7.31. Excited States via ROCIS and DFT/ROCIS¶
The ORCA program package includes the orca_rocis module to 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).
7.31.1. General Use¶
In the present implementation the orca_rocis module is only able to
perform CIS calculations on top of a high-spin ROHF reference function.
All spins of the unpaired electrons have to be coupled ferrmoagnetically
to give a total spin of \(S = \frac{1}{2}N\), where \(N\) is the number of
unpaired electrons. Other ROHF functions such as Zerner’s configuration
averaged or spin averaged ROHF cannot be used as reference. The input
for a high spin ROHF calculation is done in the %scf block.
%scf
HFTyp ROHF # Flag for ROHF
ROHF_Case HighSpin # selects the high-spin case
ROHF_NEl[1] = 4 # the number of unpaired electrons
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 program features the
ability to start a ROCIS 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. Furthermore it is
possible to invoke the orca_rocis module for closed-shell molecules.
The program will then perform a CI calculation with the provided RHF
reference function. In this case it will yield the same result as the
orca_cis program.
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 dimension of the iterative subspace is given by MaxDim \(\cdot\)
NRoots. The lowest possible choice for MaxDim is a value of 2. In
general, by choosing MaxDim \(\approx\) 5-10 times NRoots you will
achieve a more favorable convergence by the cost of an increased disk
space requirement. Increasing the NGuessMat variable will improve the
convergence of the iterative CI procedure. The amount of output produced
during the calculation is controlled via the PrintLevel variable
%rocis NRoots 3
PrintLevel 3
end
Note, that this does not influence which spectra are calculated or printed. The absorption spectrum calculated on the basis of the pure dipole approximation for your calculation is always printed. In addition, it is possible to allow for electric quadrupole and magnetic dipole contributions to the absorption spectrum as well as to calculate the CD spectrum check section (One Photon Spectroscopy) for details. By defining in the %rocis block:
%rocis
NRoots 6
DoDipoleLength true
DoDipoleVelocity true
DoHigherMoments true
DecomposeFoscLength true
DecomposeFoscVelocity true
DoFullSemiclassical true
DoCD true
end
The printed spectra look like this:
-----------------------------------------------------------------------------
ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
-----------------------------------------------------------------------------
State Energy Wavelength fosc T2 TX TY TZ
(cm-1) (nm) (au**2) (au) (au) (au)
-----------------------------------------------------------------------------
1 2635.0 3795.1 0.000000001 0.00000 0.00001 -0.00001 0.00029
2 4365.5 2290.7 0.000011416 0.00086 0.01200 -0.00864 0.02534
3 4368.2 2289.3 0.000011174 0.00084 -0.02006 0.01442 0.01523
4 5977.9 1672.8 0.000093897 0.00517 -0.04164 -0.05863 0.00000
5 65245.3 153.3 0.027669631 0.13961 -0.20555 -0.31203 -0.00023
-----------------------------------------------------------------------------
ABSORPTION SPECTRUM VIA TRANSITION VELOCITY DIPOLE MOMENTS
-----------------------------------------------------------------------------
State Energy Wavelength fosc P2 PX PY PZ
(cm-1) (nm) (au**2) (au) (au) (au)
-----------------------------------------------------------------------------
1 2635.0 3795.1 0.000000085 0.00000 -0.00000 0.00000 -0.00004
2 4365.5 2290.7 0.001777771 0.00005 -0.00315 0.00223 -0.00618
3 4368.2 2289.3 0.001850956 0.00006 0.00526 -0.00372 -0.00371
4 5977.9 1672.8 0.003237195 0.00013 0.00667 0.00937 0.00000
5 65245.3 153.3 0.057301314 0.02555 0.08779 0.13358 0.00010
-------------------------------------------------------------------
CD SPECTRUM
-------------------------------------------------------------------
State Energy Wavelength R MX MY MZ
(cm-1) (nm) (1e40*sgs) (au) (au) (au)
-------------------------------------------------------------------
1 2635.0 3795.1 0.00007 -0.00511 -0.01539 0.00021
2 4365.5 2290.7 10.02484 0.57434 -0.40490 0.42899
3 4368.2 2289.3 -10.03730 0.34432 -0.24269 -0.71470
4 5977.9 1672.8 0.01537 -0.00033 -0.00032 -0.00286
5 65245.3 153.3 -0.00865 0.00004 0.00003 -0.00005
-----------------------------------------------------------------------------------------------------
COMBINED ELECTRIC DIPOLE + MAGNETIC DIPOLE + ELECTRIC QUADRUPOLE SPECTRUM
