Dr. Eduard Matito

Quantum Chemistry


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Exhaustive Benchmark Test For Natural Orbital Functional Theory

Posted on November 17, 2015 at 10:55 AM

The most popular method in computational chemistry is density functional theory (DFT). For the past thirty years DFT has become the preferred method over ab initio calculations due to its cost-efficiency favorable ratio. Despite its success, the development of new DFT functionals is an arduous task because the physical interactions entering the Hamiltonian have to be expressed in terms of the electron density and, such expressions only exist for the external potential (e.g. the attractive electron-nucleus Coulombic potential of molecular systems). On the other hand, the density matrix functional theory (DMFT), which uses the first-order reduced density matrix (1-RDM), permits an easier construction of the Hamiltonian because the only energy component that needs to be approximated is the electron-electron repulsion (Vee). Namely, since the Hartree-Fock expression of Vee in terms of the 1-RDM is well known, only the correlation part of Vee is actually needed to construct a DMFT functional. It is thus only natural that DMFT functionals provide quite accurate energy predictions compared to DFT ones. The downside is that DMFT are computationally more expensive than DFT calculations. In the past years, there has just been a resurged interest in the DMFT functionals based on natural orbitals, in a framework known as the natural orbital functional theory (NOFT). The groups of Baerends, Lathiotakis, Csányi, Goedecker, Umrigar and Piris, among others, have been actively suggesting NOFT functionals.

Particularly interesting are the series of functionals developed by Mario Piris, PNOF1-PNOF6, who in the past ten years has put forward functionals that can deal with nondynamic correlation effects as efficiently as the well-stablished complete active space self-consistent field (CASSCF) method. Lately, his efforts focus on introducing larger dynamic correlation effects in his functionals. We have colaborated with Mario in the past, trying to find stringent conditions that DMFT functionals should fulfill or testing the limits of applicability of his latest functional, PNOF6. 

Despite the promising research behind NOFT functionals, thus far there has been no attempt to calibrate the functionals available in the literature. This information is not only useful to reveal the limitations of current functionals but it is also important to provide a test set that can be used in order to improve the new NOFT functionals. In a work that has just been accepted in J. Chem. Phys., we have used harmonium (a well-known friend from past investigations) to calibrate a set of 14 NOFT functionals together with Prof. Jerzy Cioslowski (who published relevant papers on this topic, see e.g. this and that) and Mario.

Our results reveal that most functionals performance poorly within different electron correlation regimes. Notwithstanding, the PNOF functionals perform better than most functionals, as the following plot of the correlation Vee energy in the singlet state of four-electron harmonium shows:

PNOF6 gives very accurate results in the weak- and moderate-correlation regimes and it is reasonable accurate in the strong correlation regime. In this sense, PNOF6 can be regarded as the best performing functional of the series, although our results show there is still a long way to go to achieve chemical accuracy for arbitrary correlation regimes.

The present approach not only uncovers the flaws and patent failures of the functionals but, even more importantly, allows for pinpointing their root causes. Since the approximate values of U are computed at exact 1-RDM, the test requires minimal programming, and thus is particularly useful in quick screening of new functionals. In conjuction with the previously described DMFT stringent conditions based on the local spin, these tools will be used to construct more robust natural orbital functionals.

Bonding Description of the Harpoon Mechanism

Posted on November 11, 2015 at 6:25 PM

The formation of molecules through the harpoon mechanism occurs from the interaction of two fragments, one with a low ionization potential (IP) and another that has a large electron affinity (EA). The reactants approach each other and, at a certain distance, an electron from the fragment with low IP harpoons the fragment with large EA, giving rise to a rapid electron-transfer process that is triggered by the Coulomb attraction exerted by the two fragments. Michael Polanyi, the father of the Nobel laureate John Polanyi, suggested the mechanism in 1932 to explain the large reaction cross sections observed in alkali atoms with halogen molecules. The reaction has been widely studied but, despite the intriguing reaction mechanism, its chemical bonding has not been so carefully analyzed.

In this work we perform a more exhaustive analysis of the bonding in the formation of molecules through harpoon mechanism using the electron sharing indices (ESI), the electron localization function (ELF) and the Laplacian of the electron density. Several diatomics are analyzed but the focus is put into the two lowest-lying singlet sigma states of LiH. The LiH in its ground state is formed by means of a harpoon mechanism, going through two avoided crossings, that change twice its bonding character. The single sigma excited state, shows a very peculiar behavior and likewise changes its bonding nature twice, as it also passes through two avoided crossings.

The work is part of Mauricio's thesis and it will be published in a special issue of Molecular Physics dedicated to the 65th birthday of Andreas Savin, who (aside from its important contributions to the density functional theory [DFT]) also contributed to the popularization, the understanding and interpretation of the ELF (e.g. the DFT version of the ELF) and introduce significant ideas in the field of the chemical bonding analysis. Happy birthday Andreas! 


