.. index::
single: Program; Seward
single: Seward
.. _UG\:sec\:seward:
:program:`seward`
=================
.. only:: html
.. contents::
:local:
:backlinks: none
.. xmldoc::
%%Description:
The Seward module generates one- and two-electron integrals needed
by other programs. The input contains an additional and optional
embedded input section for numerical quadrature options for the
computation of integrals associated with DFT calculations. The
embedded section starts and ends with the keywords "Grid Input"
and "End of Grid", respectively. Keywords associated with this
embedded input section is labelled "(NQ)" below.
The :program:`SEWARD` module generates one- and two-electron integrals needed
by other programs. The two-electron integrals may optionally be
Cholesky decomposed. In addition, it will serve as the input parser
for parameters related to the specification of the quadrature grid
used in numerical integration in association with DFT and reaction
field calculations.
.. .. figure:: seward.*
:width: 50%
:align: center
H. W. Seward, secretary of State in the Lincoln administration, who suggested and supervised
the 1867 purchase of Alaska from tzar Russia. Price: 2 cents an acre.
In the following three subsections we will in detail describe the input parameters
for analytic integration, numerical integration, and relativistic operators.
.. ..include:: ../integrals.inc
Analytic integration
--------------------
Any conventional ab initio quantum chemical calculation starts by
computing overlap, kinetic energy, nuclear attraction and electron
repulsion integrals. These are used repeatedly to determine the
optimal wave function and the total energy of the system under
investigation. Finally, to compute various properties of the system
additional integrals may be needed, examples include multipole moments
and field gradients.
.. _UG\:sec\:seward_description:
Description
...........
:program:`SEWARD` is able to compute the following integrals:
* kinetic energy,
* nuclear attraction,
* two electron repulsion (optionally Cholesky decomposed),
* :math:`n`\th (default :math:`n`\=2) order moments (overlap, dipole moment, etc.),
* electric field (generated at a given point by all charges in the system),
* electric field gradients (spherical gradient operators),
* linear momentum (velocity),
* orbital angular momentum,
* relativistic mass-velocity correction (1st order),
* one-electron Darwin contact term,
* one-electron relativistic no-pair Douglas--Kroll,
* diamagnetic shielding,
* spherical well potential (Pauli repulsion),
* ECP and PP integrals,
* modified kinetic energy and multipole moment integrals
(integration on a finite sphere centered at the origin) for use in
the variational :math:`R`\-matrix approach,
* external field (represented by a large number of charges and dipoles),
* angular momentum products, and
* atomic mean-field integrals (AMFI) for spin--orbit coupling.
*Note that while* :program:`SEWARD` *compute these integrals the input to
select them and their settings are put in the input of* :program:`GATEWAY`.
In general these integrals will be written to a file, possibly in
the form of Cholesky vectors (two-electron integrals only). However,
:program:`SEWARD` can also compute the orbital contributions and total components of
these properties if provided with orbital coefficients and
orbital occupation numbers.
To generate the one- and two-electron integrals
:program:`SEWARD` uses two different integration schemes. Repulsion type integrals (two-electron
integrals, electric field integrals, etc.) are evaluated by
the reduced multiplication scheme of the Rys quadrature :cite:`seward`.
All other integrals are computed by the Gauss--Hermite quadrature.
:program:`SEWARD` use spherical Gaussians as basis functions,
the only exception to this are the diffuse/polarization functions
of the 6-31G family of basis sets.
The double coset :cite:`dcf` formalism is used to treat symmetry.
:program:`SEWARD` is especially designed to handle ANO-type basis sets, however, segmented basis
sets are also processed.
At present the following limitations are built into :program:`SEWARD`:
.. include:: ../limitations.inc
.. _UG\:sec\:seward_dependencies:
Dependencies
............
:program:`SEWARD` usually runs after program :program:`GATEWAY`. In the same time, any input used
in :program:`GATEWAY` can be placed into :program:`SEWARD` input. However, it is recommended to
specify all information about the molecule and the basis set in :program:`GATEWAY` input.
:program:`SEWARD` does normally not depend on any other code, except of :program:`GATEWAY`.
There are two exceptions however.
The first one is when :program:`SEWARD` is used as a property module. In these cases the file
:file:`INPORB` has to have been generated by a wave function code. The second case, which is
totally transparent to the user, is when :program:`SEWARD` picks up the new Cartesian coordinates
generated by :program:`SLAPAF` during a geometry optimization.
.. _UG\:sec\:seward_files:
Files
.....
Input Files
:::::::::::
Apart form the standard input file
:program:`SEWARD` will use the following input files: :file:`RYSRW`, :file:`ABDATA`,
:file:`RUNFILE`, :file:`INPORB` (for calculation of properties) (:numref:`UG:sec:files_list`).
In addition, :program:`SEWARD` uses the following files:
.. class:: filelist
:file:`BASLIB`
The default directory for one-particle basis set information.
This directory contains files which are part
of the program system and could
be manipulated by the user in accordance with the instructions in
:numref:`UG:sec:the_basis_set_libraries` and following subsections.
New basis set files can be added to this directory by the local
|molcas| administrator.
:file:`QRPLIB`
Library for numerical mass-velocity plus Darwin potentials (used for ECPs).
Output files
::::::::::::
In addition to the standard output file
:program:`SEWARD` may generate the following files:
:file:`ONEINT`, :file:`ORDINT`, :file:`CHVEC`, :file:`CHRED`, :file:`CHORST`,
:file:`CHOMAP`, :file:`CHOR2F` (:numref:`UG:sec:files_list`).
.. _UG\:sec\:seward_input:
Input
.....
Below follows a description of the input to :program:`SEWARD`.
Observe that if
nothing else is requested
:program:`SEWARD` will by default compute the overlap, the
dipole, the quadrupole, the nuclear attraction, the kinetic energy,
the one-electron Hamiltonian, and the two-electron repulsion
integrals.
The input for each module is preceded by its name like: ::
&SEWARD
Argument(s) to a keyword, either individual or composed by several entries,
can be placed in a separated line or in the same line separated by a semicolon.
If in the same line, the first argument requires an equal sign after the
name of the keyword.
General keywords
::::::::::::::::
.. class:: keywordlist
:kword:`TITLe`
One line of title card follows.
