Polarizability anisotropic

Abstract We present an overview of the energy functions used in two Anisotropic Polarizable... 

As we have seen, Anisotropic Polarizable Molecular Mechanics (APMM) procedures such as SIBFA or GEM are more complex than usual classical approaches. 

Gresh N, Cisneros GA, Darden TA, Piquemal J-P (2007) Anisotropic, polarizable molecular mechanics studies of inter-, intra-molecular interactions, and ligand-macromolecule complexes. A bottom-up strategy. J Chem Theory Comput 3 1960... 

The Drude oscillators are typically treated as isotropic on the atomic level. However, it is possible to extend the model to include atom-based anisotropic polarizability. When anisotropy is included, the harmonic self-energy of the Drude oscillators becomes... 

Bernardo DN, Ding YB, Kroghjespersen K, Levy RM (1994) An anisotropic polarizable water model - incorporation of all-atom polarizabilities into molecular mechanics force-fields. J Phys Chem 98(15) 4180-4187... 

These techniques proved to be successful for the majority of the hydrocarbons, but they failed for some compounds such as phenanthrene, terphenyl, or quater-phenyl. The failure has been interpreted by the effect of the electric field on the charge distribution [190]. Actually, these molecules have strongly anisotropic polarizabilities. In a more recent study, it was demonstrated that the isomeric ratio also depends on the counterion [191]. 

The fluctuations in the orientation of anisotropically polarizable molecules in liquids also cause frequency broadening of the scattered light, as investigated for CSj in CCI4 239). CS is a highly polarizable molecule with very different polarizabilities along and perpendicular to the internuclear axis. CCU on the other hand, is a poor scatterer because it is an isotropic molecule. Thus, if CSj is mixed with CCI4, the CSj molecules can be studied in a new environment. 

This question was addressed by use of classical trajectory techniques with an ion-quadrupole plus anisotropic polarizability potential to determine the collision rate constant (k ). Over one million trajectories with initial conditions covering a range of translational temperature, neutral rotor state, and isotopic composition were calculated. The results for the thermally average 300 K values for are listed in the last column of Table 3 and indicate that reaction (11) for H2/H2, D2/D2, and HD /HD proceeds at essentially the classical collision rate, whereas the reported experimental rates for H2/D2 and D2/H2 reactions seem to be in error as they are significantly larger than k. This conclusion raises two questions (1) If the symmetry restrictions outlined in Table 2 apply, how are they essentially completely overcome at 300 K (2) Do conditions exist where the restriction would give rise to observable kinetic effects ... 

We noted in the preceding section that the polarizability of an ellipsoid is anisotropic the dipole moment induced by an applied uniform field is not, in general, parallel to that field. This anisotropy originates in the shape anisotropy of the ellipsoid. However, ellipsoids are not the only particles with an anisotropic polarizability in fact, all the expressions above for cross sections are valid regardless of the origin of the anisotropy provided that there exists a coordinate system in which the polarizability tensor is diagonal. 

In the recent work reviewed in this chapter, we have shown the creation and properties of molecular superrotors, illustrated by application of the optical centrifuge to simple diatomic molecules. The technique is certainly not limited to diatomics, and to date we have created superrotor wave packets in a range of molecules. All that is required is an anisotropic polarizability such that the molecule can be... 

The birefringence An of a nematic phase depends on the anisotropic polarizabilities a, a L and the degree of order S (Eq. (3), p. 114). The polarizabilities ae and of a nematic phase parallel and perpendicular to the director respectively obey the following relations 53)... 

Figure 9. Top An isotropic atom/molecule and crystal with isotropic polarizabilities will give rise to a spherical wave surface and index ellipsoid. Middle Another isotropic atom/molecule and crystal with larger isotropic polarizabilities will give rise to a smaller spherical wave surface and a larger spherical index ellipsoid. Bottom An anisotropic atom/molecule and crystal with anisotropic polarizabilities will give rise to an ordinary spherical wave surface and an ellipsoidal extraordinary wave surface. The index ellipsoid will have major and minor axes.

One possibility is weighting the partitioning with the original polarizabilities [108]. This may work better in the general case, but it is just as arbitrary. What will happen to local (anisotropic) polarizabilities in the condensed phases is hard to estimate without calculations. Some typical model systems can be found in Ref. [24], It is also demonstrated by the work of Augspurger and Dykstra [109] on acetylene clusters where for linear complexes an increase of the axial components of the linear and second hyperpolarizabilities are found, while van Duijnen et al. [110] for parallel clusters of butadienes and Kirtman et al. [Ill] for hexatrienes obtained a decrease in the same properties. These authors also show that well-constructed fully classical electrostatic models are able to reproduce these results. 

In the complexes [Ln(H20)y]3+, [Ln(oda)3]3, the dynamic polarization first-order electric dipole transition moment is minimized by negative interference due to the out-of-phase relation between the contributions of the [ML3] and [ML6] ligand sets [109,110]. For [Ln(oda)3]3 and other D3 complexes, only the anisotropic polarizability contributions are non-zero for AMj = 1 transitions in the [Eu(H20) ]3+ and [Eu(oda)3]3 complexes the contribution of the cross-term to the dipole strength of the 7Fo —> 5D2 and5 Do — 7F2 transitions has a magnitude comparable with that of the dominant crystal field or dynamic polarization contribution [111]. 

There exist a variety of extensions of the basic shell model. One variation for molecular systems uses an anisotropic oscillator to couple the core and shell charges,thus allowing for anisotropic polarizability in nonspherical systems. Other modifications of the basic shell model that account for explicit environment dependence include a deformable or breathing shelF ° and shell models allowing for charge transfer between neighboring sites. 

An Anisotropic Polarizable Water Model Incorporation of All-Atom Polarizabilities into Molecular Mechanics Force Fields. 

For molecules with anisotropic polarizabilities, where the assumption Piseries solution in the form times powra s of a r gM The contribution to Be of the lead term in the series proportional to vanishes on averaging over all orientations if the intomolecular potential is a function of fu only. For isotropically polarizable molecules the lead term also vanishes, leaving the series equivalent to the second term on the right side of equation 3a). The lead term in this series, (4Treo) 2<4 i2, is exactly what is obtained by setting the denominator of the second term in equation (23a) equal to one. 

Non-dipolar macromolecules. In the case of anisotropically polarizable macromolecules (JT + 0) not possessing poman t dipoles (A = 0), we obtain from (318) the following Ae variation, due solely to reorientation of induced dipoles ... 

Birefringence of Dipolar Anisotropically Polarizable Microsystems. In the general case of microsystems which are dipolar and at the same time anisotropically polarizable in an external field E, the reorientation function for the Kerr effect is given by equation (233). Graphs of this reorientation function are shown in Figure 13 against the parameter Xi at parametrical values of X = X ln for = 1,4,9,16,25, 36,. 

Dipolar, anisotropically polarizable macromolecules. If the solution contains macromolecules which are at the same time dipolar and amsotropically polarizable, one has to apply formula (318). For comprehensive analysis, the latter is more conveniently expressed in the following form ... 

---