On the Calculation of Molecular Properties of Heavy Element Systems with Ab Initio Approaches: from Gas-Phase to Complex Systems André Severo Pereira Gomes

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On the Calculation of Molecular Properties of Heavy Element Systems with Ab Initio Approaches: from Gas-Phase to Complex Systems André Severo Pereira Gomes On the calculation of molecular properties of heavy element systems with ab initio approaches: from gas-phase to complex systems André Severo Pereira Gomes To cite this version: André Severo Pereira Gomes. On the calculation of molecular properties of heavy element systems with ab initio approaches: from gas-phase to complex systems. Theoretical and/or physical chemistry. Universite de Lille, 2016. tel-01960393 HAL Id: tel-01960393 https://hal.archives-ouvertes.fr/tel-01960393 Submitted on 19 Dec 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. M´emoirepr´esent´epour obtenir le dipl^omed' Habilitation `adiriger des recherches { Sciences Physiques de l'Universit´ede Lille (Sciences et Technologies) ANDRE´ SEVERO PEREIRA GOMES Universit´ede Lille - CNRS Laboratoire PhLAM UMR 8523 On the calculation of molecular properties of heavy element systems with ab initio approaches: from gas-phase to complex systems M´emoirepr´esent´epour obtenir le dipl^omed' Habilitation `adiriger des recherches { Sciences Physiques de l'Universit´ede Lille (Sciences et Technologies) ANDRE´ SEVERO PEREIRA GOMES Universit´ede Lille - CNRS Laboratoire PhLAM UMR 8523 On the calculation of molecular properties of heavy element systems with ab initio approaches: from gas-phase to complex systems Soutenue publiquement le 16/12/2016, Membres du jury Rapporteur Hans Jørgen Aagaard Jensen Assistant Professor, Department of Chemistry and Physics, University of Southern Denmark, Odense, Denmark Rapporteur Nikolas Kaltsoyannis Professor and Head of Computational Chemistry, School of Chemistry, The University of Manchester, Manchester, UK Rapporteur Octavio Roncero Investigador Cient´ıfico,Dept. Fisica Atomica, Molecular y de Agregados, Instituto de Fisica Fundamental (C.S.I.C.), Madrid, Spain Examinateur Sylvain Cristol Professeur, Universit´ede Lille (Sciences et Technologies), Villeneuve d'Ascq, France Garant de l'habilitation Val´erieVallet Directrice de recherche au CNRS, Universit´ede Lille (Sciences et Technologies), Villeneuve d'Ascq, France c Andr´eSevero Pereira Gomes, April 11, 2017 Contents Contents 5 1 Abstract 1 2 Sommaire 3 3 Preface 5 4 Background and Motivation 7 4.1 Heavy elements from the perspective of \goal-driven" research . 7 4.2 Heavy elements from the perspective of \curiosity-driven" research . 11 4.3 This manuscript . 12 5 Electronic Structure Methods 13 5.1 Electronic structure methods for excited states . 13 5.2 The molecular Hamiltonian in the relativistic framework . 27 5.3 A comparison of IHFSCC to experiment for heavy elements . 33 5.4 Benchmaking approximate methods for small systems . 39 5.5 Towards large systems with TDDFT . 44 6 Frozen Density Embedding Methods 47 6.1 Basic Ideas and Exact Theory . 47 6.2 Approximate Embedding Methods . 54 6.3 Actinyls in Cs2UO2Cl4 .................................... 61 6.4 The shortcomings of the kinetic energy density functionals: CUO-Ng complexes . 65 6.5 FDE Second-order magnetic properties: formalism and first applications . 67 7 Perspectives 77 7.1 The treatment of electron correlation for open-shell ground and excited states . 77 7.2 The calculation of molecular properties with coupled cluster approaches . 79 7.3 Generalizing molecular properties for DFT-in-DFT and CC-in-DFT embedding . 79 7.4 Improving the accuracy of embedding approaches for strongly interacting systems . 80 7.5 Combining a molecular description of properties with a periodic description of the environment . 81 Bibliography 83 A Curriculum Vitae 107 B List of Publications 113 C Calculations on Gas-phase species 117 C.1 Paper I . 118 C.2 Paper II . 128 C.3 Paper III . 141 5 6 Contents C.4 Paper IV . 150 C.5 Paper V . 162 C.6 Paper VI . 168 C.7 Paper VI . 180 D Development of FDE and Applications to Heavy Elements 195 D.1 Paper VIII . 196 D.2 Paper IX . 207 D.3 Paper X . 219 D.4 Paper XI . 236 D.5 Paper XII . 249 D.6 Paper XIII . 263 D.7 Paper XIV . 274 List of Figures 291 List of Tables 292 Chapter 1 Abstract This work discusses theoretical approaches to model the electronic structure of species containing heavy elements { that is, those from the fifth row onwards on the periodic table { with a special emphasis on lanthanides and actinides, due to their importance in a number of technological issues and applications in fields as diverse as consumer electronics and nuclear energy. The three key ingredients which should be addressed in modeling of such systems are: (i) relativistic effects, arising from the speeds close to that of the light to which inner electrons are accelerated for heavy nuclei; (ii) electron correlation effects, due to the instantaneous interactions between the electrons as well as due to quasi-degeneracies in the electronic states in heavy