The vertical excitation means that the geometry of GS(ground state) cannot change under the transition from GS to ES(excited state). This is normally called of absorption based on frank-condon principle.

The absorption of phosphorescence involving heavy metal is processed from S0 to S1 . Then it turned triplet state with inter-system crossing due to spin-orbit coupling. Finally the triplet energy state release to singlet and triplet state (emission).

In absorption calculation, you should calculate S0 to S1 state.

In emission calculation, you should calculated S1(T) to S0 state.

Hope this help

Sunwoo Kang, thank you for take up my question. If you dont mind, i will extend a bit on the topic.

I trying to find answer for two questions.

- Triplet transition in the absorption spectra (i.e 3MLCT, beside the common singlet MLCT). In many closed-shell complexes with heavy metal, such as Os(II), there would appear triplet MLCT absorption. That is experimental fact. I looking to assign that bands theoretically.

In Gaussian, i found a option TDDFT option, start from optimized ground singlet state, do a TD=(triplet, nstates=n). The result of this calculation are excitation energy, unfortunately, but understandably, all f=0.0000. I was wondering is that possible to use those excitation energies to assign 3MLCT bands?

- Second question involves emission energy from triplet state T1-So. I read several papers (they dont say how they do it, technically), in which, they optimized the lowest triplet excited state as one of the steps to determine emission. (From T1 geometry, they can use TDDFT or DeltaSCF to drive emission energy). So my question if how to set up the command for Gaussian to run the optimization for T1 state, which return to my question in the topic.

Thank you, a bit too long. Really appreciate if you could share your experience helping me to learn more about it!

I added a diagram showing the T1 state that i aim to get the optimized geometry.

Thanks!

You are almost there: if you have optimized both the ground and triplet T1 states, then your diagram are incomplete. Consider this one below (I did not put the vibrational states): with this kind of diagram you will be able to get not only the vertical transition, but also the adiabatic one - this should improve your obtained results.

Thank you Horacio Alves. I agree, my diagram is not accurate infact. Just want to highlight the T1 state of interest. I am looking for the command in the input file of Gaussian.

Be careful, I think there is not a specific command for that in Gaussian. You have to consider the total energies from the last SCF cycle, which are in Hartrees, the TDDFT ones (VT) which are in eV, and the total energy of the ground state with the atomic coordinates of the optimized T1 state. It sounds tricky.

Dear Haracio,

Thank you for spending time with my problem. I think the aproach you mention would be useful to calculate emission energy by deltaSCF aproach, in which, the different in energy of optimized T1 - energy of singlet state at T1 geometry = emission energy.

I try to find the way to optimize the first triplet excited state T1 as it is a important step to determin emission energy.

I would like to add a reference (10.1021/jp020927g), in which triplet transitions were calculated. All the oscilator strength are 0.

I was very confusing, and try to figure out.

I found papers, where they state: "Thirty-two singlet excited states and eight triplet excited states(43, 44) were determined starting from S1−4(optimized singlet state) geometries;" 10.1021/ja8025906

"Time-dependent DFT (TD-DFT)(14) calculations were also performed to get singlet and triplet transition energies, on the basis of the structures optimized in their ground state" 10.1021/ja4065188

Does it mean that they managed to optimize excited state start from S0 configuration with TDDFT?

With this:

# td=(triplets,nstates=10, root=1) opt ub3pw91/genecp geom=connectivity

you will get the first excited triplet state optimized. In order to check, if the calculation is correct, do:

# opt ub3pw91/genecp geom=connectivity

to see if there are differences in the molecular structure(the latter deal with the singlet ground state). However, do not forget that, at both TDDFT and CIS level of calculation the obtained oscilator strength for a singlet-triplet excitation is 0, because you are dealing within the independent particle approximation and, the selection rule states that the spin difference between the excited and the ground state should be zero(http://www.chemistry.adelaide.edu.au/external/soc-rel/content/transiti.htm). It is only different from zero when the considered transition is singlet-singlet (check changing the keyword triplets to singlets). Note that it is only valid for vertical transitions, which are the results you get from a TDDFT or CIS calculations. By repeating the TDDFT optimization recipe above, changing the root to 2,3,4,... you will get the optimized 2,3,4,... triplet states. I supposed that this was done in the paper will have mentioned above

Thank you very much. I agree with you on the first suggestion setting up the calculation.For the set up # td=(triplets,nstates=10, root=1) opt ub3pw91, i would start with the optimized ground state. But i am not sure to set (charge 0, multiplicity 1) or (charge, multiplicity 3)?