-----------------------------------------------------------------------------------------------------
State Energy Wavelength D2 m2 Q2 D2+m2+Q2 D2/TOT m2/TOT Q2/TOT
(cm-1) (nm) (*1e6) (*1e6)
-----------------------------------------------------------------------------------------------------
1 2635.0 3795.1 0.00000 0.00011 0.00000 0.00000000080469 0.86010 0.13938 0.00052
2 4365.5 2290.7 0.00001 0.47866 0.00000 0.00001189497194 0.95976 0.04024 0.00000
3 4368.2 2289.3 0.00001 0.48629 0.00000 0.00001166062671 0.95830 0.04170 0.00000
4 5977.9 1672.8 0.00009 0.00001 0.00001 0.00009389664707 1.00000 0.00000 0.00000
5 65245.3 153.3 0.02767 0.00000 0.06183 0.02766969236508 1.00000 0.00000 0.00000
-----------------------------------------------------------------------------------------------------
COMBINED ELECTRIC DIPOLE + MAGNETIC DIPOLE + ELECTRIC QUADRUPOLE SPECTRUM (origin adjusted)
-----------------------------------------------------------------------------------------------------
State Energy Wavelength D2 m2 Q2 D2+m2+Q2 D2/TOT M2/TOT Q2/TOT
(cm-1) (nm) (*1e6) (*1e6)
-----------------------------------------------------------------------------------------------------
1 2635.0 3795.1 0.00000 0.00000 0.00000 0.00000000069409 0.99716 0.00016 0.00268
2 4365.5 2290.7 0.00001 0.38277 0.00039 0.00001179947536 0.96753 0.03244 0.00003
3 4368.2 2289.3 0.00001 0.36798 0.00045 0.00001154275975 0.96808 0.03188 0.00004
4 5977.9 1672.8 0.00009 0.00000 0.00001 0.00009389663928 1.00000 0.00000 0.00000
5 65245.3 153.3 0.02767 0.00003 0.06176 0.02766969232228 1.00000 0.00000 0.00000
Furthermore like in TD-DFT (section Use of TD-DFT for the Calculation of X-ray Absorption Spectra) 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.
For the Fe K-edge XAS spectrum of [FeCl\(_4\)]\(^{2-}\). This will result in addition to the following tables for the velocity representation:
-------------------------------------------------------------------------------------------------------------
COMBINED ELECTRIC DIPOLE + MAGNETIC DIPOLE + ELECTRIC QUADRUPOLE SPECTRUM (Origin Independent, Velocity)
-------------------------------------------------------------------------------------------------------------
State Energy Wavelength P2 m2 Q2 P2+m2+Q2+PM+PO P2/TOT m2/TOT Q2/TOT
(cm-1) (nm) (*1e6) (*1e6)
-------------------------------------------------------------------------------------------------------------
1 57131638.5 0.2 0.00000 0.00000 3.75184 0.00000375184371 0.00000 0.00000 1.00000
2 57131638.5 0.2 0.00000 0.00000 3.75184 0.00000375184267 0.00000 0.00000 1.00000
3 57145543.6 0.2 0.00007 0.00000 3.46619 0.00007086820341 0.95853 0.00000 0.04891
4 57145543.6 0.2 0.00007 0.00000 3.46620 0.00007078008474 0.95972 0.00000 0.04897
5 57145543.6 0.2 0.00007 0.00000 3.46620 0.00007084079919 0.95889 0.00000 0.04893
11 57351031.6 0.2 0.00000 0.00000 0.00000 0.00000000000002 0.99463 0.00618 0.00216
12 57351031.6 0.2 0.00000 0.00000 0.00000 0.00000000000001 0.00000 0.00000 0.00000
13 57351031.6 0.2 0.00000 0.00000 0.00000 0.00000000000002 0.99414 0.00692 0.00217
15 57354687.7 0.2 0.00000 0.00000 0.00000 0.00000000000888 0.00898 0.00000 0.00002
-------------------------------------------------------------------------------------------------------------
COMBINED ELECTRIC DIPOLE + MAGNETIC DIPOLE + ELECTRIC QUADRUPOLE SPECTRUM (Exact Formulation, Velocity)
-------------------------------------------------------------------------------------------------------------
State Energy Wavelength P2 m2 Q2 Exact Osc. Strength P2/TOT m2/TOT Q2/TOT
(cm-1) (nm) (*1e6) (*1e6)
-------------------------------------------------------------------------------------------------------------
1 57131638.5 0.2 0.00000 0.00000 3.02719 0.00000302719471 0.00000 0.00000 1.00000
2 57131638.5 0.2 0.00000 0.00000 2.66225 0.00000266224706 0.00000 0.00000 1.00000
3 57145543.6 0.2 0.00007 0.00000 3.46619 0.00007092969904 0.95853 0.00000 0.04891
4 57145543.6 0.2 0.00007 0.00000 3.46620 0.00007074406444 0.95972 0.00000 0.04897
5 57145543.6 0.2 0.00007 0.00000 3.46620 0.00007075200792 0.95889 0.00000 0.04893
11 57351031.6 0.2 0.00000 0.00000 0.00000 0.00000000000002 0.99463 0.00618 0.00216
12 57351031.6 0.2 0.00000 0.00000 0.00000 0.00000000000001 0.98256 0.01631 0.00209
13 57351031.6 0.2 0.00000 0.00000 0.00000 0.00000000000002 0.99414 0.00692 0.00217
15 57354687.7 0.2 0.00000 0.00000 0.00000 0.00000000001200 0.00898 0.00000 0.00002
....
