5.7. Excited States via ROCIS and ROCIS/DFT¶
The ORCA program package can perform configuration interaction with single excitations (CIS) calculations using a restricted open-shell Hartee-Fock (ROHF) reference function. It produces excitation energies, absorption energies and CD intensities. It was designed with the aim to reproduce and - even more importantly - reliably predict transition metal L-edges as observed in X-ray absorption spectroscopy (XAS).
The original ROCIS implementation [587], [588] is able to perform the CIS calculations only on top of a high-spin ROHF reference function. Starting in ORCA 6.0 the new General Spin ROCIS (GS-ROCIS) implementation [589] is also available upon request by the user. This new implementation can perform the CIS calculation on top of any spin coupling situation obtained with the CSF-ROHF method. This includes the high-spin situations covered previously by the original implementation.
5.7.1. General Description¶
5.7.1.1. General Spin ROCIS¶
The GS-ROCIS method is described as follows:
Starting from a reference CSF constructed in the genealogical coupling scheme (obtained by a CSF-ROHF calculation),
four classes of excited CSFs are defined according to the occupation number of the orbitals involved in the excitation.
These excitation classes are:
DOMO to SOMO excitations - \(\left| \Phi_i^t \right\rangle\)
SOMO to VMO excitations - \(\left| \Phi_t^a \right\rangle\)
DOMO to VMO excitations - \(\left| \Phi_i^a \right\rangle\)
DOMO to VMO excitations coupled with SOMO to SOMO excitations - \(\left| \Phi_{ui}^{at} \right\rangle\)
This way, the GS-ROCIS wavefunction is defined as:
Where the expansion coefficients \(c_p^q\) are determined in the CI procedure.
GS-ROCIS can be requested by:
%rocis
DoGenROCIS true # Turns the general-spin ROCIS procedure on
ReferenceMult 1 # The reference wavefunction multiplicity (it needs to agree with the ROHF solution)
end
A number of basic variables in the %rocis block control the settings
of the Davidson procedure that is used to solve the CI problem:
%rocis
NRoots 6 # Number of desired roots.
MaxDim 5 # Davidson expansion space = MaxDim * NRoots.
ETol 1e-6 # Energy convergence tolerance.
RTol 1e-6 # Residual vector convergence tolerance.
MaxIter 35 # Maxmimum number of iterations.
NGuessMat 512 # Dimension of the guess matrix: 512x512.
end
The amount of output produced during the calculation is controlled via the PrintLevel variable:
%rocis
PrintLevel 3
end
Note, that this does not influence which spectra are calculated or printed.
The orca_rocis module provides two ways of choosing the orbital
excitation space: by orbital energy or orbital number. In the former
case an energy window has to be specified and the program will then take
all orbitals, whose orbital energies lie within this window, into
account. Note, that one actually has to define two orbital windows: One
for the donor and the second for the acceptor orbital. The input of the
windows is done as an array: The first two numbers define the donor
space while the last two numbers define the acceptor space.
%rocis
NRoots 3
EWin = -5,5,-5,5
end
The default is to keep core orbitals and very high lying virtual orbitals out of their respective orbital excitation spaces. Since these orbitals span a space that is usually not reachable with regular UV/Vis spectroscopy, this is a reasonable approximation. One has to keep in mind that an orbital energy window makes only sense if the orbitals used in the calculation have a well-defined orbital energy. As a consequence one cannot use an orbital energy window for a calculation with localized orbitals. The second way to specify the excitation space is by orbital numbering.
%rocis
NRoots 3
OrbWin = 1,13,9,22
end
In restricted calculations only one set of spatial orbitals is created. Hence it is not necessary to provide orbital windows for \(\alpha\) and \(\beta\) electrons separately. Of course, only doubly or singly occupied orbitals can act as donor orbitals and only singly and nonoccupied orbitals can act as acceptor orbitals. The program recognises nonoccupied orbitals in the donor space and doubly occupied orbitals in the acceptor space and removes both.
The absorption spectrum calculated on the basis of the pure dipole approximation for your calculation is always printed.
Furthermore like in TD-DFT (section Excited States via RPA, CIS, TD-DFT and SF-TDA) or CASSCF one may obtain intensities by evaluating the 2nd order oscillation strengths, or the full semi-classical oscillation strengths.
The exact oscillation strengths behave like the multipole expansion in the velocity representation.
They are by definition origin independent they do not suffer from artificial negative values like the multipole moments beyond 1st order.
They are used with the multipole moments up to 2nd order to regenerate the electric dipole, electric quadrupole and magnetic dipole contributions in either length or the velocity representation.
%rocis
DoDipoleLength true
DoDipoleVelocity true
DecomposeFosc true
DoFullSemiclassical true
DoCD true
end
Further details can be found in the section One Photon Spectroscopy.
The user can control which orbital excitations to include in the ROCIS problem:
%rocis
Do_is true # Include DOMO->SOMO excitations
Do_sa true # Include SOMO->Virtual excitations
Do_ia true # Include DOMO->Virtual excitations
Do_ista true # Include DOMO->SOMO coupled to
# SOMO->Virtual excitations with s not equal t
# For GS-ROCIS, the following excitation is included in the DOMO->VMO class
# Only on the original ROCIS implementation it is a separate class.
Do_isa true # Include DOMO->SOMO coupled to
# SOMO->Virtual excitations with s = t
end
By default, all excitations are included.
When the program finishes the ROCIS calculation it gives the excitation energy together with the composition for each root and the respective spin coupling situation. According to the number of labels of the respective functions \(\left|\Phi \right\rangle\), contributions from excited configuration state functions belonging to the different excitation classes are given by two, three or four numbers.
STATE 16 Exc. Energy: 27294.664mEh 742.726eV 5990486.3cm**-1
8->50 : 0.0145 (-0.120499) : spin coupling: +1-1+1+1+1+1
8->51 : 0.0317 (0.178098) : spin coupling: +1+1+1+1+1-1
8->51 : 0.2212 (-0.470333) : spin coupling: +1+1-1+1+1+1
8->51 : 0.4135 (-0.643076) : spin coupling: +1-1+1+1+1+1
6->46 ; 48->51 : 0.0843 (-0.290338) : spin coupling: +1 2+1 0+1+1
6->47 ; 49->51 : 0.1252 (-0.353805) : spin coupling: +1+1 2+1 0+1
7->46 ; 49->51 : 0.0452 (-0.212665) : spin coupling: +1 2+1+1 0+1
7->47 ; 48->51 : 0.0133 (0.115519) : spin coupling: +1+1 2 0+1+1
7->49 ; 46->51 : 0.0109 (0.104242) : spin coupling: +1 0+1+1 2+1
Furthermore the ROCIS is able to calculate the effect of spin-orbit coupling (SOC) on the calculated ground and excited states. It introduces SOC in the framework of quasi-degenerate perturbation theory (QDPT). The SOC Hamiltonian is diagonalized in the basis of the calculated ROCIS states \(\left| \Psi_I^{SM} \right\rangle\), where \(I\) is the root label and \(S\) and \(M\) are the spin and magnetic spin quantum numbers, respectively[654], [587].
%rocis
rel
DoSOC true # invokes the calculation of SOC effects
TEMPERATURE 10 # temperature for SOC corrected spectra in Kelvin
end
end
After the SOC calculation the program will produce additional spectra
for the SOC corrected results. The spectra contain transitions from the
\(2S+1\) lowest lying states into all excited states, where S is the spin
quantum number of the electronic ground state. These \(2S+1\) lowest
states may be split up in the order of 1-100 cm\(^{-1}\). Due to the small
magnitude of the splitting, all of the \(2S+1\) states
can be significantly populated even at low temperatures. Experimentally,
the intensity of a given transition is dependent on the population of
the corresponding initial state. With the TEMPERATURE keyword the
population of the theoretically calculated states can be manipulated by
the varying the fictive temperature of the system. It has to be
mentioned that the electric quadrupole transitions between spin-orbit
coupled states are not well defined and are likely to give unreasonable
results. Hence it is recommended to use the Decomposefosc keyword only
for calculations that do not include SOC.
