Polarizability. Magnetic Susceptibility

For these physical properties only theoretical results from a simple ab initio FSGO calculation are available. The average polarizability a = 4.107 and the molar, dia-, and paramagnetic susceptibilities (in 10 emu/mol) Xm = 16.430, %d = 21.482, %p = 5.053 were obtained. 

---

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 calculation and analysis of various properties of the reaction complex such as dipole moment, polarizability, magnetic susceptibility, etc., as a function of s complements the description. 

The polarizability, ionization potential, and magnetic susceptibility data from the last edition of the Landolt-Bornstein tables are given in Table I for the inert gases and for H2, Na, Ci2, and CH4. The coefficients of the dipole-dipole or R 6 potential term are... 

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. 

If the electron-cloud radius yrms were exactly equal to the structural radius r, Wasastjerna s criterion would be obviously true. But in fact, for ions r ce. 2 yrms (Table 3). Hence the criterion needs justification. It is obviously most probable for isoelectronic ions (cp. Eauling (/)), but the electron-cloud radii should refer to the ions in the crystals, not to the free ions. For, with a gross difference between crystal and free-ion electron-cloud radii for the hydride ion, there may be significant differences for others 40). For the crystals the electron-cloud radii could be obtained either from polarizeability or from magnetic susceptibility. The theory of polarizeability is less certain and there is a considerable correction to infinite wavelength. We therefore adopt the magnetic evidence. But this must be corrected for the inner shell contribution (Table 3). 

Magnetic susceptibilities Zeeman and Faraday effects polarizability 594... 

Polarizability will be dealt with first because it is the easiest of the three properties to calculate and has certainly received the most attention. Many of the conclusions also apply to x and a, which are dealt with in much less detail. In each section we have tried to pick out the most important methods and consider them in detail at the expense of the less useful methods. Thus, for example, although the variational technique of Karplus and Kolker is simpler than the other uncoupled Hartree-Fock perturbation methods, it is not a very useful technique for calculating polarizabilities. It is very useful for calculations of magnetic susceptibility, however, where many other techniques are inappropriate. 

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. 

---