Coulomb repulsion energy

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 ... 

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... 

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... 

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 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. ... 

Imagine a model hydrogen molecule with non-interacting electrons, such that their Coulomb repulsion is zero. Each electron in our model still has kinetic energy and is still attracted to both nuclei, but the electron motions are completely independent of each other because the electron-electron interaction term is zero. We would, therefore, expect that the electronic wavefunction for the pair of electrons would be a product of the wavefunctions for two independent electrons in H2+ (Figure 4.1), which I will write X(rO and F(r2). Thus X(ri) and T(r2) are molecular orbitals which describe independently the two electrons in our non-interacting electron model. 

The first term on the right-hand side is a contribution from external fields, usually zero. The second term is the contribution from the kinetic energy and the nuclear attraction. The third term is the Coulomb repulsion between the electrons, and the final term is a composite exchange and correlation term. 

In order to get an estimate of the order of magnitude of the correlation energy, Froman makes it plausible that the correlation energy should be roughly proportional to the total Coulomb repulsion energy of all the electrons within the system, and he suggests the formula... 

The Mg + dicadon [42] with AN+2 (N= 1) valence electrons has a stable structure in agreanent with the rule, but this is a local energy minimum. The linear structure is more stable because it minimizes the Coulomb repulsion. This is in contrast to the tetrahedral stmcture of the Li dication with two electrons (N= 0). The six electron systems caimot form closed-shell structures in the tetrahedron, but the two electron systems can do. 

Hindered Rotation (Figure 4b). This mode characterizes the orientational energy associated with the bond. For HoO the tilt energy Is very small ( . 1 eV) until the protons get close to the surface and the Coulomb repulsion takes over abruptly, resulting In a... 

The asymptotic energy values obtained by a configuration interaction calculation at 25 a.u. corrected by the coulombic repulsion term (the l/R" term has been neglected) are seen to be in quite good agreement with experiment (Table 3). 

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