element species that often possess unpaired d or f electrons; and (iii) environment effects arising from the interaction of the heavy element species with surrounding molecules, since these are often found in the condensed phase. We begin by briefly reviewing the approaches used to describe electron correlation and relativis- tic effects before turning our attention to the four-component intermediate Hamiltonian Fock-space coupled cluster (4c-IHFSCC) method in order to first establish its accuracy with respect to available experimental results and later show how served as a reference method to which more approximate ones were assessed. From this assessment it is then possible to pick the most suitable approaches to, for instance, treat treat large molecular systems which are beyond the reach of very accurate (and therefore computationally very costly) approaches. Next we briefly review the frozen density embedding (FDE) method, a formally exact approach that myself and others use as a framework to devise computationally efficient schemes to account for environment effects on the aforementioned electronic structure approaches. Application of these approximate schemes to heavy element systems are discussed in order to show that FDE can be quite accurate describe environment effects (notably in the absence of strong interactions such as covalent bonds between subsystems), thus allowing one to use approaches such as 4c-IHFSCC to obtain electronic spectra or ionization energies. 1 Chapter 2 Sommaire Cet ouvrage pr´esente des approches th´eoriquesapplicables `ala mod´elisationde la structure ´electronique d'esp`ecescontenant des ´el´ements lourds { c'est `adire, ceux qui se situent au-del`ade la cinqui`eme p´eriode de la classification p´eriodique { avec un int´er^etparticulier port´eaux lanthanides et actinides `acause de leur importance dans des domaines si vari´esque les appareils ´electroniquesou l'´energie nucl´eaire. La mod´elisationde la structure ´electroniquepour tels syst`emes requiert la prise en compte de trois ingr´edients : (i) des effets relativistes d^uaux vitesses tr`es´elev´eesdes ´electronsdu cœur, caus´ees par la forte attraction des noyaux lourds ; (ii) des effets de corr´elation´electronique issus non seulement de l'interaction instantan´eeentre ´electronsmais aussi de la quasi-d´eg´en´erescencessouvent pr´esentes dans des ´el´ements lourds poss´edant des couches ´electroniques d et f partiellement remplies ; et (iii) des effets de l'environnement sur les propri´et´esdes mol´eculescontenant les ´el´ements lourds, car celles-ci se trouvent en g´en´eralen phase condens´ee. Nous commen¸conspar une br`eve r´evisiondes approches utilis´eespour d´ecrirela corr´elation ´electroniqueet les effets relativistes avant de nous pencher sur la m´ethode intermediate Hamiltonian Fock-space coupled cluster `aquatre composantes (4c-IHFSCC), de fa¸con`a´etablirsa pr´ecisionpar rapport `ades r´esultatsexp´erimentaux et ensuite montrer comment celle-ci peut ^etreutilis´eecomme m´ethode de r´ef´erencepour l'´evaluation d'approches plus approxim´ees. Ces comparaisons nous ont permis ensuite de choisir les approches les plus ad´equatespour le traitement de syst`emesmol´eculaires plus ´etendus,qui seraient impossibles `atraiter avec des m´ethodes plus pr´ecises(et par cons´equent plus co^uteuses). Ensuite nous pr´esentons la m´ethode frozen density embedding (FDE), une approche formelle- ment exacte que moi-m^emeet d'autres utilisons comme point de d´epartpour concevoir des m´ethodes efficaces du point de vue computationnel afin de d´ecrireles effets de l'environnement dans le cadre des calculs de structure ´electronique. Nous discutons aussi de l'application de ces m´ethodes com- putationnelles `ades syst`emescontenant des ´el´ements lourds pour montrer qu'elles sont capables de tr`esbien d´ecrireles effets de l'environnement (notamment dans l'absence de interactions fortes telles que des liaisons chimiques entre sous-syst`emes),permettant ainsi l'utilisation d'approches telles que 4c-IHFSCC pour obtenir des spectres ´electroniquesou des ´energiesd'ionisation. 3 Chapter 3 Preface This manuscript describes my scientific activities on the calculation of molecular properties for systems containing heavy elements such as actinides, lanthanides and transition metals, carried out during my time as Postdoctoral researcher at the Free University (VU) Amsterdam under the supervision of Lucas Visscher (2005-2006, 2007-2009), at the Universit´ede Strasbourg (2006-2007) under the supervision of Trond Saue, and at the Universit´ede Lille 1 (2009), and following my appointment at CNRS as researcher (charg´ede recherche) in 2009. The main focus of my first year as postdoc in Amsterdam was on exploring how to execute computational chemistry codes in grid environments, but I profited from this period to start exploring with Ivan Infante the use of accurate, wavefunction-based (WFT) electronic structure methods such as Fock-space coupled cluster (FSCC) to obtain the electronic states of actinyl ions.
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