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@@ -16,20 +16,28 @@ The input contains two files:
    - `pair_style lj/charmm/coul/long 8.0 10.0` This is the line that specifies that we are using the *lj/charmm/coul/charmm* *pair_style*. If a different *pair_style* was selected, then `PairLJCharmmCoulLong::compute` would not be executed, and the optimizations would not have any impact. Moreover, the `8.0`and `10.0` represent the *cutoff distances*, which can have an impact to the execution of the function. For more information, check the LAMMPS [documentation](https://docs.lammps.org/pair_charmm.html#pair-style-lj-charmm-coul-long-command).
 - `data.protein`: contains the initial data for the atoms in the simulation and their properties
 
-# Algorithm and Data structures
+# Overview of Algorithm and Data structures
 
-
-FIXME neighbor
 LAMMPS computes interactions between atoms.
-If a pair of atoms are "neighbors" (that is, they are placed  the *pair_style* cutoff distance), it produces a *short-range* interaction in "real space" and is computed using a *pair_style*.
-If atoms aren't within the cutoff distance, these become *long-range* interactions in "reciprocal space" (FFT domain).
+If a pair of atoms are "neighbors" (that is, the distance between them is smaller than the *pair_style* cutoff distance), it produces a *short-range* interaction in real space and is computed using a *pair_style*.
+If atoms aren't within the cutoff distance, these become *long-range* interactions in reciprocal space (FFT domain).
 The `PairLJCharmmCoulLong::compute` computes short-range interactions.
 
 File `neigh_list.h` contains the `int **firstneigh` array.
 Note that the `**` denotes that it is a double pointer or pointer to pointer.
 In other words, `int **firstneigh` is a pointer to an array of pointers to arrays of `int`.
 
-`firstneigh[i]` contains an array of the 
+`firstneigh[i]` contains an array of the atoms `j` that are neighbors of atom `i`.
+In this protein input, there are 32.000 `i` atoms.
+For example, `firstneigh[i][0]` would be the first neighbor of atom `i`.
+Both `i` and are atoms `firstneigh[i][0]`, and are represented using a 32 bit `int`.
+To retrieve the properties of an atom, this `int` value needs to be used as an index for the arrays found in file `atom_vec.h` or `atom.h` such as `double **x` (position), `**f` (force) or `*q` (charge).
+`x` and `f` are pointer to pointer since the second index in needed to split the magnitudes in XYZ components.
+
+Function `PairLJCharmmCoulLong::compute` has an inner and an outer for loop.
+the outer loop (i-loop) iterates through all 32.000 atoms in the protein simulation, while the inner loop (j-loop) iterates through each atom `j` that is a neighbor of `i`.
+
+For each pair of atoms `i, j`, the algorithm first computes the distance between the two atoms, and if it is smaller than the cutoff distance, 
 
 atom_vec.h -> contains `**x` and `**f` (3D)
 neigh_list.h -> contains `**firstneigh` (for each i, store array of neighbors j)