# Blog Archives

## Orbital Contributions to Excited States

This is a guest post by our very own Gustavo “*Gus*” Mondragón whose work centers around the study of excited states chemistry of photosynthetic pigments.

When you’re calculating excited states (no matter the method you’re using, TD-DFT, CI-S(D), EOM-CCS(D)) the analysis of the orbital contributions to electronic transitions poses a challenge. In this post, I’m gonna guide you through the CI-singles excited states calculation and the analysis of the electronic transitions.

I’ll use adenine molecule for this post. After doing the corresponding geometry optimization by the method of your choice, you can do the excited states calculation. For this, I’ll use two methods: CI-Singles and TD-DFT.

The route section for the CI-Singles calculation looks as follows:

%chk=adenine.chk

%nprocshared=8

%mem=1Gb

#p CIS(NStates=10,singlets)/6-31G(d,p) geom=check guess=read scrf=(cpcm,solvent=water)

adenine excited states with CI-Singles method

0 1

--blank line--

I use the same geometry from the optimization step, and I request only for 10 singlet excited states. The CPCP implicit solvation model (solvent=water) is requested. If you want to do TD-DFT, the route section should look as follows:

%chk=adenine.chk

%nprocshared=8

%mem=1Gb

#p FUNCTIONAL/6-31G(d,p) TD(NStates=10,singlets) geom=check guess=read scrf=(cpcm,solvent=water)

adenine excited states with CI-Singles method

0 1

--blank line--

Where FUNCTIONAL is the DFT exchange-correlation functional of your choice. Here I strictly not recommend using B3LYP, but CAM-B3LYP is a noble choice to start.

Both calculations give to us the excited states information: excitation energy, oscillator strength (as *f* value), excitation wavelength and multiplicity:

Excitation energies and oscillator strengths:

Excited State 1: Singlet-A 6.3258 eV 196.00 nm f=0.4830 <S**2>=0.000

11 -> 39 -0.00130

11 -> 42 -0.00129

11 -> 43 0.00104

11 -> 44 -0.00256

11 -> 48 0.00129

11 -> 49 0.00307

11 -> 52 -0.00181

11 -> 53 0.00100

11 -> 57 -0.00167

11 -> 59 0.00152

11 -> 65 0.00177

The data below corresponds to all the electron transitions involved in this excited state. I have to cut all the electron transitions because there are a lot of them for all excited states. If you have done excited states calculations before, you realize that the HOMO-LUMO transition is always an important one, but not the only one to be considered. Here is when we calculate the *Natural Transition Orbitals *(NTO), by these orbitals we can analyze the electron transitions.

For the example, I’ll show you first the HOMO-LUMO transition in the first excited state of adenine. It appears in the long list as follows:

35 -> 36 0.65024

The 0.65024 value corresponds to the transition amplitude, but it doesn’t mean anything for excited state analysis. We must calculate the NTOs of an excited state from a new Gaussian input file, requesting from the checkpoint file we used to calculate excited states. The file looks as follows:

%Oldchk=adenine.chk

%chk=adNTO1.chk

%nproc=8

%mem=1Gb

#p SP geom=allcheck guess=(read,only) density=(Check,Transition=1) pop=(minimal,NTO,SaveNTO)

I want to say some important things right here for this last file. See that no level of theory is needed, all the calculation data is requested from the checkpoint file “adenine.chk”, and saved into the new checkpoint file “adNTO1.chk”, we must use the previous calculated density and specify the transition of interest, it means the excited state we want to analyze. As we don’t need to specify charge, multiplicity or even the comment line, this file finishes really fast.

After doing this last calculation, we use the new checkpoint file “adNTO1.chk” and we format it:

formchk -3 adNTO1.chk adNTO1.fchk

If we open this formatted checkpoint file with GaussView, chemcraft or the visualizer you want, we will see something interesting by watching he MOs diagram, as follows:

We can realize that frontier orbitals shows the same value of 0.88135, which means the real transition contribution to the first excited state. As these orbitals are contributing the most, we can plot them by using the cubegen routine:

cubegen 0 mo=homo adNTO1.fchk adHOMO.cub 0 h

This last command line is for plotting the equivalent as the HOMO orbital. If we want to plot he LUMO, just change the “homo” keyword for “lumo”, it doesn’t matter if it is written with capital letters or not.

