MOLPRO

14 INTEGRATION 85
14.2 INTEGRAL-DIRECT CALCULATIONS (GDIRECT)
References:
Direct methods, general: M. Schütz, R. Lindh, and H.-J. Werner, Mol. Phys. 96, 719 (1999).
Linear scaling LMP2: M. Schütz, G. Hetzer, and H.-J. Werner J. Chem. Phys. 111, 5691 (1999).
All methods implemented in MOLPRO apart from full CI (FCI) and perturbative triple excitations
(T) can be performed integral-direct, i.e., the methods are integral driven with the two-electron
integrals in the AO basis being recomputed whenever needed, avoiding the bottleneck of storing
these quantities on disk. For small molecules, this requires significantly more CPU time, but
reduces the disk space requirements when using large basis sets. However, due to efficient
prescreening techniques, the scaling of the computational cost with molecular size is lower in
integral-direct mode than in conventional mode, and therefore integral-direct calculations for
extended molecules may even be less expensive than conventional ones. The break-even point
depends strongly on the size of the molecule, the hardware, and the basis set. Depending on
the available disk space, calculations with more than 150–200 basis functions in one symmetry
should normally be done in integral-direct mode.
Integral-direct calculations are requested by the DIRECT or GDIRECT directives. If one of these
cards is given outside the input of specific programs it acts globally, i.e. all subsequent calculations
are performed in integral-direct mode. On the other hand, if the DIRECT card is part
of the input of specific programs (e.g. HF, CCSD), it affects only this program. The GDIRECT
directive is not recognized by individual programs and always acts globally. Normally, all calculations
in one job will be done integral-direct, and then a DIRECT or GDIRECT card is
required before the first energy calculation. However, further DIRECT or GDIRECT directives
can be given in order to modify specific options or thresholds for particular programs.
The integral-direct implementation in MOLPRO involves three different procedures: (i) Fock
matrix evaluation (DFOCK), (ii) integral transformation (DTRAF), and (iii) external exchange
operators (DKEXT). Specific options and thresholds exist for all three programs, but it is also
possible to specify the most important thresholds by general parameters, which are used as
defaults for all programs.
Normally, appropriate default values are automatically used by the program, and in most cases
no parameters need to be specified on the DIRECT directive. However, in order to guarantee
sufficient accuracy, the default thresholds are quite strict, and in calculations for extended
systems larger values might be useful to reduce the CPU time.
The format of the DIRECT directive is
DIRECT, key1=value1, key2=value2. . .
The following table summarizes the possible keys and their meaning. The default values are
given in the subsequent table. In various cases there is a hierarchy of default values. For instance,
if THREST D2EXT is not given, one of the following is used: [THR D2EXT, THREST DTRAF,
THR DTRAF, THREST, default]. The list in brackets is checked from left to right, and the first
one found in the input is used. default is a default value which depends on the energy threshold
and the basis set (the threshold is reduced if the overlap matrix contains very small eigenvalues).
General Options (apply to all programs):
THREST
Integral prescreening threshold. The calculation of an integral
shell block is skipped if the product of the largest estimated integral
value (based on the Cauchy-Schwarz inequality) and the
largest density matrix element contributing to the shell block is