# Dynamical processes in complex quantum systems: from theoretical developments to energy harvesting and storage (DYNAPLEX)

#### MEC y MICINN

*Status: finished project*

**Contract Number:**

*FIS2010-21282-C02-01*

Advancements in new technologies, including the pressing need for energy conservation, storage, and conversion, require new materials. In this respect corrosion protection, new semiconductors, batteries, and catalysis quite obviously represent some of the crucial research areas. For example, the light-conversion process in photovoltaic devices ("artificial photosynthesis") or photo-catalytic water splitting cells (a carbon neutral way to produce hydrogen for a "hydrogen-based economy") takes place on the atomic or molecular scale. Current experimental techniques, however, lack the necessary resolution or the data is convoluted by intrinsic or extrinsic factors (temperature, defects, impurities, solvents, etc.). Therefore many open questions in the fundamental understanding of photovoltaic and photo-catalytic processes remain, whose resolution would expedite progress in device design. This is the domain of theoretical spectroscopy - the domain of quantum-mechanical calculations of elementary excitations on the atomic scale and clearly the domain of application of the present DynaPlex project.

The goal of the project has been divided in three main subjects according to the nature of the activities being performed. First, Fundamental issues and methodological developments to handle charge-transfer processes, highly correlated oxides and Mott-insulators, and develop new algorithms to address molecular dynamics including non-adiabatic effects, electron delocalization, and bond-breaking phenomena. Second, a set of Practical objectives ranging from photocatalysis to thermoelectricity and energy harvesting in hybrid solar cells. Finally, Biophysics and biotechnology looks at the control of nanocapilarity by light, the photophysics of fluorescent proteins, and the microscopic mechanisms behind the first step of photosynthesis (towards "artificial photosynthetic" units). Achieving a "first-principles spatially and time resolved multi-scale spectroscopic modelling tool-box" not only means meeting the challenges of clean energy solutions, but also many other old and new challenges appearing in material science, chemistry, biomedicine, and nanotechnology as well.

## Open positions

**INTRODUCTION**

__ General description of the project__

Our goal with this project is to consolidate an interdisciplinary world-reference Spanish collaborative team in Theoretical Condensed Matter and Computational Physics in what is now starting to be known as Theoretical Spectroscopy. With this goal in mind, we will provide a general ab-initio toolbox (theoretical framework), that can be used to describe, explain, and predict the structural, chemical, and spectroscopic properties of atoms, molecules, clusters, surfaces, and solids, (without the inclusion of any external, semi-empirical or empirical, parameters in order not to bias its predictions or its interpretations of experiments). Besides theoretical and consequent computing implementations we will address highly relevant topics in nano- and bio-physics and material science.

Spectroscopy essentially deals with the excitation of a system as a response to an external perturbation. To interpret or design this kind of experiments, one needs to make use of theoretical approaches beyond the present standard model of solid-state physics, namely density-functional theory (DFT). In fact, DFT is a ground-state theory and, in principle, by solving the Kohn-Sham (KS) equations one can have access to properties like the electronic density or the total energy of the system. These calculations can be done in a very efficient way adopting the local-density approximation (LDA) or even more sophisticated approximations. However, the eigenvalues of the Kohn-Sham equations cannot be interpreted as excitation energies. An accurate description of such excited states can be obtained in the framework of many-body perturbation theory (MBPT) or, in certain cases, using time-dependent density functional theory (TDDFT). They are complementary approaches. MBPT has a relative conceptual clarity and therefore allows one to find good approximations, but calculations are in general very demanding. DFT-based approaches are more efficient, but a fully reliable description of exchange-correlation (XC) effects within TDDFT is difficult to obtain. For these reasons, a great effort in the last years has been made in combining the advantages of both methods.