--------------------------------------------------------------------------------------------------------
SOC CORRECTED ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
--------------------------------------------------------------------------------------------------------
Transition Energy Energy Wavelength fosc(D2) D2 |DX| |DY| |DZ|
(eV) (cm-1) (nm) (*population) (au**2) (au) (au) (au)
--------------------------------------------------------------------------------------------------------
0-5.0A -> 1-5.0A 0.000000 0.0 0.0 0.000000000 0.00000 0.00000 0.00000 0.00000
2-5.0A -> 3-5.0A 0.000000 0.0 2927278012.6 0.000000000 0.00000 0.00000 0.00000 0.00000
3-5.0A -> 4-5.0A 0.000001 0.0 2013441147.3 0.000000000 0.00000 0.00000 0.00000 0.00000
2-5.0A -> 4-5.0A 0.000001 0.0 1192923906.3 0.000000000 0.00000 0.00000 0.00000 0.00000
1-5.0A -> 2-5.0A 0.000002 0.0 559585326.1 0.000000000 0.00000 0.00000 0.00000 0.00000
0-5.0A -> 2-5.0A 0.000002 0.0 554991701.4 0.000000000 0.00000 0.00000 0.00000 0.00000
1-5.0A -> 3-5.0A 0.000003 0.0 469780906.9 0.000000000 0.00000 0.00000 0.00000 0.00000
0-5.0A -> 3-5.0A 0.000003 0.0 466539107.5 0.000000000 0.00000 0.00000 0.00000 0.00000
1-5.0A -> 4-5.0A 0.000003 0.0 380906816.8 0.000000000 0.00000 0.00000 0.00000 0.00000
0-5.0A -> 4-5.0A 0.000003 0.0 378772788.3 0.000000000 0.00000 0.00000 0.00000 0.00000
4-5.0A -> 5-5.0A 715.072294 5767447.6 1.7 0.000853852 0.00024 0.00000 0.01494 0.00454
3-5.0A -> 5-5.0A 715.072294 5767447.6 1.7 0.000001143 0.00000 0.00021 0.00018 0.00050
2-5.0A -> 5-5.0A 715.072295 5767447.6 1.7 0.000001245 0.00000 0.00024 0.00053 0.00012
1-5.0A -> 5-5.0A 715.072297 5767447.6 1.7 0.000000330 0.00000 0.00000 0.00029 0.00010
0-5.0A -> 5-5.0A 715.072297 5767447.6 1.7 0.000024144 0.00001 0.00000 0.00251 0.00076
4-5.0A -> 6-5.0A 715.089740 5767588.3 1.7 0.000002661 0.00000 0.00067 0.00036 0.00042
3-5.0A -> 6-5.0A 715.089741 5767588.3 1.7 0.000008083 0.00000 0.00000 0.00145 0.00045
2-5.0A -> 6-5.0A 715.089742 5767588.3 1.7 0.000775076 0.00022 0.00001 0.01423 0.00432
1-5.0A -> 6-5.0A 715.089744 5767588.4 1.7 0.000000497 0.00000 0.00002 0.00015 0.00035
0-5.0A -> 6-5.0A 715.089744 5767588.4 1.7 0.000001537 0.00000 0.00056 0.00035 0.00007
4-5.0A -> 7-5.0A 715.115140 5767793.2 1.7 0.000001500 0.00000 0.00027 0.00020 0.00056
3-5.0A -> 7-5.0A 715.115141 5767793.2 1.7 0.000834113 0.00024 0.00001 0.01476 0.00449
2-5.0A -> 7-5.0A 715.115141 5767793.2 1.7 0.000008694 0.00000 0.00002 0.00150 0.00050
1-5.0A -> 7-5.0A 715.115143 5767793.2 1.7 0.000000562 0.00000 0.00026 0.00025 0.00018
0-5.0A -> 7-5.0A 715.115143 5767793.2 1.7 0.000003341 0.00000 0.00036 0.00031 0.00085
4-5.0A -> 8-5.0A 715.184940 5768356.2 1.7 0.000000146 0.00000 0.00004 0.00020 0.00001
3-5.0A -> 8-5.0A 715.184940 5768356.2 1.7 0.000019943 0.00001 0.00206 0.00012 0.00120
...
If the PrintLevel value is set to 3 or higher, the program will print
out the composition of the SOC corrected states in the basis of states
\(\left| \Psi_I^{SM} \right\rangle\).
Eigenvectors of SOC calculation:
the threshold for printing is: 0.010000
weight real image : Root Block Spin Ms
State 0: 0.00 cm**-1 0.00000 eV
0.135363 -0.028407 0.366819 : 0 0 2 2
0.181749 0.224125 0.362653 : 0 0 2 1
0.367330 -0.135925 -0.590639 : 0 0 2 0
0.180828 0.039792 -0.423372 : 0 0 2 -1
0.134728 0.185875 0.316510 : 0 0 2 -2
State 1: 0.00 cm**-1 0.00000 eV
0.078367 -0.271364 0.068762 : 0 0 2 2
0.306783 0.460606 0.307612 : 0 0 2 1
0.228162 0.440545 0.184613 : 0 0 2 0
0.307656 -0.543907 -0.108722 : 0 0 2 -1
0.079031 -0.142362 -0.242414 : 0 0 2 -2
State 2: 0.02 cm**-1 0.00000 eV
0.416636 0.252581 0.594003 : 0 0 2 2
0.072004 -0.082420 0.255363 : 0 0 2 1
0.022669 -0.134504 0.067662 : 0 0 2 0
0.071994 0.254211 0.085850 : 0 0 2 -1
0.416695 -0.326890 -0.556631 : 0 0 2 -2
State 3: 0.02 cm**-1 0.00000 eV
0.080023 -0.256741 0.118772 : 0 0 2 2
0.319001 0.556244 0.097947 : 0 0 2 1
0.201858 -0.134225 0.428768 : 0 0 2 0
0.319074 0.512787 0.236903 : 0 0 2 -1
0.080042 0.143270 0.243959 : 0 0 2 -2
State 4: 0.03 cm**-1 0.00000 eV
0.289609 -0.315623 -0.435879 : 0 0 2 2
0.120461 0.303600 -0.168190 : 0 0 2 1
0.179979 -0.232115 -0.355108 : 0 0 2 0
0.120448 0.275975 -0.210441 : 0 0 2 -1
0.289502 -0.272469 -0.463963 : 0 0 2 -2
State 5: 5767447.63 cm**-1 715.07230 eV
0.191190 -0.086278 0.428656 : 1 0 2 2
0.061035 -0.247045 -0.001820 : 1 0 2 1
0.055460 -0.038920 0.232262 : 1 0 2 0
0.061035 -0.234143 -0.078813 : 1 0 2 -1
0.191190 -0.058171 0.433366 : 1 0 2 -2
0.109587 -0.316206 -0.097982 : 2 0 2 2
0.026192 -0.108605 -0.119987 : 2 0 2 1
0.010968 0.017308 -0.103287 : 2 0 2 0
0.026192 -0.141786 0.078029 : 2 0 2 -1
0.109587 0.330874 0.010450 : 2 0 2 -2
0.015452 0.114128 -0.049265 : 3 0 2 2
0.041882 -0.204634 -0.002607 : 3 0 2 1
0.027697 0.027504 -0.164135 : 3 0 2 0
0.041882 -0.194305 -0.064244 : 3 0 2 -1
0.015452 -0.091834 -0.083778 : 3 0 2 -2
State 6: 5767588.34 cm**-1 715.08974 eV
0.198585 -0.131642 0.425741 : 1 0 2 2
0.047453 -0.161434 0.146261 : 1 0 2 1
0.019867 -0.139025 -0.023213 : 1 0 2 0
0.047453 0.105160 0.190773 : 1 0 2 -1
0.198585 0.013812 -0.445415 : 1 0 2 -2
0.160559 -0.388214 -0.099243 : 2 0 2 2
0.044707 -0.072788 -0.198517 : 2 0 2 1
0.014352 -0.118163 -0.019729 : 2 0 2 0
0.044707 0.133333 -0.164102 : 2 0 2 -1
0.160559 -0.399398 -0.032262 : 2 0 2 -2
0.012669 -0.111020 -0.018537 : 3 0 2 0
...