These spectra are plotted by calling:
orca_mapspc MyOutput.out ABS/ABSV/CD/ABSQ/ABSOI/ABSVOI -eV -x0(start) -x1(stop)
-w(width) -n(points)
In particular ABSOI and ABSVOI will plot the exact transition moments spectra at the Length and Velocity representations (For the multiple expansion contributions).
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.
Starting from ORCA 4.0 the basis set definition on ORCA has changed.
This also affects the definition of the auxiliary basis set when the
DoRI keyword is set. ROCIS will then only allow in the mainline /C
auxiliary basis sets to be set (i.e. def2-TZVP/C). As these basis are
usually optimised on the presence of effective core potentials (ECPs)
they are generally not recommended for core-electron calculations. The
/J auxiliary basis set need to be used and they are specified in the
following way.
%basis
AuxC "def2/J"
end
! def2-TZVP def2-TZVP/C TightSCF SlowConv
%SCF HFTyp ROHF
ROHF_Case HighSpin
ROHF_Nel[1] = 1
End
%ROCIS NROOTS 5
DoRI true # invokes the RI approximation
DoHigherMoments true
end
* xyz 0 2
N 0 0 0
O 0 0 1.15
*
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 many-electron expansion space of a ROCIS calculation in ORCA is divided into five classes. Using second quantised replacement operators \(E_{p}^{q} =\hat{{a} }_{q\alpha }^{\uparrow } \hat{{a} }_{p\alpha } +\hat{{a} }_{q\beta }^{\uparrow } \hat{{a} }_{p\beta }\) they take the form[726].
The orbital label \(i\) denotes a doubly occupied orbital, \(s\) and \(t\) refer to singly occupied orbitals and orbital label \(a\) corresponds to a virtual orbital. The form of the excitation classes ensures that all excited states are eigenfunctions of the \(\hat{{S} }^{2}\)-operator and have the same total spin \(S\) as the electronic ground state. Each of the five excitation classes can be switched on or off manually.
%rocis
NRoots 3
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
Do_isa true # Include DOMO->SOMO coupled to
# SOMO->Virtual excitations with s = t
# ---------------------------------
# by default all switches for the
# excitation classes are set to
# ``true''
# ---------------------------------
end
Formally, the \(\left| \Phi_{ti}^{as} \right\rangle\) and \(\left| \Phi_{ti}^{at} \right\rangle\) excitation classes can be regarded as double excitations. When the program finishes the ROCIS calculation it gives the excitation energy together with the composition for each root. 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 5 Exc. Energy: 297.279mEh 8.089eV 65245.3cm**-1
47->50 : 0.2196
47->51 : 0.0138
37->50 : 0.1165
41->50 : 0.0960
38->46 ; 47->50 : 0.0103
37->46 ->50 : 0.0150
37->47 ->50 : 0.0938
37->48 ->50 : 0.0179
37->49 ->50 : 0.0179
41->46 ->50 : 0.0174
41->47 ->50 : 0.0585
41->48 ->50 : 0.0213
41->49 ->50 : 0.0211
Furthermore the orca_rocis module 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[621], [726].
%rocis
NRoots 3
OrbWin = 1, 3 ,9 ,22
SOC true # invokes the calculation of SOC effects
TEMPERATURE 10 # temperature for SOC corrected spectra in Kelvin
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 DoHigherMoments keyword only
for calculations that do not include SOC.
