Equation-of-motion coupled-cluster theory based on the 4-component Dirac-Coulomb(-Gaunt) Hamiltonian:Energies for single electron detachment, attachment, and electronically excited states

<p>This entry contains the figures included in the paper titled "Equation-of-Motion Coupled-Cluster Theory based on the 4-component Dirac--Coulomb(--Gaunt) Hamiltonian. Energies for single electron detachment, attachment and electronically excited states", by Avijit Shee, Trond Saue, Lucas Visscher and Andre Severo Pereira Gomes.</p> <p>It accompanies the dataset found at the DOI: 10.5281/zenodo.1320320</p> <p>There are three figures that use the (original) png files included in <a href="https://zenodo.org/api/files/7bda2e2b-ac69-41aa-a21e-821e88bfb973/original-figures.tar.bz2">original-figures.tar.bz2 </a>:</p> <p>figure 1: Potential energy curves of the spin-orbit split X²Π and A²Π states of the XO molecules, obtained with EOM-IP and the ²DCG^M Hamiltonian.</p> <p>figure 2: Internuclear distances (in Angstrom), harmonic vibrational frequencies (in cm⁻¹) and the vertical Ω = 3/2 − 1/2 energy difference (in eV) for the X²Π and A²Π states of the XO molecules, obtained with EOM-IP and the ²DCG^M Hamiltonian.</p> <p>figure 3: SO-ZORA/QZ4P/Hartree-Fock (ADF) spinor magnetization plots (isosurfaces at 0.03 a.u.) and energies (in Eh) for the valence spinors of the XO⁻ species (from left to right: X = Cl, Br, I, At, Ts).</p

Molecular properties via a subsystem density functional theory formulation: A common framework for electronic embedding

In this article, we present a consistent derivation of a density functional theory (DFT) based embedding method which encompasses wave-function theory-in-DFT (WFT-in-DFT) and the DFT-based subsystem formulation of response theory (DFT-in-DFT) by Neugebauer [J. Neugebauer, J. Chem. Phys. 131, 084104 (2009)10.1063/1.3212883] as special cases. This formulation, which is based on the time-averaged quasi-energy formalism, makes use of the variation Lagrangian techniques to allow the use of non-variational (in particular: coupled cluster) wave-function-based methods. We show how, in the time-independent limit, we naturally obtain expressions for the ground-state DFT-in-DFT and WFT-in-DFT embedding via a local potential. We furthermore provide working equations for the special case in which coupled cluster theory is used to obtain the density and excitation energies of the active subsystem. A sample application is given to demonstrate the method. © 2012 American Institute of Physics

On the performance of the intermediate Hamiltonian Fock-space coupled-cluster method on linear triatomic molecules: The electronic spectra of NpO2+, NpO22+, and Pu O22

International audienceIn this paper we explore the use of the novel relativistic intermediate Hamiltonian Fock-space coupled-cluster method in the calculation of the electronic spectrum for small actinyl ions (NpO2+, NpO22+, and PuO22+). It is established that the method, in combination with uncontracted double-zeta quality basis sets, yields excitation energies in good agreement with experimental values, and better than those obtained previously with other theoretical methods. We propose the reassignment of some of the peaks that were observed experimentally, and confirm other assignments

Environmental effects with Frozen Density Embedding in Real-Time Time-Dependent Density Functional Theory using localized basis functions

Frozen Density Embedding (FDE) represents a versatile embedding scheme to describe the environmental effect on the electron dynamics in molecular systems. The extension of the general theory of FDE to the real-time time-dependent Kohn-Sham method has previously been presented and implemented in plane-waves and periodic boundary conditions (Pavanello et al. J. Chem. Phys. 142, 154116, 2015). In the current paper, we extend our recent formulation of real-time time-dependent Kohn-Sham method based on localized basis set functions and developed within the Psi4NumPy framework (De Santis et al. J. Chem. Theory Comput. 2020, 16, 2410) to the FDE scheme. The latter has been implemented in its "uncoupled" flavor (in which the time evolution is only carried out for the active subsystem, while the environment subsystems remain at their ground state), using and adapting the FDE implementation already available in the PyEmbed module of the scripting framework PyADF. The implementation was facilitated by the fact that both Psi4NumPy and PyADF, being native Python API, provided an ideal framework of development using the Python advantages in terms of code readability and reusability. We demonstrate that the inclusion of the FDE potential does not introduce any numerical instability in time propagation of the density matrix of the active subsystem and in the limit of weak external field, the numerical results for low-lying transition energies are consistent with those obtained using the reference FDE calculations based on the linear response TDDFT. The method is found to give stable numerical results also in the presence of strong external field inducing non-linear effects