.. xmldoc::
Enter one optional title card.
%%Keyword: Title
One line of title card follows.
:kword:`TEST`
:program:`SEWARD` will only process the input and generate a non-zero return code.
.. xmldoc::
%%Keyword: Test
SEWARD will only process the input and generate a non-zero
return code.
:kword:`ONEOnly`
:program:`SEWARD` will not compute the two-electron integrals.
.. xmldoc::
%%Keyword: Oneonly
SEWARD will not compute the two-electron integrals.
:kword:`NODKroll`
:program:`SEWARD` will not compute Douglas--Kroll integrals.
.. xmldoc::
%%Keyword: NoDK
SEWARD will not compute Douglas-Kroll integrals.
:kword:`DIREct`
Prepares for later integral-direct calculations. As with keyword
:kword:`OneOnly`, :program:`SEWARD` will evaluate no two-electron integrals.
.. xmldoc::
%%Keyword: Direct
Prepares for later integral-direct calculations. As with keyword
oneonly, SEWARD will evaluate no two-electron integrals.
:kword:`EXPErt`
Sets "expert mode", in which various default settings are
altered. Integral-direct calculations will be carried out
if the two-electron integral file is unavailable.
.. xmldoc::
Activates expert mode which will deactivate some checks. This will, for
example, allow the used to combine relativistic and non-relativistic basis sets.
%%Keyword: Expert
Sets "expert mode", in which various default settings are
altered. Integral-direct calculations will be carried out
if the two-electron integral file is unavailable.
:kword:`CHOLesky`
:program:`SEWARD` will Cholesky decompose the two-electron integrals using
default configuration (in particular, the decomposition threshold is
1.0d-4) of the decomposition driver.
The decomposition threshold can be changed using keyword :kword:`THRC`.
Default is to not decompose.
.. xmldoc::
.. xmldoc::
%%Keyword: Cholesky
Cholesky decompose the two-electron integrals using default settings.
:kword:`1CCD`
:program:`SEWARD` will Cholesky decompose the two-electron integrals using
the one-center approximation.
The decomposition threshold can be changed using keyword :kword:`THRC`.
Default is to not decompose.
.. xmldoc::
%%Keyword: 1CCD
One-center Cholesky decomposition of the two-electron integrals.
:kword:`THRCholesky`
Specify decomposition threshold for Cholesky decomposition of two-electron integrals
on the next line. Default value: 1.0d-4.
.. xmldoc::
%%Keyword: ThrCholesky
Specify decomposition threshold for Cholesky decomposition of two-electron integrals.
:kword:`SPAN`
Specify span factor (0 :math:`<` span :math:`\leq` 1) for Cholesky decomposition of two-electron integrals on the next line.
Span=1 implies full pivoting, Span=0 means no pivoting. If the span factor is too low, numerical errors may cause
negative diagonal elements and force the program to quit; if the span factor is too large, the execution time may
increase. Default value: 1.0d-2.
.. xmldoc::
%%Keyword: Span
Specify span factor (in between, but not equal to, 0 and 1) for Cholesky decomposition of two-electron integrals on the next line.
:kword:`LOW Cholesky`
:program:`SEWARD` will Cholesky decompose the two-electron integrals using
low accuracy (threshold 1.0d-4)
configuration of the decomposition driver.
Default is to not decompose.
.. xmldoc::
%%Keyword: Low
Cholesky decompose the two-electron integrals using low accuracy settings. Recommended.
:kword:`MEDIum Cholesky`
:program:`SEWARD` will Cholesky decompose the two-electron integrals using
medium accuracy (threshold 1.0d-6)
configuration of the decomposition driver.
Default is to not decompose.
.. xmldoc::
%%Keyword: Medium
Cholesky decompose the two-electron integrals using medium accuracy settings.
:kword:`HIGH Cholesky`
:program:`SEWARD` will Cholesky decompose the two-electron integrals using
high-accuracy (threshold 1.0d-8)
configuration of the decomposition driver.
Default is to not decompose.
.. xmldoc::
%%Keyword: High
Cholesky decompose the two-electron integrals using high accuracy settings.
:kword:`LDF`
Local Density Fitting: :program:`SEWARD` will fit each AO product using only auxiliary functions centered on the two parent atoms.
Fitting coefficients are computed and stored for use in later modules (only non-hybrid KS-DFT at the moment).
Requires an auxiliary basis set (generated by RICD in Gateway or externally defined).
Can not be combined with Cholesky and (global) DF/RI. LDF is turned off by default.
.. xmldoc::
%%Keyword: LDF
Local Density Fitting using auxiliary functions centered on the two parent atoms of each AO product.
:kword:`LDF1`
Local Density Fitting using auxiliary functions centered on the two parent atoms of each AO product. Equivalent to keyword :kword:`LDF`.
.. xmldoc::
%%Keyword: LDF1
Local Density Fitting using auxiliary functions centered on the two parent atoms of each AO product. Equivalent to keyword LDF.
:kword:`LDF2`
LDF using auxiliary functions centered on the two parent atoms of each AO product as well as the two-center functions required to achieve the given target accuracy.
.. xmldoc::
%%Keyword: LDF2
Local Density Fitting using auxiliary functions centered on the two parent atoms of each AO product as well as the two-center functions required to achieve the given target accuracy.
:kword:`TARGet accuracy`
Specify the target accuracy for LDF2 on the next line. Default value: threshold used to generate the aCD or acCD auxiliary basis set
(or 1.0d-4 in case of externally defined auxiliary basis sets).
.. xmldoc::
%%Keyword: TARG
Specify the target accuracy for LDF2 on the next line. Default value: threshold used to generate the aCD or acCD auxiliary basis set (or 1.0d-4 in case of externally defined auxiliary basis sets).
:kword:`APTH`
Specify the LDF/LDF2 atom pair prescreening threshold on the next line, thus defining which atom pairs are considered significant.
Default value: the target accuracy or the cutoff threshold for primitive integral evaluation, whichever is smaller.
.. xmldoc::
%%Keyword: APTH
Specify the LDF/LDF2 atom pair prescreening threshold on the next line, thus defining which atom pairs are considered significant. Default value: the target accuracy or the cutoff threshold for primitive integral evaluation, whichever is smaller.