-------------------------------------------------------------------------------
SPIN ORBIT CORRECTED ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
-------------------------------------------------------------------------------
States Energy Wavelength fosc T2 TX TY TZ
(cm-1) (nm) (au**2) (au) (au) (au)
-------------------------------------------------------------------------------
0 1 5.6 0.0 0.000000000 0.00000 0.00003 0.00002 0.00000
0 2 6.2 0.0 0.000000000 0.00000 0.00000 0.00000 0.00005
0 3 23.7 422287.3 0.000000000 0.00000 0.00000 0.00000 0.00000
0 4 23.7 421562.8 0.000000000 0.00000 0.00018 0.00025 0.00000
0 5 2621.7 3814.3 0.000000000 0.00000 0.00000 0.00001 0.00005
0 6 2622.0 3813.9 0.000000000 0.00000 0.00003 0.00012 0.00000
0 7 2634.7 3795.5 0.000000095 0.00002 0.00388 0.00273 0.00049
0 8 2634.9 3795.2 0.000000103 0.00002 0.00039 0.00027 0.00495
0 9 2639.5 3788.6 0.000000001 0.00000 0.00001 0.00001 0.00036
0 10 4223.6 2367.6 0.000000103 0.00002 0.00043 0.00029 0.00390
0 11 4223.9 2367.5 0.000000120 0.00002 0.00348 0.00236 0.00046
0 12 4296.3 2327.6 0.000000696 0.00010 0.00562 0.00842 0.00000
0 13 4357.6 2294.8 0.000000002 0.00000 0.00001 0.00001 0.00049
0 14 4418.1 2263.4 0.000005778 0.00083 0.00653 0.00468 0.02762
0 15 4422.1 2261.4 0.000005517 0.00079 0.02184 0.01559 0.00832
0 16 4488.2 2228.0 0.000000001 0.00000 0.00004 0.00006 0.00038
0 17 4524.2 2210.3 0.000000001 0.00000 0.00030 0.00018 0.00000
0 18 4597.2 2175.2 0.000000027 0.00000 0.00023 0.00016 0.00191
0 19 4597.4 2175.2 0.000000051 0.00001 0.00213 0.00153 0.00023
0 20 6043.6 1654.6 0.000047989 0.00502 0.04104 0.05779 0.00000
0 21 6049.5 1653.0 0.000000014 0.00000 0.00109 0.00057 0.00001
0 22 6051.3 1652.5 0.000000021 0.00000 0.00001 0.00004 0.00150
0 23 6069.7 1647.5 0.000000000 0.00000 0.00005 0.00007 0.00000
0 24 6069.9 1647.5 0.000000028 0.00000 0.00098 0.00138 0.00000
0 25 65281.7 153.2 0.014223474 0.13787 0.20423 0.31010 0.00023
0 26 65281.7 153.2 0.000000035 0.00000 0.00032 0.00048 0.00011
0 27 65281.7 153.2 0.000009000 0.00009 0.00522 0.00774 0.00001
0 28 65281.7 153.2 0.000007207 0.00007 0.00460 0.00698 0.00000
0 29 65281.7 153.2 0.000047448 0.00046 0.01179 0.01791 0.00001
1 2 0.6 0.0 0.000000000 0.00000 0.00001 0.00001 0.00000
1 3 18.1 553477.5 0.000000000 0.00000 0.00000 0.00000 0.00009
1 4 18.1 552233.6 0.000000000 0.00000 0.00006 0.00004 0.00000
1 5 2616.1 3822.5 0.000000063 0.00001 0.00006 0.00003 0.00261
1 6 2616.4 3822.1 0.000000060 0.00001 0.00211 0.00144 0.00006
1 7 2629.1 3803.6 0.000000143 0.00002 0.00225 0.00321 0.00003
1 8 2629.3 3803.3 0.000000002 0.00000 0.00015 0.00025 0.00040
1 9 2633.9 3796.7 0.000000271 0.00003 0.00011 0.00008 0.00538
1 10 4218.0 2370.8 0.000000005 0.00000 0.00031 0.00046 0.00019
...
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 : Root Spin Ms
State 0: 0.00 cm**-1 0.00000 eV
0.378045 : 0 2 2
0.235825 : 0 2 0
0.378045 : 0 2 -2
State 1: 5.61 cm**-1 0.00070 eV
0.496236 : 0 2 2
0.496236 : 0 2 -2
State 2: 6.20 cm**-1 0.00077 eV
0.496291 : 0 2 1
0.496291 : 0 2 -1
Further details of the SOC calculation such as the procedure of SOC
integral calculation can be controlled via the %rel block (section
Relativistic Options.