Further details of the SOC calculation such as the procedure of SOC
integral calculation can be controlled via the %rel block (section
Relativistic Calculations.
5.7.1.2. Original ROCIS Implementation¶
It is still possible to use the original implementation of ROCIS[587], [588] which is able to perform CIS calculations only on top of a high-spin ROHF reference function. All spins of the unpaired electrons have to be coupled ferromagnetically to give a total spin of \(S = \frac{1}{2}N\), where \(N\) is the number of unpaired electrons.
The usage of the original ROCIS implementation can be requested by:
%rocis
DoGenROCIS false
end
In our experience ROHF calculations suffer a lot from convergence problems. UHF calculations generally exhibit better convergence properties. In most cases the quasi-restricted orbitals (qro’s) of a UHF calculation resemble the ROHF orbitals. Thus the original ROCIS features the ability to start a calculation on top of a UHF calculation. It will automatically create the qro’s and build the reference determinant with them. If one wants to avoid the (small) errors that are introduced by this procedure, one may take the qro’s of a UHF calculation as starting orbitals for a subsequent ROHF calculation.
5.7.1.3. ROCIS/DFT¶
Important
Currently,
ROCIS/DFTis not implemented for the general-spin (GS-ROCIS) procedure.
For many transition metal compounds the description of the electronic ground and excited states by Hartree-Fock theory and CIS is of rather poor quality. Especially covalency and relative spin state energetics are not reproduced correctly. This in turn might lead to wrong intensity distributions in the calculated L-edge spectra. In the majority of these cases the quality of the description and hence the predicted L-edge spectra can be significantly improved with the ROCIS/DFT method[587]. It features the usage of a restricted open-shell Kohn-Sham matrix as reference and also uses the DFT orbitals for setting up the excited configuration state functions in the CI expansion. The two electron integrals that include the DFT orbitals are scaled according to their nature and their position in the CI matrix by the parameters \(c_{1}\), \(c_{2}\) and \(c_{3}\). They all lie in the interval [0;1]. Parameters \(c_{1}\) and \(c_{2}\) scale coulomb- and exchange- like terms in the diagonal part of the CI matrix, whereas \(c_{3}\) reduces the size of all off-diagonal elements of the CI matrix. For example:
The three default parameters \(c_{1} = 0.18\), \(c_{2} = 0.20\) and \(c_{3} = 0.40\) have been optimized for a test set of molecules and their excited states on a B3LYP/def2-TZVP(-f) level of theory but can be freely chosen[587]. It is most likely that for a different combination of test molecules, functional and basis set, a different set of parameters gives better results. Since the parameters are chosen with regard of a good “balance” between orbital energies, Coulomb and exchange integrals, a new set of parameters should at least crudely resemble their relative proportions.
The ROCIS/DFT method can be requested by the following keywords:
%rocis
DoGenROCIS false # ROCIS/DFT is available only for the high-spin implementation of ROCIS.
DoDFTCIS true # Switches on the ROCIS/DFT method.
DFTCIS_c = 0.18, 0.20, 0.40 # Array input of the three parameters.
end
5.7.1.4. Resolution of the Identity¶
If calculations on large molecules are conducted, the integral transformation will be the most time-consuming part. Therefore it is strongly recommended to use the resolution of the identity (RI) approximation in those cases. It effectively reduces the computational costs of the transformation step by only introducing minor errors to the calculation. It has to be kept in mind that in order to keep the introduced errors small, one has to provide a reasonable auxiliary basis sets along with your normal basis set input.
! def2-SVP def2-SVP/C TightSCF
%scf
HFTyp ROHF
ROHF_Case HighSpin
ROHF_Nel[1] = 1
end
%rocis
NRoots 5
DoRI true # invokes the RI approximation
end
* xyz 0 2
N 0 0 0
O 0 0 1.15
*
5.7.2. Core PNO-ROCIS, PNO-ROCIS/DFT¶
It has been shown [655] that it is possible to combine the powerful machinery of Pair Natural Orbitals (PNOs) with the ROCIS and ROCIS/DFT methods to formulate the core PNO-ROCIS and PNO-ROCIS/DFT methods. The usage of PNOs here is somewhat unconventional since they are not used to treat electron correlation effects in a state specific manner. Rather, the PNOs are used to identify the relevant part of the virtual space that can be reached by excitation out of local core orbitals. This subspace of the virtual space is local, thus leading to a linear scaling, state universal method.
The PNO-ROCIS calculations can be requested with the following keywords:
%rocis
DoPNO true # Flag to call the PNO truncation
TCutPNO 1e-11 # Threshold to cutout the PNO populations
XASElems 0 # Number of the involved element to the calculated core XAS calculation
end
As shown in reference[655], a universal TCutPNO 1e-11 threshold can be defined for all edges provided that the PNOs are constructed by taking into account all the available core orbitals in the systems. For example in the case of a 1st row transition metal this will be the 9 1s, 2s, 2p, 3s and 3p MOs. These orbitals will be identified automatically by the program provided that the elements for which the XAS calculation will be performed are specified within the XASElems keyword.
===============================================================
Core PNO/ROCIS truncation
===============================================================
...
================================================================
TCutPNO: 1.000e-13
Virtual orbitals before selection: 303 ... 2772 (2470 MO's)
Virtual orbitals after selection: 303 ... 558 (256 MO's)
PNO transformation completed in: 3253.03 sec
================================================================
From this point and on the programm will proceed the usual way. This will result in extraordinary computation speeding ups without loss in accuracy.
5.7.3. Transition Metal L-Edges with ROCIS or DFT/ROCIS¶
The ROCIS method was designed to calculate transition metal L-edge spectra of large molecules as they are observed in X-ray absorption spectroscopy (XAS). An L-edge results when an electron is promoted from the 2p shell of a transition metal ion into the valence d shell by an X-ray photon. Strong spin-orbit coupling in the 2p shell and p-d coupling phenomena complicate the interpretation and even more so the prediction of these spectra. It has to be kept in mind that the present program applies a variety of approximations which might lead to observable deviations from experimentally determined spectra. However, we believe that the results obtained from the program are in general qualitatively correct and in most cases accurate close to the experimental uncertainty. In cases where quantitative accuracy is not met, the provided results might still give some insight into the mechanisms of intensity distribution in the spectra.
The special input structure for orbital windows described in Excited States with Restricted Open-shell CIS - ROCIS allows the user to restrict the donor orbital space to the transition metal 2p shell. The acceptor orbital space is the same as in regular UV/Vis spectroscopy. It should include all singly occupied molecular orbitals and as many virtual orbitals as one can afford in the calculation (preferably all). The number of roots should be chosen large enough so that at least all 2p-3d single excitations are calculated. In many cases even more roots are required since doubly excited or charge transfer states may become important. Moreover the strong SOC apparent in the 2p shell of transition metal ions necessitates the additional calculation of excited states with a total spin of \(S' = S + 1\) and \(S' = S -1\) where \(S\) is the total spin of the electronic ground state. Accordingly, additional excitation classes introduce excited configuration state functions with a lower and higher spin multiplicity.
for \(S' = S + 1\):
DOMO to SOMO excitations - \(\left| \Phi_i^{t+} \right\rangle\)
SOMO to VMO excitations - \(\left| \Phi_t^{a+} \right\rangle\)
DOMO to VMO excitations - \(\left| \Phi_i^{a+} \right\rangle\)
for \(S' = S -1\):
DOMO to SOMO excitations - \(\left| \Phi_i^{t-} \right\rangle\)
SOMO to VMO excitations - \(\left| \Phi_t^{a-} \right\rangle\)
DOMO to VMO excitations - \(\left| \Phi_i^{a-} \right\rangle\)
SOMO to SOMO excitations - \(\left| \Phi_t^{u-} \right\rangle\)
Note
Depending on the ground state multiplicity and/or occupation of the involved orbitals, some excitations are not possible. The program automatically includes only the allowed excitations into the respective multiplicities.
