  Orbital-free density functional theory (OF-DFT) runs at low computational
cost that scales linearly with the number of simulated atoms, making it
suitable for large-scale material simulations. It is generally considered that
OF-DFT strictly requires the use of local pseudopotentials, rather than
orbital-dependent nonlocal pseudopotentials, for the calculation of
electron-ion interaction energies, as no orbitals are available. This is
unfortunate situation since the nonlocal pseudopotentials are known to give
much better transferability and calculation accuracy than local ones. We report
here the development of a theoretical scheme that allows the direct use of
nonlocal pseudopotentials in OF-DFT. In this scheme, a nonlocal pseudopotential
energy density functional is derived by the projection of nonlocal
pseudopotential onto the non-interacting density matrix (instead of 'orbitals')
that can be approximated explicitly as a functional of electron density. Our
development defies the belief that nonlocal pseudopotentials are not applicable
to OF-DFT, leading to the creation of an alternate theoretical framework of
OF-DFT that works superior to the traditional one.
