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Subsections
6.9 RASSI  A RAS State Interaction Program
Program RASSI (RAS State Interaction) computes matrix elements
of the Hamiltonian and other operators in a wave function basis, which
consists of individually optimized CI expansions from the RASSCF
program. Also, it solves the Schrödinger equation within the space of
these wave functions. There are many possible applications for such type
of calculations. The first important consideration to have into account
is that RASSI computes the interaction among RASSCF states
expanding the same set of configurations, that is,
having the same active space size and number of electrons.
The RASSI program is routinely used to compute electronic
transition moments, as it is shown in the Advanced Examples in the
calculation of transition dipole moments for the
excited states of the thiophene molecule using CASSCFtype wave functions.
By default the program will compute the matrix elements and expectation values
of all the operators for which SEWARD has computed the integrals
and has stored them in the ONEINT file.
RASSCF (or CASSCF) individually optimized states are interacting and
nonorthogonal. It is imperative when the states involved have different
symmetry to transform the states to a common eigenstate basis in such
a way that the wave function remains unchanged. 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 analysis of the original states in terms of RASSI eigenstates is
very useful to identify spurious local minima and also to inspect the
wave functions obtained in different singleroot RASSCF calculations,
which can be mixed and be of no help to compare the states.
Finally, the RASSI program can be applied in situations when
there are two strongly interacting states and there are two very different
MCSCF solutions. This is a typical situation in transition metal chemistry
when there are many close states associated each one to a configuration
of the transition metal atom. It is also the case when there are two
close quasiequivalent localized and delocalized solutions. RASSI
can provide with a single set of orbitals able to represent, for instance,
avoided crossings. RASSI will produce a
number of files containing the natural orbitals for
each one of the desired eigenstates to be used in subsequent calculations.
RASSI requires as input files the ONEINT and ORDINT
integral files and the JOBIPH files from the RASSCF program
containing the states which are going to be computed. The JOBIPH files
have to be named consecutively as JOB001, JOB002, etc.
The input for the RASSI module has to contain at least
the definition of the number of states available in each of the input
JOBIPH files. Figure 6.11 lists the input file
for the RASSI program in a calculation including two JOBIPH
files (2 in the first line), the first one including three roots (3 in the first
line) and the second five roots (5 in the first line). Each one of the
following lines lists the number of these states within each JOBIPH file.
Also in the input, keyword NATOrb indicates that three files
(named sequentially NAT001, NAT002, and NAT003) will
be created for the three lowest eigenstates.
Figure 6.11:
Sample input requesting the RASSI module to calculate the matrix elements and expectation values for eight interacting RASSCF states

&RASSI
NROFjobiph= 2 3 5; 1 2 3; 1 2 3 4 5
NATOrb= 3
The RASSI section of the MOLCAS output is basically divided
in three parts. Initially, the program prints the information about the
JOBIPH files and input file, optionally prints the wave functions,
and checks that all the configuration spaces are the same in all the
input states. In second place RASSI prints the expectation
values of the oneelectron operators, the Hamiltonian matrix, the
overlap matrix, and the matrix elements of the oneelectron operators,
all for the basis of input RASSCF states. The third part starts with
the eigenvectors and eigenvalues for the states computed in
the new eigenbasis, as well as the overlap of the computed eigenstates
with the input RASSCF states. After that, the expectation values and
matrix elements of the oneelectron operators are repeated on the
basis of the new energy eigenstates. A final section informs about
the occupation numbers of the natural orbitals computed by
RASSI, if any.
In the Advanced Examples a detailed example of how to interpret
the matrix elements output section for the thiophene molecule is
displayed. The rest of the output is selfexplanatory. It has to be
remembered that to change the default origins for the one electron
operators (the dipole moment operator uses the nuclear charge
centroid and the higher order operators the center of the nuclear
mass) keyword CENTer in GATEWAY must be used.
Also, if multipoles higher than order two are required, the
option MULTipole has to be used in GATEWAY.
The program RASSI can also be used to compute a spinorbit Hamiltonian
for the input CASSCF wave functions as defined above. The keyword AMFI
has to be used in SEWARD to ensure that the corresponding integrals
are available.
Figure 6.12:
Sample input requesting the RASSI module to calculate and diagonalize the spinorbit Hamiltonian the ground and triplet excited state in water.

