Molecule polarizability

Dispersion Interactions From Atoms-in-Molecules Polarizability to Local Softness.410... 

The intrinsic atom-in-molecule polarizabilities were tested by us [99] for their performance in the calculation of the dispersion energy for a set of Van der Waals complexes, at their equilibrium geometry using a DFT- B3LYP computational ansatz combined with an aug-cc-pVTZ basis set for the calculation of the (Mf) values using Van Alsenoy s STOCK program, also used to partition the polarizabilities [100]. 

As a further step currently under investigation, the relationship between local polarizability and local softness is studied with the aim to substitute atom-in-molecule polarizabilities by atom-condensed softness values. In this way, conceptual DFT could be exploited in a computational strategy, an ansatz rarely used until now, the best known example being the electronegativity equalization method [101]. 

Ion-radicals have, as a rule, a deeper coloring than the initial neutral molecules. An unpaired electron on the MO increases the molecule polarizability and facilitates its excitation by light. This enhances the intensity of absorption and shifts it to the region of higher wavelengths. Therefore, ion-radicals are quite easily revealed via electron spectroscopy. This method is often applied to investigate the ion-radical reaction kinetics and establish the significance of ion-radical pathway. 

The velocity of light passing through a polymer is affected by the polarity of the bonds in the molecule. Polarizability P is related to the molecular weight per unit volume, M, and density p as follows (the Lorenz-Lorentz relationship) ... 

In examining the Debye, Keesom, and London equations we see that (a) they share as a common feature an inverse sixth-power dependence on the separation and (b) the molecular parameters that describe the polarization of a molecule, polarizability and dipole moment, serve as proportionality factors in these expressions. For a full discussion of the experimental determination of a0 and p, a textbook of physical chemistry should be consulted (Atkins 1994). For our purposes, it is sufficient to note that the molar polarization of a substance can be related to its relative dielectric constant e, by... 

Figure 8. Dipole coupling shifts (experimental points) as function of coverage in Stage 1, compared with theoretical shifts for random (S ) and regular (S oc 3/2) distributions assuming free molecule polarizabilities...

Hence, N and O are less polarizable than C and H, even though they form more polar molecules. Polarizability increases with atomic radius, since the electrons are less tightly bound. Therefore, S is more polarizable than N. 

ISS data have been recorded in many pure and mixed molecular liquids [34,49, 75, 83, 83-85], In most cases, the data are not described precisely by Eq. (27). Rather, an additional decay component appears at intermediate times (decay times 500 fs). This has been interpreted [49, 84] in terms of higher order polarizability contributions to C (t) which represent translational motions, an interpretation supported by observations in CCI4 (whose single-molecule polarizability anisotropy vanishes by symmetry). This interpretation is not consistent with several molecular dynamics simulations of CSj [71, 86]. An alternative analysis has been presented [82] that incorporates theoretical results showing that even the single-molecule orientational correlation function C (t) should in fact show decay on the 0.5-ps time scale of cage fluctuations [87, 88]. 

Figure 21. One-dimensional elTective potential i (R) for ion-dipole interactions for dipole locking parameter C = 0,2,4, and 6. Distance Rf, is (oui /kT), where q is ion charge and a is molecule polarizability.

Certainly, the discrete SWB model is rather crude. It does not take into account the long-range nature of Coulomb interaction, although it is of great significance for aqueous systems. Moreover, this model does not consider molecules polarizability and other effects related to the non-additivity of intermolecular interaction. Therefore it is quite surprising to observe a close correlation between the theoretical predictions based on the SWB model and contemporary quantum-chemical calculations. Some of the coincidences are listed below. 

Another scheme to calculate and interpret macroscopic nonlinear optical responses was formulated by Mukamel and co-workers [112 114] and incorporated intermolecular interactions as well as correlation between matter and the radiation field in a consistent way by using a multipolar Hamiltonian. Contrary to the local field approximation, the macroscopic susceptibilities cannot be expressed as simple functionals of the single-molecule polarizabilities, but retarded intermolecular interactions (polariton effects) can be included. 

PVOL Polarization volume of the molecule (polarizability) divided by its... 

Table CXLII. Heats of Sublimation Calculated from Dispersion cules possess greater Forces between Atoms and Molecules polarizabilities and the...

Molecule Polarizability Ref. Molecule Polarizability Ref. Molecule Polarizability Ref. 

Related to this feature, the two lone pairs of electrons on the oxygen atom render a water molecule polarizable to electric fields from other molecules or from a charged surface. Thus, water molecules can respond to the changing of charge distribution in an external solute (or surface) to lower the energy of an... 

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