# Category Archives: Spectroscopy

## Geometry Optimizations for Excited States

Electronic excitations are calculated vertically according to the Frank—Condon principle, this means that the geometry does not change upon the excitation and we merely calculate the energy required to reach the next electronic state. But for some instances, say calculating not only the absorption spectra but also the emission, it is important to know what the geometry minimum of this final state looks like, or if it even exists at all (Figure 1). Optimizing the geometry of a given excited state requires the prior calculation of the vertical excitations whether via a multireference method, quantum Monte Carlo, or the Time Dependent Density Functional Theory, TD-DFT, which due to its lower computational cost is the most widespread method.

Most single-reference treatments, ab initio or density based, yield good agreement with experiments for lower states, but not so much for the higher excitations or process that involve the excitation of two electrons. Of course, an appropriate selection of the method ensures the accuracy of the obtained results, and the more states are considered, the better their description although it becomes more computationally demanding in turn.

In Gaussian 09 and 16, the argument to the ROOT keyword selects a given excited state to be optimized. In the following example, five excited states are calculated and the optimization is requested upon the second excited state. If no ROOT is specified, then the optimization would be carried out by default on the first excited state (Where L.O.T. stands for Level of Theory).

`#p opt TD=(nstates=5,root=2) L.O.T.`

Gaussian16 includes now the calculation of analytic second derivatives which allows for the calculation of vibrational frequencies for IR and Raman spectra, as well as transition state optimization and IRC calculations in excited states opening thus an entire avenue for the computation of photochemistry.

If you already computed the excited states and just want to optimize one of them from a previous calculation, you can read the previous results with the following input :

`#p opt TD=(Read,Root=N) L.O.T. Density=Current Guess=Read Geom=AllCheck`

Common problems. The following error message is commonly observed in excited state calculations whether in TD-DFT, CIS or other methods:

`No map to state XX, you need to solve for more vectors in order to follow this state.`

This message usually means you need to increase the number of excited states to be calculated for a proper description of the one you’re interested in. Increase the number N for nstates=N in the route section at higher computational cost. A rule of thumb is to request at least 2 more states than the state of interest. This message can also reflect the fact that during the optimization the energy ordering changes between states, and can also mean that the ground state wave function is unstable, i.e., the energy of the excited state becomes lower than that of the ground state, in this case a single determinant approach is unviable and CAS should be used if the size of the molecule allows it. Excited state optimizations are tricky this way, in some cases the optimization may cross from one PES to another making it hard to know if the resulting geometry corresponds to the state of interest or another. Gaussian recommends changing the step size of the optimization from the default 0.3 Bohr radius to 0.1, but obviously this will make the calculation take longer.

`Opt=(MaxStep=10)`

If the minimum on the excited state potential energy surface (PES) doesn’t exist, then the excited state is not bound; take for example the first excited state of the H2 molecule which doesn’t show a minimum, and therefore the optimized geometry would correspond to both H atoms moving away from each other indefinitely (Figure 2). Nevertheless, a failed optimization doesn’t necessarily means the minimum does not exist and further analysis is required, for instance, checking the gradient is converging to zero while the forces do not.

## Density Keyword in Excited State Calculations with Gaussian

I have written about extracting information from excited state calculations but an important consideration when analyzing the results is the proper use of the keyword density.

This keyword let’s Gaussian know which density is to be used in calculating some results. An important property to be calculated when dealing with excited states is the change in dipole moment between the ground state and any given state. The Transition Dipole Moment is an important quantity that allows us to predict whether any given electronic transition will be allowed or not. A change in the dipole moment (i.e. non-zero) of a molecule during an electronic transition helps us characterize said transition.

Say you perform a TD-DFT calculation without the density keyword, the default will provide results on the lowest excited state from all the requested states, which may or may not be the state of interest to the transition of interest; you may be interested in the dipole moment of all your excited states.

Three separate calculations would be required to calculate the change of dipole moment upon an electronic transition:

1) A regular DFT for the ground state as a reference
2) TD-DFT, to calculate the electronic transitions; request as many states as you need/want, analyze it and from there you can see which transition is the most important.
3) Request the density of the Nth state of interest to be recovered from the checkpoint file with the following route section:

`# TD(Read,Root=N) LOT Density=Current Guess=Read Geom=AllCheck`

replace N for the Nth state which caught your eye in step number 2) and LOT for the Level of Theory you’ve been using in the previous steps. That should give you the dipole moment for the structure of the Nth excited state and you can compare it with the one in the ground state calculated in 1). Again, if density=current is not used, only properties of N=1 will be printed.

