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Subsections
8.41 rassi
The
RASSI (RAS State Interaction) program forms overlaps and
other matrix
elements of the Hamiltonian and other operators
over a wave function basis, which consists of RASSCF wave functions,
each with an individual set of orbitals. It is extensively used
for computing dipole oscillator strengths, but any
oneelectron operator, for which the Seward has computed
integrals to the ORDINT file, can be used, not just dipole
moment components.
Also, it solves the Schrödinger
equation projected on the space spanned by these wave functions,
i.e., it forms noninteracting linear combinations of the input
state functions, and computes matrix elements over the resulting
eigenbasis as well.
Finally, using these spinfree eigenstates as a basis, it can
compute spinorbit interaction matrix elements, diagonalize
the resulting matrix, and compute various matrix elements over
the resulting set of spinorbit eigenstates.
If only matrix
elements of some oneelectron operator(s), such as the dipole
transition moments, are required, the calculation of Hamiltonian
matrix elements and the transformation to the eigenbasis of this
matrix can be skipped. However, if any states have the same symmetry
and different orbitals, it is desirable to use the transitions strengths
as computed between properly noninteracting and orthonormal states.
The reason is that the individually optimized RASSCF states are
interacting and nonorthogonal, and the main error in the computed
transition matrix elements is the difference in electronic dipole
moment times the overlap of any two states involved. For excited
states, the overlap is often in the order of 10%.
Please note: Due to the increasing number of calculations done with
a hundred input states, or more, there has been a demand to change
the output. Until MOLCAS6.2, the default assumption has been to print
all expectation values and matrix elements that can be computed from
the selection of oneelectron integrals. From 6.4, this is requested by
keywords, see the keyword list below for XVIN, XVES, XVSO, MEIN,
MEES, and MESO.
Apart from computing oscillator strengths, overlaps and Hamiltonian
matrix elements can be used to compute electron transfer rates, or
to form quasidiabatic states and reexpress matrix elements over a
basis of such states.
The CSF space of a RASSCF wave function is closed under deexcitation.
For any given pair of RASSCF wave functions, this is used in the
way described in reference [82] to allow the pair of orbital
sets to be transformed to a biorthonormal pair, while simultaneously
transforming the CI expansion coefficients so that the wave functions
remain unchanged. The basic principles are the same as in the earlier
program [83], but is adapted to allow RASSCF as well as
CASSCF wave functions. It uses internally a Slater determinant
expansion. It can now use spindependent operators,
including the AMFI spinorbit operator, and can compute matrix elements
over spinorbit states, i.e. the eigenstates of the sum of the
spinfree hamiltonian and the spinorbit operator.
One use of the RASSI eigenstates is to resolve ambiguities due
to the imperfect description of highly excited states.
Association between individually optimized states and the exact
electronic eigenstates is often not clear, when the calculation
involves several or many excited states. The reason is that the
different states each use a different set of orbitals. The State
Interaction calculation gives an unambiguous set of noninteracting and
orthonormal eigenstates to the projected Schrödinger equation, and
also the overlaps between the original RASSCF wave functions and the
eigenstates. The latter is a very efficient diagnostic, since it
describes the RASSCF states in terms of one single wavefunction basis
set.
To make the last point clear, assume the following situation:
We have
performed three RASSCF calculations, one where we optimize for the
lowest state, one for the first excited state, and one for the 2nd
excited state in the same symmetry. The active orbitals are fairly
much mixed around, so a simple inspection of the CI coefficient is
insufficient for comparing the states. Assume that for each state, we
have calculated the three lowest CI roots. It can now happen, that the
2nd root of each calculation is a fair approximation to the exact 2nd