Inclusion of configuration state functions with higher or lower
multiplicity is invoked with the keywords DoLowerMult and
DoHigherMult, respectively.
%rocis
DoLowerMult true #Invokes a CI calculation #with S'=S-1
DoHigherMult true #Invokes a CI calculation #with S'=S+1
end
The program will conduct a separate Davidson procedure for each multiplicity. Subsequently it gives the excitation energies and compositions of the calculated excited states for all included multiplicities.
Here is an example calculation of L-edge XAS on [FeCl\(_4\)]\(^{2-}\):
# [Fe(II)Cl4]2- - ROCIS - L-edge
!x2c x2c-SVPall AutoAux TightSCF
%pal
nproc 12
end
%scf
HFTyp ROHF
ROHF_CASE HIGHSPIN
ROHF_NEL[1] 4
end
%rocis
DoGenROCIS true
ReferenceMult 5
NRoots 50
OrbWin 6,8,0,2000
DoPNO true
TCutPNO 1e-11
XASelems 0
rel
DoSOC true
end
DoHigherMult true
DoLowerMult true
DoRI true
Decomposefosc true
end
*xyz -2 5
Fe -0.009575 0.000087 0.011550
Cl -1.774578 -1.558533 -0.219791
Cl -0.681385 1.874633 1.289404
Cl 0.666770 0.847828 -2.091305
Cl 1.756927 -1.164015 1.071196
end
After all CI calculations are finished, the program gives a list of all calculated roots with their excitation energies and their multiplicities. It is this number that will be referred to as label \(I\) in the decomposition of spin-orbit coupled states in the basis \(\left| \Psi_{I}^{SM} \right\rangle\). It is very important to note, that when states with different multiplicities are calculated this number might deviate from the number that appears in the respective CI part of the output. If one gets confused about the numbering of the states, the state energies might act as a guideline through the output of the program.
-------------------
Excitation energies
-------------------
--------------------------------------------------------------------------------
ROOT Mult Excitation energy[Eh] [cm-1] [eV]
--------------------------------------------------------------------------------
0 5 0.00000000 0.00 0.000
1 5 26.41778649 5798033.94 718.865
2 5 26.42452401 5799512.66 719.048
3 5 26.42621555 5799883.91 719.094
4 5 26.44615744 5804260.65 719.637
5 5 26.45323131 5805813.18 719.829
6 5 26.47192609 5809916.21 720.338
7 5 26.47357807 5810278.78 720.383
8 5 26.48177016 5812076.74 720.606
9 5 26.49063895 5814023.21 720.847
10 5 26.50722706 5817663.88 721.298
11 5 26.50759779 5817745.25 721.308
12 5 26.50982238 5818233.49 721.369
13 3 26.55037043 5827132.76 722.472
14 3 26.58407940 5834531.02 723.390
15 3 26.58587963 5834926.12 723.439
16 3 26.58857702 5835518.13 723.512
17 3 26.59674863 5837311.59 723.734
18 3 26.59825865 5837643.00 723.775
19 3 26.61152227 5840554.03 724.136
20 3 26.61806435 5841989.85 724.314
21 3 26.62812795 5844198.56 724.588
22 3 26.63079807 5844784.58 724.661
23 3 26.63345218 5845367.09 724.733
24 3 26.64337021 5847543.85 725.003
25 3 26.65680719 5850492.92 725.369
26 3 26.66486245 5852260.85 725.588
27 3 26.66512507 5852318.49 725.595
28 3 26.66741755 5852821.63 725.657
29 3 26.68096811 5855795.63 726.026
30 3 26.68291870 5856223.74 726.079
31 3 26.68410859 5856484.89 726.112
32 3 26.68502036 5856685.00 726.136
33 3 26.68625712 5856956.44 726.170
34 3 26.68835097 5857415.98 726.227
35 3 26.69951161 5859865.46 726.531
36 3 26.70277202 5860581.04 726.619
37 3 26.71055426 5862289.04 726.831
38 3 26.71604333 5863493.75 726.980
39 3 26.71631714 5863553.85 726.988
40 3 26.71801283 5863926.01 727.034
41 3 26.71869535 5864075.80 727.053
42 3 26.71953590 5864260.28 727.076
43 3 26.72200411 5864801.99 727.143
44 3 26.72811146 5866142.40 727.309
45 3 26.73591005 5867853.99 727.521
46 3 26.73675062 5868038.48 727.544
47 3 26.75216877 5871422.37 727.964
48 3 26.78204828 5877980.17 728.777
49 7 27.21891306 5973860.90 740.664
50 7 27.21926225 5973937.54 740.674
51 7 27.21931555 5973949.24 740.675
52 5 27.26974929 5985018.16 742.048
53 5 27.26978849 5985026.77 742.049
54 5 27.27023065 5985123.81 742.061
55 5 27.29466376 5990486.26 742.726
56 5 27.29677691 5990950.04 742.783
57 5 27.31333680 5994584.52 743.234
58 7 27.31641173 5995259.39 743.317
59 5 27.31967798 5995976.24 743.406
60 7 27.32002169 5996051.68 743.416
...
Without SOC the spin exclusion rule applies which means that only excited states with a total spin equal to the ground state spin (\(S' = S\)) give rise to non-vanishing intensities. Hence, only these transitions are listed in the spectra before SOC.
------------------------
ROCIS-EXCITATION SPECTRA
------------------------
Center of mass = ( -0.0160, 0.0000, 0.0229)
Reading integrals ...
Reading the Dipole integrals ... done
Reading the Linear Momentum integrals ... done
Reading the Angular momentum integrals ... done
Reading the Quadrupole integrals ... done
Reading the Higher Moment integrals ... done
--------------------------------------------------------------------
Using One-Photon Spectroscopy Tool
--------------------------------------------------------------------
----------------------------------------------------------------------------------------------------
ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
----------------------------------------------------------------------------------------------------
Transition Energy Energy Wavelength fosc(D2) D2 DX DY DZ
(eV) (cm-1) (nm) (au**2) (au) (au) (au)
----------------------------------------------------------------------------------------------------
0-5A -> 1-5A 718.864517 5798034.0 1.7 0.007967331 0.00045 0.00001 -0.02035 0.00619
0-5A -> 2-5A 719.047854 5799512.7 1.7 0.000032204 0.00000 0.00123 -0.00019 -0.00052
0-5A -> 3-5A 719.093883 5799883.9 1.7 0.000038607 0.00000 -0.00060 -0.00039 -0.00130
0-5A -> 4-5A 719.636530 5804260.7 1.7 0.000000074 0.00000 -0.00004 -0.00001 -0.00005
0-5A -> 5-5A 719.829019 5805813.2 1.7 0.000257559 0.00001 -0.00007 -0.00364 0.00116
0-5A -> 6-5A 720.337730 5809916.2 1.7 0.045609938 0.00258 -0.04638 0.00619 0.01987
0-5A -> 7-5A 720.382683 5810278.8 1.7 0.043374431 0.00246 0.02031 0.01315 0.04327
0-5A -> 8-5A 720.605601 5812076.7 1.7 0.000000543 0.00000 0.00005 0.00005 0.00016
0-5A -> 9-5A 720.846933 5814023.2 1.7 0.180244898 0.01021 0.00031 0.09663 -0.02948
0-5A -> 10-5A 721.298318 5817663.9 1.7 0.084488140 0.00478 -0.02823 -0.01833 -0.06040
0-5A -> 11-5A 721.308407 5817745.3 1.7 0.085964316 0.00486 0.06366 -0.00850 -0.02719
0-5A -> 12-5A 721.368941 5818233.5 1.7 0.000000007 0.00000 -0.00000 0.00002 0.00001
0-5A -> 13-5A 742.047603 5985018.2 1.7 0.002287503 0.00013 0.00507 0.00276 0.00962
0-5A -> 14-5A 742.048670 5985026.8 1.7 0.002278095 0.00013 0.00999 -0.00164 -0.00477
0-5A -> 15-5A 742.060702 5985123.8 1.7 0.001342355 0.00007 0.00019 0.00823 -0.00246
0-5A -> 16-5A 742.725560 5990486.3 1.7 0.000418059 0.00002 0.00197 0.00126 0.00419
0-5A -> 17-5A 742.783062 5990950.1 1.7 0.000464555 0.00003 0.00461 -0.00063 -0.00197
0-5A -> 18-5A 743.233680 5994584.5 1.7 0.000000003 0.00000 -0.00001 -0.00000 -0.00001
0-5A -> 19-5A 743.406232 5995976.3 1.7 0.000000000 0.00000 -0.00000 -0.00000 -0.00000
0-5A -> 20-5A 743.562910 5997239.9 1.7 0.000577479 0.00003 0.00001 0.00538 -0.00165
0-5A -> 21-5A 743.597306 5997517.4 1.7 0.000009265 0.00000 -0.00029 -0.00017 -0.00063
0-5A -> 22-5A 743.658216 5998008.6 1.7 0.000010720 0.00000 -0.00070 0.00011 0.00029
0-5A -> 23-5A 744.043391 6001115.3 1.7 0.000081920 0.00000 -0.00088 -0.00059 -0.00184
0-5A -> 24-5A 744.092953 6001515.0 1.7 0.000301862 0.00002 -0.00017 -0.00389 0.00119
...