Review on Aromaticity and Electron Delocalization

Posted on September 6, 2015 at 12:00 PM

We have recently published together with Ferran Feixas, Jordi Poater and Miquel Solà a review on Chemical Society Reviews (from RSC) covering the last 12 years studying the connections between aromaticity and electron delocalization. During this time we have developed a series of aromaticity indices (PDI, FLU, ING and INB) and constructed aromaticity tests (1 and 2) that allow a more reliable description of aromaticity not only in organic molecules but also inorganic molecules such as the all-metal clusters. These tools have been implemented in our own computational code (ESI-3D) and have been applied to a plethora of systems.

Miquel Solà, who has supervised the theses of the three of us (Jordi, Ferran and me) received the invitation from the editorial board of the Chemical Society Reviews who has published our work this week, including the inside cover of the journal that has been designed by Ferran.

In this link you can find the article or ask for a reprint if you don't have access.

The Electronic Structure of the Al3 Anion: Is it Aromatic?

Posted on June 19, 2015 at 9:25 PM

Our first article since I joined the Basque Country has just appeared online. The work has been carried out in close collaboration with Txema Mercero, Jesus Ugalde, Fernando Ruiperez, Xabi Lopez and Ivan Infante. The paper deals with the aromatic character of Al3- in various electronic states. Highly-accurate ab initio calculations (CASSCF) were performed in the lowest-lying singlet, triplet and quintet states. These states were found to be of significant multideterminant character, thus preventing the application of Hückel's rule or a simple molecular orbital analysis. The study of multicenter delocalization indices shed some light on the aromaticity of these species, which are found to be more aromatic than Al42- in its ground-state singlet configuration. 

This communication was published in Chem. Eur. J., whose editor selected it as a very important and invited us to publish a frontispieces, including the image you find below. Should you be interested in this work do not hesitate to request a reprint.

PhD Student position in Computational Chemistry

Posted on June 17, 2015 at 9:50 AM

PhD-student position available to perform the doctoral thesis in Donostia (Spain) under the supervision of Dr. Eduard Matito to work on some of the these subjects: (i) development of new DFT functionals; (ii) chemical bonding and aromaticity from electron delocalization measures. Dr. Matito works in the Donostia International Physics Center (DIPC) leading a group of four people that is part of a bigger laboratory working in diverse research subjects including method development, aluminum (III) interaction with bioligands, noncovalent and hydrogen-bond interactions, spin-flip methods for excited states, nanoclusters, chemical bonding and aromaticity.


Candidates should have completed a BSc. and a MSc., preferably in chemistry or physics, and have a good background in computational and theoretical chemistry. The candidate will enjoy a three-year contract of 16,422€/year (minimal salary in Spain ca. 9,034.20€) at the University of the Basque Country in Donostia. Donostia, the 2016 European Capital of Culture, is one of Spain’s most attractive, charming and popular cities, a sophisticated coastal gem situated in the north of the peninsula surrounded by hills and offering a lively beach front, a range of natural beauty and a unique gastronomical experience. The fellowship includes the payment of the doctoral studies, the possibility to perform short stays in other research centers and a fourth year of contract (19,000€/year) if the candidate obtains her/his PhD degree before the end of the third year. In addition, the group normally covers the expenses to attend a conference or a summer school every year.


The deadline to submit paperwork is the 29th of June at 15:00. Applicants should contact Dr. Matito ([email protected]) for futher details as soon as possible (the application procedure requires some paperwork that usually takes some days to obtain). Please include a CV with your e-mail.

More details in this website.

NLOP-DFT awarded with the MINECO project

Posted on May 21, 2015 at 9:50 AM

In the last years we have been working together with Josep Maria Luis on the ability of density functional theory (DFT) to reproduce nonlinear optical properties (NLOP). We started by studing the so-called catastrophe of DFT to reproduce polarizabilities and second-order polarizability on long conjugated chains as the size of chain increases. We supervised together the Bachelor Thesis of Natalia Abulí and recently the Erasmus stay of Sebastian Sitkiewicz, both devoted to this research topic. 

DFT has found applications on a wide variety of scientific areas due to its remarkable combination of efficiency and accuracy. It is being applied with success to the fields of bioinorganic chemistry, material science, drug design, biochemistry and nano-technology, among many others. The exact density functional expressions of many energy components have not been found, and as a result, the construction of new functionals in DFT has become a complicated task, often untangled by the recourse of fitting parameters with the aid of experimental results. In this regard, the errors in DFT calculations are hardly predictable and for each new scientific challenge functionals must be calibrated against the expensive standard ab initio methods to assess their performance. DFT has reached a state of saturation, and the design of new strategies for constructing DFT functionals is now of utmost importance.

