Réunion GDR 2013 Résumés

Présentations de revue (Mercredi)

Perspectives on density-functional theory and density-matrix functional theory

Evert Jan Baerends

Vrije Universiteit Amsterdam, Netherlands & Pohang University of Science and Technology, South Korea

Perspectives on strongly correlated electrons

Garnet Chan

Princeton University, USA

Perspectives on coupled-cluster methods

Jürgen Gauss

Johannes Gutenberg-Universität Mainz, Germany

Perspectives on correlated linear-scaling methods

Christian Ochsenfeld

Ludwig-Maximilian University of Munich, Germany

Présentations courtes (Jeudi et Vendredi)

A multi-state multi-reference coupled cluster formalism

Jean-Paul Malrieu

Laboratoire de Chimie et Physique Quantiques, Université de Toulouse et CNRS, Toulouse.

This work first returns on the intrinsic difficulties of multi-reference coupled cluster (MR-CC) formalisms. They may be formulated either in an effective Hamiltonian frame or in an intermediate effective Hamiltonian (IEH) one. In the former case complete model space approach being intractable, the incomplete model space approach is re-examined, and is formulated in terms of an IEH, despite the fact that the model space dimension is equal to the number of desired roots. Some of its drawbacks are illustrated on the magnetic systems problem. Then one proposes a multi-root complete active space (CAS)-based CC-SD, which only handles single and double excitation operators, generalising a previously proposed State Specific MR-CC formalism. The method proceeds through an iterative dressing of the matrix elements between the singles and doubles and the CAS determinants.

Reference

J. P. Malrieu, Mol. 
Phys. 111, 2451 (2013)

Fonctions d’onde multi-déterminantales sélectionnées pour les calculs Monte Carlo quantique

Emmanuel Giner

Laboratoire de Chimie et Physique Quantiques, Université de Toulouse et CNRS, Toulouse.

On sait que les méthodes Monte Carlo quantique (quantum Monte Carlo, QMC) sont d’autant plus précises et rapides que la fonction d’onde d’essai utilisée est de bonne qualité. En particulier, il est important de disposer de fonctions d’onde d’essai avec des "noeuds" (hypersurface de dimension 3N-1 où la fonction d’onde s’annule) les plus exacts possibles. Dans ce travail nous proposons de construire la fonction d’essai à partir d’une méthode d’interaction de configuration où les déterminants sont sélectionnés à l’aide d’un critère perturbatif (méthode de type CIPSI). Un des avantages de ce type de fonctions d’onde par rapport à des fonctions d’onde CASSCF ou basées sur des interactions de configuration tronquées sur un critère de degré d’excitations (IC des simples et des doubles par exemple) est que les déterminants de poids les plus forts entrent les premiers dans le développement (avec un degré d’excitation qui peut maintenant être variable), ce qui permet ainsi de limiter le développement à un nombre raisonnable de déterminants. Un autre point important est que les coefficients des déterminants de la fonction d’onde étant optimisés de manière déterministe par la diagonalisation de la matrice hamiltonienne dans la base de déterminants sélectionnés, on n’a plus nécessairement besoin d’avoir recours à l’étape d’optimisation stochastique de nombreux paramètres (linéaires/non linéaires) qui est une étape habituelle avec les autres fonctions d’onde. Nous présentons ici plusieurs applications (atome d’oxygène, molécule F2, potentiel d’ionisation de Cu, petits peptides, etc.) qui illustrent l’intérêt de la méthode et ses différents aspects.

Reference

E. Giner, A. Scemama, M. Caffarel, "Using perturbatively selected configuration interaction in quantum Monte Carlo calculations" Can.J. Chem. 91(9), 879-885 (2013).

