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6.34 seward

The 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.

In the following three subsection we will in detail describe the input parameters for analytic integration, numerical integration, and reaction fields.

6.34.1 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.


6.34.1.1 Description

SEWARD is able to compute the following integrals:
  • kinetic energy,
  • nuclear attraction,
  • two electron repulsion (optionally Cholesky decomposed),
  • n'th (default 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 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.

In general these integrals will be written to a file, possibly in the form of Cholesky vectors (two-electron integrals only). However, 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 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 [104]. All other integrals are computed by the Gauss-Hermite quadrature. 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 [105] formalism is used to treat symmetry. 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 SEWARD:


Max number of unique basis functions: 2000
Max number of symmetry independent centers: 500
Highest angular momentum: 15
Highest symmetry point group: D2h



6.34.1.2 Dependencies

SEWARD usually runs after program GATEWAY. In the same time, any input used in GATEWAY can be placed into SEWARD input. However, it is recommended to specify all information about the molecule and the basis set in GATEWAY input.

SEWARD does normally not depend on any other code, except of GATEWAY. There are two exceptions however. The first one is when SEWARD is used as a property module. In these cases the file INPORB has to have been generated by a wave function code. The second case, which is totally transparent to the user, is when SEWARD picks up the new Cartesian coordinates generated by SLAPAF during a geometry optimization.


6.34.1.3 Files

6.34.1.3.1 Input Files

Apart form the standard input file SEWARD will use the following input files: RYSRW, ABDATA, RUNFILE, INPORB (for calculation of properties) ([*]). In addition, SEWARD uses the following files:
FileContents
BASLIBThe 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 the section [*] and following subsections. New basis set files can be added to this directory by the local MOLCAS administrator.
QRPLIBLibrary for numerical mass-velocity plus Darwin potentials (used for ECPs).

6.34.1.3.2 Output files

In addition to the standard output file SEWARD may generate the following files: ONEINT, ORDINT, CHVEC, CHRED, CHORST, CHOMAP, CHOR2f ([*]).


6.34.1.4 One-Electron Integral Labels

The storage of one-electron integrals on disk is facilitated by the one-electron integral I/O facility. The internal structure of the one-electron file and the management is something which the user normally do not need to worry about. However, for the general input section of the FFPT, the user need to know the name and structure of the internal labels which the one-electron integral I/O facility associates with each type of one-electron integral. The labels are listed and explained here below for reference. The component index is also utilized by the one-electron integral I/O facility to discriminate the various components of the one-electron integrals of a certain type, for example, the dipole moment integrals have three components (1=x-component, 2=y-component, 3=z-component). The component index is enumerated as a canonical index over the powers of the Cartesian components of the operator (e.g. multipole moment, velocity, electric field, etc.). The order is defined by following pseudo code,

      Do ix = nOrder, 0, -1
         Do iy = nOrder-ix, 0, -1
            iz = nOrder-ix-iy
         End Do
      End Do,
where nOrder is the total order of the operator, for example, nOrder=2 for the electric field gradient and the quadrupole moment operator.

Label Explanation
'Mltpl nn' the nn'th order Cartesian multipole moments.
'MltplS ' the overlap matrix used in the semi-empirical NDDO method.
'Kinetic ' the kinetic energy integrals.
'Attract ' the electron attraction integrals.
'AttractS' the electron attraction integrals used in the semi-empirical NDDO method.
'PrjInt ' the projection integrals used in ECP calculations.
'M1Int ' the M1 integrals used in ECP calculations.
'M2Int ' the M2 integrals used in ECP calculations.
'SROInt ' the spectrally resolved operator integrals used in ECP calculations.
'XFdInt ' the external electric field integrals.
'MassVel ' the mass-velocity integrals.
'Darwin ' the Darwin one-electron contact integrals.
'Velocity' the velocity integrals.
'EF0nnnnn' the electric potential at center nnnnn.
'EF1nnnnn' the electric field at center nnnnn.
'EF2nnnnn' the electric field gradient at center nnnnn.
'AngMom ' the angular momentum integrals.
'DMS ' the diamagnetic shielding integrals.
'Wellnnnn' the nnnn'th set of spherical well integrals.
'OneHam ' the one-electron Hamiltonian.
'AMProd ' the hermitized product of angular momentum integrals.
'AMFI ' the atomic mean field integrals.


