The ORCA program package includes the orca_rocis module to performconfiguration interaction with single excitations (CIS) calculationsusing a restricted open-shell Hartee-Fock (ROHF) reference function. Itproduces excitation energies, absorption energies and CD intensities. Itwas designed with the aim to reproduce and - even more importantly -reliably predict transition metal L-edges as observed in X-rayabsorption spectroscopy (XAS).
7.31.1. General Use ¶
In the present implementation the orca_rocis module is only able toperform CIS calculations on top of a high-spin ROHF reference function.All spins of the unpaired electrons have to be coupled ferrmoagneticallyto give a total spin of \(S = \frac{1}{2}N\) , where \(N\) is the number ofunpaired electrons. Other ROHF functions such as Zerner’s configurationaveraged or spin averaged ROHF cannot be used as reference. The inputfor 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 convergenceproblems. UHF calculations generally exhibit better convergenceproperties. In most cases the quasi-restricted orbitals (qro’s) of a UHFcalculation resemble the ROHF orbitals. Thus the program features theability to start a ROCIS calculation on top of a UHF calculation. Itwill automatically create the qro’s and build the reference determinantwith them. If one wants to avoid the (small) errors that are introducedby this procedure, one may take the qro’s of a UHF calculation asstarting orbitals for a subsequent ROHF calculation. Furthermore it ispossible to invoke the orca_rocis module for closed-shell molecules.The program will then perform a CI calculation with the provided RHFreference 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 settingsof 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. Ingeneral, by choosing MaxDim \(\approx\) 5-10 times NRoots you willachieve a more favorable convergence by the cost of an increased diskspace requirement. Increasing the NGuessMat variable will improve theconvergence of the iterative CI procedure. The amount of output producedduring the calculation is controlled via the PrintLevel variable
%rocis NRoots 3 PrintLevel 3 end
Note, that this does not influence which spectra are calculated orprinted. The absorption spectrum calculated on the basis of the puredipole approximation for your calculation is always printed. Inaddition, it is possible to allow for electric quadrupole and magneticdipole contributions to the absorption spectrum as well as to calculatethe 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 obtainintensities by evaluating the 2nd order oscillation strengths, orthe full semi-classical oscillation strengths.
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The exact oscillation strengths behave like the multipole expansionin the velocity representation.
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They are by definition origin independent they do not suffer fromartificial negative values like the multipole moments beyond 1storder.
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They are used with the multipole moments up to 2nd order toregenerate the electric dipole, electric quadrupole and magneticdipole contributions in either length or the velocityrepresentation.
For the Fe K-edge XAS spectrum of [FeCl \(_4\) ] \(^{2-}\) . This will resultin 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 momentsspectra at the Length and Velocity representations (For the multipleexpansion contributions).
If calculations on large molecules are conducted, the integraltransformation will be the most time-consuming part. Therefore it isstrongly recommended to use the resolution of the identity (RI)approximation in those cases. It effectively reduces the computationalcosts of the transformation step by only introducing minor errors to thecalculation. It has to be kept in mind that in order to keep theintroduced errors small, one has to provide a reasonable auxiliary basissets 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 theDoRI 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 areusually 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 thefollowing way.
%basisAuxC "def2/J" end
! def2-TZVP def2-TZVP/C TightSCF SlowConv%SCF HFTyp ROHFROHF_Case HighSpinROHF_Nel[1] = 1End%ROCISNROOTS 5DoRI true# invokes the RI approximationDoHigherMoments trueend* xyz 0 2N 0 0 0O 0 0 1.15*
The orca_rocis module provides two ways of choosing the orbitalexcitation space: by orbital energy or orbital number. In the formercase an energy window has to be specified and the program will then takeall orbitals, whose orbital energies lie within this window, intoaccount. Note, that one actually has to define two orbital windows: Onefor the donor and the second for the acceptor orbital. The input of thewindows is done as an array: The first two numbers define the donorspace 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 virtualorbitals out of their respective orbital excitation spaces. Since theseorbitals span a space that is usually not reachable with regular UV/Visspectroscopy, this is a reasonable approximation. One has to keep inmind that an orbital energy window makes only sense if the orbitals usedin the calculation have a well-defined orbital energy. As a consequenceone cannot use an orbital energy window for a calculation with localizedorbitals. The second way to specify the excitation space is by orbitalnumbering.
%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 occupiedorbitals can act as donor orbitals and only singly and nonoccupiedorbitals can act as acceptor orbitals. The program recognisesnonoccupied orbitals in the donor space and doubly occupied orbitals inthe acceptor space and removes both.
