Neste trabalho foram estudados os complexos de transferência (CTC) de carga formados por iodeto com os derivados piridínicos C4(4CP)+ e C3bis(4CP)2+ em solução. A formação de um CTC é caracterizada pelo surgimento de uma nova banda no espectro eletrônico de absorção, em solventes orgânicos como acetonitrila. Este tipo de sistema tem recebido muito interesse em diversos campos como, por exemplo, eletrônica orgânica, espectroscopia não linear, bioquímica, no ramo farmacêutico, etc. O complexo C4(4CP)+I- é caracterizado por uma banda de transferência de carga com máximo em 421 nm em acetonitrila. Cálculos das propriedades eletrônicas e das energias de excitação do complexo foram realizados usando a teoria do funcional da densidade e a teoria do funcional da densidade dependente do tempo. O emprego de funcionais de troca e correlação com correções de longo alcance foi essencial para a obtenção de resultados acurados para as energias de excitação. Usando os funcionais CAM-B3LYP e B97X-D, associados ao modelo contínuo PCM, foi possível descrever muito bem o máximo da banda experimental. No caso do C3bis(4CP)2+ foram encontradas diferentes estruturas possíveis para o complexo, que podem ser formadas pela associação de um ou dois I-. Em todos os casos apenas um dos I- participa da excitação, o que explica a estequiometria 1:1 observada experimentalmente. Uma visão mais aprofunda do comportamento do complexo em solução foi obtida usando a dinâmica molecular clássica. O campo de força foi ajustado para reproduzir os resultados de uma dinâmica por primeiros princípios de vácuo. A dinâmica clássica mostrou não haver dissociação em acetonitrila no complexo formado com o C3bis(4CP)2+. A banda calculada a partir das configurações amostradas da dinâmica está em excelente acordo com o resultado experimental. / In this work, we have studied theoretically charge-transfer complexes (CTC) formed by pyridinium derivatives with iodide. The formation of a CTC is characterized by the appearance of a new absorption band on the electronic spectra, in organic polar solvents like acetonitrile. These type of systems have recently received much interest in a broad variety of fields, for example, organic electronics, nonlinear spectroscopy, medical biochemistry, pharmaceutical industry, etc. The C4(4CP)+I- complex is characterized by the charge-transfer band with a maximum at 421 nm in acetonitrile. We have used density functional theory (DFT) and time dependent density functional theory (TDDFT) to calculate electronic properties and the excitation energies of the complex. Functionals with long-range corrections were essential in describing the charge-transfer excitations. CAM-B3LYP and wB97X-D associated with the polarizable continuum model predicts CT excitations in good agreement with experiment. Our results also indicates the existence of different conformations for the complex formed by the C3bis(4CP)2+ with iodide. Complexes were formed by the association of one or two I- to C3bbis(4CP)2+, but the charge transfer excitations were calculated from only one iodide to the aromatic ring, what explain why the stoichiometry 1:1 was observed. A better description of the complex in solution was obtained using classical molecular dynamics. The OPLS-AA force field was fine-tuned to reproduce the results of a first principle molecular dynamics for the complex. No dissociation were observed. The calculated charge-transfer band using configurations sampled from molecular dynamics is in excellent agreement with experiment.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-09-04T14:24:54Z No. of bitstreams: 1 rodrigofragadealmeida.pdf: 7192674 bytes, checksum: 6ae959161ccde060e031fade5c149253 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-09-04T15:52:10Z (GMT) No. of bitstreams: 1 rodrigofragadealmeida.pdf: 7192674 bytes, checksum: 6ae959161ccde060e031fade5c149253 (MD5) / Made available in DSpace on 2018-09-04T15:52:10Z (GMT). No. of bitstreams: 1 rodrigofragadealmeida.pdf: 7192674 bytes, checksum: 6ae959161ccde060e031fade5c149253 (MD5) Previous issue date: 2018-07-30 / A busca por fontes renováveis de energia cresce cada vez mais em diversas regiões do mundo devido a demanda crescente e pela poluição gerada pelo uso de combustíveis fósseis. A energia solar é uma fonte renovável e inesgotável de energia que pode ser aproveitada diretamente por diversos tipos de células solares. Entre estes variadostipos, as células solares sensibilizadas por