Polarizability of atoms and molecules

Concluding remarks and recapitulation. Rdated electric field-induced phenomena non-linear polarizabilities of atoms and molecules radial and angular correlations fluctuations of molecular fields. 

There exist various reviews of the methods by which the electric and magnetic polarizabilities of atoms and molecules can be establidied. Particularly valuable are the comprehensive artides of Le Ffevre on the determination of the anisotropy of optical polarizability from molecular refraction measurements and Kerr effect and, recently, on the role of molecular polarizability in chemistry. Bothorel reviews the method of deternuning optical anisotropy from direct measurements of depolarized scattered laser light intensity and its particular utility in the study of n-alkanes. Stein et al have latdy discussed the polarizability anisotropy of macromolecules. 

Non-lineax Polarizabilities of Atoms and Molecules 377 Radial and Angular Molecular Correlations 379... 

Numerical values of linear and non-linear polarizabilities of atoms and molecules calculated theoretically and determined from experimental data. Only mean values are given a = (ou + a%i + 033)/s, b = (6u3 + 6333 +... 

It has long been recognized that the polarizabilities of atoms and molecules can be correlated with their volumes [153-158], For a uniform conducting sphere of radius R and volume V, the relationship is exact [87] ... 

Bogaard, M. P, Orr, B. J. (1975). Electric Dipole Polarizabilities of Atoms and Molecules. In A. D. Buckingham (Ed.), International review of science, physical chemistry, molecular structure, and properties, series 2 (Vol. 2, p. 149). London Butterworths. 

Sometimes it is stated that dispersion is a quantum mechanical effect and induction is not. Thus, some clarifying comments are at place here. From the general viewpoint, all effects including polarizability are quantum mechanical in their origin because the polarizability of atoms and molecules is a quantum mechanical quantity and can be assessed only in the framework of quantum mechanics. However, once calculated, one can think of polarizability in classical terms representing a quantum molecular object as a classical oscillator with the mass equal to the polarizability, which is not specified in the classical framework. This is definitely wrong from a fundamental viewpoint, but, as it usually appears with harmonic models, a quantum mechanical calculation and such a primitive classical model give basically... 

Sideline. In 1850 Mossotti and in 1879 Clausius showed that for any given substance the ratio (e — l)/(e + 2) should be (and indeed is) proportional to the density of the substance. Luckily, the static electric diple polarizability oc is very close to the atomic volume (or the molecular volume). Decades before the advent of X-ray structure determination, Eq. (5.10.19) allowed estimates of the size of atoms and molecules from measures of the density and the dielectric constant. 

Ty). Numerous authors have discussed certain special aspects of refractive index theory in simple dense fluids, macromolecular fluids and in fluids near the critical point. Also, various experimental studies of jRm have been carried out for simple fluids and water. " Frequency-dependent polarizabilities of atoms and simple molecules have been calculated. ... 

The Role of Non-linear Polarizability. We have just proved that the anisotropic molar saturation constants are non-zero even in liquids consisting of atoms and non-polar molecules. Beside the previous statistical-fluctuational processes, simple liquids reveal mechanisms that are due to the non-linear polarizabilities of atoms and such molecules. This is so because, in general, in addition to linear electric polarizability in the form (288), if a suffidently strong electric field is applied, we have to deal with the non-linear polarizability ... 

Linear electric polarizabilities of atoms and polarizability anisotropies of molecules have been rather extensively evaluated by using more or less approximate wavefunctions and various perturbation methods. Note-... 

Electronegativities calculated using other definitions have been correlated with different properties of atoms and molecules, such as bond force constant of binary hydrides, ionization potential of atoms [23], polarizability [24,25], etc. Studies on the bond critical points of binary [26] and diatomic [26] hydrides provided correlation between the properties calculated at the bond critical points and the electron-attracting power of an atom [26]. 

Polarizabilities for atoms and molecules in excited states are found to be larger than for ground states and may be positive or negative. Molecular polarizabilities are very slightly temperature dependent since the size of the molecule depends on its rovibra-tional state. Only in the case of dihydrogen has this effect been studied enough to warrant consideration in Table 3. 

The most fundamental starting point for any theoretical approach is the quantum mechanical partition function PF), and the fundamental connection between the partition function and the corresponding thermodynamic potential. Once we have a PF, either exact or approximate, we can derive all the thermodynamic quantities by using standard relationships. Statistical mechanics is a general and very powerful tool to connect between microscopic properties of atoms and molecules, such as mass, dipole moment, polarizability, and intermolecular interaction energy, on the one hand, and macroscopic properties of the bulk matter, such as the energy, entropy, heat capacity, and compressibility, on the other. 

Reshetmkov N, Curtis LJ, Brown MS, Irwing RE (2008) Determination of polarizabilities and lifetimes for the Mg, Zn, Cd and Hg isoelectronic sequences. Physica Scripta 77 015301 Wasastjema JA (1922) About the formation of atoms and molecules explained using the dispersion theory. Z phys Chem 101 193-217... 

At present, in spite of the well-known fact that the interaction of atoms and molecules leads to the changing of their multipole moments and (hyper)polariz-abilities [1-3], only the simple moments and polarizabilities of interacting molecules such as interaction-induced dipole moments and dipole polarizabilities have widely studied. Nevertheless, the induced dipole moments and polarizabilities play the important role in understanding the collision-induced absorption, collision-induced Rayleigh scattering or collision-induced Raman light scattering [4-9],... 

Methods to compute the interaction energy of a cluster of atoms and molecules have been developed at different levels of sophistication. The development of quantum chemical methods and computers has permitted us to accurately model the interaction energy of assembhes of molecules. During the last decades, Anthony Stone has played a prominent role in the endeavour of accurately modelling molecular properties and interactions from quantum chemistry. The IMPT theory, models of distributed multipoles, distributed polarizabilities, distributed dispersion coefficients, anisotropic repulsion, developed by Stone and collaborators, allow us to build accurate interaction potentials from quantiun chemistry. 

Bonin K D and Kresin V V 1997 Electric-dipole Polarizabilities of Atoms, Molecules and Clusters (Singapore World Scientific)... 

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