Coulomb interaction basic principles

Atomic and molecular species identification via motional resonance-based detection is also possible in more complex systems, namely in large multispecies ion crystals of various size, shape, and symmetry [47,52,70] (Figure 18.19). The basic principle of the method is as follows. The radial motion of the ions in the trap is excited using an oscillating electric field of variable frequency applied either to an external plate electrode or to the central trap electrodes. When the excitation field is resonant with the oscillation mode of one species in the crystal, energy is pumped into the motion of that species. Some of this energy is distributed through the crystal, via the Coulomb interaction. This, in turn, leads to an increased temperature of the atomic coolants and modifies their fluorescence intensity, which can be detected. 

DFT uses the electron density as the fundamental variable used to describe the electrons and not the electronic wavefunction. For N electrons, this means that the basic variable of the system depends only on the three spatial coordinates x, y, and 2, rather than 3N degrees of freedom. Useful applications of DFT are based on approximations for the exchange-correlation functional. The exchange-correlation fimctional describes the effects of the Pauli exclusion principle and the Coulomb potential beyond a pure electrostatic interaction of the electrons. Unfortunately, the exact functional is not known for anything but the free electron gas. Still, the various approximations of DFT include electron correlation in some form, which gives this method a powerful advantage over wavefunction-based methodology. 

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