In MBPT the key variables are the Green's functions, which describe the propagation of effective particles ("quasiparticles") and give access to one-particle excitations, as measured in photoemission, or to neutral excitations, as measured e.g. in optical absorption, electron-energy loss (EELS) or inelastic X-ray scattering (IXS). Standard theoretical techniques in this context are the GW approximation for photoemission and the Bethe-Salpether equation (BSE) for absorption, EELS and IXS. In the GW approximation one takes for the self-energy, which is a non-local, non-Hermitian, and frequency-dependent potential, the product of the Green's function G and the dynamically screened Coulomb interaction W. In this way, one neglects the so-called vertex corrections, which are responsible, for instance, for excitonic effects in the screening. Then, in the BSE one further takes into account the interaction between the electron and the hole, which constitute the neutral excitations that are directly probed by absorption experiments. One can use TDDFT to address neutral excitations, but then one has to find reliable approximations to describe the electron exchange and correlation (XC) terms. This has the added difficulty of it being necessary to have the correct description of the dynamic effects within the XC potential, which is also indispensable to analyze nonlinear phenomena (e.g. for femtosecond or attosecond dynamics) where the response of the electron system to an external probe cannot be treated as a perturbation. Concerning the linear-response regime there have been very interesting progresses in the representation of the dynamic part of the XC kernel, which have provided a way of describing adequately excitonic effects in a broad class of materials, ranging from nanosystems to bulk solids. In correlated materials, thanks to their extreme sensitivity, even local excitations with light can trigger a macroscopic phase transition by virtue of a cooperative interaction of the different degrees of freedom of the system (e.g. electronic, structural, and magnetic). Hence, photoinduced phase transitions provide an important approach to investigate the physical pathway connecting different correlated electron states as well as their mutual competition. On the other side, time-resolved spectroscopy measurements of photoinduced phase transitions are very demanding, because they require a simultaneous access to the femtosecond dynamics of more than one degree of freedom of the system.

There have been impressive improvements in this field during the last few years, including new theoretical paradigms and the development of more efficient computational tools (from our presently running national project fancy-nano). This allows us to tackle the ab-initio description of a wide range of systems, which combine structural complexity and a rich phenomenology. Thus, theoretical spectroscopy has become a powerful tool with predictive accuracy. Nevertheless, still there are many open theoretical questions, the need of new methodological implementations of the latest theoretical developments and, what is more important, application fields (basically within the nano- and bio-technology, functionalized materials design and, in general, in complex systems) that ask for an extensive use of ab-initio tools.

Based on these motivations the proposed project, Dynamical processes in complex quantum systems: from theoretical developments to energy harvesting and storage (DynaPlex), will directly address fundamental problems related to the characterization of the electronic properties and its application to complex systems. These properties, regardless of the object being studied and their static (structural) or dynamic character (response or transport), will be determined by applying and developing common theoretical (DFT, TDDFT, MBPT) and computational tools where the participating researchers have a well-recognized expertise. To organize the description of the planed activities we have divided the project in three different, although interconnected, branches. First, we will consider basic research challenges concerning the development of new theoretical tools and its implementation on suitable computer codes. This includes the critical discussion of the approximations that build the state-of-the-art ab-initio calculations of electronic structure and the theoretical spectroscopy. Second, we will tackle the study of specific problems having special relevance in applied nanoscience such as molecular electronics, new photovoltaic materials, thermoelectricity, and photocatalysis. Finally, a third research line will be devoted to applications in biological processes, a field where one of the partners (Donostia) has gained a worldwide recognition in the last years.

The collaboration with other groups will be essential for the successful enforcement of the whole research. In this respect, we must mention that the two partners (Donostia and Madrid) are playing an active role in the development of the European Theoretical Spectroscopy Facility (ETSF) (URL: http://www.etsf.eu). The ETSF is a distributed knowledge network that provides theoretical expertise to further the understanding of the properties of materials, chemicals, and biological processes for applications across both public and private sectors. Donostia hosts the Vice-presidency for Scientific Development of the ETSF, and its activities will greatly help the proper attainment of the different research lines within the DynaPlex project. Reciprocally, some of the research objectives of the proposed project will contribute to the consolidation of the leading scientific role of Spain in the ESTF venture. This international projection constitutes a significant benefit for the project, whose main scientific aspects are described in the following.

__ Fundamental theoretical issues and methodological developments__

The proponents have made important contributions to the foundations of DFT, TDDFT, and MBPT. Then, theoretical developments will constitute an essential part of the proposed activities that, on the other hand, are required ingredients to fulfil the more applied objectives.

The simulation of molecular systems as energy-conserving, closed quantum mechanical objects is an idealization since every system interacts with its environment to a certain degree. However, due to obvious reasons, most of the molecular electronic structure approaches to date have concentrated on the simulation of time-independent or time-dependent systems that do not interact with quantum environments. To fill this gap, we will pursue a consistent formulation of time-dependent DFT for open quantum systems (F1), an activity that will be complemented with a more fundamental study of quantum phase transitions (F2).

The study of molecular aggregates has opened a number of questions about the intrinsic nature of the chemical bond (F3), which explains their stability and chemical properties. Many of these aggregates lie in the nanoscale and, therefore, their chemical properties show remarkable differences with respect to the basic molecular constituents. Although quantum-chemistry calculations are feasible for these systems, we want to address a more fundamental understanding of the chemical bond in such systems. We will study the electron localization in molecular bonds and the electronic delocalization that appears in molecular aggregates. The well-known method of the electron localization function (ELF) and Bader’s theory of atoms in molecules (AIM) will provide the theoretical framework to study these respective issues.