corante (DSSCs em inglês) se mostram promissoras devido à sua alta eficiência. Das variadas moléculas usadas como sensibilizador neste tipo de célula, as mais eficientes são os complexos polipiridínicos de rutênio(II). Diversas propriedades são importantes para que uma molécula seja aplicável em uma DSSC como um sensibilizador eficiente, entre elas uma larga e intensa absorção na região visível e infravermelho próximo do espectro eletromagnético e um potencial redox que permita que o sensibilizador seja regenerado pelo par redox,que também faz parte da célula. Neste trabalhofoi construída uma metodologia computacional baseada em dados experimentais que leva a resultados com pequenos desviospara o cálculo de potenciais redox e espectros eletrônicosde complexos cis-[Ru(R2-phen)(dcbpy)(NCS)2], sendo dcbpy a 4,4’-dicarboxi-2,2’-bipiridina e R2-phen a 1,10-fenantrolina com substituintes R nas posições 4 e 7.Parao cálculo de potenciais redox foi aplicadaa teoria do funcional da densidade (DFT) e paraasimulação dosespectroseletrônicosa DFT dependente do tempo (TDDFT). Com esta metodologia, novos complexos foram avaliados e suas propriedades estudadas visando estimar as suas eficiências se aplicados a DSSCs. Os novos complexos que apresentaram melhores resultados,em ordem do menos para o mais promissor,são aqueles com substituintes R = 2-piridil, 2-(5-etilfuril), 2-benzotiazolil. / The search for renewable energy sources grows increasingly in many regions of the world due to the crescent demand and pollution generated by the use of fossil fuels.The solar energy is a renewable and endless source of energy, which may be harnessed directly with different types of solar cells. Among thesevaried types, the dye-sensitized solar cells (DSSCs) present themselves to be promising owing to their high efficiency. Fromthe many molecules used as sensitizers in this kind of cell, the most efficient are thepolypyridinicruthenium(II) complexes. Different properties are important for a molecule to be applicable in a DSSC as an efficient sensitizer, among them a broad and intense absorption in the visible and near infrared region of the electromagnetic spectrum and a redox potential that allows the sensitizer to be regenerated by the redox couple,that is also part of the cell. In this work wasbuilt a computational methodologybased on experimental datawhich gives results with small deviations, for the calculation of redox potentials and electronic spectra of complexes cis-[Ru(R2-phen)(dcbpy)(NCS)2], where dcbpy is the4,4’-dicarboxylic acid 2,2’-bipyridineandR2-phenthe1,10-phenanthrolinewith R substituents on the positions 4 and 7. For the calculation of redox potentials, was applied the density functional theory (DFT) and for the electronic spectra simulations, the time-dependent DFT (TDDFT). With this methodology, new complexes where evaluated and their properties studied intending to estimate their efficiencies if applied to DSSCs. The new complexes that presented better results, in order from the less to the most promising, were those with substituents R = 2-pyridyl, 2-(5-ethylfuryl) and 2-benzothiazolyl.

As transições eletrônicas que apresenta as energias mais baixas no retinal e em quatro retinais sintéticos foram analisadas em dois diferentes ambientes: no vácuo e ligados à proteína bacterioopsina por uma base de Schiff protonada, utilizando diversos métodos de química teórica. Os resultados aqui apresentados fornecem indicativos de que três estados eletrônicos estão envolvidos na formação da primeira banda de absorção dos aldeídos, enquanto que, no caso dos compostos ligados à proteína apenas dois estados estariam envolvidos. As análises discutidas neste trabalho também sugerem uma possível explicação para o envolvimento de dois estados eletrônicos excitados no processo de fotoisomerização do retinal ligado à bacterioopsina. / Low-lying electronic transitions of retinal and of four synthetic retinals were analyzed in two different environments: in vacuum and linked to bacterioopsin through a protonated Schiff base, employing several methods of theoretical chemistry. The results here reported suggest that the first absorption band of the aldehydes involves three electronic states, while for the case of protein linked compounds, two states would be embraced. Our discussions also provided a possible explanation about the involvement of two electronic excited states in the photoisomerization process of retinal linked to bacterioopsin.

