Real-Time Propagation TDDFT and Density Analysis for Exciton Couplings Calculations in Large Systems

Photo-active systems are characterized by their capacity of absorbing light energy and transforming it. Usually, more than one chromophore is involved in the light absorption and excitation transport processes in complex systems. Linear-Response Time-Dependent Density Functional (LR-TDDFT) is commonly used to identify excitation energies and transition properties by solving well-known Casida's equation for single molecules. However, this methodology is not useful in practice when dealing with multichromophore systems. In this work, we extend our local density decomposition method that enables to disentangle individual contributions into the absorption spectrum to computation of exciton dynamic properties, such as exciton coupling parameters. We derive an analytical expression for the transition density from Real-Time Propagation TDDFT (P-TDDFT) based on Linear Response theorems. We demonstrate the validity of our method to determine transition dipole moments, transition densities and exciton coupling for systems of increasing complexity. We start from the isolated benzaldehyde molecule, perform a distance analysis for $\pi$-stacked dimers and finally map the exciton coupling for a 14 benzaldehyde cluster.Comment: 32 pages, 8 figures; added references in introductions, typos fixe

Error estimation in IBM Quantum Computers

One of the main important features of the noisy intermediate-scale quantum (NISQ) era is the correct evaluation and consideration of errors. In this paper, we analyze the main sources of errors in current (IBM) quantum computers and we present a useful tool (TED-qc) designed to facilitate the total error probability expected for any quantum circuit. We propose this total error probability as the best way to estimate the fidelity in the NISQ era, mainly because we do not have to compare our quantum calculations with any classical one. In order to contrast the robustness of our tool we compute the total error probability that may occur in three different quantum models: 1) the four-electron Ising model, 2) the Quantum-Phase Estimation (QPE) and 3) the Grover's algorithm. For each model, we compute a statistically significant sample size for both the expectation value of the related observable and the fidelity, comparing them with the value calculated in the simulator as a function of the error probability. The analysis is satisfactory in more than the $99\%$ of the cases. In addition, we study how the error mitigation techniques are able to eliminate the noise induced during the measurement.Comment: 9 pages, 8 figure

A Definition of the Magnetic Transition Temperature Using Valence Bond Theory

Macroscopic magnetic properties are analyzed using Valence Bond theory. Commonly the critical temperature TC for magnetic systems is associated with a maximum in the energy-based heat capacity Cp(T). Here a more broadly applicable definition of the magnetic transition temperature TC is described using the spin moment expectation value (i.e., applying the spin exchange density operator) instead of energy. Namely, the magnetic capacity Cs(T) reflects variation in the spin multiplicity as a function of temperature, which is shown to be related to ∂[χT(T)]/∂T. Magnetic capacity Cs(T) depends on long-range spin interactions that are not relevant in the energy-based heat capacity Cp(T). Differences between Cs(T) and Cp(T) are shown to be due to spin order/disorder within the crystal that can be monitored via a Valence Bond analysis of the corresponding magnetic wave function. Indeed the concept of the Boltzmann spin-alignment order is used to provide information about the spin correlation between magnetic units. As a final illustration, the critical temperature is derived from the magnetic capacity for several molecular magnets presenting different magnetic topologies that have been experimentally studied. A systematic shift between the transition temperatures associated with Cs(T) and Cp(T) is observed. It is demonstrated that this shift can be attributed to the loss of long-range spin correlation. This suggests that the magnetic capacity Cs(T) can be used as a predictive tool for the magnetic topology and thus for the synthetic chemists

