Distributed polarizabilities

The induction energy is inlierently non-additive. In fact, the non-additivity is displayed elegantly in a distributed polarizability approach [28]. Non-additive induction energies have been found to stabilize what appear to be highly improbable crystal structures of the alkalme earth halides [57]. 

Garmer DR, Stevens WJ (1989) Transferability of molecular distributed polarizabilities from a simple localized orbital based method. J Phys Chem 93 8263... 

Inserting the multipole expansions of the operators rfj1 and rfA with respect to the pairs of sites (a, b) and (a1, b ), respectively, and defining the distributed polarizability tensor,... 

Le Sueur CR, Stone AJ (1993) Practical schemes for distributed polarizabilities. Mol Phys 78 1267-1291... 

Angyan JG, Jansen G, Loos M, H attig C, Hess BA (1994) Distributed polarizabilities using the topological theory of atoms in molecules. Chem Phys Lett 219 267-273... 

Higher + Electronic + Interaction with the environment Spatio-temporal structure (flexibility, conformation) Electronic properties (electron distribution, polarizability, ionisation) Solvation, hydration, partitioning, intermolecular interactions Conformational energy diagrams, computer display Molecular orbitals, electrostatic potential maps Computer display... 

Method (III) attempts to include a discrete molecular description of the solvent structure around a central solute molecule. The solute molecule is described, again, through a QM calculation while the spatial distribution, charge distribution, polarizabilities etc. of the adjacent part of the solvent is represented by a parametrized molecular mechanics (MM) model. The parametrization may be achieved through high level calculations on the isolated solvent molecules. 

Intermolecular dispersion energies are calculated as a sum of pixel-pixel terms in a London-type expression, involving the above defined distributed polarizabilities and an overall oscillator strength > Eos To avoid singularities (as before described) due to very short pixel-pixel distances in an inverse sixth-power formula, each term in the sum is damped, as it is shown here for the molecule A...molecule B interaction ... 

Various shape complementarity measures can also be determined based on shape codes. This is an important problem since molecular recognition usually depends on the complementarity of local regions of molecules, where complementarity may refer to electron distributions, polarizability properties, electrostatic potentials, or simply geometric considerations. The powerful topological techniques are suitable for the quantification of the degree of molecular complementarity and can be used as tools for the study of molecular recognition. 

Because of intense theoretical work in this area, dynamic aspects of structure such as rotational barriers of methyl substituents and deviations from planarity have been treated in Section 9.01.2.1. For the same reason, calculated heats of formation, total energies, resonance energies, aspects of delocalization and conjugation, homodesmotic stabilization energies, electron distribution, polarizability and magnetic and bond-order-based aromaticity indexes have been discussed in Section 9.01.2.8. Complexation of the parent 1 by water has also been considered (Section 9.01.2.12). 

Misquitta, A. J., Stone, A. J., and Price, S. L. [2008a]. Accurate induction energies for small organic molecules. 2. development and testing of distributed polarizability models against SAPT[DFT] energies,/ Chem. Theory Comput 4, pp. 19-32, doi 10.1021/ct700105f. 

Figure 8.3 Ab Initio polarization energies (kcal/mol] for the Ca(II]-H20 complex, computed using the CSOV procedure (blue], polarization energy computed using (1] distributed polarlzabllltles+ab-lnltio fields (grey), (11] distributed polarizabilities +GEM with (green] and (111] without fields damping (red].

Misquitta, A. ]., and Stone, A. J. (2006]. Distributed polarizabilities obtained using a constrained density-fitting algorithm, /. Chem. Phys. 124, p. 024111. 

The use of several expansion centers surely improves the situation. The averaged value of dipole first polarizability a can be satisfactorily expressed as a sum of transferable group contributions, but the calculations of IND with distributed polarizabilities are rather unstable, probably divergent, and it is convenient to limit the calculation to the first term alone, as is actually done in almost all the practical implementations. Instability and lack of convergence are factors suggesting an accurate examination of the function to fit the opportune values for these distributed a polarizabilities. 

Electronic distribution polarizability, inductive effects, charge, and dipoles. 

Dehez et al. probed the accxnacy of a novel approach for evaluating induction energies. Fully distributed polarizabihty models obtained with AIM are used to generate large grids of induction energies much more rapidly than with a finite perturbation approach. Test calculations show that this method is able to provide compact, yet optimal distributed polarizability models. 

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