Anisotropy dipole polarizability

In linear, spherical and synnnetric tops the components of a along and perpendicular to the principal axis of synnnetry are often denoted by a and respectively. In such cases, the anisotropy is simply Aa = tty -If the applied field is oscillating at a frequency w, then the dipole polarizability is frequency dependent as well a(co). The zero frequency limit of the dynamic polarizability a(oi) is the static polarizability described above. 

The isotropic dipole polarizability a, the dipole polarizability anisotropy Aa and the isotropic traceless quadrupole polarizability C are defined as... 

The simplified schematic in Figure 2a shows the essential features of the effect. Optically anisotropic molecules in the solution are preferentially oriented by the applied field E(t), resulting in a difference of refractive indices for components of polarized light parallel and perpendicular to the bias field which is measured as a birefringence. The basic theoretical problem is to evaluate this effect in terms of anisotropies of polarizability Aa. referred to molecular axes which produce a time dependent effect when the molecules are preferentially oriented by the field. For no anisotropy in absence of the field, the effect must be an evgn function of field strength, and at low fields proportional to E. A remarkable feature of the effect is that for molecules with permanent dipole moments the response af-... 

Table XXXIII compares the estimated a with those computed. The accuracy of this simple estimator suggests that the isotropic polarizability is significantly determined by the heavy atoms, not the hydrogens, and that multiple bonds are, as expected, less polarizable. The anisotropy of the dipole polarizability, of course, has very much to do with the hydrogens.

Ilias et al 6 have made a detailed study of the electric dipole moment and static dipole polarizability of HI. Relativistic correlated CCSD(T) calculations have been made. The authors believe that the remaining discrepancies between theory and experiment, particularly in the polarizability anisotropy, cannot be reconciled and that the experimental data must be inaccurate. 

Table 8. The static dipole polarizability for the ground state and the first excited singlet state of pyrimidine in a.u. Coupled cluster values from [121]. The polarizability anisotropy parameter is defined as y = + a )/2 — Reproduced from [58]...

Table 13 Experimental and theoretical dipole moments p№ and dipole polarizability anisotropy for some small molecules. The theoretical results have been obtained using Hartree-Fock (HF), LDA, and GGA methods, and all quantities are given in atomic units. From ref. 80...

Approximate variation of the frequency-dependent polarizability a(v) from V = 0 up to the first dipole-allowed electronic transition, of energy the static dipole polarizability is a(0) infrared contributions ignored The photon frequency is v the polarizability anisotropy (the difference between polarizabilities parallel and perpendicular to the molecular axis) is y(v)... 

Ab initio and DFT Calculations on Diatomic Molecules. - Jaszunski, Klopper and Noga" describe an analysis of the static dipole polarizability of the Hc2 dimer using high precision CCSD(T) calculations. The results for the polarizability and its anisotropy are not significantly different from CCSD results in the literature and serve to confirm their accuracy. 

Polarizabilities of carbon dioxide and carbodiimide. Assessment of theoretical model dependencies on dipole polarizabilities and dipole polarizability anisotropies ... 

Optical Polarizability and Its Anisotropy. The polarizability, a, the constant of proportionality between the induced dipole moment, /j., and the intensity of the applied electric field, E, is of primary importance and is given by (6)... 

Anisotropy in the Rg-HX system (Rg = rare gas, X = F, Cl) is largely determined by the R induction term, involving the dipole polarizability of the rare gas atom and the dipole and quadrupole moments of the hydride molecule [80]. The corresponding dispersion term, involving frequency-dependent polarizabilities, gives further stabilization to the H-bonding in these complexes. 

The Kerr effect is also often used to determine the polarizabilities of molecules [1,9, 10]. In the general case, the Kerr constant has a complicated relation with the polarizability anisotropy, dipole moment and hyperpolarizability of a molecule. As a result, the problem of a separation of the contributions to the Kerr constant from these values is appeared. The separation diflhculties lead to the increase of errors of the method (10-20 %). Only for the gas media composed of non-polar molecules... 

The analysis of Fig. (5.1) shows that the analytical description of A y may be effectively used for / > 11 a.u. Naturally, for shorter R the analytical values of APg, y are noticeably differ from ab initio values due to exchange interactions appeared in this range. It is also noticeable that the exchange interaction is the most important for the Afi component. Such behavior of Aj is consistent with results of the asymptotic model of exchange interactions for van der Waals complexes [54, 60]. The strong anisotropy of the exchange effects was also observed for the case of collision-induced dipole moments and dipole polarizabilities in ion-atom pairs [61]. 

Fernandez et al calculated the frequency dependent interaction-induced second hyperpolarizability of two argon atoms. Subsequently, they evaluated the dielectric, the refractivity, the Kerr and the hyperpolarizability second virial coefficients. They obtained the interaction-induced mean and the anisotropy of the dipole polarizability and the mean second hyperpolarizability of Ai2 in the range of internuclear separations defined by 5 < R/ao < 30 at the CCSD level of theory, keeping the ten innermost MO frozen. They tested several basis sets at the experimental bond length of the argon dimer. Their final choice for the calculations was a d-aug-cc-pVTZ-33211 basis. 

A very accurate determination of the interaction-induced polarizability of He2 at the experimental internuclear separation of 5.6 ao was reported by Jaszunski et al The authors used a very large Ils8p6d5f4g3h basis set for He and high-precision explicitly correlated R12 methods. Their most accurate results for the mean and the anisotropy polarizability were calculated at the CCSD(T)-R12 level of theory and are are aint= 0.00104 and Aa = 0.06179 e ao Eh These values represent reference estimates of the interaction-induced dipole polarizability of two helium atoms. 

Maroulis et al. ° constructed five new, carefully optimized, xenon-specific gaussian-type basis sets. Their size ranges from B1 =[9s8p7dll] to B5 = [9s8p7d5f3g]. The interaction-induced dipole polarizability of the xenon dimer was calculated for a wide range of internuclear separations 4[Pg.37]

Aa = anisotropy of polarizability, Aa>0 P = angle between the molecular long axis and the dipole moment /t k = Boltzmann constant... 

The anisotropy of the electric dipole polarizability can be determined in Rayleigh scattering experiments, where the observed depolarization of the incident light is a function of (ctanis) (Bonin and Kresin 1997). 

The properties that are routinely computed and discussed are the mean (or average) static dipole polarizability (a), the anisotropy (Act) of the polarizability tensor, the vector component of the first hyperpolarizabUity tensor in the direction of the ground state permanent dipole moment (/3 ), the total first-order hyperpolarizabUity tot, and the scalar component of the second hyperpolarizability tensor y. Those quantities are related to the experiment and in terms of the Cartesian components are defined as... 

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