VARIATIONAL DERIVATION AND EXTENSIONS OF DISTRIBUTED APPROXIMATING FUNCTIONALS

Extensions of the ''Distributed Approximating Functional'' (DAF) appro ach to approximating functions and their derivatives are given. The me thod, although inherently approximate, can be made arbitrarily accurat e, numerically stable, and computationally efficient by appropriate ch oice of parameters. It also provides approximate representations of qu antum operators which are analytic and which can be made arbitrarily a ccurate. Differences between the DAFs and more standard basis set appr oaches are discussed in order to clarify the properties of the DAFs. S ome illustrative examples are given.