7.31.2. Transition Metal L-Edges with ROCIS or DFT/ROCIS¶
The orca_rocis program 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 General Use 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. 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 four additional excitation classes introduce excited configuration state functions with a lower and higher spin multiplicity. They feature the second quantized spin raising and lowering operators \(\hat{{S} }_{pq}^{+} =\hat{{a} }_{q\alpha}^{\uparrow} \hat{{a} }_{p\beta }\), \(\hat{{S} }_{pq}^{-} =\hat{{a} }_{q\beta}^{\uparrow } \hat{{a} }_{p\alpha }\).
Inclusion of configuration state functions with higher or lower
multiplicity is invoked with the keywords DoLowerMult and
DoHigherMult, respectively.
%rocis
NRoots 20
SOC true
DoRI true
PrintLevel 3
DoLowerMult true #Invokes a CI calculation #with S'=S-1
DoHigherMult true #Invokes a CI calculation #with S'=S+1
OrbWin = 6,8,0,2000
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. 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.
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.
--------------------------------------------------------------------------------
ROOT Mult Excitation energy[Eh] [cm-1] [eV]
--------------------------------------------------------------------------------
0 5 0.00000000 0.00 0.000
1 5 26.24822856 5760820.28 714.251
2 5 26.24833619 5760843.90 714.254
3 5 26.27159871 5765949.43 714.887
4 5 26.27982129 5767754.08 715.110
5 5 26.30321870 5772889.22 715.747
6 5 26.30458669 5773189.46 715.784
7 5 26.33143414 5779081.79 716.515
8 5 26.33600432 5780084.83 716.639
9 5 26.33865219 5780665.97 716.711
10 5 26.34522494 5782108.52 716.890
11 5 26.34577552 5782229.36 716.905
12 5 26.35183534 5783559.34 717.070
13 3 26.42121780 5798787.03 718.958
14 3 26.42122881 5798789.45 718.958
...
42 7 27.22926558 5976133.02 740.946
43 7 27.23201078 5976735.52 741.021
44 7 27.23280499 5976909.83 741.042
45 7 27.23594814 5977599.67 741.128
46 7 27.23865050 5978192.77 741.201
47 7 27.26590445 5984174.32 741.943
48 7 27.26597947 5984190.78 741.945
49 7 27.26604364 5984204.87 741.947
50 3 27.29447169 5990444.10 742.720
51 3 27.30121861 5991924.88 742.904
52 3 27.30655497 5993096.08 743.049
53 3 27.30685328 5993161.55 743.057
54 3 27.31274496 5994454.62 743.218
55 7 27.52164817 6040303.58 748.902
56 7 27.52433114 6040892.42 748.975
57 7 27.52448641 6040926.50 748.979
58 7 27.53903479 6044119.50 749.375
59 7 27.53935644 6044190.10 749.384
------------------------
ROCIS-EXCITATION SPECTRA
------------------------
NOTE: At this point no SOC is included!!!
Hence only transitions to states with the same spin multiplicity
as the ground state are observed!!!
Center of mass = ( -0.0011, -0.0021, 0.0000)
Calculating the Dipole integrals ... done
Transforming integrals ... done
Calculating the Linear Momentum integrals ... done
Transforming integrals ... done
-----------------------------------------------------------------------------
ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
-----------------------------------------------------------------------------
State Energy Wavelength fosc T2 TX TY TZ
(cm-1) (nm) (au**2) (au) (au) (au)
-----------------------------------------------------------------------------
1 5760820.3 1.7 0.000985130 0.00006 0.00612 -0.00434 0.00011
2 5760843.9 1.7 0.000777158 0.00004 -0.00008 0.00006 0.00666
3 5765949.4 1.7 0.000000036 0.00000 0.00000 0.00001 -0.00004
4 5767754.1 1.7 0.000007564 0.00000 0.00033 0.00057 -0.00000
5 5772889.2 1.7 0.025379335 0.00145 -0.00031 0.00021 -0.03804
6 5773189.5 1.7 0.026898175 0.00153 0.03203 -0.02254 -0.00039
7 5779081.8 1.7 0.000000323 0.00000 -0.00006 -0.00009 -0.00008
8 5780084.8 1.7 0.001711738 0.00010 -0.00572 -0.00805 0.00001
9 5780666.0 1.7 0.113054940 0.00644 -0.04616 -0.06564 -0.00001
10 5782108.5 1.7 0.151287595 0.00861 0.00073 -0.00052 0.09281