The many-electron expansion space of a ROCIS calculation in ORCA isdivided 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 [ 725 ] .
(7.236) ¶ \[\begin{split}\begin{array}{l} \left| \Phi_i^s \right\rangle= E_{i}^{s} \left| 0 \right\rangle\\ \left| \Phi_s^a \right\rangle= E_{s}^{a} \left| 0 \right\rangle\\ \left| \Phi_i^a \right\rangle= \frac{1}{\sqrt 2 }E_{i}^{a} \left| 0 \right\rangle\\ \left| \Phi_{ti}^{as} \right\rangle=E_{t}^{a} E_{i}^{s} \left| 0 \right\rangle\\ \left| \Phi_{ti}^{as} \right\rangle= \frac{1}{\sqrt 6 }\left( E_{i}^{a} -2E_{s}^{a} E_{i}^{s} \right)\left| 0 \right\rangle\\ \end{array}\end{split}\]
The orbital label \(i\) denotes a doubly occupied orbital, \(s\) and \(t\) refer to singly occupied orbitals and orbital label \(a\) corresponds to avirtual orbital. The form of the excitation classes ensures that allexcited states are eigenfunctions of the \(\hat{{S} }^{2}\) -operator andhave the same total spin \(S\) as the electronic ground state. Each of thefive 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 regardedas double excitations. When the program finishes the ROCIS calculationit gives the excitation energy together with the composition for eachroot. According to the number of labels of the respective functions \(\left|\Phi \right\rangle\) , contributions from excited configurationstate functions belonging to the different excitation classes are givenby 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 ofspin-orbit coupling (SOC) on the calculated ground and excited states.It introduces SOC in the framework of quasi-degenerate perturbationtheory (QDPT). The SOC Hamiltonian is diagonalized in the basis of thecalculated ROCIS states \(\left| \Psi_I^{SM} \right\rangle\) , where \(I\) isthe root label and \(S\) and \(M\) are the spin and magnetic spin quantumnumbers, respectively [ 621 ] , [ 725 ] .
%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 spectrafor the SOC corrected results. The spectra contain transitions from the \(2S+1\) lowest lying states into all excited states, where S is the spinquantum number of the electronic ground state. These \(2S+1\) loweststates may be split up in the order of 1-100 cm \(^{-1}\) . Due to the smallmagnitude of the splitting, all of the \(2S+1\) statescan be significantly populated even at low temperatures. Experimentally,the intensity of a given transition is dependent on the population ofthe corresponding initial state. With the TEMPERATURE keyword thepopulation of the theoretically calculated states can be manipulated bythe varying the fictive temperature of the system. It has to bementioned that the electric quadrupole transitions between spin-orbitcoupled states are not well defined and are likely to give unreasonableresults. Hence it is recommended to use the DoHigherMoments keyword onlyfor 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 printout 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 MsState 0: 0.00 cm**-1 0.00000 eV 0.378045 : 0 2 2 0.235825 : 0 2 0 0.378045 : 0 2 -2State 1: 5.61 cm**-1 0.00070 eV 0.496236 : 0 2 2 0.496236 : 0 2 -2State 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 SOCintegral calculation can be controlled via the %rel block (section Relativistic Options .
The orca_rocis program was designed to calculate transition metalL-edge spectra of large molecules as they are observed in X-rayabsorption spectroscopy (XAS). An L-edge results when an electron ispromoted from the 2p shell of a transition metal ion into the valence dshell by an X-ray photon. Strong spin-orbit coupling in the 2p shell andp-d coupling phenomena complicate the interpretation and even more sothe prediction of these spectra. It has to be kept in mind that thepresent program applies a variety of approximations which might lead toobservable deviations from experimentally determined spectra. However,we believe that the results obtained from the program are in generalqualitatively correct and in most cases accurate close to theexperimental uncertainty. In cases where quantitative accuracy is notmet, the provided results might still give some insight into themechanisms of intensity distribution in the spectra.
The special input structure for orbital windows described in General Use allows the user to restrict thedonor orbital space to the transition metal 2p shell. The acceptororbital space is the same as in regular UV/Vis spectroscopy. It shouldinclude all singly occupied molecular orbitals and as many virtualorbitals as one can afford in the calculation. The number of rootsshould be chosen large enough so that at least all 2p-3d singleexcitations are calculated. In many cases even more roots are requiredsince doubly excited or charge transfer states may become important.Moreover the strong SOC apparent in the 2p shell of transition metalions necessitates the additional calculation of excited states with atotal spin of \(S' = S + 1\) and \(S' = S -1\) where \(S\) is the total spinof the electronic ground state. Accordingly four additional excitationclasses introduce excited configuration state functions with a lower andhigher spin multiplicity. They feature the second quantized spin raisingand lowering operators \(\hat{{S} }_{pq}^{+} =\hat{{a} }_{q\alpha}^{\uparrow} \hat{{a} }_{p\beta }\) , \(\hat{{S} }_{pq}^{-} =\hat{{a} }_{q\beta}^{\uparrow } \hat{{a} }_{p\alpha }\) .
