Polímeros conjugados semicondutores tem atraído grande interesse nas últimas décadas devido às possíveis aplicações como componentes ativos em aplicações optoeletrônicas. A adequação destes semicondutores orgânicos para a fabricação de dispositivos depende do entendimento e controle de propriedades eletrônicas básicas: gap fundamental (Eg) e potencial de ionização (IP). Nesse contexto, estudos teóricos baseados em cálculos de primeiros princípios tem se mostrado muito úteis, uma vez que possibilitam a simulação de processos físicos em condições ideais, onde se pode analisar as propriedades eletrônicas de polímeros desconsiderando efeitos do ambiente ou desordem estrutural. A Teoria do Funcional da Densidade (DFT) tem se tornado o método mais comum para o cálculo da estrutura eletrônica do estado fundamental de uma ampla variedade de materiais orgânicos complexos. Embora cálculos DFT baseados na diferença de energias totais tem sido aplicados com sucesso para estimar IPs de moléculas pequenas, este método falha nas propriedades de sistemas conjugados longos. Realmente, a capacidade preditiva da DFT padrão com respeito as propriedades espectroscópicas é frequentemente limitada, entretanto o tratamento adequado das excitações eletrônicas através de abordagens de muitos corpos é ainda muito difícil para materiais orgânicos complexos. Funcionais híbridos que misturam uma fração () de troca exata (EX) não-local ao correspondente semi-local representam uma boa alternativa, embora a quantidade ideal de EX seja, em geral, dependente do sistema. Neste trabalho, adotamos um esquema não-empírico baseado na aproximação G0W0 para identificar o valor ótimo de para o funcional híbrido PBE no qual a correção de autoenergia para o orbital mais alto ocupado (HOMO) de Kohn-Sham generalisado é minimizado. Estudamos, com base nessa estratégia, a dependência com o comprimento das propriedades eletrônicas básicas em uma família de oligômeros conjugados 1D de trans-poliacetileno (TPA). Nossos cálculos mostram que a fração EX ótima (dependente do tamanho) incorporada ao PBEh reproduz com precisão os IPs experimentais determinados em fase gasosa, / Semiconducting conjugated polymers have attracted considerable interest over the past decades due to the promising applications as active components for optoelectronic applications. The suitability of such organic semiconductors for device fabrication relies on quantitative understanding and control of basic electronic properties: fundamental gap (Eg) and ionization potential (IP). In this context, theoretical studies based on first principles approaches have proven useful, through simulating physical processes in ideal conditions, in which one might analyse the electronic properties of polymers apart from the effects of the surrounding environment or structural disorder. Density Functional Theory (DFT) has become an usual choice for calculating the ground state electronic structure of a wide variety of complex organic materials. Although DFT calculations based on total energy differences have been successfully applied to estimate IPs of small molecules, they fail for properties of long conjugated systems. Indeed, the predictive ability of standard DFT with respect to spectroscopic properties is often limited, however a proper treatment of the electronic excitations through many-body approaches is still very difficult for complex organic materials. Hybrid functionals that mix a fraction (_) of nonlocal exact exchange (EX) with the semilocal counterpart represent a good alternative, although the ideal amount of EX is usually system dependent. In this work, we adopt a non-empirical scheme based on the G0W0 approximation to identify the optimum _ value for the PBE hybrid functional for which the self-energy correction to the generalized Kohn-Sham highest occupied molecular orbital (HOMO) is minimized. Based on this strategy we study the size dependence of the basic electronic properties in a family of 1D _-conjugated oligomers of trans-polyacetylene (TPA). Our calculations demonstrate that the size dependent optimal EX fraction incorporated in PBEh accurately reproduces IPs from experimental gas phase data, although no particular constraint has been imposed a priori. Furthermore, we note that the optimum _-value decreases exponen tially with chain length going from _ w0.85 for the smaller oligomer (ethylene, n=1) up to _ w0.75 extrapolated for an isolated TPA chain. The accuracy of our optimized PBEh in predicting IPs and Eg is superior to other conventional mean field approaches, as demonstrated for a selected set of conjugated molecules such as acenes and phenylenes. As a result, we can obtain good estimations for the energy barriers of electron transfer in organic/organic interfaces. On the other extreme, we analyse the influence of exact exchange on the electronic structure of the prototypical metal system gold (Au), commonly used as electrode in organic devices. In this case, we confirm the expected result that the insertion of even a small fraction of EX into PBE functional distorts the Au band structure, worsening the description of electronic properties compared to regular PBE. We then proceed to analyse the factibility of studying polymer/metal interface systems using pure DFT. Our calculations reveal that the result is too system-dependent: for the TPA/Au(111) interface, an artificial charge transfer takes place at interface due to an underestimation of the IPs of the conjugated system inherent to the underlying DFT approximation. Finally, our study emphasizes the importance of a physically motivated choice of EX fraction in hybrid functionals for accurately predicting both ionization potentials and fundamental gaps of organic semiconductors relevant for nanoelectronics.