Electronic Descriptors for Supervised Spectroscopic Predictions

Spectroscopic properties of molecules holds great importance for the description of the molecular response under the effect of an UV/Vis electromagnetic radiation. Computationally expensive ab initio (e.g. MultiConfigurational SCF, Coupled Cluster) or TDDFT methods are commonly used by the quantum chemistry community to compute these properties. In this work, we propose a (supervised) Machine Learning approach to model the absorption spectra of organic molecules. Several supervised ML methods have been tested such as Kernel Ridge Regression (KRR), Multiperceptron Neural Networs (MLP) and Convolutional Neural Networks. The use of only geometrical descriptors (e.g. Coulomb Matrix) proved to be insufficient for an accurate training. Inspired on the TDDFT theory, we propose to use a set of electronic descriptors obtained from low-cost DFT methods: orbital energy differences, transition dipole moment between occupied and unoccupied Kohn-Sham orbitals and charge-transfer character of mono-excitations. We demonstrate that with this electronic descriptors and the use of Neural Networks we can predict not only a density of excited states, but also getting very good estimation of the absorption spectrum and charge-transfer character of the electronic excited states, reaching results close to the chemical accuracy (~2 kcal/mol or ~0.1eV)

Pitfalls on evaluating pair exchange interactions for modelling molecule-based magnetism

Molecule-based magnetism is a solid-state property that results from the microscopic interaction between magnetic centres or radicals. The observed magnetic response is due to unpaired electrons whose coupling leads to a particular magnetic topology. Therefore, to understand the magnetic response of a given molecule-based magnet and reproduce the available experimental magnetic properties by means of statistical mechanics, one has to be able to determine the value of the J(AB) magnetic exchange coupling between radicals. The calculation of J(AB) is thus a key point for modelling molecule-based magnetism. In this Perspectives article, we will build upon our experience in modelling molecular magnetism to point out some pitfalls on evaluating J(AB) couplings. Special attention must be paid to the cluster models used to evaluate J(AB), which should account for cooperative effects among J(AB) interactions and also consider the environment (counterions, hydrogen bonding) of the two radicals whose interaction has to be evaluated. It will be also necessary to assess whether a DFT-based or a wavefunction-based method is best to study a given radical. Finally, in addition to model and method, the J(AB) couplings have to be able to adapt to changes in the magnetic topology due to thermal fluctuations. Therefore, it is most important to appraise in which systems molecular dynamics simulations would be required. Given the large number of issues one must tackle when choosing the correct model and method to evaluate J(AB) interactions for modelling magnetic properties in molecule-based materials, the "human factor" is a must to cross-examine and challenge computations before trusting any result.MD, JRA, and JJN acknowledge financial support from MINECO (CTQ2017-87773-P/AEI/FEDER, UE), Spanish Structures Excellence Maria de Maeztu program (MDM-2017-0767), and Catalan DURSI (2017SGR348)

Pitfalls on evaluating pair exchange interactions for modelling molecule-based magnetism

Molecule-based magnetism is a solid-state property that results from the microscopic interaction between magnetic centres or radicals. The observed magnetic response is due to unpaired electrons whose coupling leads to a particular magnetic topology. Therefore, to understand the magnetic response of a given molecule-based magnet and reproduce the available experimental magnetic properties by means of statistical mechanics, one has to be able to determine the value of the JAB magnetic exchange coupling between radicals. The calculation of JAB is thus a key point for modelling molecule-based magnetism. In this Perspectives article, we will build upon our experience in modelling molecular magnetism to point out some pitfalls on evaluating JAB couplings. Special attention must be paid to the cluster models used to evaluate JAB, which should account for cooperative effects among JAB interactions and also consider the environment (counterions, hydrogen bonding) of the two radicals whose interaction has to be evaluated. It will be also necessary to assess whether a DFT-based or a wavefunction-based method is best to study a given radical. Finally, in addition to model and method, the JAB couplings have to be able to adapt to changes in the magnetic topology due to thermal fluctuations. Therefore, it is most important to appraise in which systems molecular dynamics simulations would be required. Given the large number of issues one must tackle when choosing the correct model and method to evaluate JAB interactions for modelling magnetic properties in molecule-based materials, the "human factor" is a must to cross-examine and challenge computations before trusting any result

