Electronic quantum exchange

Keywords Halogen bonds Bader s atoms-in-molecules theory Energy decomposition Interacting quantum atoms scheme Electrostatic interactions Electronic quantum exchange... 

In the previous section we presented the semi-classical electron-electron interaction we treated the electrons quantum mechanically but assumed that they interact via classical electromagnetic fields. The Breit retardation is only an approximate treatment of retardation and we shall now consider a more consistent treatment of the electron-electron interaction operator that also provides a bridge to relativistic DFT, which is current-density functional theory. For the correct description we have to take the quantization of electromagnetic fields into account (however, we will discuss only old, i.e., pre-1940 quantum electrodynamics). This means the two moving electrons interact via exchanged virtual photons with a specific angular frequency u>... 

The Fock operator determines three sets of information for each electron i (1) the kinetic energy term of the electron (—1/2V ), (2) an attraction term with each nucleus, A, (—EZA/r,A), and (3) the interaction of the electron with all the other electrons in the molecule. This average force is treated by the (IJjj — Kjj) term and can be described as the potential felt by a single electron in the field of the other i — 1 electrons in the molecule. A few words about the components of this last term in the Fock operator are in order. J is called the coulomb operator and is identified as the classical repulsion between electrons. The exchange integral K is due to the quantum mechanical effect of spin correlation, an intrinsic property of the electron that keeps apart electrons of the same spin. This operator has a stabilizing effect on the energy of the system. 

VWN(Vosko, Wilk, Nusair)(12) p / +correl. PZ(Perdew, Zunger) (1J) electron gas exchange and correlation from accurate Quantum Monte Carlo calcs, of Ceperley and Alder (14)... 

The effect under consideration, firstly observed in II-2O - D-2O mixtures [Chatzidimitriou-Dreismann 1997 (a)], has been attributed to sub-femtosecond QE of a proton with (i) adjacent particles (electrons and nuclei) caused by mutual Coulombic interactions [Chatzidimitriou-Dreismann 2001 Chatzidimitriou-Dreismann 2003 (b) Chatzidimitriou-Dreismann 2004 (a)], or (ii) an adjacent second proton due to quantum exchange correlations [Karlsson 2000 Karlsson 2002 (c) Karlsson 2003 (a)]. However, the recent NCS results from liquid HD (Sec. 5) clearly contradict the possibility (ii). Results from samples with various isotopic H D compositions indicate that this effect is mainly of intramolecular origin [Chatzidimitriou-Dreismann 2002 (a)]. We attribute the striking effect to light H atoms, rather than to heavier atoms G or O. 

Takagahara T. (1993a), Effects of dielectric confinement and electron-hole exchange interaction on excitonic states in semiconductor quantum dots , Phys. Rev. B 47, 4569-4584. 

A) Schematic diagram of the scanning tunneling microscope (STM) in which a tip of atomic dimensions glides across an atomic surface but does not touch it. Electrons are exchanged between the surface and the probe tip by quantum mechanical tunneling. B) The quantum corral was made by moving 48 iron atoms into a circle. 

This is shown in Fig. 22.8, which in addition contains two points from electron Compton scattering on hydrogen molecules. Those were obtained by Cooper et al. [16] and have been introduced at 37° (which corresponds to their -values) on the 0-scale. Their positions support the theory given above (which should be applicable also to electron Compton scattering), a 31 % anomaly for H2 and no anomaly for HD molecules (no quantum exchange effect). 

Exchange interactions are purely quantum-mechanical interactions, acting even on distant electrons. Due to these interactions, total electronic energies are lowered, stabilizing electronic states. A significant proportion of the exchange interactions is taken up by the self-interactions of the electrons themselves. Exchange selfinteractions correspond to the Ka terms in Eq. (2.45) and cancel out with 7,, terms. 

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