&RASSI
NROFjobiph= 2 1 1; 1; 1
Spinorbit
Ejob
The first JOBMIX file contains the wave function for the ground state and
the second file the ^{3}B_{2} state discussed above. The keyword Ejob
makes the RASSI program use the CASPT2 energies which have been
written on the JOBMIX files in the diagonal of the spinorbit
Hamiltonian. The output of this calculation will give four spinorbit states and
the corresponding transition properties, which can for example be used to
compute the radiative lifetime of the triplet state.
Keyword  Meaning

NROFjob  Number of input files, number of roots, and roots for each file

EJOB/HDIAG  Read energies from input file / inline

SPIN  Compute spinorbit matrix elements for spin properties



6.9.3 CASVB  A nonorthogonal MCSCF program
CASVB is a program for carrying out quite general types of
nonorthogonal MCSCF calculations, offering, for example, all the advantages
associated with working within a valence bond formalism.
Warning: as for any general MCSCF program, one may experience convergence
problems, (e.g., due to redundant parameters), and the nonorthogonal
optimization of orbitals can furthermore give linear dependency problems.
Several options in CASVB can help overcoming these difficulties.
This program can be used in two basic modes:
 a)
 fully variational optimization
 b)
 representation of CASSCF wavefunctions using
overlap (relatively inexpensive) or energybased criteria.
CASVB executes the following logical steps:
Setup of wavefunction information, starting guess generation, one, or several,
optimization steps, various types of analysis of the converged solution.
6.9.4 CASVB input
CASVB attempts to define defaults for as many input quantities as
possible, so that in the simplest case no input to the CASVB module
is required.
Sample input for a CASVB calculation on the lowest singlet state of CH_{2}:
&GATEWAY
coord
3
ch2 molecule
C 0.000000 0.000000 0.000000
H 0.000000 0.892226 0.708554
H 0.000000 0.892226 0.708554
group= x y; basis= sto3g
&SEWARD
&SCF
&RASSCF
nactel= 6 0 0; inactive= 1 0 0 0; ras2= 3 1 2 0
lumorb
&CASVB
6.9.5 CASVB output
The amount of output in CASVB depends heavily on the setting of the
PRINT levels. In case of problems with convergence behaviour it is
recommended to increase these from their rather terse default values.
In the following the main features of the output are outlined, exemplified by
the job in the input above. Initially, all relevant information
from the previous RASSCF calculation is recovered from the
JOBIPH interface file, after which the valence bond wavefunction
information is summarized, as shown below. Since
spatial configurations have not been specified explicitly in this example, a
single covalent configuration is chosen as default. This gives 5 spinadapted
VB structures.
Number of active electrons : 6
active orbitals : 6
Total spin : 0.0
State symmetry : 1
Spatial VB configurations

Conf. => Orbitals
1 => 1 2 3 4 5 6
Number of VB configurations : 1
VB structures : 5
VB determinants : 20
The output from the following optimization steps summarizes only the most
relevant quantities and convergence information at the default print level. For
the last optimization step, for example, The output below thus
states that the VB wavefunction was found by maximizing the overlap with a
previously optimized CASSCF wavefunction (output by the RASSCF
program), and that the spin adaptation was done using the YamanuchiKotani
scheme. Convergence was reached in 7 iterations.
 Starting optimization  step 3 
Overlapbased optimization (Svb).
Optimization algorithm: dFletch
Maximum number of iterations: 50
Spin basis: Kotani

Optimization entering local region.
Converged ... maximum update to coefficient: 0.59051924E06
Final Svb : 0.9978782695
Number of iterations used: 7
Finally in the output below the converged
solution is printed; orbital coefficients (in terms of the active CASSCF MOs)
and structure coefficients. The overlap between orbitals are generally of
interest, and, as also the structures are nonorthogonal, the structure weights
in the total wavefunction. The total VB wavefunction is not symmetryadapted
explicitly (although one may ensure the correct symmetry by imposing constraints
on orbitals and structure coefficients), so its components in the various
irreducible representations can serve to check that it is physically plausible
(a well behaved solution generally has just one nonvanishing component).
Next follows the oneelectron density with naturalorbital analysis, again with
quantities printed in the basis of the active CASSCF MOs.
Orbital coefficients :

