How to construct the code for center of mass of a droplet

Dear all,

I would like to construct a code to describe the center of mass of a droplet, with water and ions. For example, the following trajectory file shows the water coordinates as: 57SOL OW 36289 17.563 14.835 0.520

   57SOL    HW1  36290  17.602  14.916   0.487 

   57SOL    HW2  36291  17.571  14.843   0.615  

   58SOL     OW   36292  17.588  14.547   0.457  

   58SOL    HW1  36293  17.573  14.642   0.458 

   58SOL    HW2  36294  17.521  14.512   0.516  

   59SOL     OW   36295  11.747  17.611   1.159  

   59SOL    HW1  36296  11.714  17.522   1.174 

   59SOL    HW2  36297  11.740  17.624   1.064

To describe the center of mass of each molecule, I used: for i = 1:length(x)/3

   xcm(i) = (x(i*3-2)*massO + x(i*3-1)*massH + x(i*3)*massH)/massWater;

   ycm(i) = (y(i*3-2)*massO + y(i*3-1)*massH + y(i*3)*massH)/massWater;

   zcm(i) = (z(i*3-2)*massO + z(i*3-1)*massH + z(i*3)*massH)/massWater;
end

Then, the center of mass of a droplet (100% water) defined by:

cmx = sum(xcm)/length(x)*3;

cmy = sum(ycm)/length(y)*3;

cmz = sum(zcm)/length(z)*3;

My question is, for a droplet consisting of H2O, H3O, and Chloride ions, how does one describe the center of mass of each molecule/ion using the for-loop, and then using the xcm(i), ycm(i), and zcm(i) to determine the center of the droplet?

Below is an example coordinate file showing (partially) two water molecules, two H3O ions, and two Chloride ions:

 2015SOL     OW  42163  17.143  16.975   0.502 
 2015SOL    HW1  42164  17.175  17.038   0.567 
 2015SOL    HW2  42165  17.222  16.937   0.464 
 2016SOL     OW  42166  16.088  17.097   0.778 
 2016SOL    HW1  42167  16.094  17.182   0.734 
 2016SOL    HW2  42168  16.159  17.098   0.843 
.                                              
.                                              
.                                              

 2035H3O     OW  42241  17.895  20.054   0.561 
 2035H3O    H31  42242  17.836  20.100   0.492 
 2035H3O    H32  42243  17.970  20.114   0.593 
 2035H3O    H33  42244  17.930  19.964   0.527 
 2036H3O     OW  42245  13.948  17.327   0.503 
 2036H3O    H31  42246  13.875  17.348   0.571 
 2036H3O    H32  42247  13.978  17.410   0.452 
 2036H3O    H33  42248  14.026  17.276   0.544 
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.                                              
.                                              
 2037CLA     CL  42249  13.862  17.882   1.754 
 2038CLA     CL  42250  16.686  17.457   0.667

Thanks in advance.

Regards, Kester

[Image Analyst]

Can you attach a diagram? I know of center of mass for a photo but not for a trajectory. How does a trajectory have a center of mass?

[Kester Wong]

Hi Image Analyst,

Thank you for the reply. The trajectory is essentially XYZ coordinates of each water molecule; as we may know water has three atoms, hence the center of mass of a water molecule is extracted from the three XYZ coordinates.

The center of mass of each water molecule then gets represented by a "dot" as shown in the diagram, whereby the center of mass of the droplet can then be calculated.

In my water droplets, I also have H3O and Chloride ions, as mentioned in the post. As for chloride, the center of mass is unchanged (since it is represented by a XYZ coordinate). I would like to know how to construct such a code that collectively describes the center of mass of H2O, H3O, and chloride ions; then compute the center of mass of the droplet.