Molecular modeling, electronic polarizability

The molecular electronic polarizability is one of the most important descriptors used in QSPR models. Paradoxically, although it is an electronic property, it is often easier to calculate the polarizability by an additive method (see Section 7.1) than quantum mechanically. Ah-initio and DFT methods need very large basis sets before they give accurate polarizabilities. Accurate molecular polarizabilities are available from semi-empirical MO calculations very easily using a modified version of a simple variational technique proposed by Rivail and co-workers [41]. The molecular electronic polarizability correlates quite strongly with the molecular volume, although there are many cases where both descriptors are useful in QSPR models. 

FORMALISMS FOR THE EXPLICIT INCLUSION OF ELECTRONIC POLARIZABILITY IN MOLECULAR MODELING AND DYNAMICS STUDIES... 

Classical anharmonic spring models with or without damping [9], and the corresponding quantum oscillator models seem well removed from the molecular problems of interest here. The quantum systems are frequently described in terms of coulombic or muffin tin potentials that are intrinsically anharmonic. We will demonstrate their correspondence after first discussing the quantum approach to the nonlinear polarizability problem. Since we are calculating the polarization of electrons in molecules in the presence of an external electric field, we will determine the polarized molecular wave functions expanded in the basis set of unperturbed molecular orbitals and, from them, the nonlinear polarizability. At the heart of this strategy is the assumption that perturbation theory is appropriate for treating these small effects (see below). This is appropriate if the polarized states differ in minor ways from the unpolarized states. The electric dipole operator defines the interaction between the electric field and the molecule. Because the polarization operator (eq lc) is proportional to the dipole operator, there is a direct link between perturbation theory corrections (stark effects) and electronic polarizability [6,11,12]. 

The recent progress of computational quantum chemistry has made it possible to get realistic descriptions of vibrational frequencies for polyatomic molecules in solution. The first attempt in this direction was made by Rivail el al. [1] by exploiting a semiempirical QM molecular model coupled with a continuum description of the medium to compute vibrational frequency shifts for molecular solutes. An extension to ab initio QM methods, including the treatment of electron correlation effects and electrical and mechanical anharmonicities, was then proposed [2 1] in the framework of the Polarizable Continuum Model (PCM). 

Structures and substitution patterns of bridge elements in ID tt systems conjugation efficiency. The electronic requirements for optimum molecular second-order polarizabilities devised on the basis of the two-state model (see pp. 143 and 168) and the technical requirements to translate molecular properties into stable bulk materials partially coincide with the requirements for dyes in classical domains of application, e.g. in textile dyeing and colour... 

The above results are consistent with a molecular model of adsorption that assumes liaison of substituent Z of Z(CH2) H sorbates with the phenyl group of poly(Sty-co-DVB) absorbents. When Z is a halogen atom, this liaison is postulated to involve the non-bonded electrons on Z with the pi-electrons of a phenyl group as indicated in Fig. 37a (when the adsorbed molecule is represented by ZCRR R") and in Fig. 37b (when ZCRR R" is Z(CH2)nH). The order observed for a0 (Eq. 30) as a function of Z is consistent with the assumption that the inherent dynamic adsorption density of such molecules on the adsorption site (in this case the phenyl groups of the polymer) varies with the polarity and polarizability of substituent Z, and inversely with the bulkiness of that substituent. 

It should be clear from the above that because of sustained efforts over many decades, significant progress has now been achieved in the understanding of the freezing of water into ice. However, there stiU remain many unsolved problems in this area. For example, we do not yet have a quantitative theory of the nucleation of ice in supercooled water. The molecular models we use in simulations are perhaps too primitive, as most of them do not include the polarizabihty of water molecules. The polarizability of water is large due to the two lone pairs of electrons on the lone oxygen atom. Perhaps one would need to consider quantum simulations to fully understand the freezing of ice. 

Lopes PEM, Roux B, MacKereU AD. Molecular modeling and dynamics studies with explicit inclusion of electronic polarizability theory and applications. Theor Chem Aa. 2009 124(l-2) ll-28. http //dx.doi.Org/10.1007/s00214-009-0617-x. 

An electrostatic interaction model has been presented for the calculation of the static electronic polarizability of hydrocarbons, which, contrary to previous models, can describe aliphatic, olefinic, and aromatic systems. It is based on the representation of the C and H atoms by induced electric charges and dipoles, where the actual values of the charges and dipoles are those that minimize the electrochemical energy of the molecule. The electrostatic interactions are described in terms of normalized propagators, which improves both the consistency and the numerical stability of the technique. The calibration of the model is sought by reproducing the molecular polarizabilities obtained by current density functional theory for a set of 48 reference structures. An excellent agreement with the reference data has been obtained as evidenced by the relative errors on the mean molecular polarizabilities of 0.5, 1.4, and 1.9% for alkanes, alkenes, and aromatic molecules, respectively. 

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