(7.237) ¶ \[\begin{split} \begin{array}{r}\left. \begin{array}{l}\left| \Phi_{i}^{\left(t-\right)} \right\rangle =\sqrt{ \frac{2{S}'+1}{2{S}'+2} } S_{ti}^{-} \left| 0 \right\rangle-\sum\limits_{u \neq t}^{\text{SOMO}} {\frac{1}{\sqrt{2{S}'+1}}\frac{1}{\sqrt{2{S}'+2} }S_{uu}^{-} E_{i}^{t} \left|0 \right\rangle} \\\left| \Phi_{i}^{\left(t-\right)} \right\rangle =\sqrt{ \frac{2{S}'+1}{2{S}'+2} } S_{ti}^{-} \left| 0 \right\rangle-\sum\limits_{u \ne t}^{\text{SOMO} } { \frac{1}{\sqrt{ 2{S}'+1} }\frac{1}{\sqrt{ 2{S}'+2} }S_{uu}^{-} E_{i}^{t} \left|0 \right\rangle} \\\left| \Phi_{i}^{\left(a-\right)} \right\rangle =\sqrt{ \frac{2{S}'+1}{2{S}'+3} } S_{ai}^{-} \left| 0 \right\rangle-\sum\limits_{t}^{\text{SOMO} } { \sqrt{\frac{\left({ S}' +1\right)^2 - { S}'^2}{\left({ S}'+1\right)\left(2{S}'+3\right)} }\frac{1}{\sqrt{ 2\left(2{S}'+2\right)} } S_{tt}^{-} E_{i}^{a} \left|0 \right\rangle}\\\hspace{2cm}+ \sum\limits_{t, u \ne t}^{\text{SOMO} } { \sqrt{\frac{2}{\left(2{S}'+2\right)\left(2{S}'+3\right)} }\sqrt{\frac{1}{\left(2{S}'+2\right)2\left(2{S}'+1\right)} } S_{tt}^{-} S_{uu}^{-} S_{ai}^{+} \left|0 \right\rangle}\end{array}\right\} \quad S' = S-1 \\\left. \left| \Phi_{i}^{a^+} \right \rangle = S_{ai}^{+} \left| 0 \right \rangle \right\} \quad { S}' = S +1 \end{array}\end{split}\]
Inclusion of configuration state functions with higher or lowermultiplicity 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 eachmultiplicity. Subsequently it gives the excitation energies andcompositions of the calculated excited states for all includedmultiplicities. After all CI calculations are finished, the programgives a list of all calculated roots with their excitation energies andtheir multiplicities. It is this number that will be referred to aslabel \(I\) in the decomposition of spin-orbit coupled states in the basis \(\left| \Psi_{I}^{SM} \right\rangle\) . It is very important to note, thatwhen states with different multiplicities are calculated this numbermight deviate from the number that appears in the respective CI part ofthe output. If one gets confused about the numbering of the states, thestate energies might act as a guideline through the output of theprogram.
Without SOC the spin exclusion rule applies which means that onlyexcited states with a total spin equal to the ground state spin( \(S' = S\) ) give rise to non-vanishing intensities. Hence, only thesetransitions 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 multiplicityas the ground state are observed!!!Center of mass = ( -0.0011, -0.0021, 0.0000)Calculating the Dipole integrals ... doneTransforming integrals ... doneCalculating the Linear Momentum integrals ... doneTransforming 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, theprogram 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 MsState 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 generatea plot of the intensity vs the excitation energy. The orca_mapspc program applies Gaussian type lineshape functions to the calculatedtransitions with a user-defined FWHM. One has to provide someinformation for the program such as the name of the output file, thetype of spectrum you wish to plot, the energy range and the like. It isinvoked 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 calculationfollowed by the type of spectrum that should be plotted. In the case oftransition metal L-edges it is an absorption spectrum after the SOCcorrection. 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 thespecific calculation. As a result, one obtains a .plt and a .stk file. The .plt file contains five columns. In the first column onefinds the energy and in the second the total intensity. Columns three tofive contain the x-,y- and z-components of the transition moment. Note,that the distribution of the transition moment among its spatialcomponents depends on the orientation of your molecular axis system. The .stk file contains a list of all transitions with their respectivetransition energy and intensity. A more detailed description of the orca_mapspc program and its usage can be found in chapter orca_mapspc .
