Polarizabilities dipole definition

VIII. ADDITIVITY OF GROUP DIPOLES AND POLARIZABILITIES A. Definition of Group Moments... 

General properties and definitions of polarizabilities can be introduced without invoking the complete DFT formalism by considering first an elementary model the dipole of an isolated, spherical atom induced by a uniform electric field. The variation of the electronic density is represented by a simple scalar the induced atomic dipole moment. This coarse-grained (CG) model of the electronic density permits to derive a useful explicit energy functional where the functional derivatives are formulated in terms of polarizabilities and dipole hardnesses. 

Within the mixed quantum/classical approach, at each time step in a classical molecular dynamics simulation (that is, for each configuration of the bath coordinates), for each chromophore one needs the transition frequency and the transition dipole or polarizability, and if there are multiple chromophores, one needs the coupling frequencies between each pair. For water a number of different possible approaches have been used to obtain these quantities in this section we begin with brief discussions of each approach to determine transition frequencies. For definiteness we consider the case of a single OH stretch chromophore on an HOD molecule in liquid D2O. 

Any molecule has an infinity of excited orbitals in the continuum above the first ionization energy. The electric dipole polarizability is connected partly with a few of these continuum orbitals and partly with the valence orbitals (7). If the simultaneous formation of empty orbitals of X, but with the continuum, it is reasonable to think of M being polarized by X. The population of the continuum orbitals of X is expected to be the more... 

Measurements of dipole moments, Kerr constants, and dielectric absorption have been employed (81RCR336) widely to obtain information on the conformational equilibrium in acyl heterocycles. Details on conformer structures and populations depend on the choice of additive scheme, group moments, or polarizability tensor in the case of Kerr constants. Several early conclusions, especially for furan- and thiophene-2-carboxaldehyde, appeared contradictory, owing to the choice of these quantities. A more precise definition of polarizability tensors for several heterocycles and a choice of group moments and additive schemes tested on a large amount of available experimental results and supported by accurate theoretical calculations have led to more confidence in the use of experimental dipole moments and Kerr constants in conformational analysis. A limitation of the method is that the... 

The dielectric constant of the vaccum c(j is included in the susceptibility definitions as SI units are used throughout this work. The analogous definition can be applied to the microscopic polarization p of a molecule with the molecular dipole moment jli and the polarizabilities a,/3, and y instead of the static polarization P (0) and the susceptibilities y-P. 

In quantum mechanics the definition of molecular polarizabilities is given through time-dependent perturbation theory in the electric dipole approximation. These expressions are usually given in terms of sums of transition matrix elements over energy denominators involving the full electronic structure of the molecule [42]. 

For vapors, the local field vanishes because of the spherical symmetry and eqs A.5 and A.6 provide good agreement with experiment. However, for liquids one can no longer use eq A.6 for the polarizability in the Lorentz— Debye model. Indeed, for liquid water, eq A.5 diverges for values of y about 4 times smaller than the value of y for its vapor, which at 300 K is y = ye 4 yd = 32.3 x 10 40 C2 m2 J "1. One can regard eq A.5 as the definition of the molecular polarizability and calculate y in terms of the macroscopic dielectric constant e. The lower value of the polarizability in liquid than in vapor can be explained in the framework of the Lorentz—Debye model by the hindered rotation of the permanent dipole moment by the neighboring molecules in the condensed state. 

Over the last years, the basic concepts embedded within the SCRF formalism have undergone some significant improvements, and there are several commonly used variants on this idea. To exemplify the different methods and how their results differ, one recent work from this group [52] considered the sensitivity of results to the particular variant chosen. Due to its dependence upon only the dipole moment of the solute, the older approach is referred to herein as the dipole variant. The dipole method is also crude in the sense that the solute is placed in a spherical cavity within the solute medium, not a very realistic shape in most cases. The polarizable continuum method (PCM) [53,54,55] embeds the solute in a cavity that more accurately mimics the shape of the molecule, created by a series of overlapping spheres. The reaction field is represented by an apparent surface charge approach. The standard PCM approach utilizes an integral equation formulation (IEF) [56,57], A variant of this method is the conductor-polarized continuum model (CPCM) [58] wherein the apparent charges distributed on the cavity surface are such that the total electrostatic potential cancels on the surface. The self-consistent isodensity PCM procedure [59] determines the cavity self-consistently from an isodensity surface. The UAHF (United Atom model for Hartree-Fock/6-31 G ) definition [60] was used for the construction of the solute cavity. 