The second on "singlet ground state" i did not think of it. That suggestion is very useful to me.

May i add one more question, so what we are talking now is the first triplet excited state T1. I understand that correspond to the electron configuration of (a)1b(1)- two electron, two different orbitals, same spin of 1/2.

Although not common, i do read people mentioned the "triplet ground state" for close-shell system. Doest it mean T0 state, where two electrons are at the SAME ORBITAL but have the same spin of 1/2 each (2x1/2+1 =3). Do you think my interpretation of "triplet ground state" is wrong?

I ask this question as it relates to other aproach, optimize T0, then do normal TDDFT to get to excited state.

Thank you!

First, the transition from singlet GS to triplet ES always shows oscillation strength due to the spin forbidden transition. But if you considered the spin-orbit coupling between singlet GS to triplet ES, you can get the oscillation strength.

Second, just use TD(NSTATE=x, triplet, root=x) option in route section in gaussian input file using singlet GS optimized structure. Also, you should mentioned singlet in input file.

Hope this help

Thank you all, Sunwoo Kang and Horacio Alves (I should address you all Dr. infact).

So to summarize, to optimize the lowest lying triplet excited state, i will need to do:

- Optimize singlet ground state.

- Base on that optimized geometry, spinmultiplicity =1, run #td=(triplet, nstates=10,root=1), opt, Ub3lyp, freq.

The nstates should be much larger than root, otherwise cal. would terminate with error "Must solve more vector in order to follow the state". Did i summarize your instructure fairly?

Thank you!

root=1 command means optimize first excited state geometry (This is the default in gaussian 09). nstate=x command means that it can show lots of transition property (excitation energy and probability of related states)

So, it can summarize that you can get the first excited state geometry and ten transition property using # opt td(nstate=10,singlet or triplet, root=1)

Thank you! It seems to be clear to me what i should do to get T1 now. But comes the technical problem, I start from optimized ground state geometry with

# opt freq td=(triplets,nstates=26,root=1) ub3pw91/genecp (26 states already), but still ends up with error message.

"You need to solve for more vectors in order to follow this state."

The triplet excitation energies were successfully calculated. Then it moved to do optimization, but just for 1 or 2 cycle then stop with the above error.

Hi,

The problem is related to the fact that the TD-DFT procedures uses the Davidson approach for calculating the energies of only part of the overwelming gigant one- electron excitation CI matrix. In this approach only a smaller group of those excitation is used to get the lovest requested excited states. Soem time the umber of excited determinant is not enoough to locate the complete expansion eneded for the calculation of the requested excited states and the program issues an erro you cna try to use the IOp(9/76=XX) where XX is a starting number of states where to start the search for the needed eigenvalues of the CI matrix. Frequently the caclulation of the exciatation energies converges because the convergence criteria are different for the calculation of the excited states. In fact for calculating the gradients a better converged eigenfunctions in the CI space are needed. This is particularly sensitive if the triplet states are required because the starting guess is a singlet and not a triplet if you start using as a reference state the singlet S0. Some other problem can be sometime related to the fact that the reference configuration does not represent carefully the molecular state because it is defined by more than one Slater determinat and in this case it should be necessary to use e multireference starting guess for the claculation. This is not yet implemented in Gaussian.

Thank you very much, Professor Francesco Lelj. I will try to add the keyword IOp in the command. I realized that there are number of papers reported working with optimizing triplet states. It is also quite relevent to my research field so i try to figure out how to perform the calculation.

Thank you!

I think i would step back one step. Just focus on the calculation bellow to get triplet excitation energy

------------------------------------

# td=(triplets,nstates=6) b3pw91/genecp geom=connectivity

0 1

coordinate

Ru 0

SDD

****

C H N 0

6-31G*

****

Ru 0

SDD

"

I found that the transition always have unexpectedly MUCH smaller energy compare to singlet transition or even observed emission. Would you suggest any possible problem?

