Atomic repulsion

The method employed for an initial effort to explore a complex reaction sequence should be fast and inexpensive, but sufficiently reliable to enable meaningful deductions concerning structures and relative energies to be made. The results can then be usefully employed as starting points for more elaborate and accurate methods for detailing the energy hypersurfaces. For this study we have chosen to use Anderson s modification (27) of extended Hiickel theory (MEHT). MEHT differs from EHT by the inclusion of a pair-wise correction for atom-atom repulsions. 

First, as we have seen in examples on the previous pages, bond angles in molecules tend to open up as much as possible as a result of Ihe repulsions between the electrons bonding the substituents to the central atoms. Repulsions between... 

Figure 34 Ratio of individual atom-repulsion coefficients for the two ends of each bidentate ligand in cis-[M(bidentate)2-(unidentate)2] as a function of normalized bite b. Upper curve, R(unidentate/bidentate) = 1.5 middle curve, R(uni-dentate, bidentate) = 1.0 lower curve, Rfunidentate/bidentate) = 0.75...

By adjusting the calculated to the observed wave numbers, the following five Urey-Bradley force constants have been obtained for Se6 (in N/cm) K = 1.188 (bond stretching), H = 0.102 (bond-angle bending), F = 0.082 (next nearest atom repulsion), Y = 0.242 (torsion), and P = 0.207 (bond-bond interaction) (18,19). 

Ajj/rij12 is a repulsive force (i.e., a positive contribution to the potential energy) and BA 6 is an attractive force between nonbonded atoms i and j. Other exponential forms, such as the Buckingham potential, can also be used to describe atomic repulsion.51 A similar equation can be used to describe H-bonds using different constants ... 

Sheer congestion of donor atoms around the metal ion and concomitant inter-donor atom repulsions makes these high coordination numbers difficult to attain. They are often associated with multidentate ligands with a small bite angle such as nitrate that take up little space in the coordination sphere, either alone, as in (Ph4As)2[Eu(N03)5] or in combination with other ligands, as in Ln(bipy)2(N03)3, Ln(terpy)(N03)3(H20) (Ln = Ce-Ho), and crown ether complexes (Section 4.3.7) such as Ln(12-crown )(N03)3(Ln = Nd-Lu). Other crown ether complexes can have 11 and 12 coordination, e.g. Eu(15-crown-5)(N03)3 (Ln = Nd-Lu) and Ln(18-crown-6)(N03)3(Ln = La, Nd). 

Steric considerations (interdonor atom repulsions) make coordination numbers of 10 or more difficult, so fewer examples are known and, moreover, small differences between different types of polyhedra make assignment of a particular geometry difficult. Most examples involve nitrate, either alone (Section 3.7.7), or in combination with other polydentate ligands such as crown ethers (Section 3.7.8). Near-icosahedral geometries are found for regular 12-coordinate complexes such as Pr(naph)6 + and Ln(N03)6. ... 

Atomic repulsion and induced dipole-induced dipole dispersive attraction are typically described by a Lennard-Jones function [16,17] ... 

Rules 1-3) (a) in a face-to-face interaction K-atom repulsion dominates ... 

In many applications, it is more computationally convenient to express the S functions in terms of the scalar products between the unit local axis vectors (xj, yi, and X2, ya, i) and the unit intermolecular vector R. This set of variables is highly redundant, but easily calculated from the local axis vector information in most simulations. As an illustration. Table 1 gives the S functions that are important in describing the anisotropy of the atom-atom repulsion between an N atom in pyridine and a hydrogen-bonding proton of methanol. 

Another simpler systematic potential was derived for chlorine, using the two atomic sites for the distributed multipoles and dispersion coefficients. The anisotropic atom-atom repulsion potential was derived from the overlap model, with the proportionality constant and one major anisotropic coefficient being adjusted by empirical fitting to the crystal structure. This empirical adjustment appeared to effectively absorb the missing contributions, including the many-body effects, because the potential was able to reproduce a wide range of properties of the solid and liquid from Monte Carlo simulations. 

Here qi is the effective charge of an atom is a dispersion interaction constant and Ay and bij are parameters of the Born - Mayer atom-atom repulsion potential. To calculate the long range Coulomb term in Eq. (1) one generally has to employ the Ewald summation technique. To obviate this inconvenience, the Coulomb term has been multiplied by the screening factor (and the dispersion term has been neglected) ... 

A much wider class, however, is presented by adsorbents where the adsorbed molecules interact directly with the inorganic mineral surface. In this case, a simple account of dispersion attraction and short-range atom-atom repulsion forces would not suffice, for polarization interaction is expected to play a major role. The corresponding approach employed will be demonstrated using the molecular-statistical interpretation of the expe-... 

Once more the molecular-statistical method based on a microscopic model of the mi-croporous adsorbent leads to quite satisfactory agreement with the experimental data provided that the essential interactions of the adsorbed molecule with the adsorbent surface, including polarization and dispersion attraction, and short-range atom-atom repulsion, are taken into account. 

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