The performance of approximate equation of motion coupled cluster for valence and core states of heavy element systems

The equation of motion coupled cluster singles and doubles model (EOM-CCSD) is an accurate, black-box correlated electronic structure approach to investigate electronically excited states and electron attachment or detachment processes. It has also served as a basis for developing less computationally expensive approximate models such as partitioned EOM-CCSD (P-EOM-CCSD), the second-order many-body perturbation theory EOM (EOM-MBPT(2)), and their combination (P-EOM-MBPT(2)) [S. Gwaltney et al., Chem. Phys. Lett. 248, 189-198 (1996)]. In this work we outline an implementation of these approximations for four-component based Hamiltonians and investigate their accuracy relative to EOM-CCSD for valence excitations, valence and core ionizations and electron attachment, and this for a number of systems of atmospheric or astrophysical interest containing elements across the periodic table. We have found that across the different systems and electronic states of different nature considered, partition EOM-CCSD yields results with the largest deviations from the reference, whereas second-order based approaches tend show a generally better agreement with EOM-CCSD. We trace this behavior to the imbalance brought about by the removal of excited state relaxation in the partition approaches, with respect to degree of electron correlation recovered.Comment: 5 figures, 4 table

Implementation of relativistic coupled cluster theory for massively parallel GPU-accelerated computing architectures

In this paper, we report a reimplementation of the core algorithms of relativistic coupled cluster theory aimed at modern heterogeneous high-performance computational infrastructures. The code is designed for efficient parallel execution on many compute nodes with optional GPU coprocessing, accomplished via the new ExaTENSOR back end. The resulting ExaCorr module is primarily intended for calculations of molecules with one or more heavy elements, as relativistic effects on electronic structure are included from the outset. In the current work, we thereby focus on exact 2-component methods and demonstrate the accuracy and performance of the software. The module can be used as a stand-alone program requiring a set of molecular orbital coefficients as starting point, but is also interfaced to the DIRAC program that can be used to generate these. We therefore also briefly discuss an improvement of the parallel computing aspects of the relativistic self-consistent field algorithm of the DIRAC program

Relativistic EOM-CCSD for Core-Excited and Core-Ionized State Energies Based on the Four-Component Dirac–Coulomb(−Gaunt) Hamiltonian

We report an implementation of the core–valence separation approach to the four-component relativistic Hamiltonian-based equation-of-motion coupled-cluster with singles and doubles theory (CVS-EOM-CCSD) for the calculation of relativistic core-ionization potentials and core-excitation energies. With this implementation, which is capable of exploiting double group symmetry, we investigate the effects of the different CVS-EOM-CCSD variants and the use of different Hamiltonians based on the exact two-component (X2C) framework on the energies of different core-ionized and -excited states in halogen- (CH3I, HX, and X–, X = Cl–At) and xenon-containing (Xe, XeF2) species. Our results show that the X2C molecular mean-field approach [Sikkema, J.; J. Chem. Phys. 2009, 131, 124116], based on four-component Dirac–Coulomb mean-field calculations (2DCM), is capable of providing core excitations and ionization energies that are nearly indistinguishable from the reference four-component energies for up to and including fifth-row elements. We observe that two-electron integrals over the small-component basis sets lead to non-negligible contributions to core binding energies for the K and L edges for atoms such as iodine or astatine and that the approach based on Dirac–Coulomb–Gaunt mean-field calculations (2DCGM) are significantly more accurate than X2C calculations for which screened two-electron spin–orbit interactions are included via atomic mean-field integrals

