Atom-centered pair potentials

For the interpretation of the measurements information on the structure of the clusters is very important. An ab initio calculation at one point of the total energy surface of a more than three-atom cluster including effects of correlation is a state-of-the-art task. A complete mapping of the surface is impossible. Therefore, we have used a model which is based on a reliable multi—center pair potential. Then the equilibrium geometries and total energy minima are determined by minimizing the intermolecular energy with respect to the molecular positions. To initiate a... 

In a statistical Monte Carlo simulation the pair potentials are introduced by means of analytical functions. In the election of that analytical form for the pair potential, it must be considered that when a Monte Carlo calculation is performed, the more time consuming step is the evaluation of the energy for the different configurations. Given that this calculation must be done millions of times, the chosen analytic functions must be of enough accuracy and flexibility but also they must be fastly computed. In this way it is wise to avoid exponential terms and to minimize the number of interatomic distances to be calculated at each configuration which depends on the quantity of interaction centers chosen for each molecule. A very commonly used function consists of a sum of rn terms, r being the distance between the different interaction centers, usually, situated at the nuclei. In particular, non-bonded interactions are usually represented by an atom-atom centered monopole expression (Coulomb term) plus a Lennard-Jones 6-12 term, as indicated in equation (51). 

The OPLS model is an example of pair potential where non-bonded interactions are represented through Coulomb and Lennard-Jones terms interacting between sites centred on nuclei (equation (51). Within this model, each atomic nucleus has an interaction site, except CH groups that are treated as united atoms centered on the carbon. It is important to note that no special functions were found to be needed to describe hydrogen bonding and there are no additional interaction sites for lone pairs. Another important point is that standard combining rules are used for the Lennard-Jones interactions such that An = (Ai As )1/2 and Cu = (C Cy)1/2. The A and C parameters may also be expressed in terms of Lennard-Jones o s and e s as A = 4ei Oi and C ... 

Figure 9.9 Calculated atom jumps in the core of a E5 symmetric (001) tilt boundary in b.c.c. Fe. A pair-potential-molecular-dynamics model was employed. For purposes of clarity, the scales used in the figure are [130] [310] [001] = 1 1 5. All jumps occurred in the fast-diffusing core region. Along the bottom, a vacancy was inserted at B, and subsequently executed the series of jumps shown. The trajectory was essentially parallel to the tilt axis. Near the center of the figure, an atom in a B site jumped into an interstitial site at I. At the top an atom jumped between B, I and B sites. From Balluffi et al. [14],...

If a more complex adsorbate is being studied, (N2, CO2, water, etc.) the orientation dependence should be added to the model. For the linear Nj molecule, e.g., a three-site L-J pair potential is typically used [17]. The three sites correspond to the N atoms and the center of mass. The interaction between the atomic sites is taken to be a L-J 12-6 potential function, and partial charges are placed on the three sites in the molecule to reproduce the known quadrupole moment. 

The treatment described in the last section is appropriate for both atomic and molecular fluids, as the coordinate representation of each particle included the possibility of molecular orientation. This approach is convenient if the pair potential can be written as a function of the molecular coordinates In many circumstances, however, the interaction between two molecules can best be written as the sum of pairs of site-site interactions, where typically the sites are the centers of the constituent atoms. If a and y label sites on molecules 1 and 2, respectively, then the total interaction between the two molecules is given by... 

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