6.34.1.5 Input

Below follows a description of the input to SEWARD. Observe that if nothing else is requested 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.

6.34.1.5.1 General keywords

KeywordMeaning
TITLeOne line of title card follows.
TESTSEWARD will only process the input and generate a non-zero return code.
ONEOnlySEWARD will not compute the two-electron integrals.
NODKrollSEWARD will not compute Douglas-Kroll integrals.
DIREctPrepares for later integral-direct calculations. As with keyword OneOnly, SEWARD will evaluate no two-electron integrals.
EXPErtSets ``expert mode'', in which various default settings are altered. Integral-direct calculations will be carried out if the two-electron integral file is unavailable.
CHOLeskySEWARD will Cholesky decompose the two-electron integrals using default configuration (in particular, the decomposition threshold is 1.0d-4) of the decomposition driver. The configuration may be tailored using the ChoInput section. Default is to not decompose.
LOW CholeskySEWARD will Cholesky decompose the two-electron integrals using low-accuracy (threshold 1.0d-4) configuration of the decomposition driver (the configuration may be tailored using the ChoInput section). Default is to not decompose.
MEDIum CholeskySEWARD will Cholesky decompose the two-electron integrals using medium-accuracy (threshold 1.0d-6) configuration of the decomposition driver (the configuration may be tailored using the ChoInput section). Same as Cholesky. Default is to not decompose.
HIGH CholeskySEWARD will Cholesky decompose the two-electron integrals using high-accuracy (threshold 1.0d-8) configuration of the decomposition driver (the configuration may be tailored using the ChoInput section). Default is to not decompose.
FAKE CD/RIIf CD/RI vectors are already available, SEWARD will not redo work!
JMAXThe 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.
SYMMetrySee the the description in the manual for the program GATEWAY
BASIs SetSee the the description in the manual for the program GATEWAY
ZMATSee the the description in the manual for the program GATEWAY
NOGUessorbDisable automatic generation of starting orbitals with the GuessOrb procedure.
NODEleteDo not delete any orbitals automatically.
SDELeteSet 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 NODElete.
TDELeteSet 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 NODElete.
ECPShowForce SEWARD to print ECP parameters.
AUXShowForce SEWARD to print auxiliary basis set parameters.
BSSHowForce SEWARD to print basis set parameters.
VERboseForce SEWARD to print a bit more verbose.

6.34.1.5.2 Cholesky specific keywords

KeywordMeaning
CHOInputThis marks the start of a Cholesky input section for modifying the default configuration of the decomposition driver. Below follows a description of the options associated with the decomposition configuration. The options may be given in any order, and they are all optional except for ENDChoinput which marks the end of the CHOInput section.

Keywords affecting the accuracy of the decomposition:

THRCholesky
Set threshold for convergence of the Cholesky decomposition. The real entry on the subsequent line specifies the threshold. This keyword defines the formal accuracy of the decomposition. However, it may also be affected by the screening settings specified by the following keywords. Default value: 1.0D-4.
PREScreen
Turn on diagonal prescreening. Default is off.
PREThreshold
Turn on diagonal prescreening and set threshold. The real entry specifies the diagonal prescreening threshold. Default is 1.0d-16.
NOPRescreen
Turn off diagonal prescreening. This is the default.
DMP1
Set "first" screening damping for setting up the first reduced set (i.e., the effective dimension of the diagonal and, consequently, of the Cholesky vectors). The real entry specifies the damping. Default value ranges from 1.0d5 to 1.0d0 depending on the decomposition threshold.
DMP2
Set "second" screening damping for setting up the second (and later) reduced set (i.e., the effective dimension of the updated diagonal and, consequently, of the Cholesky vectors). The real entry specifies the damping. Default value ranges from 1.0d5 to 1.0d0 depending on the decomposition threshold.
SCREen
Enable screening of diagonal during decomposition (using the first and second screening dampings given above). Default is to use screening (making this keyword redundant).
NOSCreen
Disable screening of diagonal during decomposition (in which case the dampings above are only used for statistics). Default is to use screening.
ABSOlute
Use absolute value of diagonal elements in screening procedure. This may leave in small negative diagonal elements arising from numerical inprecision. The default is to use absolute value.
NOABsolute
Do not use absolute value of diagonal elements in screening procedure. This will eliminate any small negative diagonal elements arising from numerical inprecision. The default is to use absolute value.
Special keyword needed to run the Cholesky version of CASPT2:
REORder vectors
Reorder vectors into full (i.e., canonical) storage after decomposition. The resulting files are significantly larger than the original ones.

