Subject: fitting problem

From: "Gavin Tsai" <[email-masked]>
Date: Mon, 9 Nov 1998 12:44:03 -0600

Dear all,
    
        I try to use Hessian biased singular value decomposition (HBFF/SVD)
    method to optimize the potential form and Force Field constants to
    perform the vibration frequency calculations of some medium size
    molecules.  This method is based on singular value decomposition (SVD)
    of Jacobian which is the partial derivatives in force(F) and Hessian(H)
    with respect to FF parameters (geometry (c) and force constants (k) ).
    The Jacobian matrix has four main componets
    
    [ dF/dc, dF/dk ]
    [ dH/dc, dH/dk],
    
    with [dF/dk,dH/dk] being much smaller than [ dF/dc, dH/dc].

      My question is as below:
    
       Because of the different magnitudes of the components of the Jacobian
    matrix, the step change for the carestian coordinates is acceptable, but
    is very SMALL for the force contsnts.  I multiplied the step change of
    force constants by a scaling factor, but it is not very efficient
    because of their different magnitudes ( e.g. stretching force constants
    > bending force constants > cross term force constants). 

     In brief, Is there any efficient method to fit different magnitudes  of parameters
(like coordinates amd force constants)? Is there any suggestions on how to nondimensitionize this Jacobian Matrix?
    
       Any suggestions will be welcomed and appreciated.  I will summarize the responses. Thanks!
    
    Gavin Tsai