:kword:`CLDF`
Constrained LDF/LDF2: specify constraint order on the next line (-1 for unconstrained, 0 for charge constraint). Default: unconstrained LDF.
.. xmldoc::
%%Keyword: CLDF
Constrained LDF/LDF2: specify constraint order on the next line (-1 for unconstrained, 0 for charge constraint). Default: unconstrained LDF.
.. xmldoc::
:kword:`FAKE CD/RI`
If CD/RI vectors are already available, :program:`SEWARD` will not redo work!
.. xmldoc::
%%Keyword: FAKE
If CD/RI vectors are already available, SEWARD will not redo work!
.. :kword:`MOLPro`
The integrals are normalized as in the program package
:program:`MOLPRO`. The default is the normalization
according to the double coset representatives (DCR) formalism
for conventional calculations; for Cholesky decomposition, the
default is the :kword:`MOLECULE` normalization (except when AMFI or
Douglas--Kroll is specified, where the DCR formalism is again
default).
.. .. xmldoc:: %%Keyword: MOLPRO
The integrals are normalized as in the program package
MOLPRO. The default is the normalization
according to the double coset representatives (DCR) formalism
for conventional calculations; for Cholesky decomposition, the
default is the MOLECULE normalization (except when AMFI or
Douglas-Kroll is specified, where the DCR formalism is again
default).
.. :kword:`MOLEcule`
The integrals are normalized as in the integral program
:program:`MOLECULE`. The default is the normalization
according to the double coset representatives (DCR) formalism
for conventional calculations; for Cholesky decomposition, the
default is the :kword:`MOLECULE` normalization (except when AMFI or
Douglas--Kroll is specified, where the DCR formalism is again
default).
.. .. xmldoc:: %%Keyword: MOLECULE
The integrals are normalized as in the integral program
MOLECULE. The default is the normalization
according to the double coset representatives (DCR) formalism
for conventional calculations; for Cholesky decomposition, the
default is the MOLECULE normalization (except when AMFI or
Douglas-Kroll is specified, where the DCR formalism is again
default).
.. xmldoc::
.. :kword:`MOLCas`
The integrals are normalized according to the double coset
representatives (DCR) formalism. This is the default for
conventional calculations. The default for Cholesky decompositions
is the :kword:`MOLECULE` normalization (except when AMFI or
Douglas--Kroll is specified, where the DCR formalism is again
default).
.. .. xmldoc:: %%Keyword: MOLCAS
The integrals are normalized according to the double coset
representatives (DCR) formalism. This is the default
for conventional calculations; for Cholesky decomposition, the
default is the MOLECULE normalization (except when AMFI or
Douglas-Kroll is specified, where the DCR formalism is again
default).
:kword:`JMAX`
The integer entry on the next line is the highest rotational quantum
number for which
:program:`SEWARD` will compute the rotational energy within the
rigid rotor model. The default value is 5.
.. xmldoc:: %%Keyword: JMAX
The integer entry on the next line is the highest rotational quantum
number for which
SEWARD will compute the rotational energy within the
rigid rotor model. The default value is 5.
:kword:`SYMMetry`
See the the description in the manual for the program :program:`GATEWAY`.
.. :kword:`SKIP`
The subsequent entry contains a sequence of integers, one for
each irreducible representation. By setting an integer to a nonzero
value all basis functions from the corresponding
irreducible representation will be removed.
The default is to skip no basis functions.
.. .. xmldoc:: %%Keyword: Skip
The subsequent entry contains a sequence of integers, one for
each irreducible representation. By setting an integer to a nonzero
value all basis functions from the corresponding
irreducible representation will be removed.
.. :kword:`NOTAbles`
Indicates that no tables will be used for the the roots and weights
of the Rys polynomials. The default is to use tables.
This option is used to verify the data base for
the calculation of roots and weights. Observe that the activation of
this option will make the program perform rather slow.
.. .. xmldoc:: %%Keyword: Notables
Indicates that no tables will be used for the the roots and weights
of the Rys polynomials. The default is to use tables.
:kword:`BASIs Set`
See the the description in the manual for the program :program:`GATEWAY`.
:kword:`ZMAT`
See the the description in the manual for the program :program:`GATEWAY`.
:kword:`XBAS`
See the the description in the manual for the program :program:`GATEWAY`.
:kword:`XYZ`
See the the description in the manual for the program :program:`GATEWAY`.
:kword:`NOGUessorb`
Disable automatic generation of starting orbitals with the GuessOrb procedure.
.. xmldoc::
%%Keyword: NOGUESSORB
Disable automatic generation of starting orbitals with the GuessOrb procedure.
:kword:`NODElete`
Do not delete any orbitals automatically.
.. xmldoc::
.. xmldoc::
%%Keyword: NODElete
Do not delete any orbitals automatically.
:kword:`SDELete`
Set the threshold for deleting orbitals based on the eigenvalues of the overlap matrix.
All eigenvalues with eigenvectors below this threshold will be deleted.
If you want no orbitals deleted use keyword :kword:`NODElete`.
.. xmldoc::
%%Keyword: SDELete
Set the threshold for deleting orbitals based on the eigenvalues of the overlap matrix.
:kword:`TDELete`
Set the threshold for deleting orbitals based on the eigenvalues of the kinetic energy matrix.
All eigenvalues with eigenvectors above this threshold will be deleted.
If you want no orbitals deleted use keyword :kword:`NODElete`.
.. xmldoc::
%%Keyword: TDELete
Set the threshold for deleting orbitals based on the eigenvalues of the kinetic energy matrix.
.. xmldoc::
:kword:`VERBose`
Force :program:`SEWARD` to print a bit more verbose.
.. xmldoc::
%%Keyword: Verbose
Force SEWARD to print a bit more verbose.
:kword:`EMBEdding`
Reads in an embedding potential from a file. It can also write out the
density and the electrostatic potential on a grid. It is a block keyword
which *must* be ended with :kword:`ENDEmbedding`.
.. xmldoc::
%%Keyword: Embedding
Reads in an embedding potential from a file and can output the density and ESP on a grid.
The subkeywords are:
:kword:`EMBInput` ---
Specifies the path to the file which contains the embedding potential
(e.g. ``EMBI=myEmbPot.dat``). The file contains a potential given on a grid. It
has the number of grid points in the first line. Then in five columns
data for each grid point is given (x, y, z, weight of this grid point,
value of the potential). Default is ``EMBPOT``.
