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Understanding and Minimizing Density Functional Failures Using Dispersion Corrections

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Understanding and Minimizing Density Functional Failures Using Dispersion Corrections Understanding and Minimizing Density Functional Failures Using Dispersion Corrections THÈSE NO 5535 (2012) PRÉSENTÉE LE 23 octobre 2012 À LA FACULTÉ DES SCIENCES DE BASE LABORATOIRE DE DESIGN MOLÉCULAIRE COMPUTATIONNEL PROGRAMME DOCTORAL EN CHIMIE ET GÉNIE CHIMIQUE ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES PAR Stephan Niklaus STEINMANN acceptée sur proposition du jury: Prof. J. Zhu, président du jury Prof. A.-C. Corminboeuf, directrice de thèse Dr I. Tavernelli, rapporteur Dr A. Tkatchenko, rapporteur Dr T. A. Wesolowski, rapporteur Suisse 2012 To Schrödinger’s cat Il n’est pas de destin qui ne se surmonte par le mépris. — Albert Camus, Le mythe de Sisyphe But it ain’t about how hard ya hit. It’s about how hard you can get it and keep moving forward. — Rocky Balboa Acknowledgements First and foremost, my advisor Prof. Clémence Corminboeuf has fostered my scientific curios- ity and provided the framework of the four years I spent happily pursuing the doctoral studies here in Lausanne. I am immensely grateful to her for having accepted me in her group and for believing more in me than I ever did myself. In particular, I have profited tremendously from her constant availability to share her opinion and to discuss various chemical questions. If this thesis is written well, it is because of all the great help and advices Clémence has given me. The members of the “Laboratory for Computational Molecular Design” have never failed to support me. Since my early days, I admire Matthew Wodrich’s love for alkanes and Fabrice Avaltroni’s passion for Bash-scripting and Daniel Jana’s remarkable aptitude to make beautiful pictures. The three have really got me started in the lab and never complained when I wasted their time by asking stupid questions. Only few months after I started, Jérôme Gonthier joined the lab and became essentially my “brother in arms”: every day we have discussed our research and shared our enthousiasm about the latest articles or conferences; furthermore, I am very grateful for his corrections of the French abstract. Tanya Todorova has brought many joyful moments to our lunch breaks: she transforms even the most insignificant event into a funny story! I will leave the LCMD wondering: does Laëtita Bomble complain more or less than me? In any case, I enjoyed the discussion with her, even though I rarely agreed with her; after all: where is the discussion if everyone shares the same opinion? I warmly welcome Riccardo Petraglia, who carries on the flame of dispersion corrections. Taking care of students has provided me welcome excuses to take a break, as Matthieu Mottet has pointed out. In addition to my four brothers, the friends in Basel have also been very supportive. In particular, Franziska Hofmann has kept me motivated and while Andrin Bürgin has regularly reminded me how strange the world I am living in is, Jörg Duschmalé shared my passion for the beauty of exactly this world, where doing science is more imperative than earning money. My deepest gratitude goes to my parents, who have never questioned any of my decisions and let me pursue my way between books, chemistry and the computer. More direct contributions to this thesis have been made by Gabor Csonka, who has brought our attention to the Tang and Toennies damping function, further discussions about damping functions with Alexandre Tkatchenko, Zhengting Gan and Jing Kong from Q-Chem Inc. who provided their source code and Stan Gisbergen and Pier Philipsen from SCM who helped with the implementation in ADF. I am also very grateful to Tomasz Wesolowski, Alexandre Tkatchenko and Ivano Tavernelli for having accepted to be on my jury. Finally, the Swiss NSF Grant 200021_121577/1, and EPFL are respectfully acknowledged for their financial support. v Abstract This thesis introduces original formalisms to achieve an accurate description of dispersion interactions within the framework of density functional theory. The presented research focuses on two specific objectives related to density functional approximations: (1) the development and implementation of dispersion corrections that dramatically reduce the failures for both inter- and intramolecular interaction energies and (2) the identification of the key factors at the origin of the errors in thermochemistry. Kohn-Sham density functional theory has become the preferred methodology for modeling the energy and structural properties of large molecules, yet common semilocal and hybrid approximations are affected by well-known deficiencies as illustrated by both the delocaliza- tion error and their inability to accurately describe omnipresent long-range (van der Waals) interactions. After