After calculation of SOC in the basis of all calculated ROCIS roots, the
program prints out the composition of the spin-orbit coupled states (if
PrintLevel >2) and the corresponding absorption spectrum.
Eigenvectors of SOC calculation:
the threshold for printing is: 0.010000
weight real image : Root Block Spin Ms
State 0: 0.00 cm**-1 0.00000 eV
0.135363 -0.028407 0.366819 : 0 0 2 2
0.181749 0.224125 0.362653 : 0 0 2 1
0.367330 -0.135925 -0.590639 : 0 0 2 0
0.180828 0.039792 -0.423372 : 0 0 2 -1
0.134728 0.185875 0.316510 : 0 0 2 -2
State 1: 0.00 cm**-1 0.00000 eV
0.078367 -0.271364 0.068762 : 0 0 2 2
0.306783 0.460606 0.307612 : 0 0 2 1
0.228162 0.440545 0.184613 : 0 0 2 0
0.307656 -0.543907 -0.108722 : 0 0 2 -1
0.079031 -0.142362 -0.242414 : 0 0 2 -2
State 2: 0.02 cm**-1 0.00000 eV
0.416636 0.252581 0.594003 : 0 0 2 2
0.072004 -0.082420 0.255363 : 0 0 2 1
0.022669 -0.134504 0.067662 : 0 0 2 0
0.071994 0.254211 0.085850 : 0 0 2 -1
0.416695 -0.326890 -0.556631 : 0 0 2 -2
State 3: 0.02 cm**-1 0.00000 eV
0.080023 -0.256741 0.118772 : 0 0 2 2
0.319001 0.556244 0.097947 : 0 0 2 1
0.201858 -0.134225 0.428768 : 0 0 2 0
0.319074 0.512787 0.236903 : 0 0 2 -1
0.080042 0.143270 0.243959 : 0 0 2 -2
State 4: 0.03 cm**-1 0.00000 eV
0.289609 -0.315623 -0.435879 : 0 0 2 2
0.120461 0.303600 -0.168190 : 0 0 2 1
0.179979 -0.232115 -0.355108 : 0 0 2 0
0.120448 0.275975 -0.210441 : 0 0 2 -1
0.289502 -0.272469 -0.463963 : 0 0 2 -2
State 5: 5767447.63 cm**-1 715.07230 eV
0.191190 -0.086278 0.428656 : 1 0 2 2
0.061035 -0.247045 -0.001820 : 1 0 2 1
0.055460 -0.038920 0.232262 : 1 0 2 0
0.061035 -0.234143 -0.078813 : 1 0 2 -1
0.191190 -0.058171 0.433366 : 1 0 2 -2
0.109587 -0.316206 -0.097982 : 2 0 2 2
0.026192 -0.108605 -0.119987 : 2 0 2 1
0.010968 0.017308 -0.103287 : 2 0 2 0
0.026192 -0.141786 0.078029 : 2 0 2 -1
0.109587 0.330874 0.010450 : 2 0 2 -2
0.015452 0.114128 -0.049265 : 3 0 2 2
0.041882 -0.204634 -0.002607 : 3 0 2 1
0.027697 0.027504 -0.164135 : 3 0 2 0
0.041882 -0.194305 -0.064244 : 3 0 2 -1
0.015452 -0.091834 -0.083778 : 3 0 2 -2
State 6: 5767588.34 cm**-1 715.08974 eV
0.198585 -0.131642 0.425741 : 1 0 2 2
0.047453 -0.161434 0.146261 : 1 0 2 1
0.019867 -0.139025 -0.023213 : 1 0 2 0
0.047453 0.105160 0.190773 : 1 0 2 -1
0.198585 0.013812 -0.445415 : 1 0 2 -2
0.160559 -0.388214 -0.099243 : 2 0 2 2
0.044707 -0.072788 -0.198517 : 2 0 2 1
0.014352 -0.118163 -0.019729 : 2 0 2 0
0.044707 0.133333 -0.164102 : 2 0 2 -1
0.160559 -0.399398 -0.032262 : 2 0 2 -2
0.012669 -0.111020 -0.018537 : 3 0 2 0
...
Energy levels: cm-1 eV Boltzmann populations for T = 300.00 K
0 : 0.000 0.0000 2.00e-01
1 : 0.000 0.0000 2.00e-01
2 : 0.018 0.0000 2.00e-01
3 : 0.021 0.0000 2.00e-01
4 : 0.026 0.0000 2.00e-01
--------------------------------------------------------------------------------------------------------
SOC CORRECTED ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
--------------------------------------------------------------------------------------------------------
Transition Energy Energy Wavelength fosc(D2) D2 |DX| |DY| |DZ|
(eV) (cm-1) (nm) (*population) (au**2) (au) (au) (au)
--------------------------------------------------------------------------------------------------------
0-5.0A -> 1-5.0A 0.000000 0.0 0.0 0.000000000 0.00000 0.00000 0.00000 0.00000
2-5.0A -> 3-5.0A 0.000000 0.0 2927278012.6 0.000000000 0.00000 0.00000 0.00000 0.00000
3-5.0A -> 4-5.0A 0.000001 0.0 2013441147.3 0.000000000 0.00000 0.00000 0.00000 0.00000
2-5.0A -> 4-5.0A 0.000001 0.0 1192923906.3 0.000000000 0.00000 0.00000 0.00000 0.00000
1-5.0A -> 2-5.0A 0.000002 0.0 559585326.1 0.000000000 0.00000 0.00000 0.00000 0.00000
0-5.0A -> 2-5.0A 0.000002 0.0 554991701.4 0.000000000 0.00000 0.00000 0.00000 0.00000
1-5.0A -> 3-5.0A 0.000003 0.0 469780906.9 0.000000000 0.00000 0.00000 0.00000 0.00000
0-5.0A -> 3-5.0A 0.000003 0.0 466539107.5 0.000000000 0.00000 0.00000 0.00000 0.00000
1-5.0A -> 4-5.0A 0.000003 0.0 380906816.8 0.000000000 0.00000 0.00000 0.00000 0.00000
0-5.0A -> 4-5.0A 0.000003 0.0 378772788.3 0.000000000 0.00000 0.00000 0.00000 0.00000
4-5.0A -> 5-5.0A 715.072294 5767447.6 1.7 0.000853852 0.00024 0.00000 0.01494 0.00454
3-5.0A -> 5-5.0A 715.072294 5767447.6 1.7 0.000001143 0.00000 0.00021 0.00018 0.00050
2-5.0A -> 5-5.0A 715.072295 5767447.6 1.7 0.000001245 0.00000 0.00024 0.00053 0.00012
1-5.0A -> 5-5.0A 715.072297 5767447.6 1.7 0.000000330 0.00000 0.00000 0.00029 0.00010
0-5.0A -> 5-5.0A 715.072297 5767447.6 1.7 0.000024144 0.00001 0.00000 0.00251 0.00076
4-5.0A -> 6-5.0A 715.089740 5767588.3 1.7 0.000002661 0.00000 0.00067 0.00036 0.00042
3-5.0A -> 6-5.0A 715.089741 5767588.3 1.7 0.000008083 0.00000 0.00000 0.00145 0.00045
2-5.0A -> 6-5.0A 715.089742 5767588.3 1.7 0.000775076 0.00022 0.00001 0.01423 0.00432
1-5.0A -> 6-5.0A 715.089744 5767588.4 1.7 0.000000497 0.00000 0.00002 0.00015 0.00035
0-5.0A -> 6-5.0A 715.089744 5767588.4 1.7 0.000001537 0.00000 0.00056 0.00035 0.00007
4-5.0A -> 7-5.0A 715.115140 5767793.2 1.7 0.000001500 0.00000 0.00027 0.00020 0.00056
3-5.0A -> 7-5.0A 715.115141 5767793.2 1.7 0.000834113 0.00024 0.00001 0.01476 0.00449
2-5.0A -> 7-5.0A 715.115141 5767793.2 1.7 0.000008694 0.00000 0.00002 0.00150 0.00050
1-5.0A -> 7-5.0A 715.115143 5767793.2 1.7 0.000000562 0.00000 0.00026 0.00025 0.00018
0-5.0A -> 7-5.0A 715.115143 5767793.2 1.7 0.000003341 0.00000 0.00036 0.00031 0.00085
4-5.0A -> 8-5.0A 715.184940 5768356.2 1.7 0.000000146 0.00000 0.00004 0.00020 0.00001
3-5.0A -> 8-5.0A 715.184940 5768356.2 1.7 0.000019943 0.00001 0.00206 0.00012 0.00120
2-5.0A -> 8-5.0A 715.184941 5768356.2 1.7 0.000019954 0.00001 0.00119 0.00064 0.00197
