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Interatomic forces in an ensemble via vector analysis

  1. Nov 23, 2009 #1
    Hi all,

    My question is about obtaining the force between two particular atoms in an ensemble. Please excuse my ignorance on this topic. I can calculate all the forces in the system by the Hellmann–Feynman theorem using any quantum mechanical code. This is the print out from such a code:

    Forces on atoms are in units of Ry/au
    atom 1 force = 0.00166685 -0.00270340 -0.00251785
    atom 2 force = -0.00060500 -0.00337831 0.00397175
    atom 3 force = 0.00306646 -0.00125532 -0.00156902
    atom 4 force = -0.00081405 -0.00165894 0.00224862

    The atomic positions are, in fractional coordinates:
    1 0.494721110 0.619850102 0.464420445
    2 0.296515967 0.455429577 0.485041062
    3 0.263967419 0.580233832 0.449392069
    4 0.490069979 0.402504092 0.458079571

    As I understand it, the force on atom 1 in the direction of atom 2 is given by:

    F(1,2)= (R(1,2)dotF1)*R(1,2),

    Where the directional vector is R(1,2) = P2-P1/|P2-P1| and P1 and P2 are the positions of the atoms 1 and 2.

    The above gives:

    F(1,2)= -0.001278802 0.00172051 -0.0002 and |F(1,2)| = 0.25835556 which is repulsive

    Furthermore, how about the force on atom two in the direction of atom one? By the same approach this force is 0.002931211 which is also repulsive.

    Is it true then to think that, the 1-2 inter-atomic force is, given by F(1,2)+F(2,1)??

    Any help on this topic would be greatly appreciated!! Thank you very much in advance!!

  2. jcsd
  3. Nov 23, 2009 #2


    User Avatar
    Science Advisor

    As an approximation yes, if they're only bound to eachother. If either has bonds to other atoms then you've got a more complicated situation.
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