## NIST CCCBDB – Vibrational Scaling Factors & ThermoChem Data

The Computational Chemistry Comparison and Benchmark DataBase (CCCBDB) from the National Institute of Standards and Technology (NIST) collects experimental and calculated thermochemistry—related values for 1968 common molecules, constituting a vast source of benchmarks for various kinds of calculations.

In particular, scaling factors for vibrational frequencies are very useful when calculating vibrational spectra. These scaling factors are arranged by levels of theory ranging from HF to MP2, DFT, and multireference methods. These scaling factors are obtained by least squares regression between experimental and calculated frequencies for a set of molecules at a given level of theory.

Aside from vibrational spectroscopy, a large number of structural and energetic properties can be found and estimated for small molecules. A quick formation enthalpy can be calculated from experimental data and then compared to the reported theoretical values at a large number of levels of theory. Moments of inertia, enthalpies, entropies, charges, frontier orbital gaps, and even some odd values or even calculations gone awry are pointed out for you to know if you’re dealing with a particularly problematic system. The CCCB Database includes tutorials and input/output files for performing these kinds of calculations around thermochemistry, making it also a valuable learning resource.

Every computational chemist should be aware of this site, particularly when collaborating with experimentalists or when carrying calculations trying to replicate experimental data. The vastness of the site calls for a long dive to explore their possibilities and capabilities for more accurate calculations.

## Natural Transition Orbitals (NTOs) Gaussian

The canonical molecular orbital depiction of an electronic transition is often a messy business in terms of a ‘chemical‘ interpretation of ‘which electrons‘ go from ‘which occupied orbitals‘ to ‘which virtual orbitals‘.

Natural Transition Orbitals provide a more intuitive picture of the orbitals, whether mixed or not, involved in any hole-particle excitation. This transformation is particularly useful when working with the excited states of molecules with extensively delocalized chromophores or multiple chromophoric sites. The elegance of the NTO method relies on its simplicity: separate unitary transformations are performed on the occupied and on the virtual set of orbitals in order to get a localized picture of the transition density matrix.

[1] R. L. Martin, J. Chem. Phys., 2003, DOI:10.1063/1.1558471.

In Gaussian09:
After running a TD-DFT calculation with the keyword TD(Nstates=n) (where n = number of states to be requested) we need to take that result and launch a new calculation for the NTOs but lets take it one step at a time. As an example here’s phenylalanine which was already optimized to a minimum at the B3LYP/6-31G(d,p) level of theory. If we take that geometry and launch a new calculation with the TD(Nstates=40) in the route section we obtain the UV-Vis spectra and the output looks like this (only the first three states are shown):

```Excitation energies and oscillator strengths:

Excited State 1: Singlet-A 5.3875 eV 230.13 nm f=0.0015 <S**2>=0.000
42 -> 46 0.17123
42 -> 47 0.12277
43 -> 46 -0.40383
44 -> 45 0.50838
44 -> 47 0.11008
This state for optimization and/or second-order correction.
Total Energy, E(TD-HF/TD-KS) = -554.614073682
Copying the excited state density for this state as the 1-particle RhoCI density.

Excited State 2: Singlet-A 5.5137 eV 224.86 nm f=0.0138 <S**2>=0.000
41 -> 45 -0.20800
41 -> 47 0.24015
42 -> 45 0.32656
42 -> 46 0.10906
42 -> 47 -0.24401
43 -> 45 0.20598
43 -> 47 -0.14839
44 -> 45 -0.15344
44 -> 47 0.34182

Excited State 3: Singlet-A 5.9254 eV 209.24 nm f=0.0042 <S**2>=0.000
41 -> 45 0.11844
41 -> 47 -0.12539
42 -> 45 -0.10401
42 -> 47 0.16068
43 -> 45 -0.27532
43 -> 46 -0.11640
43 -> 47 0.16780
44 -> 45 -0.18555
44 -> 46 -0.29184
44 -> 47 0.43124```

The oscillator strength is listed on each Excited State as “f” and it is a measure of the probability of that excitation to occur. If we look at the third one for this phenylalanine we see f=0.0042, a very low probability, but aside from that the following list shows what orbital transitions compose that excitation and with what energy, so the first line indicates a transition from orbital 41 (HOMO-3) to orbital 45 (LUMO); there are 10 such transitions composing that excitation, visualizing them all with canonical orbitals is not an intuitive picture, so lets try the NTO approach, we’re going to take excitation #10 for phenylalanine as an example just because it has a higher oscillation strength:

```%chk=Excited State 10: Singlet-A 7.1048 eV 174.51 nm f=0.3651 <S**2>=0.000
41 -> 45 0.35347
41 -> 47 0.34685
42 -> 45 0.10215
42 -> 46 0.17248
42 -> 47 0.13523
43 -> 45 -0.26596
43 -> 47 -0.22995
44 -> 46 0.23277```

