Usually, for the relatively
large MP2 energy jobs (i.e., approximately 150 AOs or more), the new MP2 program is definitely the method that is to be
used. This program is intended to handle large systems (up to 500 AOs or more)
efficiently. It is direct, fast, and requires much less memory as compared to other MP2
methods. Its main features are as follows:
- Memory requirements scale as approximately N2.
The other MP2 programs currently implemented in the GAMESS scale
as at least N3 for the segmented transformation and as A N2
for the alternative integral transformation. Here, A and N are the number of
active orbitals and the total number of MOs, respectively.
- Disk requirements scale as A2N2.
They scale as A2(N-A)2
for the alternative integral transformation. The segmented transformation does not use
temporary disk storage.
- The disk I/O is used, but to a very limited degree. Therefore, the CPU utilization is
usually 90% or even better.
The CPU utilization is usually less than 50% for other MP2
transformation methods working in the conventional mode, while, in the direct mode, there
is a very serious overhead because of the multiple reevaluation of 2-electron integrals.
- Asymptotically, the FLOPs count is about a half or even better as compared to other MP2
energy transformation methods.
- It uses SMP more efficiently.
- On the other hand, it requires the 2-electron AO integrals to be reevaluated four
times. This cost is fixed and does not depend on the details of the MP2 calculation
performed.
To
give one an idea about the program capabilities, we list here the timings obtained for a
relatively large test job, namely RHF+MP2 (D2h group,
but no symmetry was used during integral transformation) calculation with 512 basis
functions (10 core, 87 active, and 415 virtual orbitals), which uses 9,000,000
words of memory and approximately 9.5 GBytes of disk.
The dual processor 300 MHz Pentium II
system working under Windows NT 4.0 Workstation was used for the tests.
The total execution (real) time for this job
was about 13.4 hours with a single processor, and about 8.5 hours with both processors.
Comment:
In the above calculations, we used the PC GAMESS version 4.4. The corresponding times are
only 5.75 and 4.5 hours when the test was carried out on the same system but with the
newer PC GAMESS v. 5.0. The performance is improved mainly due to the much more efficient
usage of the sparsity of 2e integrals inside MP2 code in
the newer PC GAMESS version. Indeed, the AO integral list for the model system is very
sparse (approximately 2.5-3.0 percents of all integrals are nonzero).