Polímeros conjugados semicondutores tem atraído grande interesse nas últimas décadas devido às possíveis aplicações como componentes ativos em aplicações optoeletrônicas. A adequação destes semicondutores orgânicos para a fabricação de dispositivos depende do entendimento e controle de propriedades eletrônicas básicas: gap fundamental (Eg) e potencial de ionização (IP). Nesse contexto, estudos teóricos baseados em cálculos de primeiros princípios tem se mostrado muito úteis, uma vez que possibilitam a simulação de processos físicos em condições ideais, onde se pode analisar as propriedades eletrônicas de polímeros desconsiderando efeitos do ambiente ou desordem estrutural. A Teoria do Funcional da Densidade (DFT) tem se tornado o método mais comum para o cálculo da estrutura eletrônica do estado fundamental de uma ampla variedade de materiais orgânicos complexos. Embora cálculos DFT baseados na diferença de energias totais tem sido aplicados com sucesso para estimar IPs de moléculas pequenas, este método falha nas propriedades de sistemas conjugados longos. Realmente, a capacidade preditiva da DFT padrão com respeito as propriedades espectroscópicas é frequentemente limitada, entretanto o tratamento adequado das excitações eletrônicas através de abordagens de muitos corpos é ainda muito difícil para materiais orgânicos complexos. Funcionais híbridos que misturam uma fração () de troca exata (EX) não-local ao correspondente semi-local representam uma boa alternativa, embora a quantidade ideal de EX seja, em geral, dependente do sistema. Neste trabalho, adotamos um esquema não-empírico baseado na aproximação G0W0 para identificar o valor ótimo de para o funcional híbrido PBE no qual a correção de autoenergia para o orbital mais alto ocupado (HOMO) de Kohn-Sham generalisado é minimizado. Estudamos, com base nessa estratégia, a dependência com o comprimento das propriedades eletrônicas básicas em uma família de oligômeros conjugados 1D de trans-poliacetileno (TPA). Nossos cálculos mostram que a fração EX ótima (dependente do tamanho) incorporada ao PBEh reproduz com precisão os IPs experimentais determinados em fase gasosa, / Semiconducting conjugated polymers have attracted considerable interest over the past decades due to the promising applications as active components for optoelectronic applications. The suitability of such organic semiconductors for device fabrication relies on quantitative understanding and control of basic electronic properties: fundamental gap (Eg) and ionization potential (IP). In this context, theoretical studies based on first principles approaches have proven useful, through simulating physical processes in ideal conditions, in which one might analyse the electronic properties of polymers apart from the effects of the surrounding environment or structural disorder. Density Functional Theory (DFT) has become an usual choice for calculating the ground state electronic structure of a wide variety of complex organic materials. Although DFT calculations based on total energy differences have been successfully applied to estimate IPs of small molecules, they fail for properties of long conjugated systems. Indeed, the predictive ability of standard DFT with respect to spectroscopic properties is often limited, however a proper treatment of the electronic excitations through many-body approaches is still very difficult for complex organic materials. Hybrid functionals that mix a fraction (_) of nonlocal exact exchange (EX) with the semilocal counterpart represent a good alternative, although the ideal amount of EX is usually system dependent. In this work, we adopt a non-empirical scheme based on the G0W0 approximation to identify the optimum _ value for the PBE hybrid functional for which the self-energy correction to the generalized Kohn-Sham highest occupied molecular orbital (HOMO) is minimized. Based on this strategy we study the size dependence of the basic electronic properties in a family of 1D _-conjugated oligomers of trans-polyacetylene (TPA). Our calculations demonstrate that the size dependent optimal EX fraction incorporated in PBEh accurately