1-5.0A -> 8-5.0A 715.184943 5768356.2 1.7 0.000507851 0.00014 0.00004 0.01152 0.00348
0-5.0A -> 8-5.0A 715.184943 5768356.2 1.7 0.000022305 0.00001 0.00003 0.00240 0.00077
4-5.0A -> 9-5.0A 715.206052 5768526.4 1.7 0.000049980 0.00001 0.00006 0.00360 0.00113
3-5.0A -> 9-5.0A 715.206053 5768526.4 1.7 0.000007590 0.00000 0.00077 0.00040 0.00119
...
The obtained spectra can be prepared for ploting with the use of orca_mapspc.
Check section orca_mapspc for details.
5.7.4. Resonant Inelastic Scattering Spectroscopy¶
5.7.4.1. General¶
Starting from ORCA version 4.0 ROCIS module can be used to calculate RIXS spectra
The present implementation is directly based on the Kramers Heisenerg Dirac (KDH) expression formula for near resonant and resonant conditions
The resonance scattering cross section for total and direct cases, averaged over all orientations of the molecule and integrated over all directions and polarizations of scattered radiation is given in equations:
Interference effects can be then derived in a straightforward way from equation:
In order to access RIXS spectroscopy in the ROCIS module one needs in addition to specify a 2nd donor space. This is specified by defining an OrbWin array with 6 elements: The first four elements define the ranges of the two donor spaces while the last two elements the respective acceptor space range.
OrbWin = 0,0,2,4,45,60
An important difference with respect to the conventional ROCIS or DFT/ROCIS calculations is the fact that two donor spaces of very different energy ranges are involved (e.g. K-edge, L-edge) which requires to restrict somewhat the acceptor space and saturate it with as many states as possible.
The main calling commands in order to perform a RIXS calculation within both ROCIS and CASSCF blocks are the following:
RIXS true. Similar to absorption spectroscopy, this requests the RIXS calculation to be performed based on the calculated non-relativistic ground state multiplicity States
RIXSSOC true. By turning-on this flag the RIXS is calculated by taking in account the relativistically corrected Ms States.
Elastic true. This flag indicates whether the resonant condition in which the initial and Final states coincide should be taken into account. Note that the intensity of this spectral feature might be overestimated as presently the non resonant terms are not treated
The respective ROCIS input reads then as follows:
!B3LYP def2-TZVP SlowConv
%Basis
AuxC "def2/J"
end
%ROCIS
NRoots 200
PrintLevel 3
MaxCore 4000
DoRI true
DoHigherMult true
SOC true
RIXS true # Request RIXS calculation (NoSOC)
RIXSSOC true # Request RIXS calculation (with SOC)
Elastic true # Request RIXS calculation (Elastic)
DoDFTCIS true
DFTCIS_c =0.18,0.20,0.40
OrbWin = 2,4,25,33,0,100
end
* xyzfile 2 2 test.xyz
When running the calculation one can monitor if the requested NRoots were sufficient enough to select the states dominated by both the donor orbital spaces
--------------------------------------------------------------------------------
ROOT Mult Excitation energy[Eh] [cm-1] [eV]
--------------------------------------------------------------------------------
0 2 0.00000000 0.00 0.000
1 2 0.06611737 14511.08 1.799
2 2 0.07728471 16962.03 2.103
3 2 0.07732428 16970.72 2.104
...
84 2 33.75471831 7408304.35 918.513
85 2 33.77073325 7411819.22 918.948
86 2 33.77076955 7411827.19 918.949
87 4 34.06882971 7477243.83 927.060
88 2 34.07021441 7477547.74 927.098
...
If that is not the case the respective RIXS calculations will not be performed and a Warning Message will be generated:
Making the RIXS files ...
WARNING!: Flag for RIXS property calculation was identified but
there is zero number of Intermediate and/or Final states:
No Cross-Section properties will be evaluated ...Skipping this part
TIP: Increase the number of NRoots and/or decrease or increase
the acceptor orbital space
...Done
A successful run on the other hand will generate the following messages for RIXS and RIXSSOC calculations.
----------------------------------------------------------------------------------
ROCIS RIXS SPECTRUM
----------------------------------------------------------------------------------
Making the RIXS data files for Inelastic and Elastic Scattering
Ground State: 1
Intermediate States: 21
Final States: 59
The RIXS cross section will be generated from:
60 Ground-Final State Pairs and 21 Intermediate States/Pair
Calculating Intensities...
10% done
20% done
30% done
40% done
50% done
60% done
70% done
80% done
90% done
100% done
Storing the files...All Done
----------------------------------------------------------------------------------
----------------------------------------------------------------------------------
ROCIS RIXSSOC SPECTRUM
----------------------------------------------------------------------------------
Making the RIXS-SOC data files for Inelastic and Elastic Scattering
Ms States: 2
Intermediate States: 78
Final States: 214
The RIXS cross section will be generated from:
432 Ground-Final State Pairs and 78 Intermediate States/Pair
Calculating Intensities...
10% done
20% done
30% done
40% done
50% done
60% done
70% done
80% done
90% done
100% done
Storing the files...All Done
----------------------------------------------------------------------------------
In both cases the number of involved Initial, Final and Intermediate states is specified explicitly.
For example in the case of RIXSSOC 2 Ms Ground states, 78 Intermediate states and 214 Final states are involved. Then the RIXS cross section for elastic and inelastic scattering will be generated by 432 (2*(2+214)) Ground-Final State-Pairs and 78 Intermediate States per Ground-Final state pair.
