6.6. Excited States Calculations¶
A plethora of methods to compute excited states exists in ORCA . In the following section, we illustrate typical single-reference approaches. Multi-reference methods, such as NEVPT2 or MRCI, are described elsewhere in the manual.
6.6.1. Excited States with RPA, CIS, CIS(D), ROCIS and TD-DFT¶
ORCA features a module to perform TD-DFT, single-excitation CI (CIS) and RPA. The module works with either closed-shell (RHF or RKS) or unrestricted (UHF or UKS) reference wavefunctions. For DFT models the module automatically chooses TD-DFT and for HF wavefunctions the CIS model. If the RI approximation is used in the SCF part it will also be used in the excited states calculation. A detailed documentation is provided in section Excited States via RPA, CIS, TD-DFT and SF-TDA.
6.6.1.1. General Use¶
In its simplest form it is only necessary to provide the number of roots sought:
! B3LYP DEF2-SVP
%TDDFT NROOTS 10
TRIPLETS TRUE
END
* int 0 1
C 0 0 0 0.00 0.0 0.00
O 1 0 0 1.20 0.0 0.00
H 1 2 0 1.08 120 0.00
H 1 2 3 1.08 120 180.00
*
The triplets parameter is only valid for closed-shell references. If chosen as true the program will also determine the triplet excitation energies in addition to the singlets. We will discuss many more options in the following sections.
6.6.1.2. Spin-Flip¶
The collinear spin-flip version of CIS/TDA (always starting from an open-shell reference!) can be invoked in a similar manner, using:
%tddft
nroots 5
sf true
end
Please check Sec. Collinear Spin-Flip TDA (SF-TD-DFT) for more details on how to use it, and how to understand its results.
6.6.1.3. Population analysis¶
If you want to print excited-state charges and bond orders, you can use UPOP TRUE under %TDDFT to get the analysis from the unrelaxed density and !ENGRAD if you want to use the relaxed density. Multiple states can be indicated by the IROOTLIST and TROOTLIST keywords. For more details please check Sec. Population Analysis of Excited States.
6.6.1.4. Use of TD-DFT for the Calculation of X-ray Absorption Spectra¶
In principle X-ray absorption spectra are “normal” absorption spectra that are just taken in a special high-energy wavelength range. Due to the high energy of the radiation employed (several thousand eV), core-electrons rather than valence electrons are excited. This has two consequences: a) the method becomes element specific because the core-level energies divide rather cleanly into regions that are specific for a given element. b) the wavelength of the radiation is so short that higher-order terms in the expansion of the light-matter interaction become important. Most noticeably, quadrupole intensity becomes important.
X-ray absorption spectra can be generally divided into three regions: a) the pre-edge that corresponds to transitions of core electrons into low lying virtual orbitals that lead to bound states. b) the rising edge that corresponds to excitations to high-lying states that are barely bound, and c) the extended X-ray absorption fine structure region (EXAFS) that corresponds to electrons being ejected from the absorber atom and scattered at neighbouring atoms.
With the simple TD-DFT calculations described here, one focuses the attention on the pre-edge region. Neither the rising edge nor the EXAFS region are reasonably described with standard electronic structure methods and no comparison should be attempted. In addition, these calculations are restricted to K-edges as the calculation of L-edges is much more laborious and requires a detailed treatment of the core hole spin orbit coupling.
It is clearly hopeless to try to calculate enough states to cover all transitions from the valence to the pre-edge region. Hence, instead one hand-selects the appropriate donor core orbitals and only allows excitations out of these orbitals into the entire virtual space. This approximation has been shown to be justified.[200] One should distinguish two situations: First, the core orbital in question may be well isolated and unambiguously defined. This is usually the case for metal 1s orbitals if there is only one metal of the given type in the molecule. Secondly, there may be several atoms of the same kind in the molecule and their core orbitals form the appropriate symmetry adapted linear combinations dictated by group theory. In this latter case special treatment is necessary: The sudden approximation dictates that the excitations occurs from a local core orbital. In previous versions of the program you had to manually localize the core holes. In the present version there is an automatic procedure that is described below.
A typical example is TiCl\(_4\). If we want to calculate the titanium K-edge, the following input is appropriate:
! BP86 ZORA ZORA-def2-TZVP(-f) SARC/J TightSCF
%tddft OrbWin[0] = 0,0,-1,-1
NRoots 25
DoHigherMoments true
DoFullSemiclassical true
end
* int 0 1
Ti 0 0 0 0 0 0
Cl 1 2 3 2.15 0 0
Cl 1 2 3 2.15 109.4712 0
Cl 1 2 3 2.15 109.4712 120
Cl 1 2 3 2.15 109.4712 240
*
Note
The absolute transition energies from such calculations are off by a few hundred electron volts due to the shortcomings of DFT. The shift is constant and very systematic for a given element. Hence, calibration is possible and has been done for a number of edges already. Calibration depends on the basis set!
Electric quadrupole contributions and magnetic dipole contributions have been invoked with
DoHigherMoments true(check section One Photon Spectroscopy for more information), which is essential for metal edges. For ligand edges, the contributions are much smaller.OrbWinis used to select the single donor orbital (in this case the metal 1s). The LUMO (45) and last orbital in the set (174) are selected automatically if “-1” is given. This is different from previous program versions where the numbers had to be given manually.
The output contains standard TD-DFT output but also:
--------------------------------------------------------------------------------------------------------------------------------
ABSORPTION SPECTRUM COMBINED ELECTRIC DIPOLE + MAGNETIC DIPOLE + ELECTRIC QUADRUPOLE SPECTRUM
--------------------------------------------------------------------------------------------------------------------------------
Transition Energy Energy Wavelength fosc(D2) fosc(M2) fosc(Q2) fosc(D2+M2+Q2) D2/TOT M2/TOT Q2/TOT
(eV) (cm-1) (nm) (au) (au*1e6) (au*1e6)
--------------------------------------------------------------------------------------------------------------------------------
This section contains the relevant output since it combines electric dipole, electric quadrupole and magnetic dipole transition intensities into the final spectrum. Importantly, there is a gauge issue with the quadrupole intensity: the results depend on the where the origin is placed. We have proposed a minimization procedure that guarantees the fastest possible convergence of the multipole expansion.[201]
The spectra are plotted by calling
orca_mapspc MyOutput.out ABSQ -eV -x04890 -x14915 -w1.3
Starting from ORCA version 4.1 one may obtain origin independent transition moments formulations which can be combined 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 representations. This requires in addition to the electric dipole (D), electric quadrupole (Q) and magnetic dipole (m) intensities the corresponding electric dipole - magnetic quadrupole (DM) and the electric dipole - electric octupole (DO) intensities.[811][95]. See also section General Use.
These spectra are requested by (check section One Photon Spectroscopy for more information)
DoHigherMoments true
DecomposeFoscLength true
DecomposeFoscVelocity true
Resulting in:
--------------------------------------------------------------------------------------------------------------------------------
ABSORPTION SPECTRUM COMBINED ELECTRIC DIPOLE + MAGNETIC DIPOLE + ELECTRIC QUADRUPOLE SPECTRUM (Origin Independent, Length)
--------------------------------------------------------------------------------------------------------------------------------
Transition Energy Energy Wavelength fosc(D2) fosc(M2) fosc(Q2) fosc(D2+M2+Q2+DM+DO) D2/TOT M2/TOT Q2/TOT
(eV) (cm-1) (nm) (au) (au*1e6) (au*1e6)
--------------------------------------------------------------------------------------------------------------------------------
...
---------------------------------------------------------------------------------------------------------------------------------
ABSORPTION SPECTRUM COMBINED ELECTRIC DIPOLE + MAGNETIC DIPOLE + ELECTRIC QUADRUPOLE SPECTRUM (Origin Independent, Velocity)
---------------------------------------------------------------------------------------------------------------------------------
Transition Energy Energy Wavelength fosc(P2) fosc(M2) fosc(Q2) fosc(P2+M2+Q2+PM+PO) P2/TOT M2/TOT Q2/TOT
(eV) (cm-1) (nm) (au) (au*1e6) (au*1e6)
---------------------------------------------------------------------------------------------------------------------------------
...
