Coulombic electronic energy

Fourier Series for the Total Electrostatic Energy The Coulombic electronic energy of a continuous charge distribution is defined as... 

The quaniity, (R). the sum of the electronic energy computed 111 a wave funciion calculation and the nuclear-nuclear coulomb interaciion .(R.R), constitutes a potential energy surface having 15X independent variables (the coordinates R j. The independent variables are the coordinates of the nuclei but having made the Born-Oppenheimer approximation, we can think of them as the coordinates of the atoms in a molecule. 

The iotal energy of a system is equal to the sum of the electronic energy and the Coulombic nuclear repulsion energy ... 

The fact that H commutes with Ez, Ex, and Ey and hence E2 is a result of the fact that the total coulombic potential energies among all the electrons and the nucleus is invariant to rotations of all electrons about the z, x, or y axes (H does not commute with L ) since if... 

The second term on the right-hand side is the coulombic potential energy for the attraction between charges —e and +e a distance r apart. The first term contains the reduced mass /r, equal to - - m ), for the system of an electron of mass and a proton of mass m. ... 

In an electron-excited X-ray spectrum the discrete X-ray lines are superimposed on a continuous background this is the well-known bremsstrahlung continuum ranging from 0 to the primary energy Eq of the electrons. The reason for this continuum is that because of the fundamental laws of electrodynamics, electrons emit X-rays when they are decelerated in the Coulomb field of an atom. As a result the upper energy limit of X-ray quanta is identical with the primary electron energy. 

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... 

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... 

HMO calculations of the pi electronic energies of the radicals were done using the values of coulomb and bond integrals suggested by Streitwieser (5). The only exception to these integral values was for the case of a heteroatom (with lone electron pair) bonded to the radical center carbon. The bond integrals for this case were chosen to be one-half the values suggested by Streitwieser ... 

Mohr, P.J. (1992) Self-energy correction to one-electron energy levels in a strong Coulomb field. Physical Review A, 46, 4421-4424. 

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