eigenstate, and the same with the 3rd, or possibly that the order gets
interchanged in one or two of the calculation. In that case, a RASSI
calculation with these 9 states will give three improved solutions
close to the original ones, and of course 6 more that are considered
to be the removed garbage. The overlaps will confirm that each of the
input states consists mainly of one particular out of the three lowest
eigenstates. This situation is the one we usually assume, if no
further information is available.
However, it happens that the active orbitals of the three calculations
do not span approximately the same space. The orbital optimization
procedure has made a qualitatively different selection of correlating
orbitals for the three different calculation. Then the RASSI
calculation may well come out with 4 lowest roots that overlap
strongly with the original RASSCF states. This may change the
assignments and may also give valuable information about the
importance of some state. The natural orbitals of the eigenstates will
show that the active space used in the RASSCF was in some way
inappropriate.
Another bothersome situation is also solved by the RASSI method. The
analysis of the original states in terms of RASSI eigenstates may
reveal that the three optimized RASSCF states consists mainly of TWO
low RASSI eigenstates! This is because the RASSCF optimization
equations are nonlinear and may sometimes offer spurious extra
solutions. Two of the calculations are in this case to be regarded
qualitatively, as two different (local) solutions that
approximate (imperfectly) the same excited state. Also in this case, the
natural orbitals will probably offer a clue to how to get rid of the
problem. Extra solutions rarely occur for low states in CASSCF
calculations, provided a generous active space can be afforded.
Problems occur when the active space is too small, and in
particular with general RASSCF calculations.
A further application is the preparation of a suitable orbital basis
for a subsequent CI calculation. Note that such an application also
allows the use of badly converged RASSCF wave functions, or of RASSCF
wave functions containing multiple minima solutions close to a common
exact eigenstate. In effect, the RASSI program cleans up the situation
by removing the errors due to bad convergence (pushing the errors into
a garbage part of the spectrum). This requires that the set of input
states (9 in this example) provides flexibility enough to remove at
least a major part of the error. As one would expect, this is usually
true: The erratic nonconvergent, or the too slowly convergent, error
mode is to a large extent spanned by the few lowest RASSCF wave
functions.
Finally, there are situations where there is no problem to obtain
adiabatic RASSCF solutions, but where it is still imperative to use
RASSI natural orbitals in a subsequent CI. Consider the case of
transition metal chemistry, where there is in general two or more
electronic states involved. These states are supposed to interact
strongly, at least within some range of interatomic distances. Here,
an MCSCF solution, such as RASSCF, will have at least two very
different solutions, one associated with each configuration of the
transition metal atom. Using one set of orbitals, one electronic state
has a reasonably described potential energy curve, while other states
get pushed far up in energy. Using another set of orbitals, another
state gets correctly described. In no calculation with a single
orbital set do we obtain the avoided crossings, where one switches
from one diabatic state to another. The only way to accomplish this is
via a RASSI calculation. In this case, it is probably necessary also to
shift the energies of the RASSCF states to ensure that the crossing
occur at the correct places. The shifts can be determined by
correcting the atomic spectrum in the separatedatoms limit.
Note, however, that most of the problems described above can be
solved by performing stateaveraged RASSCF calculations.
8.41.1 Dependencies
The RASSI program needs one or more JOBIPH files produced
by the RASSCF program. Also, it needs a ONEINT file from
SEWARD, with overlap integrals and any oneelectron
property integrals for the requested matrix elements. If Hamiltonian
matrix elements are used, also the ORDINT file is needed.
8.41.2 Files
File  Contents