Thank you!

Hi Mer, if you are intrested to T1, I suggest to optimize the geometry by unrestricted approach ( the usual way Gaussian use when you declare different spin state than Singlet) and then use the geometry as input to the optimization using TDDFT. UKS procdure is faster if you need only the T1. Higher Triplet states can not be optimized using the Urestricted approach unless they belong to a different symmetry form the one of the lowest energy state of the same multiplicity because of the variational approach. This plunges the wavevefunction of the given multiplicity always to the lowest energy one for the given symmetry.

If your molecules belongs to C1 you can get only the T1 with this procedure.

As far as the problem of the too low triplet energy I suggest you to read the paper of Bredas group http://dx.doi.org/10.1063/1.3663856.

I too found always the triplet states to "red" than the experimental ones and I am still looking for a solution. It looks that the geometry of the triplet state is always too much stable compared to the Singlet or that is too much destabilized at the Triplet geometry.

Regards

Francesco

Dear Professor Francesco Lelj

Thank you very much for your advice. I thought about optimizing the Ti triplet excited state using unrestricted procedure also. But I am also interested in T2 state. In fact, i try to make a simple comparision between spin density or pair of NTO orbitals between T1 and T2 state to explain for the experimental observation of dual emission.

I found three aproaches for emission energy estimation, either via TDDFT calculation based on triplet-optimized geometries; deltaSCF or HSOMO(triplet)-HOMO(singlet). But all three methods require triplet states to be optimized.

Is there any possible way around, Professor?

Best regards,

Mer Mercurate

Dear Mer ( by the way is Mer your name and Mercurate your family name or the other way around ? :-),

The HSOMO and HOMO is not a very accurate approach because in this way you disregard the the electron electron contribution to the energy.

Delta SCF is not practical in this case unless you have symmetry and as I told you previously you the second triplet belongs to a different symmetry than T1 ( Why do you call it T0 if it isn't the ground state or has your molecule a Triplet ground state ? What is your molecule) So the only way is to use the CIS or the TD DFT approach or even more correlated methods which I think are not viable if your molecule has many electrons and atoms or you have a lot of computer power.

In the CIS/ TDDFT case are you interested in the vertical or relaxed process ?

In the former case if you are interested in the vertical absorption from the T1 ( your T0), use the geometry optimized at the ub3lyp level or other viable methods ( UMP3 P) for the calculations of the energies of the other triplet states by TDDFT. In this case it is not necessary that you define the root=1 option because it is the default. If you want the NTO or other properties of the the different Tn you need to add the keyword Density=current and then in succesive calculations compute the NTO for each state you are interested in. See the Gaussian Manual in the keyword Properties

A second suggestion is not to use just the B3LYP. It is an "old" functional that does not show the correct long range behaviour. I suggets to test some newer one and at least to compare a couple more of the new ones avilable in Gaussian and that have a correct long range behaviour or even a range separate behaviour as CAM-B3LYP

Give a look at the DFT part of the Gaussian09 manual on line.

Hope this will help!

Francesco

Dear Professor Francesco Leji,

Thank you very much for your very detailed reply.

I was wrong to put it T0. It should be T1 as my molecules are derivative of Ru(bpy)3 2+ which has singlet ground state. (Actually, i was confused when some published papers use the term T0 - triplet ground state along with S0 singlet ground state; i will try to figure out why they use the term T0 for their closed-shell system).

Regarding HSOMO-HOMO energy, yes, that is not very popular approach. I only found it on publish from Prof. Mark Thompson's group mainly, i think.

Regarding basis set: Thank you for your advice, very much.

Actually, what i am trying to do is very closed to your iridium pyridine imines paper published on Dalton this year (Dalton Trans.,2014,43,4026), certainly i would not be able to go that high-level and details. I just try to write a short paragraph to support my explaination of experimental observation in my thesis. (And more importantly, i feel quite exciting to learn this method). It was lucky enough for me to have you here along with your published works. I so far particularly like the part on DeltaSCF emission energy ΔE(T1@T1:S0@T1) and your comment on the possibility of ISC based on similarity of optimized S1 and T1 structure. I would like to try to follow your approach for my compounds.

