Can electrons move as slowly as nuclei? Something about the Born Oppenheimer Approximation and electron-pairing medium in high temperature copper-oxide superconductors

Real-time evolution of the electron densities under excitations in La₂CuO₄ was calculated by the time-dependent density functional theory (TDDFT). The author found, for the first time, the electrons (the electron cloud of Cu²⁺) in high temperature copper-oxide superconductors (La₂CuO₄) can move as slowly as nuclei. Under excitations, the electron cloud of Cu²⁺ changes obviously and the characteristic frequencies are 83 meV and 36 meV, respectively, for two different modes. The results are unexpected and close to that of lattice vibrations, because the change of the electron density should be very quick according to the Born Oppenheimer Approximation. The results show that the electron cloud of Cu²⁺ (just like the lattice) can be the electron-pairing medium in high temperature copper oxide superconductors.