You must realize that the Natural Transition Orbitals are quite different from Molecular Orbitals. For visual comparisson, I’ve printed also the molecular orbitals, given from the optimization and from excited states calculations, without calculating NTOs:

These are the molecular frontier orbitals, plotted with Chimera with 0.02 as the isovalue for both phase spaces:

The frontier NTOs look qualitatively the same, but that’s not necessarily always the case:

If we analyze these NTOs on a hole-electron model, the HOMO refers to the *hole* space and the LUMO refers to the *electron* space.

Maybe both orbitals look the same, but both frontier orbitals are quite different between them, and these last orbitals are the ones implied on first excited state of adenine. The electron transition will be reported as follows:

If I can do a graphic summary for this topic, it will be the next one:

NTOs analysis is useful no matter if you calculate excited states by using CIS(D), EOM-CCS(D), TD-DFT, CASSCF, or any of the excited states method of your election. These NTOs are useful for population analysis in excited states, but these calculations require another software, MultiWFN is an open-source code that allows you to do this analysis, and another one is called TheoDORE, which we’ll cover in a later post.

## XVIII RMFQT

It was my distinct pleasure for me to participate in the organization of the latest edition of the Mexican Meeting on Theoretical Physical Chemistry, RMFQT which took place last week here in Toluca. With the help of the School of Chemistry from the Universidad Autónoma del Estado de México.

This year the national committee created a Lifetime Achievement Award for Dr. Annik Vivier, Dr. Carlos Bunge, and Dr. José Luis Gázquez. This recognition from our community is awarded to these fine scientists for their contributions to theoretical chemistry but also for their pioneering work in the field in Mexico. The three of them were invited to talk about any topic of their choosing, particularly, Dr. Vivier stirred the imagination of younger students by showing her pictures of the times when she used to hangout with Slater, Roothan, Löwdin, etc., it is always nice to put faces onto equations.

Continuing with a recent tradition we also had the pleasure to host three invited plenary lectures by great scientists and good friends of our community: Prof. William Tiznado (Chile), Prof. Samuel B. Trickey (USA), and Prof. Julia Contreras (France) who shared their progress on their recent work.

As I’ve abundantly pointed out in the past, the RMFQT is a joyous occasion for the Mexican theoretical community to get together with old friends and discuss very exciting research being done in our country and by our colleagues abroad. I’d like to add a big shoutout to Dr. Jacinto Sandoval-Lira for his valuable help with the organization of our event.

## Useful Thermochemistry from Gaussian Calculations

Statistical Mechanics is the bridge between microscopic calculations and thermodynamics of a particle ensemble. By means of calculating a partition function divided in electronic, rotational, translational and vibrational functions, one can calculate all thermodynamic functions required to fully characterize a chemical reaction. From these functions, the vibrational contribution, together with the electronic contribution, is the key element to getting thermodynamic functions.

Calculating the Free Energy change of any given reaction is a useful approach to asses their thermodynamic feasibility. A large negative change in Free Energy when going from reagents to products makes up for a quantitative spontaneous (and exothermic) reaction, nevertheless the rate of the reaction is a different story, one that can be calculated as well.

Using the **freq** option in your route section for a Gaussian calculation is mandatory to ascertain the current wave function corresponds to a minimum on a potential energy hypersurface, but also yields the thermochemistry and thermodynamic values for the current structure. However, thermochemistry calculations are not restricted to minima but it can also be applied to transition states, therefore yielding a full thermodynamic characterization of a reaction mechanism.

A regular **freq** calculation yields the following output (all values in atomic units):

Zero-point correction= 0.176113 (Hartree/Particle) Thermal correction to Energy= 0.193290 Thermal correction to Enthalpy= 0.194235 Thermal correction to Gibbs Free Energy= 0.125894 Sum of electronic and zero-point Energies= -750.901777 Sum of electronic and thermal Energies= -750.884600 Sum of electronic and thermal Enthalpies= -750.883656Sum of electronic and thermal Free Energies= -750.951996

For any given reaction say A+B -> C one could take the values from the last row (lets call it G) for all three components of the reaction and perform the arithmetic: DG = GC – [GA + GB], so products minus reagents.

By default, Gaussian calculates these values (from the previously mentioned partition function) using normal conditions, T = 298.15 K and P = 1 atm. For an assessment of the thermochemistry at other conditions you can include in your route section the corresponding keywords **Temperature=**x.x and **Pressure=**x.x, in Kelvin and atmospheres, respectively.

