Kirkwood-Onsager

Ab initio SCRF/MO methods have been applied to the hydrolysis and methanol-ysis of methanesulfonyl chloride (334). ° The aminolysis by aromatic amines of sulfonyl and acyl chlorides has been examined in terms of solvent parameters, the former being the more solvent-dependent process.Solvent effects on the reactions of dansyl chloride (335) with substituted pyridines in MeOH-MeCN were studied using two parameters of Taft s solvatochromatic correlation and four parameters of the Kirkwood-Onsager, Parker, Marcus and Hildebrand equations. MeCN solvent molecules accelerate charge separation of the reactants and stabilize the transition... 

An important difference between the Bom and Kirkwood-Onsager formulae is that the... 

The Kirkwood-Onsager equations can be generalized to include multipole moments higher dian the dipole, leading to the expression... 

Nach der Kirkwood-Onsager-Beziehung (160, 206, 214) ist fur den Logarith-mus des Produktverhaltnisses eine lineare Abhangigkeit zu erwarten, falls... 

The exciplex or CIP is treated as a dipole of radius q and dipole moment p. The last term in Eq. (15) describes the energy of this dipole, based on the Kirkwood-Onsager model (assuming formation of a spherical complex) [14]. Thus, an exciplex or CIP is stabilized by Coulombic interactions and by solvation. The solvation energy is expected to be favored by increasing solvent polarity and a large dipole... 

Some exciplexes, however, can be stabilized in polar solvents because of favorable orbital interactions, electrostatic effects, or a Kirkwood-Onsager solvation energy term [18]. For example, in polar solvents an exciplex structure with a large dipole moment can be stable with respect to solvent-separated and free ions (Fig. 8). The lifetimes of these exciplexes should then be sufficiently long to allow for observation. In fact, there is evidence to support exciplex emission even in polar solvents. Eisenthal and coworkers, for example, observed the exciplex emission of 9-anthracene-(CH2)3-iV,JV-dimethylaniline systems in acetonitrile [19] ... 

A similar treatment for a point dipole of magnitude p, in a sphere of radius a yields the Kirkwood—Onsager result > ... 

As emphasized, the Born—Kirkwood—Onsager (BKO) approach includes only the solute s monopole and dipole interaction with the continuum. That is, the full classical multipolar expansion of the total solute charge distribution is truncated at the dipole term. This simplification of the electronic distribution fails most visibly for neutral molecules whose dipole moments vanish as a result of symmetry. A distributed monopole or distributed dipole model is more... 

The Born—Kirkwood—Onsager model, however, is particularly simple to implement its advantages include the ability to use correlated wavefunc-tions220,222 and to calculate analytic first and second derivatives.- T2i9,22o such, the BKO or Onsager model (the latter considers only the dipole-—not the charge—and hence is appropriate only for neutral solutes) is available in many standard programs,2i . 228,229 and it is widely employed. 

Applications of the Born—Kirkwood-Onsager model at the ab initio level include investigations of solvation effects on sulfamic acid and its zwitterion,23i an examination of the infrared spectra of formamide and formamidic acid,222 and a number of studies focusing on heterocyclic tautomeric equilibria.222,232,233 a more detailed comparison of some of the heterocyclic results is given later. The gas phase dipole moment depends on basis set, and systematic studies of this dependence are available. Furthermore, the effects of basis set choice and level of correlation analysis have been explored in solvation studies as well,222,233 but studies to permit identification of particular trends in their impact on the solvation portion of the calculation are as yet insufficient. 

Reaction Fields from Higher Order Multipolar Expansions Generalizations of the Born—Kirkwood—Onsager model have appeared which extend the multipole series to arbitrarily high order.20,62,144,234-236 ybis approach yields... 

Born—Kirkwood—Onsager Reaction Field The theory underlying the implementation of the BKO model at the semiempirical level is no different from that presented in Equations [22] and [23], although the approximations inherent to various levels of semiempirical theory make certain technicalities of the... 

The aqueous solvation free energies of the four tautomers available to the 5-(2H)-isoxazolone system have also been studied using a variety of continuum models (Table 7). Hillier and co-workers - " have provided data at the ab initio level using the Born-Kirkwood-Onsager model, the classical multipolar expansion model (up to I = 7), and an ab initio polarized continuum model. We examined the same BKO model with a different cavity radius and the AMl-SMl and AMl-SMla o- models, and Wang and Ford have performed calculations with the AMl-PCM model. 

Nearly symmetrical molecules deserve special mention. Benzene and piperazine are uncharged and have no dipole moment, so the Born-Kirkwood-Onsager model predicts AGs — 0- However, AM1-SM2 predicts —0.5 and —7.8 kcal/mol, respectively, in good agreement with the experimental -0.9 and -7.4 kcal/mol. In benzene the result comes as the sum of a hydrophobic AGcds = 1.4 kcal/mol and a hydrophilic AGe p = —2.0 kcal/mol whereas in piperazine both terms are hydrophilic (AG ds 4.1 kcal/mol, AGg p = —3.7 kcal/ mol), and they reinforce each other. Similar reinforcement occurs in many other compounds [e.g., p-bromophenol (AGs -4.4 kcal/mol, AGg p = —2.7 kcal/mol)], in which case AM1-SM2 predicts AGs 7.0 kcal/mol versus an experimental value of —7.1 kcal/mol. 

G. E. Chudinov and D. V. Napolov, Chem. Phys. Lett., 201, 250 (1993). A New Method of Geometry Optimization for Molecules in Solution in the Framework of the Born-Kirkwood-Onsager Approach. 

M. V. Basilevsky and G. E. Chudinov, Dynamics of charge transfer chemical reactions in a polar medium within the scope of the Born-Kirkwood-Onsager model, Chem. Phys. 157, 327-344 (1991). 

Dip a2/V Kirkwood-Onsager dipole solvent index [(dipole momentj /volume]... 

The traditional treatment regarding medium effects is the dielectric continuum model in the Kirkwood-Onsager theory [76]. This simple model assumes that the solvation energy arises from the electrostatic interaction between the solutes and... 

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