Quantum Monte Carlo study of protonated water dimer

Mario Dagrada

Institut de Minéralogie et des Physique des Milieux Condensés, Université Pierre et Marie Curie et CNRS, Paris

In this talk I present a theoretical study of the molecular complex H5O2+ taken as simple model for proton transfer in aqueous systems; the computations are performed with a highly-correlated quantum Monte Carlo (QMC) approach. By means of a Jastrow correlated variational wave function, we have been able to reach the coupled cluster accuracy, not only in the energetics but also in the geometry of the complex. Both energetics and geometry are in strong disagreement with the GGA-DFT based calculations, commonly used to simulate the thermodynamics of proton transfer. The consequences of this disagreement will be discussed. We will show how a QMC framework, which is able to deal also with the nuclear forces, is a promising candidate to study the physics of proton transfer, where precision beyond chemical accuracy (~0.3 kcal/mol) is needed.

Numerical correlation-energy functional for lattice density-functional theory: A systematic approach to the ground-state properties of strongly correlated systems

Matthieu Saubanère* and G. M. Pastor

Institut für Theoretische Physik, Universität Kassel, Germany

*Present affiliation: Institut Charles Gerhardt, Université Montpellier 2 et CNRS, Montpellier

We present an accurate method to determine ground-state properties of strongly-correlated electrons decribed by lattice-model Hamiltonians. In lattice density-functional theory (LDFT) the basic variable is the one-particle density matrix $\gamma$. From the HK theorem, the ground state Energy $E_{gs}[\gamma_{gs}] = \min_{\gamma} E[\gamma]$ is obtained by minimizing the energy over all the representable $\gamma$. The energy functional can be divided into two contributions: the kinetic-energy functional, which linear dependence on $\gamma$ is axactly known, and the correlation-energy functional $W[\gamma]$, which approximation constitutes the actual challenge. Within the framework of LDFT, we develope a numerical approach to $W[\gamma]$, which involves the exact diagonalisation of an effective many-body Hamiltonian of a cluster surrounded by an effective field. This effective Hamiltonian depends on the density matrix $\gamma$. In this talk we discuss the formulation of the method and its application to the Hubbard and single-impurity Anderson models in one and two dimensions. The accuracy of the method is deponstrated by comparison with the Bethe-Ansatz solution (1D), density-matrix renormalization group calculations (1D), and quantum Monte Carlo simulations (2D).

Etude DFT et multi configurationelle de la spectroscopie et de la fragmentation du cation de la benzophénone

Noura Khemiri¹, Sabri Messaoudi¹, Manef Abderrabba¹ et Majdi Hochlaf²

¹ Laboratoire Matériaux, Molécules et Applications, Institut Préparatoire aux Etudes Scientifiques et Techniques, La Marsa, Université de Carthage, Tunisie

² Laboratoire Modélisation et Simulation Multi Echelle, Université Paris-Est et CNRS, Marne-la-Vallée

Nous avons étudié les géométries du cation de la benzophénone et des deux produits résultants de sa fragmentation par la méthode de la théorie de la fonctionnelle de la densité. Nos calculs ont été réalisés en phase gazeuse en utilisant la Base aug-cc-pVTZ et la fonctionnelle PBE1PBE. Nous avons déterminé les paramètres des structures optimisées ainsi que leurs fréquences harmoniques. Nous sommes entrain d'étudier leurs fréquences anharmoniques. Nous avons déterminé les états électroniques excités de la benzophénone ionisée par la méthode multi configurationelle CASSCF et nous avons tracé les courbes d'énergie correspondantes à ces états en fonction de la distance entre les deux produits de la fragmentation. Nos résultats ont été comparés aux résultats expérimentaux de la spectroscopie et de la fragmentation du cation de la benzophénone obtenus au Synchrotron Soleil dans l'équipe de Benoit Soep.

L'approche Broken Symmetry dans le formalisme UDFT : prise en compte de la corrélation statique

Asma Marzouk

Laboratoire de dynamique interactions et réactivité, Université Pierre et Marie Curie et CNRS, Paris

Les systèmes fortement corrélés constituent une sérieuse difficulté pour les méthodes mono-déterminantales de la Chimie Quantique. La description correcte de la structure électronique et la surface de potentiel de la molécule Cr2 n'a pu être réalisée que par une méthode MRCI en plus de 1 billion de configurations.[1] Nous allons montré que l'approche BS-UDFT est capable de reproduire les données les plus fiables d'une manière satisfaisante. En mettant en valeurs les avantages de cette technique, nous insisterons également sur ses limites. Nous utiliserons trois exemples simples, Cr2, [2] Ti2O [3] et (CoO2)(O2)2 [4] pour illustrer notre démarche.