(Huge) **Disclaimer**: Although calculating the thermochemistry of any reaction by means of DFT calculations is a good (and potentially very useful) guide to chemical reactivity, getting quantitative results require of high accuracy methods like G3 or G4 methods, collectively known as Gn mehtods, which are composed of pre-defined stepwise calculations. The sequence of these calculations is carried out automatically; no basis set should be specified. Other high accuracy methods like CBS-QB3 or W1U can also be considered whenever Gn methods are too costly.

## Computational Chemistry from Latin America

The video below is a sad recount of the scientific conditions in Mexico that have driven an enormous amount of brain power to other countries. Doing science is always a hard endeavour but in developing countries is also filled with so many hurdles that it makes you wonder if it is all worth the constant frustration.

That is why I think it is even more important for the Latin American community to make our science visible, and special issues like this one from the International Journal of Quantum Chemistry goes a long way in doing so. This is not the first time IJQC devotes a special issue to the Comp.Chem. done south of the proverbial border, a full issue devoted to the Mexican Physical Chemistry Meetings (RMFQT) was also published six years ago.

I believe these special issues in mainstream journals are great ways of promoting our work in a collected way that stresses our particular lines of research instead of having them spread a number of journals. Also, and I may be ostracized for this, but I think coming up with a new journal for a specific geographical community represents a lot of effort that takes an enormous amount of time to take off and thus gain visibility.

For these reasons I’ve been cooking up some ideas for the next RMFQT website. I don’t pretend to say that my colleagues need any shoutouts from my part -I could only be so lucky to produce such fine pieces of research myself- but it wouldn’t hurt to have a more established online presence as a community.

¡Viva la ciencia Latinoamericana!

## XVI Mexican Meeting on Phys.Chem.

A yearly tradition of this Comp.Chem. lab and many others throughout our nation is to attend the Mexican Meeting on Theoretical Physical Chemistry to share news, progress and also a few drinks and laughs. This year the RMFQT was held in Puebla and although unfortunately I was not able to attend this lab was proudly represented by its current members. Gustavo Mondragón gave a talk about his progress on his photosynthesis research linking to the previous work of María Eugenia Sandoval already presented in previous editions; kudos to Gustavo for performing remarkably and thanks to all those who gave us their valuable feedback and criticism. Also, five posters were presented successfully, I can only thank the entire team for representing our laboratory in such an admirable way, and a special mention to the junior members, I hope this was the first of many scientific events they attend and may you deeply enjoy each one of them.

Among the invited speakers, the RMFQT had the honor to welcome Prof. John Perdew (yes, the **P** in PBE); the team took the opportunity of getting a lovely picture with him.

Here is the official presentation of the newest members of our group:

**Alejandra Barrera** (hyperpolarizabilty calculations on hypothetical poly-calyx[n]arenes for the search of NLO materials)

**Fernando Uribe** (Interaction energy calculations for non-canonical nucleotides)

**Juan Guzmán** (Reaction mechanisms calculations for catalyzed organic reactions)

We thank the organizing committee for giving us the opportunity to actively participate in this edition of the RMFQT, we eagerly await for next year as every year.

## XIth Mexican Reunion on Theoretical Physical Chemistry

For over a decade these meetings have gathered theoretical chemists every year to share and comment their current work and to also give students the opportunity to interact with experienced researchers, some of which in turn were even students of Prof. Robert Parr, Prof. Richard Bader or Prof. Per Olov Löwdin. This year the Mexican Meeting on Theoretical Physical Chemistry took place last weekend in Toluca, where CCIQS is located. You can find links to this and previous meetings here. We participated with a poster which is presented below (in Spanish, sorry) about our current research on the development of calixarenes and tia-calixarenes as drug carriers. In this particular case, we presented our study with the drug IMATINIB (Gleevec as branded by Novartis), a powerful tyrosinkynase inhibitor widely employed in the treatment of Leukaemia.

The International Journal of Quantum Chemistry is dedicating an issue to this reunion. As always, this meeting posed a great opportunity to reconnect with old friends, teachers, and colleagues as well as to make new acquaintances; my favourite session is still the beer session after all the seminars! Kudos to María Eugenia “Maru” Sandoval-Salinas for this poster and the positive response it generated.