Long-range Coulombic interactions

Calculation of the energies and forces due to the long-range Coulomb interactions between charged atoms is a major problem in simulations of biological molecules (see Chapter 5). In an isolated system the number of these interactions is proportional to N-, where N is the number of charged atoms, and the evaluation of the electrostatic interactions quickly becomes intractable as the system size is increased. Moreover, when periodic... 

Monte Carlo simulations [17, 18], the valence bond approach [19, 20], and g-ology [21-24] indicate that the Peierls instability in half-filled chains survives the presence of electron-electron interactions (at least, for some range of interaction parameters). This holds for a variety of different models, such as the Peierls-Hubbard model with the onsite Coulomb repulsion, or the Pariser-Parr-Pople model, where also long-range Coulomb interactions are taken into account ]2]. As the dimerization persists in the presence of electron-electron interactions, also the soliton concept survives. An important difference with the SSH model is that neu-... 

In 1995, one of the authors (A.K.) introduced the state of a molecule embedded in a perfect conductor as an alternative reference state, which is almost as clean and simple as the vacuum state. In this state the conductor screens all long-range Coulomb interactions by polarization charges on the molecular interaction surface. Thus, we have a different reference state of noninteracting molecules. This state may be considered as the North Pole of our globe. Due to its computational accessibility by quantum chemical calculations combined with the conductor-like screening model (COSMO) [21] we will denote this as the COSMO state. 

This simple result may be improved in various ways first, we may relax the "static approximation and keep the plasma assumption (315). In order to eliminate the divergences brought in by the long-range Coulomb interactions (114), it is then necessary to sum over an infinite class of diagrams, known as the ring... 

The Coulomb interaction is long-range, which necessitates use of special numerical methods for efficient simulation.30 When one tries to understand the glass transition in a chemically realistic model, these long-range Coulomb interactions add further numerical overhead so that the most extensive glass transition simulations of realistic models were done for apolar molecules. 

The threshold for positronium formation in collisions of positrons with atoms and molecules is an example of a general class of thresholds in collision processes where there is no residual long-range Coulomb interaction between the constituent subsystems in either the initial or final states. Since the original work of Wigner (1948), there has been much discussion of the effect of the opening of a new channel on those already... 

Real proteins are built up both from hydrophobic and polar amino acid residues, some of the latter can be charged. Many of the conformational and collective properties of proteins are due to a complex interplay between short-range (hydrophobic) effects and long-range (Coulomb) interactions. Electrostatic effects can also determine some of the unique solution properties of globular proteins. We have already discussed the results of simulations... 

PB equation is based on the mean-field approximation, where ions are treated as continuous fluid-like particles moving independendy in a mean electric potential. The theory ignores the discrete ion properties such as ion size, ion-ion correlation and ion fluctuations. Fail to consider these properties can cause inaccurate predictions for RNA folding, especially in the presence of multivalent ions which are prone to ion correlation due to the strong, long-range Coulomb interactions. For example, PB cannot predict the experimentally observed attractive force between DNA helices in multivalent ion solutions. 

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