Polarizabilities of atoms

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

Polarizabilities of atoms, 75, 76, 125 Polarization of bonds, 207 Potential energy surfaces, see Potential surfaces... 

FIGURE 14.5 The polarizability of atoms tends to decrease from left to right jeross a period and to increase down a group. 

Neon and xenon are gases at room temperature, but both become liquids if the temperature is low enough. Draw a molecular picture showing the relative sizes and polarizabilities of atoms of neon and xenon, and use the picture to determine which substance has the lower boiling point. 

High polarizibility of atoms or ions requires easy hybridization and/or large size. We see that for both copper and bismuth we have ample opportunity for hybridization that could lead to high polarizibility. For copper, it is 3d-4s hybridization for bismuth, it is 6s-6p hybridization. We expect this polarizibility to be more pronounced for the lower oxidation states of bismuth and copper. Oxygen polarizibility (2s-2p) may also be significant. 

These methods have been applied to calculate the polarizabilities of atoms,31 and the long-ranged forces between atoms,33 with a typical calculated accuracy of 10 % or less. Thus, we have been able to estimate successfully the significant features of zero-point fluctuations of atomic dipole moments, without actually solving the quantum equations of motion to obtain all the excited state energies and wave functions. 

The dimensions of the polarizability a are those of volume. The polarizability of a metallic Bphere is equal to the volume of the sphere, and we may anticipate that the polarizabilities of atoms and ions will be roughly equal to the atomic or molecular volumes. The polarizability of the normal hydrogen atom is found by an accurate quantum-mechanical calculation to be 4.5 ao that is, very nearly the volume of a sphere with radius equal to the Bohr-orbit radius a0 (4.19 a ). 

Bonin, K.D. and V V. Kresin Electric Polarizabilities of Atoms. Molecules ami Clusters. Wot Id Scientific Publishing Company Inc., River Edge, NJ. 1997. 

Bonin KD, Kresin VV (1997) Electric dipole polarizabilities of atom molecules and clusters. World Scientific, Singapore... 

K. Coutinho, S. Canuto, Sequential Monte Carlo/quantum mechanics study of the dipole polarizability of atomic liquids The argon case, in Atoms, Molecules and Clusters in Electric Fields. Theoretical Approaches to the Calculation of Electric Polarizabilities, ed. by G. Maroulis (Imperial College Press, London, 2006), pp. 405 120... 

Since the suggestion of the sequential QM/MM hybrid method, Canuto, Coutinho and co-authors have applied this method with success in the study of several systems and properties shift of the electronic absorption spectrum of benzene [42], pyrimidine [51] and (3-carotene [47] in several solvents shift of the ortho-betaine in water [52] shift of the electronic absorption and emission spectrum of formaldehyde in water [53] and acetone in water [54] hydrogen interaction energy of pyridine [46] and guanine-cytosine in water [55] differential solvation of phenol and phenoxy radical in different solvents [56,57] hydrated electron [58] dipole polarizability of F in water [59] tautomeric equilibrium of 2-mercaptopyridine in water [60] NMR chemical shifts in liquid water [61] electron affinity and ionization potential of liquid water [62] and liquid ammonia [35] dipole polarizability of atomic liquids [63] etc. 

Refs. [i] Bottcher CJF (1973) Theory of electric polarization Dielectrics in static fields, vol. 1. (1978) Dielectrics in time-dependent fields, vol. 2. Elsevier, Amsterdam [ii] Tide DR (2003) Dipole Moments. In Tide DR (ed) CRC handbook of chemistry and physics, 84til edn. CRC Press, Boca Raton, pp 9-42 - 9-51 [Hi] Miller TM (2003) Atomic and molecular polarizabilities. In Tide DR (ed) CRC handbook of chemistry and physics, 84th edn. CRC Press, Boca Raton, pp 10-163 -10-177 [ivJFred-erikse HPR (2003) Polarizabilities of atoms and ions in solids. In LideDR (ed) CRC handbook of chemistry and physics, 84til edn. CRC Press, Boca Raton, pp 12-17 -12-18... 

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. 

Hitherto, theoretical calculations have been carried out for a few multipole polarizabilities only, i.e. for field-gradient-induced quadrupole polarizabilities of atoms and ions [defined by the tensor of... 

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 ... 

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

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-... 

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 +... 

A. D. Buckingham and K. L. Clarke. Long-range effects of molecular interactions on the polarizability of atoms. Chem. Phys. Lett., 57 321-325 (1978). 

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] ... 

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