References

[1] H. Dachsel, R. J. Harrison, D. A. Dixon, J. Phys. Chem. A 1999, 103, 152-155

[2] K. E. Edgecombe, A. D. Becke, Chemical Physics Letters 1995, 244,427-432

[3] A. Marzouk, H. Bolvin, P. Reinhardt, L. Manceron, J.P. Perchard, B. Tremblay, M.E. Alikhani, J. Phys. Chem. A (Submitted)

[4] A. Marzouk, D. Danset, M.F. Zhou, Y. Gong, M. E. Alikhani, L. Manceron , J. Phys. Chem. A 2011, 115, 9014–9021

Random-phase approximation correlation energies from Lanczos chains and an optimal basis set: Theory and applications to the benzene dimer

Dario Rocca

Laboratoire de Cristallographie, Résonance Magnétique et Modélisations, Université de Lorraine and CNRS, Nancy

A new ab initio approach is introduced to compute the correlation energy within the adiabatic connection fluctuation dissipation theorem in the random phase approximation [1]. First, an optimally small basis set to represent the response functions is obtained by diagonalizing an approximate dielectric matrix containing the kinetic energy contribution only. Then, the Lanczos algorithm is used to compute the full dynamical dielectric matrix and the correlation energy. The convergence issues with respect to the number of empty states or the dimension of the basis set are avoided and the dynamical effects are easily kept into account. To demonstrate the accuracy and efficiency of this approach the binding curves for three different configurations of the benzene dimer are computed: T-shaped, sandwich, and slipped parallel.

Reference

[1] D. Rocca, 2013 (submitted)

Analytical gradients of random phase approximation correlation energies in range-separated-hybrid context: Theory and implementation

Bastien Mussard

Laboratoire de Cristallographie, Résonance Magnétique et Modélisations, Université de Lorraine and CNRS, Nancy

In view of the recent revival of interest in the Random Phase Approximation (RPA) in a range-separated hybrid (RSH) context as a method to calculate ground-state correlation energies of electronic systems, in particular systems where long-range electron-electron interaction play an important role, we propose a method to obtain the gradient of RSH-RPA energies. Taking advantage of the Lagrangian formalism and using several versions of the Riccati equations associated to the RPA problem (which are in some cases equivalent to the rCCD expressions), we obtain a compact matrix formulation for the energy gradient. The resulting algebra is implemented in the Molpro program suite, exploiting analogies with the analytical gradient of the Møller–Plesset (MP2) energy. Simple test cases and examples of geometry optimizations will be shown.

Noyau de corrélation Bethe-Salpeter dépendant de la fréquence pour le calcul des énergies d’excitation en TDDFT

Elisa Rebolini, Julien Toulouse et Andreas Savin

Laboratoire de Chimie Théorique, Université Pierre et Marie Curie et CNRS, Paris

Bien que la théorie de la fonctionnelle de la densité dépendante du temps (TDDFT) [1] soit devenue une méthode de référence pour le calcul des énergies d’excitation dans des systèmes de taille moyenne, les approximations usuelles telles que l’approximation adiabatique et les approximations (semi)-locales ne sont pas la panacée. En effet, les excitations simples vers des états de valence bas en énergie sont bien décrites, mais les énergies vers les états de Rydberg plus hauts en énergie sont largement sous-estimées. De plus, les excitations à transfert de charge ou présentant un caractère multiple sont extrèmement mal (voire pas du tout) décrites dans ces approximations.La séparation de portée de l’interaction éléctronique [2] réalisée sur la partie d’échange du noyau a permis de résoudre les cas du transfert de charge et des états de Rydberg en introduisant une partie d’échange non-local à longue portée [3, 4]. Cependant, le problème des excitations multiples demeure. En effet, pour les traiter en restant dans un formalisme mono-déterminantal, un noyau dépendant de la fréquence est nécessaire [5]. Afin de les prendre en compte, nous avons étendu la séparation de portée au noyau de corrélation et proposons un noyau de corrélation au deuxième ordre de perturbation basée sur le noyau de Bethe-Salpeter utilisé en physique de la matière condensée [7, 6]. Dans cette présentation, je vais présenter la dérivation de ce noyau ainsi que quelques résultats préliminaires.