Back to my problem, I am trying to get optimized geometries of the second and the first triplet excited state (T2 and T1), as i have two different phosphorescent emissive excited states. If i could get the optimize geometries, i would try to do as follow to estimate emission energies.

- Start with singlet multiplicity; optimized T2 geometry; td=triplet then take the first excitation as emission energy; Similarly for T1.

- DeltaSCF; substract the energy different between two states of the same geometry (follow your paper)

They are all vertical emission energies, as i understand.

How do you think about the approach. That is what i plan, as i currently struggling with optimize excited state with TDDFT. I understand that it is not likely the data could be use. But i am really want to see how it work.

Thank you very much. I really appreciate your very kind help!

And please just call me Mer.

Best regards,

Mer Mecurate

Dera Mer,

thank you for your kind words!

If I understand well you want to justify the presence of a double emissions in your emission spectra. From what you say I guess that your molecule doesnt' have any symmetry if the substitution on the bipy ligands are not the same and at most it belongs to the C3 point group so you don't have much room to get many different irrep in the triplet states.

So you are left with the UKS for the T1 and the TDDFT approach for the higher energy triplet states.

I didn't understend your statetment:

DeltaSCF; substract the energy different between two states of the same geometry (follow your paper)

Emission should be related to the difference between the T1@T! and S0@T1 ( following the notation of our paper on Dalton). So the second emission should be T2@T2 and S0@T2. This means that you need to optimize the T2 with TDDFT approach.

I suggests you to start with the the T1 geometry you got by UKS ( +2 3 charge multpliciti input in gaussian).

Probably what you will find is that they are too "red" compared to the experimental values.

As I told you the convergence of the triplet geometry is very tricky using the Singlet S0 wavefunction as reference. I never tried using the Triplet T1 as a reference for the optimization of T1 and than recomputing just the S0 energy (i.e, without reoptimizing the geometry) using the geometry of the Triplet states optimized by TDDFT. The problem of the gemetry optimization in TDDFT is related to the tollerance of the wavefunction which is 10-6. Triplets are very slow to get that value so at least to see if you can get an optimized geometry and then refine it, try to increase the valuet to 10-5 or 10-4 ( I guess this is the value it is used just for computing the energies). The only risk is that the gradient are not stable enough and the geometry optimization goes wandering around without finding the minimum. So it is safe to check the optimization frequently to see how it behaves.

Furthermore use the IOp(9/76 =XX) and then use the smallest number of triplet you need+2, i.e. Nstates=4. In fact frequently those that are hard to cenverge are the higer energy one.

By the way what version of Gaussian09 are you using ? I guess D01 because it has more keywords to hande the TDDFT calculations ( look to the on-line manual)

The other danger you can stumble in in the optimization is that while the geometry changes the former T2 became T1. So you have to check the composition of the states in terms of the involved one electron excitation ( those with the arrow -> in the Gaussian aoutput). Some time changing the geometry the T1 goes above the T2 so T2 becomes T1 and the other way around. If you are lucky once it happened it does not go back during the optimization and it converges to the wanted state. If you sse thei behaviour it could means that the two triplets crosses and this could be only a computation a problem but it could also mean that the geometry relaxation mixes the two states and that the energy hyper surface could be very complex and that the Born-Oppenheimer approximation breaks down.

If I have time I'll try the procedure with the Ru(Bipy)3 2+ .

Let me know how it is going.

Regards

Francesco (just call me that way ! ! ) : -)

Dear Professor Francesco,

Thank you very much for your reply. I delayed to post the reply to do some more reading.

I would like first to clear some points you mentioned:

- I am using Gaussian 09 Revision A.02.

- My molecules have either C2 rotational axis or no symmetry (Ru(bpy)2(modified bpy/phen)2+).

- DeltaSCF, as i try to learn from your papers. I plan to estimate emission energy by taking the energy difference T1@T1 -S0@T1.

