EOMCCSD overestimates the first excitation energy of Styrene
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All the excitation energies by me are vertical.
For GAMESS B3LYP optimized non-planar styrene, EOMCCSD(6-31+G*) gives /eV (8 states using symmetry A, macOS 2020R1 binarry, 6 states using the compiled with intel MKL and openmpi on Ubuntu18.04)
4.927
4.927
4.927
6.245
6.615
6-311+G** oscillator strengths can be accepted
Left eomccsd oscillator strength of the first(degenerate) and the second
OSCILLATOR STRENGTH 0.00350026 0.00553708 0.00000077
...
OSCILLATOR STRENGTH 0.00002559 0.00006540 0.01118304
CR_EOMCCSD(T) gives
delta-CR-EOMCC(2,3)
(2,3),D (2,3),A (2,3),B (2,3),C
4.434 4.485 4.514 4.434
5.905 5.937 5.954 5.905
6.278 6.310 6.326 6.278
(T)/R
4.344
5.926
6.301
DEL(IIA) DEL(IIB)
DEL(IIC) DEL(IID)
4.347 4.393
4.280 4.280
5.930 5.954
5.902 5.902
6.305 6.329
6.278 6.278
No state is missing.
Theoretical Study of the Ground and Excited Singlet States of Styrene
gives
4.51
5.35
5.91
(vertical PPP-CI)
the experimental ones indexed there
0-0
4.31
4.88(combinatrion)
The experimental vertical indexed in Vibronic spectra of the lower excited singlet states of styrene:
A Time Dependent Density Functional Theory study is 4.43 and 5.21.
Dalton SOPPA(CCSD) (6-31+G*) with the GAMESS optimized structure gives
4.27
4.94
5.98
Very Best Regards!
Hi, @xiongyan21,
Sorry for late replying, but you should post the GAMESS-related question into GAMESS ML, https://groups.google.com/g/gamess?pli=1
Pygamess is a simple GAMESS python wrapper library.
GAMESS MCPDFT can employ aldet wiith soscf and mp2 to generate OPTIMIZED MCSCF MO-S and using aldet and fullnr CI to do multiconfigurational pair-density theory.
It seems operating system, MPI, or the version will affect the convengence, e.g., using 2020R1 binary for mac(possibly no longer updated) some 4 state-average cannot converge but the compiled one on Ubuntu18.04 with open MPI can for the same number active orbitals and electrons targeting the same requested states, but when the requested state is reduced, the former one can converge, and they got the same excitation energies and groud state excitation energy, and close subsequent state energy if present,
Multiconfiguration pair-density functional theory developed by Prof. Truhlar's group, which can deal with strongly correlated systems, eliminate delocalization errors, but not doubly count electron correlations, is an creation integrating the strengths of WFT and DFT.
It seems operating system, MPI, or the version will affect the convengence, e.g., using 2020R1 binary for mac some 4 state-average cannot converge but the compiled one on Ubuntu18.04 with open MPI can for the same number active orbitals and electrons targeting the same requested states, but when the requested state is reduced, the former one can converge, and they got the same excitation energies and groud state excitation energy, and similar subsequent state energy if present, e.g.,
STATE 4 TOTAL MC-PDFT ENERGY = -309.0226093294
STATE 4 TOTAL MC-PDFT ENERGY = -309.0226080596
Multiconfiguration pair-density functional theory developed by Prof. Truhlar's group, which can deal with strongly correlated systems, eliminate delocalization errors, but not doubly count electron correlations, is an creation integrating the strengths of WFT and DFT.
It seems eDFT, unable to get S0-S2 for now, cannot converge for styrene,
It is said in one article of Dr. Micheal Filatov, then in Universität Bonn, eDFT "enables one to account for strong non-dynamic electron correlation in the ground and excited states of molecular systems in a transparent and accurate fashion"
MR-SPIN-FLIP TDDFT, which can treat spin-contamination, developed by Dr. Micheal Filatov in Ulsan National Institute of Science and Technology and Dr. Cheol Ho Choi in Kyungpook National University et al, and contributed by Drs.Komarov, Lee, Filatov, and Choi with PBE0 and 6-31+G** gives
~|2.1|% from the experimental first
~|10.7|%from the experimental second
~|0.8|% from the experimental second
but the following oscillator strength
0.7528
0.0548
0.5903
CAMB3LYP gives the second
~|4.4|% from the experimental second
deviating form those.