For many transition metal compounds the description of the electronicground and excited states by Hartree-Fock theory and CIS is of ratherpoor quality. Especially covalency and relative spin state energeticsare not reproduced correctly. This in turn might lead to wrong intensitydistributions in the calculated L-edge spectra. In the majority of thesecases the quality of the description and hence the predicted L-edgespectra can be significantly improved with the DFT/ROCISmethod [ 725 ] . It features the usage of a restricted open-shellKohn-Sham matrix as reference and also uses the DFT orbitals for settingup the excited configuration state functions in the CI expansion. Thetwo electron integrals that include the DFT orbitals are scaledaccording to their nature and their position in the CI matrix by theparameters \(c_{1}\) , \(c_{2}\) 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. Forexample:
(7.238) ¶ \[\begin{split}\begin{array}{l} H_{ia,ia}^{\text{DFT/ROCIS} } =F_{aa}^{C\left( \text{KS} \right)} -F_{ii}^{C\left( \text{KS}\right)} -c_{1} \left({ ii\vert aa} \right)+2c_{2} \left({ ia\vert ia}\right) \\ H_{ia,jb}^{\text{DFT/ROCIS} } =c_{3} \left\{{ \delta_{ij} F_{ab}^{C\left( \text{KS}\right)} -\delta_{ab} F_{ji}^{C\left( \text{KS} \right)} -\left({ ij\vert ab}\right)+2\left({ ia\vert jb} \right)} \right\} \end{array}\end{split}\]
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 theirexcited states on a B3LYP/def2-TZVP(-f) level of theory but can befreely chosen [ 725 ] . It is most likely that for a differentcombination of test molecules, functional and basis set, a different setof parameters gives better results. Since the parameters are chosen withregard of a good “balance” between orbital energies, Coulomb andexchange integrals, a new set of parameters should at least crudelyresemble their relative proportions.
! B3LYP def2-TZVP(-f) TightSCF%BasisAuxC "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
7.31.3. Natural Transition Orbitals/ Natural Difference Orbitals ¶
Likewise to CIS and TD-DFT (section Natural Transition Orbitals ) The nature of thecalculated excited states in ROCIS and DFT/ROCIS can be analyzed byusing the Natural Transition Orbitals (NTO) or Natural DifferenceOrbitals (NDO) machineries. [ 687 ] Note that:
-
The NTO analysis is based on the transition density between groundand excited states. Hence is valid for singly excited states and forstates of the same multiplicity.
-
The NDO analysis on the otherhand is somewhat more flexible in thisrespect as it is based on the difference density between ground andexcited states.
-
Presently, only one analysis (NTO or NDO) can be performed at a timewhile 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%BasisAuxC "def2/J"end%ROCIS NRoots 40PrintLevel 3MaxCore 4000MaxDim 360SOC trueDoRI trueDoNTO trueDoNDO trueNDOThresh/NTOThresh 1e-4NDOStates/NTOStates= 1,2,3,4,5,6,7,8,9,10,13,14,15DoLowerMult trueDoHigherMult trueDoDFTCIS trueDFTCIS_c = 0.18, 0.20, 0.40OrbWin = 6,8,0,2000end* xyz -2 5Fe -17.84299991694815 -0.53096694321123 6.09104775508499Cl -19.84288422845700 0.31089495619796 7.04101319789001Cl -17.84298666758073 0.11868125024595 3.81067954087770Cl -17.84301352218429 -2.87052442818457 6.45826391412877Cl -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------------------------------------------doneSolving eigenvalue problem for the Occupied space ... doneSolving eigenvalue problem for the Acceptor space ... doneNatural Transition Orbitals were saved in nto.14.ntoThreshold for printing occupation numbers 1.0e-04E= 25.447756 au 692.469 eV 5585137.0 cm**-149[0] -> 46[1] : n= 0.3905690948[0] -> 47[1] : n= 0.0861937447[0] -> 48[1] : n= 0.00441125
-------------------------------------------------NATURAL DIFFERENCE ORBITALS FOR STATE 14-----------------------------------------------doneSolving eigenvalue problem for the Occupied space ... doneSolving eigenvalue problem for the Acceptor space ... doneNatural Difference Orbitals were saved in ndo.14.ndoThreshold for printing occupation numbers 1.0e-04E= 25.447756 au 692.469 eV 5585137.0 cm**-149[0] -> 46[1] : n= 0.8117321748[0] -> 47[1] : n= 0.1790369947[0] -> 48[1] : n= 0.0116585946[0] -> 49[1] : n= 0.0092273845[0] -> 50[1] : n= 0.00112567
For closed shell cases the orbitals are save in similar way to TDDFT andCIS (section Natural Transition Orbitals ). In the case of open shellcases for convenience donor orbitals are saved with orbital operator 0while acceptor orbitals with orbital operator 1. This needs to bespecified 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 therelativistically corrected states located at 705.5 eV (when shifted withrespect to experiment). It can be seen that these states contain forexample significant contributions from state 14. NTO or NDO analysisthen shows that this state is dominated by the spin conserving DOMO-SOMO \(2p_z-3d_{yz}\) single electron excitation.