11 5782229.4 1.7 0.147199895 0.00838 0.07488 -0.05266 -0.00088
12 5783559.3 1.7 0.000000026 0.00000 0.00001 -0.00001 0.00004
28 5960986.7 1.7 0.004292708 0.00024 -0.00881 -0.01263 -0.00000
29 5963084.1 1.7 0.001638281 0.00009 -0.00774 0.00553 0.00006
30 5963136.7 1.7 0.001369356 0.00008 -0.00005 0.00003 -0.00869
31 5963484.9 1.7 0.000935993 0.00005 0.00415 0.00587 -0.00000
32 5968477.0 1.7 0.000661255 0.00004 0.00493 -0.00349 -0.00007
33 5968705.6 1.7 0.000607238 0.00003 0.00006 -0.00004 0.00579
35 5970943.7 1.7 0.000000001 0.00000 0.00000 0.00000 -0.00001
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 : Root Spin Ms
State 0: 0.00 cm**-1 0.00000 eV
0.129027 : 0 2 2
0.741116 : 0 2 0
0.129027 : 0 2 -2
-------------------------------------------------------------------------------
SPIN ORBIT CORRECTED ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
-------------------------------------------------------------------------------
States Energy Wavelength fosc T2 TX TY TZ
(cm-1) (nm) (au**2) (au) (au) (au)
-------------------------------------------------------------------------------
0 1 0.0 0.0 0.000000000 0.00000 0.00000 0.00000 0.00000
0 2 0.8 0.0 0.000000000 0.00000 0.00000 0.00000 0.00000
0 3 0.8 0.0 0.000000000 0.00000 0.00000 0.00000 0.00000
0 4 1.0 0.0 0.000000000 0.00000 0.00000 0.00000 0.00000
0 5 5729330.4 1.7 0.000080556 0.00002 0.00013 0.00009 0.00464
0 6 5729330.4 1.7 0.000096984 0.00003 0.00415 0.00295 0.00013
0 7 5731365.3 1.7 0.000000001 0.00000 0.00001 0.00000 0.00000
0 8 5731365.4 1.7 0.000000000 0.00000 0.00000 0.00000 0.00001
0 9 5733452.5 1.7 0.000058329 0.00002 0.00323 0.00227 0.00004
0 10 5733477.2 1.7 0.000066389 0.00002 0.00003 0.00002 0.00421
0 11 5734964.4 1.7 0.000000034 0.00000 0.00005 0.00007 0.00004
0 12 5737151.2 1.7 0.000047769 0.00001 0.00208 0.00291 0.00000
With the aid of the orca_mapspc program it is possible to extract a
.plt file from the printed spectra, which then can be used to generate
a plot of the intensity vs the excitation energy. The orca_mapspc
program applies Gaussian type lineshape functions to the calculated
transitions with a user-defined FWHM. One has to provide some
information for the program such as the name of the output file, the
type of spectrum you wish to plot, the energy range and the like. It is
invoked in the command line and the parameters are given as arguments:
orca_mapspc FeIICl4.out socabs -eV -w1 -n3000 -x0710 -x1740
The first argument has to be the output file of your calculation
followed by the type of spectrum that should be plotted. In the case of
transition metal L-edges it is an absorption spectrum after the SOC
correction. The arguments “-eV” (use electron Volt as energy unit),
“-w1” (FWHM \(=\) 1eV), “-n3000” (use 3000 grid points), “-x0710” and
“-x1740” (energy range: 710 to 740 eV) have to be adapted to the
specific calculation. As a result, one obtains a .plt and a .stk
file. The .plt file contains five columns. In the first column one
finds the energy and in the second the total intensity. Columns three to
five contain the x-,y- and z-components of the transition moment. Note,
that the distribution of the transition moment among its spatial
components depends on the orientation of your molecular axis system. The
.stk file contains a list of all transitions with their respective
transition energy and intensity. A more detailed description of the
orca_mapspc program and its usage can be found in chapter
orca_mapspc.
Fig. 7.31 Comparison of the experimentally observed (black) and calculated ROCIS (red) Fe L-edge of [FeCl\(_4\)]\(^{2-}\). The red bars highlight the contribution of individual states to the total spectrum. The calculation was performed using the TZVP basis set.¶
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 DFT/ROCIS method[726]. 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[726]. 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.