The Origin Independent transition moments spectra are plotted by calling:
orca_mapspc MyOutput.out ABSOI/ABSVOI -eV -x04890 -x14915 -w1.3
Although the multipole moments up to 2nd order:
Only approximate origin independence is achieved by using the length approximation for distances from the excited atom up to about 5 Angstrom.
Can form negative intensities which can be partly cured by using larger basis sets.
Starting from ORCA version 6.0 the full semi-classical ligth-matter interaction[95][398][528] can be computed by including the keyword:
DoFullSemiclassical true
Resulting in:
-----------------------------------------------------------------------------
ABSORPTION SPECTRUM VIA FULL SEMI-CLASSICAL FORMULATION
-----------------------------------------------------------------------------
Transition Energy Energy Wavelength fosc(FFMIO)
(eV) (cm-1) (nm)
-----------------------------------------------------------------------------
The full-semiclassical transition moments:
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.
Now, let us turn to the Cl K-edge. Looking at the output of the first calculation, we have:
----------------
ORBITAL ENERGIES
----------------
NO OCC E(Eh) E(eV)
0 2.0000 -180.132624 -4901.6579
1 2.0000 -101.520058 -2762.5012
2 2.0000 -101.520052 -2762.5010
3 2.0000 -101.520048 -2762.5010
4 2.0000 -101.520048 -2762.5010
5 2.0000 -19.823233 -539.4176
6 2.0000 -16.411730 -446.5859
7 2.0000 -16.411729 -446.5858
8 2.0000 -16.411729 -446.5858
9 2.0000 -9.280963 -252.5478
10 2.0000 -9.280957 -252.5477
11 2.0000 -9.280953 -252.5476
12 2.0000 -9.280953 -252.5476
13 2.0000 -7.037815 -191.5087
14 2.0000 -7.037805 -191.5084
15 2.0000 -7.037791 -191.5080
16 2.0000 -7.037791 -191.5080
17 2.0000 -7.035288 -191.4399
18 2.0000 -7.035287 -191.4399
....
And looking at the energy range or the orbital composition, we find that orbitals 1 through 4 are Cl 1s-orbitals. They all have the same energy since they are essentially non-interacting. Hence, we can localize them without invalidating the calculation. To this end, you can invoke the automatic localization for XAS which modifies the input to:
! BP86 ZORA ZORA-def2-TZVP(-f) SARC/J TightSCF
%tddft XASLoc[0] = 1,4
OrbWin[0] = 1,1,-1,-1
NRoots 25
DoHigherMoments true
DoFullSemiclassical true
end
* int 0 1
Ti 0 0 0 0 0 0
Cl 1 2 3 2.15 0 0
Cl 1 2 3 2.15 109.4712 0
Cl 1 2 3 2.15 109.4712 120
Cl 1 2 3 2.15 109.4712 240
*
This localizes the orbitals 1 through 4 of operator 0 (the closed-shell) and then allows excitations (arbitrarily) from core hole 1 only. You could choose any of the three other localized 1s orbitals instead without changing the result. You could even do all four core holes simultaneously (they produce identical spectra) in which case you have the entire ligand K-edge intensity and not just the one normalized to a single chlorine (this would be achieved with
OrbWin[0] = 1,4,-1,-1).If you have a spin unrestricted calculation, you need to give the same
XASLocandOrbWininformation for the spin-down orbitals as well.
Quite nice results have been obtained for a number of systems in this way.[713]
6.6.1.5. Excited State Geometry Optimization¶
For RPA, CIS, TDA and TD-DFT the program can calculate analytic
gradients. With the help of the IRoot keyword, a given state can be
selected for geometry optimization. Note however, that if two states
cross during the optimization it may fail to converge or fail to
converge to the desired excited state (see section
Root Following Scheme for Difficult Cases below)! If
you want to follow a triplet state instead of the singlet, please set
IROOTMULT to TRIPLET.
! HF DEF2-SVP Opt
%CIS NRoots 1
IRoot 1
end
* int 0 1
C 0 0 0 0.00 0.0 0.00
O 1 0 0 1.20 0.0 0.00
H 1 2 0 1.08 120 0.00
H 1 2 3 1.08 120 180.00
*
Note that this example converges to a saddle point as can be verified
through a numerical frequency calculation (which is also possible with
the methods mentioned above). The excited state relaxed density matrix
is available from such gradient runs (MyJob.cisp when using the
KeepDens keyword) and can be used for various types of analysis. Note
that the frozen core option is available starting from version 2.8.0.
6.6.1.5.1. Root Following Scheme for Difficult Cases¶
In case there is a root flipping after a step during the geometry optimization, it might be impossible to converge an excited state geometry using the regular methods. To help in those cases, the flag FOLLOWIROOT might be set to TRUE. Then, excited state wavefunction will be analyzed and compared with the reference one (more below), and the IROOT will be automatically adjusted to keep homing the target state.
One example of such a calculation is:
! wB97X OPT
%TDDFT
NROOTS 5
IROOT 3
FOLLOWIROOT TRUE
END
* xyz 0 1
N 0.0 0.0 0.0
H 0.0 0.0 1.0
H 0.0 -0.9 0.5
H 0.0 0.9 0.5
*
This will ask for an optimization of the third excited state of ammonia. At some point, there is a state crossing and what was state 3 now becomes state 2. The algorithm will recognize this and automatically change the IROOT flag, to keep following the same state. FOLLOWIROOT also works with spin-adapted triplets and spin-flip states.
In cases where you want to keep the comparison only with the density from the very first computed excited state, e.g. the one you get on the first cycle of a geometry optimization, you can use FIRKEEPFIRSTREF, as in:
%TDDFT
NROOTS 5
IROOT 3
FOLLOWIROOT TRUE
FIRKEEPFIRSTREF TRUE # default false
END
6.6.1.5.2. Criteria to Follow IROOTs - starting from ORCA6¶
Starting from ORCA6 we have a much more robust algorithm to follow these excited states, inspired by some of the recent literature [820] [135]. The algorithm now works as follows, after each excited state calculation using CIS/TDDFT:
Given a reference state, take all states within an energy difference of up to 1 eV to it. We don’t want to check states that are too far apart in energy. Controlled by
%TDDFT FIRENTHRESH 1.0 END, number in eV.Now take all states with a difference of \(\hat{S}^2\) not larger than 0.5. We don’t want to compare singlets to triplets. Controlled by
%TDDFT FIRS2THRESH 0.5 END.Calculate the overlap between the transition densities of all states with the reference - this is the core part.
In case there is ambiguity - that is if two states have overlaps differing by only 0.05 - take the one with the closer transition dipole angle. Controlled by
%TDDFT FIRSTHRESH 0.05 END.Update the IROOT to the state that went best on all these tests.
Note
These FIR keywords are specific to Follow IRoot.
Now by default we might also update the reference state from time to time in case the separation of states is very clear. The way it work is:
If the best overlap is larger than
FIRMINOVERLAP, which is 0.5 by default andFIRDYNOVERLAPisFALSE, we will assume that the overlap is good enough and we will always update the reference. However, the default isFIRDYNOVERLAP TRUE, which means also have a second check for robustness.If
FIRDYNOVERLAP TRUEand the best overlap is larger than 0.5 (orFIRMINOVERLAP), we will check for theratiobetween the best and the second best states. If thisratiois between 0.3 and 0.6 (controlled by%TDDFT FIRDYNOVERRATIO 0.3,0.6 END), it means that there is a clear separation between the best and the second best and the reference can be updated safely. If the ratio is too close to 1, both states are too similar and it would be dangerous to update the reference state. If it is too close to zero, they are easy to distinguish and we don’t need to update the reference yet [820].
Important
It is important to stress that this will not necessarily solve all problems (root flipping can be particularly bad if the system is highly symmetric), for the excited states may change too much during the optimization. If that happens, it is advisable to restart the calculation after some steps and check which IROOT you still want. This can also be used when calculating numerical gradients and Hessians, in case you suspect of root flipping after the displacements.
