Cation of Time-Dependent Density- Functional Theory Algorithms for Gaussian- and Wavelet-Based Pro- Grams

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Cation of Time-Dependent Density- Functional Theory Algorithms for Gaussian- and Wavelet-Based Pro- Grams THÈSE Pour obtenir le grade de DOCTEUR DE L’UNIVERSITÉ DE GRENOBLE Spécialité : Chimie physique Arrêté ministérial : 7 Août 2006 Présentée par Bhaarathi Natarajan Thèse dirigée par Mark Earl Casida et codirigée par Thierry Deutsch préparée au sein Département de Chimie Moléculaire (DCM) et de Chimie et Science du Vivant (CSV) Implementation, Testing, and Appli- cation of Time-Dependent Density- Functional Theory Algorithms for Gaussian- and Wavelet-based Pro- grams Thèse soutenue publiquement le Laboratoire de Chimie Théorique , devant le jury composé de : Prof. Éric Suraud Laboratoire de Physique Théorique - IRSAMC University Paul Sabatier Toulouse 3 118 Route de Narbonne, 31062 Toulouse cedex , Président Prof. Dietrich Förster CPMOH, University of Bordeaux 1, 351 Cours de la Liberation, 33405 Talence, France, Rapporteur Prof. Jürg Hutter Physical Chemistry Institute, University of Zurich, Winterthurerstrasse 190, CH- 8057 Zurich, Switzerland, Rapporteur Dr. Valérie Véniard Laboratoire des Solides Irradiés, École Polytechnique, 91128 Palaiseau Cedex, France, Examinateur Dr. Miguel Alexandre Lopes Marques Laboratoire de Physique de la Matière Condensée et Nanostructures, Univer- sité Lyon 1 et CNRS, 43 blv. du 11 novembre 1918, 69622 Villeurbanne Cedex, France, Examinateur Mark E. Casida Laboratoire de Chimie Théorique, Département de Chimie Moléculaire (DCM), Université Joseph Fourier, Grenoble, France , Directeur de thèse Thierry Deutsch Institut Nanosciences et Cryogénie, SP2M/L-Sim, CEA cedex 9, 38054 Grenoble, FRANCE , Co-Directeur de thèse Bhaarathi NATARAJAN: PhD Thesis, Implementation, Testing, and Ap- plication of Time-Dependent Density-Functional Theory Algorithms for Gaussian- and Wavelet-Based Programs , © March 3, 2012 Dedicated to my parents. ABSTRACT The interaction of light with matter is a well-established domain of physical science. For a chemical physicist, this interaction may be used as a probe (spectroscopy) or to induce chemical reactions (photo- chemistry.) Photochemical reaction mechanisms are difficult to study experimentally and even the most sophisticated modern femtosecond spectroscopic studies can benefit enormously from the light of theoret- ical simulations. Spectroscopic assignments often also require theoret- ical calculations. Theoretical methods for describing photoprocesses have been developed based upon wave-function theory and show remarkable success when going to sophisticated higher-order approxi- mations. However such approaches are typically limited to small or at best medium-sized molecules. Fortunately time-dependent density- functional theory (TD-DFT) has emerged as a computationally-simpler method which can be applied to larger molecules with an accuracy which is often, but not always, similar to high-quality wave-function calculations. Part of this thesis concerns overcoming difficulties in- volving the approximate functionals used in present-day TD-DFT. In particular, we have examined the quality of conical intersections when the Ziegler-Wang noncollinear spin-flip approach is used and have shown that the spin-flip approach has merit as a particular solution in particular cases but is not a general solution to improving the de- scription of conical intersections in photochemical simulations based upon TD-DFT. Most of this thesis concerns algorithmic improvements aimed at either improving the analysis of TD-DFT results or extending practical TD-DFT calculations to larger molecules. The implementa- tion of automatic molecular orbital symmetry analysis in de Mon2k is one contribution to improving the analysis of TD-DFT results. It also served as an introduction to a major programming project. The major methodological contribution in this thesis is the implementation of Casida’s equations in the wavelet-based code Big DFT and the subse- quent analysis of the pros and cons of wavelet-based TD-DFT where it is shown that accurate molecular orbitals are more easily obtained in Big DFT than with de Mon2k but that handling the contribution of unoccupied orbitals in wavelet-based TD-DFT is potentially more problematic than it is in a gaussian-based TD-DFT code such as de - Mon2k. Finally the basic equations for TD-DFT excited state gradients are derived. The thesis concludes with some perspectives about future work. v RÉSUMÉ L’interaction entre la matiére et le rayonnement est un domaine bien établi de la physique. Pour un physico-chimiste, cette interaction peut être utilisée comme une sonde (spectroscopie) ou pour provoquer des réactions chimiques (photo-chimie). Les mécanismes des réac- tions photochimiques sont difficiles à étudier expèrimentalement et même les études