Aug-cc-pvdz B3LYP gives the relative deviance
~|5.5|% from the experimental first
~|13.2|%from the experimental second
~|0.9|% from the experimental second
All the above calculations use GAMESS, otherwise stated.
Very Best Regards!
EOMCCSD slso overestimates the first excitation energies of cyclopetadiene (6-311++G(2d,2p）optimized) with aug-cc-pvdz using GAMESS
5.667
5.712
6.332
6.388
6.551
The experimental data indexed in Electronic excitation and ionization spectra of cyclopentadiene:
Revisit by the symmetry-adapted cluster–configuration interaction method
is 5.26 or 5.34, and 5.68
The SAC-CI data in the reference is 5.54 5.58
In On the vertical excitation energy of cyclopentadiene, aug-cc-pVdz CCSDT 5.9 CCSDT-3 5 .9 CCSD 6.01
aug-cc-pvqz 5.68
cr-eomccsdt
(2,3).C
5.279
5.480
6.113
6.162
6.323
Perhaps black-boxed coupled cluster methods does not considered the facts about molecules. thus not performing very well here.
For the first excitation states, Reks eDFT ( camqtp01 ~ |1.1|% from 5.26, |2.6%| from 5.34), MR-Spin-Flip DFT (|2.7|% from 5.34,~|1.3|% from 5.26, camqtp01), also black-boxed, even the former one in transparent way, and multiconfiguration pair-density theory using tpbe perform well, and LC-BLYP gives LC-BLYP: |5.1|% from 5..26, >6% from 5.34.
Basis sets can change not only the value but also the degeneracy of styrene,
using 6-31+G**,
4.917
4.917
6.626
6.626
Larger basis sets for cr-eomccsdt calculation for styrene is under calculation, e.g., AUG-CC-PVDZ. It is very computer resource demanding.
EOMCCSD
4.901
4.901
6.643
...
the first state is doubly degenerate.
Although the calculation is being undertaken, that of the second state > 5.8
oscillator strength
0.00350026 0.00553708 0.00000077
0.00000002 0.00000005 0.00000373
Anyway, EOMCCSD overestimates the excitation en
ergies of styrene, giving degeneracy states when compared with the experimental data, but cr-eomccsdt ( disk, memory, and CPU demanding) may correct them,
Basis sets has a significant effect on EOMCCSD for cyclopentadiene
spherical 6-31+G**
eomccsd
5.850
6.179
6. 658
6.767
7.223
7.223
cr-eomccsdt
(2,3),C
5.455
5.903
6.395
6.494
6.959
6-311+G**
eomccsd
5.775
6.071
6.666
6.501
6.852
7.289
cr-eomccsdt
(2,3),C
5.362
5.793
6.399
6.501
6.852
This calculation is OK with GAMESS 2021 R1 but fails, getting segmaentation fault with GAMESS 2022R2, both compiled on Ubuntu18.04 with GCC 7.5, Intel MKL, and openmpi, and 6-31+G** for styrene also fails, getting
Intel MKL ERROR: Parameter 2 was incorrect on entry to DGEHD2.
When nuact is changed from 7 to 8, the error becomes
Intel MKL ERROR: Parameter 3 was incorrect on entry to DGEHD2.
It is stated on the network for installation to use LAPACK for this version
Very Best Regards!
Using MRSF-TDDFT with B3LYP and aug-cc-pvdz, the oscillator strengths of the first four states are 0.7659,0.0245, 0.6152, and 0.0119, and the first and the third vertical excitation energies are ~|0.023|% and ~|1.3|% deviating from the experimental 0-0 in Theoretical Study of the Ground and Excited Singlet States of Styrene, the second and the fourth ones are 4.520 and 5.163, respectively.
Reks eDFT with B3LYP and DH(d,p) gives the first excitation energy of ~|5|% deviating from the above experimental value.
The first IPs with Dyson EKT from LC-BLYP REKS and MRSF TDDFT in GAMESS using DH(d,p) are all ~|1|% deviating from the adiabatic experimental value in A study of phenylacetylene and styrene, and their argon complexes PA-Ar and ST-Ar with laser threshold photoelectron spectroscopy .