Each set of NTOs for each transition must be calculated separately. First, copy you filename.chk file from the TD-DFT result to a new one and name it after the Nth state of interest as shown below (state 10 in this case). NOTE: In the route section, replace N with the number of the excitation of interest according to the results in filename.log. Run separately for each transition your interested in:

```#chk=state10.chk

#p B3LYP/6-31G(d,p) Geom=AllCheck Guess=(Read,Only) Density=(Check,Transition=N) Pop=(Minimal,NTO,SaveNTO)

0 1
--blank line--```

By requesting SaveNTO, the canonical orbitals in the state10.chk file are replaced with the NTOs for the 10th excitation, this makes it easier to plot since most visualizers just plot whatever set of orbitals they read in the chk file but if they find the canonical MOs then one would need to do some re-processing of them. This is much more straightforward.

Now we format our chk files into fchk with the formchk utility:

`formchk -3 filename.chk filename.fchkformchk -3 state10.chk state10.fchk`

If we open filename.fchk (the file where the original TD-DFT calculation is located) with GaussView we can plot all orbitals involved in excited state number ten, those would be seven orbitals from 41 (HOMO-3) to 47 (LUMO+2) as shown in figure 1.

If we now open state10.fchk we see that the numbers at the side of the orbitals are not their energy but their occupation number particular to this state of interest, so we only need to plot those with highest occupations, in our example those are orbitals 44 and 45 (HOMO and LUMO) which have occupations = 0.81186; you may include 43 and 46 (HOMO-1 and LUMO+1, respectively) for a much more complete description (occupations = 0.18223) but we’re still dealing with 4 orbitals instead of 7.

The NTO transition 44 -> 45 is far easier to conceptualize than all the 10 combinations given in the canonical basis from the direct TD-DFT calculation. TD-DFT provides us with the correct transitions, NTOs just paint us a picture more readily available to the chemist mindset.

NOTE: for G09 revC and above, the %OldChk option is available, I haven’t personally tried it but using it to specify where the excitations are located and then write the NTOs of interest into a new chk file in the following way, thus eliminating the need of copying the original chk file for each state:

`%OldChk=filename.chk%chk=stateN.chk`

NTOs are based on the Natural Hybrid orbitals vision by Löwdin and others, and it is said to be so straightforward that it has been re-discovered from time to time. Be that as it may, the NTO visualization provides a much clearer vision of the excitations occurring during a TD calculation.

Thanks for reading, stay home and stay safe during these harsh days everyone. Please share, rate and comment this and other posts.

## Gustavo “Gus” Mondragón M.Sc. – Thesis Defense

We celebrate the successful thesis defense of Gustavo “Gus” Mondragón who has now completed his Masters degree and is now on to getting a PhD in our group. Gustavo has worked on the search for multiexcitonic states and their involvement in the excitonic transference between photosynthetic pigments, specifically between bacteriochlorophyll-d molecules (BChl-d) from the bchQRU chlorosome whose whole structure is shown in the gallery below. To this end, Gustavo has studied and implemented the Restricted Active Space method with double spin flip (RAS-2SF) with the use of QChem5.0, a method that has required the use and understanding of states with high multiplicities. Additionally, Gustavo has investigated the influence of the environment within the chlorosome by performing ONIOM calculations for the spectroscopic properties of a BChl-d dimer, finding albeit qualitatively a batochromic effect, probably an expected result but nonetheless an impressive feat for the level of theory selected.

There’s still a lot of work to do in this line of research and although we’re eager to publish our results in this excitonic transference mechanism we want to be completely sure that we’re taking every possibility into consideration so we don’t incur into any inconsistencies.

Gustavo cultivates many research interests from excited states of these pigments to biochemical processes that require the use of various tools; I’m sure his permanence in our lab will bring lots of interesting results. Congratulations, Gus! Thank you for your hard work.

With pleasure I announce that last week our very own Gustavo “Gus” Mondragón became the fifth undergraduate student from my lab to defend his BSc thesis and it has to be said that he did it admirably so.

Gus has been working with us for about a year now and during this time he not only worked on his thesis calculating excited states for bacteriochlorophyl pigments but also helped us finishing some series of calculations on calix[n]arene complexes of Arsenic (V) acids, which granted him the possibility to apear as a co-author of the manuscript recently published in JIPH. Back in that study he calculated the interaction energies between a family of calix macrocycles and arsenic acid derivatives in order to develop a suitable extracting agent.

For his BSc thesis, Gus reproduced the UV-Vis absorption spectra of bacteriochlorophyll-a pigments found in the Fenna-Matthews-Olson complex of photosynthetic purple bacteria using Time Dependent Density Functional Theory (TD-DFT) with various levels of theory, with PBEPBE yielding the best results among the tried set. These calculations were performed at the crystallographic conformation and at the optimized structure, also, in vacuo results were compared to those in implicit solvent (SMD, MeOH). He will now move towards his masters where he will further continue our research on photosynthesis.