In DynaPlex, we will put considerable effort in the construction of reliable functional approaches for applications of DFT and TDDFT (F4). This topic is rather broad and includes the development of “orbital-free” functionals for the electron exchange energy showing a favourable scaling with respect to the system size, correlation-energy functionals based on a recent generalized hydrodynamic approximation to evaluate dispersion van der Waals forces, and new forms for the exchange-correlation kernel aimed to describe double excitations properly. The study of degenerate confined systems (F5) is closely related to this research line, as it provides a stringent assessment of existing functional approaches and provides clues for further improvement, with relevance in the characterization of biomolecular systems and molecular dissociation.

Another objective is a better understanding of strong electronic correlation in transition-metal oxides (F6). We aim at filling the gap between the field of parameter-free methods (TDDFT, GW) and modelling based on parametrized Hamiltonians (Hubbard, Anderson, etc.). Novel theoretical developments, such as the GW+Dynamical mean field theory (DMFT) scheme, will be treated within this objective.

We will also investigate the Mott transition in a hydrogen chain using variational Monte Carlo simulations (F7). This type of phase transition is due to strong electronic correlations, which are beyond the realm of standard local or semi-local Density Functional Theory approximations. Besides the physical insights, we will provide a stringent benchmark system to assess the reliability of new DFT tools.

The implementation of the effective optimized potential (OEP) method in LCAO formalism (F8) is a methodological objective motivated by the necessity of robust, reliable, and reasonably fast computational tools able to study charge-transfer excitations in large biomolecules or molecular aggregates. Such processes can be studied using well-known quantum chemistry methods such as CAS-SCF, CASPT2 or CASR3. However, they do not show good scaling properties with the system size and therefore are unsuitable, for instance, when analyzing organic materials that are relevant in the development of new photovoltaic cells.

__ Practical objectives (applications)__

The ab-initio study of photocatalysis and quantum transport in low-dimensional systems (P1) will be our first objective under this section. We will concentrate on the study of the electronic, structural, and spectroscopic properties of 1D and 2D systems for nanoelectronics, nanosensing, and photocatalysis. Regarding transport properties, the analyses are often done using standard DFT-based methods. To circumvent their inherent limitations, we will use an approach based on advanced van der Waals functionals for structural properties and GW-or TDDFT-based approaches to quantum transport instead. In a last stage, we will contribute to close the gap between coherent transport calculations and actual realizations by using “divide-and-conquer” strategies. On the other hand, hydrogen production via photocatalysis has important implications due to the increasing need for cleaner burning fuels and more viable forms of renewable energy. In this process, TiO2 has been the catalyst of choice. We will pursue the description of the photocatalytic activity of the metal oxide through an accurate description of optical excitations in the material using TDDFT.

A second objective is the TDDFT description of quantum transport in molecular electronics devices (P2). The TDDFT-based approach to quantum transport is a very promising alternative, since it allows the description of many-body effects at a relatively affordable computational cost. In this objective we will apply this technique to realistic macromolecular juntions and compare the results with ongoing experimental measurements.

Our next goal is the first-principles analysis of thermoelectric materials (P3). As it is well known, a temperature gradient can produce electrical energy via the Seebeck’s thermoelectric effect, and the reverse operation (Peltier effect) is also possible. Both have found technological applications, but mostly confined in the realm of scientific laboratories because of the lack of efficient materials. We could improve such efficiency by increasing the electric conductance or by reducing the thermal conductivity. Unfortunately, neither are independent in bulk materials, and little can be done to vary them separately. However, the two are almost independent in nanosystems and this opens the way to mainstream applications. We will pursue a unified microscopy theory of thermal and electrical transport beyond linear response. To do so, we will use the Stochastic TDDFT, which combines a stochastic approach to investigate the dynamics of a system couplet to its environment and the DFT methods to study the time evolution of a many particle system. This will allow us to evaluate the thermoelectric efficiency for a range of nanostructures.

Finally, we will investigate nanostructures with actual interest in the development of a new generation of solar cells. In particular, we will focus on dye-sensitized semiconductor solar cells. In this type of devices, organic dyes are adsorbed on a highly porous nanocrystalline TiO2. Visible light excites the dye-sensitizer molecules from the ground state, which is located energetically in the semiconductor band gap, to an excited state resonant with the TiO2 conduction band. The electron is transferred to the semiconductor on an ultrafast timescale, travelling to one of the electrodes. Since changes in the geometry of the oxide substrate can improve the overall efficiency of the device, we will study the photoabsorption properties of small organic chromophores adsorbed on TiO2 extended structures (P4).