reproduces IPs from experimental gas phase data, although no particular constraint has been imposed a priori. Furthermore, we note that the optimum _-value decreases exponen tially with chain length going from _ w0.85 for the smaller oligomer (ethylene, n=1) up to _ w0.75 extrapolated for an isolated TPA chain. The accuracy of our optimized PBEh in predicting IPs and Eg is superior to other conventional mean field approaches, as demonstrated for a selected set of conjugated molecules such as acenes and phenylenes. As a result, we can obtain good estimations for the energy barriers of electron transfer in organic/organic interfaces. On the other extreme, we analyse the influence of exact exchange on the electronic structure of the prototypical metal system gold (Au), commonly used as electrode in organic devices. In this case, we confirm the expected result that the insertion of even a small fraction of EX into PBE functional distorts the Au band structure, worsening the description of electronic properties compared to regular PBE. We then proceed to analyse the factibility of studying polymer/metal interface systems using pure DFT. Our calculations reveal that the result is too system-dependent: for the TPA/Au(111) interface, an artificial charge transfer takes place at interface due to an underestimation of the IPs of the conjugated system inherent to the underlying DFT approximation. Finally, our study emphasizes the importance of a physically motivated choice of EX fraction in hybrid functionals for accurately predicting both ionization potentials and fundamental gaps of organic semiconductors relevant for nanoelectronics.

Le présent travail concerne l’avancement des approximations de l’énergie d’échange- corrélation (XC) de la théorie fonctionnelle de la densité (DFT) de Kohn-Sham (KS) basée sur l’approche du facteur de corrélation (CF). Le travail est organisé en trois parties où chaque partie est construite sur des modèles et méthodes précédents. La première partie du travail introduit une nouvelle condition physique à travers la déri- vation du développement en série du quatrième ordre du trou d’échange exact. La dérivation détaillée des formules requises est suivie d’une analyse approfondie qui montre que le terme de quatrième ordre peut ajouter des informations supplémentaires importantes qui sont par- ticulièrement pertinentes pour les molécules par rapport aux atomes. Sur la base de ces résultats, nous explorons les fonctionnelles d’échange qui dépendent du terme de quatrième ordre de l’expansion du trou d’échange. Nous constatons également que les développements d’ensembles de base gaussiens, fréquemment utilisés dans les codes de structure électronique, donnent des représentations insatisfaisantes du terme de quatrième ordre. La deuxième partie de ce travail porte sur la mise en œuvre de nouvelles versions du modèle CF initial [J. P. Precechtelova, H. Bahmann, M. Kaupp et M. Ernzerhof, J. Chem. Phys. 143, 144102 (2015)] dans lequel le trou XC est approximé. Étant donné que diverses contraintes satisfaites par le trou XC sont connues, des approximations peuvent être conçues pour éviter en grande partie des ajustements empiriques. Dans l’approche CF, le trou XC est écrit comme le produit d’un trou d’échange multiplié par un facteur de corrélation. Une contrainte importante satisfaite par le modèle CF est qu’il reproduit correctement l’éner- gie d’échange exacte dans la limite de haute densité. Ceci est réalisé en utilisant l’énergie d’échange exacte par particule comme variable d’entrée, c’est-à-dire que le modèle CF s’ap- puie sur l’échange exact. Des variations du modèle CF initial sont proposées qui assurent que la réponse exacte est obtenue dans la limite homogène. De plus, nous appliquons une correction à la profondeur du trou XC qui est conçue pour capturer une forte corrélation. Les fonctions d’échange-corrélation qui s’appuient sur un échange exact, comme les hybrides, échouent souvent pour les systèmes qui présentent une corrélation électronique importante. Malgré ce fait et malgré la réduction de l’empirisme à un seul paramètre dans CF, des énergies