Static charge distribution, molecular

A physical property equal in magnitude to the electrostatic energy between the static charge distribution, p(r), of an atomic or molecular system and a positive unit point charge located at r. The electrostatic potential V(r) produced at any point r by the electrons and nuclei (A) of the system is given by... 

Several issues remain to be addressed. The effect of the mutual penetration of the electron distributions should be analyzed, while the use of theoretical densities on isolated molecules does not take into account the induced polarization of the molecular charge distribution in a crystal. In the calculations by Coombes et al. (1996), the effect of electron correlation on the isolated molecule density is approximately accounted for by a scaling of the electrostatic contributions by a factor of 0.9. Some of these effects are in opposite directions and may roughly cancel. As pointed out by Price and coworkers, lattice energy calculations based on the average static structure ignore the dynamical aspects of the molecular crystal. However, the necessity to include electrostatic interactions in lattice energy calculations of molecular crystals is evident and has been established unequivocally. 

The application of a static electric field polarizes the electronic charge distribution and leads to changes in molecular magnetic susceptibility and nuclear... 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

These examples demonstrate that molecular structure and its stability are predicted by a theory which uses only the information contained in the quantum mechanical state function and that the static and dynamic properties of a bond can be characterized in terms of the properties of the charge density at the bond critical point. The values of Pb, ab, e, and V Pb enable one to translate the predicted electronic effects of orbital models into observable consequences in the charge distribution. 

The polarizability of an atom or molecule describes the response of the electron cloud to an external field. The atomic or molecular energy shift KW due to an external electric field E is proportional to i for external fields that are weak compared to the internal electric fields between the nucleus and electron cloud. The electric dipole polarizability a is the constant of proportionality defined by KW = -0(i /2. The induced electric dipole moment is aE. Hyperpolarizabilities, coefficients of higher powers of , are less often required. Technically, the polarizability is a tensor quantity but for spherically symmetric charge distributions reduces to a single number. In any case, an average polarizability is usually adequate in calculations. Frequency-dependent or dynamic polarizabilities are needed for electric fields that vary in time, except for frequencies that are much lower than electron orbital frequencies, where static polarizabilities suffice. 

Debye-Falkenhagen-type forces do not suffer from the vanishing of the rotationally averaged interaction since they arise from a force due to induction which can track the rotation of the particle. Unlike the Keesom force in which, in principle, the interaction of distributed point charges are considered, induction forces are dependent upon a collective molecular or material property, the static dielectric constant. Definition of the domain of validity for the classical calculation is required and has been given in the case of metals [5.17]. Those authors pointed out that if the surface of the metal were taken at the center of mass of the surface charge distribution, then classical electrostatic calculations would be valid. 

Davidson s (Appendix E) algorithms. A two-dimensional real space representation of the resulting transition density matrices is convenient for an analysis and visualization of each electronic transition and the molecular optical response in terms of excited-state charge distribution and motions of electrons and holes (Section IIC). Finally, the computed vertical excitation energies and transition densities may be used to calculate molecular spectroscopic observables such as transition dipoles, oscillator strengths, linear absorption, and static and frequency-dependent nonlinear response (Appendix F). The overall scaling of these computations does not exceed X in time and in memory (A being the... 

The static dipole polarizabilities of alkali dimers have been calculated as a function of the internuclear distance and of the vibrational index for both their electronic ground state and lowest triplet state. The method is based on /-dependent pseudopotentials for atomic core representation, Gaussian basis sets, effective core potentials to account for core polarization, the evaluation of molecular orbitals by the restricted HF method, and then a full valence Cl treatment. For all alkali pairs, the parallel and perpendicular components of the ground state a at equilibrium distance Rg scale as the cube of Re, which can be related to a simple electrostatic model of an ellipsoidal charge distribution. So, for the ground state, the longitudinal polarizability exhibits a maximum at a distance corresponding to 1.3-1.5 times the equilibrium distance. 

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