Important
This algorithm is completely general and should work for any excited state method, as long as there are transition densities. We will include more methods in the future when possible.
6.6.1.6. Doubles Correction¶
For CIS (and also for perturbatively corrected time-dependent double-hybrid functionals) the program can calculate a doubles correction to the singles-only excited states. The theory is due to Head-Gordon and co-workers [371].
%cis dcorr n # n=1,2,3,4 are four different algorithms that
# lead to (essentially) the same result but differ
# in the way the rate-limiting steps are handled
Spin-component scaling versions of CIS(D) can be evoked in the %cis block by setting DOSCS TRUE and the four scaling parameters, as defined by Head-Gordon and co-workers [718], in the following order: same-spin indirect term (CTss), opposite-spin indirect term(CTos), same-spin direct term(CUss), and opposite-spin direct term(CUos). Note that this implementation only works for the version with the parameter \(\lambda=1\) as defined in Ref. [718]. The example below shows how to apply the SCS-CIS(D) version with \(\lambda=1\) whose usage has been advocated in Ref. [311]. The user is able to specify other scaling parameters.
%cis
dcorr # n=1,2,3,4
doscs true # set SCS-CIS(D) to true (default: false)
scspar 0.333, 1.2, 0.43, 1.24 #SCS-CIS(D) scaling parameters in this order
CTss, CTos, CUss, CUos
end
Note the use of commas to separate the parameters. These parameters do not communicate with the SCS/SOS parameters set for ground-state SCS/SOS-MP2 in the %mp2 block.
Note
CIS(D) is often a quite big improvement over CIS.
The cost of the (D) correction is O(N\(^{5})\) and therefore comparable to RI-MP2. Since there are quite a few things more to be done for (D) compared to RI-MP2, expect the calculations to take longer. In the most elementary implementation the cost is about two times the time for RI-MP2 for each root.
The (D) correction is compatible with the philosophy of the double-hybrid density functionals and should be used if these functionals are combined with TD-DFT. The program takes this as the default but will not enforce it. The (D) correction can be used both in a TD-DFT and TDA-DFT context.
In our implementation it is only implemented together with the RI approximation and therefore you need to supply an appropriate (“/C”) fitting basis.
The program will automatically put the RI-MP2 module into operation together with the (D) correction. This will result in the necessary integrals becoming available to the CIS module.
Singlet-triplet excitations can be calculated by setting TRIPLETS TRUE in the %cis or %tddft blocks, respectively. The implementation has been tested for double hybrids in Ref. [145].
For spin-adapted triplets (TRIPLETS TRUE), the only option available currently is DCORR 1.
Spin-component and spin-opposite scaling techniques for double-hybrids within the TD- and TDA-DFT frameworks, as defined by Schwabe and Goerigk [772], can be evoked in the same way in the %tddft block as described for SCS-CIS(D) above. While user-defined parameters can be entered in such a way, a series of new functionals are available through normal keywords, which use the herein presented SCS/SOS-CIS(D) implementation. [147] See Sec. Choice of Functional for a list of those functionals.
6.6.1.7. Spin-orbit coupling¶
It also possible to include spin-orbit coupling between singlets and triplets calculated from TD-DFT by using quasi-degenerate perturbation theory (please refer to the relevant publication [198]), similarly to what is done in ROCIS. In order to do that, the flag DOSOC must be set to TRUE. The reduced matrix elements are printed and the new transition dipoles between all SOC coupled states are also printed after the regular ones. This option is currently still not compatible with double hybrids, but works for all other cases including CPCM. All the options regarding the SOC integrals can be altered in the %rel block, as usual.
%CIS DOSOC TRUE END
Please have in mind that, as it is, you can only calculate the SOC between excited singlets and the spin-adapted triplets. There is no SOC starting from a UHF/UKS wavefunction. If you want more information printed such as the full SOC matrix or triplet-triplet couplings, please set a higher PRINTLEVEL.
6.6.1.7.1. SOC and ECPs¶
ORCA currently does not have SOC integrals for ECPs, and these are by default ignored in the SOC module. If you try to use ORCA together with ECPs, an abort message will be printed. If you absolutely need to use ECPs, for instance for embedded potentials, please use:
%TDDFT FORCEECP TRUE END
OBS.: Do not use ECPs in atoms where SOC might be important. In that case, always use all-electron basis functions or the results will not make sense.
6.6.1.7.2. Geometry Optimization of SOC States¶
If you want to compute geometries for the SOC states, just choose SOCGRAD TRUE and a given IROOT. The weigthed “unrelaxed” gradient will then be calculated after selecting the CIS/TD-DFT states with contribution larger than 0.01%. Each gradient will be calculated separately and, after that, the final SOC gradient will be computed as a weighted sum. Setting IROOT 0 in this case corresponds to ask for the SOC ground state, which is NOT necessarily equal to the ground state from HF/DFT.
6.6.1.8. Transient spectra¶
If one wants to compute transient spectra, or transition dipoles
starting from a given excited state, the option DOTRANS must be set to
TRUE and an IROOT should be given for the initial state (the default is
1). If DOTRANS ALL is requested instead, the transition dipoles between
all states are computed. The transient transition dipoles will then be
printed after the normal spectra. This option is currently only
available for CIS/TDA and is done usng the expectation value formalism,
as the other transition dipole moments in ORCA.
%cis
DOTRANS TRUE
#or
DOTRANS ALL
end
6.6.1.9. Non-adiabatic coupling matrix elements¶
The CIS module can compute the non-adiabatic coupling matrix elements (NACME) between ground and an excited state given by an IROOT, \(\langle \Psi_{GS} | \frac{\partial}{\partial R_x} | \Psi_{IROOT} \rangle\) [783]. These can also include LR-CPCM effects if !CPCM(solvent) is chosen in the main input, ZORA effects and will make use of RIJ and COSX, if they are chosen for the SCF. The usage is simple, e.g.:
!PBE0 DEF2-SVP TIGHTSCF
%TDDFT NROOTS 5
IROOT 2
NACME TRUE
END
* xyz 0 1
O 0.000000000 0.000000000 0.611403292
C 0.000000000 0.000000000 -0.613232096
H 0.931880792 0.000000000 -1.200880848
H -0.931880792 0.000000000 -1.200880848
*
By choosing NACME TRUE under %TDDFT, a regular gradient calculation will be done, and the NACMEs will be computed together with it. After the usual gradient output, the NACMEs will be printed as:
---------------------------------
CARTESIAN NON-ADIABATIC COUPLINGS
<GS|d/dx|ES>
---------------------------------
1 O : -0.161958900 -0.000000135 0.000001029
2 C : -0.088213027 -0.000000024 0.000000167
3 H : 0.226241398 0.000000001 -0.109102154
4 H : 0.226241406 -0.000000000 0.109102161
Difference to translation invariance:
: 0.2023108777 -0.0000001585 0.0000012017
Norm of the NACs ... 0.4002363416
RMS NACs ... 0.1155382798
MAX NAC ... 0.2262414063
6.6.1.9.1. NACMEs with built-in electron-translation factor¶
As you can see, the calculation above does not have full translation invariance! That is a feature of NACs calculated from CI wavefunctions, due to the Born-Oppenheimer approximation. It can be somehow fixed by including the so-called “electron-translation factors” (ETFs) [252], and those are added with ETF TRUE under %TDDFT. By now using the input:
!PBE0 DEF2-SVP
%TDDFT NROOTS 5
IROOT 2
NACME TRUE
ETF TRUE
END
* xyz 0 1
O 0.000000000 0.000000000 0.611403292
C 0.000000000 0.000000000 -0.613232096
H 0.931880792 0.000000000 -1.200880848
H -0.931880792 0.000000000 -1.200880848
*
one gets the following output:
---------------------------------
CARTESIAN NON-ADIABATIC COUPLINGS
<GS|d/dx|ES>
with built-in ETFs
---------------------------------
1 O : -0.071334028 -0.000001941 0.000003727
2 C : -0.362514525 -0.000000130 -0.000000776
3 H : 0.217014763 0.000000003 -0.128968922
4 H : 0.217014813 -0.000000002 0.128968939
Difference to translation invariance:
: 0.0001810232 -0.0000020693 0.0000029689
Norm of the NACs ... 0.5137724505
RMS NACs ... 0.1483133313
MAX NAC ... 0.3625145251
where the residual translation variance is due to the DFT and COSX grids only.
