Calculation on this system for the ti 2 cl 2 cp 4

calculation on this system. For the
Ti
2
Cl
2
Cp
4
system (Figure 8), the TZV basis set as defined in GAMESS
35
was employed,
yielding 486 basis functions. A ZAPT2 gradient calculation on the lowest energy triplet state
of this system involves 108 doubly occupied orbitals and two singly occupied orbitals, and
requires 30.5 MWords of replicated memory and 2470 MWords of distributed memory. Six
processors of the IBM cluster are required in order to run a calculation on this system. For
the iron-porphyrin:imidazole system (Figure 9), two basis sets were used. The smaller basis

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set consists of the MIDI basis set 46 with d polarization functions, and a calculation with this
basis set has 493 basis functions. The larger basis set consists of the TZV basis set with d
and p polarization functions, and a calculation with this basis set has 728 basis functions. For
the triplet state, 110 orbitals are doubly occupied and two orbitals are singly occupied. A
ZAPT2 gradient calculation with the smaller basis set requires 32.1 MWords of replicated
memory and 2635 MWords of distributed memory, which corresponds
to the memory
allotted to seven processors on the IBM system. A similar calculation with the larger basis
set requires 52.1 MWords of replicated memory and 5536 MWords of distributed memory,
which corresponds to memory allotted to 15 processors on the IBM system.
Table 1 lists the wall clock time in seconds for a ZAPT2 gradient calculation on 1, 2,
4, 8, 16, 32, and 64 processors for the molecules benchmarked in this study. Tables 2 and 3
list the associated speedups and parallel efficiencies, respectively. The speedups may be
visualized in Figure 10. Some superlinear speedup is noted for Ti
2
Cl
2
Cp
4
with the TZV basis
set and Fe-porphyrin:imidazole with the MIDI(d) basis set with 16 processors and for the Fe-
porphyrin:imidazole with the TZV(d,p) basis set with 32 and 64 processors. Most likely, this
is due to an unusually long time for the run with 16 processors. Calculations investigating
this hypothesis are in progress. The parallel efficiency for the ZAPT2 gradients is at least
85% on 32 processors and at least 73% on 64 processors for the systems examined in this
analysis. As the size of the system increases, the parallel efficiency tends to increase as the
time required for computation grows faster than the time required for communication.
ZAPT2 gradients require much less memory and computational time than similar
UMP2 gradient calculations. A UMP2 gradient calculation on the Au
3
H
4
system requires 18
MWords of replicated memory and 647 MWords of distributed memory, so it requires two

229
processors on the IBM cluster. This UMP2 calculation takes 79828 seconds, which is
approximately a factor of three times the time required for a ZAPT2 gradient calculation
(28292 seconds). For Au
5
H
4
, a UMP2 gradient calculation requires 59.2 MWords of
replicated memory and 3911 MWords of distributed memory. This would require the use of
11 processors on the IBM system. For a calculation with 16 processors on this system, the
UMP2 gradient step takes 98418 seconds in