On the problem of fitting many-body potentials. I. The minimal maximum error scheme and the paradigm of metal systems

Issues involved in fitting a semiempirical potential, such as the choice of a goodness criterion, selection of fitting quantities (properties), ascription of the degree of importance to the individual members of a fitting set, etc., all of which affect the outcome of a fitting procedure, are addressed and analyzed. The minimal maximum error fitting scheme is implemented to obtain the values of the parameters of the Gupta-type potential for nickel. The subtleties of this potential, one of which is that only four of its five parameters are independent, and their implications are pointed out and discussed. The resulting values of the parameters for nickel are analyzed and compared with those obtained in earlier studies.