7.31.4. Resonant Inelastic Scattering Spectroscopy ¶
7.31.4.1. General ¶
Starting from ORCA version 4.0 ROCIS module can be used to calculateRIXS spectra
The present implementation is directly based on the Kramers HeisenergDirac (KDH) expression formula for near resonant and resonant conditions
\[\left|{ {\alpha _{\rho \lambda } }({E_{ex} },{E_{sc} }) } \right|_{Total}^2 = { \sum\limits_F { \left|{ \sum\limits_V { \frac{{\left\langle F \right|{ m_\rho }\left| V \right\rangle\left\langle V \right|{ m_\lambda }\left| I \right\rangle} }{{{E_{VI} } - { E_{ex} } - i\frac{1}{2}{\Gamma _V} }} } } \right|} ^2}\left\{{ \frac{{{\Gamma _F} }}{{{{({E_{FV} } - { E_{ex} } + { E_{sc} }) }^2} + \frac{1}{4}{\Gamma _F}^2} }} \right\}\]
\[\left|{ {\alpha _{\rho \lambda } }({E_{ex} },{E_{sc} },V) } \right|_{resonant}^2 = \sum\limits_F { {{\left|{ \left\langle F \right|{ m_\rho }\left| V \right\rangle} \right|}^2}{{\left|{ \left\langle V \right|{ m_\lambda }\left| I \right\rangle} \right|}^2} } f({E_{VI} },{E_{FV} },{E_{ex} },{E_{sc} },{\Gamma _V},{\Gamma _F})\]
\[\left|{ {\alpha _{\rho \lambda } }({E_{VI} },{E_{sc} }) } \right|_{Direct}^2 = \sum\limits_V { \left|{ {\alpha _{\rho \lambda } }({E_{VI} },{E_{sc} },V) } \right|_{resonant}^2}\]
The resonance scattering cross section for total and direct cases,averaged over all orientations of the molecule and integrated over alldirections and polarizations of scattered radiation is given inequations:
\[\sigma _{_{RXES} }^{Total}({E_{ex} },{E_{sc} }) = \frac{{8\pi E_{sc}^3{E_{ex} }} }{{9{c^4} }}\sum\limits_{\rho ,\lambda = x,y,z} { \left|{ {\alpha _{\rho \lambda } }({E_{ex} },{E_{sc} }) } \right|_{Total}^2}\]
\[\sigma _{_{RXES} }^{Direct}({E_{ex} },{E_{sc} }) = \frac{{8\pi E_{sc}^3{E_{ex} }} }{{9{c^4} }}\sum\limits_{\rho ,\lambda = x,y,z} { \left|{ {\alpha _{\rho \lambda } }({E_{ex} },{E_{sc} }) } \right|_{Direct}^2}\]
Interference effects can be then derived in a straightforward way fromequation:
\[\sigma _{RXES}^{interference}(E_{ex}^{},E_{sc}^{}) = \sigma _{RXES}^{Total}(E_{ex}^{},E_{sc}^{}) - \sigma _{RXES}^{Direct}(E_{ex}^{},E_{sc}^{})\]
In order to access RIXS spectroscopy in the ROCIS module one needs inaddition to specify a 2nd donor space. This is specified by defining anOrbWin array with 6 elements: The first four elements define the rangesof the two donor spaces while the last two elements the respectiveacceptor space range.
OrbWin = 0,0,2,4,45,60
An important difference with respect to the conventional ROCIS orDFT/ROCIS calculations is the fact that two donor spaces of verydifferent energy ranges are involved (e.g. K-edge, L-edge) whichrequires to restrict somewhat the acceptor space and saturate it with asmany states as possible.
The main calling commands in order to perform a RIXS calculation withinboth ROCIS and CASSCF blocks are the following:
-
RIXS true. Similar to absorption spectroscopy, this requests theRIXS calculation to be performed based on the calculatednon-relativistic ground state multiplicity States
-
RIXSSOC true. By turning-on this flag the RIXS is calculated bytaking in account the relativistically corrected Ms States.