Made available in DSpace on 2017-07-24T19:37:54Z (GMT). No. of bitstreams: 1 Ageo Meier Andrade.pdf: 3358892 bytes, checksum: c2798e568b2f1bcb11fc21644c783df2 (MD5) Previous issue date: 2016-02-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The search for materials with conductive capacity has been gaining attention in the scienti c community for its many technological applications. Moreover, understanding the charge transport phenomena in these materials it is still seen as a challenge to the scientic community. Poly (3,4-ethylenedioxythiophene), PEDOT features desirable characteristics where planar molecular structure ensures process of charge transfer and charge separation. In the investigation of these properties, computational tools emerge as an alternative with low nancial cost when compared to experimental techniques. Knowing that several semi-empirical methodologiess are available and the class of conductive polymers exhibit unique macromolecular characteristics; the objective of this study was to investigate the structural properties of 1-EDOT to 10-EDOT by the latest methodologies available in MOPAC2012 program, that is, PM6, PM7 and RM1. It was found that among them, PM6 methodology provided good results, especially for presenting the planar polymer chain to oligomers of 2-EDOT to 10-EDOT. DFT calculations have been used for organic polymeric systems with conductive characteristics and has evolved as a major computational tools for electronic properties. Thus, for 1-EDOT to 10-EDOT optimized by PM6 methodology, single point calculations were applied using DFT B3LYP/6-31++G(d,p) obtaining information related to the charge transport, especially reducing band-gap energy, border orbital location and formation of an intramolecular charge hall. From these informations, were investigated electrostatic potential map and Density of States (DOS) based on energy levels. In computational analysis of excited states, calculations based on TDDFT using B3LYP/6-31+G were applied to molecular systems, where it was possible to investigate discrete levels of excitation energy in the UV-visible range. In small oligomers of 1-EDOT to 6-EDOT using PM6 optimized structures such calculations showed the possibility of investigating the main configuration related to discrete levels, showing the reduction in energy required for excitation with increasing polymer chain for this material. Having noted both the reduction of energy band-gap and the singlet excitation energy, relatedto increasing polymeric chain, it was investigated these properties for a macromolecular system considering infinite oligomers. In this analysis, linear regression applied to the results of 2-EDOT to 6-EDOT had the lowest band-gap energy. Subsequently, band-gap energy was related to the wavelength of maximum absorption of the singlet excitation energy. It was concluded that it is possible to apply semi-empirical calculations followed by single-pint DFT and TDDFT calculations in the investigation of conductive properties of polymeric materials providing significant results to understand charge transport and the prediction of structural and electronic properties. / A busca por materiais com capacidades condutoras vem ganhando atenção na comunidade científica por suas inúmeras aplicações tecnológicas. Além disso, o entendimento do fenômeno de transporte de carga continua sendo visto como um desafio para a comunidade cientifica. Poli (3,4-etilenodioxitiofeno), PEDOT apresenta caracteristicas condutoras desejáveis porque sua estrutura molecular planar garante que haja o processo de transferência e separação de carga. Na investigação dessa propriedade, ferramentas computacionais surgem como uma alternativa de baixo custo financeiro quando comparados a técnicas experimentais. Sabendo que diversas metodologias semi-empíricas estão disponíveis e que a classe de polímeros condutores apresentam caracteressticas macromoleculares únicas; objetivou-se neste estudo a investigação das propriedades estruturais de 1-EDOT a 10-EDOT pelas mais recentes metodologias disponíveis no programa MOPAC2012, isto é, PM6, PM7 e RM1. Verificou-se que dentre elas, a metodologia PM6 forneceu bons resultados em relação aos resultados experimentais, principalmente por apresentar a cadeia polimérica planar para oligômeros de 2-EDOT a 10-EDOT. Cálculos em DFT tem sido usados para sistemas poliméricos orgânicos com características condutoras e evoluiu como uma das principais ferramentas computacionais para propriedades eletrônicas. Sendo assim, foram aplicados cálculos pontuais em DFT usando B3LYP/6-31++G(d,p)) de 1-EDOT a 10-EDOT a partir de estruturas otimizadas em PM6 obtendo-se informações relevantes ao transporte de carga, principalmente, redução da energia de band-gap, localizaçãoo dos orbitais de fronteiras e formação de um corredor de carga intramolecular. Investigou-se a partir destas informações o mapa de potencial eletrostático e a Densidade de Estados (DOS) por meio dos níveis discretos de energia. Na análise computacional de estados excitados, cálculos baseados em TDDFT usando B3LYP/6-31+G foram aplicados a sistemas moleculares, onde é possível investigar níveis discretos de excitação na faixa do UV-Visível. Nos pequenos oligomeros de 1-EDOT a 6-EDOT, utilizando a estrutura otimizada em PM6, tais cálculos mostraram a possibilidade de investigar as principais configurações de excitação do estado singlete em níveis discretos, mostrando a redução da energia necessária para excitação com o aumento da cadeia polimérica para esse material. Por ter verificado tanto a redução da energia de band-gap quanto da energia de excitação de singlete, e que ambos s~ao relacionados ao aumento da cadeia polimérica, investigou-se a previsão por extrapolação para um sistema macromolecular com infinitos oligômeros. Nessa análise, a regressão linear aplicada aos resultados de 2-EDOT a 6-EDOT apresentou a menor energia de band-gap. Posteriormente, o band-gap foi relacionado ao comprimento de onda máximo da absorção de singlete. Concluiu-se que é possível aplicar cálculos semi-empíricos em conjunto com cálculos pontuais em DFT e TDDFT na investigação de propriedades condutoras de materiais poliméricos proporcionando resultados expressivos para entender o transporte de carga e a prediação de propriedades estruturais e eletrônicas.