Références

[1] M. E. Casida. In D. P. Chong, editor, Recent Advances in Density Functional Methods, Part I, page 155. World Scientific, Singapore, 1995.

[2] Andreas Savin. On degeneracy, near-degeneracy and density functional theory. In Recent Developements and Applications of Modern Density Functional Theory, page 327. 1996.

[3] Y. Tawada, T. Tsuneda, S. Yanagisawa, T. Yanai, and K. Hirao. J. Chem. Phys., 120 :8425, 2004.

[4] E. Rebolini, A. Savin, and J. Toulouse. Mol. Phys., 2013.

[5] Giovanni Onida, Lucia Reining, and Angel Rubio. Rev. Mod. Phys., 74 :601, 2002.

[6] E. Rebolini, J. Toulouse, and A. Savin. Concepts and Methods in Modern Theoretical Chemistry, Vol. 1 : Electronic Structure and Reactivity, chapter 18. CRC Press, 2013.

[7] G. Strinati. Application of the Green’s functions method to the study of the optical properties of semicon- ductors. La Rivista del Nuovo Cimento (1978-1999), 11(12) :1–86, 1988.

On the combination of range-separated density-functional perturbation theory with optimized effective potential techniques

Alexandrina Stoyanova¹ , Yann Cornaton² , Andrew M. Teale^3,4 , and Emmanuel Fromager²

¹ Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany

² Laboratoire de Chimie Quantique, Institut de Chimie, Université de Strasbourg et CNRS, Strasbourg

³ Center for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, Norway

⁴ Cripps Computing Centre South, University of Nottingham, UK

In this presentation, we will explore the combination of Møller-Plesset second-order (MP2) perturbation theory and optimized effective potential (OEP) techniques in the context of range-separated density functional theory (srDFT). The rigorous merge of a MP2 treatment of the long-range electron-electron interaction with density functional approximations for the short-range counterpart has been formulated in a number of studies [1–4] and applied for example, using various local and semi-local functionals, to the dispersion forces in rare gas complexes, see, e.g., Ref. 2. These approaches have been referred to as MP2-srDFT [3,4] or range separated hybrid approaches with second order perturbation corrections (RSH+MP2) [1,2]. Within the framework of those srDFT formalisms, we considered recently5 an alternative separation of the short-range exchange and correlation energies, proposed initially by Toulouse et al. [6] , which permits, unlike in MP2-srDFT, to treat explicitly the short-range exchange energy (at the Hartree-Fock (HF) level) as well as the coupling between long- and short-range correlations at the MP2 level. In this new scheme5 , the MP2 energy contributions are based on the orbitals and orbital energies for the auxiliary long-range interacting system that are obtained using an approximate short-range LDA (srLDA) potential at the HF long-range level. In the present work, we will go beyond the LDA and utilize OEP techniques to obtain (more) accurate short-range exchange-correlation potentials (i.e., srOEPs) and orbitals, respectively. As a first approximation, the srOEPs obtained at the long-range HF level will be studied that include no long- and long-/short-range MP2 contributions to the srOEP [7]. The performance of this MP2-srOEP approach will be illustrated by results for the interaction energies of rare gas dimers.

References

[1] J Angyan, Y. Gerber, A. Savin and J. Toulouse, Phys. Rev. A 72, 012510 (2005).

[2] Y.C. Gerber and J.G. Angyan J. Chem. Phys. 126, 044103 (2007).

[3] E. Fromager and H. J. Aa. Jensen, Phys. Rev. A 78, 022504 (2008).

[4] E. Fromager and H. J. Aa. Jensen, J. Chem. Phys. 135, 034116 (2011).