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light–matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).This work was supported by the European Research Council (Grant No. ERC-2015-AdG694097), the Cluster of Excellence “Advanced Imaging of Matter” (AIM), Grupos Consolidados (IT1249-19), and SFB925. The Flatiron Institute is a division of the Simons Foundation. X.A., A.W., and A.C. acknowledge that part of this work was performed under the auspices of the U.S. Department of Energy at Lawrence Livermore National Laboratory under Contract No. DE-AC52-07A27344. J.J.-S. gratefully acknowledges the funding from the European Union Horizon 2020 Research and Innovation Program under the Marie Sklodowska-Curie Grant Agreement No. 795246-StrongLights. J.F. acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG Forschungsstipendium FL 997/1-1). D.A.S. acknowledges University of California, Merced start-up funding.Peer reviewe

Estudi Teòric mitjançant Mètodes "Bottom-Up" de la Interacció Magnètica en Sòlids Moleculars

[cat] Aquesta tesi doctoral s'emmarca dins de la Química Computacional. Usant el procediment de Primers Principis Bottom-Up, es pot relacionar les propietats magnètiques microscòpiques d'un cristall moleculars (interaccions magnètics, J) amb les macroscòpiques. Aquesta relació té lloc a partir de la definició de la topologia magnètica. Els projectes desenvolupats al llarg de la tesi han permès establir els mecanismes d'interacció magnètica de diversos cristalls moleculars, buscant així ampliar el coneixement sobre els factors que regulen el comportament magnètic, i continuar una base de dades per trobar una relació magnetoestructural que permeti el disseny racional de materials magnètics amb propietats tecnològiques desitjades. Els tres primers capítols presenten una introducció i una descripció detallada del procediment de Primers Principis Bottom-Up aixi com els fonaments teòrics necessaris. El capítol 4 està dedicat a l'estudi dels mecanismes d'interacció magnètica a través de l'espai o aquella que és assistida. S'ha estudiat la influència en la transmissió de la interacció magnètica de l'anell de piridina entre dos radicals de verdazil en el cristall de verdazil-piridil:hidroquinona. El capítol 5 es centra en l'estudi de l'efecte cooperatiu en la propagació de les interaccions magnètiques. Aquí, s'ha estudiat un gran ventall de cristalls moleculars que presenten diferents topologies magnètiques (d'1D a 3D), i s'ha investigat el canvi de la resposta magnètica. Cal remarcar que tots els resultats de l'estudi teòric del magnetisme d'aquests cristalls han estat contrastats amb dades experimentals. Així doncs, el primer compost estudiat és el cristall CUPZ(N03)2, el qual es considera un prototip de cadena antiferromagnètica, i s'intenta donar una explicació al canvi de dimensionalitat magnètica observat en experiments recents. En segon lloc, es disposa l'estudi del magnetisme del cristall [(dmpyH)2CuBr4] el qual presenta una comportament magnètic d'strong-rail spin-ladder. En aquest treball s'argumenta la necessitat d'incorporar els contraions en el càlcul de les l. Emmarcats en aquesta topologia, es mostren els resultats obtinguts en la comparació de dos cristalls anàlegs, Cu(2,3-dmpz)Ch y Cu(2,3-dmpz)Br2. Les diferències en el comportament magnètic es poden argumentar en base als resultats de l'estudi teòric. El següent apartat està dedicat a l'estudi del cristall [(5MAP)2CuBr4]. L'estudi teòric demostra un comportament com bulk antiferromagnet, corrobora la dificultat de discriminar entre topologies 2D i 3D a partir de mesures de la susceptibilitat magnètica. El quart projecte d'aquest capítol estudia compostos que presenten un comportament magnètic tridimensional. Es descriu el comportament del cristall [(5FAP) 2CuCI4], ja que experimentalment no es podia assignar correctament els valors de les interaccions magnètiques per falta de models analítics 3D. També es descriu el comportament de bulk ferromagnet del compost [p-02N-C6F6-CNSSN]. Comparant els valors de les temperatures de transició magnètica obtingudes per altres cristalls orgànics es conclou que la T(c) no només depèn de la magnitud de les J, sinó també de la topologia. Finalment, es va estudiar la importància de l'ús d'estructures cristal.lines determinades a una temperatura pròxima a la que té lloc el fenomen a estudiar. Es mostra el canvi de dimensionalitat magnètica que presenta el cristall [(dmpyH)2CuBr4] en anar dismimuïnt la temperatura. L'últim capítol té un caràcter més fonamental on s'analitza les expressions i derivacions de les propietats magnètiques macroscòpiques i es donen els primers passos per interpretar la informació continguda en la funció d'ona magnètica. Es presenten els resultats inicials de l'estudi a nivell quàntic del magnetisme en cristalls moleculars, fent una nova interpretació de les expressions i dels fenòmens magnètics que comporten. Aquest anàlisi es fa a partir de Ies dades que s'obtenen en la diagonalització de l'Hamiltonià de Heisenberg com són les energies i multiplicitats d'spin dels nivells magnètics, així com per primera vegada dels valors de la matriu de densitat d'intercanvi d'spin [Pij].[eng] This PhD Thesis is embedded on the Computational Chemistry field. The First Principles Bottom-Up Procedure allows us to relate the microscopic magnetic properties of molecular crystals (i.e. the magnetic interaction values with the macroscopic magnetic properties (magnetic susceptibility magnetization M or heat capacity Cp). This relationship comes from the most important step in our work procedure: the description of the magnetic topology.. First, the study of the different magnetic interaction mechanisms and its competition are studied, i.e. the direct through space mechanism vs. the assisted through molecule magnetic interaction. Then, the study of the cooperative effects of the magnetic interaction propagation will be detailed. Keeping in mind this objective, the magnetism of a big variety of real molecular magnets which present different magnetic topology (from 1D to 3D) have been investigated. This study allows us to increase the knowledge about the factors that governs the macroscopic magnetic behaviour, and able us to construct a database to find a magneto-structural relationship to make a rational design of new magnetic materials with desired properties. Finally, the derivations and expressions of the macroscopic magnetic properties have been reviewed in order to make the first step to get a physical interpretation of the information contained therein the magnetic wave function

