Analysis of difference in two geometrical structures

A utility tool is provided to analyze the difference between two geometrical coordinates in two xyz files which store Cartesian coordinates. The following three analyses are supported: a root mean square of deviation (RMSD) between two Cartesian coordinates defined by

$${\rm RMSD} = \sqrt{\frac{\sum_i^{N_{\rm atom}} (R_i-R_i^0)^2}{N_{\rm atom}}}$$

a mean deviation (MD) between two Cartesian coordinates defined by

$${\rm MD} = \frac{\sum_i^{N_{\rm atom}} \vert R_i-R_i^0 \vert}{N_{\rm atom}}$$

and a mean deviation between bond lengths (MDBL) defined by

$${\rm MDBL} = \frac{\sum_i^{N_{\rm bond}} \vert BL_i-BL_i^0 \vert}{N_{\rm bond}}$$

where $N_{\rm atom}$ and $N_{\rm bond}$ are the number of atoms and the number of bonds with bond length (BL) within a cutoff radius. Also, the deviation vector between xyz coordinate of each atom is output to a xsf file, 'dgeo_vec.xsf', in the XCrySDen format. If you analyze the difference between two geometries, this tool would be useful.

(1) Compiling of diff_gcube.c

There is a file 'diff_gcube.c' in the directory 'source'. Compile the file as follows:

    % gcc diff_geo.c -lm -o diff_geo
  

When the compile is completed normally, then you can find an executable file 'diff_geo' in the directory 'source'. Please copy the executable file to the directory 'work'.

(2) Calculation of the difference

You can find the following usage in the header part of diff_geo.c.

     usage: 
              ./diff_geo file1.xyz file2.xyz -d rmsd

        option
           -d rmsd      a root mean square of deviation
           -d md        a mean deviation
           -d mdbl 2.2  a mean deviation between bond lengths, 
                        2.2 (Ang) means a cutoff bond length which
                        can be taken into account in the calculation

If you want to know RMSD between two Cartesian coordinates, run as follows:

    % ./diff_geo file1.xyz file2.xyz -d rmsd
  

The calculated result appears in the standard output (your display). Also, a xsf file 'dgeo_vec.xsf' is generated in the XCrySDen format, which stores the difference between Cartesian coordinates of each atom in a vector form. This file can be visualized using 'Display$\to$Forces' in XCrySDen. When MDBL is calculated, please give a cutoff bond length (Å). Bond lengths below the cutoff bond length are taken into account for the RMSD calculation. Figure 43 shows vectors corresponding to the deviation of atomic coordinates in optimized structures and the difference of total charge density between a neutral and one electron doped glycine molecule. We see that the large structural change seems to take place together with the large charge deviation. This example illustrates that the tool would be useful when we want to know how the structure is changed by the charge doping and the electric field.

Figure: (a) Vectors corresponding to the deviation of atomic coordinates in optimized structures and (b) the difference of total charge density between a neutral and one electron doped glycine molecule. These figures were visualized by XCrySDen. In Fig. (b) blue and red colors indicate the decrease and increase of total charge density, respectively.