Before starting any energy calculations, the geometry and basis set must be defined in GEOMETRY
and BASIS
blocks, respectively. By default, two electron integrals are evaluated once and stored on disk. This behaviour may be overridden by using the input command gdirect
(see section INTEGRAL-DIRECT CALCULATIONS (GDIRECT)) to force evaluation of integrals on the fly. Molpro checks if the one-and two-electron integrals are available for the current basis set and geometry, automatically computing them if necessary. The program also recognizes automatically if only the nuclear charges have been changed, as is the case in counterpoise calculations. In this case, the two-electron integrals are not recomputed.
By default a point charge nuclear model is used for all atoms. Alternatively, a Gaussian nuclear model can be used by setting
SET,FNUC=1
before the first energy evaluation (a value of 0 corresponds to a point charge nucleus). Alternatively, this also can be given as an option to the INT
command:
INT,FNUC=1
If the integrals are stored on disk, immediately after evaluation they are sorted into complete symmetry-packed matrices, so that later program modules that use them can do so as efficiently as possible. As discussed above, it is normally not necessary to call the integral and sorting programs explicitly, but sometimes additional options are desired, and can be specified using the INT
command, which should appear after geometry and basis specifications, and before any commands to evaluate an energy.
INT
, [[NO]SORT
,] [SPRI=
value]
SORT
, [SPRI=
value]
INT,NOSORT;SORT
can be used to explicitly separate the integral evaluation and sorting steps, for example to collect separate timing data. With value set to more than 1 in the SPRI
option, all the two-electron integrals are printed.
The detailed options for the integral sort can be specified using the AOINT
parameter set, using the input form
AOINT
, key1=value1, key2=value2, $\dots$
AOINT
can be used with or without an explicit INT
command.
The following summarizes the possible keys, together with their meaning, and default values.
GTHRESH,TWOINT
)molpro
(standard Molpro
record on file 1) and eaf
(Exclusive-access file). eaf
is permissible only if the program has been configured for MPP usage, and at present molpro
is implemented only for serial execution. molpro
is required if the integrals are to be used in a restart job. For maximum efficiency on a parallel machine, eaf
should be used, since in that case the integrals are distributed on separate processor-local files.
For backward-compatibility purposes, two convenience commands are also defined: COMPRESS
is equivalent to AOINT,COMPRESS=1
, and NOCOMPRESS
is equivalent to AOINT,COMPRESS=0
.
It is possible to import the second-quantised hamiltonian completely from outside Molpro
. In order to do so, it is necessary to set up a job that simulates the desired calculation by having a basis set of exactly the same dimensions as the one to be imported. One can then import the hamiltonian using the command
HAMILTONIAN
,filename
filename is the name of a file that contains the hamiltonian in FCIDUMP format, which can be produced using Molpro’s {FCI,DUMP=}
facility, or by another method.
Note that this facility is fragile, and is limited to energy-only calculations. Attempts to calculate gradients or other properties will inevitably fail. At present, the implementation does not support the use of point-group symmetry.
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 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. Exceptions are currently full CI (FCI), perturbative triple excitations (T), UMP2
, RMP2
, CPP
, MRCI-F12
, and RS2-F12
. 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).
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 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 MO-coefficients (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
$\ge 0$: full screening enabled.
SCREEN
$\lt 0$: THRPROD
is unused. No density screening in direct SCF.
SCREEN
$\lt -1$: THRINT
is unused.
SCREEN
$\lt -2$: 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.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 7-10 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).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 ${\tt SCREEN}$ 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
.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].
THR_D2EXT
General threshold for generation of 2-external integrals. If given, this is used as a default for all D2EXT
thresholds described below.THREST_D2EXT
Prescreening threshold for generation of 2-external integrals.
Defaults: [THR_D2EXT
, THREST_DTRAF
, THR_DTRAF
, THREST
, default].
THRINT_D2EXT
Integral threshold for generation of 2-external integrals.
Defaults: [THR_D2EXT
, THRINT_DTRAF
, THR_DTRAF
, THRINT
, default].
THRPROD_D2EXT
Product threshold for generation of 2-external integrals.
Defaults: [THR_D2EXT
, THRPROD_DTRAF
, THR_DTRAF
, THRPROD
, default].
THR_D3EXT
General threshold for generation of 3-external integrals. If given, this is used as a default for all D3EXT
thresholds described below.THREST_D3EXT
Prescreening threshold for generation of 3-external integrals.
Defaults: [THR_D3EXT
, THREST_DTRAF
, THR_DTRAF
, THREST
, default].
THRINT_D3EXT
Integral threshold for generation of 3-external integrals.
Defaults: [THR_D3EXT
, THRINT_DTRAF
, THR_DTRAF
, THRINT
, default].
THRPROD_D3EXT
Product threshold for generation of 3-external integrals.
Defaults: [THR_D3EXT
, THRPROD_DTRAF
, THR_DTRAF
, THRPROD
, default].
THR_D4EXT
General threshold for generation of 4-external integrals. If given, this is used as a default for all D4EXT
thresholds described below.THREST_D4EXT
Prescreening threshold for generation of 4-external integrals.
Defaults: [THR_D4EXT
, THREST_DTRAF
, THR_DTRAF
, THREST
, default].
THRINT_D4EXT
Integral threshold for generation of 4-external integrals.
Defaults: [THR_D4EXT
, THRINT_DTRAF
, THR_DTRAF
, THRINT
, default].
