MPEOE (method)


MPEOE ("modified partial equalization of orbital electronegativity") is a fast method for the determination of empirical net atomic charges [1,2]. In this method, the net atomic charge on atom A is obtained by an iterative process. The process starts from an initial charge distribution, usually zero net atomic charges on all atoms, except on atoms in groups with non zero formal charge, where the sum of the net atomic charges should equal the formal charge. In each iteration, fractional charges are transferred between directly bonded atoms from the less electronegative to the more electronegative atom. The amount of charge transferred is equal to the difference of electronegativities, multiplied by an exponentially decaying bond type dependent damping factor. The electronegativities are assumed to be linear functions of the net atomic charge. The process attains convergence when the maximum amount of charge transferred along any bond is less than a given threshold. Using the notation

electronegativity of atom A in iteration n,
net atomic charge on atom A at end of iteration n,
charge transferred along bond AB in iteration n,
damping factor for charge transfer along bond AB,
factor in linear dependence of electonegativity on net charge,
electronegativity of the positive ion A+,

the following formulae are used to compute net atomic charges in iteration n:  

     for each atom A, compute electronegativity:
     for each bond AB, compute damping factor dn:
     for each bond AB, compute charge transferred from A to B:
     for each atom A, compute new net atomic charge:

The parameters ,, (atom parameters) and  (bond parameters) are stored in the Wit!P library file mpeoe.wlb, from where they are read at program start-up. The parameters in this file were determined by a least squares parameter fitting procedure to produce net atomic charges which closely resemble charges from the MSI Quanta / CHARMm 22 all-hydrogen parameter set. The hidden (i.e. not accessible through any of the menus) MPEOE command may be used to derive alternative parameter sets.

Note: MPEOE charge calculations are always done for complete connected fragments.


References:

1. K.T. No, J.A. Grant, and H.A. Scheraga:
Determination of net atomic charges using a modified partial equalization of orbital electronegativity method. 1. Application to neutral molecules as models for polypeptides.
J. Phys. Chem., 94:4732-4739, 1990.

2. K.T. No, J.A. Grant, M.S. Jhon, and H.A. Scheraga:
Determination of net atomic charges using a modified partial equalization of orbital electronegativity method. 2. Application to ionic and aromatic molecules as models for polypeptides.
J. Phys. Chem., 94:4740-4746, 1990.



A.Widmer, NIBR/CPC/CSG-SB