Atomic interactions, computation

Klepeis, J. L. I. P. Andronlakis M. G. Ierapetritou, et al. Predicting Solvated Peptide Configuration via Global Minimization of Energetic Atom-to-Atom Interactions. Comput Chem Eng 22 765-788 (1998). 

Statistical mechanical theory and computer simulations provide a link between the equation of state and the interatomic potential energy functions. A fluid-solid transition at high density has been inferred from computer simulations of hard spheres. A vapour-liquid phase transition also appears when an attractive component is present hr the interatomic potential (e.g. atoms interacting tlirough a Leimard-Jones potential) provided the temperature lies below T, the critical temperature for this transition. This is illustrated in figure A2.3.2 where the critical point is a point of inflexion of tire critical isothemr in the P - Vplane. 

In order to improve parallelism and load balancing, a hybrid force-spatial decomposition scheme was adopted in NAMD 2. Rather than decomposing the nonbonded computation into regions of space or pairwise atomic interactions, the basic unit of work was chosen to be interactions between atoms... 

The AMBERforce field expects lone pairs to be added to all sulfur atoms and computes the interactions as if these lone pairs were atoms with a specific type just like any other atom. The templates automatically add the expected lone pairs to sulfur atoms when usin g th e AMBER force field. 

Arestraint (not to be confused with a Model Builder constraint) is a user-specified one-atom tether, two-atom stretch, three-atom bend, or four-atom torsional interaction to add to the list of molecular mechanics interactions computed for a molecule. These added interactions are treated no differently from any other stretch, bend, or torsion, except that they employ a quadratic functional form. They replace no interaction, only add to the computed interactions. 

LJ) potential (6). The diffusing atoms also have LJ forces between them. Atoms interact with a ghost atom in the substrate that is subjected to random and dissipative forces that closely match the forces exerted by a neighboring shell of atoms in the crystal. In this way the MD computation is limited to a relatively small number of mobile atoms and their ghost atoms, and the influence of the large number of atoms in the crystal is represented by the forces applied to the ghost atom. 

When addressing problems in computational chemistry, the choice of computational scheme depends on the applicability of the method (i.e. the types of atoms and/or molecules, and the type of property, that can be treated satisfactorily) and the size of the system to be investigated. In biochemical applications the method of choice - if we are interested in the dynamics and effects of temperature on an entire protein with, say, 10,000 atoms - will be to run a classical molecular dynamics (MD) simulation. The key problem then becomes that of choosing a relevant force field in which the different atomic interactions are described. If, on the other hand, we are interested in electronic and/or spectroscopic properties or explicit bond breaking and bond formation in an enzymatic active site, we must resort to a quantum chemical methodology in which electrons are treated explicitly. These phenomena are usually highly localized, and thus only involve a small number of chemical groups compared with the complete macromolecule. 

This computation involves of course all possible atom-atom interaction pairs—a relatively small population compared to the vast number of interorbital integrals that must be computed during MO calculations. As a consequence of these features, the molecular mechanics calculations far exceed in accuracy and speed the two other methods mentioned above. 

Medium-range interactions can be defined as those which dominate the dynamics when atoms interact with energies within a few eV of their molecular binding energies. These forces determine a majority of the physical and chemical properties of surface reactions which are of interest, and so their incorporation in computer simulations can be very important. Unfortunately, they are usually many-body in nature, and can require complicated functional forms to be adequately represented. This means that severe approximations are often required when one is interested in performing molecular dynamics simulations. Recently, several potentials have been semi-empirically developed which have proven to be sufficiently simple to be useful in computer simulations while still capturing the essentials of chemical bonding. 

Under the Born-Oppenheimer approximation, two major methods exist to determine the electronic structure of molecules The valence bond (VB) and the molecular orbital (MO) methods (Atkins, 1986). In the valence bond method, the chemical bond is assumed to be an electron pair at the onset. Thus, bonds are viewed to be distinct atom-atom interactions, and upon dissociation molecules always lead to neutral species. In contrast, in the MO method the individual electrons are assumed to occupy an orbital that spreads the entire nuclear framework, and upon dissociation, neutral and ionic species form with equal probabilities. Consequently, the charge correlation, or the avoidance of one electron by others based on electrostatic repulsion, is overestimated by the VB method and is underestimated by the MO method (Atkins, 1986). The MO method turned out to be easier to apply to complex systems, and with the advent of computers it became a powerful computational tool in chemistry. Consequently, we shall concentrate on the MO method for the remainder of this section. 

So, for each snapshot of the simulation that contributes to the ensemble (by either MC or MD evaluation), we compute the energy differential for all of the atoms interacting with Hb rather than Ha. In Figure 12.1, the particular case of one of the hydrogen atoms on a first-shell water molecule is illustrated. As this is a non-bonded interaction in each case, the contribution from Hd in a simple force field might be... 

MO Coefficients for Fluorine Atomic Orbitals Computed from F19 Hyperfine Interactions"... 

In practice, empirical or semi-empirical interaction potentials are used. These potential energy functions are often parameterized as pairwise additive atom-atom interactions, i.e., Upj(ri,r2,..., r/v) = JT. u ri j), where the sum runs over all atom-atom distances. An all-atom model usually requires a substantial amount of computation. This may be reduced by estimating the electronic energy via a continuum solvation model like the Onsager reaction-field model, discussed in Section 9.1. 

The dispersion and repulsion contributions have been modelled and computed with a variety of approaches [3,8], The most diffused PCM version adopts the procedure developed by Floris and Tomasi [10], based on atom-atom interaction parameters, proposed by Caillet and Claverie from crystallographic data [11] ... 

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