5.7.4.2. Processing the spectra with orca_mapspc¶
By calling orca_mapspc with the following keywords:
orca_mapspc test.el_inel.rocis.rixssoc RIXS -x0871 -x1876 -x2-1 -x34 -w0.4 -g0.4
-l -n125 -m125 -dx20 -eaxis1
The program will process the test.el_inel.rocis.rixssoc file with the
following parameters:
Energy range along x : 871-876 eV
Energy range along y: -1-34 eV
-l indicates Lorentzian broadening
Width along x (gamma): 0.4 eV
Width along y (gamma): 0.4 eV
Points along x: 125
Points along y:125
Shift to be applied along Incident energy/Emission axis: 20 eV
The y axis will be Energy Transfer axis. If -eaxis2 is the y axis will be then Emission Energy axis
All this information is printed during the data processing:
Mode is RIXS
Using Lorentzian shape
Cannot read the paras.inp file ...
taking the line width parameter from the command line
Cannot read the udex.inp file ...
taking the excitation energy ranges from the command line
Cannot read the udem.inp file ...
taking the emission energy ranges from the command line
Cannot read the gfsp.inp file ...
No Ground-Final State Pairs will be evaluated
---------------------------------------------------------------------------------
PLOTTING RIXS SPECTRA
---------------------------------------------------------------------------------
Input File : test.el_inel.rocis.rixssoc
Incident Energy Excitation axis : 871.000 ... 876.000 eV 125 points
Energy transfer axis : -1.000 ... 4.000 eV 125 points
Incident Energy Shift : 20.000 eV
Lorenzian Linewidth along Incident Axis : 0.400 eV
Lorenzian Linewidth along Energy Transfer/Emission Axis : 0.400 eV
y axis : 1 -> Energy transfer
Number of user defined cuts at constant Excitation Energy axis: 0
Number of user defined cuts at constant Emission/Energy Transfer Energy axis : 0
Making checks...Done
Proccessing data...
10% done
20% done
...
100% done
RIXS-plotting done
Incident Energy range: 845.800 ... 869.249
Emission/Energy-transfer range: 0.000 ... 4.853
Now storing the 2D file...
Done
Making the Integrated spectra along Energy Transfer/Emission axis... Done
Making the Integrated spectra along Incident axis... Done
All Done
---------------------------------------------------------------------------------
Successful run will generate the following files: The RIXS planes of the Total, Direct and Interference RIXS intensity as indicated in the above equations:
test.el_inel.rocis.rixssoc.total_rixs.dat
test.el_inel.rocis.rixssoc.direct_rixs.dat
test.el_inel.rocis.rixssoc.interference_rixs.dat
In addition one obtains the integrated spectra at constant Incident energies (CIE):
test.el_inel.rocis.rixssoc.dw.dat
as well as at constant Emission/Energy Transfer energies (CEE/CET):
test.el_inel.rocis.rixssoc.wex.dat
Fig. 5.25 DFT/ROCIS calculated RIXS planes for \({[Cu{(N{H_3})_4}]^{2 - } }\). Left: Total RIXS Intensity, Middle: Direct RIXS intensity and Right: Interference RIXS intensity. Lorentzian lineshape broadening with constant widths along Incident and Energy Transfer axis (0.5 and 0.2 eV respectively) were used throughout.¶
5.7.4.3. Generating Cuts¶
Cuts along x and y axis can be generated with two ways:
1) At first, this action can be performed by adding the following
keywords: uex and udw accounting for generating cuts at constant
Incident Energies (CIE) and at constant Emission (CEE)/or at constant
Energy Transfer (CET) respectively, together with the desired number of
cuts.
2) Alternatively, the energies of the desired cuts can be specified as lists in the files udex.inp (user defined excitations) udem.inp (user defined emissions)
For example if in udex.inp one specifies:
872.5
874.2
and for the cuts along Energy Transfer axis one just specify -udw3
orca_mapspc test.el_inel.rocis.rixssoc RIXS -x0871 -x1876 -x2-1 -x34 -w0.4 -g0.4
-l -n125 -m125 -dx20 -eaxis1 -udw3
Then at the end one gets:
Making the specified cuts (2) at constant Excitation Energy axis...
Writing file: test.el_inel.rocis.rixssoc_872.50.rxes_vs.dat ...Done
Writing file: test.el_inel.rocis.rixssoc_872.50.rxes_fs.dat ...Done
Writing file: test.el_inel.rocis.rixssoc_874.20.rxes_vs.dat ...Done
Writing file: test.el_inel.rocis.rixssoc_874.20.rxes_fs.dat ...Done
Done
Making the specified cuts (3) at constant Emission/Energy Transfer axis...
Writing file: test.el_inel.rocis.rixssoc_-1.00.xas_vs.dat ...Done
Writing file: test.el_inel.rocis.rixssoc_-1.00.xas_fs.dat ...Done
Writing file: test.el_inel.rocis.rixssoc_1.50.xas_vs.dat ...Done
Writing file: test.el_inel.rocis.rixssoc_1.50.xas_fs.dat ...Done
Writing file: test.el_inel.rocis.rixssoc_4.00.xas_vs.dat ...Done
Writing file: test.el_inel.rocis.rixssoc_4.00.xas_fs.dat ...Done
Done
All Done
---------------------------------------------------------------------------------
The files *_rxes_fs.dat are RXES spectra containing all individual
contributions from all Final states together with the Direct, the Total
and the Interference contributions at the given constant Incident
Energy.
Similarly, the *_rxes_vs.dat are RXES spectra containing individual
contributions of the Intermediate states, together with the Direct the
Total and the Interference contributions at the given constant Incident
Energy
Likewise, the respective *_xas_fs.dat and *_xas_vs.dat are XAS type
spectra with individual contributions at a given constant Emission or
Energy transfer Energy
These files are Energy vs Intensity files and read like:
1) for *fs.dat
X S- 1( 0- 0) S- 2( 0- 1) DIRECT TOT INTERFERENCE
2) for *vs.dat
X S- 1( 45) S- 2( 47) DIRECT TOT INTERFERENCE
In the first case S -1(0-0) represents the individual contribution of a given Ground-Final state pair. The numbering follows the numbering of the output file e.g.:
Eigenvalues: cm-1 eV Boltzmann populations at T = 300.000 K
0: 0.0000 0.0000 3.44e-01
1: 8.3818 0.0010 3.31e-01
Hence, in this case S -1 represents the elastic scattering intensity.
In the second case S -1(45) represents the individual contribution of a given Intermediate state.
44: 66918.6071 8.2968 1.43e-140
45: 6996678.8061 867.4775 0.00e+00
46: 6996693.0276 867.4793 0.00e+00
In this case S -1 represents the intensity contribution of the first Intermediate state.
Starting from ORCA 4.2 in every RIXS requested calculation the Off resonant XES spectrum is automatically generated in every RIXS requested calculation.
----------------------------------------------------------------------------------
ROCIS RIXS SPECTRUM
----------------------------------------------------------------------------------
Making the RIXS data files for Inelastic and Elastic Scattering
Ground State: 1
Intermediate States: 28
Final States: 588
The RIXS cross section will be generated from:
589 Ground-Final State Pairs and 28 Intermediate States/Pair
The Off-Resonance XES spectrum will be printed
Calculating Intensities...
10% done
20% done
30% done
40% done
50% done
60% done
70% done
80% done
90% done
100% done
Printing the XES spectrum and Storing the files...
-------------------------------------------------------------------------------------
X-RAY EMISSION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
-------------------------------------------------------------------------------------
Transition Energy INT TX TY TZ
(eV) (fosc) (au) (au) (au)
-------------------------------------------------------------------------------------
1 589 -> 0 6403.377 0.000000000721 0.00000 0.00000 0.00000
2 590 -> 0 6403.380 0.000000000083 -0.00000 0.00000 0.00000
3 591 -> 0 6403.685 0.000873238810 0.00236 0.00000 0.00000
4 592 -> 0 6404.766 0.000000000154 0.00000 0.00000 0.00000
5 593 -> 0 6408.288 0.000000006850 -0.00001 0.00000 0.00000
6 594 -> 0 6408.295 0.000034710300 -0.00047 0.00000 0.00000
...