Les réponses optiques d'agrégats de métaux nobles sont caractérisées par une absorption intense, situées dans le domaine UV-Visible, et appelée plasmon de surface localisé. Pour des particules de plusieurs nanomètres de diamètre, le phénomène de plasmon peut être interprété par des modèles semi-classiques ou classiques comme la théorie de Mie, mais ces modèles trouvent leur limite lorsque la taille du système diminue. La théorie de la fonctionnelle de la densité dépendante du temps (TDDFT) est une approche entièrement quantique qui permet d'appréhender le phénomène de plasmon en reproduisant la réponse optique de petits agrégats d'argent, composés de quelques atomes à quelques centaines d'atomes. Dans ce contexte, nous avons réalisé des calculs TDDFT avec une fonctionnelle de type Range-Separated-Hybrid (RSH) sur des agrégats contenant entre 8 et 147 atomes d'argent. Les spectres obtenus sont en excellent accord avec les données expérimentales et les réponses optiques calculées perme ttent de retrouver les prédictions du modèle en couches. Nous présentons des outils permettant d'identifier et de caractériser les excitations plasmoniques dans le formalisme de la TDDFT. Les effets de l'environnement sur la réponse optique des agrégats sont également étudiés, avec notamment la présentation d'une méthodologie permettant de reproduire les spectres mesurés sur des agrégats d'argent piégés dans des matrices de gaz rare. Les effets de l'oxydation et les effets induits par une matrice de silice sur la réponse optique des agrégats sont également étudiés / Optical responses of noble metal clusters are characterized by a strong absorption in the UV-Visible range called localized surface plasmon. For clusters of several nanometers, the plasmon phenomenon can be interpreted by semi-classical or classical model, as the Mie theory, but those models can not describe the optical response of small-size clusters. The time dependent density functional theory (TDDFT) is a quantum method that allow to understand the plasmon phenomenon by reproducing the optical response of small silver cluster, made of a few tens or hundreds atoms. In this context, we performed TDDFT calculation using Range-Separated Hybrid (RSH) functionals over cluster containing between 8 and 147 silver atoms. The obtained spectra are in excellent agreement with the experimental ones and the calculated optical response allows to recover the shell model prediction. We present some tools that allow to identify and characterize plasmonic excitations within the TDDFT framework. The effect of the surrounding medium over the optical response of clusters are studied, in particular we will present a methodology that allow to reproduce spectra measured over clusters trapped in rare gas matrix. The effects of the oxidation and the effects induced by a silica matrix over the optical response of clusters are also studied

As transições eletrônicas que apresenta as energias mais baixas no retinal e em quatro retinais sintéticos foram analisadas em dois diferentes ambientes: no vácuo e ligados à proteína bacterioopsina por uma base de Schiff protonada, utilizando diversos métodos de química teórica. Os resultados aqui apresentados fornecem indicativos de que três estados eletrônicos estão envolvidos na formação da primeira banda de absorção dos aldeídos, enquanto que, no caso dos compostos ligados à proteína apenas dois estados estariam envolvidos. As análises discutidas neste trabalho também sugerem uma possível explicação para o envolvimento de dois estados eletrônicos excitados no processo de fotoisomerização do retinal ligado à bacterioopsina. / Low-lying electronic transitions of retinal and of four synthetic retinals were analyzed in two different environments: in vacuum and linked to bacterioopsin through a protonated Schiff base, employing several methods of theoretical chemistry. The results here reported suggest that the first absorption band of the aldehydes involves three electronic states, while for the case of protein linked compounds, two states would be embraced. Our discussions also provided a possible explanation about the involvement of two electronic excited states in the photoisomerization process of retinal linked to bacterioopsin.