:kword:`OUTGrid` ---
Specifies the path to a file containing a grid on which the output is
produced. It is only needed if you want to have the data on a grid different
from the one given in :kword:`EMBInput`. The columns for the potential and weights
are not needed in this file (and also not read in).
:kword:`WRDEnsity` ---
Switches on the calculation of the final electron density on a grid. The
output file path must be specified along with this keyword (e.g. ``WRDE=myDens.dat``).
:kword:`WREPotential` ---
Switches on the calculation of the electrostatic potential on a grid. The
output file path must be specified along with this keyword (e.g. ``WREP=myESP.dat``).
:kword:`ENDEmbedding` ---
Ends the :kword:`EMBEdding` section. This keyword *must* be present.
The :kword:`EMBEdding` feature is currently only supported by the SCF part of |molcas|.
.. xmldoc::
Keywords associated to one-electron integrals
:::::::::::::::::::::::::::::::::::::::::::::
.. class:: keywordlist
:kword:`MULTipoles`
Entry which specifies the highest order of the
multipole for which integrals will be generated. The default center
for the dipole moment operator is the origin.
The default center for the higher order operators is the
center of the nuclear mass.
The default is to do up to quadrupole moment integrals (2).
.. xmldoc::
.. xmldoc::
%%Keyword: Multipoles
Entry which specifies the highest order of the
multipole for which integrals will be generated.
For details consult the manual.
:kword:`CENTer`
This option is used to override the default selection of the origin
of the multipole moment operators.
On the first entry add an integer entry specifying the number of
multipole moment operators for which the origin of expansion
will be defined.
Following this, one entry for each operator, the order of
the multipole operator and the coordinates of the center (in au) of
expansion are specified.
The default is the origin for 0th and 1st multipoles, and the center of mass for higher-order multipoles.
.. xmldoc::
%%Keyword: Center
This option is used to override the default selection of the origin
of the multipole moment operators.
On the first entry specify the number of such modifications.
On the following entries enter first the order of the multipole moment operators
followed by the coordinates of the origin of the operator.
:kword:`RELInt`
Requests the computation of mass-velocity and one-electron Darwin
contact term integrals for the calculation of a first order correction
of the energy with respect to relativistic effects.
.. xmldoc::
%%Keyword: Relint
Requests the computation of mass-velocity and one-electron Darwin
contact term integrals for the calculation of a first order correction
of the energy with respect to relativistic effects.
.. :kword:`BSSMethod`
Request that the one-electron Hamiltonian include the scalar relativistic
effects according to the so-called Barysz--Sadlej--Snijders transformation.
.. .. xmldoc:: %%Keyword: BSSmethod
Request that the one-electron Hamiltonian include the scalar relativistic
effects according to the so-called Barysz-Sadlej-Snijders transformation.
.. xmldoc::
:kword:`RELAtivistic`
Request arbitrary scalar relativistic Douglas--Kroll--Hess (DKH) correction to the one-electron Hamiltonian
and the so-called picture-change correction to the property integrals (multipole moments
and electronic potential related properties). An argument of the form ``RXXPyy`` follows.
Here XX represents the order of the DKH correction to the one-electron Hamiltonian and
yy the order of the picture-change correction. The character P denotes the parameterization
used in the DKH procedure.
The possible parametrizations P of the unitary transformation used
in the DKH transformation supported by |molcas| are:
.. container:: list
``P=O``: Optimum parametrization (OPT)
``P=E``: Exponential parametrization (EXP)
``P=S``: Square-root parametrization (SQR)
``P=M``: McWeeny parametrization (MCW)
``P=C``: Cayley parametrization (CAY)
Hence, the proper keyword for the 4th order relativistically corrected one-electron
Hamiltonian and 3rd order relativistically corrected
property integrals in the EXP parameterization would read as R04E03. If yy is larger than XX it is set to
XX. If yy is omitted it will default to same value as XX. Recommended orders and parametrization is
R02O02.
Since the EXP parameterization employs a fast algorithm, it is
recommended for high order DKH transformation.
.. xmldoc::
%%Keyword: RELAtivistic
Request arbitrary scalar relativistic Douglas-Kroll-Hess (DKH) correction to the one-electron Hamiltonian
and the so-called picture-change correction to the property integrals (multipole moments
and electronic potential related properties). An argument of the form RXXPyy follows
Here XX represents the order of the DKH correction to the one-electron Hamiltonian and
yy the order of the picture-change correction. The character P denotes the parameterization
used in the DKH procedure.
The possible parametrizations P of the unitary transformation used
in the DKH transformation supported by MOLCAS are:
||(P=O) Optimum parametrization (OPT);
||(P=E) Exponential parametrization (EXP);
||(P=S) Square-root parametrization (SQR);
||(P=M) McWeeny parametrization (MCW);
||(P=C) Cayley parametrization (CAY).
Hence, the proper keyword for the 4th order relativistically corrected one-electron
Hamiltonian and 3rd order relativistically corrected
property integrals in the EXP parameterization would read as R04E03. If yy is larger than XX it is set to
XX. If yy is omitted it will default to same value as XX. Recommended orders and parametrization is
R02O02.
Since the EXP parameterization employs a fast algorithm, it is
recommended for high order DKH transformation.
:kword:`RLOCal`
Request local approximation to the relativistic exact decoupling approaches such
as X2C, BSS and DKH. This option cannot be used together with point group symmetry.
.. xmldoc::
%%Keyword: Rlocal
Request local approximation to the relativistic exact decoupling approaches such
as X2C, BSS and DKH. This option cannot be used together with point group symmetry.
.. xmldoc::
:kword:`Grid Input`
Specification of numerical quadrature parameters, consult the numerical quadrature section of this
manual.
Additional keywords for property calculations
:::::::::::::::::::::::::::::::::::::::::::::
.. class:: keywordlist
:kword:`VECTors`
Requests a property calculation. For this purpose a file,
:file:`INPORB`,
must be available, which contains the MO's and occupation numbers
of a wave function. A custom filename can be given with :kword:`FileOrb`.