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

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

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

On the calculation of molecular properties of heavy element systems with ab initio approaches: from gas-phase to complex systems

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 relativistic 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.Cet ouvrage présente des approches théoriques applicables à la modélisation de la structure électronique d’espèces contenant des éléments lourds – c’est à dire, ceux qui se situent au-delà de la cinquième période de la classification périodique – avec un intérêt particulier porté aux lanthanides et actinides à cause de leur importance dans des domaines si variés que les appareils électroniques ou l’énergie nucléaire. La modélisation de la structure électronique pour tels systèmes requiert la prise en compte de trois ingrédients : (i) des effets relativistes dû aux vitesses très élevées des électrons du cœur, causées par la forte attraction des noyaux lourds ; (ii) des effets de corrélation électronique issus non seulement de l’interaction instantanée entre électrons mais aussi de la quasi-dégénérescences souvent présentes dans des éléments lourds possédant des couches électroniques d et f partiellement remplies ; et (iii) des effets de l’environnement sur les propriétés des molécules contenant les éléments lourds, car celles-ci se trouvent en général en phase condensée. Nous commençons par une brève révision des approches utilisées pour décrire la corrélation électronique et les effets relativistes avant de nous pencher sur la méthode intermediate Hamiltonian Fock-space coupled cluster à quatre composantes (4c-IHFSCC), de façon à établir sa précision par rapport à des résultats expérimentaux et ensuite montrer comment celle-ci peut être utilisée comme méthode de référence pour l’évaluation d’approches plus approximées. Ces comparaisons nous ont permis ensuite de choisir les approches les plus adéquates pour le traitement de systèmes moléculaires plus étendus, qui seraient impossibles à traiter avec des méthodes plus précises (et par conséquent plus coûteuses). Ensuite nous présentons la méthode frozen density embedding (FDE), une approche formellement exacte que moi-même et d’autres utilisons comme point de départ pour concevoir des méthodes efficaces du point de vue computationnel afin de décrire les effets de l’environnement dans le cadre des calculs de structure électronique. Nous discutons aussi de l’application de ces méthodes computationnelles à des systèmes contenant des éléments lourds pour montrer qu’elles sont capables de très bien décrire les effets de l’environnement (notamment dans l’absence de interactions fortes telles que des liaisons chimiques entre sous- systèmes), permettant ainsi l’utilisation d’approches telles que 4c-IHFSCC pour obtenir des spectres électroniques ou des énergies d’ionisation

Reassessing the potential of TlCl for laser cooling experiments via four-component correlated electronic structure calculations

Following the interest in the experimental realization of laser cooling for thallium fluoride (TlF), determining the potential of thallium chloride (TlCl) as a candidate for laser cooling experiments has recently received attention from a theoretical perspective [Yuan et al., J. Chem. Phys. 149, 094306 (2018)]. From these ab initio electronic structure calculations, it appeared that the cooling process, which would proceed from transitions between a3Π0+ and X1ς0+ states, had as a potential bottleneck the long lifetime (6.04 μs) of the excited state a3Π0+, that would make it very difficult to experimentally control the slowing zone. In this work, we revisit the electronic structure of TlCl by employing four-component Multireference Configuration Interaction (MRCI) and Polarization Propagator (PP) calculations and investigate the effect of such approaches on the computed transition dipole moments between a3Π0+ and a3Π1 excited states of TlCl and TlF (the latter serving as a benchmark between theory and experiment). Whenever possible, MRCI and PP results have been cross-validated by four-component equation of motion coupled-cluster calculations. We find from these different correlated approaches that a coherent picture emerges in which the results of TlF are extremely close to the experimental values, whereas for TlCl the four-component calculations now predict a significantly shorter lifetime (between 109 and 175 ns) for the a3Π0+ than prior estimates. As a consequence, TlCl would exhibit rather different, more favorable cooling dynamics. By numerically calculating the rate equation, we provide evidence that TlCl may have similar cooling capabilities to TlF. Our analysis also indicates the potential advantages of boosting stimulated radiation in optical cycles to improve cooling efficiency