! B3LYP def2-TZVP(-f) TightSCF
%Basis
AuxC "def2/J"
end
%ROCIS
NRoots 20
DoRI true
SOC true
DoHigherMult true
PrintLevel 3
OrbWin = 5,7,50,60
DoDFTCIS true #switches on the DFT/ROCIS method
DFTCIS_c = 0.18, 0.20, 0.40 #Array input of the three parameters
end
Fig. 7.32 Comparison of the experimentally observed (black) and calculated (red) Ti L-edge of [Cp\(_2\)TiCl\(_2\)]. The red bars highlight the contribution of the individual states to the total spectrum. The pure ROCIS method (left) predicts a wrong L\(_3\)-L\(_2\) intensity ratio and strongly overestimates the splitting of the satellite features to the main bands. Better results are obtained with the DFT/ROCIS method (right).¶
7.31.3. 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.[687] Note that:
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.
An example is given below for [FeCl\(_4\)]\(^{2-}\):
!B3LYP def2-TZVP Conv TightSCF LargePrint PAL4
%Basis
AuxC "def2/J"
end
%ROCIS
NRoots 40
PrintLevel 3
MaxCore 4000
MaxDim 360
SOC true
DoRI true
DoNTO true
DoNDO true
NDOThresh/NTOThresh 1e-4
NDOStates/NTOStates= 1,2,3,4,5,6,7,8,9,10,13,14,15
DoLowerMult true
DoHigherMult true
DoDFTCIS true
DFTCIS_c = 0.18, 0.20, 0.40
OrbWin = 6,8,0,2000
end
* xyz -2 5
Fe -17.84299991694815 -0.53096694321123 6.09104775508499
Cl -19.84288422845700 0.31089495619796 7.04101319789001
Cl -17.84298666758073 0.11868125024595 3.81067954087770
Cl -17.84301352218429 -2.87052442818457 6.45826391412877
Cl -15.84311566482982 0.31091516495189 7.04099559201853
*
Then the respective NTO and NDO analysis for state 15 is given below:
------------------------------------------
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.
In practice one can use this machinery to analyze for example the relativistically corrected states located at 705.5 eV (when shifted with respect to experiment). It can be seen that these states contain for example significant contributions from state 14. NTO or NDO analysis then shows that this state is dominated by the spin conserving DOMO-SOMO \(2p_z-3d_{yz}\) single electron excitation.
Fig. 7.33 DFT/ROCIS calculated L3 XAS spectrum of [Fe(Cl) \(_4\)]\(^{2-}\) together with NDO analysis for state 14. Constant broadening \(0.5\) eV and isovalue for the orbital plots \(0.03\) a.u. is used throughout¶
7.31.4. Resonant Inelastic Scattering Spectroscopy¶
7.31.4.1. 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.
7.31.4.2. 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. 7.34 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.¶
7.31.4.3. 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
7.31.5. Core PNO-ROCIS, PNO-ROCIS/DFT¶
It has been shown recently[545] that it is possible to combine the powerful machinery of the 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:
...
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
OrbWin = 0,0,0,2000
...
As has been shown in reference[545] a universal TCutPNO 1e-11 threshhold can be defined for all edges provided that the PNOs are constructed by taking into account all the availiable 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 element or the elements for which the XAS calculation will be performed are specified within the XASElems keyword. In the following example these correspond to Core MOs 36-44. Note that the CoreMOs list should not be confused with the OrbWin which is used to specify the excitation space that will be actually used in the actual calculation.
===============================================
Core PNO/ROCIS truncation
================================================
------------------------------------------------
Calculating Integrals...
------------------------------------------------
...
------------------------------------------------
Calculating Guess Amplitudes and Densities...
------------------------------------------------
----------------------------------------------------------------
The densities will be generated from the Detected Core MOs:
----------------------------------------------------------------
MO= 36, E= -261.246087 Eh
MO= 37, E= -31.777896 Eh
MO= 38, E= -27.263122 Eh
MO= 39, E= -27.263122 Eh
MO= 40, E= -27.263122 Eh
MO= 41, E= -3.914132 Eh
MO= 42, E= -2.457405 Eh
MO= 43, E= -2.457405 Eh
MO= 44, E= -2.457405 Eh
Alternativelly one can also use the CoreMOs keyword to individual select the respective CoreMOs
...
DoPNO true #Flag to call the PNO truncation
TCutPNO 1e-11#Threshold to cutout the PNO populations
CoreMOs 0,1,6,7,8,29,30,31,32 #The core MOs for the selected element
#to perform the XAS calculation
OrbWin = 0,0,0,2000
...