Warning
These are the recommended NACs to be used with any kind of dynamics or conical intersection optimization, otherwise moving the center of mass of you system would already change the couplings!
6.6.1.10. Numerical non-adiabatic coupling matrix elements¶
The numerical non-adiabatic coupling matrix elements between ground and excited states from CIS/TD-DFT can be calculated in a numerical fashion, by setting the NumNACME flag on the main input line:
! NumNACME
ORCA will then calculate both the NACMEs and the numerical gradient for a given IROOT at the same cost. Please be careful with the SCF options and GRID sizes since there are displacements involved, for more information check Numerical Gradients. All options regarding step size and so on can be changed from %NUMGRAD.
These are current implemented in both RHF/RKS and UHF/UKS, but only for CIS/TDA and RPA/TD-DFT, no multireference methods yet. For the latter case, the overlap of the \(| X -Y \rangle\) vector is used [517].
6.6.1.11. Restricted Open-shell CIS¶
In addition to the CIS/TD-DFT description of excited states, ORCA
features the orca_rocis module to perform configuration interaction
with single excitations calculations using a restricted open-shell
Hartree–Fock (ROHF) reference. It can be used to calculate excitation
energies, absorption intensities and CD UHFintensities. In general,
ROCIS calculations work on restricted open-shell HF reference functions
but in this implementation it is possible to enter the calculations with
RHF (only for closed-shell molecules) or UHF reference functions as
well. If the calculation starts with an UHF/UKS calculation, it will
automatically produce the quasi-restricted orbitals which will then be
used for the subsequent ROCIS calculations. Note that if the reference
function is a RHF/RKS function the method produces the CIS results. The
module is invoked by providing the number of roots sought in the
%rocis block of the input file:
! SVP TightSCF
%rocis NRoots 2
MaxDim 5 #Davidson expansion space = MaxDim * NRoots
end
* xyz -2 2
Cu 0.00 0.00 0.00
Cl 2.25 0.00 0.00
Cl -2.25 0.00 0.00
Cl 0.00 2.25 0.00
Cl 0.00 -2.25 0.00
*
In this example the MaxDim parameter is given in addition to the
number of roots to be calculated. It controls the maximum dimension of
the expansion space in the Davidson procedure that is used to solve the
CI problem.
The use of ROCIS is explained in greater detail in section Excited States via ROCIS and DFT/ROCIS.
Starting from ORCA 6.0, the General-Spin ROCIS (GS-ROCIS) implementation is available.
This new implementation can handle arbitrary CSFs as references. For this,
one would use the CSF-ROHF method to obtain the reference wavefunction for
which ROCIS will be performed. The GS-ROCIS calculation can be invoked as follows:
%scf
HFTyp ROHF
ROHF_CASE USER_CSF or AF_CSF
etc.
end
%rocis
DoGenROCIS true # Turns the General-Spin ROCIS procedure on
ReferenceMult 1 # The reference wavefunction multiplicity (it needs to agree with the ROHF solution)
etc.
end
Currently, there is no DFT/ROCIS implemented for the General-Spin procedure. Spin-Orbit coupling is also not available in the present version.
6.6.2. Excited States for Open-Shell Molecules with CASSCF Linear Response (MC-RPA)¶
ORCA has the possibility to calculate excitation energies, oscillator and rotatory strengths for CASSCF wave functions within the response theory (MC-RPA) formalism.[380, 417, 902] The main scope of MC-RPA is to simiulate UV/Vis and ECD absorption spectra of open-shell molecules like transition metal complexes and organic radicals. MC-RPA absorption spectra are usually more accurate than those obtained from the state-averaged CASSCF ansatz as orbital relaxation effects for excited states are taken into account. The computational costs are ususally larger than those of SA-CASSCF and should be comparable to a TD-DFT calculation for feasible active space sizes.
6.6.2.1. General Use¶
MC-RPA needs a converged state-specific CASSCF calculation of the electronic ground state. The only necessary information that the user has to provide is the desired number of excited states (roots). All other keywords are just needed to control the Davidson algorithm or post process the results. A minimal input for calculating the four lowest singlet excited states of ethylene could like the following:
#
# CASSCF + MCRPA for C2H4
#
! DEF2-SVP DEF2-TZVP/C VeryTightSCF
%casscf
nel 2
norb 2
mult 1
nroots 1
gtol 1e-6
etol 1e-10
end
%mcrpa
nroots 8
end
* int 0 1
C 0 0 0 0 0 0
C 1 0 0 1.3385 0 0
H 1 2 0 1.07 120 0
H 1 2 3 1.07 120 180
H 2 1 3 1.07 120 0
H 2 1 3 1.07 120 180
*
After the residual norm is below a user-given threshold TolR we get
the following information
Final Eigenvalues
State Eigenvalue RMSD error Converged
0 0.3352792890 2.4181038930e-07 T
1 0.3484190806 9.8077823429e-07 T
2 0.3514832140 2.7908735363e-07 T
3 0.3741119713 2.9210937348e-07 T
4 roots were CONVERGED within 19 iterations!
64 Sigma vectors were computed in total!
and the absorption and ECD spectrum
----------------------------------------------------------------------------------------------------
ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
----------------------------------------------------------------------------------------------------
Transition Energy Energy Wavelength fosc(D2) D2 DX DY DZ
(eV) (cm-1) (nm) (au**2) (au) (au) (au)
----------------------------------------------------------------------------------------------------
0-1A -> 1-1A 9.123912 73589.3 135.9 0.430770278 1.92711 -1.38820 0.00000 -0.00000
0-1A -> 2-1A 9.483952 76493.2 130.7 0.009915149 0.04267 -0.00000 0.00000 -0.20657
0-1A -> 3-1A 9.564384 77142.0 129.6 0.000000000 0.00000 -0.00000 0.00000 -0.00000
0-1A -> 4-1A 10.180358 82110.1 121.8 0.000000000 0.00000 0.00000 0.00000 0.00000
0-1A -> 5-1A 10.187869 82170.7 121.7 0.000000000 0.00000 0.00000 -0.00000 0.00000
0-1A -> 6-1A 10.995304 88683.1 112.8 0.000000000 0.00000 -0.00000 -0.00000 -0.00000
0-1A -> 7-1A 12.188654 98308.1 101.7 0.000000000 0.00000 0.00000 -0.00000 -0.00000
0-1A -> 8-1A 12.543751 101172.2 98.8 0.000000000 0.00000 -0.00000 0.00000 0.00000
...
------------------------------------------------------------------------------------------
CD SPECTRUM VIA TRANSITION VELOCITY DIPOLE MOMENTS
------------------------------------------------------------------------------------------
Transition Energy Energy Wavelength R MX MY MZ
(eV) (cm-1) (nm) (1e40*cgs) (au) (au) (au)
------------------------------------------------------------------------------------------
0-1A -> 1-1A 9.123912 73589.3 135.9 -0.00000 -0.00000 -0.00000 -0.00000
0-1A -> 2-1A 9.483952 76493.2 130.7 0.00000 -0.00000 -0.00000 0.00000
0-1A -> 3-1A 9.564384 77142.0 129.6 0.00000 0.69943 -0.00000 0.00000
0-1A -> 4-1A 10.180358 82110.1 121.8 -0.00000 0.15776 0.00000 -0.00000
0-1A -> 5-1A 10.187869 82170.7 121.7 0.00000 0.00000 -0.73302 0.00000
0-1A -> 6-1A 10.995304 88683.1 112.8 -0.00000 0.00000 -0.54038 -0.00000
0-1A -> 7-1A 12.188654 98308.1 101.7 -0.00000 0.00000 0.00000 -0.00000
0-1A -> 8-1A 12.543751 101172.2 98.8 0.00000 0.00000 0.00000 -0.90854
6.6.2.2. Capabilities¶
At the moment, we can simulate UV/Vis and ECD absorption spectra by
computing excitation energies, oscillator and rotatory strengths. The
code is parallelized and the computational bottleneck is the integral
direct AO-Fock matrix construction. All intermediates that depend on the
number of states are stored on disk, which makes the MC-RPA
implementation suitable for computing many low-lying electronic states
of larger molecules. Abelian point-group symmetry can be exploited in
the calculation (up to D\(_{\textrm{2h} }\)). But there are no
calculations of spin-flip excitations possible at the moment. That means
all excited states will have the same spin as the reference state, which
is specified in the %casscf input block.