Keywords for selecting decomposition algorithm:

TWOStep
Use two-step algorithm. This is the default algorithm, as it is usually the fastest. However, the performance is dependent on memory availability. NOTE: the two-step algorithm can not be restarted!
ONEStep
Use one-step algorithm. This is the original algorithm, not used by default.
NAIVe
Use ``naive'' algorithm. Stop after the first step of the two-step algorithm. Not recommended, as it is highly inaccurate.
PARAllel
Emulate the special algorithm used for parallel Cholesky decomposition. Mostly for debugging purposes.

Keywords for controlling output:

PRINt
Set print level. The integer entry on the subsequent line specifies the print level. Default value: 1. (translation of print levels: 0 - silent, 1 - terse, 2 - terse but with additional timings info, 3 - detailed, 4 - verbose, 5 - debug, 6 or larger - insane.)

Keywords for restarting the decomposition (note that restart is not possible in parallel):

RSTDiagonal
Do not compute initial diagonal. Instead, read diagonal from file CHODIAG which must be available. Also needed is the CHRED file(s). Default is to not restart.
RSTCholesky
Restart Cholesky decomposition procedure from Cholesky vectors available on disk using default restart model (see below). Files needed: CHVEC, CHRED, CHORST, and CHOMAP. Note that currently it is not possible to restart calculations using the TWOStep algorithm. Default is to not restart.
RSTModel
Set Cholesky decomposition restart model. The integer entry specifies the restart model (-1 = use configuration from restart file and ignore input configuration, 0 = abort if discrepancies are detected between input and configuration on disk, +1 = use input configuration and ignore configuration on disk). Default value: -1. Note: setting the restart model will automatically trigger a restart (i.e., RSTCholesky is a short-hand for the default restart model). Also, note that currently it is not possible to restart calculations using the TWOStep algorithm.

Keywords specifying dimensions of some central index arrays:

CHOMax
Set the maximum number of Cholesky vectors per irreducible representation. The integer entry specifies the maximum. This is used to allocate index arrays. Default value: 20 times the number of basis functions in the largest irreducible representation.
REDMax
Set the maximum number of reduced sets (i.e., integral passes). The integer entry specifies the maximum. This is used to allocate index arrays. Default value: the number of irreducible representations times the maximum number of Cholesky vectors.

Keywords for setting algorithmic details:

VBUFfer
Set the fraction of memory to use as global Cholesky vector buffer. Default: 0.35d0.
SPAN
Set the span defining the max. ratio between the qualified and globally largest diagonals allowed during decomposition. The real entry on the subsequent line specifies the span. Default value: 1.0D-2.
MINQualified
Set the minimum number of qualified diagonals needed to proceed to decomposition procedure. The integer value specifies the minimum. Default value: 50.
MAXQualified
Set the maximum number of diagonals that can be qualified per irreducible representation. The integer entry specifies the maximum. Default value: 100.
QFRAction
Set the memory fraction that may be used to store qualified integral columns. during integral evaluation as well as during vector computation. Thus, this may force the number of qualified to be less than the minimum number given through MINQualified (thereby saving memory for other processes such as the reading of previous vectors). The two integers (N1 N2) specify the ratio N1/N2 of available memory. Default values: N1=1, N2=3.
MXSHell pair
Set the maximum number of shell pair distributions (**|AB) that are allowed to be calculated before proceeding to decomposition procedure. The integer value specifies the maximum. Default is generic: calculate as many shell pair distributions as needed to meet the MINQualified requirement above.
ADDRessing
Set type of I/O used for Cholesky vectors (1 for word-addressable files, 2 for direct-access files). The integer on the next line specifies the addressing mode. Default: 1 (WA-files).
IOVEctor
Set algorithm used for reading vectors. The integer specifies the algorithm according to
  1. Read vectors from same reduced set (rs) and copy from rs to rs (rs2rs/batch algorithm).
  2. Read vectors across reduced sets into a small buffer and do rs2rs copying (buffer/rs2rs algorithm). The size of the buffer is determined on the basis of memory availability.
  3. Read vectors across reduced sets into a large buffer without reordering at the time of read. (lrgbuf/rs2rs). The size of the buffer is determined on the basis of memory availability and as close as possible to the memory fraction specified by keyword FRACtion.
  4. Read vectors across reduced sets into a fixed-size buffer without reordering at the time of read. (fxdbuf/rs2rs). The size of the buffer can be controlled by the keyword FRACtion.
The default is 3.
FRACtion
Set the memory fraction that may be used as I/O vector buffer. Two integers (N1 N2) specify the ratio N1/N2 of available memory. Default values: N1=2, N2=3. Note that the this is the fraction of memory available at the time of reading the vectors from disk and that the buffer is de-allocated again after reading. Thus, the N1/N2 fraction of memory will not interfere with the memory availability in other parts of the code such as integral evaluation.
MXSUbtraction
Set the max. number of vectors in the subtraction part (i.e. dimension the matrix multiplication). An integer specifies this number. Default: max. number of qualified columns (set by keyword MAXQualified.
IFCSeward
Set interface to the integral evaluation of SEWARD (1 for storing full integral shell quadruple, 2 for extracting integrals directly in reduced set). Default: 2 (extract in reduced set). Note that 1 (store full shell quadruple) requires significantly more memory.

Keywords for calculating the integral diagonal:

BUFFersize
Set size (in double precision words) of the buffer used during evaluation of the integral diagonal. An integer entry specifies the size. Default value: 1000000 (or the amount needed to store the entire diagonal, if this is smaller).
THRDiagonal
Set screening threshold for initial diagonal. The real entry on the subsequent line specifies the threshold. Default value: 0.0D0. WARNING: all integral diagonals smaller than the threshold will be unconditionally discarded in the course of calculating the initial diagonal.
Keywords for debugging:
CHECk configuration only
Abort calculation after checking decomposition configuration. May be used to check input for inconsistencies. Default is to not abort.
CHKAll integrals
Check all integrals after completing decomposition. This option is mostly for debugging and consumes significant amounts of CPU time. Default is to not check.
CHKSpecified integral columns
Check specified integral columns (shell pairs) after completing decomposition. The integer entry on the subsequent line specifies the number of shell pair columns to check. This option is mostly for debugging and consumes significant amounts of CPU time. Default is to not check.
CHKMinimum number of integral columns
Check a minimal integral columns (shell pairs) after completing decomposition. Which columns are checked depends on the decomposition at hand. This option is mostly for debugging and may consume significant amounts of CPU time. Default is to not check.
DIACheck
Check the integral diagonal during decomposition by computing the diagonal from Cholesky vectors and comparing to the one stored in core. The real number specifies the tolerance of the check. Default is not to check.
HALT
Halt execution after decomposition. Default is not to halt.
TRCNegative
Trace negative diagonal elements during decomposition. Default is not to trace.

Finally,

ENDChoinput
Marks the end of the Cholesky input section. This card is mandatory.

