Reaction field effect

Rashin, A.A., M.A. Bukatin, J. Andzelm, and T. Hagler. 1994. Incorporation of reaction field effects into density functional calculations for molecules of arbitrary shape. Biophys. Chem. 51, 375. 

The reaction field effects are easily incorporated as an additional term in the Kohn-Sham matrix, given by ... 

The reactant R2 can also be considered to be a solvent molecule. The global kinetics become pseudo first order in Rl. For a SNl mechanism, the bond breaking in R1 can be solvent assisted in the sense that the ionic fluctuation state is stabilized by solvent polarization effects and the probability of having an interconversion via heterolytic decomposition is facilitated by the solvent. This is actually found when external and/or reaction field effects are introduced in the quantum chemical calculation of the energy of such species [2]. The kinetics, however, may depend on the process moving the system from the contact ionic-pair to a solvent-separated ionic pair, but the interconversion step takes place inside the contact ion-pair following the quantum mechanical mechanism described in section 4.1. Solvation then should ensure quantum resonance conditions. 

Interactions between a solute and a solvent may be broadly divided into three types specific interactions, reaction field and Stark effects, and London-van-der-Waals or dispersion interactions. Specific interactions involve such phenomena as ion pair formation, hydrogen bonding and ir-complexing. Reaction field effects involve the polarization of the surrounding nonpolar solvent by a polar solute molecule resulting in a solvent electric field at the solute molecule. Stark effects involve the polarization of a non-polar solute by polar solvent molecules Dispersion interactions, generally the weakest of the three types, involves nonpolar solutes and nonpolar solvents via snap-shot dipole interactions, etc. For our purposes it is necessary to develop both the qualitative and semiquantita-tive forms in which these kinds of interactions are encountered in studies of solvent effects on coupling constants. 

All of the interaction mechanisms described above are expected to produce electric fields in the solute cavity. In the case of specific interactions and reaction field effects these electric fields are expected to have some specific orientation with respect to the solute coordinate system. Dispersion forces and Stark effects are not expected to have any specific orientation with respect to the solute. Magnetic field effects seem unlikely to be important in light of the well-known invariance of coupling constants to changes of the external magnetic field. However, it is conceivable that a solvent magnetic reaction field might... 

It is noteworthy that the quite polar compounds CH3CN and CH3CC13 which are not expected to hydrogen bond, but which do have significant dipoles and hence might display reaction field effects show AJ values of 0.33 and 0.52 Hz respectively precisely the range of values predicted by Raynes 1S). 

Investigation of the concentration dependence of/13 of trichloroethylene and cis 1,2-dichloroethylene (Table 8) over the range of 50-100 mole % showed a small but significant change. Both cis and trans isomers of the dichloro and dibromoethylenes show the same slopes for the concentration dependence (Figs. 1 and 2). This is inconsistent with the idea of a reaction field effect since... 

It is interesting that the difference between A / for the cis isomer and AJ for the trans isomer (Table 7) is approximately 0.7 Hz in each case about the same as the value of AJ observed for the 1,1-isomer. For either cis-trans pair it might be assumed that both isomers experience a solvent- C-X bond interaction, whereas the cis isomer also experiences a reaction field effect. The 1,1 isomer also experiences C-X interaction with the solvent, but since the halogens are removed from the vicinity of the C-H bonds this has little effect on lJl3... 

Thus, AJ for the 1,1-isomer reflects only a reaction field effect. Further, the 0.7 Hz change or difference is the same range as the theoretically predicted effect of 0.3 -0.5 Hz for a through space electric field. 

As implied above, the principal interaction mechanism for polar solutes seems to be the reaction field effect. Specific interactions, notably hydrogen bonding, are also common. For non-polar solutes dispersion interactions seem to predominate. None of the investigations reported to date have developed completely satisfactory solutions to the interaction question, but it appears from the most recent studies that all interaction mechanisms are present in all systems. Most authors have simply reported the dominant effect for the particular case with which they were concerned. Particularly intriguing is the indication that dispersion interactions and reaction field effects produce the opposite affect on coupling constants. 

The corresponding PCM expressions (2.193) and (2.194) show that the same physical effects are considered the static cavity field effects are explicitly represented by the matrices m°, while the static reaction field effects are implicit in the coupled perturbed HF (or KS) equations which determine the derivative of the density matrix. 

Thole, B.T. and Duijnen P.Th. van, Reaction field effects on proton transfer in the active site of Actinidin. Biophysical Chemistry (1983) 18 53-59. 

This equation takes account of the fact that to maintain T we have kept the dielectric medium in contact with a heat bath with which it can exchange heat to maintain thermal equilibrium. Equation [8] provides the simplest example of a reaction field effect. The electric field is in general given... 

