Kinetic energy interacting

An electron with a hi kinetic energy, interacting with atoms, has an ai roximately equal probability of produdng either excitation or ionization (exdtation is sli tly more probable in the case of interaction with a molecule). A soni-classica] model of such a collision can be viewed as follows. The electron passing closdy by an atom produces in it an electric field due to Coulombic force. This fidd (its component perpendicular to the dectron trajectory) causes a puls acting on the atom components. This perturbation of tls atom can be theoretically understood as equivalent to the effect of a beam of photons with frequencies corresponding to the Fourier components of the pulse [17]. 

Metastable noble gas atoms with low kinetic energy " interact with the tails of the wave function of the surface atoms (and adsorbed species [93]) and eject electrons from the uppermost surface layer exclusively [77] as they cannot penetrate into the surface [94]. As a consequence, the kinetic energy distribution of ejected electrons (MIES spectrum) contains information on the electronic states of the solid surface [77] also known as SDOS (Surface DOS) [93]. 

Here H stands for the one-electron part (kinetic energy + interaction with all the nuclei) of the chain and the elements of the charge-bond order matrix ,(qj - ( 2 defined as a generalization of the definition given by Coulson as... 

As the kinetic energy involved in the system goes higher, the interaction of energetic particles is more and more localized near the nuclei. When the interaction distance is much smaller than interatomic distances in the system, the BCA is valid ... 

Thus E. is the average value of the kinetic energy plus the Coulombic attraction to the nuclei for an electron in ( ). plus the sum over all of the spin orbitals occupied in of the Coulomb minus exchange interactions. If is an occupied spin orbital, the temi [J.. - K..] disappears and the latter sum represents the Coulomb minus exchange interaction of ( ). with all of the 1 other occupied spin orbitals. If is a virtual spin orbital, this cancellation does not occur, and one obtains the Coulomb minus exchange interaction of cji. with all N of the occupied spin orbitals. 

This gives the total energy, which is also the kinetic energy in this case because the potential energy is zero within the box , m tenns of the electron density p x,y,z) = (NIL ). It therefore may be plausible to express kinetic energies in tenns of electron densities p(r), but it is by no means clear how to do so for real atoms and molecules with electron-nuclear and electron-electron interactions operative. 

Kolm and Sham [25] decompose G[p] into the kinetic energy of an analogous set of non-interacting electrons with the same density p(r) as the interacting system. 

Flere we distinguish between nuclear coordinates R and electronic coordinates r is the single-particle kinetic energy operator, and Vp is the total pseudopotential operator for the interaction between the valence electrons and the combined nucleus + frozen core electrons. The electron-electron and micleus-micleus Coulomb interactions are easily recognized, and the remaining tenu electronic exchange and correlation... 

Here, t is the nuclear kinetic energy operator, and so all terms describing the electronic kinetic energy, electron-electron and electron-nuclear interactions, as well as the nuclear-nuclear interaction potential function, are collected together. This sum of terms is often called the clamped nuclei Hamiltonian as it describes the electrons moving around the nuclei at a particular configrrration R. 

The f operators are the usual kinetic energy operators, and the potential energy V(r,R) includes all of the Coulomb interactions ... 

There is a very convenient way of writing the Hamiltonian operator for atomic and molecular systems. One simply writes a kinetic energy part — for each election and a Coulombic potential Z/r for each interparticle electrostatic interaction. In the Coulombic potential Z is the charge and r is the interparticle distance. The temi Z/r is also an operator signifying multiply by Z r . The sign is - - for repulsion and — for atPaction. 

To provide further insight why the SCF mean-field model in electronic structure theory is of limited accuracy, it can be noted that the average value of the kinetic energy plus the attraction to the Be nucleus plus the SCF interaction potential for one of the 2s orbitals of Be with the three remaining electrons in the s 2s configuration is ... 

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