  A new method for implementing the kinetic energy operator for real-space,
grid-based electronic structure codes is developed. It is based on multi-order
Adaptive Finite Differencing (AFD) and uses atomic pseudo orbitals produced by
the corresponding pseudopotential codes to optimize the standard finite
difference (SFD) operators for improved accuracy. Results are presented for a
variety of test systems and Bravais lattice types, including the well-known
Delta test for 71 elements in the periodic table, the Mott insulator NiO, and
borax decahydrate, which contains covalent, ionic, and hydrogen bonds. The
tests show that an 8th-order AFD operator leads to the same average Delta value
as that achieved by plane-wave codes and is typically far more accurate and a
much lower computational cost than a 12th-order SFD operator. The scalability
of real-space electronic calculations is demonstrated for a 2,016-atom NiO
cell, for which the computational time decreases nearly linearly when scaled
from 18 to 144 CPU-GPU nodes.