ORDINT*  Ordered twoelectron integral file produced by the SEWARD
program. In reality, this is up to 10 files in a multifile system,
named ORDINT, ORDINT1,...,ORDINT9. This is necessary on some platforms
in order to store large amounts of data.

ONEINT  The oneelectron integral file from SEWARD

JOBnnn  A number of JOBIPH files from different RASSCF jobs.
An older naming convention assumes file names JOB001, JOB002, etc. for these files.
They are automatically linked to default files named $Project.JobIph,
$Project.JobIph01, $Project.JobIph02, etc. in directory $WorkDir,
unless they already exist as files or links before the program starts.
You can set up such links yourself, or else you can specify file names
to use by the keyword IPHNames.

JOBIPHnn  A number of JOBIPH files from different RASSCF jobs.
The present naming convention assumes file names JOBIPH, JOBIPH01, etc. for
such files, when created by subsequent RASSCF runs, unless
other names were specified by input.
They are automatically linked to default files named $Project.JobIph,
$Project.JobIph01, $Project.JobIph02, etc. in directory $WorkDir,
unless they already exist as files or links before the program starts.
You can set up such links yourself, or else you can specify file names
to use by the keyword IPHNames.

File  Contents

SIORBnn  A number of files containing natural orbitals, (numbered sequentially as
SIORB01, SIORB02, etc.)
If you do not like these names, you must set up links yourselves, except
for the first one: SIORB01 is automatically linked to a default file
named $Project.SiOrb in directory $WorkDir, if it does not already
exists as a file or a link before the program starts. You must set up the
other files yourself.

TOFILE  This output is only created if TOFIle is given in the input.
It will contain the transition density matrix computed by Rassi.
Currently, this file is only used as input to QmStat.

EIGV  Like TOFILE this file is only created if TOFIle is given
in the input. It contains auxiliary information that is picked up
by QmStat.

8.41.3 Input
This section describes the input to the
RASSI program in the MOLCAS program system,
with the program name:
&RASSI
When a keyword is followed by additional mandatory lines of input,
this sequence cannot be interrupted by a comment line. The first 4
characters of keywords are decoded. An unidentified keyword makes the
program stop.
8.41.3.1 Keywords
Keyword  Meaning

CHOInput  This marks the start of an input section for modifying
the default settings of the Cholesky RASSI.
Below follows a description of the associated options.
The options may be given in any order,
and they are all optional except for
ENDChoinput which marks the end of the CHOInput section.
 NoLK
 Available only within ChoInput. Deactivates the ``Local Exchange'' (LK) screening algorithm [81] in computing
the Fock matrix. The loss of speed compared to the default algorithm can be substantial, especially for electronrich systems.
Default is to use LK.
 DMPK
 Available only within ChoInput. Modifies the thresholds used in the LK screening.
The keyword takes as argument a (double precision) floating point (nonnegative) number used
as correction factor for the LK screening thresholds.
The default value is 1.0d1. A smaller value results in a slower but more accurate calculation.
Note: the default choice of the LK screening thresholds is tailored to achieve as much as possible an
accuracy of the RASSI energies consistent with the choice of the Cholesky decomposition
threshold.
 NODEcomposition
 Available only within ChoInput. The inactive Exchange contribution to the Fock matrix is computed using inactive canonical orbitals
instead of (localized) ``Cholesky MOs''.
This choice is effective only in combination with the LK screening.
Default is to use Cholesky MOs. Note: the Cholesky MOs in RASSI are computed by decomposing the
density type supermatrix
where is the corresponding canonical
MOs matrix for the state A and B.When computing the coupling between 2 different
states A and B, only for the first state we use pure Cholesky MOs. The invariance of the Fock matrix
is then ensured by rotating the orbitals of B according to the orthogonal matrix defined in A
through the Cholesky localization. These orbitals used for B are therefore called ``pseudo Cholesky MOs''.
 TIME
 Activates printing of the timings of each task of the Fock matrix build.
Default is to not show these timings.
 MEMFraction
 Set the fraction of memory to use as global Cholesky vector buffer.
Default: for serial runs 0.0d0; for parallel runs 0.3d0.

MEIN  Demand for printing matrix elements of all selected oneelectron
properties, over the input RASSCF wave functions.

MEES  Demand for printing matrix elements of all selected oneelectron
properties, over the spinfree eigenstates.

MESO  Demand for printing matrix elements of all selected oneelectron
properties, over the spinorbit states.

PROPerty  Replace the default selection of oneelectron operators, for which
matrix elements and expectation values are to be calculated, with a
usersupplied list of operators.
From the lines following the keyword the selection list is
read by the following FORTRAN code:
READ(*,*) NPROP,(PNAME(I),ICOMP(I),I=1,NPROP)
NPROP is the number of selected properties, PNAME(I) is a
character string with the label of this operator on SEWARD's
oneelectron integral file, and ICOMP(I) is the component number.
The default selection is to use dipole and/or velocity integrals, if
these are available in the ONEINT file. This choice is replaced by the
userspecified choice if the PROP keyword is used.
Note that the character strings are read using list directed input and
thus must be within single quotes, see sample input below.
For a listing of presently available operators, their labels, and
component conventions, see
SEWARD program description.

SOCOupling  Enter a positive threshold value. Spinorbit interaction matrix
elements over the spin components of the spinfree eigenstates
will be printed, unless smaller than this threshold.
The value is given in cm^{1} units. The keyword is
ignored unless an SO hamiltonian is actually computed.