The DIRAC code for relativistic molecular calculations

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree?Fock, Kohn?Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.Fil: Saue, Trond. Université Paul Sabatier; Francia. Centre National de la Recherche Scientifique; FranciaFil: Bast, Radovan. Uit The Arctic University Of Norway; NoruegaFil: Gomes, André Severo Pereira. University Of Lille.; Francia. Centre National de la Recherche Scientifique; FranciaFil: Jensen, Hans Jorgen Aa.. University of Southern Denmark; DinamarcaFil: Visscher, Lucas. Vrije Universiteit Amsterdam; Países BajosFil: Aucar, Ignacio Agustín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; Argentina. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Física; ArgentinaFil: Di Remigio, Roberto. Uit The Arctic University of Norway; NoruegaFil: Dyall, Kenneth G.. Dirac Solutions; Estados UnidosFil: Eliav, Ephraim. Universitat Tel Aviv.; IsraelFil: Fasshauer, Elke. Aarhus University. Department of Bioscience; DinamarcaFil: Fleig, Timo. Université Paul Sabatier; Francia. Centre National de la Recherche Scientifique; FranciaFil: Halbert, Loïc. Centre National de la Recherche Scientifique; Francia. University Of Lille.; FranciaFil: Hedegård, Erik Donovan. Lund University; SueciaFil: Helmich-Paris, Benjamin. Max-planck-institut Für Kohlenforschung; AlemaniaFil: Ilias, Miroslav. Matej Bel University; EslovaquiaFil: Jacob, Christoph R.. Technische Universität Braunschweig; AlemaniaFil: Knecht, Stefan. Eth Zürich, Laboratorium Für Physikalische Chemie; SuizaFil: Laerdahl, Jon K.. Oslo University Hospital; NoruegaFil: Vidal, Marta L.. Department Of Chemistry; DinamarcaFil: Nayak, Malaya K.. Bhabha Atomic Research Centre; IndiaFil: Olejniczak, Malgorzata. University Of Warsaw; PoloniaFil: Olsen, Jógvan Magnus Haugaard. Uit The Arctic University Of Norway; NoruegaFil: Pernpointner, Markus. Kybeidos Gmbh; AlemaniaFil: Senjean, Bruno. Universiteit Leiden; Países BajosFil: Shee, Avijit. Department Of Chemistry; Estados UnidosFil: Sunaga, Ayaki. Tokyo Metropolitan University; JapónFil: van Stralen, Joost N. P.. Vrije Universiteit Amsterdam; Países Bajo

La méthode Equation of Motion Coupled Cluster pour la modélisation des états excités et propriétés des molécules contenant des éléments lourds

In this thesis, we seek to obtain certain molecular properties for species containing heavy elements or presenting atmospheric interests. For this, we use techniques to characterize the core electrons, with ionization potentials (IP) or with excitation energies (EE), allowing for example to respectively interpret X-ray Photoelectron Spectroscopy(XPS) and X-ray Absorption Spectroscopy (XAS). We also seek to characterize valence electrons through the polarizability, which is used for example to develop force fields. When we work with heavy elements or with core electrons, we must take relativistic effects into account. We therefore used the Dirac-Coulomb(-Gaunt) Hamiltonian. Furthermore, to compare our results with experiments, we need precise methods. Thus, we will work with the Coupled-Cluster (CC) method, and will use the Equation of Motion Coupled-Cluster (EOM-CC) method to obtain the IPs, EEs and electron affinities (EA). However, these two elements (4-component Hamiltonians and post-Hartree-Fock methods) imply considerable computational costs, requiring the resources of High Performance Computing (HPC) platforms.This thesis presents a study of the Core-Valence Separation (CVS) method, which will allow us to reach the properties of core electrons (IP and EE) with EOM-CC. We provide a detailed investigation of the performance of different Hamiltonians, in particular the exact two-component molecular mean field Hamiltonian. Second, we will focus on the perturbative approximations (Partioned and Many Body Perturbation Theory 2d order (MBPT (2)) to be applied to the EOM-CC matrix to limit computational costs, including for core processes. Finally, we present the work carried out in Exacorr, a new relativistic coupled cluster implementation for hybrid and massively parallel architectures. We will finish by outlining the formalism and working equations for the Linear Response Coupled-Cluster (LRCC) method, through which analytical (frequency-dependent) molecular polarizabilities can be obtained.Dans cette thèse, nous cherchons à obtenir certaines propriétés moléculaires pour des espèces contenant des éléments lourds ou présentant des intérêts atmosphériques. Pour cela, nous utilisons des techniques permettant de caractériser les électrons de cœur, avec les potentiels d'ionisation (IP) ou avec les énergies d'excitation (EE), offrant la possibilité par exemple d'interpréter respectivement les expériences X-ray Photoelectron Spectroscopy (XPS) et X-ray Absorption Spectroscopy (XAS).Nous cherchons également à caractériser les électrons de valence au travers de la polarisabilité qui est utilisée par exemple pour développer des champs de force. Quand nous travaillons avec des éléments lourds ou avec des électrons de cœur, il faut prendre en compte les effets relativistes. Nous avons donc employé l'hamiltonien de Dirac-Coulomb(-Gaunt). De plus, pour comparer nos résultats aux expériences, il nous faut des méthodes précises. Ainsi, nous travaillerons avec la méthode Coupled-Cluster (CC) et pour obtenir les (IP), les (EE) et également les affinités électroniques (EA), nous utiliserons " Equation of Motion Coupled-Cluster " (EOM-CC). Cependant, ces deux éléments (hamiltoniens à 4-composantes et méthodes post-Hartree-Fock) impliquent des coûts de calcul considérables, nécessitant les ressources de plateformes de " High Performance Computing " (HPC).Cette thèse se présentera donc selon les éléments décrits précédemment. Premièrement, nous étudierons la méthode Core-Valence Separation (CVS) qui nous permettra, à partir de EOM-CC, d'atteindre les propriétés des électrons de cœur (IP et EE). Comme ces électrons sont proches du noyau où les effets relativistes sont les plus importants, nous étudierons différents hamiltoniens, notamment "exact two-component molecular mean field Hamiltonian ". Deuxièmement, nous nous intéresserons aux approximations perturbatives (" Partioned " et " Many Body Perturbation Theory 2d order " (MBPT(2)) à appliquer à la matrice EOM-CC pour limiter les coûts computationnels.Enfin, nous présenterons des travaux réalisés sur Exacorr, une nouvelle implémentation de Coupled-Cluster relativiste pour les architectures hybrides et massivement parallèles., un nouveau module de parallélisation des calculs pour des architectures hybrides et massivement parallèles. Nous terminerons en décrivant le formalisme et les équations de travail de la méthode Linear Response Coupled-Cluster (LRCC), grâce à laquelle des polarisabilités moléculaires analytiques (dépendantes de la fréquence) peuvent être obtenues