THRPROD_D4EXT
Product threshold for generation of 4-external 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.DMP2
): DMP2
Selects the transformation method for direct MP2
:
DMP2
=$-1$: 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 semi-direct 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 2-external integrals in DMP2. If given, this is used as a default for all DMP2
thresholds described below.THREST_DMP2
Prescreening threshold for generation of 2-external integrals.
Defaults: [THR_DMP2
, THREST_DTRAF
, THR_DTRAF
, THREST
, default].
THRINT_DMP2
Integral threshold for generation of 2-external integrals.
Defaults: [THR_DMP2
, THRINT_DTRAF
, THR_DTRAF
, THRINT
, default].
THRPROD_DMP2
Product threshold for generation of 2-external integrals
Defaults: [THR_DMP2
, THRPROD_DTRAF
, THR_DTRAF
, THRPROD
, default].
LMP2
): DTRAF
Selects the transformation method for direct LMP2
:
DTRAF
$\geq 0$: generates the 2-external 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
$= -1$: generates the 2-external 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 PAO-based local correlation treatments).
DTRAF
$= -2$: 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
$= -1$. Note, that neither DTRAF
$= -1$ nor DTRAF
$= -2$ work in the context of LMP2 gradients.
THR_LMP2
General threshold for generation of 2-external 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 2-external 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 $(\mu \mu | \nu \nu)$
Default: THREST_LMP2
DKEXT
): DKEXT
Selects driver for DKEXT
.
DKEXT=-1
: use paging algorithm (minimum memory). This is automatically used if in-core algorithm would need more than one integral pass.
DKEXT
=0: use in-core algorithm, no integral triples.
DKEXT
=1: use in-core algorithm and integral triples.
DKEXT
=2: use in-core algorithm and integral triples if at least two integrals of a triple differ.
DKEXT
=3: use in-core algorithm and integral triples if all integrals of a triple differ.
SCREEN_DKEXT
if given, replaces value of ${\tt SCREEN}$ 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
$\ge 1$).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.
Default values and alias names for direct options. |
||
---|---|---|
Parameter | Alias | Default value |
SCREEN | $1$ | |
MAXRED | $7$ | |
VARRED | 1.d-7 | |
SWAP | $1$ | |
SWAP_DFOCK | SWAP |
|
DMP2 | DTRAF | $-1$ |
PAGE_DTRAF | PAGE | $1$ |
SCREEN_DTRAF | SCREEN |
|
MAXSHLQ1_DTRAF | NSHLQ1 | $32$ |
MINSHLQ1_DTRAF | $0$ | |
MAXSHLQ2_DTRAF | NSHLQ2 | $16$ |
MINSHLQ2_DTRAF | 0 | |
MAXCEN_DTRAF | 0 | |
PRINT_DTRAF | $-1$ | |
SWAP_DTRAF | SWAP |
|
DKEXT | DRVKEXT | $3$ |
SCREEN_DKEXT | SCREEN |
|
MAXSIZE_DKEXT | $0$ | |
MINSIZE_DKEXT | $5$ | |
MAXCEN_DKEXT | $1$ | |
PRINT_DKEXT | $-1$ | |
SWAP_DKEXT | SWAP |
|
MXMBLK_DKEXT | depends on hardware (-B parameter on molpro command) |
Default thresholds and alias names for direct calculations |
||
---|---|---|
Parameter | Alias | Default value |
THREST | THRAO | $\min(\Delta E \cdot 1.d-2,1.d-9)^{a,b}$ |
THRINT | THRSO | $\min(\Delta E \cdot 1.d-2,1.d-9)^{a,b}$ |
THRPROD | THRP | $\min(\Delta E \cdot 1.d-3,1.d-10)^{a,b}$ |
THRMAX | 1.d-8$^b$ | |
THREST_DSCF | THRDSCF | $\le$ 1.d-10 (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$^c$] |
THRINT_DMP2 | THRSO_DMP2 | [THR_DMP2 , THRINT_DTRAF , default$^c$] |
THRPROD_DMP2 | THRP_DMP2 | [THR_DMP2 , THRPROD_DTRAF , default$^c$] |
THR_LMP2 | THRLMP2 | THR_DTRAF |
THREST_LMP2 | THRAO_LMP2 | [THR_LMP2 , THREST_DTRAF , default$^c$] |
THRQ1_LMP2 | THRQ1 | [THR_LMP2 , THRPROD_DTRAF , default$^c$] |
THRQ2_LMP2 | THRQ2 | [THR_LMP2 , THRINT_DTRAF , default$^c$] |
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) $\Delta E$ is the requested accuracy in the energy (default 1.d-6).
b) The thresholds are reduced if the overlap matrix has small eigenvalues.
c) The default thresholds for DMP2 and LMP2 are $0.1 \cdot {\Delta E}$.
$method=[hf,mp2,ccsd,qci,bccd,multi,mrci,acpf,rs3] !some methods basis=vdz !basis geometry={o;h1,o,r;h2,o,r,h1,theta} !geometry gdirect !direct option r=1 ang,theta=104 !bond length and angle do i=1,#method !loop over methods $method(i) !run method(i) e(i)=energy !save results in variables dip(i)=dmz enddo table,method,e,dip !print table of results
This job produces the following table:
METHOD E DIP HF -76.02145798 0.82747348 MP2 -76.22620591 0.00000000 CCSD -76.23580191 0.00000000 QCI -76.23596211 0.00000000 BCCD -76.23565813 0.00000000 MULTI -76.07843443 0.76283026 MRCI -76.23369819 0.76875001 ACPF -76.23820180 0.76872802 RS3 -76.23549448 0.75869972