Electronic charge density instantaneous

For an individual molecule, fluctuations of the instantaneous electronic charge density away from its quantum mechanical average are characterized by the fluctuation-dissipation theorem (3, 4). The molecule is assumed to be in equilibrium with a radiation bath at temperature T then in the final step of the derivation, the limit is taken as T — 0. The fluctuation correlations, which are defined by... 

Jj( 1) is the potential energy of interaction between the point charge of electron 1 and electron 2 considered to be smeared out into a hypothetical charge cloud of charge density (charge per unit volume) - e)Hartree-Fock method considers average interelectronic interactions, rather than instantaneous inter-... 

In contrast to the above situation, based on an average charge density (pa), one may identify another dynamical regime where the solvent electronic timescale is fast [50-52] relative to that of the solute electrons (especially, those participating in the ET process). In this case, H F remains as in Equation (3.106), treated at the Born-Oppenheimer (BO) level (i.e., separation of electronic and nuclear timescales), but HFF is replaced by an optical RF operator involving instantaneous electron coordinates [52] ... 

This description disregards instantaneous effects due to solvent polarization induced by the change in charge density associated with the electronic transition [19]. In principle such effects may be appreciable [24], but we will shortly show (section 3) that the solvatochromic behaviours of merocyanines can be correctly predicted in terms of the only effects related to the dielectric constant of the solvent. 

For the spectroscopic applications, it would be again instructive to separate the noninertial and inertial components of the electrostatic polarization of the dielectric medium. The first of them corresponds to the electrostatic polarization of the electron charge distribution in the solvent that is supposedly instantaneous as compared to any electronic or conformational transition of the solute. The second component arises from the orientational polarization of the solvent molecules in the electrostatic field of the solute. The noninertial polarization can be described by the optical dielectric permittivity of the solvent that corresponds to the infinite frequency of external electromagnetic field (e Ud) whereas the inertial polarization represents the slow, orientational part of the total dielectric constant of the solvent, s. In order to separate the noninertial polarization, it is helpful to determine the solute charge density as the sum of the respective nuclear and electronic parts... 

The subscripts refer to frequency, a sine wave parameter. Doo is the surface charge density at t = 0+, which is after the step but so early that only apparently instantaneous polarization mechanisms have come to effect (high frequency e.g., electronic polarization). The capacitor charging current value at t = 0 is infinite, so the model has some physical flaws. Do is the charge density after so long time that the new equilibrium has been obtained and the charging current has become zero. With a single Debye dispersion, this low-frequency value is called the static value (see Section 6.2.1). t is the exponential time constant of the relaxation process. 

The image forces are those induced by the appearance of the fictitious charge on the metal (image charge) created by the ion s charge. Similarly to the adsorbed water molecules (Section 6.7.2), ions also experience dispersion forces due to the induction of instantaneous fluctuations in the electron density clouds of continuous atoms—the adsorbed ion and the metal atom. Both these forces are of attractive character and were discussed in Section 6.7.2. 

The strength of the London interaction depends on the polarizability, a (alpha), the ease with which the electron cloud can be distorted. This dependence is reasonable, because the nuclei in highly polarizable molecules have only weak control over the surrounding electrons, so there can be big fluctuations in electron density and hence large instantaneous partial charges. It turns out that the potential energy of the London interaction varies as the sixth power of the separation of two molecules ... 

London dispersion force induced dipole-induced dipole The above two examples required a permanent charge to induce a dipole in a nonpolar molecule. A nonpolar molecule may also induce a temporary dipole on its identical neighbor in a pure substance. These forces occur because at any given moment, electrons are located within a certain region of the molecule, and the instantaneous location of electrons will induce a temporary dipole on neighboring molecules. For example, an isolated helium atom consists of a nucleus with a 2+ charge and two electrons in a spherical electron density cloud. An attraction of He atoms due to London dispersion forces (shown at right by the dashed line) occurs because when the electrons... 

In the formulation of Eq. (17 12), the solute-solvent interaction was assumed to be pairwise additive. When the QM/MM method is employed as introduced in Section 17.2.3, the electron density of the QM solute is determined through the interaction with a number of solvent molecules. The instantaneous electrostatic interaction between the point charges and the wavefunctions in the potential Eels is expressed as... 

Car-Parrinello techniques have been used to describe classical variables whose behavior, like quantum electrons in the Born-Oppenheimer approximation, is nearly adiabatic with respect to other variables. In simulations of a colloidal system consisting of macroions of charge Ze, each associated with Z counterions of charge —e, Lowen et al. [192] eliminated explicit treatment of the many counterions using classical density functional theory. Assuming that the counterions relax instantaneously on the time-scale of macroion motion, simulations of the macroion were performed by optimizing the counterion density at each time step by simulated annealing. 

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