SOPROPerty  Enter a usersupplied selection of oneelectron operators, for which
matrix elements and expectation values are to be calculated over the
of spinorbital eigenstates. This keyword has no effect unless the
SPIN keyword has been used. Format: see PROP keyword.

SPINorbit  Spinorbit interaction matrix elements will be computed. Provided that
the ONEL keyword was not used, the resulting Hamiltonian including the
spinorbit coupling, over a basis consisting of all the spin components
of wave functions constructed using the spinfree eigenstates, will be
diagonalized. NB: For this keyword to have any effect, the SO integrals
must have been computed by SEWARD! See AMFI keyword in SEWARD documentation.

ONEL  The twoelectron integral file will not be accessed. No Hamiltonian
matrix elements will be calculated, and only matrix elements for the
original RASSCF wave functions will be calculated.
ONEE is a valid synonym for this keyword.

JVAlue  For spinorbit calculations with single atoms, only: The output lines
with energy for each spinorbit state will be annotated with the
approximate J and Omega quantum numbers.

OMEGa  For spinorbit calculations with linear molecules, only: The output lines
with energy for each spinorbit state will be annotated with the
approximate Omega quantum number.

NROF jobiphs  Number of
JOBIPH files used as input. This keyword should be
followed by the number of
states to be read from each JOBIPH. Further, one line per
JOBIPH is required with a list of the states to be
read from the particular file. See sample input below.
Alternatively, the first line can contain the number of JOBIPH used
as input followed by the word ALL , indicating that all states
will be taken from each file. In this case no further lines are required.
For JOBIPH file names, see the Files section.
Note: If this keyword is missing, then by default all files named 'JOB001',
'JOB002', etc. will be used, and all states found on these files will be
used.

IPHNames  Followed by one entry for each JOBIPH file to be used, with the
name of each file. Note: This keyword presumes that the number of
JOBIPH files have already been entered using keyword NROF.
For default JOBIPH file names, see the Files section.
The names will be truncated to 8 characters and converted to uppercase.

SHIFt  The next entry or entries gives an energy shift for each wave function,
to be added to diagonal elements of the Hamiltonian matrix.
This may be necessary e.g. to ensure that an energy crossing occurs
where it should. NOTE: The number of states must be known
(See keyword NROF) before this input is read.
In case the states are not orthonormal, the actual quantity added to
the Hamiltonian is 0.5D0*(ESHFT(I)+ESHFT(J))*OVLP(I,J). This is necessary
to ensure that the shift does not introduce artificial interactions.
SHIFT and HDIAG can be used together.

HDIAg  The next entry or entries gives an energy for each wave function,
to replace the diagonal elements of the Hamiltonian matrix.
Nonorthogonality is handled similarly as for the SHIFT keyword.
SHIFT and HDIAG can be used together.

NATOrb  The next entry gives the number of eigenstates, for which natural
orbitals will be computed. They will be written, formatted, commented,
and followed by natural occupancy numbers, on one file each.
For file names, see the Files section.
The format allows their use as standard orbital input files to
other MOLCAS programs.

ORBItals  Print out the Molecular Orbitals read from each
JOBIPH file.

OVERlaps  Print out the overlap integrals between the various orbital sets.

CIPRint  Print out the CI coefficients read from
JOBIPH.

THRS  The next line gives the threshold for printing CI coefficients. The
default value is 0.05.

DIPR  The next entry gives the threshold for printing dipole intensities.
Default is 1.0D5.

QIPR  The next entry gives the threshold for printing quadrupole intensities.
Default is 1.0D5.
Will overwrite any value chosen for dipole intesities.

QIALL  Print all quadrupole intensities.

RFPE  RASSI will read from RUNOLD (if not present defaults to RUNFILE) a response field contribution
and add it to the Fock matrix.

HCOM  The spinfree Hamiltonian is computed.

HEXT  It is read from the following few lines, as a triangular matrix: One element
of the first row, two from the next, etc, as listdirected input of reals.

HEFF  A spinfree effective Hamiltonian is read from JOBIPH instead of being computed.
It must have been computed by an earlier program. Presently, this is done by
a multistate calculation using CASPT2. In the future, other programs may add
dynamic correlation estimates in a similar way.

EJOB  The spinfree effective Hamiltonian is assumed to be diagonal, with energies
being read from a JOBMIX file from a multistate CASPT2 calculation.
In the future, other programs may add dynamic correlation estimates in a similar way.