The simplest quantum mechanical Hamiltonian operator that includes reaction field effects for neutral solutes is ... 

M. M. Karelson, A. R. Katritzky, and M. C. Zerner, Int. j. Quantum Chem., Symp., 20, 521 (1986). Reaction Field Effects on the Electronic Distribution and Chemical Reactivity of Molecules. 

A. R. Katritzky and M. Karelson,/. Am. Chem. Soc., 113, 1561 (1991). AMI Calculations of Reaction Field Effects on the Tautomeric Equilibria of Nucleic Acid Pyrimidine and Purine Bases and Their 1-Methyl Analogues. 

Onsager model—reaction field effects. In the simplest form of this model a chosen molecule is represented by a spherical cavity of suitable volume filled with fluid of relative permittivity c , containing a rigid dipole of value fi. This p, is chosen so that if py is the measured vacuum dipole moment of the molecule, = (c , + 2)py/3. Correct calculation of the orienting couple on the dipole due to a given external field leads to the Onsager relation... 

Although neutral methanol and ammonia are more stable in vacuo than their ions, the reaction field is capable of inverting this gap. At 3.0A as the spherical cavity radius, the diionic form becomes more stable. The tetrahedral substrate can approach the dyad to a shorter distance than the planar substrate. The repulsive barrier occurs at distances shorter than 2.5A for the planar, but only at 2.0A for the tetrahedral. The tetrahedral substrate is more stabilized by the reaction field effect than the planar substrate, due to an increase in the in-vacuo dipole moment of the tetrahedral. The reaction field is supposed to mimic the protein surrounding, and it is proposed that the protein stabilizes the diionic form even though the simulation of the reaction field is not sufficient to obtain a realistic interpretation. This study indicates a tendency to tetrahedralization of the model substrate at distances characteristic of the Michaelis-Menten complex formation. The authors believe that this must affect intermolecular interactions of large substrates. 

Zhan, C.G., Chipman, D.M. Reaction field effects on nitrogen shielding. J. Chem. Phys. 1999, 110(3), 1611-22. 

The continuum model has been applied to an experimental study of the solvent effect on the 6-chloro-2-hydroxypyridine/6-chloro-2-pyridone equilibrium in a variety of essentially non-hydrogen-bonding solvents (Beak et al., 1980). In this study, a plot of log A nh/oh) versus (e - 1)/ (2e + 1), the solvent dielectric term, yielded a linear least-squares fit with a slope of 2.5 0.2, an intercept of -1.71, and a correlation coefficient of 0.9944. This result was used to estimate the gas phase free-energy difference of 9.2 kJ mole-1, which compares favorably with the observed value of 8.8 kJ mole-1 for this system. The authors also reported that alcohol solvents are correlated fairly well in this study but that other solvents seem to be divided into two classes, those that are electron-pair donors and those that are electron-pair acceptors in a hydrogen bond. The hydrogen bonding effect is assumed to be independent from the reaction field effect and is included in the continuum model by means of the Kamlet and Taft (1976) empirical parameters. The interested reader is referred to the original paper for a detailed discussion of the method and its application. 

It shows the relevant (system) part of the density operator at time r (1) coupled to the bath (2), propagated in the bath subspace from time r to time t (3) and affecting again the system via the system-bath coupling (4). This is a mathematical expression of what we often refer to as a reaction field effect The system at some time r appears to act on itself at some later time t, and the origin of this action is the reaction of the system at time t to the effect made by the same system on the bath at some earlier time r. 

The mechanism of liver alcohol dehydrogenase (LADH) has been extensively studied. For a recent overview the reader is referred to Ref [93]. Reaction field effects on the transition structure of model hydride transfer systems have been calculated at ab initio 4-3IG basis set level [93, 94]. The active site of enzymes are usually assumed to be designed to receive molecules in the transition state for the reaction they catalyze. This special sort of surrounding medium effects has been computationally documented recently [95]. From the reaction geodesic passing through the transition state for hybride transfer in the pyridium cation/methanolate model system, only the TS-structure could be fitted into the LADH active site. The normal mode analysis carried out on the TS showed an excellent agreement with isotopic substitution experiments [95]. Reaction field calculations on this model systems have also been performed. For an overview of biomolecular interactions the reader is referred to Ref [96]. 

Karelson, M. M. Katritzky, A. R. Zerner, M. C. Reaction field effects on the electron distribution and chemical reactivity of molecules. Int. J. Quantum... 

To end this short section on reaction field effects, we remark on another imphcation of the calculation of free-energy second derivatives, that is, that the assessment of a complete equiUbrium scheme or the account for vibrational and/or electronic nonequihbrium solvent effects [203,204] should be done (see below for more details on this subject). 

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