The Equation of Motion Coupled Cluster method for modeling excited states and properties of molecules containing heavy elements

Dans cette thèse, nous cherchons à obtenir certaines propriétés moléculaires pour des espèces contenant des éléments lourds ou présentant des intérêts atmosphériques. Pour cela, nous utilisons des techniques permettant de caractériser les électrons de cœur, avec les potentiels d'ionisation (IP) ou avec les énergies d'excitation (EE), offrant la possibilité par exemple d'interpréter respectivement les expériences X-ray Photoelectron Spectroscopy (XPS) et X-ray Absorption Spectroscopy (XAS).Nous cherchons également à caractériser les électrons de valence au travers de la polarisabilité qui est utilisée par exemple pour développer des champs de force. Quand nous travaillons avec des éléments lourds ou avec des électrons de cœur, il faut prendre en compte les effets relativistes. Nous avons donc employé l'hamiltonien de Dirac-Coulomb(-Gaunt). De plus, pour comparer nos résultats aux expériences, il nous faut des méthodes précises. Ainsi, nous travaillerons avec la méthode Coupled-Cluster (CC) et pour obtenir les (IP), les (EE) et également les affinités électroniques (EA), nous utiliserons " Equation of Motion Coupled-Cluster " (EOM-CC). Cependant, ces deux éléments (hamiltoniens à 4-composantes et méthodes post-Hartree-Fock) impliquent des coûts de calcul considérables, nécessitant les ressources de plateformes de " High Performance Computing " (HPC).Cette thèse se présentera donc selon les éléments décrits précédemment. Premièrement, nous étudierons la méthode Core-Valence Separation (CVS) qui nous permettra, à partir de EOM-CC, d'atteindre les propriétés des électrons de cœur (IP et EE). Comme ces électrons sont proches du noyau où les effets relativistes sont les plus importants, nous étudierons différents hamiltoniens, notamment "exact two-component molecular mean field Hamiltonian ". Deuxièmement, nous nous intéresserons aux approximations perturbatives (" Partioned " et " Many Body Perturbation Theory 2d order " (MBPT(2)) à appliquer à la matrice EOM-CC pour limiter les coûts computationnels.Enfin, nous présenterons des travaux réalisés sur Exacorr, une nouvelle implémentation de Coupled-Cluster relativiste pour les architectures hybrides et massivement parallèles., un nouveau module de parallélisation des calculs pour des architectures hybrides et massivement parallèles. Nous terminerons en décrivant le formalisme et les équations de travail de la méthode Linear Response Coupled-Cluster (LRCC), grâce à laquelle des polarisabilités moléculaires analytiques (dépendantes de la fréquence) peuvent être obtenues.In this thesis, we seek to obtain certain molecular properties for species containing heavy elements or presenting atmospheric interests. For this, we use techniques to characterize the core electrons, with ionization potentials (IP) or with excitation energies (EE), allowing for example to respectively interpret X-ray Photoelectron Spectroscopy(XPS) and X-ray Absorption Spectroscopy (XAS). We also seek to characterize valence electrons through the polarizability, which is used for example to develop force fields. When we work with heavy elements or with core electrons, we must take relativistic effects into account. We therefore used the Dirac-Coulomb(-Gaunt) Hamiltonian. Furthermore, to compare our results with experiments, we need precise methods. Thus, we will work with the Coupled-Cluster (CC) method, and will use the Equation of Motion Coupled-Cluster (EOM-CC) method to obtain the IPs, EEs and electron affinities (EA). However, these two elements (4-component Hamiltonians and post-Hartree-Fock methods) imply considerable computational costs, requiring the resources of High Performance Computing (HPC) platforms.This thesis presents a study of the Core-Valence Separation (CVS) method, which will allow us to reach the properties of core electrons (IP and EE) with EOM-CC. We provide a detailed investigation of the performance of different Hamiltonians, in particular the exact two-component molecular mean field Hamiltonian. Second, we will focus on the perturbative approximations (Partioned and Many Body Perturbation Theory 2d order (MBPT (2)) to be applied to the EOM-CC matrix to limit computational costs, including for core processes. Finally, we present the work carried out in Exacorr, a new relativistic coupled cluster implementation for hybrid and massively parallel architectures. We will finish by outlining the formalism and working equations for the Linear Response Coupled-Cluster (LRCC) method, through which analytical (frequency-dependent) molecular polarizabilities can be obtained