[5] Y. Cornaton, A. Stoyanova, H. J. Aa. Jensen and E. Fromager, Phys. Rev. A 88, 022516 (2013).

[6] J. Toulouse, P. Gori-Giorgi, and A. Savin, Theor. Chem. Acc. 114, 305 (2005).

[7] A. Stoyanova, Y. Cornaton, A. M. Teale and E. Fromager in preparation.

Connexion adiabatique généralisée pour un ensemble d’états excités partiellement occupés : exemple de H2

Odile Franck*, Emmanuel Fromager

Laboratoire de Chimie Quantique, Institut de Chimie, Université de Strasbourg et CNRS, Strasbourg

* Affiliation actuelle : Laboratoire de Chimie Théorique, Université Pierre et Marie Curie et CNRS, Paris

Dans ce travail nous avons étudié la possibilité de décrire les états excités en utilisant une méthode DFT indépendante du temps. C’est en principe possible en considérant un ensemble comprenant l’état fondamental et tous les états excités jusqu’à celui que l’on souhaite décrire. La DFT pour les ensembles a été formulée initialement par Theophilou [1] pour les equi-ensembles puis généralisée par Gross et al. [2] en se basant sur le principe variationnel de Rayleigh-Ritz. Dans notre étude nous nous sommes limités à un ensemble de deux états non dégénérés. Nous avons introduit une connexion adiabatique généralisée pour les ensembles (GACE) [3] le long de laquelle, à la différence de la connexion adiabatique traditionnelle [4], la densité est maintenue constante lorsque la force d’interaction mais également le poids de l’ensemble varient. En utilisant une transformée de Legendre-Fenchel [5, 6, 7] pour les ensembles nous avons construit cette GACE pour H2 en base minimale. Nous avons ainsi obtenu puis testé une approximation simple pour l’énergie d’échange-corrélation d’un ensemble de deux états.

References

[1] A. K. Theophilou, J. Phys. C 12, 5419 (1978).

[2] E. K. U. Gross, L. N. Oliveira, W. Kohn, Phys. Rev. A 37, 2809 (1988).

[3] O. Franck, E. Fromager, submitted to Mol. Phys., arXiv:1308.4596(2013).

[4] A. Nagy, Int. J. Quantum Chem. 56, 225 (1995).

[5] H. Eschring, The Fundamentals of Density Functional Theory, 2nd ed. (Eagle, Meipzig, 2003; Edition am Gutenbergplatz), Edition am Gutenbergplatz.

[6] W. Kutzelnigg, J. Mol. Structure: TEOCHEM 768, 163 (2006)

[7] R. van Leeuwen, Adv. Quantum Chem. 43, 25 (2003)

Liens entre DFT quantique et classique et le problème de la corrélation en DFT classique

Daniel Borgis

Département de Chimie, PASTER, Ecole Normale Supérieure, Paris

Je montrerai les liens entre fonctionnelle de la densité électronique en chimie quantique et fonctionnelle de la densité classique en mécanique statistique et j'essaierai d'établir comment des concepts développés DFT électronique peuvent s'appliquer en DFT classique pour résoudre des problèmes d'intérêt physico-chimique: solvatation moléculaire, interfaces complexes, reconnaissance moléculaire. La réciproque est-elle vraie ? Je monterai comment se pose le problème de la corrélation en DFT classique.

Towards systematically improvable models for heavy elements in condensed phase with frozen density embedding

Andre S. P. Gomes¹, Christoph R. Jacob², Florent Real¹, Lucas Visscher³, Valerie Vallet¹

¹ Labo. PhLAM, Université de Lille 1 et CNRS, Villeneuve d’Ascq

² Karlsruhe Institute of Technology, Center for Functional Nanostructures and Institute of Physical Chemistry, Karlsruhe, Germany

³ Amsterdam Center for Multiscale Modeling, Section Theoretical Chemistry, Faculty of Sciences, VU University Amsterdam, Amsterdam, The Netherlands