For S0-T1, MRSF-TDDFT pbe0 gives an RE ~|10.3|% deviating from the experimental one indexed in The Low-Lying Singlet-Triplet Transitions of Phenylacetylene and Styrene:Analysis of the Vibronic Structure; REKS eDFT BLYP gives 3.29 eV.
There is one article for S0-T1 gaps, Performance Analysis and Optimization of Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) for Vertical Excitation Energies and Singlet−Triplet Energy Gaps using MRSF TDDFT.
MRSF TDDFT using BLYP and aug-cc-pvdz gives an RE ~|5.4|% deviating from the experimental 0-0 indexed in the above reference.
There is also an reference Accurate Spin−Orbit Coupling by Relativistic Mixed-Reference Spin-Flip-TDDFT for spin-orbit coupling, where it is said "The SOC-MRSF code is being tested and available soon".
Using NWCHEM7.2.0, and the input similar to the QA test with LC-wPBE and still with odft the following is given
Alpha Orbitals
State Energy (eV) Error (eV)
-----------------------------------
...
@gw 26 -10.448 0.000
@gw 27 -8.810 0.001
@gw 28 -8.054 0.001
Beta Orbitals
State Energy (eV) Error (eV)
-----------------------------------
...
@gw 26 -10.448 0.000
@gw 27 -8.810 0.001
@gw 28 -8.054 0.001
For cyclopentadiene using C1 symmetry, the REs of CDGW orbital energies with NWCHEM7.2.0 (LC-wPBE) and EOMCCSD (ccpv-dz) with GAMESS(not including a quartet state with those experimental PES values indexed in Electronic excitation and ionization spectra of cyclopentadiene:Revisit by the symmetry-adapted cluster–configuration interaction method are aounrd |5.6|%, |1.4|%, |1.2|%, |1.2|%, |3.5|%, |1.4|%, |0.1|%, |4|%, |0.5|%, |1.1|%; |1.9|%, |0.25|%,|1.3|% , |1.3|%,|1.1|%,|1.3|%, |0.6|%, |0.7|%,|3.2|%, |1.3|%.
MRSF DYSON EKT (aug-cc-pvdz,camqtp01)) gives the following RE about |0.9|%, |4.6|%, |6|%,|3|%,|1.5|%, |1.9|%, |3.6|%,|7.1|%, |3.1|%,|1.4|%;
16 17
ENERGY -0.475995 -0.412437
STRENGTH 1.000060 0.997526
REKS eDFT EKT (6-31+G**, camqtp01 gives around |1|%,|3.9|%, |5.8|%, |2.8|%, |1.05|%, |1.6|%, |3.3|%,|3.8|%,|2.9|%, |1.2|%.
e.g.,
16 17
ENERGY -0.474414 -0.409496
STRENGTH 1.000050 0.995428.
A A
GAMESS EOMCCSDt gives the REs of IPs ( not including the quartet one) ~|1|%, |0.7|% ... deviating from the above GW ones from NWCHEM7.2.0.
Input similar to gw_closedshell gets the same results of alpha
Alpha Orbitals
State Energy (eV) Error (eV)
-----------------------------------
...
@gw 26 -10.448 0.000
@gw 27 -8.810 0.001
@gw 28 -8.054 0.001
GAMESS ECOMCCSD for cc-pvdz gives /hartree for styrene
-0.4090 -3372 -0.3031
---- SUMMARY OF IP-EOMCCSD(2H-1P) CALCULATIONS ----
SPIN IONIZATION TOTAL
SYMM MULT ENERGY (H) ENERGY (H) ITERATIONS
A 2 0.3049581931 -308.4056824211 CONVERGED
A 2 0.3334425873 -308.3771980269 CONVERGED
GAMESS MRSF TDDFT 6-31G** PBE0 DYSON orbital
...
26 27 28 29
ENERGY -0.319602 -0.272301 -0.236159 -0.055287
STRENGTH 1.011090 0.999756 0.985039 0.057278
LC-BLYP aug-cc-pvdz
...
26 27 28 29
ENERGY -0.413732 -0.354006 -0.314657 -0.059935
STRENGTH 0.994581 0.999594 1.009403 0.044700
REKS eDFT DH(d,p)
26 27 28 29
ENERGY -0.404961 -0.346274 -0.315127 -0.084561
STRENGTH 0.999758 0.999316 0.996229 0.008749
Of course I will check the RE calculations, in case the data be wrong copied from the outputs into a sheet.
