14.3 INTEGRALDIRECT 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).
Most methods implemented in MOLPRO can be performed integraldirect,
i.e., the methods are integral driven with
the twoelectron integrals in the AO basis being recomputed whenever needed, avoiding the bottleneck
of storing these quantities on disk. Exceptions are currently
full CI (FCI), perturbative triple excitations (T), UMP2, RMP2, CPP, MRCIF12, and RS2F12.
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 integraldirect mode than in conventional mode, and therefore integraldirect
calculations for extended molecules may even be less expensive than conventional ones.
The breakeven 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 150200 basis
functions in one symmetry should normally be done in integraldirect mode.
Integraldirect 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 integraldirect 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 integraldirect, 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 integraldirect 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 CauchySchwarz inequality) and the
largest density matrix element contributing to the shell block is smaller
than this value. In DTRAF and DKEXT effective density matrices
are constructed from the MO coefficients and amplitudes, respectively.
 THRINT
 Integral prescreening threshold. This applies to the product
of the exact (i.e. computed) integral value and a density matrix.
This threshold is only used in DTRAF and DKEXT. A shell block
of integrals is skipped if the product of the largest integral and the
largest element of the effective density matrix contributing to the shell block
is smaller than this threshold. If it is set negative,
no computed integrals will be neglected.
 THRPROD
 Prescreening threshold for products of integrals and MOcoefficients (DTRAF)
or amplitudes (DKEXT). Shell blocks of MO coefficients or amplitudes are
neglected if the product of the largest integral in the shell block and
the largest coefficient is smaller than this value. If this is set negative,
no product screening is performed.
 THRMAX
 Initial value of the prescreening threshold THREST for DFOCK and DKEXT
in iterative methods (SCF, CI, CCSD). If nonzero, it will also
be used for DKEXT in MP3 and MP4(SDQ) calculations.
The threshold will be reduced to THREST once a certain accuracy has been
reached (see VARRED), or latest
after MAXRED iterations. In CI and CCSD calculations,
also the initial thresholds THRINT_DKEXT and THRPROD_DKEXT are
influenced by this value. For a description, see THRMAX_DKEXT.
If THRMAX=0, the final thresholds will be used from the beginning in all
methods.
 SCREEN
 Enables or disables prescreening.
SCREEN: full screening enabled.
SCREEN: THRPROD is unused. No density screening in direct SCF.
SCREEN: THRINT is unused.
SCREEN: THREST is unused.
 MAXRED
 Maximum number of iterations after which thresholds are reduced to their final values
in CI and CCSD calculations. If MAXRED=0, the final thresholds
will be used in CI and CCSD from the beginning (same as
THRMAX=0, but MAXRED has no effect on DSCF. In the latter case
a fixed value of 10 is used.
 VARRED
 Thresholds are reduced to their final values if the sum of squared amplitude changes
is smaller than this value.
 SWAP
 Enables or disables label swapping in SEWARD. Test purpose only.
 Specific options for direct SCF (DFOCK):
 THREST_DSCF
 Final prescreening threshold in direct SCF.
If given, it replaces the value of THREST.
 THRMAX_DSCF
 Initial prescreening threshold in direct SCF. This is used for the first 710 iterations.
Once a certain accuracy is reached, the threshold is reduced to THREST_DSCF
 SWAP_DFOCK
 Enables or disables label swapping in fock matrix calculation (test purpose only).
 General options for direct integral transformation (DTRAF):
 PAGE_DTRAF
 Selects the transformation method.
PAGE_DTRAF=0: use minimum memory algorithm, requiring
four integral evaluations.
PAGE_DTRAF=1: use paging algorithm,leading
to the minimum CPU time (one integral evaluation for DMP2/LMP2 and two otherwise).
 SCREEN_DTRAF
 If given, replaces value of for DTRAF.
 MAXSHLQ1_DTRAF
 Maximum size of merged shells in the first quarter transformation step
(0: not used).
 MINSHLQ1_DTRAF
