Dynamical cluster approximation

Jarrell s methodology [11,13], referred to as the dynamical cluster approximation (DCA), is quite novel as it leads to analytic self-energies that are k dependent while preserving lattice periodicity. 

These similarities are once again a consequence of the plume expansion. During the expansion, collisions become less frequent and the rates of ion-molecule reactions decrease. Because matrix is normally in considerable excess, the last reactions of any ion wUl nearly always be with matrix neutrals. This is fortunate for understanding MALDI spectra, because simple bimolecular matrix-analyte reactions are the limiting reactions. Quantitative understanding of complex processes in dynamic cluster or dense plume environments is not necessary, at least to a good first approximation. 

Repeat this example using 2060 water cells and 40 solute cells in the Example 4.2 Parameter Setup. This is approximately a 2% solution. Repeat the dynamics again with a higher concentration such as 2020 water cells and 80 solute cells, using Example 4.2 Parameter Setup. Compare the structures of water as characterized by their fx profiles and average cluster sizes. Some measures of the structure change in water as a fimction of the concentration are shown in Table 4.2. 

We wanted to extend this approach to include dynamical effects on line shapes. As discussed earlier, for this approach one needs a trajectory co t) for the transition frequency for a single chromophore. One could extract a water cluster around the HOD molecule at every time step in an MD simulation and then perform an ab initio calculation, but this would entail millions of such calculations, which is not feasible. Within the Born Oppenheimer approximation the OH stretch potential is a functional of the nuclear coordinates of all the bath atoms, as is the OH transition frequency. Of course we do not know the functional. Suppose that the transition frequency is (approximately) a function of a one or more collective coordinates of these nuclear positions. A priori we do not know which collective coordinates to choose, or what the function is. We explored several such possibilities, and one collective coordinate that worked reasonably well was simply the electric field from all the bath atoms (assuming the point charges as assigned in the simulation potential) on the H atom of the HOD molecule, in the direction of the OH bond. 

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