1 2 3 4 5 6
1 0.43397359 0.43397359 0.79451779 0.68987187 0.79451780 0.68987186
2 0.80889967 0.80889967 0.05986171 0.05516284 0.05986171 0.05516284
3 0.00005587 0.00005587 0.20401015 0.20582094 0.20401016 0.20582095
4 0.39667145 0.39667145 0.00000000 0.00000000 0.00000000 0.00000000
5 0.00000001 0.00000001 0.53361427 0.65931951 0.53361425 0.65931952
6 0.00000000 0.00000000 0.19696124 0.20968879 0.19696124 0.20968879
Overlap between orbitals :

1 2 3 4 5 6
1 1.00000000 0.68530352 0.29636622 0.25477647 0.29636623 0.25477647
2 0.68530352 1.00000000 0.29636622 0.25477647 0.29636623 0.25477646
3 0.29636622 0.29636622 1.00000000 0.81994979 0.35292419 0.19890631
4 0.25477647 0.25477647 0.81994979 1.00000000 0.19890634 0.04265679
5 0.29636623 0.29636623 0.35292419 0.19890634 1.00000000 0.81994978
6 0.25477647 0.25477646 0.19890631 0.04265679 0.81994978 1.00000000
Structure coefficients :

0.00000000 0.00000001 0.09455957 0.00000000 0.99551921
Saving VB wavefunction to file VBWFN.
Saving VB CI vector to file JOBIPH.
Svb : 0.9978782695
Evb : 38.4265149062
ChirgwinCoulson weights of structures :

VB spin+space (norm 1.00000000) :
0.00000000 0.00000000 0.00211737 0.00000000 1.00211737
VB spin only (norm 0.38213666) :
0.00000000 0.00000000 0.00894151 0.00000000 0.99105849
Symmetry contributions to total VB wavefunction :

Irreps 1 to 4 : 0.10000000E+01 0.15118834E17 0.17653074E17 0.49309519E17
Energies for components > 1d10 :

Irreps 1 to 4 : 0.38426515E+02 0.00000000E+00 0.00000000E+00 0.00000000E+00
Oneelectron density :

1 2 3 4 5 6
1 1.98488829 0.00021330 0.00011757 0.00000000 0.00000000 0.00000000
2 0.00021330 1.90209222 0.00006927 0.00000000 0.00000000 0.00000000
3 0.00011757 0.00006927 0.02068155 0.00000000 0.00000000 0.00000000
4 0.00000000 0.00000000 0.00000000 0.09447774 0.00000000 0.00000000
5 0.00000000 0.00000000 0.00000000 0.00000000 1.97572540 0.00030574
6 0.00000000 0.00000000 0.00000000 0.00000000 0.00030574 0.02213479
Natural orbitals :

1 2 3 4 5 6
1 0.99999668 0.00000000 0.00257629 0.00000000 0.00000000 0.00005985
2 0.00257628 0.00000000 0.99999668 0.00000000 0.00000000 0.00003681
3 0.00005995 0.00000000 0.00003666 0.00000000 0.00000001 1.00000000
4 0.00000000 0.00000000 0.00000000 1.00000000 0.00000001 0.00000000
5 0.00000000 0.99999999 0.00000000 0.00000000 0.00015650 0.00000000
6 0.00000000 0.00015650 0.00000000 0.00000001 0.99999999 0.00000001
Occupation numbers :

1 2 3 4 5 6
1 1.98488885 1.97572545 1.90209167 0.09447774 0.02213475 0.02068154
6.9.6 Viewing and plotting VB orbitals
In many cases it can be helpful to view the shape of the converged valence bond
orbitals. MOLCAS therefore provides two facilities for doing this. For the
Molden program, an interface file is generated at the end of each
CASVB run (see also Section ). Alternatively a
CASVB run may be followed by RASSCF
(Section ) and GRID_IT
(Section ) with the VB specification, in order to
generate necessary files for viewing with LUSCUS.
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Up: 6. Program Based Tutorials
Previous: 6.8 CASPT2
