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Example 2: Transforming a bent three body system from Cartesian to internal coordinates

  • Page ID
    2246
  • [ "article:topic", "Graduate", "Franzen", "Author tag:Franzen" ]

     

    The first task is determine the elements of the B matrix. We have:

    where X12 = cosq and Y12 = sinq. Bx1 = cosq and Bx2 = -cosq, By1 = sinq and By2 = -sinq, for the 1-2 coordinate and since X23 = 1 and Y23 = 0 we have Bx2 = 1 and Bx3 = -1, for the 2-3 coordinate.

    Given the above values we have for the angle coordinate Bx1 = -sinq/r12, Bx3 = 0 and Bx2 = sinq/r12. We also calculate By1 = cosq/r12, By3 = -1/r23, and therefore By2 = 1/r23 � cosq/r12.

     

    The B-matrix is:

     

    Dx1

    Dx2

    Dx3

    Dy1

    Dy2

    Dy3

    Dr12

    cosq

    -cosq

    0

    sinq

    -sinq

    0

    Dr23

    0

    -1

    1

    0

    0

    0

    Dq

    -sinq/r12

    sinq/r12

    0

    cosq/r12

    1/r23-cosq/r12

    -1/r23