Coulombic poles

The Coulomb-pole removed transition operator satisfies the equation... 

This singularity structure from the Borel sum differs somewhat from the singularity structure predicted from the coulombic poles of... 

In 1995, one of the authors (A.K.) introduced the state of a molecule embedded in a perfect conductor as an alternative reference state, which is almost as clean and simple as the vacuum state. In this state the conductor screens all long-range Coulomb interactions by polarization charges on the molecular interaction surface. Thus, we have a different reference state of noninteracting molecules. This state may be considered as the North Pole of our globe. Due to its computational accessibility by quantum chemical calculations combined with the conductor-like screening model (COSMO) [21] we will denote this as the COSMO state. 

The latter variable eliminates a finite range [42] of convergence of series both of X at 2 i e, because of a pole due to intemuclear coulombic repulsion as / 0, and of y at V2 Re, for a similar phenomenon as oo. Expressions for Fy in terms of coefficients cj in the latter series are available in a large consistent collection in Fortran coding [43] up to Cio such expressions, readily calculated, through symbolic computation with efficient procedures [44], first in terms of coefficients and thence converted to bj or Cj as required, are further converted to Fortran or C code for numerical applications. 

M = z f Ffi, where ja is the magnetic permeability of the medium (assumed to be equal to unity for air) F, the force at a point in magnetic field and r the distance between the poles. It follows that F = mm V jur2 ESU ate based on the strength of electrical charges (q and q ) q = Fk, where k is the specific inductive capacity ot dielectric constant (assumed as unity for air F, the force between two charges and r the distance. It follows that F =qqVkc2(See also " Electrostatic Law of Coulomb )... 

Magnetic fields exist when two poles of the opposite orientation are present the north pole and the south pole. Two magnetic poles of strengths m1 and m2 placed at a distance of d meters apart in a medium of relative permeability equal to pR will exert a force (F) on each other given by Coulomb s law, which states ... 

That is, is due to the Coulomb and exchange interactions. Ignoring the exchange interaction and carrying out the multi-pole expansion for the Coulomb interaction yield... 

The above resolvent operator Hi E) refers to the operator H° including only the Coulomb interaction between the subsystems. Its poles ) are those eigenvalues of H° which differ from those in the subspace Im P by transfers of one electron between the M- and R-systems. We denote these states as p — /. ) or /. — p) with respect to the direction of the transfers. The energies in the expression in eq. (1.242) are defined by the ionization potentials Ip and electron affinities Afl, Ap of the subsystems ... 

The simplest description of the effect of the central ion on the surrounding ligands reduces to that of the Coulomb field affecting the positions of the poles of the Green s... 

The expression (1.69) for e is quite general in the sense that it gives the response of the crystal to an external field of any wave vector. In particular the poles of s(K, (o) provide, over the whole Brillouin zone, the dispersion curves of the new elementary excitations built up by coulombic and retarded interactions. 

Unit pole a unit pole is one that will repel with a force of one dyne an equal and similar pole placed 1.0 cm away in a vacuum the repulsion obeys Coulomb s law a unit magnetic pole has not been isolated... 

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