The variety of interaction potentials

In the preceding sections we have examined the definition of the eomponents of the intermolecular potential, paying attention mostly to rigorous methods and to some approximations based on these methods. 

The beginning of qualitative and semi-quantitative eomputational studies on the properties of liquids dates back at least to the 1950s, and in the early years of these studies, the computational resources were not so powerful as they are today. For this reason, for many 

W e shall try to give a eursory view of the variety of intermolecular potentials in use for liquid systems, paying more attention to the simplest ones. We shall almost completely neglect potentials used in other fields, sueh as the scattering of two isolated molecules, the determination of speetroseopie properties of dimers and trimers, and the accurate study of local chemical interactions, which all require more sophisticated potentials. 

Our exposition will not try to classify potentials according to such criteria, but simply show the variety of potentials in use. We shall pay attention to the description adopted for a single molecule, that must then be combined with that adopted for the interaction partners. In particular, we shall consider the number of sites and the shape of the molecule used in each description. 

The number of sites reflects the possibility we have examined, and advocated, of using many-center expansions to improve the representation. Each expansion center will be a site. There are models with one, two, and more sites. This sequence of increasing complexity reaches the number of heavy atoms of the molecule and then the whole number of atoms, including hydrogens. It is not limited to the nuclei as expansion sites. There are potentials introducing other locations of sites, in substitution or in addition to the nuclei. For example potentials widely used in simulations adopt for water a four-site model other potentials (rarely used in simulations) prefer to use the middle of the bonds instead of (or in addition to) nuclei. Each site of the molecule must be combined with the sites of the second (and other) molecule to give the potential. 

The shape of the molecule reflects the effect of the exchange-repulsion interaction. For almost all many-site models the shape is not given, but it implicitly results to be that of the xmion of the spheres centered on the expansion sites provided by a somce of exchange-repulsion potential. There are some simple models in which the shape is explicitly stated. There will be spheres, ellipsoids, cylinders and more complex shapes, as fused spheres, spherocylinders, etc. Some typical examples are reported in Table 8.5. 

---

For readers wishing to reach a better appreciation of papers regarding the formulation of interaction potentials, we add that there is another way of introducing electron correlation effects in the calculations. It is based on the density functional theory (DFT). There is a variety of DFT methods (detailed information can be found in the quoted monograph ) a family of these methods again makes use of MOs they are called hybrid functional methods and give, on average, better results than other correlated methods at a lower computational cost. 

However, further experimentation embracing a variety of ternary systems will be required to determine the degree of interaction between such multiple centers. Preliminary results for Fe W0, confirm the superposition of two characteristic sets of interband transitions. The optical band gap and flat-band potential are essentially the same as in FeNbO, but the quantum efficiency is considerably greater. This suggests that there may be some enhancement of the photoresponse due to interaction between the iron and tungsten centers. 

The helix-loop-helix (HLH) dimerization domain is quite distinct from the helix-turn-helix motif described above (which is involved in DNA binding not dimerization) and must not be confused with it. The HLH domain consists of two a-helices separated by a nonhelical loop. The C-terminal a-helix has hydrophobic amino acids on one face. Thus two transcription factor monomers, each with an HLH motif, can dimerize by interaction between the hydrophobic faces of the two C-terminal a-helices. Like the leucine zipper (see above), the HLH motif is often found in transcription factors that contain basic DNA binding domains. Again, like the leucine zipper, the HLH motif can dimerize transcription factor monomers to form either homodimers or heterodimers. This ability to form heterodimers markedly increases the variety of active transcription factors that are possible and so increases the potential for gene regulation. 

These methods were selected for different reasons, but mainly for their flexibility and novelty. Rhizon samplers represent the current equivalent of porous cups, widely used in the recent past centrifugation is possibly the current most widely used method because of the ease and the ready availability of the requisite equipment in most laboratories squeezing is a novel alternative, since it has been used on soils recently (Di Bonito, 2005) and has the potential to access water contained in small pores soil suspension or saturation extracts constitute a valid alternative, especially when batch experiments are carried out (Degryse et al., 2003). Furthermore, these methods are capable to perform fractionated extraction on the soil, whereby a combination of the methods can be used to provide soil water originating from a wider range of pores, which can present a variety of interactions with the soil matrix and possibly different chemistry. 

The phase shifts <5, are calculated by standard partial-wave scattering theory. It involves the electron-atom interaction potential of the muffin-tin model. There are a variety of ways to obtain this potential, which consists of electrostatic and exchange parts (spin dependence may be included, especially when the spin polarization of the outgoing electrons is of interest). One usually starts from known atomic wave functions within one muffin-tin sphere and spherically averages contributions to the total charge density or potential from nearby... 

---