It is also possible to analyze and visualize the ground-to-excited-state transitions by means of natural transition orbitals[562] (NTO), which is explained in more detail in section Excited States via MC-RPA.
For further details, please study our recent publications[379, 380].
6.6.3. Excited States with EOM-CCSD¶
The methods described in the previous section are all based on the single excitation framework. For a more accurate treatment, double excitations should also be considered. The equation of motion (EOM) CCSD method (and the closely related family of linear response CC methods) provides an accurate way of describing excited, ionized and electron attached states based on singles and doubles excitations within the coupled-cluster framework. In this chapter, the typical usage of the EOM-CCSD routine will be described, along with a short list of its present capabilities. A detailed description will be given in Section Excited States via EOM-CCSD.
6.6.3.1. General Use¶
The simplest way to perform an EOM calculation is via the usage of the
EOM-CCSD keyword, together with the specification of the desired
number of roots:
! RHF EOM-CCSD cc-pVDZ TightSCF
%mdci
nroots 9
end
*xyz 0 1
C 0.016227 -0.000000 0.000000
O 1.236847 0.000000 -0.000000
H -0.576537 0.951580 -0.000000
H -0.576537 -0.951580 -0.000000
*
The above input will call the EOM routine with default settings. The main output is a list of excitation energies, augmented with some further state specific data. For the above input, the following output is obtained:
----------------------
EOM-CCSD RESULTS (RHS)
----------------------
IROOT= 1: 0.147823 au 4.022 eV 32443.5 cm**-1
Amplitude Excitation
0.107945 4 -> 8
0.665496 7 -> 8
0.104633 7 -> 8 6 -> 8
Ground state amplitude: 0.000000
Percentage singles character= 92.32
IROOT= 2: 0.314133 au 8.548 eV 68944.3 cm**-1
Amplitude Excitation
0.671246 7 -> 9
Ground state amplitude: -0.000000
Percentage singles character= 90.42
IROOT= 3: 0.343833 au 9.356 eV 75462.6 cm**-1
Amplitude Excitation
-0.670633 5 -> 8
-0.112538 6 -> 8 5 -> 8
Ground state amplitude: 0.000000
Percentage singles character= 92.00
IROOT= 4: 0.364199 au 9.910 eV 79932.5 cm**-1
Amplitude Excitation
0.102777 4 -> 10
-0.484661 6 -> 8
0.438311 7 -> 10
-0.167512 6 -> 8 6 -> 8
Ground state amplitude: -0.021060
Percentage singles character= 87.22
IROOT= 5: 0.389398 au 10.596 eV 85463.0 cm**-1
Amplitude Excitation
0.646812 4 -> 8
-0.122387 7 -> 8
0.171366 7 -> 8 6 -> 8
Ground state amplitude: 0.000000
Percentage singles character= 87.47
IROOT= 6: 0.414587 au 11.281 eV 90991.4 cm**-1
Amplitude Excitation
-0.378418 6 -> 8
-0.537292 7 -> 10
-0.124246 6 -> 8 6 -> 8
Ground state amplitude: -0.061047
Percentage singles character= 89.13
IROOT= 7: 0.423861 au 11.534 eV 93026.7 cm**-1
Amplitude Excitation
0.673806 7 -> 11
Ground state amplitude: 0.000000
Percentage singles character= 93.14
IROOT= 8: 0.444201 au 12.087 eV 97490.8 cm**-1
Amplitude Excitation
0.664877 6 -> 9
0.130475 6 -> 9 6 -> 8
Ground state amplitude: -0.000000
Percentage singles character= 87.17
IROOT= 9: 0.510514 au 13.892 eV 112044.8 cm**-1
Amplitude Excitation
-0.665791 6 -> 10
0.114259 6 -> 15
-0.124374 6 -> 10 6 -> 8
Ground state amplitude: -0.000000
The IP and EA versions can be called using the keywords IP-EOM-CCSD
and EA-EOM-CCSD respectively. For open-shell systems (UHF reference
wavefunction), IP/EA-EOM-CCSD calculations require an additional
keywords. Namely, an IP/EA calculation involving the removal/attachment
of an \(\alpha\) electron is requested by setting the DoAlpha keyword to
true in the %mdci block, while setting the DoBeta keyword to true
selects an IP/EA calculation for the removal/attachment of a \(\beta\)
electron. Note that DoAlpha and DoBeta cannot simultaneously be true
and that the calculation defaults to one in which DoAlpha is true if
no keyword is specified on input. A simple example of the input for a
UHF IP-EOM-CCSD calculation for the removal of an \(\alpha\) electron is
given below.
! IP-EOM-CCSD cc-pVDZ
%mdci
DoAlpha true
NRoots 7
end
*xyz 0 3
O 0.0 0.0 0.0
O 0.0 0.0 1.207
*
6.6.3.2. Capabilities¶
At present, the EOM routine is able to perform excited, ionized and
electron attached state calculations, for both closed- or open-shell
systems, using RHF or UHF reference wavefunctions, respectively. It can
be used for serial and parallel calculations. The method is available in
the back-transformed PNO and DLPNO framework enabling the calculation of
large molecules - see Section
Excited States with PNO based coupled cluster methods and Section
Excited States with DLPNO based coupled cluster methods. In the closed-shell case (RHF), a
lower scaling version can be invoked by setting the CCSD2 keyword to
true in the %mdci section. The latter is a second order approximation to
the conventional EOM-CCSD. For the time being, the most useful
information provided is the list of the excitation energies, the
ionization potentials or the electron affinities. The ground to excited
state transition moments are also available for the closed-shell
implementation of EE-EOM-CCSD.
6.6.4. Excited States with ADC2¶
Among the various approximate correlation methods available for excited states, one of the most popular one is algebraic diagrammatic construction(ADC) method. The ADC has it origin in the Green’s function theory. It expands the energy and wave-function in perturbation order and can directly calculate the excitation energy, ionization potential and electron affinity, similar to that in the EOM-CCSD method. Because of the symmetric eigenvalue problem in ADC, the calculation of properties are more straight forward to calculate than EOM-CCSD. In ORCA, only the second-order approximation to ADC(ADC2) is implemented. It scales as O(\(N^{5}\)) power of the basis set.
6.6.4.1. General Use¶
The simplest way to perform an ADC2 calculation is via the usage of the
ADC2 keyword, together with the specification of the desired number of
roots:
! ADC2 cc-pVDZ cc-pVDZ/C TightSCF
%mdci
nroots 9
end
*xyz 0 1
C 0.016227 -0.000000 0.000000
O 1.236847 0.000000 -0.000000
H -0.576537 0.951580 -0.000000
H -0.576537 -0.951580 -0.000000
*
The above input will call the ADC2 routine with default settings. The main output is a list of excitation energies, augmented with some further state specific data. The integral transformation in the ADC2 implementation of ORCA is done using the density-fitting approximation. Therefore, one need to specify an auxiliary basis. For the above input, the following output is obtained:
----------------------
ADC(2) RESULTS (RHS)
----------------------
IROOT= 1: 0.146914 au 3.998 eV 32243.8 cm**-1
Amplitude Excitation
-0.116970 4 -> 8
-0.672069 7 -> 8
IROOT= 2: 0.286012 au 7.783 eV 62772.3 cm**-1
Amplitude Excitation
-0.659777 7 -> 9
IROOT= 3: 0.341919 au 9.304 eV 75042.4 cm**-1
Amplitude Excitation
-0.676913 5 -> 8
IROOT= 4: 0.352206 au 9.584 eV 77300.2 cm**-1
Amplitude Excitation
-0.126824 4 -> 10
0.360690 6 -> 8
-0.547669 7 -> 10
IROOT= 5: 0.393965 au 10.720 eV 86465.3 cm**-1
Amplitude Excitation
-0.551344 6 -> 8
-0.363451 7 -> 10
-0.109270 6 -> 8 6 -> 8
IROOT= 6: 0.404946 au 11.019 eV 88875.5 cm**-1
Amplitude Excitation
0.669682 4 -> 8
-0.126557 7 -> 8
IROOT= 7: 0.412800 au 11.233 eV 90599.2 cm**-1
Amplitude Excitation
0.100274 4 -> 11
0.671884 7 -> 11
IROOT= 8: 0.439251 au 11.953 eV 96404.6 cm**-1
Amplitude Excitation
-0.674114 6 -> 9
-0.104541 6 -> 9 6 -> 8
IROOT= 9: 0.486582 au 13.241 eV 106792.5 cm**-1
Amplitude Excitation
-0.654624 5 -> 9
The transition moment for ADC2 in ORCA is calculated using an EOM-like expectation value approach, unlike the traditionally used intermediate state representation. However, the two approaches gives almost identical result.