- T0(?) ground state. I got confused by papers from a group at North Dakota State University (a paper on Dalton- DOI: c2dt32153j and an IC paper- doi: ic400683u) on Pt(bpy)(diacetylide)2+ and Pt(C^N^N)Cl complexes. They optimize S0 and ALSO "triplet ground state T0 (?)"; From "triplet ground state T0", vertical excitation is calculated then the first excitation energy happens to be close to emission energy (?). Then they analyze the NTO orbitals and made comments. I may have missed her points, but still can not figure out the meaning of ground state T0.

Back to the main problem.

Having your comments and advices in mind, i tried to do some more reading the last few days. As you mentioned, it is difficult to optain optimized T1 by TDDFT with S0 wavefunction as reference. The chance of successful optimization T1 and T2 would drop dramatically if apply to a series of several compounds, I believe.

Also, it may be the case, similar to singlet, excitation energies are not well-seperated, then the T2 may not be the origin of the second emission but higher triplet excited state (Tn) [my thought].

I think that it doest seem to be very practically feasible to solve the emission problem using this T1 T2 optimization aproach, at least to me, within my candidature.

So I try to simplify the problems, by not to optimize higher triplet excited state but only do the optimization for S0 and T1. and then:

- For the lower energy emission, originated from T1: I try to follow analysis in your papers and use deltaSCF to estimate emission energy.

- For higher emission (if any), performing a TDDFT, use T1 optimized-geometry as singlet ground state then calculate # td=triplet, nstate=xx; unrestricted COM-B3LYP; PCM solvent effect and then comments based on NTOs analysis.

It is my plan. It would be very much appreciated if you have any comment or sugestion for that.

Thank you very much, and i wish you a great week ahead!

Best regards,

Mer Mercurate

Ref:

Dalton paper: http://pubs.rsc.org/en/content/articlelanding/2013/dt/c2dt32153j#!divAbstract

ic paper: http://pubs.acs.org/doi/abs/10.1021/ic400683u

Hi Mer !,

I'll give a look at the paper whose reference you sent me

What I can figure out without reading yet the paper is that, being a Pt complex, for some reason it is a high spin system an then, as in case of tetrahedral Ni complexes, some time they get as a ground state a triplet ( i.e., the the high spin counterpart of the low spin d8 ). So they call it T0 for signifying that it was the ground state.

As for your problem I suggest to check if in case of the C2 point group system you have the luck that the two triplets belongs to two different irreps. If so you can try the Urestricted approach on both. Owing to the variational theorem you can get the geometries for the triplet states belonging to the two irreps. Then you can try to do an educated guess of the geoemtries of the other complexes which are only some derivative and hoping that the main geometry of the derivative ( at least for what concerns the coordination to the metal and largest part of the molecule) is not changed, use that geometry for the calculation of the Triplet states emission as you suggested.

This could be a small improvement on your suggestion of using the geometry of the T1 for the higher energy triplets ( T2) . Though your suggestion at least does not use the S0 geometry, it is more apt to study the absorption from the T1 toward higher triplet states than the emission from T2 toward S0.

It is anyway an attempt to tackle the problem.

As a second caveat: are you sure that the emission spectrum is due to a second triplet and its shape is not because a vibronic structure ? If so, you see more than one maximum but it is the vibronic sequence not the emission from another triplet causing its shape.

Though in case of transition metals frequently are reported more than one triplet emission it is need a strong reason (Leroy-Lhez, S.; Belin, C.; D’Aleo, A.; Williams, R. M.; De Cola, L.; Fages, F. Supramol. Chem. 2003, 15, 627-637; Ford, W. E.; Rodgers, M. A. J. J. Phys. Chem. 1992, 96, 2917-2920. ; Lavie-Cambot, A.; Lincheneau, C.; Cantuel, M.; Leydet, Y.; McClenaghan, N. D. Chem. Soc. Rev. 2010, 39, 506-515.) for the molecule not to drop down to the most stable triplet ( processes that are very fast in the picosecond time scale. See the paper Phys.Chem.Chem.Phys. 2014, 16, 219 DOI: 10.1039/c3cp53886a ) and than emits toward S0 ( in organic phothochemistry emission from the lowest energy excited state is frequently called the Kasha rule). For engendering a dual emission you need that the internal corversion must be slower than the emission from the triplet. On the other hand this is in general intrinsically very slow because it depends only on the Spin Orbit coupling (SOC). Hence you should strongly hamper the T2 not to decay to T1. This appens for example in case of Pyrene complexes where the emission is from a triplet of pyrene and from that one on the remaining molecule. But in this case the conformation of the pyrene moiety w.r.t. the rest of the molecule segregates its electronic structure from the remaining ligand and metal. Hence the two triplets behave as if they were in two separate molecules decaying almost independently (though they are able to exchange energy by some coupling mecahnism like Dexter one (Dexter, D. L. J. Chem. Phys. 1953, 21, 836-850).)

