How to calculate center of mass of the polymer from atomic coordinates?

[Kimko]

Homework Statement

Please help me calculate the center of mass of the polymer (radius) from atomic coordinates (more than 2000) given in Armstrongs. Can anyone help with the formula? I need to calculate the radius of gyration of the polymer. Thanks.

Homework Equations

The Attempt at a Solution

 

[Dick]

The center of mass is equal to the sum the atoms positions times their masses all divided by the total mass.

 

[Kimko]

Can you please show me how to calculate it using the following coordinates?
Coordinates
ATOM 60 -4.062 10.538 11.856 H
ATOM 61 -2.514 15.625 6.177 N
ATOM 62 -2.780 16.719 5.186 C
ATOM 63 -3.809 17.716 5.736 C
ATOM 64 -4.444 17.483 6.747 O

Thank you.

 

[Dick]

(-4.062 10.538 11.856)*mass(H)+(-2.514 15.625 6.177)*mass(N)+ etc etc. Then divide that by mass(H)+mass(N)+mass(C)+mass(C)+mass(O). To multiply or divide a vector by a number just multiply or divide each component. To add two vectors add component by component.

 

[Kimko]

I did it the way you sad and my result is -0.46791 20.58064 19.18521 =Ravg.
Please help how I put it into my formula: Rg= [1/N sum/Ri-Ravg/^2]^(1/2)

 

[Dick]

Your result is wrong. For example, you've got z=19.18. That's bigger than all of your other z coordinates. Show me how you computed the z coordinate of the center of mass and I'll tell what you did wrong.

 

[Kimko]

I used all 2000 atomic coordinates in excel, not only those 5. I need to know how to convert
my result in one number that I can use in my formula to calculate Rg. Thanks.

 

[Dick]

Well then. So you've got R_avg. Then you just have to sum (R_i-R_avg)^2. If R_i=(xi,yi,zi) and R_avg=(xa,ya,za), (R_i-R_avg)^2=(xi-xa)^2+(yi-ya)^2+(zi-za)^2.