proton of the H bond is substituted by deuterium All the damping mechanisms induce approximately a l/y/2 low-frequency shift of the first moment and a 1 / y/2 narrowing of the breadth, which is roughly in agreement with experiment. As a consequence, the isotope effect does not allow us to distinguish between the two damping mechanisms. 

---