.. xmldoc::
.. xmldoc::
%%Keyword: Vectors
Requests a property calculation. For this purpose an INPORB file must be available.
:kword:`FILEorb`
The next line specifies the filename containing the orbitals and occupation numbers
from which the properties will be computed. By default a file named :file:`INPORB`
will be used.
.. xmldoc::
%%Keyword: FileOrb
The next line specifies the filename containing the orbitals and occupation numbers
from which the properties will be computed. By default a file named INPORB
will be used.
:kword:`ORBCon`
The keyword will force :program:`SEWARD`
to produce a list of the orbital
contributions to the properties being computed. The default is to
generate a compact list.
.. xmldoc::
%%Keyword: Orbcon
The keyword will force SEWARD to produce a list of the orbital
contributions to the properties being computed. The default is to
generate a compact list.
:kword:`THRS`
The real entry on the following line specifies the threshold for
the occupation number of an orbital in order for the
:kword:`OrbCon`
option to list the contribution of that orbital to a property.
The default is 1.0d-6.
.. xmldoc::
Specify the threshold for the occupation number of a orbital to allow that
this orbital is included when listing orbital contributions to properties.
%%Keyword: Thrs
The real entry on the following line specifies the threshold for
the occupation number of an orbital in order for the
keyword "OrbCon" option to list the contribution of that orbital to a
property. The default is 1.0d-6.
:kword:`ORBAll`
When :kword:`OrbCon` is present, the keyword will force
:program:`SEWARD` to produce a list of the computed properties
of all orbitals (including unoccupied orbitals), and the
properties are not weighted by orbital occupation numbers.
The total electronic and nuclear
contributions printed are the same as those printed by using
:kword:`OrbCon` without :kword:`OrbAll`.
.. xmldoc::
%%Keyword: OrbAll
Print computed properties for all orbitals (including unoccupied orbitals),
and not weighted by orbital occupation numbers.
Requires "OrbCon".
.. xmldoc::
Keywords for two-electron integrals
:::::::::::::::::::::::::::::::::::
.. class:: keywordlist
:kword:`NOPAck`
The two-electron integrals will not be packed. The default is to
pack the two-electron integrals.
.. xmldoc::
.. xmldoc::
%%Keyword: Nopack
The two-electron integrals will not be packed. The default is to
pack the two-electron integrals.
:kword:`PKTHre`
An entry specifies the desired accuracy for the packing
algorithm, the default is 1.0d-14.
.. xmldoc::
Specifies the desired accuracy for the packing algorithm.
%%Keyword: Pkthre
An entry specifies the desired accuracy for the packing
algorithm, the default is 1.0d-14.
:kword:`STDOut`
Generate a two-electron integral file according to the standard of
version 1 of |molcas|. The default is to generate the
two-electron integrals according to the standard used since version 2 of
|molcas|.
.. xmldoc:: %%Keyword: Stdout
Generate a two-electron integral file according to the standard of
version 1 of MOLCAS. The default is to generate the
two-electron integrals according to the standard used since version 2 of
MOLCAS.
:kword:`THREshold`
Threshold for writing integrals to disk follows. The default is 1.0d-14.
.. xmldoc::
Specify the threshold for writing integrals to disk.
%%Keyword: Threshold
Threshold for writing integrals to disk follows. The default is 1.0d-14.
:kword:`CUTOff`
Threshold for ignoring the calculation of integrals based on the
pair prefactor follows. The default is 1.0d-16.
.. xmldoc::
Specify the threshold for ignoring the calculation of integrals based on the pair prefactors.
%%Keyword: Cutoff
Threshold for ignoring the calculation of integrals based on the
pair prefactor follows on the next line. The default is 1.0d-16.
.. xmldoc::
Keywords associated to electron-molecule scattering calculations within the framework of the :math:`R`\-matrix method
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
This section contains keyword which control the radial numerical integration
of the diffuse basis functions describing the scattered electrons in the
variational :math:`R`\-matrix approach. The activation of this option is controlled
by that the center of the diffuse basis is assigned the unique atom label DBAS.
.. class:: keywordlist
:kword:`RMAT`
Radius of the :math:`R`\-matrix sphere (in bohr). This sphere is centered at the
coordinate origin. The default is 10 bohr.
.. xmldoc:: %%Keyword: RMAT
Radius of the R-matrix sphere (in bohr). This sphere is centered
at the coordinate origin. Default value is set to 10 bohr.
:kword:`RMEA`
Absolute precision in radial integration.
The default is 1d-9.
.. xmldoc:: %%Keyword: RMEA
Absolute precision in radial integration for R-matrix calculation.
The default is 1d-9.
:kword:`RMER`
Relative precision in radial integration.
The default is 1d-14.
.. xmldoc:: %%Keyword: RMER
Relative precision in radial integration for R-matrix calculation.
The default is 1d-14.
:kword:`RMQC`
Effective charge of the target molecule.
This is the effective charge seen by the incident electron outside
of the :math:`R`\-matrix sphere. The default is 0d0.
.. xmldoc:: %%Keyword: RMQC
Effective charge of the target molecule for R-matrix calculation.
This is the effective charge seen by the incident electron outside
of the R-matrix sphere. The default is 0d0.
:kword:`RMDI`
Effective dipole of the target molecule.
This is the effective dipole seen by the incident electron outside
of the :math:`R`\-matrix sphere. The default is (0d0,0d0,0d0).
.. xmldoc:: %%Keyword: RMDI
Effective dipole of the target molecule for R-matrix calculation.
This is the effective dipole seen by the incident electron outside
of the R-matrix sphere. The default is (0d0,0d0,0d0).
:kword:`RMEQ`
Minimal value of the effective charge of the target molecule
to be considered. This is also the
minimal value of the components of the effective dipole
to be considered. Default is 1d-8
.. xmldoc:: %%Keyword: RMEQ
Minimal value of the effective charge of the target molecule
to be considered in R-matrix calculation. This is also the
minimal value of the components of the effective dipole
to be considered in R-matrix calculation. Default is 1d-8.
:kword:`RMBP`
Parameter used for test purposes in the definition of the
Bloch term. Default is 0d0.
.. xmldoc:: %%Keyword: RMBP
Parameter used for test purposes in the definition of the
Bloch term in R-matrix calculation. Default is 0d0.
