where

f* = f + p u. (17)

Note that Eq. (17) defines an effective force f* such that Eqs. (14) and (16) are exactly equivalent.

Equation (16) expresses the atomic displacements u in terms of G, the perfect LSGF even for lattices with defects. The effect of the defects is included exactly in f*. The LSGF G is independent of f or f* and reduces to the CGF asymptotically and smoothly

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