Revising the common understanding of metamagnetism in the molecule-based bisdithiazolyl BTDMe compound

The BDTMe molecule-based material is the first example of a thiazyl radical to exhibit metamagnetic behavior. Contrary to the common idea that metamagnetism occurs in low-dimensional systems, it is found that BDTMe magnetic topology consists of a complex 3D network of almost isotropic ferromagnetic spin-ladders that are coupled ferromagnetically and further connected by some weaker antiferromagnetic interactions. Calculated magnetic susceptibility χT(T) data is in agreement with experiment. Calculated M(H) data clearly show the typical sigmoidal shape of a metamagnet at temperatures below 2 K. The calculated critical field becomes more apparent in the dM/dH(H) plot, being in very good agreement with experiment. Our computational study concludes that the magnetic topology of BDTMe is preserved throughout the entire experimental range of temperatures (0-100 K). Accordingly, the ground state is the same irrespective of the temperature at which we study the BDTMe crystal. Revising the commonly accepted understanding of a metamagnet explained as ground state changing from antiferromagnetic to ferromagnetic, the Boltzmann population of the different states is here suggested to be the key concept: at 2 K the ground singlet state has more weight (24%) than at 10 K (1.5%), where excited states have an important role. Changes in the antiferromagnetic interactions that couple the ferromagnetic skeleton of BDTMe will directly affect the population of the distinct states that belong to a given magnetic topology and thus its magnetic response. Accordingly, this strategy could be valid for a wide range of bisdithiazolyl BDT-compounds whose magnetism can be tuned by means of weak antiferromagnetic interactions