:kword:`CELL`
Defines the three vectors of the unit cell (:math:`\vec{e}_1`, :math:`\vec{e}_2`, :math:`\vec{e}_3`).
The optional keyword
*Angstrom* before the definition of vectors would read data in Å.
Must consist of three entries (four in the case of Å) which correspond to coordinates of the vectors. All the atoms which
are defined after that key are considered as the atoms of the cell.
.. xmldoc:: %%Keyword: CELL
Defines the three vectors of the unit cell (e1,e2,e3).
The optional keyword
Angstrom before the definition of vectors would read data in A.
Must consist of three entries (four in the case of A) which correspond to coordinates of the vectors.
All the atoms which
are defined after that key are considered as the atoms of the cell.
:kword:`SPREad`
Three integer numbers :math:`n_1`, :math:`n_2`, :math:`n_3` which define the spread of the unit cell along the unit cell vectors.
For example, ``0 0 2`` would add all cell's atoms translated on :math:`-2\vec{e}_3`, :math:`-\vec{e}_3`, :math:`\vec{e}_3`, :math:`2\vec{e}_3`.
This key must be placed **before** the definition of the unit cell atoms.
.. xmldoc:: %%Keyword: SPREAD
Three integer numbers n_1, n_2, n_3 which define the spread of the unit cell along the unit cell vectors.
For example, 0 0 2 would add all cell's atoms translated on -2*e3, -e3, e3, 2*e3.
This key must be placed before the definition of the unit cell atoms.
Below follows an input for the calculation of integrals of a carbon
atom. The comments in the input gives a brief explanation of the
subsequent keywords.
.. extractfile:: ug/SEWARD.C.input
&SEWARD
Title= This is a test deck!
* Remove integrals from a specific irreps
Skip= 0 0 0 0 1 1 1 1
* Requesting only overlap integrals.
Multipole= 0
* Request integrals for diamagnetic shielding
DSHD= 0.0 0.0 0.0; 1; 0.0 0.0 0.0
* Specify a title card
* Request only one-electron integrals to be computed
OneOnly
* Specify group generators
Symmetry= X Y Z
* Enable an inline basis set
Expert
* Specify basis sets
Basis set
C.ANO-L...6s5p3d2f.
Contaminant d
C 0.0 0.0 0.0
End of basis
The basis set label and the all electron basis set library
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
.. compound::
The label, which defines the basis set for a given atom or set of atoms,
is given as input after the
keyword :kword:`Basis set`. It has the following general
structure (notice that the last
character is a period): ::
atom.type.author.primitive.contracted.aux.
where the different identifiers have the following meaning:
.. class:: whatnotlist
``atom``
Specification of the atom by its chemical symbol.
``type``
Gives the type of basis set (ANO, STO, ECP, etc.) according to
specifications given in the basis set library, *vide supra*.
Observe that the upper cased character of the type label
defines the file name in the basis directory.
``author``
First author in the publication where that basis set appeared.
``primitive``
Specification of the primitive set (e.g. 14s9p4d3f).
``contracted``
Specification of the contracted set to be selected. Some basis
sets allow only one type of contraction, others all types up
to a maximum. The first basis functions for each angular
momentum is then used.
**Note**, for the basis set types ANO and ECP, on-the-fly decontraction of the most
diffuse functions are performed in case the number of contracted functions specified in this field
exceeds what formally is specified in the library file.
``aux``
Specification of the type of AIMP, for instance, to choose between
non-relativistic and relativistic core AIMP's.
Only the identifiers ``atom``, ``type``,
and ``contracted`` have to be included in
the label. The others can be left out. However, the periods have to be
kept. Example --- the basis set label
"``C.ano-s...4s3p2d.``"
will by |molcas| be
interpreted as
"``C.ano-s.Pierloot.10s6p3d.4s3p2d.``",
which is the first
basis set in the ANO-S file in the
basis directory that fulfills the specifications given.
More information about basis set format can be found in
the section Advanced examples.
.. index::
single: Numerical Integration
.. _UG\:sec\:dft:
Numerical integration
---------------------
Various Density Functional Theory (DFT) models can be used in |molcas|.
Energies and analytical gradients are available for all DFT models.
In DFT the exact exchange present in HF theory is replaced by a more general
expression, the exchange-correlation functional, which accounts for both the exchange energy, :math:`E_{\text{X}} [P]`
and the electron correlation energy, :math:`E_{\text{C}} [P]`.
.. _UG\:sec\:df_description:
Description
...........
We shall now describe briefly how the exchange and correlation energy terms look like.
The functionals used in DFT are integrals of some function of the electron density and optionally the gradient
of the electron density
.. math:: E_{\text{X}}[P] = \int f(\rho_{\alpha}(r), \rho_{\beta}(r), \nabla \rho_{\alpha}(r), \nabla \rho_{\beta}(r))\;dr
The various DFT methods differ in which function, :math:`f`, is used for :math:`E_{\text{X}}[P]` and for :math:`E_{\text{C}}[P]`.
In |molcas| pure DFT methods are supported, together with hybrid methods, in which the exchange functional
is a linear combination of the HF exchange and a functional integral of the above form.
The latter are evaluated by numerical quadrature.
In the :program:`SEWARD` input the parameters for the numerical integration can be set up.
In the :program:`SCF` and :program:`RASSCF` inputs the keywords for
using different functionals can be specified.
Names for the various pure DFT models are given by combining the names for the exchange and correlation functionals.
The DFT gradients has been implemented for both the fixed and the moving grid approach :cite:`Johnson:93,Handy:93,Baker:94`.
The latter is known to be translationally invariant by definition and is recommended in geometry optimizations.
.. .. _UG\:sec\:dft_files:
Files
.....
.. class:: filelist
:file:`RUNFILE`
The run file will contain the parameters defining and controlling the numerical integration.
Input
.....
Below follows a description of the input to the numerical integration utility in the
:program:`SEWARD` input.
Compulsory keywords
.. class:: keywordlist
:kword:`GRID Input`
This marks the beginning of the input to the numerical integration utility.
.. xmldoc::
%%Keyword: Grid input
Specification of numerical quadrature parameters.
:kword:`END Of Grid-Input`
This marks the end of the input to the numerical integration utility.
Optional keywords
.. class:: keywordlist
:kword:`GRID`
It specifies the quadrature quality.
