Electric Polarizability. Magnetic Susceptibility

The static average electric dipole polarizability a = 4.84 was derived [1] from older data [2] for the dielectric constant, the molar refraction, and the dipole moment. A vibrational contribution avib=0.086 (0.096x10 ° C2-m2-j- formerly called atomic polarization ) was obtained 

Polarizabilities a (without the vibrational contribution) and the components a, (parallel) and (perpendicular to the molecular symmetry axis) from three theoretical calculations are given below  

Experimental and a few theoretical values for the average magnetic susceptibility x. its components Xw (parallel) and Xi (perpendicular to the molecular symmetry axis), the anisotropy Ax = Xi 5Cii. the dia- and paramagnetic contributions x and x are given in the table below. 

The experimental data (in the first row) are based on an earlier measurement of x PH, [7] (see also Phosphor C, 1965, p. 30) and on later observations of the Zeeman effect In rotational transitions of PHgD and PHDg [8]. The theoretical data (all for the experimental geometry) were often based on coupled Hartree-Fock (CHF) calculations (see the remarks)  

X and x were also calculated for different origins by a variational method yielding the susceptibilities of localized P-H bonds [16] and for the origin at the center of mass by an ab initio sum-over-states (SOS) configuration interaction method [17]. x =-40.93 was obtained from a united-atom approximation, and x was estimated to be 16.35 (or 7.70) [18]. 

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Second-order response properties, such as electric polarizabilities, magnetic susceptibilities, and atomic polar tensors, can be readily partitioned into either atomic or atom-pair contributions with the help of the theory of AIMs. The former partitioning is accomplished by taking derivatives of the pertinent first-order properties with respect to strengths of external perturbations, whereas the latter involves a somewhat more complicated (albeit more theoretically consistent) formalism. In general, the atomic and atom-pair contributions to the second-order response properties are the sums of the atomic basin and surface relaxation terms. ... 

The atomic properties satisfy the necessary physical requirement of paralleling the transferability of their charge distributions - atoms that look the same in two molecules contribute identical amounts to all properties in both molecules, including field-induced properties. Thus the atoms of theory recover the experimentally measurable contributions to the volume, heats of formation, electric polarizability, and magnetic susceptibility in those cases where the group contributions are found to be transferable, as well as additive additive [4], The additivity of the atomic properties coupled with the observation that their transferability parallels the transferability of the atom s physical form are unique to QTAIM and are essential for a theory of atoms in molecules that purports to explain the observations of experimental chemistry. 

The tensor elements of x can be determined from measurements of macroscopic magnetic susceptibility or evaluated from molecular orbital methods and approximate variation perturbation calculations. Recently, calculations of the magnetic quadrupole polarizability of closed-shell atoms, and magneto-electric susceptibilities of atoms, have been made. These matters, which relate to the behaviour of microsystems under the simultaneous action of an electric and a magnetic field, will be dealt with in detml in subsequent sections. 

Bakhshi has published two articles on this subject with titles 1 - Average electric polarizabilities and magnetic susceptibilities of hydrocarbons, alcohols, ethers, aldehydes, ketones, amines and nitriles. 2- Double-zeta pseudopotential study of methyllithium, methylberyllium and dimethylberyllium. ... 

A comprehensive theory of electric polarizabilities and magnetic susceptibilities has been developed [4-6], which accounts for the electromagnetic moments induced in the electron cloud by the switching on of an external time-dependent perturbation. 

Some of those have long been known a is the electric dipole polarizability (a symmetric polar tensor of dimension P) in length formalism, k (an asymmetric axial tensor of dimension P t) is related to the optical activity, A is the mixed dipole-quadrupole polarizability, x is the magnetic susceptibility (or magnetizability), written as a sum of diamagnetic and paramagnetic components. 

Here ao(T, V) and xo(7 > V) represent respectively the modified scalar electric polarizability and magnetic susceptibility. As before, we assume that these parameters do not depend on the intensity of the applied electromagnetic field such materials are said to be linear in their response to electromagnetic fields. Phenomena such as ferroelectricity and ferromagnetism are thus excluded from the current formulations. 

