Coulomb tail

Infinite series of Feshbach resonances due to the Coulomb tail... 

If the collision system can separate asymptotically into a pair of charged particles of opposite signs, the attractive Coulomb tail of the interaction between them supports an infinite number of bound Rydberg states in each closed channel (with a threshold energy Eth). Its coupling with open channels, if any, normally turns these bound states into an infinite series of quasi-bound... 

A less orthodox line of attack, as yet not explored to its full potential, applies from the beginning the recursion method to the solid-plus-impurity system. The direct use of memory function methods to the perturbed solid is no more difficult than for the perfect solid, with the advantage of overcoming the traditional separation of the actual Hamiltonian into a perfect part and a perturbed part. In fact, such a separation, to make any practical sense, requires that the perturbed part be localized in real space, a restriction hardly met when treating impurities with a coulombic tail. 

The extended potential with a coulombic tail of the impurity centered at the origin is simulated by... 

This result is consistent with the limiting behavior found by Holovko and Polishchuk [22] for an ion-dipole system adsorbed in ion-dipolar matrices. The Coulombic tail has to be properly dealt with in any numerical procedure to... 

Lastly we note that the width of the well identified bound states is zero. But if we diagonalize a hamiltonian with a Coulombic tail, where sits an infinity of discrete but loosely bound Rydberg states, we will reproduce in our projected calculation one discrete state which averages these states, and is surely also an admixture of continuum states. Typically cross sections to these states are small. If one is really interested in cross sections to them an adjunct basis, P, may be used which connects them to P through the potential matrix elements. A t-matrix expression which has the desired state as the final entry, but P%, as the approximate state wave function, can be used. For example, if charge transfer is responsible for a small amount of flux loss from the target nucleus it is not necessary to use a two-centered basis the procedure described can be used, e.g.,... 

The semi-local potential can be rewritten in a form that separates long and short range components. The long range component is local, and corresponds to the Coulomb tail. Choosing an arbitrary angular momentum component (usually the most repulsive one) and defining... 

Adamson, R., Dombroski, J., Gill, R (1996). Chemistry without Coulomb tails. Chemical Physics... 

LDA) In this case the as3nnptotic potential in which the orbitals are calculated lacks the Coulomb tail which is seen by Hartree-Fock orbitals,... 

To find the coefficient of the Coulomb integral for two structures, superimpose their vector-bond patterns to form the superposition pattern (Fig. 1). The Coulomb coefficient is 2 " times the sum (— 1)E for the different patterns in which each orbit serves either as the head or as the tail... 

In principle, any cycloaddition involving two dissymmetric compounds can give head-to-head or head-to-tail products. These two compounds are usually obtained in nonequal proportions whose ratio cannot be adequately explained by steric or coulombic factors.1 For example, Reaction (5.1) favors the more hindered product. In Reaction (5.2), the product is formed by creating bonds between atoms having the same charge in the starting material. 

Statistic mechanics were used by Kiefer and Wilson104 to calculate adsorption isotherms of ionic surfactants on charged solid-water interface. The effect of coulombic repulsions between the ionic heads of the surfactant species are considered, as well as the van der Waals attractions of their hydrocarbon tails. Using the method of Fowler and Guggenheim93 they obtained the equation for an adsorption isotherm ... 

To explain the enantioselectivity obtained with semi-stabilized ylides (e.g., benzyl-substituted ylides), the same factors as for the epoxidation reactions discussed earlier should be considered (see Section 10.2.1.10). The enantioselectivity is controlled in the initial, non-reversible, betaine formation step. As before, controlling which lone pair reacts with the metallocarbene and which conformer of the ylide forms are the first two requirements. The transition state for antibetaine formation arises via a head-on or cisoid approach and, as in epoxidation, face selectivity is well controlled. The syn-betaine is predicted to be formed via a head-to-tail or transoid approach in which Coulombic interactions play no part. Enantioselectivity in cis-aziridine formation was more varied. Formation of the minor enantiomer in both cases is attributed to a lack of complete control of the conformation of the ylide rather than to poor facial control for imine approach. For stabilized ylides (e.g., ester-stabilized ylides), the enantioselectivity is controlled in the ring-closure step and moderate enantioselectivities have been achieved thus far. Due to differences in the stereocontrolling step for different types of ylides, it is likely that different sulfides will need to be designed to achieve high stereocontrol for the different types of ylides. 

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