Very Best Regards!
Perhaps unusual or not?
For cyclopentadiene, if closed-shell DFT is used with SCF, the input gives
...
@gw 5 ... 2.276 *
...
@gw 16 -12.894 0.001
@gw 17 -11.266 0.001
@gw 18 -8.863 0.001
- Result did not converge
ODFT with SCF gives
@gw 16 -12.895 0.001
@gw 17 -11.266 0.001
@gw 18 -8.864 0.001
All the geometries are from GAMESS.
The HF IPs for cyclopentadiene are 8.53, 11.35,13.6... in THE ELECTRONlC STRUCTURE OF MOLECULES BY A MANY-BODY APPROACH. V. Ionization potentials and one-electron properties of cyclopentadiene and ...
Very Best Regards!
RISM-SCF-cSED just released in GAMESS may address Stoke shifts in UV, which perhaps is very difficult to converge if geometry search is employed.
Test trans_300K_emm has warnings
...
*** WARNING! ATOM 1 SHELL 1 TYPE S HAS NORMALIZATION 1.02152578
...
Using the original geometry, without cSED,,
SUMMARY OF TDDFT RESULTS
STATE ENERGY EXCITATION TRANSITION DIPOLE, A.U. OSCILLATOR
0 -> HARTREE EV X Y Z STRENGTH
0 A -248.4782526022 0.000
1 A -248.2794289623 5.410 -0.0084 0.0024 -0.0637 0.0005
....
After an cSED, excitation energy is
SUMMARY OF TDDFT RESULTS
STATE ENERGY EXCITATION TRANSITION DIPOLE, A.U. OSCILLATOR
0 -> HARTREE EV X Y Z STRENGTH
0 A -248.4482948974 0.000
1 A -248.2425777643 5.598 0.0171 -0.0070 0.0573 0.0005
...
The calculation is sophisticated and it may take long time to finish.
There is no data for hexane accompanied.
Test nh3_opt can pass(Oct. 5th) can pass.
I will not try the other test.
Very Best Regards!
Distihguished Prof. Anna Krylov, et al. have written an article Benchmarking Excited-State Calculations Using Exciton Properties which is very helpful in the understanding an excited state.
Prof. Krylov has just won the inaugural Barry Prize for Distinguished Intellectual Achievement by the American Academy of Sciences and Letters (AASL), and is called quantum chemistry pioneer by University of Southern California.
GAMESS MRSF-TDDFT, REKS eDFT, CREOMCCSD(t), also could give excitation energies of 4-dimethylaminobenzenitrile comparable to the published experimental results, and the first also can give excitation energies in hexane, S0-T1 gap in agreement with the published experimental results, all assuming ground state geometries.
Of course, I cannot understand the skillful experiments.
Using REKS eDFT in GAMESS, It seems form me the listed double excitation energy of all-trans octatetraene cannot be obtained comparable to the experimental 2 1Ag- one published and explained in Prof. Krylov et al' s article, whereas it can be compared with the 2 1Bu- one. MRSF_TDDFT B3LYP gives the first two of 3.25 and ~4.5, and the oscillator strengths ~1.4 and 0, respectively. The order: the first is Bu, the second is Ag and the third is Au, except for the ground state is Ag, is different from the commonly known.
If C2h symmetry is employed, REKS eDFT will give strange results.
GAMESS B3LYP aug-cc-pvdz gives
SUMMARY OF TDDFT RESULTS
STATE ENERGY EXCITATION TRANSITION DIPOLE, A.U. OSCILLATOR
0 -> HARTREE EV X Y Z STRENGTH
0 AG -310.6305585475 0.000
1 BU -310.4843666601 3.978 -3.8835 0.2941 -0.0000 1.4783
2 AG -310.4529638829 4.833 -0.0000 -0.0000 0.0000 0.0000
3 AU -310.4500883494 4.911 -0.0000 0.0000 0.0107 0.0000
4 BG -310.4489696252 4.941 0.0000 0.0000 0.0000 0.0000
5 AU -310.4426700555 5.113 0.0000 0.0000 -0.3449 0.0149
Energies of Low-Lying Excited States of Linear Polyenes gives experimental 1 1Ag- - 2 1Ag 32 460 +- 735 cm-1, and 1 1Ag- - 1 1Bu+ 37 110 +- 770 cm-1. I cannot understand the experiments.