What you could try is computing the vibronic structure of your T1 using Gaussian09 D01. Previous version are not as good at computing Franck-Condon factors as the D01.

In this case it is necessary to compute vibrations for the T1 and S0 in their respective optimized structure ( remember to use the option freq=(SaveNormalMode) and follow the instruction of the FC option in Gaussian). In case of T1 this can be easily done just in Urestricted way so you can compute the Hessian analytically and not in numerical way as in TDDFT( a painful and prohibitively slow computation if you have a lot of gaussian functions and no symmetry as in large C1 molecule).

In this way you can get the vibronic structure of the spectrum in absorption and emission as well and check the shape of your spectrum with the computed one. Be carefull that because you do not have the contribution of SOC the shape of the spectrum does not contain the contribution from the electronic transition probability but onle the vibrational contribution so the intensities do not reproduce the absolute value of your experimental absorption. In this way you could check if the shape of the spectrum is due to a real multiple emission or to a vibronic structure. I am assuming that you do not have any strong evidence ( e.g., multiple decay times) that the spectrum is due to multiple states decay but just the shape of the emission spectrum.

I suggest you to switch to the D01 version of Gaussian (or at least to the C01) because the A01 have some serious problem in the convergence procedure of the geometry optimization and frequently it wanders around before finding the minimum energy geometry. They improved the search in version C01 and D01

Hope this will help.

Francesco

Dear Professor Francesco,

Thank you for your post. It has always been very comprehensive and very helpful for me.

Thank you for your advice about the C and D revision of Gaussian. I currently have access only to A revision. But knowing the advantage of other version would be helpful for me, especially when i try to set up my own lab/system.

Regarding the education guess of the geoemtries for T2, I understand it is similar to what people do to get the optimization of 3MC state from the triplet MLCT, especially when the 3MC lever is slightly higher in energy. I think i will try it.

For the vibronic-structured emission, yes. Some of my compounds show vibronic-structure emission (with 1500cm-1 spacing), especially those containing organic chromophore and mainly 3LC emission. The one which i suspect dual emission havs two structureless emission bands (seperated by 4000cm-1) and also different life times. But the interesting point from your suggestion is how to use frequency calculation to address vibronic band in the absorption and emission spectra. It is really interesting to me. I do see compounds with vibronic absorption bands but i have never realized the link between theoretical frequency calculation and the shape of absorption bands. So far, to me, frequency calculation is limited to stationary/transition status check and for infrared spectroscopy only. That would be interesting to explore in the future.

Again, thank you very much for your time and patience. Your comments are very useful for me and i really appreciate your very kind help!

Thank you!

Mer Mercurate.

Best wihes for the defense of your thesis !

Francesco

Thank you very much, Professor Francesco!

I wish you all the best!

Mer Mercurate.

Please someone help me to assign the transition for emission from triplet optimized geometry with TDDFT. Especially the assignment of MLCT, pi-pi* in cyclometalated Ir complexes 

The complex emit at 551 nm

Excited State 4: Triplet-A 2.2296 eV 556.09 nm f=0.0000 =2.000

302 ->312 -0.37390

303 ->312 0.15151

303 ->313 -0.10084

306 ->312 -0.15063

307 ->312 0.43759

309 ->312 -0.15742

Excited State 5: Triplet-A 2.2697 eV 546.25 nm f=0.0000 =2.000

310 ->313 0.44514

310 ->314 -0.53390

These are the details from triplet optimized state. How to choose between these two? Please help.

Is it required to perform TDDFT on triplet optimized structure to understand the emission?

hello , this article is useful