6.34.1.5.3 Keywords associated to one-electron integrals

KeywordMeaning
MULTipolesEntry 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).
CENTerThis 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.
SDIPoleSupplement ONEINT for transition dipole moment calculations, i.e. dipole moment and velocity integrals will be computed. This option should be used whenever the RASSI program is used to compute transition moments, so that the transition moments can be evaluated in both velocity and length representation.
ANGMSupplement ONEINT for transition angular momentum calculations. Entry which specifies the angular momentum origin (in au).
DSHDRequests the computation of diamagnetic shielding integrals. The first entry specifies the gauge origin. Then follows an integer specifying the number of points at which the diamagnetic shielding will be computed. If this entry is zero, the diamagnetic shielding will be computed at each nucleus. If nonzero, then the coordinates (in au) for each origin has to be supplied, one entry for each origin.
RELIntRequests 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.
AMPRRequest the computation of angular momentum product integrals. The keyword is followed by values which specifies the angular momentum origin (in au).
RXXPyyRequest 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). 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.
RX2CRequest the scalar relativistic X2C (eXact-two-Component) corrections to the one-electron Hamiltonian as well as the property integrals.
RBSSRequest the scalar relativistic BSS (Barysz-Sadlej-Snijders) corrections to the one-electron Hamiltonian as well as the property integrals. The non-iterative scheme is employed for the construction of BSS transformation.
NOAMfiExplicit request for no computation of atomic mean-field integrals.
AMFIExplicit request for the computation of atomic mean-field integrals (used in subsequent spin-orbit calculations). These integrals are computed by default for the ANO-RCC and ANO-DK3 basis sets.
EPOTAn integer follows which represents the number of points for which the electric potential will be computed. If this number is zero, the electric field acting on each nucleus will be computed. If nonzero, then the coordinates (in au) for each point have to be supplied, one entry for each point.
EFLDAn integer follows which represents the number of points for which the electric potential and electric field will be computed. If this number is zero, the electric field acting on each nucleus will be computed. If nonzero, then the coordinates (in au) for each point have to be supplied, one entry for each point.
FLDGAn integer required which represents the number of points for which the electric potential, electric field and electric field gradient will be computed. If this number is zero, the electric field gradient acting on each nucleus will be computed. If nonzero, then the either coordinates (in au) for each point or labels for each atom center have to be supplied, one entry for each point. In case a label is supplied it must match one of those given previous in the input during specification of the coordinates of the atom centers. Using a label instead of a coordinate can e.g. be useful in something like a geometry optimization where the coordinate isn't known when the input is written.
Grid InputSpecification of numerical quadrature parameters, consult the numerical quadrature section of this manual.

6.34.1.5.4 Additional keywords for property calculations

KeywordMeaning
VECTorsRequests a property calculation. For this purpose a file, INPORB, must be available, which contains the MO's and occupation numbers of a wave function.
ORBConThe 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.
THRSThe real entry on the following line specifies the threshold for the occupation number of an orbital in order for the OrbCon option to list the contribution of that orbital to a property. The default is 1.0d-6.

6.34.1.5.5 Keywords for two-electron integrals

KeywordMeaning
NOPAckThe two-electron integrals will not be packed. The default is to pack the two-electron integrals.
PKTHreAn entry specifies the desired accuracy for the packing algorithm, the default is 1.0d-10.
STDOutGenerate 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.
THREsholdThreshold for writing integrals to disk follows. The default is 1.0d-10.
CUTOffThreshold for ignoring the calculation of integrals based on the pair prefactor follows. The default is 1.0d-10.

6.34.1.5.6 Keywords associated to electron-molecule scattering calculations within the framework of the 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 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.

KeywordMeaning
RMATRadius of the R-matrix sphere (in Bohr). This sphere is centered at the coordinate origin. The default is 10 Bohr.
RMEAAbsolute precision in radial integration. The default is 1d-9.
RMERRelative precision in radial integration. The default is 1d-14.
RMQCEffective charge of the target molecule. This is the effective charge seen by the incident electron outside of the R-matrix sphere. The default is 0d0.
RMDIEffective dipole of the target molecule. This is the effective dipole seen by the incident electron outside of the R-matrix sphere. The default is (0d0,0d0,0d0).
RMEQMinimal 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
RMBPParameter used for test purposes in the definition of the Bloch term. Default is 0d0.
CELLDefines the three vectors of the unit cell ($\vec{e_1}$,$\vec{e_2}$,$\vec{e_3}$). 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.
SPREadThree integer numbers n1, n2, n3 which define the spread of the unit cell along the unit cell vectors. For example, $0\quad 0\quad 2$ would add all cell's atoms translated on $-2\vec{e_3}$, $-\vec{e_3}$, $\vec{e_3}$, $2\vec{e_3}$. 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.