Last year we put together an ambitious research project to construct new DFT functionals that do not suffer from the above-mentioned drawback. We based the strategy on the same idea I suggested for DFTCorr, which combined with Josep Maria outstanding expertise on NLOP, resulted in the research projecte entitled: "DFT functionals for the calculation of nonlinear optical properties" (acronym: NLOPDFT). This project was submitted to 2014's call "Generación de Conocimiento" of the Spanish Ministry (MINECO) with the following team: Sebastian Sitkiewicz, Mauricio Rodríguez-Mayorga, Eloy Ramos-Córdoba, Marc Garcia-Borràs, Josep Maria Luis and myself. 

The goal of NLOPDFT is to use a genuinely new strategy to design density functionals for the calculation of NLOPs, which will lead ultimately to an all-purpose functional that yields reasonably accurate results in most applications. This strategy is physically motivated and consists in using variable amounts of the components of the exchange-correlation functionals regulated by electron correlation measures that enter into the functional expressions. Overcoming one of the most important DFT pitfalls —the description of NLOPs—, promises to furnish new functionals with the flexibility to accurately describe a wider range of properties, paving the way towards the development of all-purpose functionals. This project gives the recipe to construct an unprecedented class of local hybrid functionals and range-separate hybrids with more flexibility than its predecessors. Our preliminary results following this strategy show a drastic improvement of hybrid functionals. This project shall leap forward DFT development and make an impact in a number of fields where DFT has found applications. 


A few weeks ago, the MINECO decided to grant our project with 60,000€ and a PhD fellowship. Therefore, there is an opening for a PhD position to work in this project. The PhD fellowship is a four-year grant including a free one-year master in the MaCMOM master organized by the IQCC at the University of Girona. Interested candidates should have an excellent academic track record, preferably with a good background on computational chemistry. Prospective candidates should send their CV by e-mail to either JosepM ([email protected]) or myself ([email protected]).


[Polarizability and second-order polarizabilities in polyacetylene chains. From: Limacher et al. JCP 130, 194114 (2009)]

Hot paper published in Dalton Transactions

Posted on May 1, 2015 at 2:00 PM

Our article with Dr. Óscar Jiménez-Halla (Univ. Guanajuato, Mexico) was selected as one of the six hot articles published in Dalton Transactions in December 2014. In this paper, we performed a theoretical study of the aromaticity in the neutral an anionic borole systems synthesized in the group of Prof. Holger Braunschweig. The results show that the neutral borole structures with four π electrons are antiaromatic and become increasingly more aromatic by addition of one and two electrons, in agreement with Hückel’s rule. While the uptake of one electron to the borole leads to a nonaromatic system, addition of a second electron fully aromatizes the ring and reliefs the system from its inherent electron deficiency. It is also shown that the exocyclic substituent at the boron atom has a considerable influence on the degree of antiaromaticity in the borole ring. Substituents with π-donating abilities, such as an amino or thiophene group, seem to mitigate the destabilizing electron delocalization in the ring, whereas π-accepting groups result in an enhanced antiaromatic destabilization.

(Artwork by J. Óscar C. Jiménez Halla)

Next stage: Donostia

Posted on April 1, 2015 at 4:30 PM

At the end of 2013 I was awarded an ikerbasque fellowship. The position includes a five-year contract in the University of the Basque Country (Donostia delegation) and a very small startup budget. As a hosting group I chose the group of Jesus Ugalde, currently hosted at the Donostia International Physics Center (DIPC). By the beginning of 2015, some crew from Girona already joined the group: Mauricio Rodriguez (holding a FPU grant) and Eloy Ramos (postdoctoral position paid by the DIPC). By mid March I joined them and, so far, I have only found facilities to settle down.

By September, we will have a new team member, Mr. Sebastian Sitkiewicz, who has been awarded a scolarship to take the European Master of Theoretical Chemistry and Computational Modelling (TCCM). Irene Casademont, who had been working with Eloy and myself for the past two years, also agreed to undertake her PhD studies in Donostia. In 2016, after the courses of the Master in Advanced Catalysis and Molecular Modelling (MACMoM) finish, Irene will join our group as well. 

The five of ous, Irene, Sebastian, Mauricio, Eloy and myself will work on the next years on the development of density functional theory (DFT) and other related topics such as reduced density matrices, density matrix functional theory and time-dependent processes.

Electrides: Rare and Promising Compounds

Posted on March 25, 2015 at 5:05 PM

A few weeks ago we published our work on molecular electrides in Chemical Communications. The work has received some additional attention by Chemistry World, the blog from the Royal Society of Chemistry. In this post I will try to summarize the contents of our recently published work. 