Au cours de cette thèse on étude deux des plus populaires systèmes de nano-échelle, nano fil et points quantiques (quantum dots), dans le cadre d'une approximation basé sur des premiers principes. Afin d'atteindre cet objectif, nous avons utilisé et développé des théories plus sophistiquées qui nous ont permis d'avoir un meilleur aperçu de la façon dont les systèmes se comportent. Un aspect commun qui limite ces deux types de systèmes (nano fil et points quantiques) est la souplesse de contrôler les propriétés électroniques et optiques. Cette accordabilité des propriétés électroniques et optiques les dote d'un grand intérêt technologique, et elle est la raison de sa popularité / In this thesis we studied two of the most popular nano-scale systems, nano-wires and quantum dots, via a first-principles approach. In order to achieve this objective we have used and developed state-of-the-art theories that allowed us to have a greater insight into the the way this systems behave. One common aspect that bounds this two class of systems (nano-wires and quantum dots) is the flexibility to control their electronic and optical properties. This tunability of their electronic and optical properties, endows them of great technological interest, and is the reason behind their popularity

Cette thèse présente une étude des propriétés optiques et de la photofragmentation de biomolécules en phase gazeuse. Les expériences sont effectuées sur un piège ionique quadripolaire couplé avec des lasers UV-Visible accordables en longueur d'onde. Les molécules sont isolées en phase gazeuse au centre du piège puis irradiées par le faisceau laser. Pour les molécules polyanioniques, le canal de relaxation principal après excitation laser est l'émission d'électron. Cette perte d'un électron conduit à la formation d'un ion radicalaire. Une partie de ce travail est consacrée à l'étude de la relaxation de molécules polyanioniques après excitation laser et notamment aux mécanismes conduisant à la perte d'électron. Les expériences de photodétachement réalisées à Lyon ont été complétées par des expériences de spectroscopie de photoélectron effectuées à Karlsruhe (Pr. Kappes). La production d'anions radicalaires a un potentiel analytique important. L'un des objectifs de ce travail de thèse a été d'étudier la réactivité de ces ions radicalaires et de montrer l'intérêt de leur fragmentation pour l'analyse structurelle de peptides. L'autre objectif était de sonder les propriétés électroniques de protéines et de peptides en phase gazeuse. Pour cela, le taux de détachement d'électron a été enregistré en fonction de la longueur d'onde du laser. Nous avons notamment pu déterminer des signatures optiques pour des chromophores neutres, déprotonnés ou radicalaires au sein des protéines. Ces résultats ont été comparés à des calculs théoriques (TD DFT). / This manuscript discusses optical properties and photofragmentation of gas phase biomolecules. These experiments are performed with a quadrupolar ion trap coupled to a UV-visible tunable laser. Molecules are isolated at the center of the trap, and irradiated by the laser beam. The most intense relaxation channel observed for multiply negatively charged ions is electron emission. This loss of one electron leads to radical anion formation. The first part of this manuscript is dedicated to the study of the mechanisms leading to the electron loss. Photodetachment experiments performed in Lyon were completed by photoelectron spectroscopy experiments performed in Karlsruhe (Pr. Kappes). The radical anion production has an important analytical potential. One of the main objectives of this work was to study the reactivity of this radical anion and to show the interest of radical fragmentation for the structural analysis of peptides. An other objective was to probe electronical properties of gas phase peptides and proteins. The electron detachment yield is recorded as a function of laser wavelength. We have determinated optical fingerprints for neutral, deprotonated and radical chromophores localized in the heart of proteins. These results are compared to computational methods (TD DFT).