-
Elastic true. This flag indicates whether the resonant condition inwhich the initial and Final states coincide should be taken intoaccount. Note that the intensity of this spectral feature might beoverestimated as presently the non resonant terms are not treated
The respective ROCIS input reads then as follows:
!B3LYP def2-TZVP SlowConv%BasisAuxC "def2/J"end%ROCISNRoots 200PrintLevel 3MaxCore 4000DoRI 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 NRootswere sufficient enough to select the states dominated by both the donororbital spaces
--------------------------------------------------------------------------------ROOT Mult Excitation energy[Eh] [cm-1] [eV]--------------------------------------------------------------------------------0 2 0.00000000 0.00 0.0001 2 0.06611737 14511.08 1.7992 2 0.07728471 16962.03 2.1033 2 0.07732428 16970.72 2.104...84 2 33.75471831 7408304.35 918.51385 2 33.77073325 7411819.22 918.94886 2 33.77076955 7411827.19 918.94987 4 34.06882971 7477243.83 927.06088 2 34.07021441 7477547.74 927.098...
If that is not the case the respective RIXS calculations will not beperformed and a Warning Message will be generated:
Making the RIXS files ...WARNING!: Flag for RIXS property calculation was identified butthere is zero number of Intermediate and/or Final states:No Cross-Section properties will be evaluated ...Skipping this partTIP: 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 messagesfor RIXS and RIXSSOC calculations.
----------------------------------------------------------------------------------ROCIS RIXS SPECTRUM ----------------------------------------------------------------------------------Making the RIXS data files for Inelastic and Elastic ScatteringGround State: 1Intermediate States: 21Final States: 59The RIXS cross section will be generated from: 60 Ground-Final State Pairs and 21 Intermediate States/PairCalculating Intensities...10% done20% done30% done40% done50% done60% done70% done80% done90% done100% doneStoring the files...All Done----------------------------------------------------------------------------------
----------------------------------------------------------------------------------ROCIS RIXSSOC SPECTRUM ----------------------------------------------------------------------------------Making the RIXS-SOC data files for Inelastic and Elastic ScatteringMs States: 2Intermediate States: 78Final States: 214The RIXS cross section will be generated from: 432 Ground-Final State Pairs and 78 Intermediate States/PairCalculating Intensities...10% done20% done30% done40% done50% done60% done70% done80% done90% done100% doneStoring the files...All Done----------------------------------------------------------------------------------
In both cases the number of involved Initial, Final and Intermediatestates is specified explicitly.
For example in the case of RIXSSOC 2 Ms Ground states, 78 Intermediatestates and 214 Final states are involved. Then the RIXS cross sectionfor elastic and inelastic scattering will be generated by 432(2*(2+214)) Ground-Final State-Pairs and 78 Intermediate States perGround-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 thefollowing 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 willbe then Emission Energy axis
All this information is printed during the data processing:
Mode is RIXSUsing Lorentzian shapeCannot 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.rixssocIncident Energy Excitation axis : 871.000 ... 876.000 eV 125 pointsEnergy transfer axis : -1.000 ... 4.000 eV 125 pointsIncident Energy Shift : 20.000 eVLorenzian Linewidth along Incident Axis : 0.400 eVLorenzian Linewidth along Energy Transfer/Emission Axis : 0.400 eVy 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...DoneProccessing data...10% done20% done...100% doneRIXS-plotting doneIncident Energy range: 845.800 ... 869.249Emission/Energy-transfer range: 0.000 ... 4.853Now storing the 2D file...DoneMaking the Integrated spectra along Energy Transfer/Emission axis... DoneMaking the Integrated spectra along Incident axis... DoneAll Done---------------------------------------------------------------------------------
Successful run will generate the following files: The RIXS planes of theTotal, Direct and Interference RIXS intensity as indicated in the aboveequations:
test.el_inel.rocis.rixssoc.total_rixs.dattest.el_inel.rocis.rixssoc.direct_rixs.dattest.el_inel.rocis.rixssoc.interference_rixs.dat
In addition one obtains the integrated spectra at constant Incidentenergies (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
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 followingkeywords: uex and udw accounting for generating cuts at constantIncident Energies (CIE) and at constant Emission (CEE)/or at constantEnergy Transfer (CET) respectively, together with the desired number ofcuts.