Thank you, Gustavo, for your hard work and your sense of humor. Congratulations on this step and may many more successes come your way.

## Maru Sandoval M.Sc. – Our First Graduate Thesis

It is with great pride that I’d like to announce that for the first time we have a Masters Student graduated from this Comp.Chem. lab: María Eugenia “Maru” Sandoval-Salinas has finished her graduate studies and just last Friday defended her thesis admirably earning not only the degree of Masters of Science in Chemistry but doing so with the highest honors given by the National Autonomous University of Mexico.

Maru’s thesis is for many reasons a landmark in this lab not only because it is the first graduate thesis published from our lab but also the first document on our work about the study of Photosynthesis, a long sought after endeavor now closer to publication. It must also be said that Maru came to this lab when she was an undergraduate student five years ago when I just recently joined UNAM as a researcher fresh out of a postdoc stay. After getting her B.Sc. degree and publishing an article in JCTC (DOI: 10.1021/ct4004178) she now is about to publish more papers that I’m sure will be as highly ranked as the previous one. Thus, Maru was a pioneer in our lab giving it a vote of confidence when we had little to nothing to show for; thanks to her hard work and confidence, along with that of the students who have followed her, we managed to succeed as a consolidated research group in the field of computational chemistry.

More specifically, her thesis centered around finding a mechanism for the excitonic transference between pigments (bacteriochlorophyl-a, BChl-a) in the Fenna-Matthews-Olson (FMO) complex, a protein trimer with seven BChl-a molecules in each monomer, located between the antenna complex and the reaction center in green sulfur bacteria. Among the possible mechanisms explored were Förster’s theory, a modification to Marcus’ theory and finally we explored the possibility of Singlet Fission occurring between adjacent molecules with the help of Dr. David Casanova from the Basque Country University where Maru took a short research stay last autumn. Since nature doesn’t conform to any specific mechanism -specially in a complex arrangement such as the FMO- then it could be possible that a combination of the above might also occur but lets just wait for the papers to be published to discuss it. Calculations were performed through the TD-DFT and the C-DFT formalisms using G09 and Q-Chem; comparing experimental data in CH3OH (SMD implicit calculations with the SVWN5 functional) were undertaken previously for selection of the level of theory.

Now, after two original theses written and successfully defended, an article published in JCTC and more in process, at least five posters, a couple of oral presentations and countless hours at her desk, Maru will go pursuit a PhD abroad where I’m sure she will exceed anyone’s expectations with her work, drive, dedication and scientific curiosity. Thank you, Maru, for all your hard work and trust when this lab needed it the most, we wish you the best for you earn it. You will surely be missed.

## Simulation of Raman Spectroscopy and crystal cell effects – Selenium Carboxylate Eur. J. Inorg. Chem.

Computing spectroscopic features of molecules is always an interesting challenge, specially when intermolecular contacts are into play. Take vibrational spectroscopy for instance, all the non-covalent interactions present in a solid will have an important effect on the the calculated frequencies and their intensities. However calculating the spectroscopical properties of a solid quickly becomes a daunting task.

My colleague and friend Dr. Vojtech Jancik asked me to calculate the Raman frequencies for a new compound: Selenoyl bis-carboxylate, which according to him was very hard to obtain due to the very nature of selenium. So we performed various calculations on the isolated molecule to reproduce the measured Raman spectrum but we soon realized that a calculation on the crystal cell was needed if we wanted to get a more thorough picture of the experiment.

The level of theory used was PBEPBE/LANL2DZ. Optimization of the title structure pointed to a low coordination capacity by carboxylate groups as evidenced by the longer Se -O-C=O distances and reduced Wiberg bond indexes. A blue shift was observed for all bands and so we calculated the Raman frequencies at the crystal structure which gave us a better correspondence between spectra. Finally we computed the Raman spectra for the full unit cell comprised of four molecules with which an excellent agreement was obtained (a scaling factor of 0.8 was used).

Unfortunately we failed to further extend this calculation to a larger system with four unit cells and 32 molecules apparently due to insufficient memory; the calculation just stalled and stopped without error after consuming its time in the queue. I’ll try to take a look into it some day.

You can read the whole story in: Synthesis and Crystal Structure of the First Selenonyl Bis(carboxylate) SeO2(O2CCH3)2
Lukas Richtera · Vojtech Jancik · Joaquín Barroso‐Flores · Petr Nykel · Jiri Touzin · Jan Taraba