Coulomb repulsions

Calculate also the activation energy for the reaction, again in kcal/mol, assuming that the Coulomb repulsion maximizes at 3 -y 10 cm separation of the nuclear centers. Assuming a successful cold-fusion device, how many fusions per second would generate one horsepower (1 hp) if the conversion of heat into work were 10% efficient ... 

Here pyy r ) represents the probability density for finding the 1 electrons at r, and e / mutual Coulomb repulsion between electron density at r and r. ... 

Another example of the difficulty is offered in figure B3.1.5. Flere we display on the ordinate, for helium s (Is ) state, the probability of finding an electron whose distance from the Fie nucleus is 0.13 A (tlie peak of the Is orbital s density) and whose angular coordinate relative to that of the other electron is plotted on the abscissa. The Fie nucleus is at the origin and the second electron also has a radial coordinate of 0.13 A. As the relative angular coordinate varies away from 0°, the electrons move apart near 0°, the electrons approach one another. Since both electrons have opposite spin in this state, their mutual Coulomb repulsion alone acts to keep them apart. 

Coulomb repulsion by occupying different r giom of space in the SCF picture Is 2s, both electrons reside in the same 2s region of space. In this particular example, the electrons undergo angular correlation to avoid one another. 

Ding C F, Wang X B and Wang L S 1998 Photoelectron spectroscopy of doubly charged anions intramolecular Coulomb repulsion and solvent stabilization J. Phys. Chem. A 102 8633... 

Traditionally, for molecular systems, one proceeds by considering the electronic Hamiltonian which consists of the quantum mechanical operators for the kinetic energy of the electrons, their mutual Coulombic repulsions, and... 

The Exclusion Prin cip le is t ii an tn ni mechanical in nature, and outside the realm ofeveryday, classical" experience. Think ofii as iheinherent tendency of electron s to slay away from oneanoiher, to be m n tnally excluded. Excbi sion is due to lb c an lisymmdry of the wave function and nol to electrostatic coulomb repulsion between two electrons. Exclusion exists even m the absence of electrostatic repulsions. 

The diagonal integrals Za,a, which represent the mutual coulomb repulsions between a pair of electrons in the valence-state orbital labeled a, are calculated in terms of the valence-state IP and EA of that orbital ... 

The advantage of using electron density is that the integrals for Coulomb repulsion need be done only over the electron density, which is a three-dimensional function, thus scaling as. Furthermore, at least some electron correlation can be included in the calculation. This results in faster calculations than FIF calculations (which scale as and computations that are a bit more accurate as well. The better DFT functionals give results with an accuracy similar to that of an MP2 calculation. 

Just as for an atom, the hamiltonian H for a diatomic or polyatomic molecule is the sum of the kinetic energy T, or its quantum mechanical equivalent, and the potential energy V, as in Equation (1.20). In a molecule the kinetic energy T consists of contributions and from the motions of the electrons and nuclei, respectively. The potential energy comprises two terms, and F , due to coulombic repulsions between the electrons and between the nuclei, respectively, and a third term Fg , due to attractive forces between the electrons and nuclei, giving... 

Cationic starches show decreased gelatinization temperature range and increased hot paste viscosity. Pastes remain clear and fluid even at room temperatures and show no tendency to retrograde. This stabiUty is due to Coulombic repulsion between positively charged starch molecules in dispersion. 

CMC hydrates rapidly and forms clear solutions. Viscosity buUding is the single most important property of CMC. DUute solutions of CMC exhibit stable viscosity because each polymer chain is hydrated, extended, and independent. The sodium carboxylate groups are highly hydrated, and the ceUulose molecule itself is hydrated. The ceUulose molecule is linear, and conversion of it into a polyanion (polycarboxylate) tends to keep it in an extended form by reason of coulombic repulsion. This same coulombic repulsion between the carboxylate anions prevents aggregation of the polymer chains. Solutions of CMC are either pseudoplastic or thixotropic, depending on the type. 

DFT methods compute electron correlation via general functionals of the electron density (see Appendix A for details). DFT functionals partition the electronic energy into several components which are computed separately the kinetic energy, the electron-nuclear interaction, the Coulomb repulsion, and an exchange-correlation term accounting for the remainder of the electron-electron interaction (which is itself... 

The potential energy component is the Coulomb repulsion between each pair of charged entities (treating each atomic nucleus as a single charged mass) ... 

Coordinates can be transformed to bohrs by dividing them by Aq. Energies are measured in hartrees, defined as the Coulomb repulsion between two electrons separated by 1 bohr ... 

The ground-state electronic structure of As, as with all Group 15 elements features 3 unpaired electrons ns np there is a substantial electron affinity for the acquisition of 1 electron but further additions must be effected against considerable coulombic repulsion, and the formation of As is highly endothermic. Consistent with this there are no ionic compounds containing the arsenide ion and... 

The first two terms represent the kinetic energy of the nuclei A and B (each of mass M), whilst the fourth term represents the kinetic energy of the electron (of mass m). The fifth and sixth (negative) terms give the Coulomb attraction between the nuclei and the electron. The third term is the Coulomb repulsion between the nuclei. 1 have used the subscript tot to mean nuclei plus electron, and used a capital I. ... 

It represents the Coulomb repulsion between a pair of electrons. 

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