TOFIle  Signals that a set of files with data from Rassi should be
created. This keyword is necessary if QmStat is to be run
afterwards.

XVIN  Demand for printing expectation values of all selected oneelectron
properties, for the input RASSCF wave functions.

XVES  Demand for printing expectation values of all selected oneelectron
properties, for the spinfree eigenstates.

XVSO  Demand for printing expectation values of all selected oneelectron
properties, for the spinorbit states.

EPRG  This computes the g matrix and principal g values for the
states lying within the energy range supplied on the next line.
A value of 0.0D0 or negative will select only the ground state,
a value E will select all states within energy E of the ground state.
The states should be ordered by increasing energy in the input.
The angular momentum and spinorbit coupling matrix elements
need to be available (use keywords SPIN and PROP).
For a more detailed description see ref [84].

MAGN  This computes the magnetic moment and magnetic susceptibility.
On the next two lines you have to provide the magnetic field and
temperature data. On the first line put the number of magnetic
field steps, the starting field (in Tesla), size of the steps (in Tesla),
and an angular resolution for sampling points in case of powder magnetization
(for a value of 0.0d0 the powder magnetization is deactivated).
The second line reads the number of temperature steps, the starting
temperature (K), and the size of the temperature steps (K).
The angular momentum and spinorbit coupling matrix elements
need to be available (use keywords SPIN and PROP).
For a more detailed description see ref [85].

HOP  Enables a trajectory surface hopping (TSH) algorithm which allow
nonadiabatic transitions between electronic states during molecular
dynamics simulation with DYNAMIX program. The algorithm
computes the scalar product of the amplitudes of different
states in two consecutive steps. If the scalar product
deviates from the given threshold a transition between the states
is invoked by changing the root for the gradient computation.
The current implementation is working only with SACASSCF.

STOVerlaps  Computes only the overlaps between the input states.

TRACk  Tries to follow a particular root during an optimization.
Needs two JOBIPH files (see NrOfJobIphs) with the same
number of roots. The first file corresponds to the current iteration,
the second file is the one from the previous iteration (taken as a reference).
With this keyword RASSI selects the root from the first JOBIPH
with highest overlap with the root that was selected in the previous
iteration. It also needs MDRlxRoot, rather than RlxRoot,
to be specified in RASSCF.
No other calculations are done by RASSI when Track
is specified.

DQVD  Perfoms DQ diabatization[86] by using properties that are computed with RASSI.
One must compute 7 properties with RASSI in order for this keyword to work
(x,y,z,xx,yy,zz,1/r), and they must be specified in that order.
At present, this keyword also requires ALPHa and BETA, where
ALPHa is the parameter in front of rr and BETA is the parameter
in front of 1/r. When ALPHa and BETA are equal to zero, this
method reduces to Boys localized diabatization[87].At present, this method only works for one choice of origin for each quantity.

ALPHa  ALPHa is the prefactor for the quadrupole term in DQ diabatization. This
keyword must be used in conjunction with DQVD and BETA. You must
specify a real number (e.g. not ).

BETA  BETA is the prefactor for the electrostatic potential term in DQ diabatization. This
keyword must be used in conjunction with DQVD and ALPHa. You must
specify a real number (e.g. not ).

TRDI  Prints out the components and the module of the transition dipole
vector. Only vectors with sizes large than 1.0D4 a.u. are printed.
See also the TDMN keyword.

TDMN  Prints out the components and the module of the transition dipole
vector. On the next line, the minimum size, in a.u., for the dipole
vector to be printed must be given.

»COPY "Jobiph file 1" JOB001
»COPY "Jobiph file 2" JOB002
»COPY "Jobiph file 3" JOB003
&RASSI
NR OF JOBIPHS= 3 4 2 2  3 JOBIPHs. Nr of states from each.
1 2 3 4; 3 4; 3 4  Which roots from each JOBIPH.
CIPR; THRS= 0.02
Properties= 4; 'MltPl 1' 1 'MltPl 1' 3 'Velocity' 1 'Velocity' 3
* This input will compute eigenstates in the space
* spanned by the 8 input functions. Assume only the first
* 4 are of interest, and we want natural orbitals out
NATO= 4
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