Energy atom pair

Base pair Stacking energy Atom pair Bond energy ... 

The technique of INS is probably the least used of those described here, because of experimental difficulties, but it is also one of the physically most interesting. Ions of He" of a chosen low energy in the range 5-10 eV approach a metal surface and within an interaction distance of a fraction of a nanometer form ion-atom pairs with the nearest surface atoms. The excited quasi molecule so formed can de-excite by Auger neutralization. If unfilled levels in the ion fall outside the range of filled levels of the solid, as for He", an Auger process can occur in which an electron from the va-... 

The next higher energy orbital is much higher in energy (-0.9 au) and it is completely delocalized. The orbital surface consists of a single surface that encompasses all three atoms. This means that this orbital is simultaneously (o) bonding with respect to each CH atom pair. 

Some force fields make special provision for the mutual electrostatic potential energy of pairs of atoms that have different electronegativities. If atom A has a formal charge of i2a and atom B (distant J ab from Qa) has a formal charge of (2b, then their mutual potential energy is... 

The parameter redundancy is also the reason that care should be exercised when trying to decompose energy differences into individual terms. Although it may be possible to rationalize the preference of one conformation over another by for example increased steric repulsion between certain atom pairs, this is intimately related to the chosen functional form for the non-bonded energy, and the balance between this and the angle bend/torsional terms. The rotational banier in ethane, for example, may be reproduced solely by an HCCH torsional energy term, solely by an H-H van der Waals repulsion or solely by H-H electrostatic repulsion. Different force fields will have (slightly) different balances of these terms, and while one force field may contribute a conformational difference primarily to steric interactions, another may have the... 

In this section the several theoretical or semi-empirical formulas for the prediction of London energies are compared with experimental values. The formulas to be tested are summarized in conventional units both for unlike atom pairs and in the simplified form for pairs of like atoms as follows ... 

The Finite Range Problem. The minimum image convention requires (1) the use of interaction energy functions that are of finite range, i.e. that are non-zero only for distances below a certain limit, R. As a consequence, only a fraction of all minimum image pairs actually interact with non-zero energy this fraction must be less than ir/2d, i.e., in two dimensions maximally 0.79, in three dimensions maximally 0.52 (and actually often less than 0.3). It is desirable to efficiently eliminate from consideration all noninteracting atom pairs. 

However, the reality is considerably more complicated than the ideal model. Non-ideality of the system causes that segregation extends over more than one layer. Further, when the size of the atoms is not equal one has to consider it in the calculations. This all has been done by A.D.van Langeveld (10), who made the following assumptions on the Pt/Cu system i) segregation extends over the two outmost layers, ii) when the binding energy of pairs of atoms is e the non-ideality of an alloy AB is described by the parameter ... 

One important use of X-ray probes is in the study of local order and displacements, but this is not within the scope of the present book. The recent availability in intense synchrotron sources with selectable X-ray energies permits high-precision measurements of chemically specific atomic-pair correlations in solid solution alloys. A recent review of the technique is given by G.E. Ice and C.J. Sparks (Modern Resonant X-ray studies of alloys local order and displacement) in Annual Reviews of Materials Science 1999, 29, 25-52. 

In view of this and in line with the DFT-D approach described by Grimme [118], we have added an atom-atom pair-wise additive potential of the form Csemi-empirical energy [19-21] in order to account for dispersion effects [43], Thus the dispersion corrected semi-empirical energy ( Pm3-d) is now given by ... 

A - = hydrogen-bonded parameter specific to the atomic pair Btj = hydrogen-bonded parameter specific to the atomic pair Cy = nonbonded parameter specific to the atomic pair Eok = parameter corresponding to torsional barrier energy for a dihedral angle 0k... 

We now analyze the chemical species prevalent in water at these extreme conditions by defining instantaneous species based on the O-H bond distance. If that distance is less than a cut-off value rc, we count the atom pair as being bonded. Determining all bonds in the system gives the chemical species at each point in time. Species with lifetimes less than an O-H bond vibrational period (10 fs) are transient and do not represent bound molecules. The optimal cut-off rc between bonded and nonbonded species is given by the location of the maximum in the free energy surface.83... 

The role of the potential energy is taken by the Dyana target function [8, 28] that is defined such that it is zero if and only if all experimental distance constraints and torsion angle constraints are fulfilled and all nonbonded atom pairs satisfy a check for the absence of steric overlap. A conformation that satisfies the constraints more closely than another one will lead to a lower target function value. The exact definition of the Dyana target function is ... 

The molecular mechanics technique has been called by many different names, including Westheimer method, strain-energy method, conformational energy calculations, empirical potential energy calculations, atom-atom pair potential method, and force field calculations. Empirical force field is widely used, but somewhat long, and many authors omit empirical, leading to confusion with spectroscopic force field calculations. Molecular mechanics (11) now appears to be favored (10a) and is used (abbreviated as MM) throu out this chapter. 

In Table III, we list Ne atom pair energies in mEh. The results obtained with MP2-R12 theory using an auxiliary basis set coincide with the exact atom pair energies. Using this large auxiliary basis is equivalent with computing all three-electron integrals in an exact manner ( ). 

Atom-atom potentials have been used extensively for the study of molecular crystals, and many useful empirical parameters sets have been designed. The interaction energy of the two chains is considered to be the sum over all pairwise interactions. In the present work, such interaction is considered according to the 6-12 potential functions. The energy of an atom pair is given by an expression of the form ... 

In this expression, the dipole dipole interactions are included in the electrostatic term rather than in the van der Waals interactions as in Eq. (9.43). Of the four contributions, the electrostatic energy can be derived directly from the charge distribution. As discussed in section 9.2, information on the nonelectrostatic terms can be deduced indirectly from the charge density. The polarizability a, which occurs in the expressions for the Debye and dispersion terms of Eqs. (9.41) and (9.42), can be expressed as a functional of the density (Matsuzawa and Dixon 1994), and also obtained from the quadrupole moments of the experimental charge density distribution (see section 12.3.2). However, most frequently, empirical atom-atom pair potential functions like Eqs. (9.45) and (9.46) are used in the calculation of the nonelectrostatic contributions to the intermolecular interactions. 

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