The theoretical modeling of electronic spectra is an extremely valuable tool to aid interpret experimental results for species containing heavy elements (Ln, Ac) but remains a rather difficult task, due to the need to describe electron correlation and spin-orbit effects [1] for ground and excited states in an accurate and balanced manner. Furthermore, as most chemically interesting phenomena involving such species occur in the condensed phase, the interaction of the heavy element-containing species with its surroundings must be taken into account. This can be done by constructing appropriate structural models for the total system and applying embedding approaches [2], which have the advantage of being computationally much more efficient than standard wavefunction (WFT) or Density Functional theory (DFT) approaches. In this contribution we discuss the use of a computationally simple yet fully QM/QM embedding scheme [3] based on a subsystem formulation of DFT [4], as a means to construct structural models for uranyl (UO22+) in the Cs2UO2Cl4 host crystal. We show that with such an approach the species' low-lying electronic spectrum and ionization energies can be accurately described [5] with a relatively compact embedded model, which may provide a cost-effective route to simulate the spectra of uranyl or other actinyls in solution or at interfaces.

References

[1] I. Infante, A. S. P. Gomes and L. Visscher, J. Chem. Phys, 125, 074301 (2006); F. Real, A. S. P. Gomes, L. Visscher, V. Vallet and E. Eliav, J. Phys. Chem A., 113 (45), 12504 (2009)

[2] A.S.P. Gomes, Ch.R. Jacob, Annu. Rep. Prog. Chem., Sect. C: Phys. Chem, 108, 222 (2012)

[3] A. S. P. Gomes, Ch. R. Jacob and L. Visscher, Phys. Chem. Chem. Phys, 10, 5353 (2008)

[4] T.A. Wesolowski and A. Warshel J. Phys. Chem. 97 (1993) 8050

[5] A. S. P. Gomes, C. R. Jacob, F. Real, L. Visscher and V. Vallet, Phys. Chem. Chem. Phys, in press (2013)

An improved description of solute-solvent interactions for semiempirical (NDDO) Born-Oppenheimer molecular dynamics of biomolecular systems

Antoine Marion, F. Ingrosso, G. Monard

SRSMC, Université de Lorraine et CNRS, Vandoeuvre-lès-Nancy

Developing theoretical models and computational methods to achieve a molecular description of a system in which the quantum chemical nature of the intra- and inter-molecular interactions plays an important role is indeed a challenge, when the number of degrees of freedom is large and meaningful statistics are necessary to model the phenomenon of interest. Although outstanding progresses have been made in the past decades in performing molecular dynamics (MD) simulations with density functional theory based methods to include the quantum nature of the electrons, long time scales and/or systems containing a large number of atoms still demand very high computational costs. A reasonable compromise is represented by using a lower level of quantum chemistry to model the electronic Hamiltonian. In particular, NDDO(Neglect of Diatomic Differential Overlap)-based semiempirical methods are particularly appealing, since they can be reparametrized and improved. We recently developed a new scheme allowing us to perform reasonably long MD simulations (up to nanosecond on commodity computer) of large biomolecular systems (500-1000 atoms) with a full quantum description of the electrons at semiempirical (NDDO) level of theory, the so called SEBOMD [1] methodology (SemiEmpirical Born-Oppenheimer Molecular Dynamics). This technique has already been successfully applied to simulate liquid water [1] and N-methyl acetamide [2] in aqueous solution and aims at describing the time dependent behavior of proteins in water including key quantum effects (bond making/breaking, solvent induced polarization and IR shifts, charge transfer ...). However, before reaching this goal, we first tested the ability of SEBOMD to reproduce the behavior of small molecules of biological interest in water, typically amino acid side chains. We both study hydrophobic and hydrophilic interactions in these systems, comparing our results with available experimental data for electronic/vibrationnal properties and solute first solvation shell. Here, we present part of these results, discussing the advantages and limitations of the SEBOMD methodology.