2) Alternatively, the energies of the desired cuts can be specified aslists in the files udex.inp (user defined excitations) udem.inp (userdefined 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 ...DoneWriting file: test.el_inel.rocis.rixssoc_872.50.rxes_fs.dat ...DoneWriting file: test.el_inel.rocis.rixssoc_874.20.rxes_vs.dat ...DoneWriting file: test.el_inel.rocis.rixssoc_874.20.rxes_fs.dat ...DoneDoneMaking the specified cuts (3) at constant Emission/Energy Transfer axis...Writing file: test.el_inel.rocis.rixssoc_-1.00.xas_vs.dat ...DoneWriting file: test.el_inel.rocis.rixssoc_-1.00.xas_fs.dat ...DoneWriting file: test.el_inel.rocis.rixssoc_1.50.xas_vs.dat ...DoneWriting file: test.el_inel.rocis.rixssoc_1.50.xas_fs.dat ...DoneWriting file: test.el_inel.rocis.rixssoc_4.00.xas_vs.dat ...DoneWriting file: test.el_inel.rocis.rixssoc_4.00.xas_fs.dat ...DoneDoneAll Done---------------------------------------------------------------------------------
The files *_rxes_fs.dat are RXES spectra containing all individualcontributions from all Final states together with the Direct, the Totaland the Interference contributions at the given constant IncidentEnergy.
Similarly, the *_rxes_vs.dat are RXES spectra containing individualcontributions of the Intermediate states, together with the Direct theTotal and the Interference contributions at the given constant IncidentEnergy
Likewise, the respective *_xas_fs.dat and *_xas_vs.dat are XAS typespectra with individual contributions at a given constant Emission orEnergy 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 agiven Ground-Final state pair. The numbering follows the numbering ofthe output file e.g.:
Eigenvalues: cm-1 eV Boltzmann populations at T = 300.000 K0: 0.0000 0.0000 3.44e-011: 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 agiven Intermediate state.
44: 66918.6071 8.2968 1.43e-14045: 6996678.8061 867.4775 0.00e+0046: 6996693.0276 867.4793 0.00e+00
In this case S -1 represents the intensity contribution of the firstIntermediate state.
Starting from ORCA 4.2 in every RIXS requested calculation the Offresonant XES spectrum is automatically generated in every RIXS requestedcalculation.
----------------------------------------------------------------------------------ROCIS RIXS SPECTRUM ----------------------------------------------------------------------------------Making the RIXS data files for Inelastic and Elastic ScatteringGround State: 1Intermediate States: 28Final States: 588The RIXS cross section will be generated from: 589 Ground-Final State Pairs and 28 Intermediate States/PairThe Off-Resonance XES spectrum will be printedCalculating Intensities...10% done20% done30% done40% done50% done60% done70% done80% done90% done100% donePrinting 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 0.000002 590 -> 0 6403.380 0.000000000083 -0.00000 0.00000 0.000003 591 -> 0 6403.685 0.000873238810 0.00236 0.00000 0.000004 592 -> 0 6404.766 0.000000000154 0.00000 0.00000 0.000005 593 -> 0 6408.288 0.000000006850 -0.00001 0.00000 0.000006 594 -> 0 6408.295 0.000034710300 -0.00047 0.00000 0.00000...16490 614 -> 588 6387.989 0.000000000000 0.00000 0.00000 0.0000016491 615 -> 588 6388.222 0.000000000000 0.00000 0.00000 0.0000016492 616 -> 588 6388.881 0.000000000000 0.00000 0.00000 0.00000All 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 combinethe powerful machinery of the PNOs with the ROCIS and ROCIS/DFT methodsto formulate the core PNO-ROCIS and PNO-ROCIS/DFT methods. The usage ofPNOs here is somewhat unconventional since they are not used to treatelectron correlation effects in a state specific manner. Rather, thePNOs are used to identify the relevant part of the virtual space thatcan be reached by excitation out of local core orbitals. This subspaceof the virtual space is local, thus leading to a linear scaling, stateuniversal method.
The PNO-ROCIS calculations can be requested with the following keywords:
...DoPNO true #Flag to call the PNO truncationTCutPNO 1e-11#Threshold to cutout the PNO populationsXASElems 0 #Number of the involved element to the calculated core XAS calculationOrbWin = 0,0,0,2000...