A complete list of CoreMOs of the different atoms can be found in reference[545] The program will then proceed and generate the Core PNOs and use the TCutPNO threshold to reduce the Virtual MO space. In the following example only virtual orbitals are selected out of the total 1445 virtual MOs
TCutPNO: 1.000e-11
Virtual orbitals before selection: 368 ... 1812 (1445 MO's)
Virtual orbitals after selection: 368 ... 447 ( 80 MO's)
PNO transformation completed in: 177.09 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.
7.31.6. 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 The Multireference Correlation Module)
...
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
--------------------------------------------------------
7.31.7. Keyword List¶
%rocis
#-----------------------------------------------------------
# GENERAL KEYWORDS
#-----------------------------------------------------------
NRoots 3 # The number of desired roots
MaxDim 5 # Davidson expansion space = MaxDim * NRoots
MaxIter 35 # Maximum CI Iterations
NGuessMat 512 # The dimension of the guess matrix
ETol 1e-6 # Energy convergence tolerance
RTol 1e-6 # Residual Convergence tolerance
MaxCore 2000 # Maximum memory used during the calculation in MB
EWin= -5,5,-5,5 # Energy Window that defines orbital excitation space
OrbWin=6,8,0,2000 # Orbital Window that defines orbital excitation space
# (overrides EWin)
DoRI false # Switch for the RI approximation
DoLoc false # Switch for localization of Donor orbital space
LocMet PipekMezey # chooses the localization method:
# PipekMezey or FosterBoys.
# Abbreviations "PM" and "FB"
# are equivalent to full names.
SOC false # Switch for inclusion of SOC
TEMPERATURE 10 # The fictive temperature for the
# SOC corrected spectra
DoDFTCIS false # Switch for the DFT/ROCIS method
DFTCIS_C = 0.18, 0.20, 0.40 #Array Input of the
# three DFT/ROCIS parameters
#-----------------------------------------------------------
# FLAGS FOR EXCITATION SPACES
#-----------------------------------------------------------
Do_is true # Include DOMO->SOMO excitations
Do_sa true # Include SOMO->Virtual excitation
Do_ia true # Include DOMO->Virtual excitations
Do_ista true # Include DOMO->SOMO excitations
# coupled to SOMO->Virtual
# excitations with s not equal t
Do_isa true # Include DOMO->SOMO excitations
# coupled to SOMO->Virtual
# excitations with s = t
DoLowerMult false # Switch for excitation with S’=S-1
Do_LM_is true # Include DOMO->SOMO excitations
# with S’=S-1
Do_LM_sa true # Include SOMO->Virtual excitations
# with S’=S-1
Do_LM_ia true # Include DOMO->Virtual excitations
# with S’=S-1
Do_LM_ss true # Include SOMO->SOMO excitations
# with S’=S-1
DoHigherMult false # Switch for DOMO->Virtual
# excitations with S’=S+1
#-----------------------------------------------------------
OUTPUT KEYWORDS
#-----------------------------------------------------------
PrintLevel 3 # Controls the amount of output
# produced during the calculation
RIXS false # Perform a RIXS calculation
RIXSSOC false # Perform a RIXS calculation on the basis
# of relativistically corrected states
Elastic false # Include the elastic line in the generation
# of the RIXS or RIXSSOC spectra
PlotDiffDens = 1,2 # Array input for plotting
# difference densities of CI roots
# 1 and 2 to the ground state.
PlotSOCDiffDens=1,2 # Array input for plotting
# difference densities of SOC
# states 1 and 2 to the ground state
DoNTO false # Request Natural Transition Orbital Analysis
DoNDO false # Request Natural Difference Orbital Analysis
# (if true it switches off the NTO analysis)
NDOThresh 1e-4 # Threshold for printing occupation numbers
NTOThresh 1e-4 # Threshold for printing occupation numbers
NDOStates = 1,2 # Array input for states to be taken into account
NTOStates = 1,2 # Array input for states to be taken into account
TPrint 0.01 # Threshold for contributions to CI
# and SOC states to be printed
DoPNO false # Performs the calculation in the PNO-ROCIS framework
DoCD true # Request circular dichroism calculation
DoDipoleLength true # Request the use of electric moments in a length formulation
DoDipoleVelocity true # Request the use of electric moments in a velocity formulation
DoHigherMoments true # Request the calculation of electric quadrupole and magnetic
# dipole moments contributions
DoFullSemiclassical true # Request the calculation of complete semiclassical
# multipolar moments
DecomposeFoscLength true # Request the decomposition of the oscillator strengths
# in a multipolar expansion under a length formulation
DecomposeFoscVelocity true # Request the decomposition of the oscillator strengths
# in a multipolar expansion under a velocity formulation