Polarizability generalized

In general, polarizability increases as the orbital increases in size negative electrons orbit the positive nucleus at a greater distance in such atoms, and consequently experience a weaker electrostatic interaction. For this reason, London dispersion forces tend to be stronger between molecules that are easily polarized, and weaker between molecules that are not easily polarized. 

It might seem at first glance that arriving at the dipole moment p of an ellipsoidal particle via the asymptotic form of the potential < p is a needlessly complicated procedure and that p is simply t>P, where v is the particle volume. However, this correspondence breaks down for a void, in which P, = 0, but which nonetheless has a nonzero dipole moment. Because the medium is, in general, polarizable, uP, is not equal to p even for a material particle except when it is in free space. In many applications of light scattering and absorption by small particles—in planetary atmospheres and interstellar space, for example—this condition is indeed satisfied. Laboratory experiments, however, are frequently carried out with particles suspended in some kind of medium such as water. It is for this reason that we have taken some care to ensure that the expressions for the polarizability of an ellipsoidal particle are completely general. 

The problem is to discuss the generalized polarizability ae(1.49) with the matrix a 1 not commuting with that of the dipolar interactions, 0. To show that the pure retarded interactions may be discarded in the dynamics of mixed crystals, we assume here that the coulombic interactions are suppressed in (ft. The interaction tensor is then reduced to its retarded term (1.74). Then the dispersion is given by (1.35) ... 

In the liquid phase, calculations of the pair correlation functions, dielectric constant, and diffusion constant have generated the most attention. There exist nonpolarizable and polarizable models that can reproduce each quantity individually it is considerably more difficult to reproduce all quantities (together with the pressure and energy) simultaneously. In general, polarizable models have no distinct advantage in reproducing the structural and energetic properties of liquid water, but they allow for better treatment of dynamic properties. 

In order to determine the 2nd-order energy A2 [a, x] the knowledge of the system response quantities (generalized polarizabilities) is needed [3-8,12,80-84]. In what follows the response of the potential Ea or ,-(r), Per unit value of the displacement in the stimulus b or Xj(r ). for the fixed values of the remaining state-parameters, will be called the molecular charge sensitivity (CS). Such quantities are defined by the relevant second partial derivatives of the system electronic energy ... 

However, Equations (1) and (2) are approximations generally, polarizability cannot be regarded as a constant and the induced polarization is a non-linear function of field strength. This non-linearity becomes increasingly important at very intense electric fields. The non-linear dependence of a dipole moment on field can be expressed as a Taylor series as shown in Equations (3) and (4)... 

In general, polarizability, a, is difficult to determine experimentally. However, the ratio of the capacity of a condenser in a vacuum to that in the medium under consideration, i.e., the relative permittivity (earlier, dielectric constant), of the medium, can be measured. At low frequencies, the relative permittivity of electrical nonconductors is almost independent of the frequency. At high frequencies, the relative permittivity depends on the frequency, since the permanent dipoles are no longer able to establish a preferred orientation, because of rapid alteration of the field. 

In general, polarizability increases as the number of electrons in an atom or molecule increases. The strength of dispersion forces... 

Taking to be the general polarizability operator expressed in irreducible spherical tensor form, and making use of the well-known properties of the 3j symbols, the Raman intensity is found to be [16-18]... 

Here, a, is the principal value of the tensor of the generalized polarizability of one adsorbed molecule [Eq. (1.35)] and (W ), is the number of the adsorbed molecules per unit area that contribute to the /th component of the polarizability. The quantity on the right of Eq. (1.89) is called surface susceptibility. 

Efficient calculation of the density response function from generalized polarizabilities... 

Keywords Density response function Polarization propagator Density response kernel Generalized polarizability Polarizability Conceptual density functional theory Random phase approximation... 

Generalized polarizabilities for ultrafast quantum/molecular mechanics simulations... 

Recently we developed a quantum/molecular mechaiucs (QM/MM) method for the accurate statistical simulation of molecules in polar environments such as in aqueous solutions [30, 31], which speeds up the calculations by 4 or more orders of magnitude or more, even for relatively small solutes and at the inexpensive DFT level. The generalized polarizabilities in our protocol can be used for the efficient... 

The computational cost of the transformation in Eq. (9) is negligible compared to the cost of calculating the generalized polarizabilities, a. Compared to the method used by Geerlings et al. [29], the advantage of our method is that its resolution, i.e., the size of the sine basis, can be defined by the user and is not given by the atomic orbital basis set. The main features of the DRE do not require high resolution. The number of the expansion (sine) basis is proportional to the molecular volume and at a constant resolntion scales linearly with molecular size. This quantity determines the main computational cost, the calculation of the first-order perturbed wavefunctions by the CPHF or CPKS procedure... 

The key quantity to understanding the nonlinear optical response of a given molecule is the corresponding generalized polarizability some-... 

Polarizability is defined as the ease with which the electron cloud of an atom or molecule is distorted. In general, polarizability increases with the size of an atom and the number of electrons on an atom. The importance of London dispersion forces increases with the atom size and number of electrons... 

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