 Shells are only merged if their size is smaller than this value
(0: not used).
 MAXSHLQ2_DTRAF
 Maximum size of merged shells in the second quarter transformation step
(0: not used).
 MINSHLQ2_DTRAF
 Shells are only merged if their size is smaller than this value
(0: not used).
 MAXCEN_DTRAF
 Maximum number of centres in merged shells (0: no limit).
 PRINT_DTRAF
 Print parameter for DTRAF.
 General thresholds for all direct integral transformations:
 THR_DTRAF
 General threshold for DTRAF.
If given, this is taken as default value for all thresholds described below.
 THREST_DTRAF
 AO prescreening threshold for DTRAF.
Defaults: [THR_DTRAF, THREST, default].
 THRINT_DTRAF
 Integral threshold for DTRAF.
Defaults: [THR_DTRAF, THRINT, default].
 THRPROD_DTRAF
 Product threshold for DTRAF.
Defaults: [THR_DTRAF, THRPROD, default].
 Thresholds specific to direct integral transformations:
 THR_D2EXT
 General threshold for generation of 2external integrals.
If given, this is used as a default for all D2EXT thresholds described below.
 THREST_D2EXT
 Prescreening threshold for generation of 2external integrals.
Defaults: [THR_D2EXT, THREST_DTRAF, THR_DTRAF, THREST, default].
 THRINT_D2EXT
 Integral threshold for generation of 2external integrals.
Defaults: [THR_D2EXT, THRINT_DTRAF, THR_DTRAF, THRINT, default].
 THRPROD_D2EXT
 Product threshold for generation of 2external integrals.
Defaults: [THR_D2EXT, THRPROD_DTRAF, THR_DTRAF, THRPROD, default].
 THR_D3EXT
 General threshold for generation of 3external integrals.
If given, this is used as a default for all D3EXT thresholds described below.
 THREST_D3EXT
 Prescreening threshold for generation of 3external integrals.
Defaults: [THR_D3EXT, THREST_DTRAF, THR_DTRAF, THREST, default].
 THRINT_D3EXT
 Integral threshold for generation of 3external integrals.
Defaults: [THR_D3EXT, THRINT_DTRAF, THR_DTRAF, THRINT, default].
 THRPROD_D3EXT
 Product threshold for generation of 3external integrals.
Defaults: [THR_D3EXT, THRPROD_DTRAF, THR_DTRAF, THRPROD, default].
 THR_D4EXT
 General threshold for generation of 4external integrals.
If given, this is used as a default for all D4EXT thresholds described below.
 THREST_D4EXT
 Prescreening threshold for generation of 4external integrals.
Defaults: [THR_D4EXT, THREST_DTRAF, THR_DTRAF, THREST, default].
 THRINT_D4EXT
 Integral threshold for generation of 4external integrals.
Defaults: [THR_D4EXT, THRINT_DTRAF, THR_DTRAF, THRINT, default].
 THRPROD_D4EXT
 Product threshold for generation of 4external integrals.
Defaults: [THR_D4EXT, THRPROD_DTRAF, THR_DTRAF, THRPROD, default].
 THR_DCCSD
 General threshold for generalized transformation needed in each CCSD iteration.
If given, this is used as a default for THREST_DCCSD, THRINT_DCCSD, and
THRPROD_DCCSD described below.
 THREST_DCCSD
 Prescreening threshold for DCCSD transformation.
Defaults: [THR_DCCSD, THREST_DTRAF, THR_DTRAF, THREST, default].
 THRINT_DCCSD
 Integral threshold for DCCSD transformation.
Defaults: [THR_DCCSD, THRINT_DTRAF, THR_DTRAF, THRINT, default].
 THRPROD_DCCSD
 Product threshold for DCCSD transformation.
Defaults: [THR_DCCSD, THRPROD_DTRAF, THR_DTRAF, THRPROD, default].
 THRMAX_DCCSD
 Initial value for THREST_DCCSD in CCSD calculations.
The threshold will be reduced to THREST_DCCSD once a certain accuracy has been
reached (see VARRED), or latest after MAXRED iterations.
The initial thresholds THRINT_DCCSD and THRPROD_DCCSD are obtained by multiplying
their input (or default) values by THRMAX_DCCSD/THREST_DCCSD,
with the restriction that the initial values cannot be smaller than the final ones.
 Specific options for direct MP2 (DMP2):
 DMP2
 Selects the transformation method for direct MP2:
DMP2=: automatic selection, depending on the available memory.
DMP2=0: use fully direct method for DMP2 (min. two integral evaluations,
possibly multipassing, no disk space).
DMP2=1: use semidirect method for DMP2 (one to four integral evaluations,
depending on PAGE_DTRAF).
DMP2=2: use DKEXT to compute exchange operators in DMP2
(one integral evaluation). This is only useful in local DMP2 calculations with
many distant pairs.
 THR_DMP2
 General threshold for generation of 2external integrals in DMP2.
If given, this is used as a default for all DMP2 thresholds described below.
 THREST_DMP2
