Electron density partitioning onto atoms

In the first calculation, we propagate only the electronic wavefunction without allowing the nuclei to move. This is to study first pure charge migration. In the second calculation, the nuclei are allowed to move along with the propagation of the electronic wavefunction. In Fig. 5, the spin densities partitioned onto the atoms are plotted as a function of time in each case. The bottom half aims to represent the corresponding evolution of both the... 

However, the partitioning scheme just described can be used to decompose the electron density into atomic components. Projection onto Y< m functions yields multipoles attached to the atoms. The radial resolution is automatically as good as that of the integration. The Poisson equation, relating the static potential to the density, can then be solved with high accuracy for each multipole, since the decomposition has reduced... 

To follow the evolution of the electronic wavefunction, its spin density is computed, partitioned onto the atoms and can be decomposed in the space of the VB structures of the moat at each step of the simulation. One can then plot the electron dynamics trajectory on the moat diagram (Fig. 1) where the structures represent exclusively the nature of the electronic wavefunction in this case. Because each structure in Fig. 1 is a superposition of two resonance structures where the unpaired electron and the positive charge are interchanged, following the unpaired electron is equivalent to following the positive charge. This is how we monitor the hole dynamics. 

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