Energy, penetration

From a physical point of view, this new formulation includes exponential terms that are in agreement with the observed ab initio and experimental results. Moreover, it is easy to verify that the new expression converges to the classical one when r increases. That way, at long range, where the multipolar approximation is valid, the exponential part dies whereas, at short distances, the monopole-monopole interaction embodies a part of the penetration energy. Consequently, Emono-mono has the correct dependence at any range. 

Industry elasticity Import penetration Energy intensity Fixed and marginal costs Price Quantity Academic articles and competition inquiries Competition inquiries, analyst reports and national trade statistics The Carbon Trust and company environmental reports FAME database and competition inquiries Companies and competition inquiries Trade associations and competition inquiries... 

Penetrating Energy Earners by Means of Proton Tunneling... 

This would imply a characteristic luminosity of Lc 102°L , even for a small fraction of the solar material taking part in the reactions (i.e. e 10-2). If this was really the appropriate cross-section for the reaction, the sun would have been gone very quickly indeed. Instead the cross-sections are much less than that at the Coulomb barrier penetration energy (say at proton energies of 1 MeV), to allow for a long lifetime of the sun (in addition, weak-interaction process gives a smaller cross-section for some reactions than electromagnetic process, - see Sect. 3.1). 

The EFP method attempts to overcome this parameterization problem by including electrostatics and polarization from first principles. This represents a considerable departure from the traditional MM potentials used in biomolecular simulations. The electrostatic energy remains an approximation, however, as the multipole expansions in Ueie are left uncorrected for the effects of charge penetration (C/pen). This penetration energy, Upen, is then implicit in Urep. Thus a limitation that is characteristic of all force-field methods, from the crudest MM to the most sophisticated QM/MM, is a certain lack of generality, i.e., there are arbitrary parameters that have to be refined and fitted for a particular application. 

In the EFP approach, efforts are being made to improve this situation [120,127,128]. A general expression for the penetration energy, f/pen, for example, can be obtained by considering the Coulomb interaction between two identical spherical Gaussians [127] ... 

Kairys Y, Jensen JH. Evaluation of the charge penetration energy between non-or-thogonal molecular orbitals using the spherical Gaussian overlap approximation. Chem Phys Lett 1999 315 140-144. 

The difference between the converged multipole expansion of the electrostatic energy and is sometimes called the first-order penetration energy. The exchange-repulsion is often simply called the exchange energy. For Hartree-Fock monomer wavefunctions, g l can be divided cleanly [69] into attractive exchange and... 

Impact-Penetration Energy The puncture impact system uses a swinging pendulum arm. A round test sample, clamped around its periphery, is impacted. The penetration energy is calculated from the force necessary to break the sample. 

Mendeleev periodic table (p. 446) minimal model of a molecule (p. 489) molecular spinorbital (p. 394) molecular orbital (p. 420) occupied orbital (p. 409) open shell (p. 411) orbital centering (p. 422) orbital localization (p. 467) orbital size (p. 424) penetration energy (p. 454)... 

Electrostatic Energy in the Multipole Representation Plus the Penetration Energy... 

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