As has been shown in reference [ 545 ] a universal TCutPNO 1e-11threshhold can be defined for all edges provided that the PNOs areconstructed by taking into account all the availiable core orbitals inthe systems. For example in the case of a 1st row transition metal thiswill be the 9 1s, 2s, 2p, 3s and 3p MOs. These orbitals will beidentified automatically by the program provided that the element or theelements for which the XAS calculation will be performed are specifiedwithin the XASElems keyword. In the following example these correspondto Core MOs 36-44. Note that the CoreMOs list should not be confusedwith the OrbWin which is used to specify the excitation space that willbe 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 EhMO= 37, E= -31.777896 EhMO= 38, E= -27.263122 EhMO= 39, E= -27.263122 EhMO= 40, E= -27.263122 EhMO= 41, E= -3.914132 EhMO= 42, E= -2.457405 EhMO= 43, E= -2.457405 EhMO= 44, E= -2.457405 Eh
Alternativelly one can also use the CoreMOs keyword to individual selectthe respective CoreMOs
...DoPNO true #Flag to call the PNO truncationTCutPNO 1e-11#Threshold to cutout the PNO populationsCoreMOs 0,1,6,7,8,29,30,31,32 #The core MOs for the selected element #to perform the XAS calculationOrbWin = 0,0,0,2000...
A complete list of CoreMOs of the different atoms can be found inreference [ 545 ] The program will then proceed and generate theCore PNOs and use the TCutPNO threshold to reduce the Virtual MO space.In the following example only virtual orbitals are selected out of thetotal 1445 virtual MOs
TCutPNO: 1.000e-11Virtual 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. Thiswill result in extraordinary computation speeding ups without loss inaccuracy.
7.31.6. ROCIS Magnetic Properties ¶
Several magnetic properies are availiable in the ROCIS method Includingg-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 theEffective Hamiltonian as well in the sum over states (SOS) framework.HFCs are calculated in the SOS framework while EFGs are calculated asexpectation values. Please consult also the respective discussion in theMRCI chapter (section The Multireference Correlation Module )
...DoHeff true #Requests calculation of G-tenosrs and ZFS #in the effective Hamiltonian frameworkDoEPR true #Requests calculation of G-tenosrs, ZFS and HFCs #in the Sum over states (SOS) frameworkAtensorNuc 0 #Nuclei to account for the HFCs calculationNAtensors 1 #How many Nuclei are included in the HFCs calculationATensor 0 # Nucleus to calculate HFCs and EFGsNDoubGtensor 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 rootsMaxDim 5 #Davidson expansion space = MaxDim * NRootsMaxIter 35#Maximum CI IterationsNGuessMat 512 #The dimension of the guess matrixETol 1e-6 #Energy convergence toleranceRTol 1e-6#Residual Convergence toleranceMaxCore 2000#Maximum memory used during the calculation in MBEWin= -5,5,-5,5 #Energy Window that defines orbital excitation spaceOrbWin=6,8,0,2000#Orbital Window that defines orbital excitation space#(overrides EWin)DoRI false#Switch for the RI approximationDoLoc false#Switch for localization of Donor orbital spaceLocMet PipekMezey#chooses the localization method:#PipekMezey or FosterBoys.#Abbreviations "PM" and "FB"#are equivalent to full names.SOC false #Switch for inclusion of SOCTEMPERATURE 10#The fictive temperature for the#SOC corrected spectraDoDFTCIS false#Switch for the DFT/ROCIS methodDFTCIS_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 excitationsDo_sa true#Include SOMO->Virtual excitationDo_ia true#Include DOMO->Virtual excitationsDo_ista true#Include DOMO->SOMO excitations#coupled to SOMO->Virtual#excitations with s not equal tDo_isa true #Include DOMO->SOMO excitations#coupled to SOMO->Virtual#excitations with s = tDoLowerMult false #Switch for excitation with S’=S-1Do_LM_is true #Include DOMO->SOMO excitations#with S’=S-1Do_LM_sa true #Include SOMO->Virtual excitations#with S’=S-1Do_LM_ia true#Include DOMO->Virtual excitations#with S’=S-1Do_LM_ss true#Include SOMO->SOMO excitations#with S’=S-1DoHigherMult false #Switch for DOMO->Virtual#excitations with S’=S+1#-----------------------------------------------------------OUTPUT KEYWORDS#-----------------------------------------------------------PrintLevel 3#Controls the amount of output#produced during the calculationRIXS false #Perform a RIXS calculationRIXSSOC false #Perform a RIXS calculation on the basis#of relativistically corrected statesElastic false #Include the elastic line in the generation#of the RIXS or RIXSSOC spectraPlotDiffDens = 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 stateDoNTO false#Request Natural Transition Orbital AnalysisDoNDO false#Request Natural Difference Orbital Analysis#(if true it switches off the NTO analysis)NDOThresh 1e-4 #Threshold for printing occupation numbersNTOThresh 1e-4#Threshold for printing occupation numbersNDOStates = 1,2#Array input for states to be taken into accountNTOStates = 1,2#Array input for states to be taken into accountTPrint 0.01#Threshold for contributions to CI#and SOC states to be printedDoPNO 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
