  Accurate low-order structure factors (Fg) measured by quantitative convergent
beam electron diffraction (QCBED) were used for validation of different density
functional theory (DFT) approximations. 23 low-order Fg were measured by QCBED
for the transition metals Cr, Fe, Co, Ni, and Cu, and the transition metal
based intermetallic phases {\gamma}-TiAl, {\beta}-NiAl and {\gamma}1-FePd using
a multi-beam off-zone axis (MBOZA) method and then compared with Fg calculated
ab-initio by DFT using the local spin density approximation (LDA) and LDA+U,
and different generalized gradient approximations (GGA) functionals. Different
functionals perform very differently for different materials and crystal
structures. Among the GGA functionals, PW91 and EV93 achieve the best overall
agreement with the experimentally determined low-order Fg for the five metals,
while PW91 performs the best for the three intermetallics. The LDA+U approach,
through careful selection of U, achieves excellent matches with the
experimentally measured Fg for all the metallic systems investigated in this
paper. Similar to the band gap for semiconductors, it is proposed that
experimentally determined low-order Fg can be used to tune the U term in LDA+U
method DFT calculations for metals and intermetallics.