__ Biophysics and biotechnology__

In the last few years, novel theoretical developments and the increase of computational power have opened the room to tackle first-principles descriptions of excited-state properties of large electronic systems (thousand of atoms) of biological interest. Due to the inherent complexity of these systems and processes, theoretical studies were often done using empirical or semi-empirical models. Such models are indeed suitable to analyze the adiabatic dynamics of very large systems for long times, but they require a previous deep understanding of the system and processes themselves. Furthermore, this methodology lacks of predictive accuracy when excited-state properties are important. In this third part of the DynaPlex Project, we will try to circumvent these limitations by following a multi-scale bottom-up approach that includes several levels of theoretical description. Thus, we will use fully first-principles approaches for regions where a precise and flexible description of the processes is required; empirical Hamiltonians to analyze larger portions of the systems where excited states properties are crucial; and classical molecular mechanics or macroscopic models to incorporate the environment of the system. The first-principles approach will be based on TDDFT, which represents an ideal trade-off between accuracy and numerical cost. Besides the need to exploit the capabilities of current and near-future petaflot supercomputing, the successful completion of the selected goals requires new prescriptions of TDDFT that incorporate the relevant physics for biosystems. Hence, we cannot disentangle these set of objectives with the theoretical developments described in subsection "Fundamental theoretical...".

A first example of this multi-scale approach is the study of excited-state properties of water as it permeates through nanochannels (B1). Nanochannels (tubular structures with a diameter in the 1-100 nm range and lengths from few nanometers up to several microns) have been a hot topic in recent literature, in particular because they have many applications in very different areas: physics, chemistry, biology, optics, medicine, energy, and environmental sciences. The motivation of the present study is the fact that external fields, instead of osmotic or hydrostatic pressure, can drive the permeation of water through nanochannels. This opens the way to a whole set of nanofluidic techniques, with many potential innovative applications. The permeation mechanism has already been extensively studied, but not the changes in the properties of the water molecules themselves, the latter being our specific objective. This work will contribute to a better understanding of the mechanisms associated to both artificial nanoscale tubular structures and natural ones. This work will also provide indirect insights into what happens in biological cells, e.g. in membrane proteins, and helpful information for designing highly tuneable artificial nanochannels.

In a second objective, understanding the photophysics of fluorescent proteins (B2), we will concentrate on one of the most revolutionary achievements in molecular biology in the last years: the bioengineering of fluorescent proteins (FP). Since the first application of the Green Fluorescent Protein (GFP), the photophysical properties of such proteins have been improved and modified to optimize their application in various novel in vivo imaging techniques. The engineering of FPs has produced new variants emitting in the blue, cyan, yellow, and even far-red range of the spectrum, creating a new palette of promising new features. However, they can be limited because these new FPs lack unique characteristics of the GFP family such as brightness, photostability, and fluorescence at low pH. Therefore, a great need is perceived to better understand the photophysics of the GFP chromophore and its derivatives in the newly designed FPs, and how the protein environment controls it. Our goals will be the validation of experimentally derived models for the photo-induced processes in FPs and the systematic determination of the factors that control ab-sorption/emission wavelength, absorptivity, and ﬂuorescence quenching via internal conversion. In particular, we shall investigate the effects on the optical properties and excited-state dynamics due to the electrostatic and steric interactions in hydrogen bonded networks between chromophores and binding pockets.

The next objective, ab-initio calculation of the electronic circular dichroism for guanine-cytosine base pairs (B3) is part of the collaborative scientific activities under the ETSF initiative. The objective B3 concerns the theoretical study of the optical signals of hydrogen bonds that are involved in the triplex formation between protonated cytosine, guanine, and neutral cytosine in DNA derivatives. In particular, we evaluate, using state-of-the-art TDDFT techniques, the circular dichroism spectra to support and interpret the synchrotron radiation data. This objective is relevant not only to understand biological processes, but also for the possibility of using these molecules for molecular electronic purposes.

Finally, ab-initio simulation of photosynthesis (B4) is the most ambitious objective of our project (and a long-term one that bypasses the duration of the present project). From a molecular point of view, it is a complex process where the basic unit for light absorption is the chlorophyll molecule. It combines with other chromophores and proteins to form the different complexes that take part in photosynthetic processes. In brief, the photosynthesis begins with the absorption of light by chromophores (light harvesting), an exciton is created, and the latter travels through a network of chromophores and reaches a reaction center. Here, the exciton dissociates and the excitonic energy is transformed into chemical energy. We will focus just on the first part of the process but even in this case, this objective demands a multidisciplinary approach (theoretical spectroscopy, quantum dynamics, statistical mechanics, etc.) and high-performance computing. In addition, we will require novel theoretical formulations and, from this perspective, the DynaPlex project is the ideal framework to carry out this high-risk and cutting-edge investigation.

