PARAMETERIZATION


I. Experimental Data to be Fitted

II. Finding suitable values for VdW parameters presents one of the greatest challenges in FF development
  1. Close-packed geometry of a crystal appears to provide details of interatomic distances, but a simple deconvolution into atomic contributions is not easy. Many transactions are usually involved.
  2. Heat of sublimation data
    Crystal energetics can be calculated as a test of the parameters.
    Typically, the VdW radii are used as 'soft' parameters (i.e., the exact values have less influence upon the final geometry than the bond stretch and angle bend force constant terms. Thus, nonbonded terms are usually used to fine tune the ff
III. Electrostatic Interaction IV. Fitting parameters to data on liquid properties.

Overall quality of FF Methods:

  • Potentials: V=Vb +Vo +Vz+Vnb+Vl+...
  • Parameters:

    General Application of Force Field

      Conjugated Systems

      Bonding Less Easy to Define

      More recent controversy involving conjugated systems:
      1. Through bond coupling: dominance in filled-filled orbitals through-bond without bond lengthening
      2. [18] Annulenes {Many errors due to faulty experimental results=>bad parameterizations}

      Minimization Techniques

      Algorithms Global versus local minima:

      Steepest Descents:

      Assessment

      Conjugate Gradients:

      Newton Raphson:

    Special problem if full matrix NR min. w/
    Curtesians = inversion of F

    3n x 3n matrix with all coordinates is 6-fold singular due to 3 translational and 3 rotational degrees of freedom (only 3N-6 nonzero vibrational frequencies) 3 ways around this:

    1. Reduced matrix method.
      translation & rotation prevention by fixing
      1 atom@x=y=z=0
      2nd atom@ x=y=0........along 1 axis 3rd in a plane x=0
      =>can delete 6 egns,=>removes 6 rows and 6 ncolumns if F matrix
      =>no more singularities
      =>Problem w. oscillating when trial geom pcor
      Care must be taken not to restrict coordiantes
      F a bond length or< is restricted
    2. Generalized inverse
      • Diagonalize 3n x 3n F matrix
      • Remove 6 0 eigenvalues and corresponding eigenvectors.
      • Obtain inverse
        .......................eigenvector
        >F3n,3n-1=A3n,#n-6,3n-6 (-1) A3n-6,3n
    3. Apply Eckart constraints
      Eckart conditions fix the center if mass in space and constrain infinitesimal rotations of the molecule.
      In this method, a (3n+6) x (3n+6) matrix must be inverted, but E min is faster than other methods.

      This is just the opposite of steepest descents which
      converges slow-or diverges- when one is far from the minimum.
      ...........fast near minimum
      Characterictics of a block-diag min is like steepest descents works well for that surface <