The possible indexes that can follow are
COARSE, SG1GRID, FINE, ULTRAFINE,
following the Gaussian98 convention.
Default is FINE.
.. xmldoc::
%%Keyword: Grid (NQ)
It specifies the quadrature quality.
The possible indexes that can follow are
COARSE, SG1GRID, FINE, ULTRAFINE,
following the Gaussian98 convention.
Default is FINE.
.. :kword:`GLOBal`
It activates the use of the global partitioning technique.
.. .. xmldoc:: %%Keyword: Global
It activates the use of the global partitioning technique.
:kword:`RQUAd`
It specifies the radial quadrature scheme.
Options are LOG3 (Mura and Knowles) :cite:`Mura:96`, BECKE
(Becke) :cite:`BeckeG:88`, MHL (Murray et al.) :cite:`Murray:93`, TA (Treutler and
Ahlrichs, defined for :math:`\ce{H}`\--\ :math:`\ce{Kr}`) :cite:`Treutler:95`, and LMG (Lindh et
al.) :cite:`LMG:01`, respectively. The default is MHL.
.. xmldoc::
%%Keyword: RQuad (NQ)
It specifies the radial quadrature scheme.
Options are LOG3 (Mura and Knowles), BECKE (Becke) , MHL (Murray et a.), TA (Treutler and
Ahlrichs, defined for H-Kr), and LMG (Lindh et al.), respectively. The default is MHL.
.. xmldoc::
:kword:`GGL`
It activates the use of Gauss and Gauss--Legendre angular quadrature.
Default is to use the Lebedev angular grid.
.. xmldoc:: %%Keyword: GGL (NQ)
It activates the use of Gauss and Gauss-Legendre angular quadrature.
Default is to use the Lebedev angular grid.
:kword:`LEBEdev`
It turns on the Lebedev angular grid.
.. xmldoc:: %%Keyword: Lebedev (NQ)
It turns on the Lebedev angular grid.
:kword:`LOBAtto`
It activates the use of Lobatto angular quadrature.
Default is to use the Lebedev angular grid.
.. xmldoc:: %%Keyword: Lobatto (NQ)
It activates the use of Lobatto angular quadrature.
Default is to use the Lebedev angular grid.
:kword:`LMAX`
It specifies the angular grid size. Default is 29.
.. xmldoc::
%%Keyword: LMax (NQ)
Specifies the highest order of a real spherical harmonic which the angular grid will integrate exact. Default is 29.
:kword:`NGRId`
It specifies the maximum number of grid points to process at one instance.
Default is 128 grid points.
.. xmldoc::
%%Keyword: nGrid (NQ)
It specifies the maximum number of grid points to process at one instance.
Default is 128 grid points.
:kword:`NOPRunning`
It turns off the the angular prunning. Default is to prune.
.. xmldoc::
%%Keyword: Noprunning (NQ)
It turns off the the angular prunning. Default is to prune.
:kword:`NR`
It is followed by the number of radial grid points. Default is 75 radial grid points.
.. xmldoc::
%%Keyword: nR (NQ)
It is followed by the number of radial grid points. Default is 75 radial grid points.
.. :kword:`WHOLe`
It activates the use of routines which scan the whole atomic grid for
each sub block. Default is to only scan the relevant part.
.. .. xmldoc:: %%Keyword: Whole (NQ)
It activates the use of routines which scan the whole atomic grid for
each sub block. Default is to only scan the relevant part.
:kword:`FIXEd grid`
Use a fixed grid in the evaluation of the gradient. This corresponds to
using the grid to numerically evaluate the analytic gradient expression.
Default is to use a moving grid.
.. xmldoc::
:kword:`RTHReshold`
It is followed by the value for the the radial threshold.
Default value is 1.0D-13.
.. xmldoc::
%%Keyword: RThreshold (NQ)
Follows the value for the the radial threshold.
Default value is 1.0D-13.
:kword:`T_X`
Threshold for screening in the assembling of the density on the grid.
Default value is 1.0D-18.
.. xmldoc::
%%Keyword: T_X (NQ)
Threshold for screening in the assembling of the density on the grid.
Default value is 1.0D-18.
:kword:`T_Y`
Threshold for screening in the assembling of the integrals.
Default value is 1.0D-11.
.. xmldoc::
%%Keyword: T_Y (NQ)
Threshold for screening in the assembling of the integrals.
Default value is 1.0D-11.
:kword:`NOSCreening`
Turn off any screening in the numerical integration.
.. xmldoc::
%%Keyword: NOSCreening (NQ)
Turn off any screening in the numerical integration.
:kword:`CROWding`
The crowding factor, according to MHL, used in the pruning of the angular
grid close to the nuclei. Default value 3.0.
.. xmldoc::
%%Keyword: CROWding (NQ)
The crowding factor, according to MHL, used in the pruning of the angular
grid close to the nuclei. Default value 3.0.
.. xmldoc::
.. xmldoc::
The :program:`SCF` and :program:`RASSCF` programs have
their own keywords to decide which functionals to use in a DFT calculation.
Below follows an example of a DFT calculation with two different functionals.
.. extractfile:: ug/DFT.H.input
&GATEWAY
Basis set
H.3-21G.....
H1 0.0 0.0 0.0
End of basis
&SEWARD
Grid input
RQuad= Log3; nGrid= 50000; GGL; lMax= 26; Global
End of Grid Input
&SCF; Occupations=1; KSDFT=LDA5; Iterations= 1 1
&SCF; Occupations= 1; KSDFT=B3LYP; Iterations= 1 1
Relativistic operators
----------------------
The current different implementation of all relativistic operators in |molcas| as
described in the following sections has been programmed and tested in
Ref. :cite:`R2C_review`
Using the Douglas--Kroll--Hess Hamiltonian
..........................................
For all-electron calculations, the preferred way is to use the scalar-relativistic
Douglas--Kroll--Hess (DKH) Hamiltonian, which, in principle, is available up to arbitrary
order in Molcas; for actual calculations, however,
the standard 2nd order is usually fine, but one may use a higher order than 8th order
by default to be on the safe side.
.. compound::
The arbitrary-order Hamiltonian is activated by setting ::
RXXPyy
somewhere in the :program:`SEWARD` input, where
the ``XX`` denotes the order of the DKH Hamiltonian in the external potential.