We use the term modified electric polarizability and modified magnetic susceptibility because in the standard literature these quantities relate V io , rather than to q, and Ai to Ti, rather than to Ho-... 

The deflection of clusters by an inhomogeneous magnetic field provides an indication of their magnetic susceptibility. Similar deflection in a static electric field has also been performed for alkali beams and is planned for the transition metals in order to obtain polarizabilities as a function of cluster size. 

Similar expressions are obtained by perturbation calculations within the frame of the SCF theory of n electron systems (see Sect. 5.1) in aromatic hydrocarbons, the n electrons seem to be responsible for about one-half of the in-plane electric polarizabilities, and their contribution increases with the size of the molecule 21>. The same kind of developments can be made for magnetic susceptibilities 22 23>. 

IR), Raman nuclear magnetic resonance (NMR), electron spin resonance (ESR), Mdsbauer and vibronic circular (VCD) spectroscopy as well as electric and magnetic dipole moments, polarizability and magnetic susceptibility [83]. We shall in the following as an example discuss some applications to permanganate and related tetroxo complexes. 

Fig. II.3. Effect of fluorine substitutions on the out-of-plane minus average in-plane component of the magnetic susceptibility are shown for several aromatic rings. The difference between the Cotton-Mouton and the rotational Zeeman effect data is probably due to the neglect of the field dependence of the electric polarizability in the analysis of the Cotton-Mouton data. Note that the difference in the results for 1,2- and 1,3-difluorobenzene indicates that the ring current quenching effects of substituents strongly depend on their position...

In this expression is the electric dipole polarizability, is the mixed electric dipole-quadrupole polarizability, Xap is th magnetic susceptibility [56], rj p y and rj p ys can, respectively, be called electric dipole and electric quadrupole polarizability of the magnetic susceptibility. Quantum-mechanical definitions for these quantities within the framework of the Rayleigh-Schrddinger perturbation theory are given later. 

The CTOCD-DZ definitions for the magnetic susceptibility polarizabilities (23) and (25) can be arrived at by formally annihilating the diamagnetic contribution to the current density induced in the electrons by the uniform external magnetic field in the presence of an external electric field with a uniform EFG. 

In conclusion, summing the RHS of equations (49) and (50), the spurious gauge terms cancel each other out if the hypervirial conditions (33) and (54), and the sum rules for gauge invariance, equations (52), (53), (55), and (56) are fulfilled. Then the CO quadmpole polarizabilities of magnetic susceptibility change according to a relationship analogous to equation (41) for the electric polarizability,... 

Magnetic Susceptibility. - The definitions of the linear molecular magnetic susceptibility, Xy are analogous to those of the electric dipole polarizability, ay, and, as in the case of a, it can be defined in two ways, directly or through the expansion of the energy, W, in powers of the magnetic field, when... 

The application of refractions to the study of structures is based on comparing the experimental values with those calculated on various structural assumptions, of which the most important is additivity (Landolt, 1862) in the first approximation (within ca 10 %), the refraction of a compound is the sum of constant increments of different atoms, ions and bonds. Refractions of some isolated atoms can be measured by the deviation of an atomic beam in an inhomogeneous electric field or by spectroscopic methods. In other cases electronic polarizabilities of free atoms were calculated by ab initio methods. All available experimental and the best of the computed refractions of free atoms are presented in Table 11.5. These values can be used to calculate the energy of van der Waals interactions, magnetic susceptibility, or to establish correlations with atomic and molecular-physical properties. The formation of covalent bonds changes the refractions of isolated atoms and their values transform into the covalent refractions, which are different for isolated molecules and for crystals. Direct measurements of RI of A2 molecules or elemental solids give the most accurate information on the covalent refractions, in other cases the latter have to be calculated from molecular refractions by the additive method. 

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