For all-trans decapentaene based on ground state geometry, GAMESS MRSF TDDFT camb3lyp and aug-cc-pvdz gives
S0-T1 (3Bu) ~1.9, agreeing with MRMP corrected 1.89 in Theoretical Study of the p a p * Excited States of Linear Polyenes: The Energy Gap Between 1 1 B u + and 2 1 A g States and Their Character. It is the same as for the excite states.
All the geometries were optimized with GAMESS.
There is an reference: EXPERIMENTAL CONFIRMATION OF THE DIPOLE FORBIDDEN CHARACTER OF THE LOWEST EXCITED SINGLET STATE IN 1,3,5,7-OCTATETRAENE.
Distinguished Prof. Martin P. Head-Gordon in UC Berkeley, et at. authored an article entitled Excitation Energies from Time-Dependent Density Functional Theory for Linear Polyene Oligomers: Butadiene to Decapentaene, where the functioanls give 1 1Bu is lower than 2 1Ag, but Tamm-Dancoff approximation may change the order. His way can be a guide in the employment of DFT functionals to treat the excitation energies of polyenes.
In this reference, B3LYP gives 1 1Ag 4.83, the 1 1Bu 3..98 with oscillator strength 1.56, using Q-Chem.
Using GAMESS, Tamm-Dancoff approximation with BLYP gives
STATE ENERGY EXCITATION TRANSITION DIPOLE, A.U. OSCILLATOR
0 -> HARTREE EV X Y Z STRENGTH
0 AG -310.6807447453 0.000
1 AG -310.5274299275 4.172 0.0000 0.0000 -0.0000 0.0000
2 BU -310.5245950126 4.249 -4.6625 0.2656 -0.0000 2.2704
3 AU -310.5124375227 4.580 -0.0000 0.0000 -0.0210 0.0000
In Prof. Head-Gordon et al' s reference, they are 4.17 4.25 with oscillator strength 2.29, where the indexed experimental values are 3.97 and 4.41. Their SVWN results with Q-Chem also can be reproduced with GAMESS, because I have already repeated.
MRSF TDDFT may not give the correct order and corresponding oscillator strength, due to matrix operations, thus we should be cautious. The advantages of this method in GAMESS are very attractive, and practically, if C1 symmetry is adopted without the change of the strength order of the states when compared with experimental results, e.g., in the case of styrene and DMABN, it is reliable. It is the case for other methods.
Actually, TDDFT using aug-cc-pvdz and SVWN in the Tamm-Dancoff approximation gives the following excitation energies of styrene
SUMMARY OF TDDFT RESULTS
STATE ENERGY EXCITATION TRANSITION DIPOLE, A.U. OSCILLATOR
0 -> HARTREE EV X Y Z STRENGTH
0 A -306.7964794681 0.000
1 A -306.6320206402 4.475 0.2187 -0.2685 0.0029 0.0131
2 A -306.6155044656 4.925 -0.6753 1.5949 -0.0441 0.3621
Very Best Regards!
Multiconfiguration pair-density functional theory developed by distinguished Prof. Truhlar's group in GAMESS using tpbe and 6-311+G** can give S0-S1 and S0-S2 < 4.28 and ~4.6 eV respectively with (10,8) for DMABN.
For styrene, this method with 6-31+G** and ftpbe using (24,14) gives the following three excitation energies in terms of eV
<4.2
~5.05
~5.15
6--311+G(2d,p) (10.10) three-state average tpbe 8 states gives S0-S2 5.03 eV.
6-311+G(2d,p) (40,22) tpbe four state average 12 states S0-S1 4.49 eV.
Very Best Regards!
In 2023, distinguished Prof. Gordon et al. has published High-performance strategies for the recent MRSF-TDDFT in GAMESS, which makes this promising method very useful.
I have tried Phcz(optimizrd with 6-31+G** and B3LYP, with no imagimary frequencies), and the camqtp01 and 6-31G** ΔEST gap is ~|7.6|% deviating from the experimental one in toluene in Prediction of Excited-State Energies and Singlet−Triplet Gaps of Charge-Transfer States Using a Restricted Open-Shell Kohn−Sham Approach, assuming ground state geometry, running parallelly. For the gap, MRSF TDDFT using 6-311+G** and camqtp01 gives the RE ~|12.2|%, i.e. ~0.07 eV.