I.e., for the standard 2nd-order Hamiltonian you may use ``R02O``.
Note
in particular that the parametrization ``P`` does not affect the Hamiltonian up to
fourth order. Therefore, as long as you run calculations with DKH Hamiltonians below
5th order you may use any symbol for the parametrization as they would all yield the
same results.
The possible parametrizations ``P`` of the unitary transformation used
in the DKH transformation supported by |molcas| are:
.. container:: list
``P=O``: Optimum parametrization (OPT)
``P=E``: Exponential parametrization (EXP)
``P=S``: Square-root parametrization (SQR)
``P=M``: McWeeny parametrization (MCW)
``P=C``: Cayley parametrization (CAY)
Up to fourth order (``XX``\=04) the DKH Hamiltonian is independent of the chosen
parametrization.
Higher-order DKH Hamiltonians depend slightly on the chosen parametrization of the unitary
transformations applied in order to decouple the Dirac Hamiltonian.
Since the EXP parameterization employs a fast algorithm :cite:`DKH_polynomial`, it is recommended
for high-order DKH transformation.
For details on the arbitrary-order DKH Hamiltonians see :cite:`DKH_Theory` with respect to theory,
:cite:`DKH_Implementation` with respect to aspects of implementation, and
:cite:`DKH_Principles` with respect to general principles of DKH.
The current version of |molcas| employs different algorithms,
but the polynomial cost scheme of the DKH implementation as described in :cite:`DKH_polynomial` is
used as the default algorithm. The implementation in MOLCAS has been presented in :cite:`R2C_review`.
For details on the different parametrizations of the unitary transformations see :cite:`DKH_Parameterization`.
Douglas--Kroll--Hess transformed properties
...........................................
As mentioned above, four-component molecular property operators need to be DKH
transformed as well when going from a four-component to a two- or one-component description;
the results do not coincide with the well-known corresponding nonrelativistic expressions
for a given property but are properly picture change corrected.
.. compound::
The transformation of electric-field-like molecular property operators can be carried
out for any order smaller or equal to the order chosen for the scalar-relativistic DKH Hamiltonian.
In order to change the default transformation of order 2, you may concatenate the
input for the DKH Hamiltonian by 2 more numbers specifying the order in the property, ::
RxxPyy
where ``yy`` denotes the order of the Hamiltonian starting with first order 01.
The DKH transformation is then done automatically for all one-electron electric-field-like
one-electron property matrices.
Also note that the current implementation of both the Hamiltonian and the property
operators is carried out in the full, completely decontracted basis set of the
molecule under consideration. The local nature of the relativistic contributions is not
yet exploited and hence large molecules may require considerable computing time for
all higher-order DKH transformations.
For details on the arbitrary-order DKH properties see :cite:`DKH_Theory2` with respect to theory
and :cite:`DKH_Implementation2,R2C_review` with respect to implementation aspects.
Using the X2C/Barysz--Sadlej--Snijders Hamiltonian
..................................................
Exact decoupling of the relativistic Dirac Hamiltonian can be achieved with infinite-order
approaches, such as the so-called X2C (exact-two-component) and BSS (Barysz--Sadlej--Snijders)
method. In Molcas, both methods are available for all-electron calculations. The
evaluation of transformation matrices employs a non-iterative scheme.
.. which is superior to the iterative scheme in convergence behavior and computational cost.
The exact decoupling Hamiltonian is activated by setting either ``RX2C`` or ``RBSS``
somewhere in the :program:`SEWARD` input, where ``RX2C`` and ``RBSS`` denote using the
scalar (one-component) X2C and BSS Hamiltonian respectively. The one-electron Hamiltonian
as well as the property integrals will be transformed according to the given exact decoupling method.
In other words, all property integrals are by default picture change corrected.
The computation time of the X2C/BSS method is almost the same as of the DKH method at 8th order,
while X2C is a little bit faster than BSS since the additional free-particle Foldy--Wouthuysen
transformation is skipped in the X2C approach :cite:`R2C_review`. For molecules including only light atoms,
the DKH method with low orders (< 8) is enough to account for the relativistic effects.
.. As for heavy
elements containing molecules, DKH with low orders is not accurate enough while DKH with high
orders is computational expensive, the X2C method is then recommended in this case.
The differences between different exact decoupling relativistic methods are very small compared
to errors introduced by other approximations, such as the basis set incompleteness, approximate
density functionals, etc. Therefore, any exact decoupling model is acceptable for the
treatment of relativistic effects in molecular calculations.
For details on the exact decoupling approaches see :cite:`R2C_review` with respect to theories and
comparison of numerical results, :cite:`X2C_kut05jcp,X2C_liu06jcp,X2C_pen07jcp` for the X2C method, and
:cite:`BSS_bar97ijqc,BSS_ked07cpl` for the BSS method.
Local approximation to relativistic decoupling
..............................................
The computational cost for relativistic transformations increases rapidly if the molecule becomes
larger. The local DLU scheme :cite:`DLU_Theory` was proposed to reduce the computational cost
based on the atomic decomposition of the (unitary) decoupling transformation. It is important to note that
the DLU scheme can be applied to any kind of relativistic approaches mentioned above (i.e., DKH, BSS, and X2C). It was found :cite:`DLU_Theory`
that the DLU approximation introduces very small errors for total energies, which are less than
0.01 milli-hartree for molecules including heavy atoms.
The local approximation is activated by setting :kword:`RLOCal` somewhere in the :program:`SEWARD` input.
The direct local approximation to the Hamiltonian, called DLH in Ref. :cite:`DLU_Theory` may be activated by setting ``RLOCal=DLH``.
However, as DLH is not superior to the DLU scheme, but introduces slightly larger errors, it is not recommended.
The picture-change effect for molecular properties is automatically taken care of when a local approximation is employed for the transformed
operator. The default order of DKH transformed properties is set to the same as the order of the DKH Hamiltonian.
It is important to note the local approximation cannot be used together with point group symmetry
in the current implementation. Because the relativistic transformation is applied in the molecular
orbital (MO) representation instead of the atomic orbital (AO) representation. Thus, the program will
report an error and exit if symmetry is used.
.. xmldoc::
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