Frequency-Dependent Quadratic Response Properties and Two-Photon Absorption from Relativistic Equation-of-Motion Coupled Cluster Theory

We present the implementation of quadratic response theory based upon the relativistic equation-of-motion coupled cluster method. We showcase our implementation, whose generality allows us to consider both time-dependent and time-independent electric and magnetic perturbations, by considering the static and frequency-dependent hyperpolarizability of hydrogen halides (HX, X = F-At), providing comprehensive insights into their electronic response characteristics. Additionally, we evaluated the Verdet constant for noble gases Xe and Rn and discussed the relative importance of relativistic and electron correlation effects for these magneto-optical properties. Finally, we calculate the two-photon absorption cross sections of transition [ns1S0 → (n + 1)s1S0] of Ga+ and In+, which are suggested as candidates for new ion clocks. As our implementation allows for the use of nonrelativistic Hamiltonians as well, we have compared our EOM-QRCC results to the QR-CC implementation in the DALTON code and show that the differences between CC and EOMCC response are in general smaller than 5% for the properties considered. Collectively, the results underscore the versatility of our implementation and its potential as a benchmark tool for other approximated models, such as density functional theory for higher-order properties

Relativistic equation of motion coupled cluster theory

National audienceHeavy elements (Z > 31) are widely used in technological applications (catalysts, strong magnets, nuclear fuels etc) and, as such are intimately linked to major societal issues (nuclear waste, pollution). This makes is a pressing concern to understand their behavior in complex environments, and nowadays simulations play a key role in such efforts.These elements, however, are often not easy to simulate since, in order to understand their properties it is essential to incorporate relativistic effects (scalar relativistic effects and spin-orbit coupling) into the electronic structure calculations. This has to be done at the same footing as the treatment of electron correlation, as both effects are now understood to be non-additive [1].In this contribution we discuss our current work in the development of the equation of motion coupled cluster approach based on 4-component Hamiltonians [2], including its combination with quantum embedding approaches based on the frozen density embedding framework [3], so that both ground and excited states of complex systems can be accurately treated-and predicted whenever experiments are too difficult to perform.These approaches are showcased with examples of the determination of electron binding energies and electronically excited states of actinides in the gas phase [4], and of electron binding energies halogenated species in water droplets [5]. We will also outline our current efforts to treat larger molecular systems and other molecular properties in the DIRAC (http://diracprogram.org) program. [1] T Fleig, Chem. Phys. 2, 395 (2012); T Saue, <i>ChemPhysChem<.i> <b>12</b>, 3077 (2011)[2] A Shee, T Saue, L Visscher, ASP Gomes, <i>J. Chem. Phys.</i> <b>149</b>, 174113 (2018)[3] S Höfener, ASP Gomes, L Visscher, J. Chem. Phys. 136, 044104 (2012); <i>J. Chem. Phys.</i> <b>139</b>, 104106 (2013)[4] S Kervazo, F Réal, ASP Gomes, F Virot, V Vallet, <i>Inorg. Chem.</i> <b>58</b>, 14507 (2019)[5] Y Bouchafra, A Shee, F Réal, V Vallet, ASP Gomes, <i>Phys. Rev. Lett.</i> <b>121</b>, 266001 (2018

Investigating solvent effects on the magnetic properties of molybdate ions (MoO₄^2-) with relativistic embedding

14 pages, 6 figuresWe investigate the ability of mechanical and electronic density functional theory (DFT)-based embedding approaches to describe the solvent effects on nuclear magnetic resonance (NMR) shielding constants of the ⁹⁵Mo nucleus in the molybdate ion in aqueous solution. From the description obtained from calculations with two- and four-component relativistic Hamiltonians, we find that for such systems spin-orbit coupling effects are clearly important for absolute shielding values, but for relative quantities a scalar relativistic treatment provides a sufficient estimation of the solvent effects. We find that the electronic contributions to the solvent effects are relatively modest yet decisive to provide a more accurate magnetic response of the system, when compared to reference supermolecular calculations. We analyze the errors in the embedding calculations by statistical methods as well as through a real-space representation of NMR shielding densities, which are shown to provide a clear picture of the physical processes at play