In a particle with a polarizability a a dipole moment of size (Xj = aF is, by definition, induced in a field of strength F. [The induced moment is always directed parallel to the inducing field]. The interaction energy is here proportional to... 

In contrast to this equal propensity toward formation of a H-bond, there is a definite preference for a proton to locate on the syn side when coming much closer and forming a covalent bond. That is, the syn conformer of RCOOH is more stable than the anti structure by about 5 kcal/mol in the gas phase. If this is the case, why then is there so little apparent pK difference between the syn and anti structures The answer to this question resides in solvation phenomena. The presence of the polarizable medium preferentially stabilizes the anti conformer of the carboxylic acid due to its higher dipole moment. 

Linear Multipolar Electric Polarizabilities. Just as equation (40) served for defining the 2 -pole permanent electric moment, one can generalize the definition of the induced dipole (68) by introducing that of an induced 2 -pole moment. Assuming the inducing factor to be a uniform extamal electric field E, one has ... 

In Eq. (3), is the relevant molecular transition frequency, y is a dam >ing rate, is a polarizability, and (/) is the z-component of the total electric field in the vicinity of the molecule. If (t) were simply of the form i)Cos(fijr), then Eq. (3) is the well-known phenomenological Lorentzian oscillator model of absorption which leads to an approximate Lorentzian form for the absorption cross section [1]. Similar remarks hold for the SP dipole, fi/f), if E t) = ocos(mr), where E t) is the z-component of the total electric field near the SP dipole. The parameters 04,74 and a, in this case are chosen such that the resulting Lorentzian cross section proximates the known exact sur ce plasmon absorption cross section or its appropriate form in the quasistatic (a A=2 tic/cs) limit. Note that I am using a simplified notation compared to the various notations of Refs. [13-15]. (Relative to Ref. [13], for example, my definitions of surface plasmon dipole... 

Some molecular tensors (electric dipole polarizability, electric and magnetoelectric shielding) are origin independent, as can be immediately found by inspection of definitions (87)-(112). Other tensors depend on the origin assumed for the multipole expansion. For instance, in a change of origin... 

By the definition given above, molecular descriptors are divided into two main classes -+ experimental measurements, such as - logP, - molar refractivity, - dipole moment, -> polarizability, and theoretical molecular descriptors, which are derived from a symbolic representation of the molecule and can be further classified according to the different types of molecular representation. 

The most important electric properties are dipole moment and polarizability derivatives. The theory of dipole moment derivatives has been worked out by Bratoz (1958) and by Gerratt and Mills (1968). Both papers use the obvious definition of the dipole moment derivative the change of the dipole moment with nuclear coordinates. Komornicki and Mclver (1979) have pointed out, in an influential paper, that the alternative definition, namely the derivative of the geometrical force with respect to the electric field, is more useful, as there are only three field components versus 3N nuclear coordinates. Similarly, the polarizability derivatives can be defined as the second derivatives of the forces with respect to the field components. Komornicki and Mclver (1979) suggest numerical differentiation with respect to the field... 

This result shows that the relationship between the PZC and the work function is simple only when the dipole contributions are independent of metal nature. The contribution from the reference electrode is constant, provided the electrolyte solution remains unchanged when the polarizable metal is changed. As will be shown below, the dipole potential terms definitely depend on the nature of the metal. 

Since the pioneering work on fluorous biphase hydroformylation with a facile separation of the catalyst [13], the fluorous biphase system has been a hot favorite of organofluorine chemistry [14-22]. Thus, miscibility and immiscibility of two liquids are important physical properties for organofluorine chemistry. Curran proposed a definition of the term fluorous in 2002 [18]. His definition is based on fluorophilic and fluorophobic properties, which are controlled by the polarity of the compound. Here, the term polarity may contain not only the conventional polarity but also the electronic polarizability, because it was noted that hexafluorobenzene, which has no dipole moment, is a nonfluorous compound. 

Table 3. Relative energies (in kcal/mol) of the most stable thiouracil tautomers (for the definition see text below Eqs.(l)-(4)). Their total dipole moment (D) and dipole polarizability a (a.u., in parentheses) axe shown below the corresponding relative energy.

---