Screened Interaction Fields

Having derived the general expressions (3.23), (3.41), and (3.48) which cover all multiplet contributions to the dispersion energy, we are able to 

There is obviously screening. Let us consider two arbitrary particles 1 and 2, and let us inquire about the external field of a fluctuating dipole pi at position i-j in particle 1, see Fig. 10. The total field at position rj outside particle 1 is composed of the direct field jJjTy, the first-order polarisation field Pi T, k XkT hj of all remaining dipoles k in 1, the second-order polarisation field Pl ik XkT km remaining dipoles k, m in 1, and so on. 

Similarly, if position rj is that of a dipole j in particle 2, we find the screened reaction tensor of dipole j to be 

The screened tensors Tfy, account for screening by that particle in which the respective field originates. On substituting Tfy, into Eq. (3.41) and omitting all contributions resulting from interactions within particle 1 or within particle 2 we obtain 

The dispersion energy between two macroscopic particles 1 and 2 can be expressed in terms of the macroscopic screened interaction tensors Tf , T f. We do not need the molecular interaction tensors Tip T, - any longer. 

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G2, to G3, and to G4, the effective enhancement was 10%, 36%, and 35% larger than the value estimated by the simple addition of monomeric values. The enhancement included the local field effect due to the screening electric field generated by neighboring molecules. Assuming the chromophore-solvent effect on the second-order susceptibility is independent of the number of chro-mophore units in the dendrimers, p enhancement can be attributed to the inter-molecular dipole-dipole interaction of the chromophore units. Hence, such an intermolecular coupling for the p enhancement should be more effective with the dendrimers composed of the NLO chromophore, whose dipole moment and the charge transfer are unidirectional parallel to the molecular axis. 

Ahlstrom, M.M., Ridderstrom, M., Luthman, K. and Zamora, I. (2005) Virtual screening and scaffold hopping based on GRID molecular interaction fields. fournal of Chemical Information and Modeling, 45, 1313-1323. 

In case when the resonant screen interacts only with those field modes that propagate in solid angle A and are quantized in the same volume (Vq = Yo,N = N), from Eq. (14.20), we have... 

Here % is the dielectric constant. For more distant-lying centers the effect of molecular bonding is small and the screened interaction with the ionic field can be considered as homogeneous. Smearing out the polarization centers to a dielectric, x = 1 + gF, the summation in Eq. 3.18 gives... 

Issues of consistency arise in the combination of 1/gas, which usually includes a coulomb electrostatic term, and a continuum model of solvent electrostatic effects. It can be shown that, if the charges in the two models differ, errors in long range behavior can result because the solvent reaction field produced by one set of charges does not match the difference between vacuum and dielectrically screened interactions for a different set. The use of interior dielectric constants other than 1.0 also raises a consistency issue since most of the empirical potential energy functions that one would use for 1/gas are designed for use with s = 1 and do not include atomic polarizability, whereas the choice of Sm > 1 in the continuum model implies solute polarization. There is... 

Before running a molecular dynamics simulation with solvent and a molecular mechanics method, choose the appropriate dielectric constant. You specify the type and value of the dielectric constant in the Force Field Options dialog box. The dielectric constant defines the screening effect of solvent molecules on nonbonded (electrostatic) interactions. 

As for the dielectric constant, when explicit solvent molecules are included in the calculations, a value of 1, as in vacuum, should be used because the solvent molecules themselves will perform the charge screening. The omission of explicit solvent molecules can be partially accounted for by the use of an / -dependent dielectric, where the dielectric constant increases as the distance between the atoms, increases (e.g., at a separation of 1 A the dielectric constant equals 1 at a 3 A separation the dielectric equals 3 and so on). Alternatives include sigmoidal dielectrics [80] however, their use has not been widespread. In any case, it is important that the dielectric constant used for a computation correspond to that for which the force field being used was designed use of alternative dielectric constants will lead to improper weighting of the different electrostatic interactions, which may lead to significant errors in the computations. 

This decade also saw the first major developments in molecular graphics. The first multiple-access computer was built at MIT (the so-called project MAC), which was a prototype for the development of modern computing. This device included a high-performance oscilloscope on which programs could draw vectors very rapidly and a closely coupled trackball with which the user could interact with the representation on the screen. Using this equipment, Levinthal and his team developed the first molecular graphics system, and his article in Scientific American [25] remains a classic in the field and laid the foundations for many of the features that characterize modern day molecular graphics systems. 

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