 Prescreening threshold for generation of 2external integrals.
Defaults: [THR_DMP2, THREST_DTRAF, THR_DTRAF, THREST, default].
 THRINT_DMP2
 Integral threshold for generation of 2external integrals.
Defaults: [THR_DMP2, THRINT_DTRAF, THR_DTRAF, THRINT, default].
 THRPROD_DMP2
 Product threshold for generation of 2external integrals
Defaults: [THR_DMP2, THRPROD_DTRAF, THR_DTRAF, THRPROD, default].
 Specific options for direct local MP2 (LMP2):
 DTRAF
 Selects the transformation method for direct LMP2:
DTRAF : generates the 2external integrals (exchange operators) first in AO basis
and transforms these thereafter in a second step to the projected, local basis. The disk
storage requirements hence scale cubically with molecular size.
DTRAF : generates the 2external integrals (exchange operators) directly in
projected basis. The disk storage requirements hence scale linearly with molecular size.
This (together with PAGE_DTRAF = 0) is the recommended algorithm for very large
molecules (cf. linear scaling LMP2, chapter
32).
DTRAF : alternative algorithm to generate the exchange operators directly in
projected basis. Usually, this algorithm turns out to be computationally more expensive than
the one selected with DTRAF . Note, that neither DTRAF nor
DTRAF work in the context of LMP2 gradients.
 THR_LMP2
 General threshold for generation of 2external integrals in linear scaling LMP2.
If given, this is used as a default for all LMP2 thresholds described below.
 THREST_LMP2
 Prescreening threshold for generation of 2external integrals.
Defaults: [THR_LMP2, THREST_DTRAF, THR_DTRAF, THREST, default].
 THRQ1_LMP2
 Threshold used in the first quarter transformation.
Defaults: [THR_LMP2, THRPROD_DTRAF, THR_DTRAF, THRPROD, default].
 THRQ2_LMP2
 Threshold used in the second and subsequent quarter transformations.
Defaults: [THR_LMP2, THRINT_DTRAF, THR_DTRAF, THRINT, default].
 THRAO_ATTEN
 Special threshold for prescreening of attenuated integrals
Default: THREST_LMP2
 Options for integraldirect computation of external exchange operators (DKEXT):
 DKEXT
 Selects driver for DKEXT.
DKEXT=: use paging algorithm (minimum memory). This is automatically
used if incore algorithm would need more than one integral pass.
DKEXT=0: use incore algorithm, no integral triples.
DKEXT=1: use incore algorithm and integral triples.
DKEXT=2: use incore algorithm and integral triples
if at least two integrals of a triple differ.
DKEXT=3: use incore algorithm
and integral triples if all integrals of a triple differ.
 SCREEN_DKEXT
 if given, replaces value of for DKEXT.
 MAXSIZE_DKEXT
 Largest size of merged shells in DKEXT
(0: not used).
 MINSIZE_DKEXT
 Shells are only merged if their size is smaller than this value.
(0: not used).
 MAXCEN_DKEXT
 Maximum number of centres in merged shells (0: no limit).
 SCREEN_DKEXT
 Enables of disables screening in DKEXT.
 PRINT_DKEXT
 Print parameter for DKEXT.
 SWAP_DKEXT
 Enables of disables label swapping in DKEXT (test purpose only)
 MXMBLK_DKEXT
 Largest matrix block size in DKEXT
(only used with DKEXT).
 Thresholds for integraldirect computation of external exchange operators (DKEXT):
 THR_DKEXT
 General threshold for DKEXT.
If given, this is used as a default for all DKEXT thresholds described below.
 THREST_DKEXT
 Prescreening threshold for DKEXT.
Defaults: [THR_DKEXT, THREST, default].
 THRINT_DKEXT
 Integral threshold for DKEXT.
Defaults: [THR_DKEXT, THRINT, default].
 THRPROD_DKEXT
 Product threshold for DKEXT.
Defaults: [THR_DKEXT, THRPROD, default].
 THRMAX_DKEXT
 Initial value for THREST_DKEXT in CI, and CCSD calculations. If nonzero.
it will also be used for DKEXT in MP3 and MP4(SDQ) calculations.
The threshold will be reduced to THREST_DKEXT once a certain accuracy has been
reached (see VARRED), or latest after MAXRED iterations.
The initial thresholds
THRINT_DKEXT and THRPROD_DKEXT are obtained by multiplying
their input (or default) values by THRMAX_DKEXT/THREST_DKEXT,
with the restriction that the initial values cannot be smaller than the final ones.
For historical reasons, many options have alias names. The following tables summarize the
default values for all options and thresholds and also gives possible alias names.
Table 6:
Default values and alias names for direct options.
Parameter 
Alias 
Default value 
SCREEN 


