Distributed Multipoles and Polarizabilities

Soetens, J.-C. and Milot C., Effect of distributing multipoles and polarizabilities on molecular dynamics simulations of water. Chem. Phys. Lett. (1995) 235 22-30. 

P. Soderhjelm, J.W. Krogh, G. Karlstrom, U. Ryde, R. Lindh, Accuracy of distributed multipoles and polarizabilities Comparison between the loprop and mpprop models, J. Comput. Chem. 28 (2007) 1083. 

It is obvious from the discussion in the last sections that the evaluation of distributed multipoles and polarizabilities is not straightforward and also time consuming. In particular, for routine investigations of large extended assemblies it is desirable to have easily obtainable descriptors for local interaction patterns at hand. 

Other contributions to the interaction energy are usually less important. The induction energy can be calculated using distributed multipoles and polarizabilities for the individual molecules as for the electrostatic energy it is necesary to include contibutions at least to... 

Stone and collaborators fit the exchange-repulsion as the difference between the first-order perturbation energy obtained from the IMPT theory [24,25] for a dimer and the electrostatic energy, including induction, obtained from the distributed multipole and polarizability models that will be used to model electrostatic and polarization effects in the force field [26-29]. 

The expansion of the molecular field and field response in terms of distributed multipoles and polarizabilities is an efficient approach for solving for the first- and second-order corrections to the molecular Hamiltonian that result from a... 

In order to evaluate the distributed multipole forms of the interaction energy components we need to calculate distributed multipoles and distributed frequency-dependent polarizabilities of the interacting molecules. 

The distributed multipoles and the polarizabilities were derived from the MO s of the constitutive fragments of Lig-47, namely benzimidazole, methyl-benzene, CTU in an extended conformation, and benzene-connected dioxane. The location of the sp lone-pairs of CTU was determined on the basis of ELF [142] analyses using the TopMod package [143], and is shown in Fig. 1.10 ... 

The long-range interactions between a pair of molecules are detemiined by electric multipole moments and polarizabilities of the individual molecules. MuJtipoJe moments are measures that describe the non-sphericity of the charge distribution of a molecule. The zeroth-order moment is the total charge of the molecule Q = Yfi- where q- is the charge of particle and the sum is over all electrons and nuclei in tlie molecule. The first-order moment is the dipole moment vector with Cartesian components given by... 

Since the single-center multipole expansion of the interaction energy is divergent, one could use a kind of multicenter expansion. One can hope that the multipole expansion will provide better results if multipole moments and polarizabilities localized at various points of a molecule are used instead of global multipole moments and polarizabilities. This idea forms the basis of the so-called distributed multipole analysis of the electrostatic, induction, and dispersion interactions between molecules187 195. 

The multicenter expansion of the induction energy in terms of the distributed multipole moments and polarizabilities can be obtained is a similar way starting from Eq. (1-87) rewritten as follows,... 

Compared with the pronounced solvent-induced chemical shifts observed with ionic and dipolar solutes, the corresponding shifts of nonpolar solutes such as tetrame-thylsilane are rather small cf. Table 6-6. A careful investigation of chemical shifts of unsubstituted aromatic, as well as alternant and nonalternant, unsaturated hydrocarbons in aliphatic and aromatic non-HBD solvents by Abboud et al. has shown that the differential solvent-induced chemical shift range (relative to benzene as reference) is of the order of only —1.4...+1.0 ppm (positive values representing downfield shifts) [405]. The NMR spectra of these aromatic compounds have been shown to be sensitive to solvent dipolarity and polarizability, except in aromatic solvents, for which an additional specific aromatic solvent-induced shift (ASIS see later) has been found. There is no simple relationship between the solvent-induced chemical shifts and the calculated charge distribution of the aromatic solute molecules. This demonstrates the importance of quadrupoles and higher multipoles in solute/solvent interactions involving aromatic solutes [405]. 

Electric polarization, dipole moments and other related physical quantities, such as multipole moments and polarizabilities, constitute another group of both local and molecular descriptors, which can be defined either in terms of classical physics or quantum mechanics. They encode information about the charge distribution in molecules [Bbttcher et al, 1973]. They are particularly important in modelling solvation properties of compounds which depend on solute/solvent interactions and in fact are frequently used to represent the -> dipolarity/polarizability term in - linear solvation energy relationships. Moreover, they can be used to model the polar interactions which contribute to the determination of the -> lipophilicity of compounds. 

Note that a distinction is made between electrostatic and polarization energies. Thus the electrostatic term, Ue e, here refers to an interaction between monomer charge distributions as if they were infinitely separated (i.e., t/°le). A perturbative method is used to obtain polarization as a separate entity. The electrostatic and polarization contributions are expressed in terms of multipole expansions of the classical coulomb and induction energies. Electrostatic interactions are computed using a distributed multipole expansion up to and including octupoles at atom centers and bond midpoints. The polarization term is calculated from analytic dipole polarizability tensors for each localized molecular orbital (LMO) in the valence shell centered at the LMO charge centroid. These terms are derived from quantum calculations on the... 

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