Polarizability, electric static

A metal cluster is excited by the electromagnetic field of a light wave. The theory describing this phenomenon as the dielectric function e(ra) was developed by Drude-Lorentz-Sommerfeld (DLS). The internal field of a metal cluster is calculated by adding the boundaries of the sphere surface. Based on DLS the static electric polarizability of a simple single spherical cluster of radius r is given by ... 

The static electric dipole polarizability a of the model system investigated is therefore... 

TOO Schwerdtfeger, P. (2006) Atomic Static Dipole Polarizabilities, in Computational Aspects of Electric Polarizability Calculations Atoms, Molecules and Clusters (ed. G. Maroulis), Imperial College Press, London, pp. 1-32. 

Formal Theory A small neutral particle at equilibrium in a static electric field experiences a net force due to DEP that can be written as F = (p V)E, where p is the dipole moment vector and E is the external electric field. If the particle is a simple dielectric and is isotropically, linearly, and homogeneously polarizable, then the dipole moment can be written as p = auE, where a is the (scalar) polarizability, V is the volume of the particle, and E is the external field. The force can then be written as ... 

KEY TERMS dispersion forces nonpolar polarizability static electricity... 

To obtain a clear understanding of electrodynamic bonding, start with the field of a static electric dipole. Then, let the dipole oscillate so it emits electromagnetic waves (photons). Consider what happens when the emitted field envelopes another dipole (London, 1937). Finally, determine the factors that convert neutral molecules into dipoles (that is, their polarizabilities). 

The conventional approach used to describe the response of a molecule to a static electric field is either to perform pure electronic BO calculations or to perform calculations where the BO values are corrected for vibrational and rotational (thermal) motion of the nuclei. The vibrationally corrected polarizabilities usually do an excellent job of correcting the errors inherent in the pure electronic BO values. Bishop has written several excellent reviews on this topic [78-80]. 

The static dipole polarizability is the linear response of an atomic or molecular system to the application of a weak static electric field [1], It relates to a great variety of physical properties and phenomena [2-5]. Because of its importance, there have been numerous ab initio calculations of isolated atomic and molecular polarizabilities [6-14]. Particular theoretical attention has been dedicated to the polarizability of free atomic anions [15-21] because of its fragility and difficulty in obtaining direct experimental results. In recent years theoretical studies have... 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

A good example of the use of the electric resonance technique is the measurement of the Na nd fine structure intervals and tensor polarizabilities.38 These transitions were observed using selective field ionization, although they appear to be unlikely prospects for field ionization detection because of the small separations of the levels, 20 MHz. The nd3/2 states were selectively excited from the 3p1/2 state in a small static electric field and the = 0 transitions to the nd5/2 states induced by a... 

We have seen above how to calculate polarizabilities and hyperpolarizabilities for static electric fields. I will consider a simple oscillating electric field... 

We have performed a series of semiempirical quantum-mechanical calculations of the molecular hyperpolarzabilities using two different schemes the finite-field (FF), and the sum-over-state (SOS) methods. Under the FF method, the molecular ground state dipole moment fJ.g is calculated in the presence of a static electric field E. The tensor components of the molecular polarizability a and hyperpolarizability / are subsequently calculated by taking the appropriate first and second (finite-difference) derivatives of the ground state dipole moment with respect to the static field and using... 

Effects of a Static Electric Field on Molecular Magnetic Properties Employing the CTOCD Method Shielding Polarizabilities of CO, H20, and CH4 Compounds... 

We shall briefly review some definitions to compute molecular magnetic properties in the presence of a static electric field, L e., hypermagnetizabilities and shielding polarizabilities, Zafr and a1. ... 

In this section, a simple description of the dielectric polarization process is provided, and later to describe dielectric relaxation processes, the polarization mechanisms of materials produced by macroscopic static electric fields are analyzed. The relation between the macroscopic electric response and microscopic properties such as electronic, ionic, orientational, and hopping charge polarizabilities is very complex and is out of the scope of this book. This problem was successfully treated by Lorentz. He established that a remarkable improvement of the obtained results can be obtained at all frequencies by proposing the existence of a local field, which diverges from the macroscopic electric field by a correction factor, the Lorentz local-field factor [27],... 

In this way, the relative dielectric response to static electric fields of a gas of polarizable molecules that also bear a permanent dipole moment is... 

Similarly as the trace, the anisotropy of the polarizability tensor of diatomic colli-sional systems can also be related to some macroscopic properties, namely to the refractive properties of atomic gases. The so-called Kerr constant, the anisotropy of the refractive index in the parallel and perpendicular directions to the external static electric field is given by,... 

This polarization has two components the induced polarization P (due to movement of the centers of charge, or to the static electric dipole polarizability a of molecules) and the dipole polarization Pjt (due to the orientation of the permanent dipoles m in the applied electric field E) ... 

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. 

Terms of higher order in the field amplitudes or in the multipole expansion are indicated by. . . The other two tensors in (1) are the electric polarizability ax and the magnetizability The linear response tensors in (1) are molecular properties, amenable to ab initio computations, and the tensor elements are functions of the frequency m of the applied fields. Because of the time derivatives of the fields involved with the mixed electric-magnetic polarizabilities, chiroptical effects vanish as a> goes to zero (however, f has a nonzero static limit). Away from resonances, the OR parameter is given by [32]... 

Let us now consider the second-order molecular properties. The static electric dipole-polarizability tensor is given by the expression... 

The calculation of the molar polarizabilities, often involves statistical mechanical averaging over orientational distributions of the molecules. An important example is the distribution function w caused by dipole orientation in an externally applied static electric field E° because it describes the process of electric poling of NLO-phores. To second order in the field, the dipolar contributions to this (normalized) function are given by (100),... 

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