MAXRED 


VARRED 

1.d7 
SWAP 


SWAP_DFOCK 

SWAP 
DMP2 
DTRAF 

PAGE_DTRAF 
PAGE 

SCREEN_DTRAF 

SCREEN 
MAXSHLQ1_DTRAF 
NSHLQ1 

MINSHLQ1_DTRAF 


MAXSHLQ2_DTRAF 
NSHLQ2 

MINSHLQ2_DTRAF 

0 
MAXCEN_DTRAF 

0 
PRINT_DTRAF 


SWAP_DTRAF 

SWAP 
DKEXT 
DRVKEXT 

SCREEN_DKEXT 

SCREEN 
MAXSIZE_DKEXT 


MINSIZE_DKEXT 


MAXCEN_DKEXT 


PRINT_DKEXT 


SWAP_DKEXT 

SWAP 
MXMBLK_DKEXT 

depends on hardware (B parameter on molpro command) 
Table 7:
Default thresholds and alias names for direct calculations
Parameter 
Alias 
Default value 
THREST 
THRAO 

THRINT 
THRSO 

THRPROD 
THRP 

THRMAX 

1.d8 
THREST_DSCF 
THRDSCF 
1.d10 (depending on accuracy and basis set) 
THRMAX_DSCF 
THRDSCF_MAX 
THRMAX 
THR_DTRAF 
THRDTRAF 

THREST_DTRAF 
THRAO_DTRAF 
[THR_DTRAF, THREST] 
THRINT_DTRAF 
THRAO_DTRAF 
[THR_DTRAF, THRINT] 
THRPROD_DTRAF 
THRP_DTRAF 
[THR_DTRAF, THRPROD] 
THR_D2EXT 
THR2EXT 
THR_DTRAF 
THREST_D2EXT 
THRAO_D2EXT 
[THR_D2EXT, THREST_DTRAF] 
THRINT_D2EXT 
THRSO_D2EXT 
[THR_D2EXT, THRINT_DTRAF] 
THRPROD_D2EXT 
THRP_D2EXT 
[THR_D2EXT, THRPROD_DTRAF] 
THR_D3EXT 
THR3EXT 
THR_DTRAF 
THREST_D3EXT 
THRAO_D3EXT 
[THR_D3EXT, THREST_DTRAF] 
THRINT_D3EXT 
THRSO_D3EXT 
[THR_D3EXT, THRINT_DTRAF] 
THRPROD_D3EXT 
THRP_D3EXT 
[THR_D3EXT, THRPROD_DTRAF] 
THR_D4EXT 
THR4EXT 
THR_DTRAF 
THREST_D4EXT 
THRAO_D4EXT 
[THR_D4EXT, THREST_DTRAF] 
THRINT_D4EXT 
THRSO_D4EXT 
[THR_D4EXT, THRINT_DTRAF] 
THRPROD_D4EXT 
THRP_D4EXT 
[THR_D4EXT, THRPROD_DTRAF] 
THR_DCCSD 
THRCCSD 
THR_DTRAF 
THREST_DCCSD 
THRAO_DCCSD 
[THR_DCCSD, THREST_DTRAF] 
THRINT_DCCSD 
THRSO_DCCSD 
[THR_DCCSD, THRINT_DTRAF] 
THRPROD_DCCSD 
THRP_DCCSD 
[THR_DCCSD, THRPROD_DTRAF] 
THRMAX_DCCSD 
THRMAX_DTRAF 
THRMAX 
THR_DMP2 
THRDMP2 
THR_DTRAF 
THREST_DMP2 
THRAO_DMP2 
[THR_DMP2, THREST_DTRAF, default] 
THRINT_DMP2 
THRSO_DMP2 
[THR_DMP2, THRINT_DTRAF, default] 
THRPROD_DMP2 
THRP_DMP2 
[THR_DMP2, THRPROD_DTRAF, default] 
THR_LMP2 
THRLMP2 
THR_DTRAF 
THREST_LMP2 
THRAO_LMP2 
[THR_LMP2, THREST_DTRAF, default] 
THRQ1_LMP2 
THRQ1 
[THR_LMP2, THRPROD_DTRAF, default] 
THRQ2_LMP2 
THRQ2 
[THR_LMP2, THRINT_DTRAF, default] 
THRAO_ATTEN ] 
THRATTEN 
THREST_LMP2 
THR_DKEXT 
THRKEXT 

THREST_DKEXT 
THRAO_DKEXT 
[THR_DKEXT, THREST] 
THRINT_DKEXT 
THRSO_DKEXT 
[THR_DKEXT, THRINT] 
THRPROD_DKEXT 
THRP_DKEXT 
[THR_DKEXT, THRPROD] 
THRMAX_DKEXT 

THRMAX 
a) is the requested accuracy in the energy (default 1.d6).
b) The thresholds are reduced if the overlap matrix has small eigenvalues.
c) The default thresholds for DMP2 and LMP2 are
.
Subsections
molpro@molpro.net 20190122