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--- exercises:common:chg [2022/10/18 14:57] – jglan
+++ exercises:common:chg [2023/12/04 13:49] (current) – fnunes
@@ Line 1: / Line 1: @@
 **Charge density difference analysis** takes the difference between charge densities of the system of interest and a reference one and plots charge redistribution due to chemical bonds.
-$\Delta \rho = \rho(A-B) - \rho(A) - \rho(B)$
+$\Delta \rho = \rho_{AB} - \rho_{A} - \rho_{B}$
+where $\rho_{AB}$ is the total charge (or electron) density of the whole system, $\rho_{A}, \rho_{B}$ are the density of the corresponding isolated system.
+It requires three single-point calculations of system AB, A, and B to print the [[https://manual.cp2k.org/cp2k-2022_1-branch/CP2K_INPUT/FORCE_EVAL/DFT/PRINT/E_DENSITY_CUBE.html|electron density]] or [[https://manual.cp2k.org/cp2k-2022_1-branch/CP2K_INPUT/FORCE_EVAL/DFT/PRINT/TOT_DENSITY_CUBE.html|total density]].
+One can use [[https://www.cp2k.org/tools:cubecruncher | Cubecruncher]] to manipulate the CUBE files.
+<code>
+cubecruncher.x -i AB.cube   -subtract A.cube -o AB_A.cube
+cubecruncher.x -i AB_A.cube -subtract B.cube -o chg_dif.cube
+</code>
+This type of analysis is also useful in the case of time-dependent calculations. In this case, the difference would be taken over time, with respect to some reference snapshot (e.g. ground state).
+$\Delta \rho (t-t_0) = \rho(t) - \rho(t_0)$,
+where $\rho(t)$ is the electron density at time $t$, and $\rho(t_0)$ is the reference electron density.
+<code>
+cubecruncher.x -i elec_dens_t.cube -subtract elec_dens_t0.cube -o diff_t-t0.cube
+</code>