Effective Polarizable Bond Method

Taking acetone as an example. To model different external electric field environments, a acetone molecule is embedded in an octahedron-like T1P3P water box. A long time simulation is performed to generate an ensemble of configurations of the water molecules around the acetone while the acetone is kept fixed. A 

The polarization cost (or distortion) energy during the polarization process is given by 

The polarization process can be treated as charge transfer between atoms in a polar group. If charge transfer from atom 0 to atom C is Aq, then the final partial charge is 

The equilibrium with self energy going up and interaction energy going down can be reached by minimizing the total energy with respect to variation of Aq 

Just as in the traditional force field, the effective charge concept can also be introduced in the fluctuating charge model. 

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The entire set of molecules contained 782 bonds out of which 111 a-bonds were selected. The parameters were calculated by our methods to build a reactivity space with electronegativity difference, resonance effect parameter, bond polarizability, bond polarity, a-charge distribution, and bond dissociation energy as six coordinates. 

For many chemical problems, it is crucial to consider solvent effects. This was demonstrated in our recent studies on the hydration free energy of U02 and the model reduction of uranyl by water [232,233]. The ParaGauss code [21,22] allows to carry out DKH DF calculations combined with a treatment of solvent effects via the self-consistent polarizable continuum method (PCM) COSMO [227]. If one aims at a realistic description of solvated species, it is not sufficient to represent an aqueous environment simply as a dielectric continuum because of the covalent nature of the bonding between an actinide and aqua ligands [232]. Ideally, one uses a combination model, in which one or more solvation shells (typically the first shell) are treated quantum-mechanically, while long-range electrostatic and other solvent effects are accounted for with a continuum model. Both contributions to the solvation free energy of U02 were... 

The effect of the solvent is usually modelled either by the use of the Onsager s self consistent reaction field (SCRF) [20] or by the polarizable continuum method (PCM) [21]. With regard to the relative stability of cytosine tautomers in aqueous solution, these methods provided results [14,15] which, in spite of some discrepancies, are in reasonable agreement with experimental data [3]. However, continuum-based methods do not explicitly take into consideration the local solvent-solute interaction which is instead important in the description of the proton transfer mechanism in hydrogen-bonded systems. A reasonable approach to the problem was recently proposed [22,23] in which the molecule of interest and few solvent molecules are treated as a supermolecule acting as solute, while the bulk of the solvent is represented as a polarizable dielectric. 

In diis section a method for interpretation of Raman intensities based on further transformations of atomic polarizability tensors is presented. The formulation was recently proposed by Ehidev and Galabov [333], A new molecular quantity - effective induced bond charge, Ok introduced. The effective induced bond charges are obtained from rotation-free atomic polarizability tensors following the strate as outlined by Galabov, Dudev and nieva [146] in the infrared case (Section 4.IV). The Ok parameters are expected to be associated with polarizability properties of valence bonds. 

A common feature of the various methods that we have developed for the calculation of electronic effects in organic molecules is that they start from fundamental atomic data such as atomic ionization potentials and electron affinities, or atomic polarizability parameters. These atomic data are combined according to specific physical models, to calculate molecular descriptors which take account of the network of bonds. In other words, the constitution of a molecule (the topology) determines the way the procedures (algorithms) walk through the molecule. Again, as previously mentioned, the calculations are performed on the entire molecule. 

In 1976, Kamlet and Taft introduced their solvatochromic comparison method [25, 26], The hydrogen-bond donor acidity a and basicity /3 together with the solvent polarity and polarizability jv were employed to correlate the solvent effects on reaction rates, equilibria, and spectroscopic properties XYZ according to equations of the form... 

The Kerr constant is related to the difference between the refractive indices of the medium parallel and perpendicular to an applied field, and these may be calculated for the assumed conformations. On this basis a 50 50 A-Meax lV-Meeq equilibrium was estimated for iV-methylpiperidine and an 80% N-Hai preference for piperidine in benzene solution.116 Some theoretical support117 was produced for this latter preference in terms of a more effective overall electron bonding in the iV-Hax conformer. These results are very much out of line with those estimates based on other methods and the Kerr-constant work has been criticized3 on the grounds of insufficient accuracy in the bond polarizabilities used in the calculations.118... 

Several approaches have been made to calculate 13C chemical shifts of coumarins by MO methods. Good correlations were found between the 13C chemical shift values of coumarin (also protonated) and the n charge densities calculated by the CNDO/2 method [962], and of coumarins with it charge densities calculated by the Hiickel MO method (which, however, fails for methoxylated coumarins) [965]. Chemical shifts of mono- and dimethoxycoumarins have been correlated with parameters determined by refined INDO MO calculations, in which n bond orders, atom-atom polarizabilities, excitation energies and electron-nucleus distances were taken into consideration [966], In 3-substituted 4-hydroxy and 4-hydroxy-7-methoxycoumarins chemical shifts were found to be related to Swain and Lupton s parameters iF and M [388], according to equation 5.4 (SE = Substitution Effect) ... 

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