--------------------------------------------------------------------
SPECTRUM FOR LEFT-RIGHT TRANSITION MOMENTS
--------------------------------------------------------------------
----------------------------------------------------------------------------------------------------
ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
----------------------------------------------------------------------------------------------------
Transition Energy Energy Wavelength fosc(D2) D2 DX DY DZ
(eV) (cm-1) (nm) (au**2) (au) (au) (au)
----------------------------------------------------------------------------------------------------
0-1A -> 1-1A 3.997726 32243.8 310.1 0.000000000 0.00000 0.00000 -0.00000 0.00000
0-1A -> 2-1A 7.782776 62772.3 159.3 0.096710371 0.50720 0.00000 -0.70536 0.00000
0-1A -> 3-1A 9.304078 75042.5 133.3 0.002261744 0.00992 -0.00000 -0.00000 0.09835
0-1A -> 4-1A 9.584003 77300.2 129.4 0.007937829 0.03381 0.18502 0.00000 -0.00000
0-1A -> 5-1A 10.720332 86465.3 115.7 0.465055079 1.77067 1.32377 0.00000 0.00000
0-1A -> 6-1A 11.019150 88875.4 112.5 0.000000000 0.00000 0.00000 0.00000 0.00000
0-1A -> 7-1A 11.232869 90599.2 110.4 0.022236623 0.08080 -0.00000 0.28105 0.00000
0-1A -> 8-1A 11.952640 96404.5 103.7 0.009103120 0.03109 -0.00000 0.00000 -0.17328
0-1A -> 9-1A 13.240575 106792.5 93.6 0.071433742 0.22021 -0.46692 0.00000 0.00000
The IP and EA versions can be called using the keywords IP-ADC2 and EA-ADC2, respectively.
6.6.4.2. Capabilities¶
At present, the ADC2 module is able to perform excited, ionized and electron attached state calculations, only for closed-shell systems. No open-shell version of the ADC2 is currently available. Below are all the parameters that influence the ADC2 module.
%mdci
#ADC2 parameters - defaults displayed
NDav 20 # maximum size of reduced space (i.e. 20*NRoots)
CheckEachRoot true # check convergence for each root separately
RootHoming true # apply root homing
DoLanczos false # use the Lanczos procedure rather than Davidson
UseCISUpdate true # use diagonal CIS for updating
NInitS 0 # number of roots in the initial guess, if 0, use preset value
DoRootwise false # solves for each root separately,
# more stable for large number of roots
FOLLOWCIS false # follows the initial singles guess
end
One can notice that features available in the ADC2 module is quite limited as compared to the EOM module and the option to specifically target the core-orbitals are yet not available. A word of caution, The ‘second order black magic’ of ADC2 can fail in many of the cases. The readers are encouraged to try the DLPNO based EOM-CCSD methods(Excited States with DLPNO based coupled cluster methods) which are much more accurate and computationally efficient.
6.6.5. Excited States with STEOM-CCSD¶
The STEOM-CCSD method provides an efficient way to calculate excitation energies, with an accuracy comparable to the EOM-CCSD approach, at a nominal cost. A detailed description will be given in Section Excited States via STEOM-CCSD.
6.6.5.1. General Use¶
The simplest way to perform a STEOM calculation is using the
STEOM-CCSD keyword, together with the specification of the desired
number of roots (NRoots):
! STEOM-CCSD cc-pVDZ TightSCF
%mdci
NRoots 9 # Number of excited states
DoDbfilter true # Remove doubly excited states
end
*xyz 0 1
C 0.016227 -0.000000 0.000000
O 1.236847 0.000000 -0.000000
H -0.576537 0.951580 -0.000000
H -0.576537 -0.951580 -0.000000
*
The above input calls the STEOM routine with default settings, where,
for instance, the doubly excited states are eliminated
(DoDbFilter true). The main output is a list of excitation energies,
augmented with some further state specific data. The STEOMCC approach in
ORCA uses state-averaged CIS natural transition orbitals (NTO) for the
selection of the active space. For the above input, the following output
is obtained:
------------------
STEOM-CCSD RESULTS
------------------
IROOT= 1: 0.146552 au 3.988 eV 32164.5 cm**-1
Amplitude Excitation
0.196225 4 -> 8
-0.979974 7 -> 8
Amplitude Excitation in Canonical Basis
-0.153212 4 -> 8
0.977931 7 -> 8
-0.121980 7 -> 13
IROOT= 2: 0.308608 au 8.398 eV 67731.7 cm**-1
Amplitude Excitation
-0.141414 4 -> 9
0.988498 7 -> 9
Amplitude Excitation in Canonical Basis
-0.989700 7 -> 9
IROOT= 3: 0.336979 au 9.170 eV 73958.3 cm**-1
Amplitude Excitation
-0.994070 5 -> 8
Amplitude Excitation in Canonical Basis
0.983934 5 -> 8
-0.137018 5 -> 13
IROOT= 4: 0.362974 au 9.877 eV 79663.6 cm**-1
Amplitude Excitation
0.177265 4 -> 10
0.825223 6 -> 8
-0.500412 7 -> 10
-0.118642 7 -> 12
Amplitude Excitation in Canonical Basis
-0.152751 4 -> 10
-0.821991 6 -> 8
0.506004 7 -> 10
IROOT= 5: 0.402096 au 10.942 eV 88249.9 cm**-1
Amplitude Excitation
0.100684 5 -> 11
0.617781 6 -> 8
0.761064 7 -> 10
Amplitude Excitation in Canonical Basis
-0.612814 6 -> 8
-0.754151 7 -> 10
IROOT= 6: 0.421001 au 11.456 eV 92399.1 cm**-1
Amplitude Excitation
-0.165095 4 -> 11
0.983905 7 -> 11
Amplitude Excitation in Canonical Basis
0.121348 4 -> 11
-0.983982 7 -> 11
IROOT= 7: 0.445178 au 12.114 eV 97705.3 cm**-1
Amplitude Excitation
0.995471 6 -> 9
Amplitude Excitation in Canonical Basis
-0.989647 6 -> 9
IROOT= 8: 0.462852 au 12.595 eV 101584.3 cm**-1
Amplitude Excitation
-0.985707 4 -> 8
-0.130220 6 -> 10
Amplitude Excitation in Canonical Basis
0.975461 4 -> 8
-0.147945 4 -> 13
0.128680 6 -> 10
IROOT= 9: 0.512757 au 13.953 eV 112537.1 cm**-1
Amplitude Excitation
0.121760 4 -> 8
-0.989185 6 -> 10
Amplitude Excitation in Canonical Basis
-0.121079 4 -> 8
0.979589 6 -> 10
-0.154643 6 -> 15
The first set of excitation amplitudes, printed for each root, have been calculated in the CIS NTO (Natural Transition Orbitals) basis. The second set of amplitudes have been evaluated in the RHF canonical basis.