  &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
*  Specify  basis  sets
Basis  set
C.ANO-L...6s5p3d2f.
Contaminant  d
C  0.0  0.0  0.0
End  of  basis

6.34.1.5.7 The basis set label and the all electron basis set library

The label, which defines the basis set for a given atom or set of atoms, is given as input after the keyword Basis set. It has the following general structure (notice that the last character is a period):

\fbox{atom.type.author.primitive.contracted.aux.}

where the different identifiers have the following meaning:

IdentifierMeaning
atomSpecification of the atom by its chemical symbol.
typeGives 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.
authorFirst author in the publication where that basis set appeared.
primitiveSpecification of the primitive set (e.g. 14s9p4d3f).
contractedSpecification 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.
auxSpecification 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.

6.34.1.5.8 Basis set format

The Inline option for a basis set will read the basis set as defined by the following pseudo code.

Read Charge, lAng
Do iAng = 0, lAng
Read nPrim, nContr
Read (Exp(iPrim),iPrim=1,nPrim)
Do iPrim=1,nPrim
Read (Coeff(iPrim,iContr),iContr=1,nContr)
End Do
End Do

where Charge is the nuclear charge, lAng is the highest angular momentum quantum number, nPrim is the number of primitive functions (exponents) for a given shell, and nContr is the number of contracted functions for a given shell.

The following is an example of a DPZ basis set for carbon. Normally, however, the basis set will be read from a library file following the specified label (like, e.g., C.DZP...4s2p1d.), and not be inserted inline at the input file.



Basis  set  --  Start  defining  a  basis  set
C.DZP.Someone.9s5p1d.4s2p1d.  /  inline  --  Definition  in  input  stream
  6.0  2  --  charge,  max  l-quantum  no.
  9  4  --  no.  of  prim.  and  contr.  s-functions
4232.61  --  s-exponents
634.882
146.097
42.4974
14.1892
1.9666
5.1477
0.4962
0.1533
  .002029  .0  .0  .0  --  s-contraction  matrix
  .015535  .0  .0  .0
  .075411  .0  .0  .0
  .257121  .0  .0  .0
  .596555  .0  .0  .0
  .242517  .0  .0  .0
  .0  1.0  .0  .0
  .0  .0  1.0  .0
  .0  .0  .0  1.0
  5  2  --  no.  of  prim.  and  contr.  p-functions
18.1557  --  p-exponents
3.98640
1.14290
0.3594
0.1146
  .018534  .0  --  p-contraction  matrix
  .115442  .0
  .386206  .0
  .640089  .0
  .0  1.0
  1  1  --  no.  of  prim.  and  contr.  d-functions
  .75  --  d-exponents
  1.0  --  d-contraction  matrix
C1  0.00000  0.00000  0.00000  --  atom-label,  Cartesian  coordinates
C2  1.00000  0.00000  0.00000  --  atom-label,  Cartesian  coordinates
End  Of  Basis  --  end  of  basis  set  definition

6.34.1.5.9 The basis set label and the ECP libraries

The label within the ECP library is given as input in the line following the keyword BASIS SET. The label defines either the valence basis set and core potential which is assigned to a frozen-core atom or the embedding potential which is assigned to an environmental froze-ion. Here, all the comments made about this label in the section The basis set label and the basis set library for all-electron basis sets stand, except for the following changes:

  1. The identifier type must be ECP or PP.
  2. The identifier aux specifies the kind of the potential. It is used, for instance, to choose between non-relativistic, Cowan-Griffin, or no-pair Douglas-Kroll relativistic core potentials
    (i.e. Pt.ECP.Casarrubios.13s10p9d5f.1s2p2d1f.16e-NR-AIMP.
    or Pt.ECP.Casarrubios.13s10p9d5f.1s2p2d1f.16e-CG-AIMP.
    or Pt.ECP.Rakowitz.13s10p9d6f.5s4p4d2f.18e-NP-AIMP.)
    and to pick up one among all the embedding potentials available for a given ion
    (i.e. F.ECP.Lopez-Moraza.0s.0s.0e-AIMP-KMgF3.
    or F.ECP.Lopez-Moraza.0s.0s.0e-AIMP-CsCaF3.).