References

[1] G. Monard, M. I. Bernal-Uruchurtu, A. Van der Vaart, K. M. Merz Jr., and M. F. Ruiz-Lopez, J. Phys. Chem. 109, 3425 (2005)

[2] F. Ingrosso, G. Monard, M. Hamdi Farag, A. Bastida, and M. F. Ruiz-Lopez, J. Chem. Theory Comput. 7, 1840 (2011)

Calculation of screened coulomb interaction in strongly correlated f electron solids

Bernard Amadon, T. Applencourt and F. Bruneval

CEA

The combination of density functional theory in the local density approximation (LDA) and dynamical mean field theory (DMFT) [1] has been successful to describe localized or delocalized correlated electrons in condensed matter [2]. However, the accurate calculations of structural or spectral properties relies on the determination of the screened coulomb interactions between correlated electrons. In the last ten years, the constrained Random Phase Approximation was developped to describe the screening of correlated electrons by non correlated electrons [3]. In this presentation, we will first discuss the calculation of the screened interaction for strongly correlated metals and insulating oxides with f electrons. We will in particular discuss the importance of dynamical screening according to the system studied. Then we will show applications to DFT+DMFT calculations with a recent implementation [4].

References

[1] A. Georges et al., Rev. Mod. Phys. 68, 13 (1996)

[2] G. Kotliar et al., Rev. Mod. Phys. 78, 865 (2006)

[3] F. Aryasetiawan et al Phys. Rev. B 70, 195104 (2004)

[4] B. Amadon, Journal of Phys.: Condens. Matter 24, 075604 (2012)

Local and nonlocal correlations in strongly correlated systems: Insights into two-dimensional systems of adatoms on surfaces from self-consistently combined GW and dynamical mean field theory

Thomas Ayral^1,2, Philipp Hansmann¹, Loig Vaugier¹, Philipp Werner³, Silke Biermann^1,4

¹ Centre de Physique Théorique, Ecole Polytechnique et CNRS, Palaiseau

² Institut de Physique Théorique, CEA et CNRS, Gif-sur-Yvette

³ Department of Physics, University of Fribourg,Fribourg, Switzerland

⁴ Japan Science and Technology Agency, CREST, Kawaguchi, Japan

The properties of many strongly-correlated systems stem from the complex interplay of local and nonlocal charge and spin fluctuations, thwarting theoretical attempts at understanding their ground-state and spectral properties. We describe a method combining the so-called GW diagrammatic technique and dynamical mean- field theory and aimed at computing the momentum-resolved one- and two-particle excitations of "realistic" Hamiltonians, obtained from first principles, often characterized by both short and long-ranged interactions, with strengths ranging from weak to very strong. Accounting for one- and two-particle correlation effects in a momentum-resolved way, as well as local retardation effects due to non-local screening effects, this method not only captures the local-interaction-led metal-Mott-insulator transition, but also yields insights into charge- ordering phenomena and collective modes at high to very low temperatures and for various lattice geometries [1,2]. As an illustrative example, we will present its application to Hamiltonians describing systems of atoms adsorbed on semiconductor surfaces, and show that it successfully explains the experimentally-observed phase diagram and photoemission spectra of these materials [3].

References

[1] Thomas Ayral, Philipp Werner, and Silke Biermann, Phys. Rev. Lett. 109, 226401 (2012)

[2] Thomas Ayral, Silke Biermann, and Philipp Werner, Phys. Rev. B 87, 125149 (2013)

[3] P. Hansmann, T. Ayral, L. Vaugier, P. Werner, and S. Biermann, Phys. Rev. Lett. 110, 166401 (2013)

Diagramme de phase Hartree-Fock du gaz d'électrons homogène à 2 et 3 dimensions

Lucas Baguet

LPTMC, UPMC et CNRS, Paris

Le gaz d'électron homogène est un des modèles les plus simples de la matière condensée. Bien que les limites hautes densités (gaz de Fermi) et basses densités (cristal de Wigner) sont bien établies, le diagramme de phase complet à température nulle est toujours controversé. Notre méthode permet d'obtenir les états de plus basse énergie Hartree-Fock à toute densité, et pour des géométries variées à 2 et 3 dimensions. Nos résultats montrent que le gaz de Fermi n'est jamais le fondamental, le système préférant des structures cristallines comme le cristal de Wigner ou des ondes de densité de spin, dont la modulation évolue avec la densité (avec Q toujours inférieur à 2k_F).

