  Many-body Hamiltonians obtained from first principles generally include all
possible non-local interactions. But in dynamical mean field theory the
non-local interactions are ignored, and only the effects of the local
interactions are taken into account. The truncation of the non-local
interactions is a basis dependent approximation. We propose a criterion to
construct an appropriate localized basis in which the truncation can be carried
out. This involves finding a basis in which a functional given by the sum of
the squares of the local interactions with appropriate weight factors is
maximized under unitary transformations of basis. We argue that such a
localized basis is suitable for the application of dynamical mean field theory
for calculating material properties from first principles. We propose an
algorithm which can be used for constructing the localized basis. We test our
criterion on a toy model and find it satisfactory.