STATE # 1
SYMMETRY OF STATE = A
DRF COEF OCC VIR
--- ---- ------ ------
59 0.138358 59 -> 64
65 0.976298 65 -> 64
129 0.071301 64 -> 65
909 -0.053361 65 -> 77
1104 0.057138 65 -> 80
STATE # 2
SYMMETRY OF STATE = A
DRF COEF OCC VIR
--- ---- ------ ------
59 0.057898 59 -> 64
61 -0.120032 61 -> 64
63 0.915373 63 -> 64
125 -0.076563 60 -> 65
127 0.073208 62 -> 65
512 -0.050471 58 -> 71
517 -0.093939 63 -> 71
519 0.262264 65 -> 71
907 -0.054014 63 -> 77
909 -0.090241 65 -> 77
974 0.076855 65 -> 78
1102 0.067509 63 -> 80
Camqtp00 gives an RE ~|16|%.
BHHLYP gives an RE <|2.6|%
For S0-S1in tolune, MRSF TDDFT B3LYP and 6-31G** gives
TRANSITION EXCITATION TRANSITION DIPOLE, A.U. OSCILLATOR
EV X Y Z DIP STRENGTH
1 3.689 -1.5222 0.0059 -0.0082 1.5222 0.2094
but ΔEST is 0.227 eV.
6-311+G** makes the gap ~0.1 eV lower.
Very Best Regards!
Perhaps unusual or not? For cyclopentadiene, if closed-shell DFT is used with SCF, the input gives ... @gw 5 ... 2.276 * ... @gw 16 -12.894 0.001 @gw 17 -11.266 0.001 @gw 18 -8.863 0.001
- Result did not converge
ODFT with SCF gives @gw 16 -12.895 0.001 @gw 17 -11.266 0.001 @gw 18 -8.864 0.001
All the geometries are from GAMESS.
The HF IPs for cyclopentadiene are 8.53, 11.35,13.6... in THE ELECTRONlC STRUCTURE OF MOLECULES BY A MANY-BODY APPROACH. V. Ionization potentials and one-electron properties of cyclopentadiene and ...
Very Best Regards!
Hey @xiongyan21 , just FYI, you're tagging the wrong username! (I'm not your guy, I promise!)
Sorry. These are from outputs from NWCHEM7.2.0 calculated previously, just for a temporary try. I will no longer use it anymore and removed all the versions released from my computer on July this year and ago. I also removed all the versions of Dalton from my computers on september this year and ago, because I also will not use it anymore.
Very Best Regards!
For o-benzyne(optimized with RHF MP2), there is something baffling
Using MRSF-TDDFT and aug-cc-pcdz, the following is obtained for S0-T1 with GAMESS
B3lyp PBE0 BHHLYP
1.362 1.121 1.68
In Performance Analysis and Optimization of Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) for Vertical Excitation Energies and Singlet-Triplet Energy Gaps with 6-31G*, they are 1.22,1.29, and 1.00, respectively.
It is even more baffling regarding to the REKS eDFT results.
With GAMESS DH(d,p)
camb3lyp
56.5 kcal/mol
In Spin-restricted ensemble-referenced Kohn–Sham method: basic principles and application to strongly correlated
ground and excited states of molecules, it is 32.3 with cc-pvdz
For this molecule, REKS eDFT in GAMESS gives the S0-T1 gap
BHHLYP camqtp00 camb3lyp b3lyp blyp
2.42 2.44 2.45 2.465 2.52
Perhaps it is wrong. I don't know what causes this.
The geometry was optimized with GAMESS.
Very Best Regards!
Using GAMESS 2023 R2, test trans_opt_S0, and trans_300K_emm (with warnings) all can finish .
RISM RESULTS
-------------------------------------------------------
Delta mu (HNC ) (kcal/mol) 19.143
Delta mu (GF ) (kcal/mol) -5.556
-------------------------------------------------------
-------------------------------------------------------
RISM-SCF-cSED RESULTS(HNC )
-------------------------------------------------------
INITIAL STATE (EQ ) S_1 (a.u.) -248.24607312
FINAL STATE (NEQ) S_0 (a.u.) -248.45147606
DELTA E (eV) 5.589
-------------------------------------------------------
Why only one listed?