Spins and charges in Sr14Cu24O41

Vita Ilakovac

Laboratoire de Chimie Physique - Matière et Rayonnement, Université Pierre et Marie Curie et CNRS, Paris

The spin-chain-spin-ladder system, Sr14Cu24O41 is the parent compound of the Sr14-xCaxCu24O41 family, whose members with Ca doping close to x ≅ 11 are the first cuprate superconductors with a non-square lattice [1]. Their structure consists of CuO2 chain layers and Cu2O3 ladder planes, separated by Sr atoms. Like in other non-conventional superconductors, the interplay of spin and charge degrees of freedom is here of great interest, as the best candidate for the Cooper pair formation mechanism seems to be the spin-fluctuation-glue. These compounds have a particular type of collective spin excitations, called triplons, which we studied in Sr14Cu24O41 by Resonant Inelastic X-ray Scattering (RIXS) at the Cu L edge [2]. The distribution of charge degrees of freedom have been studied by the O K edge polarization dependent X-ray absorption (XAS) spectra few times, with different conclusions [3,4,5]. We performed a complete 316 atom antiferromagnetic unit cell LDA+U calculations of the O K edge polarization dependent low temperature XAS spectra [6] and discovered that switching on the correlations results in a strong chain hole-appeal. For the remaining small number of holes accommodated on ladders, leg sites are preferred to rung sites. The small hole affinity of rung sites explains naturally the one- dimensional to two-dimensional crossover in the underdoped part of the phase diagram of (La,Y,Sr,Ca)14Cu24O41 [7].

References

[1] M. Uehara et al., J. Phys. Soc. Jpn. 65, 2796 (1996)

[2] J. Schlappa, et al., Phys. Rev. Lett. 103, 047401 (2009)

[3] N. Nucker et al., Phys. Rev. B 62, 14384 (2000)

[4] A. Rusydi et al., Phys.Rev. B 75, 104510 (2007)

[5] E. Kabasawa et al., J. Phys. Soc. Jpn. 77, 034704 (2008)

[6] V. Ilakovac, et al., Phys. Rev. B 85, 075108 (2012)

[7] T. Vuletic et al., Phys. Rep. 428, 169 (2006)

Anharmonic free energies and vibrational frequencies from the stochastic self-consistent harmonic approximation

Ion Errea^1,2, Matteo Calandra¹, and Francesco Mauri¹

¹ IMPMC, Université Pierre et Marie Curie et CNRS, Paris

² IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

Although generally the harmonic approximation is sufficient to describe atomic vibrations both in solids and molecules, in cases when the atomic displacements largely exceed the range in which the harmonic potential is valid, it breaks down, as well as any perturbative approach to treat anharmonic effects based on it. We present a stochastic implementation of the self-consistent harmonic approximation valid to treat anharmonicity at any temperature in the non-perturbative regime and overcome these difficulties [1]. The method is based on the minimization of the free energy with respect to a trial density matrix described by an arbitrary harmonic Hamiltonian. The minimization is performed with respect to all the free parameters in the harmonic Hamiltonian, including equilibrium positions, phonon frequencies and polarization vectors.The method is suited to study thermodynamic properties, dynamical properties and anharmonic corrections to the internal parameters in the crystal or molecular structure. The gradient of the free energy is calculated following a stochastic procedure. The validity of the method is demonstrated in the strongly anharmonic palladium and platinum hydrides [1]. In both cases we predict a strong anharmonic correction of the phonon spectra, far beyond the perturbative limit. In palladium hydrides we calculate thermodynamic properties beyond the quasiharmonic approximation, and in PtH we predict that the superconducting transition temperature at 100 GPa predicted in the harmonic approximation is strongly suppressed when anharmonic effects are included.

Reference

[1] I. Errea, M. Calandra, and F. Mauri, Submmitted arXiv:1305.7123 [cond-mat.supr-con]