les plus sophistiquées de spectroscopies femtosec- ondes peuvent bénéficier énormément des simulations théoriques.Les résultats spectroscopiques d’ailleurs ont souvent besoin des calculs théoriques pour l’analyse de leurs spectres. Les méthodes théoriques pour décrire les processus photochimiques ont été principalement développées en utilisant le concept de la fonction d’onde à N corps et ont eu des succès remarquables. Cependant de telles approches sont généralement limitées à des petites ou moyennes molécules. Heureuse- ment la théorie de la fonctionnelle de la densité dépendant du temps (TD-DFT) a émergé comme une méthode simple de calcul pouvant être appliquée à des molécules plus grandes, avec une précision qui est souvent, mais pas toujours, semblable à la précision provenant des méthodes basés sur la fonction d’onde à N électrons. Une partie de cette thèse consiste à surmonter les difficultés des approxima- tions utilisées de nos jours en TD-DFT. En particulier, nous avons examiné la qualité des intersections coniques quand l’approche du retournement de spin non collinéaire de Ziegler-Wang est utilisée et nous avons montré que l’approche du retournement de spin, parfois ,améliore dans des cas particuliers, mais que c’est n’est pas une so- lution générale pour mieux décrire les intersections coniques dans les simulations photochimiques basées sur la TD-DFT. La plupart des parties de cette thèse traite d’améliorations algorithmiques, soit pour améliorer l’analyse des résultats de la TD-DFT, soit pour étendre les calculs de TD-DFT à de grandes molécules. L’implémentation de l’analyse automatique des symétries des orbitales moléculaires dans de Mon2k est une contribution pour améliorer l’analyse des résultats de la TD-DFT. Cela a aussi servi comme une introduction au projet de programmation majeur. La contribution méthodologique principale dans cette thèse est l’implémentation des équations de Casida dans le code Big DFT fondé sur le formalisme des ondelettes. Cette implé- mentation a aussi permis une analyse détaillée des arguments positifs et négatifs de l’utilisation de la TD-DFT fondée sur les ondelettes. On montre qu’il est plus facile d’obtenir des orbitales moléculaires précises qu’avec de Mon2k . Par contre, la contribution des orbitales inoccupées est plus problématiques qu’avec un code de gaussienne comme de Mon2k. Finalement, les équations de base des gradients vi analytiques des états excités sont dérivées pour la TD-DFT. La thèse se termine avec quelques perspectives de travaux futurs. vii PUBLICATIONS 1. Miquel Huix-Rotllant, Bhaarathi Natarajan, Andrei Ipatov, C. Muhavini Wawire, Thierry Deutsch, and Mark E. Casida, Phys. Chem. Chem. Phys., 12 , 12811-12825 (2010). "Assessment of Noncollinear Spin-Flip Tamm-Dancoff Approximation Time- Dependent Density-Functional Theory for the Photochemical Ring-Opening of Oxirane" 2. Mark E. Casida, Bhaarathi Natarajan, and Thierry Deutsch, in Fundamentals of Time-Dependent Density-Functional Theory , edited by Miquel A. L. Marques, N. T. Maitra, Fernando Noguiera, E. K. U. Gross, and Angel Rubio (Springer: in press). "Non- Born-Oppenheimer Dynamics and Conical Intersections", http: //arxiv.org/abs/1102.1849 3. Bhaarathi Natarajan, Luigi Genovese, Mark E. Casida, Thierry Deutsch, Olga N. Burchak, Christian Philouze, and Maxim Y. Balakirev, Chem. Phys., under review "Wavelet-Based Linear- Response Time-Dependent Density-Functional Theory", http: //arXiv:1108.3475v1 4. Bhaarathi Natarajan, Mark E. Casida, Luigi Genovese, and Thierry Deutsch, in Theoretical and Computational Developments in Modern Density Functional Theory, edited by A. K. Roy ( in press) . "Wavelets for Density-Functional Theory and for Post Depen- dent Density-Functional Theory Calculations", http://arXiv: 1110.4853v1 ix I can no other answer make, but, thanks, and thanks. — William Shakespeare ACKNOWLEDGMENTS The work in this thesis is very much an overlapping project between two different departments (Physics and Chemistry) in two different institutes (CEA and University of Grenoble.) Consequently, there are many people I would like to thank, without whom I would never have reached this level of academic achievement. First among them are my supervisors Mark E. Casida and Thierry Deutsch, both of whom are extremently patient, knowledgeable and hard-working, yet always approachable. Especially I am very grateful to Mark for his expert advice and all his time and support. Mark’s wide knowledge and his logical way of thinking have been of great value for me. His perpetual energy and enthusiasm in research have motivated all his students, including me. In addition, Mark is always accessible and willing to help his students with their research with his deep personal understanding. As a result, research life became smooth and rewarding for me. A special thanks to Dr. Luigi Genovese for fruitful discussions
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