6.6.5.2. Capabilities¶
At present, the STEOM routine is able to calculate excitation energies,
for both closed- or open-shell systems, using an RHF or UHF reference
function, respectively. It can be used for both serial and parallel
calculations. The method is available in the back-tranformed PNO and
DLPNO framework allowing the calculation of large molecules (Section
Capabilities and
Excited States with DLPNO based coupled cluster methods). In the closed-shell case (RHF), a
lower scaling version can be invoked by setting the CCSD2 keyword to
true in the %mdci section, which sets a second order approximation to
the exact parent approach. The transition moments can also be obtained
for closed- and open-shell systems. For more details see Section
Excited States via STEOM-CCSD.
6.6.6. Excited States with IH-FSMR-CCSD¶
The intermediate Hamiltonian Fock-space coupled cluster method (IH-FSMR-CCSD) provides an alternate way to calculate excitation energies, with an accuracy comparable to the STEOM-CCSD approach. A detailed description is given in Section General Description.
6.6.6.1. General Use¶
The IH-FSMR-CCSD calculation is called using the simple input keyword
IH-FSMR-CCSD and specifying the desired number of excited states
(NRoots) in the %mdci block.:
! IH-FSMR-CCSD cc-pVDZ TightSCF
%mdci
nroots 6
end
*xyz 0 1
C 0.016227 -0.000000 0.000000
O 1.236847 0.000000 -0.000000
H -0.576537 0.951580 -0.000000
H -0.576537 -0.951580 -0.000000
*
The above input will call the IH-FSMR-CCSD routine with default settings. The main output is a list of excitation energies, augmented with some further state specific data. The IH-FSMR-CCSD approach in ORCA uses state-averaged CIS natural transition orbitals(NTO) for the selection of the active space - similar to STEOM-CCSD. For the above input, the following output is obtained:
------------------
IH-FSMR-CCSD RESULTS
------------------
IROOT= 1: 0.144300 au 3.927 eV 31670.2 cm**-1
Amplitude Excitation
-0.173154 4 -> 8
-0.984515 7 -> 8
Ground state amplitude: 0.000000
Percentage Active Character 99.93
Amplitude Excitation in Canonical Basis
-0.170951 4 -> 8
0.976572 7 -> 8
-0.111271 7 -> 13
IROOT= 2: 0.309445 au 8.420 eV 67915.3 cm**-1
Amplitude Excitation
0.993733 7 -> 9
Ground state amplitude: 0.000000
Percentage Active Character 99.65
Amplitude Excitation in Canonical Basis
-0.991663 7 -> 9
IROOT= 3: 0.335928 au 9.141 eV 73727.6 cm**-1
Amplitude Excitation
0.994414 5 -> 8
Ground state amplitude: 0.000000
Percentage Active Character 98.98
Amplitude Excitation in Canonical Basis
-0.986238 5 -> 8
0.122237 5 -> 13
IROOT= 4: 0.358174 au 9.746 eV 78610.1 cm**-1
Amplitude Excitation
-0.176281 4 -> 10
0.736812 6 -> 8
-0.594366 7 -> 10
-0.213482 7 -> 12
Ground state amplitude: 0.000000
Percentage Active Character 92.76
Warning:: the state may have not converged with respect to active space
-------------------- Handle with Care --------------------
Amplitude Excitation in Canonical Basis
-0.184685 4 -> 10
0.734266 6 -> 8
0.630467 7 -> 10
IROOT= 5: 0.385852 au 10.500 eV 84684.8 cm**-1
Amplitude Excitation
-0.981051 4 -> 8
0.179230 7 -> 8
Ground state amplitude: 0.000000
Percentage Active Character 99.86
Amplitude Excitation in Canonical Basis
-0.973509 4 -> 8
0.112468 4 -> 13
-0.178795 7 -> 8
IROOT= 6: 0.445155 au 12.113 eV 97700.1 cm**-1
Amplitude Excitation
-0.996250 6 -> 9
Ground state amplitude: 0.000000
Percentage Active Character 99.38
Amplitude Excitation in Canonical Basis
-0.992457 6 -> 9
The first set of excitation amplitudes, printed for each root, have been calculated in the CIS NTO (Natural Transition Orbitals) basis. The second set of amplitudes have been evaluated in the RHF canonical basis.
6.6.6.2. Capabilities¶
At present, the IH-FSMR-CCSD routine is able to calculate excitation energies, for only closed shell systems using an RHF reference. It can be used for both serial and parallel calculations. In the closed-shell case (RHF), a lower scaling version can be invoked by using bt-PNO approximation. The transition moments and solvation correction can be obtained using the CIS approximation.
6.6.7. Excited States with PNO based coupled cluster methods¶
The methods described in the previous section are performed over a canonical CCSD or MP2 ground state. The use of canonical CCSD amplitudes restricts the use of EOM-CC and STEOM-CC methods to small molecules. The use of MP2 amplitudes is possible (e.g. the EOM-CCSD(2) or STEOM-CCSD(2) approaches), but it seriously compromises the accuracy of the method.
The bt-PNO-EOM-CCSD methods gives an economical compromise between accuracy and computational cost by replacing the most expensive ground state CCSD calculation with a DLPNO based CCSD calculation. The typical deviation of the results from the canonical EOM-CCSD results is around 0.01 eV. A detailed description will be given in Excited States using PNO-based coupled cluster.
6.6.7.1. General Use¶
The simplest way to perform a PNO based EOM calculation is via the usage of the bt-PNO-EOM-CCSD keyword, together with the specification of the desired number of roots. The specification of an auxilary basis set is also required, just as for ground state DLPNO-CCSD calculations.
! bt-PNO-EOM-CCSD def2-TZVP def2-TZVP/C def2/J TightSCF
%mdci
nroots 9
end
*xyz 0 1
C 0.016227 -0.000000 0.000000
O 1.236847 0.000000 -0.000000
H -0.576537 0.951580 -0.000000
H -0.576537 -0.951580 -0.000000
*
The output is similar to that from a canonical EOM-CCSD calculation:
----------------------
EOM-CCSD RESULTS (RHS)
----------------------
IROOT= 1: 0.145339 au 3.955 eV 31898.3 cm**-1
Amplitude Excitation
-0.402736 2 -> 8
-0.101455 2 -> 13
0.402595 3 -> 8
0.101420 3 -> 13
0.231140 6 -> 8
-0.231142 7 -> 8
Ground state amplitude: 0.000000
IROOT= 2: 0.311159 au 8.467 eV 68291.5 cm**-1
Amplitude Excitation
-0.382967 2 -> 9
0.382816 3 -> 9
0.257265 6 -> 9
-0.257276 7 -> 9
Ground state amplitude: 0.000000
IROOT= 3: 0.337350 au 9.180 eV 74039.8 cm**-1
Amplitude Excitation
0.342418 2 -> 8
0.342586 3 -> 8
-0.257991 4 -> 8
0.257936 5 -> 8
0.172202 6 -> 8
0.172230 7 -> 8
Ground state amplitude: 0.000010
IROOT= 4: 0.348181 au 9.474 eV 76416.9 cm**-1
Amplitude Excitation
0.393166 2 -> 11
-0.393020 3 -> 11
-0.246227 6 -> 11
0.246232 7 -> 11
Ground state amplitude: 0.000001
IROOT= 5: 0.354611 au 9.649 eV 77828.2 cm**-1
Amplitude Excitation
0.226219 2 -> 10
-0.226139 3 -> 10
-0.385817 4 -> 8
-0.385755 5 -> 8
-0.100298 6 -> 10
0.100300 7 -> 10
Ground state amplitude: 0.032619
IROOT= 6: 0.379574 au 10.329 eV 83307.0 cm**-1
Amplitude Excitation
0.214487 2 -> 8
-0.214423 3 -> 8
0.402942 6 -> 8
-0.402947 7 -> 8
Ground state amplitude: -0.000001
IROOT= 7: 0.386805 au 10.525 eV 84893.8 cm**-1
Amplitude Excitation
-0.337735 2 -> 10
-0.113836 2 -> 14
0.337611 3 -> 10
0.113798 3 -> 14
-0.182472 4 -> 8
-0.182457 5 -> 8
0.239131 6 -> 10
-0.239136 7 -> 10
Ground state amplitude: 0.038944
IROOT= 8: 0.440569 au 11.989 eV 96693.8 cm**-1
Amplitude Excitation
-0.463727 4 -> 9
-0.463700 5 -> 9
Ground state amplitude: -0.000004
IROOT= 9: 0.447197 au 12.169 eV 98148.3 cm**-1
Amplitude Excitation
-0.107379 2 -> 8
0.385138 2 -> 13
0.107343 3 -> 8
-0.385019 3 -> 13
-0.254544 6 -> 13
0.254548 7 -> 13
Ground state amplitude: 0.000000
The IP and EA versions can be called by using the keywords bt-PNO-IP-EOM-CCSD and bt-PNO-EA-EOM-CCSD, respectively. Furthermore, the STEOM version can be invoked by using the keywords bt-PNO-STEOM-CCSD.