DMABN fails at ------------------
RISM CALCULATION
------------------
IEXP ITER DIFF
2 20016891.582653000665232
2 2101********************
2 2201********************
2 2301********************
2 2401********************
2 2501********************
2 2601********************
2 2701********************
...
using 6-311G**
Very Best Regards!
For the S0-T2 gap of styrene, two runs give S0-T1 , and the reference to T2, respectively, together providing S0-T2 ~3.72 eV.
Although the inputs are identical except for mult=3 in the latter, the total energies for the two reference are different, thus I am not sure whether the two gaps can be additive by vector translation.
Very Best Regards!
For compound 1, cycl [3,3,3]azine, in Organic molecules with inverted gaps between first excited singlet and triplet states and appreciable fluorescence rates in MATTER, I have optimized it with GAMESS using 6-311+G(2d,p) (without imaginary frequencies).
REKS eDFT CAMQTP00 TZV gives S0-S1 1.297 eV. ΔEST 0.099 eV. REKS eDFT BLYP gives ΔEST 0.0825 eV.
MRSF TDDFT CAMQTP00 TZV give 1.065, and -0.178 ev, respective;y.
MRSF TDDFT CAMQTP00 cc-pvdz gives 1.086 and -0.160 eV, respectively; and 6-311+G(2d,p) gives 1.041 and -0.164 eV,
respectively.
Low-Lying Electronically Excited States of Cycl[ 3.3.3]azine, a Bridged 127-Perimete gives the experimental S0-S1 0.974
It seems it gave an experimental ΔEST ~ 0.042 eV, it is stated "For obvious reasons, attempts to determine the triplet energy of 1 and its derivatives by phosphorescence emission or heavy atom induced singlet-triplet absorption spectroscopy have not been successful"; "resorted to an indirect technique"; "Systematic errors in these values may also arise
from errors in the sensitizer triplet energies, but are not likely to exceed +-0.1 um-1"; "it may be expected that more elaborate calculations for 1 would tend to stabilize SI relative to TI by “dynamic spin polarization” ".
In Connections and performances of Green’s function methods for charged and neutral excitations, ADC(2), ADC(3), etc. results agree with those in the first reference, respectively, cc-pvdz used.
ADC(3)
The first reference: S0-S1 0.78 ΔEST -0.092
The second reference: S0-S1 0.87 ΔEST -0.09
There is an article titled Symmetry-Induced Singlet-Triplet Inversions in Non-Alternant Hydrocarbons in Angewandte Chemie.
It is said in the first reference "no inorganic INVEST molecule is known to date".
MRSF TDDFT LC-BLYP 6-311+G(2d,p) EKT DYSON gives the first IP is ~|6.5|% deviating from the experimental one in THE ELECTRONIC-STRUCTURE OF SOME HETEROCYCLES WITH BRIDGEHEAD NITROGEN - PHOTOELECTRON-SPECTRA AND AB-INITIO MOLECULAR-ORBITAL CALCULATIONS .
EOMCCSD cc-pvdz IP gives an RE ~{10.1|%.
Using spherical 6-311+G(2d,p), MRSF TDDFT with LC-BLYP gives
41 42 43 44
ENERGY -0.404972 -0.360978 -0.360954 -0.223816
STRENGTH 1.001706 0.999296 0.999294 0.996597
I am not sure whether the IP can be determined or not.
All the calculations using GAMESS in vacuum here are from me where the approximate linear dependence has not been treated with more accurate integral evaluation.
When small eigenvalues are not dropped out and no use of FDIFF, the B3LYP geometry is the same as the previous one.
Generally speaking, the loosening of QMTTOL is ignored, as for styrene, DMABN, etc., all having the same as those without approximate linear dependence.
the former: -517.2478577921
the latter: -517.2478577910
Frequencies differ from hundredths to thousandths, or the same from the subsequent Hessians.
MRSF TDDFT with LC-BLYP also gives identical observable quantities of excitation energies for three states( I haven't tried more ones). Here, no dirscf was used.
the former
SELECTING EXCITED STATE IROOT= 1 AT E= -516.1594417844
the latter
SELECTING EXCITED STATE IROOT= 1 AT E= -516.1594418604
The latter also gives the same Dyson ones.