Nous proposons de développer une méthodologie théorique pour étudier l’influence de stimuli externes sur les cristaux organiques. On s’intéresse en particulier au mécanochromisme, aggregation-induced emission, et le transfet des protons. Ces phénomènes, récemment observés expérimentalement, sont encore mal compris et il n’existe pas à l’heure actuelle de méthodologie bien définie pour les comprendre. Cette thèse développera les outils de modélisation des couplages des propriétés optiques aux phénomènes d’aggregation, réactivité et de déformation á l'etat solide. / To develop a theoretical methodology to study the influence of external stimuli on fluorescent crystals. We are particularly interested in excited state reactivity, aggregation-enhanced fluorescence and responses to mechanical stimuli. Such phenomena are often not yet understood at a molecular level, a problem exacerbated by the absence of adequate and cost-efficient computational models. This thesis counters this problem by developing a method capable of describing the solid state environment in the context of excited-state calculations at the quantum level.

La réponse linéaire de la théorie de la fonctionnelle de la densité dépendante du temps est étudiée dans le cadre du formalisme d'ondelettes du code BigDFT, qui permet d'exprimer les fonctions d'onde électroniques sur une grille de simulation dans l'espace réel. L'objectif est de déterminer un spectre d'excitations de référence pour un système et un potentiel d'échange-corrélation donnés.Il apparaît que seule une partie du spectre, concernant les transitions entre orbitales liées, peut être facilement amenée à convergence par rapport aux paramètres d'entrée de BigDFT, que sont l'extension de la grille de simulation et le nombre d'orbitales du continuum qui sont considérées pour le calcul des spectres. L'énergie de la dernière orbitale inoccupée utilisée dans les calculs se révèle d'ailleurs être un paramètre plus important que ce nombre d'orbitales inoccupées. La justification vient de l'étude de la complétude des bases formées par les orbitales de l'état fondamental du système. Tout ceci permet de porter un regard neuf sur les résultats obtenus avec le formalisme à base gaussienne, tel qu'implémenté dans le code NWChem.En ce qui concerne la convergence du spectre de plus haute énergie, concernant des transitions entre orbitales occupées et orbitales inoccupées du continuum, l'espoir d'une convergence se heurte au problème du tassement du continuum. Il faut alors songer à une manière différente de capter l'information contenue dans ce continuum.Le formalisme des états résonants, dont les fondements ont été posés lors de la première moitié du XXème siècle, est une piste très encourageante pour cela. Une étude préliminaire dans le cas du puits de potentiel carré à une dimension est donc présentée. La première étape a consisté en la détermination de ces états résonants, dont les énergies et fonctions d'onde sont complexes. Une normalisation a notamment pu leur être attribuée. Il est ensuite montré, sous certaines conditions, que la base formée par les états propres de ce potentiel, dont une partie est constituée par les états du continuum, peut être efficacement remplacée par une base discrète et complète faite d'états résonants. Des applications numériques montreront qu'ils peuvent être avantageusement utilisés pour définir la fonction de Green ou encore calculer la propagation temporelle d'un paquet d'onde. / The linear response on the time-dependent density functional theory is studied in the wavelets formalism used in the BigDFT code, that allows the representations of electronic wave-functions on a simulation grid in real space. The goal of this study is to determine a reference excitation spectrum for a given system and exchange-correlation potential.It appears that only one part of the spectrum can be easily brought to convergence with respect to the input parameters of BigDFT, which are the simulation grid extension and the number of unoccupied continuum orbitals considered in the spectrum calculation. The energy of the last unoccupied orbital used actually proves to be more important as a parameter than this number of unoccupied orbitals. This is justified by the study of the completeness of the basis sets made of the ground state orbitals of the system. This gives another point of view regarding spectrum obtained by using the Gausian basis sets formalism, as the one implemented in the code NWChem.As to the convergence of the spectrum at higher energy, concerning transitions between occupied orbitals and unoccupied orbitals of the continuum, the hope for a convergence faces the problem of the continuum collapse. One therefore has to think of another way of retrieving the data contained in this continuum.The resonant states formalism, whose foundations were laid in the first half of the 20th century, is very encouraging in this regard. A preliminary study in the case of the one-dimension square well potential is therefore presented. The first step consisted in the determination of these resonant states, whose energies and wavefunctions are complex valued in general. Their normalization was also clearly defined. It is then shown, under certain conditions, that the basis set formed by the eigenstates of this potential, including the continuum states, can be efficiently replaced by a discrete and complete basis set made of resonant states. Numerical applications also show that these states can also be advantageously used to define the Green's function or even compute the time propagation of a wavepacket.