Ionic compounds are chemical compounds consisting of positive and negative ions held together by electrostatic forces. For instance, in sodium chloride ⎯commonly known as table salt⎯ the anionic part (negative ion) is Cl- and the cationic part (positive ion) is Na+. Electrides are unique ionic compounds where the anionic part is constituted only by isolated electrons. This feature grants electrides many different properties. Thus far, only solid-state electrides have been reported and despite there have been some suggestions of molecular electrides in the literature, their electronic structure has not been confirmed as a true electride one.

James L. Dye is the father of electrides: he postulated its existence in 1960s, synthesized and characterized the first electride in 1980s, and it was the first to produce a room-temperature-stable organic electride in 2005. The first room-temperature-stable electride was inorganic and due to Prof. Hosono, see below).

Barely a handful of electrides have been synthesized and only three of them are stable at room temperature. Electrides show particular magnetic (exalted susceptibilities), chemical (organic synthesis, preparation of nanoscale metal and alloy particles), electric (an ideal electride should be a (Mott) insulator) and optical properties (low optical spectra peaks as compared to alkali anions; large nonlinear optical properties). Large second hyperpolarizabilities make electrides of high interest due to their potential utilization in optical and opto-electronic devices. Indeed, electrides have found a plethora of diverse applications, including the catalysis of the ammonia synthesis, its usage as reversible H2 storage devise, electron emitters and chemical reagents —to mention a few. All these applications are due to the group of Prof. Hosono, who synthesized the last two electrides: [Ca24Al28O68]·4e− and [Ca2N]+·e−

Unfortunately, electrides are difficult to synthesize and identify because their experimental characterization is only possible by indirect means. The density of a free electron (or a handful of them) is not large enough to be located in the X-ray of a crystal structure. As a consequence, the presence of isolated electrons in electrides always comes from indirect evidences such as the similarity of this structure with analog alkalides, the chemical shift of the corresponding cation (133Cs), EPR studies, magnetic susceptibilities, electrical resistivity or optical reflectance experiments. These evidences merely suggest the presence of an electride; they do not guarantee its existence.

In our paper we provide an unambiguous computational means to distinguish electrides from similar species, proving the existence of some electrides in gas phase. In contrast with solid state, we use the term molecular electrides for the gas-phase species. The molecular electrides studied in this work were previously characterized by frontier molecular orbital analysis and large nonlinear optical properties. Namely, these studies found an occupied orbital with large density values in the vicinity of the position where one would expect the isolated electron of the electride. Some works also included large second hyperpolarizabilities to support the discovery of a molecular electride. However, neither of these criteria are enough to assess the existence of an electride, as we have also proved in this work.

The electron localization function (ELF) and the non-nuclear attractors of the electron density were used to characterize solid-state electrides. Our study proves that these properties are actually necessary conditions for the existence of electrides. However, these features also show in molecules that do not have an electride structure such as acetylene. In our work we show that large nonlinear optical properties can be used in conjunction with the latter techniques to unambiguously characterize electrides.

The electronic structure of electrides shows an important signature: a maximum of the electron density in a non-nuclear position. This rare feature opens a new route towards the design of new electrides. We currently study the possibility to enforce non-nuclear maxima of the electron density (NNA). Since NNA are not a frequent feature of molecular densities, its mere existence increases the probability of having an electride. We believe that learning how to construct molecules with NNAs could pave the way towards the design of new electrides.

AccuCT. Eloy's Marie Curie Project

Posted on March 20, 2015 at 5:30 PM

Eloy and I have been working together for the past two years. At some point, it occurred to us studying the first stages of the physical processes taking place in dye-sensitized solar cells (DSSC). It all started as a mere simple exercise to motivate young students to try computational chemistry research. Little by little, we have familiarized ourselves with the computational techniques used (there is still a long way to go) and that's how we started working on charge-transfer and time-dependent processes. The natural tool to study time-dependent processes in large molecules is the well-known time-dependent density funcional theory (TDDFT). Since I was already working on the design of new DFT methods, it was only natural to apply the same strategy to time-dependent DFT. Merging all these pieces is how AccuCT (after the development of an accurate charge-transfer computational method), Eloy's postdoctoral subject, was born. 

The project was then put down into words and submitted to the cruelly competitive Marie Curie Global Fellowship application. The good news came at the beginning of this year: his project was granted. This is awesome news for Eloy's research career and it also guarantees the funds to carry out AccuCT. The project will start on 2016, when Eloy will move to Martin Head-Gordon's group in Berkeley and it will finish in 2018, a year we will spend working together at the DIPC. 

Addendum 11/05/2015:

Some statistics about the MSCA-IF-2014-GF have been leaked. The % success is 11.2% (all proposals) and the Spanish success is 7.6% (only 14 proposals granted).