6.6.7.2. Capabilities¶
All of the features of canonical EOM-CC and STEOM-CC are available in the PNO based approaches for both closed- and open-shell systems.
6.6.8. Excited States with DLPNO based coupled cluster methods¶
The DLPNO-STEOM-CCSD method uses the full potential of DLPNO to reduce the computational scaling while keeping the accuracy of STEOM-CCSD.
Important: DLPNO-STEOM-CCSD is currently only available for closed-shell systems!
6.6.8.1. General Use¶
The simplest way to perform a DLPNO based STEOM calculation is via the
usage of the STEOM-DLPNO-CCSD keyword, together with the specification
of the desired number of roots. The specification of an auxiliary basis
set is also required, just as for ground state DLPNO-CCSD calculations.
As any CCSD methods, it is important to allow ORCA to access a significant amount of memory. In term of scaling the limiting factor of the method is the size of temporary files and thus the disk space. For molecules above 1500 basis functions it starts to increase exponentially up to several teraoctets.
Here is the standard input we would recommend for STEOM-DLPNO-CCSD calculations. More information on the different keywords and other capabilities are available in the detailed part of the manual Excited States via STEOM-CCSD, Excited States via DLPNO-STEOM-CCSD. The following publications referenced some applications for this method either in organic molecules [100], [805] or for Semiconductors [213].
! STEOM-DLPNO-CCSD def2-TZVP def2-TZVP/C def2/J TightSCF
%mdci
NRoots 6
DoRootWise true
OThresh 0.005
VThresh 0.005
TCutPNOSingles 1e-11
NDAV 400
DoStoreSTEOM true
DoSimpleDens false
AddL2Term True
DTol 1e-5
end
* xyz 0 1
C 0.016227 -0.000000 0.000000
O 1.236847 0.000000 -0.000000
H -0.576537 0.951580 -0.000000
H -0.576537 -0.951580 -0.000000
*
The output is similar to that from a canonical DLPNO-STEOM-CCSD calculation:
------------------
STEOM-CCSD RESULTS
------------------
IROOT= 1: 0.144275 au 3.926 eV 31664.7 cm**-1
Amplitude Excitation
-0.142146 4 -> 8
-0.988793 7 -> 8
Ground state amplitude: -0.000000
Percentage Active Character 99.79
Amplitude Excitation in Canonical Basis
-0.134936 4 -> 8
-0.955031 7 -> 8
0.236745 7 -> 13
IROOT= 2: 0.308093 au 8.384 eV 67618.5 cm**-1
Amplitude Excitation
-0.971471 7 -> 9
-0.214898 7 -> 10
Ground state amplitude: -0.000000
Percentage Active Character 99.67
Amplitude Excitation in Canonical Basis
-0.956930 7 -> 9
0.236567 7 -> 11
-0.102574 7 -> 16
IROOT= 3: 0.331796 au 9.029 eV 72820.8 cm**-1
Amplitude Excitation
0.993677 5 -> 8
Ground state amplitude: -0.000000
Percentage Active Character 98.87
Amplitude Excitation in Canonical Basis
-0.957218 5 -> 8
0.250144 5 -> 13
0.105963 5 -> 18
IROOT= 4: 0.346876 au 9.439 eV 76130.5 cm**-1
Amplitude Excitation
-0.104900 4 -> 10
0.198181 7 -> 9
-0.972571 7 -> 10
Ground state amplitude: 0.000000
Percentage Active Character 99.65
Amplitude Excitation in Canonical Basis
0.100880 4 -> 11
0.218876 7 -> 9
0.956922 7 -> 11
-0.113898 7 -> 19
IROOT= 5: 0.347460 au 9.455 eV 76258.7 cm**-1
Amplitude Excitation
-0.139550 4 -> 11
-0.106648 4 -> 12
-0.801181 6 -> 8
-0.455618 7 -> 11
-0.302466 7 -> 12
Ground state amplitude: 0.027266
Percentage Active Character 87.08
Warning:: the state may have not converged with respect to active space
-------------------- Handle with Care --------------------
Amplitude Excitation in Canonical Basis
-0.163789 4 -> 10
-0.785695 6 -> 8
0.159147 6 -> 13
-0.527842 7 -> 10
0.133087 7 -> 17
IROOT= 6: 0.379059 au 10.315 eV 83193.9 cm**-1
Amplitude Excitation
-0.983700 4 -> 8
0.155238 7 -> 8
Ground state amplitude: -0.000000
Percentage Active Character 99.48
Amplitude Excitation in Canonical Basis
-0.951092 4 -> 8
0.235048 4 -> 13
0.157713 7 -> 8
STEOM-CCSD done ( 2.4 sec)
Transforming integrals ... done
--------------------------------------------------------------------
UNRELAXED EXCITED STATE DIPOLE MOMENTS
--------------------------------------------------------------------
E(eV) DX(au) DY(au) DZ(au) |D|(D)
IROOT= 0: 0.000 -0.928848 -0.000000 -0.000000 2.360944
IROOT= 1: 3.926 -0.627710 -0.000000 -0.000002 1.595512
IROOT= 2: 8.384 1.034480 -0.000000 -0.000000 2.629438
IROOT= 3: 9.029 -0.401280 -0.000000 0.000000 1.019972
IROOT= 4: 9.439 -0.250433 0.000000 0.000002 0.636550
IROOT= 5: 9.455 0.304050 0.000000 -0.000000 0.772833
IROOT= 6: 10.315 -1.244475 0.000000 0.000000 3.163205
--------------------------------------------------------------------
...
----------------------------------------------------------------------------------------------------
ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
----------------------------------------------------------------------------------------------------
Transition Energy Energy Wavelength fosc(D2) D2 DX DY DZ
(eV) (cm-1) (nm) (au**2) (au) (au) (au)
----------------------------------------------------------------------------------------------------
0-1A -> 1-1A 3.925923 31664.7 315.8 0.000000000 0.00000 -0.00000 -0.00000 0.00000
0-1A -> 2-1A 8.383625 67618.5 147.9 0.088173876 0.42929 -0.00000 0.65546 -0.00000
0-1A -> 3-1A 9.028624 72820.8 137.3 0.000908615 0.00411 0.00000 -0.00000 -0.06033
0-1A -> 4-1A 9.438972 76130.5 131.4 0.057997877 0.25080 0.00000 -0.49380 -0.00000
0-1A -> 5-1A 9.454876 76258.7 131.1 0.029389253 0.12687 0.35160 -0.00000 -0.00000
0-1A -> 6-1A 10.314723 83193.9 120.2 0.000000000 0.00000 -0.00000 0.00000 0.00000
...
STEOM-CCSD done in ( 1.3)
The IP and EA versions can be called by using the keywords IP-EOM-DLPNO-CCSD and EA-EOM-DLPNO-CCSD, respectively. As in canonical STEOM-CCSD, the first set of excitation amplitudes, printed for each root, are calculated in the CIS NTO (Natural Transition Orbitals) basis, while the second set is evaluated in the RHF canonical basis.
6.6.9. Excited States with DeltaSCF¶
The DeltaSCF approach can converge the SCF directly to excited states. Since this method involves
a few more details, it is more thoroughly described on its specific section, please check DeltaSCF: Converging to Arbitrary Single-Reference Wavefunctions.