16490 614 -> 588 6387.989 0.000000000000 0.00000 0.00000 0.00000
16491 615 -> 588 6388.222 0.000000000000 0.00000 0.00000 0.00000
16492 616 -> 588 6388.881 0.000000000000 0.00000 0.00000 0.00000
All Done
----------------------------------------------------------------------------------
Hence also the myfile-rixs.out file can also be processed with the
orca_mapspc to generate the respective XES spectra:
orca_mapspc myfile_rixs.out XES/XESSOC -x06000 -x16500 -w2.0 -eV -n10000
5.7.5. ROCIS Magnetic Properties¶
Several magnetic properies are availiable in the ROCIS method Including g-tensors (G-Matrix), zero field splittings (ZFS), hyperfine couplings (HFCs) and electric field gradients (EFGs).
The g-tensors as well as the zfs are calculated on the basis of the Effective Hamiltonian as well in the sum over states (SOS) framework. HFCs are calculated in the SOS framework while EFGs are calculated as expectation values. Please consult also the respective discussion in the MRCI chapter (section Multireference Configuration Interaction and Pertubation Theory (uncontracted))
...
DoHeff true # Requests calculation of G-tenosrs and ZFS
# in the effective Hamiltonian framework
DoEPR true # Requests calculation of G-tenosrs, ZFS and HFCs
# in the Sum over states (SOS) framework
AtensorNuc 0 # Nuclei to account for the HFCs calculation
NAtensors 1 # How many Nuclei are included in the HFCs calculation
ATensor 0 # Nucleus to calculate HFCs and EFGs
NDoubGtensor 1 # Kramers doublets to account for the g tensor calculations
...
This will enter the calculation in the ROCIS Spin Hamiltonian section
--------------------------------------------------------
ROCIS SPIN HAMILTONIAN PROPERTIES
--------------------------------------------------------
5.7.6. Natural Transition Orbitals/ Natural Difference Orbitals¶
Likewise to CIS and TD-DFT (section Natural Transition Orbitals) The nature of the calculated excited states in ROCIS and DFT/ROCIS can be analyzed by using the Natural Transition Orbitals (NTO) or Natural Difference Orbitals (NDO) machineries.[656]
Note
The NTO analysis is based on the transition density between ground and excited states. Hence is valid for singly excited states and for states of the same multiplicity.
The NDO analysis on the otherhand is somewhat more flexible in this respect as it is based on the difference density between ground and excited states.
Presently, only one analysis (NTO or NDO) can be performed at a time while when both flags are on the NTO analysis switches off.
To request for NTOs or NDOs the user needs to provide which states are to be calculated:
DoNTO true
NTOStates = 1,2,3,4,5,6,7,8,9,10,13,14,15
DoNDO true
NDOStates = 1,2,3,4,5,6,7,8,9,10,13,14,15
Which gives:
------------------------------------------
NATURAL TRANSITION ORBITALS FOR STATE 14
------------------------------------------
done
Solving eigenvalue problem for the Occupied space ... done
Solving eigenvalue problem for the Acceptor space ... done
Natural Transition Orbitals were saved in nto.14.nto
Threshold for printing occupation numbers 1.0e-04
E= 25.447756 au 692.469 eV 5585137.0 cm**-1
49[0] -> 46[1] : n= 0.39056909
48[0] -> 47[1] : n= 0.08619374
47[0] -> 48[1] : n= 0.00441125
-------------------------------------------------
NATURAL DIFFERENCE ORBITALS FOR STATE 14
-----------------------------------------------
done
Solving eigenvalue problem for the Occupied space ... done
Solving eigenvalue problem for the Acceptor space ... done
Natural Difference Orbitals were saved in ndo.14.ndo
Threshold for printing occupation numbers 1.0e-04
E= 25.447756 au 692.469 eV 5585137.0 cm**-1
49[0] -> 46[1] : n= 0.81173217
48[0] -> 47[1] : n= 0.17903699
47[0] -> 48[1] : n= 0.01165859
46[0] -> 49[1] : n= 0.00922738
45[0] -> 50[1] : n= 0.00112567
For closed shell cases the orbitals are save in similar way to TDDFT and
CIS (section Natural Transition Orbitals).
In the case of open shell
cases for convenience donor orbitals are saved with orbital operator 0
while acceptor orbitals with orbital operator 1. This needs to be
specified in the orca_plot program and should not be confused with the
spin-up and spin-down orbitals in the UHF and UKS cases.
5.7.7. Keyword List¶
Keyword |
Option / Value |
Description |
|---|---|---|
|
|
Requests the GS-ROCIS method (default: |
|
|
Sets the multiplicity for the reference CSF for the GS-ROCIS method. |
|
|
The number of desired roots. |
|
|
Davidson expansion space = MaxDim * NRoots. |
|
|
Maximum CI Iterations. |
|
|
The dimension of the guess CI matrix. |
|
|
Energy convergence tolerance. |
|
|
Residual Convergence tolerance. |
|
|
Maximum memory used by the ROCIS moduleduring the calculation in MB. |
|
|
Energy Window that defines orbital excitation space. |
|
|
Orbital Window that defines orbital excitation space (overrides EWin). |
|
|
Switch for localization of Donor orbital space (default: |
|
|
Obital window for the localization scheme. |
|
|
Chooses the Pipek Mezey localization method. |
|
Chooses the Foster Boys localization method. |
|
|
|
Performs the calculation in the PNO-ROCIS framework (default: |
|
|
Threshold for PNO selection. |
|
|
Selects from which atoms are the core MOs going to be used in the PNO procedure. |
|
|
Chooses the Pipek Mezey localization method. |
|
Chooses the Foster Boys localization method. |
|
|
|
Request Natural Transition Orbital Analysis (default: |
|
|
Threshold for printing occupation numbers. |
|
|
Array input for states to be taken into account. |
|
|
Request Natural Difference Orbital Analysis (default: |
(if true it switches off the NTO analysis) |
||
|
|
Threshold for printing occupation numbers. |
|
|
Array input for states to be taken into account. |
|
|
Controls the amount of output produced during the calculation. |
|
|
Include DOMO->SOMO excitations. |
|
|
Include SOMO->Virtual excitation. |
|
|
Include DOMO->Virtual excitations. |
|
|
Include DOMO->SOMO excitations coupled to SOMO->Virtual excitations with s\(\neq{}\)t. |
|
|
Include DOMO->SOMO excitations coupled to SOMO->Virtual excitations with s\(=\) t. |
(only used in the original ROCIS implementation) |
||
|
|
Switch for excitation with S’=S-1. |
|
|
Include DOMO->SOMO excitations with S’=S-1. |
|
|
Include SOMO->Virtual excitations with S’=S-1. |
|
|
Include DOMO->Virtual excitations with S’=S-1. |
|
|
Include SOMO->SOMO excitations with S’=S-1. |
|
|
Switch for excitations with S’=S+1. |
|
|
Include DOMO->SOMO excitations with S’=S+1. |
|
|
Include SOMO->Virtual excitations with S’=S+1. |
|
|
Include DOMO->Virtual excitations with S’=S+1. |
|
|
Request circular dichroism calculation. |
|
|
Request the use of electric moments in a length formulation (default: |
|
|
Request the use of electric moments in a velocity formulation (default: |
|
|
Request the calculation of complete semiclassical multipolar moments (default: |
|
|
Request the decomposition of the oscillator strengths in a multipolar expansion. (default: |
|
|
Requests a RIXS calculation (default: |
|
|
Perform a RIXS calculation on the basis of relativistically corrected states (default: |
|
|
Include the elastic line in the generation of the RIXS or RIXSSOC spectra (default: |
|
|
Array input for plotting difference densities of CI roots to the ground state. |
|
|
Array input for plotting difference densities of SOC states to the ground state. |
|
|
Threshold for contributions to CI and SOC states to be printed. |
|
Signals the begining of the relativistic block. |
|
|
|
Requests the inclusion of spin-orbit coupling (part of the |
|
|
Requests the calculation of MCD spectra (part of the |
|
|
Sets external magnetic field (part of the |
|
|
Sets the temperature for the SOC spectra (part of the |