If Spherical harmonics are not used, it gives
SELECTING EXCITED STATE IROOT= 1 AT E= -516.1704143263
but the observable excited quantities are the same.
Dyson ones become
41 42 43 44
ENERGY -0.404935 -0.360949 -0.360924 -0.223802
STRENGTH 1.001708 0.999295 0.999293 0.996595
Very Best Regards!
For Hexa)thiophene), when the geometry is optimized with DFTB3 in GAMESS with 3OB-3-1, and in dioxane, the excitation
energy is ~|3.8|% deviating from 2.85 eV, calculated with long-range corrected DFTB2 when emu=0.25 using accompanied OB2W0PT3 pararameters.
Whether spherical harmonics is used, the geometries optimized are the same.
It is said OB3W0PT3 should be used with LC-DFTB (EMU=0.3) in GAMESS manual.
EMU=0.2 gives an RE ~|5.6|%. Oscillator strength 2.7895.
The first is the strongest in both.
EMU=0.3 gives
SUMMARY OF TDDFT RESULTS
STATE ENERGY EXCITATION TRANSITION DIPOLE, A.U. OSCILLATOR
0 -> HARTREE EV X Y Z STRENGTH
0 A -76.2873200255 0.000
1 A -76.1888683575 2.679 -0.0083 -0.0007 -0.0000 0.0000
2 A -76.1860855119 2.755 0.0003 -0.0000 0.0000 0.0000
3 A -76.1850985865 2.782 6.2701 0.9508 0.0018 2.7407
4 A -76.1611442789 3.433 -0.0027 -0.0009 -0.0000 0.0000
When ispher was not used, it gave
SUMMARY OF TDDFT RESULTS
STATE ENERGY EXCITATION TRANSITION DIPOLE, A.U. OSCILLATOR
0 -> HARTREE EV X Y Z STRENGTH
0 A -76.2873200255 0.000
1 A -76.1888683575 2.679 -0.0083 -0.0007 -0.0000 0.0000
2 A -76.1860855119 2.755 0.0003 -0.0000 0.0000 0.0000
3 A -76.1850985865 2.782 6.2701 0.9508 0.0018 2.7407
4 A -76.1611442789 3.433 -0.0027 -0.0009 -0.0000 0.0000
...
Mio-1-1 parametrs give very low excitation energies.
Very Best Regards!
Distinguished Prof. M. Gordon et al. have published an article in 2023, titled The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures .
It is stated " Over the last four decades, the focus of the development of GAMESS has been increasingly on enabling accurate calculations on large molecular systems so that direct connections can be made with experiments".
Very Best Regards!
There is an article titled The inverted singlet–triplet gap: a vanishing myth? questioning the inverted gaps, in Frontiers in Chemistry, reviewed by Prof. Silva who wrote On the Inverted Singlet-Triplet Gaps and Their Relevance to Thermally-Activated Delayed Fluorescence in Journal of Physical Chemistry Letters, et al.
The former article said "Seemingly, the phenomenon of inverted singlet–triplet gaps tends to vanish the closer we
observe". "It is thus not certain what sign of the STG even higher levels of electronic structure would
predict. The STGs of heptazine and related compounds are small, very small, and their accurate determination including their sign remains, thus, a challenge for both theory and experiments".
It is unusual that when using MRSF- TDDFT, in tolune LC-BLYP gives the gap -2.078, and S0-S1 0.124; and in vacuum LC-BLYP gives 0.234 and 1.581.
The gap by MRSF-TDDFT camqtp01 6-311+G** for Phcz in vacuum is |0.1| eV deviating form the above one in toluene, which can be expected.
Very Best regards!
Photochemistry of carbon nitrides and heptazine derivatives, and Singlet-Triplet Inversion in Heptazine and in Polymeric Carbon Nitrides_, deal with the experimental absoptions of TAHz in toluene, and the latter also gives the experimental one of Hz in toluene, and it is said "The lowest absorption band of the T 1 state (0.94 eV, 1322 nm) is substantially lower in energy than the lowest absorption band of the S 1 state (1.98 eV, 627 nm)".
I cannot understand the experiments, cannot interpret the spectra, and cannot compare the theoretical and experimental data, thus will not try camqtp00 in solvents and any other functionals further.
In addition, it seems it is difficult to find experimental data for inverted singlet-triplet gap compounds which are perhaps rare up to now.
Very Best Regards!