Dipole Models

The quality of the results that can be obtained with point charge or dipole models depends critically on the input solvation shell structure. In view of the computer power available today, taking the most rigorous route... 

Mattliew, M. K., and Balaram, A., 1983. A helix dipole model for alamedii-cin and related tran.smembrane channels. FEES Letters 157 1-5. 

FIGURE 2.4. A schematic description of the Langevin Dipole model. The figure illustrates the three steps involved in constructing the model. 

Langevin dipoles, 52, 53, 125 Langevin dipoles model, 49-53, 50. See also Protein dipoles-Langevin dipole model for catalytic effect of carbonic anhydrase, 199... 

LD model, see Langevin dipoles model (LD) Linear free-energy relationships, see Free energy relationships, linear Linear response approximation, 92,215 London, see Heitler-London model Lysine, structure of, 110 Lysozyme, (hen egg white), 153-169,154. See also Oligosaccharide hydrolysis active site of, 157-159, 167-169, 181 calibration of EVB surfaces, 162,162-166, 166... 

Page, M. I., and Jencks, W. P., entropic hypothesis of enzyme catalysis, 224-225 Papain, Cys-His proton transfer in, 140-143 Pauling, Linus, view of enzyme catalysis, 208 PDLD model, see Protein dipoles-Langevin dipoles model (PDLD)... 

Protein dipoles-Langevin dipoles model (PDLD), 123-125,124 Protein potential surfaces, see Enzyme potential surfaces... 

Pulsed source techniques have been used to study thermal energy ion-molecule reactions. For most of the proton and H atom transfer reactions studied k thermal) /k 10.5 volts /cm.) is approximately unity in apparent agreement with predictions from the simple ion-induced dipole model. However, the rate constants calculated on this basis are considerably higher than the experimental rate constants indicating reaction channels other than the atom transfer process. Thus, in some cases at least, the relationship of k thermal) to k 10.5 volts/cm.) may be determined by the variation of the relative importance of the atom transfer process with ion energy rather than by the interaction potential between the ion and the neutral. For most of the condensation ion-molecule reactions studied k thermal) is considerably greater than k 10.5 volts/cm.). 

The results in Table IV suggest that the condensation reactions cannot be described adequately by the ion-induced dipole model. In this regard the results agree with conventional studies which have frequently found a higher power inverse dependence of the cross-section on the field strength E for condensation reactions than for hydrogen transfer reactions. 

In this instance, the (5)-enantiomer data have been negated prior to plotting. From previous discussion of the antisymmetry of the parameters under enantiomer exchange (e.g., Section III.A) it is recognized that it is then to be expected that the (R)- and (5)-enantiomer data should fall on the same experimental trend line. That they do indeed do so shows, as was argued in the Section IV.A for fenchone, that the behavior is at least qualitatively in accord with a pure electric dipole model. Furthermore, combining two distinct data sets [(/ )- and (5)-enantiomers] in this manner provides a consistency check on the reproducibility of the PECD data. It seems good practice to include measurement of both enantiomers, where this is feasible, in an experimental study. 

Schmickler, W., A jellium-dipole model for the double layer, J. Electroanal. Chem., 150, 19 (1983). 

Thole s polarizability parameters were selected to optimize the molecular polarizabilities for a set of 16 molecules. The method was later expanded to fit 52 molecules [146], It must be emphasized that this electric-field damping method is totally independent of the polarization scheme used. For the Drude and fluctuating charge methods only /i(r) is required, whereas for methods based on induced dipoles both /i(r) and /2(r) are necessary. In the context of the induced dipole model other models were proposed since the formula of Thole does not provide enough attenuation. For example, in Ref. [152] the field is evaluated using... 

When the Drude particles are treated adiabatically, a SCF method must be used to solve for the displacements of the Drude particle, d, similarly to the dipoles Jtj in the induced dipole model. The implementation of the SCF condition corresponding to the Born-Oppenheimer approximation is straightforward and the real forces acting on the nuclei must be determined after the Drude particles have attained the energy minimum for a particular nuclear configuration. In the case of N polarizable atoms with positions r, the relaxed Drude particle positions r + d5CF are found by solving... 

This equation is the equivalent of Eq. (9-12) for the induced dipole model but has one important difference. Equation (9-13), the derivative of Eq. (9-12), is linear and standard matrix methods can be used to solve for the p. because Eq. (9-12) is a quadratic function of p , while Eq. (9-54) is not a quadratic function of d and thus matrix methods are usually not used to find the Drude particle displacements that minimize the energy. 

An important alternative to SCF is to extend the Lagrangian of the system to consider dipoles as additional dynamical degrees of freedom as discussed above for the induced dipole model. In the Drude model the additional degrees of freedom are the positions of the moving Drude particles. All Drude particles are assigned a small mass mo,i, taken from the atomic masses, m, of their parent atoms and both the motions of atoms and Drude particles (at positions r, and rdj = r, + d, ) are propagated... 

Stern HA, Rittner F, Berne BJ, Friesner RA (2001) Combined fluctuating charge and polarizable dipole models application to a five-site water potential function. J Chem Phys 115(5) 2237-2251... 

It is generally thought that the ER effect happens only in nonconducting oils. Here an ER effect in solid-like matrices such as polymer gels will be discussed. The nature of the ER effect in polymer gels will be explained using the point dipole model in [44],... 

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