proposing an improved variant of “classical” atom pairwise dispersion correction, we formulate an efficient dispersion correction that is dependent upon the electron density. In contrast to the schemes that are typically applied, these dispersion coefficients reflect the charge-distribution within a molecule. Additionally, the use of density overlaps allows for distinguishing of non-bonded regions from bonded atom pairs, which eliminates the correction at covalent distances. A clear advantage of the proposed dDsC scheme is its ability to improve the performance of a variety of standard density functionals for both hydrocarbon reaction energies and typical weak interaction energies simultaneously. The density dependence also offers advantages for highly polarized and charged systems. Interaction energies of ground-state charge-transfer complexes and ¼-dimer radical cations are illustrative examples for which the delocalization error partially counterbalances the missing dispersion. We demonstrate, however, that, in practical situations, dispersion en- ergy corrections are mandatory. Following van der Waals interactions, (long-range) “exact” exchange has been identified as the second most important ingredient for obtaining robust results. The versatile methodology devised herein reveals the “true” performance of stan- dard approximations and promises many fruitful applications from metal-organic catalysis to organic-electronics. Keywords: density functional theory, van der Waals interactions, London dispersion, disper- sion correction, hydrocarbon, charge-transfer complex, charge-carrier vii Résumé Cette thèse introduit des formulations originales pour obtenir une description précise des interactions de dispersion dans le cadre de la théorie de la fonctionelle de la densité basée sur le formalisme Kohn-Sham (KS-DFT). La recherche présentée ici se concentre sur deux objectifs spécifiques : 1) le développement et l’implémentation de corrections qui réduisent considérablement les erreurs des fonctionelles de la densité pour les interactions de disper- sion inter- et intramoléculaires ; 2) l’identification des principales origines des erreurs des fonctionelles standard. La DFT s’est imposée comme la méthode de choix pour la modélisation de l’énergie et des propriétés structurelles de molécules de grande taille. Néanmoins, les approximations semi- locales et hybrides entraînent des défaillances bien connues, par exemple l’erreur de délocali- sation et leur incapacité á décrire fidèlement les interactions omniprésentes de longue portée (van der Waals). Ayant proposé une version améliorée d’une correction interatomique « classique » pour la dispersion, nous formulons ensuite une correction efficace qui dépend de la densité. A la différence de l’approche typiquement utilisée, nos coefficients de dispersion reflètent la dis- tribution de la charge électronique. De plus, le recouvrement des densités atomique permet de distinguer les contactes non-liants des liaisons chimiques, éliminant ainsi la correction dans les distances covalentes. L’avantage incontestable de l’approche proposée, dDsC, réside dans sa capacité d’améliorer conjointement les énergies de réaction d’hydrocarbures et les interactions faibles pour une grande sélection de fonctionelles standard. De plus, les systèmes chargés ou fortement polarisés bénéficient grandement de la dépendance de la densité. Des complexes de transfert de charge et des cations radicalaires de dimères ¼ sont étudiés en tant qu’exemples illustratifs de la compensation partielle entre le manque de dispersion et l‘erreur de délocalisation. Nous démontrons qu’en pratique les corrections de dispersion sont indispensables. Une fois les interactions de van der Waals prises en compte, l’échange « exact » (á longue portée) est l’ingrédient le plus important pour obtenir des résultats robustes. La méthodologie polyvalente présenté ici révèle la « vraie » performance des fonctionelles standard et laisse entrevoir des applications dans des domaines aussi divers que la catalyse organométallique et l’électronique organique. Mots-clés : théorie de fonctionelle de la densité, interactions de van der Waals, dispersion de London, correction de dispersion, hydrocarbure, complexe de transfert de charge, porteur de charge. ix Contents Acknowledgementsv Abstract vii Résumé ix Table of Contents xi 1 Introduction 1 2 Theoretical Background5 2.1 Dispersion Interactions.................................5 2.2 Density Functional Theory...............................8 2.2.1 Principles.....................................9 2.2.2 Failures....................................... 13 3 Unified Inter- and Intramolecular Dispersion Correction Formula for Generalized Gradient Approximation Density Functional Theory 21 3.1 Introduction........................................ 21 3.2 Computational Methods................................
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