### Objectives

The research objectives of the coordinated project DynaPlex are built around the latest developments of theoretical condensed matter techniques applied to the ab-initio description of electron dynamical processes. Whereas some of the objectives lie in the field of pure basic research, focusing on fundamental aspects of electronic structure properties, other ones try to push the limits in the ab-initio description of electron properties of real materials. The latter form a series of ambitious and cutting-edge investigations with a direct and immediate impact in the emerging fields of applied nanoscience and biophysics. In spite of the diversity of topics, all of them can be tackled under a coordinated effort thanks to their common methodological background. As a whole, the proposed project is a good example of synergy between formal development and applicability, where theoretical approaches, advanced numerical simulations, and comparison with experimental results coexist.

The members of the two groups have a well-recognised experience in the development and application of first-principles techniques for electronic structure. They have been able to build a stable collaborative scheme embedded in a broader European project (the ETSF), which provides the required human power and the international umbrella to fulfil the very different objectives of the project.

The diversity of research topics prevents one from defining a single starting hypothesis. On the contrary, the project tries to give some responses to the growing necessity for general explanation and analysis of electron processes in new realizations that, in many cases, have a clear implication in applied science. However, let us remark again that this diversity of objectives start from common methodological approaches on which the DynaPlex project is firmly based.

__ FUNDAMENTAL ISSUES AND METHODOLOGICAL DEVELOPMENTS__:

For the systems and processes to be studied in this project we need to develop new functionals able to handle charge-transfer processes, highly-correlated oxides and Mott-insulators, new theoretical frameworks to address molecular dynamics including non-adiabatic effects and bond-breaking phenomena, and implementations with favourable scaling with system size, all this not only for ground state but also for excited state properties . An important step forward in the proposal is the description of systems out of equilibrium. This field is completely new in density-functional schemes and will have tremendous implications to address transport (electronic and heat) as well as biological processes across many time and spatial scales. The specific objectives are the following:

F1: Development of a time-dependent density functional theory for open systems.

F2: Analysis of the canonical typicality in the framework of quantum phase transitions.

F3: Study of the localization and delocalization in the chemical bonding. A quantum chemistry approach.

F4: Construction of advanced functionals for DFT and TDDFT applications.

F5: Assessment of energy functionals in degenerated confined systems.

F6: Reach a better understanding of strong electronic correlation in transition-metal oxides.

F7: Study of the Mott transition in hydrogen chains using quantum Monte Carlo simulations.

F8: Development of a LCAO-based implementation for evaluating advanced XC potentials.

__PRACTICAL OBJECTIVES (APPLICATIONS)__:

We will apply the already developed techniques in the group (based on previous projects) and the new ones developed under objectives F to some selected highly topical applications: from photocatalysis, to thermoelectricity and energy harvesting in hybrid solar cells. Aspects such as thermal and electronic transport (triggered by the external light source) will be addresses in detail.

P1: Ab-initio description of photocatalysis in low-dimensional systems.

P2: A TDDFT approach to quantum transport: application to molecular electronics.

P3: First-principles analysis of thermoelectric materials.

P4: First-principle modelling of the excitation processes in dye-sensitized oxide-nanostructures for photovoltaic applications.

__BIOPHYSICS AND BIOTECHNOLOGY__:

The main goal here is to use density-functional and correlated approaches together with classical and coarse-grained schemes to handle the dynamics of biological systems triggered out-of-equilibrium by an external source. We will look to nanocapilarity control by light, fluorescent proteins as well as look at the microscopic mechanisms behind the first step of photosynthesis to try to pin-down the main effects and have a good starting point toward the development of "artificial photosynthetic" units (a long-term goal which is clearly beyond the present project).

We will address specific topics on each subject. The results will build the basis for future research in the Donostia group in this field, on which the team is already investing many human resources.

B1: Study of excited-state properties of confined water as it permeates through carbon nanotubes.

B2: Further understanding the photophysics of fluorescent proteins.

B3: Ab-initio calculation of the electronic circular dichroism for guanine-cytosine base pairs.

B4: Ab-initio simulation of photosyntesis.

### Personal

Donostia: A. Rubio. M. Gatti, L. Stella, D. Mowbray, R. D'Agosta

Madrid: P. Gª Aldea, J.E. Alvarellos, P. Gª González, Fernández

Bruno Torcal (phD student; supervisors: Prof. Rubio and Dr. Wanko)