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

1. Oct 2, 2007

Kimko

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 2, 2007

Dick

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

3. Oct 2, 2007

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.

4. Oct 2, 2007

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.

5. Oct 2, 2007

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)

6. Oct 2, 2007

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.

7. Oct 2, 2007

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.

8. Oct 2, 2007

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.