To measure the performance of the D&C algorithm with increasing system size,
the density matrix was computed for various supercells of crystalline neon with
a face centred cubic crystal structure (from the Inorganic Crystal Structure
Database [14]). The time taken to compute the density matrix
with varying systems size is shown in Figure 3. The scaling is
nearly linear. The nonlinear part of the scaling comes from computing the
Fermi energy for the system. Figure 4 shows the time
taken to set up and compute the electronic structure of the subsystems. This
shows almost perfect linear scaling, and also shows that a substantial part of
the run time is spent computing the Fermi energy. Improvements to the
algorithm to compute the Fermi energy should be a priority in the continuation
of this work.
Figure 3:
The time taken to compute the density matrix using the divide and
conquer algorithm as a function of system size. The algorithm displays near
linear scaling.

Figure 4:
The CPU time taken to converge the SCF for all subsystems using the
D&C algorithm. This shows near perfect linear scaling. Further investigation
is needed to reduce the time taken to calculate the Fermi energy for the
system.

Daniel R. Jones 20111206