  3. The identifier contracted is used here in order to produce the actual basis set out of the basis set included in the ECP library, which is a minimal basis set (in general contraction form) augmented with some polarization, diffuse, ... function. It indicates the number of s, p, ..., contracted functions in the actual basis set, the result being always a many-primitive contracted function followed by a number of primitives. As an example, At.ECP.Barandiaran.13s12p8d5f.3s4p3d2f.17e-CG-AIMP. will generate a (13,1,1/12,1,1,1/8,1,1/5,1) formal contraction pattern which is in this case a (13,1,1/12,1,1,1/7,1,1/5,1) real pattern. Other contraction patters should be input ``Inline".

  4. The user is suggested to read carefully section [*] of the tutorials and examples manual before using the ECP utilities.


6.34.2 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, EX [P] and the electron correlation energy ,EC [P].


6.34.2.1 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
\begin{displaymath}
E_X[P] = \int f(\rho_{\alpha}(r), \rho_{\beta}(r), \nabla \rho_{\alpha}(r), \nabla \rho_{\beta}(r)) dr
\end{displaymath} (6.15)

The various DFT methods differ in which function, f, is used for EX[P] and for EC[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 SEWARD input the parameters for the numerical integration can be set up. In the SCF and 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 [106,107,108]. The latter is known to be translationally invariant by definition and is recommended in geometry optimizations.

6.34.2.2 Input

Below follows a description of the input to the numerical integration utility in the SEWARD input.

Compulsory keywords
KeywordMeaning
GRID InputThis marks the beginning of the input to the numerical integration utility.
END Of Grid-InputThis marks the end of the input to the numerical integration utility.

Optional keywords
KeywordMeaning
GRIDIt specifies the quadrature quality. The possible indexes that can follow are COARSE, SG1GRID, FINE, ULTRAFINE following the Gaussian98 convention. Default is FINE.
RQUAdIt 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.
GGL It activates the use of Gauss and Gauss-Legendre angular quadrature. Default is to use the Lebedev angular grid.
LEBEdevIt turns on the Lebedev angular grid.
LOBAttoIt activates the use of Lobatto angular quadrature. Default is to use the Lebedev angular grid.
LMAXIt specifies the angular grid size. Default is 29.
NGRIdIt specifies the maximum number of grid points to process at one instance. Default is 5500 grid points.
NOPRunningIt turns off the the angular prunning. Default is to prune.
NR It is followed by the number of radial grid points. Default is 75 radial grid points.
FIXEd gridUse 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.
MOVIng gridUse a moving grid in the evaluation of the gradient. This correspond to evaluating the gradient of the numerical expression of the DFT energy. This is the default.
THREsholdIt is followed by the value for the the radial threshold. Default value is 1.0D-13.
T_XThreshold for screening in the assembling of the density on the grid. Default value is 1.0D-18.
T_YThreshold for screening in the assembling of the integrals. Default value is 1.0D-11.
NOSCreeningTurn off any screening in the numerical integration.
CROWdingThe crowding factor, according to MHL, used in the pruning of the angular grid close to the nuclei. Default value 3.0.

The SCF and 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.



  &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

6.34.2.3 Relativistic operators

The current different implementation of all relativistic operators in MOLCAS as described in the following subsubsections has been programmed and tested in Ref.[109]

6.34.2.4 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 that 8th order by default to be on the safe side.

The arbitrary-order Hamiltonian is activated by setting

RXXPyy

somewhere in the 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:

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 [110], it is recommended for high-order DKH transformation.

For details on the arbitrary-order DKH Hamiltonians see [111] with respect to theory, [112] with respect to aspects of implementation, and [113] 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 [110] is used as the default algorithm. The implementation in MOLCAS has been presented in [109].

For details on the different parametrizations of the unitary transformations see [114].

6.34.2.5 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.

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 [115] with respect to theory and [116,109] with respect to implementation aspects.

6.34.2.6 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.

The exact decoupling Hamiltonian is activated by setting either RX2C or RBSS somewhere in the 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[109]. For molecules including only light atoms, the DKH method with low orders (<8) is enough to account for the relativistic effects.

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 [109] with respect to theories and comparison of numerical results, [117,118,119] for the X2C method, and [120,121] for the BSS method.


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