d’atomisation précises sont obtenues pour des composés de métaux de transition fortement corrélés. Le modèle CF montre des résultats significativement supérieurs aux fonctionnelles populaires comme Perdew-Burke-Ernzerhof (PBE), PBE hybride et Tao-Perdew-Staroverov- Scuseria (TPSS). La troisième partie du travail s’appuie sur les modèles CF précédents développés dans notre groupe et aborde l’erreur d’auto-interaction à un électron et introduit un modèle de facteur de corrélation modifié où f C (r, u) est construit tel qu’il se réduit à un dans les régions à un électron d’un système à plusieurs électrons. Ce trou XC avec une correction d’auto- interaction est ensuite utilisé pour générer la fonctionnelle énergie XC correspondante. La nouvelle fonctionnelle est évaluée en l’implémentant dans un programme KS et en calculant diverses propriétés moléculaires. Nous constatons que, dans l’ensemble, une amélioration significative est obtenue par rapport aux versions précédentes du modèle de facteur de cor- rélation. / The present work is concerned with the advancement of approximations to the exchangecorrelation (XC) energy of Kohn-Sham (KS) density functional theory (DFT) based on the correlation factor (CF) approach. The work is organized in three parts where each part is build upon previous models and methods. The first part of the work introduces a new physical condition through the derivation of the fourth-order series expansion of the exact exchange hole. The detailed derivation of the required formulas is followed by a thorough analysis that shows that the fourth-order term can add important additional information that is particularly relevant for molecules compared to atoms. Drawing on these findings, we explore exchange functionals that depend on the fourth-order term of the expansion of the exchange hole. We also find that Gaussian basis set expansions, frequently used in electronic structure codes, result in unsatisfactory representations of the fourth-order term. The second part of this work addresses the implementation of new versions of the initial CF model [J. P. Precechtelova, H. Bahmann, M. Kaupp, and M. Ernzerhof, J. Chem. Phys. 143, 144102 (2015)] in which the XC hole is approximated. Since various constraints satisfied by the XC hole are known, approximations to it can be designed which largely avoid empirical adjustments. In the CF approach, the XC-hole is written as a product of an exchange hole times a correlation factor. An important constraint satisfied by the CF model is that it correctly reproduces the exact exchange energy in the high density limit. This is achieved by employing the exact exchange-energy per particle as an input variable, i.e., the CF model builds on exact exchange. Variations of the initial CF model are proposed which ensure that the exact answer is obtained in the homogeneous limit. Furthermore, we apply a correction to the depth of the XC-hole that is designed to capture strong correlation. Exchangecorrelation functionals that build on exact exchange, such as hybrids, often fail for systems that exhibit sizeable electron correlation. Despite this fact and despite the reduction of empiricism to a single parameter within CF, accurate atomization energies are obtained for strongly-correlated transition metal compounds. The CF model significantly improves upon widely used functionals such as Perdew-Burke-Ernzerhof (PBE), PBE hybrid, and Tao-Perdew-Staroverov-Scuseria (TPSS) density functionals. The third part of the work builds on the previous CF models developed in our group and addresses the one-electron, self-interaction error and introduces a modified correlation factor model where fC(r, u) is constructed such that it reduces identically to one in oneelectron regions of a many-electron system. This self-interaction corrected XC-hole is then used to generate the corresponding XC-energy functional. The new functional is assessed by implementing it into a KS program and by calculating various molecular properties. We find that, overall, a significant improvement is obtained compared to previous versions of the correlation factor model.