Interoperable workflows by exchanging grid-based data between quantum-chemical program packages.

Quantum-chemical subsystem and embedding methods require complex workflows that may involve multiple quantum-chemical program packages. Moreover, such workflows require the exchange of voluminous data that go beyond simple quantities, such as molecular structures and energies. Here, we describe our approach for addressing this interoperability challenge by exchanging electron densities and embedding potentials as grid-based data.

Formulation and Implementation of Frequency-Dependent Linear Response Properties with Relativistic Coupled Cluster Theory for GPU-Accelerated Computer Architectures.

We present the development and implementation of relativistic coupled cluster linear response theory (CC-LR), which allows the determination of molecular properties arising from time-dependent or time-independent electric, magnetic, or mixed electric-magnetic perturbations (within a common gauge origin for the magnetic properties) as well as taking into account the finite lifetime of excited states in the framework of damped response theory. We showcase our implementation, which is capable to offload the computationally intensive tensor contractions characteristic of coupled cluster theory onto graphical processing units, in the calculation of (a) frequency-(in)dependent dipole-dipole polarizabilities of IIB atoms and selected diatomic molecules, with a particular emphasis on the calculation of valence absorption cross sections for the I molecule; (b) indirect spin-spin coupling constants for benchmark systems such as the hydrogen halides (HX, X = F-I) as well the HSe-HO dimer as a prototypical system containing hydrogen bonds; and (c) optical rotations at the sodium D line for hydrogen peroxide analogues (HY, Y = O, S, Se, Te). Thanks to this implementation, we are able to show the similarities in performance, but often the significant discrepancies, between CC-LR and approximate methods such as density functional theory.

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.

Core Excitations of Uranyl in CsUOCl from Relativistic Embedded Damped Response Time-Dependent Density Functional Theory Calculations.

X-ray spectroscopies, by their high selectivity and sensitivity to the chemical environment around the atoms probed, provide significant insights into the electronic structures of molecules and materials. Interpreting experimental results requires reliable theoretical models, accounting for environmental, relativistic, electron correlation, and orbital relaxation effects in a balanced manner. In this work, we present a protocol for the simulation of core excited spectra with damped response time-dependent density functional theory based on the Dirac-Coulomb Hamiltonian (4c-DR-TD-DFT), in which environmental effects are accounted for through the frozen density embedding (FDE) method.

Frozen-Density Embedding for Including Environmental Effects in the Dirac-Kohn-Sham Theory: An Implementation Based on Density Fitting and Prototyping Techniques.

Frozen density embedding (FDE) represents an embedding scheme in which environmental effects are included from first-principles calculations by considering the surrounding system explicitly by means of its electron density. In the present paper, we extend the full four-component relativistic Dirac-Kohn-Sham (DKS) method, as implemented in the BERTHA code, to include environmental and confinement effects with the FDE scheme (DKS-in-DFT FDE). The implementation, based on the auxiliary density fitting techniques, has been enormously facilitated by BERTHA's python API (PyBERTHA), which facilitates the interoperability with other FDE implementations available through the PyADF framework.

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.

Assessing MP2 frozen natural orbitals in relativistic correlated electronic structure calculations.

The high computational scaling with the basis set size and the number of correlated electrons is a bottleneck limiting applications of coupled cluster algorithms, in particular for calculations based on two- or four-component relativistic Hamiltonians, which often employ uncontracted basis sets. This problem may be alleviated by replacing canonical Hartree-Fock virtual orbitals by natural orbitals (NOs). In this paper, we describe the implementation of a module for generating NOs for correlated wavefunctions and, in particular, second order Møller-Plesset perturbation frozen natural orbitals (MP2FNOs) as a component of our novel implementation of relativistic coupled cluster theory for massively parallel architectures [Pototschnig et al.

Simulating core electron binding energies of halogenated species adsorbed on ice surfaces and in solution relativistic quantum embedding calculations.

In this work, we investigate the effects of the environment on the X-ray photoelectron spectra of hydrogen chloride and chloride ions adsorbed on ice surfaces, as well as of chloride ions in water droplets. In our approach, we combine a density functional theory (DFT) description of the ice surface with that of halogen species using the recently developed relativistic core-valence separation equation of motion coupled cluster (CVS-EOM-IP-CCSD) the frozen density embedding formalism (FDE), to determine the K and L edges of chlorine. Our calculations, which incorporate temperature effects through snapshots from classical molecular dynamics simulations, are shown to reproduce experimental trends in the change of the core binding energies of Cl upon moving from a liquid (water droplets) to an interfacial (ice quasi-liquid layer) environment.

Environment Effects on X-Ray Absorption Spectra With Quantum Embedded Real-Time Time-Dependent Density Functional Theory Approaches.

In this work we implement the real-time time-dependent block-orthogonalized Manby-Miller embedding (rt-BOMME) approach alongside our previously developed real-time frozen density embedding time-dependent density functional theory (rt-TDDFT-in-DFT FDE) code, and investigate these methods' performance in reproducing X-ray absorption spectra (XAS) obtained with standard rt-TDDFT simulations, for model systems comprised of solvated fluoride and chloride ions ([X@ , X = F, Cl). We observe that for ground-state quantities such as core orbital energies, the BOMME approach shows significantly better agreement with supermolecular results than FDE for the strongly interacting fluoride system, while for chloride the two embedding approaches show more similar results. For the excited states, we see that while FDE (constrained not to have the environment densities relaxed in the ground state) is in good agreement with the reference calculations for the region around the K and L edges, and is capable of reproducing the splitting of the 1s (n + 1)p final states ( + 1 being the lowest virtual p orbital of the halides), it by and large fails to properly reproduce the 1s (n + 2)p states and misses the electronic states arising from excitation to orbitals with important contributions from the solvent.

Electronic spectra of ytterbium fluoride from relativistic electronic structure calculations.

We report an investigation of the low-lying excited states of the YbF molecule-a candidate molecule for experimental measurements of the electron electric dipole moment-with 2-component based multi-reference configuration interaction (MRCI), equation of motion coupled cluster (EOM-CCSD) and the extrapolated intermediate Hamiltonian Fock-space coupled cluster (XIHFS-CCSD). Specifically, we address the question of the nature of these low-lying states in terms of configurations containing filled or partially-filled Yb 4f shells. We show that while it does not appear possible to carry out calculations with both kinds of configurations contained in the same active space, reliable information can be extracted from different sectors of Fock space-that is, by performing electron attachment and detachment IHFS-CCSD and EOM-CCSD calculation on the closed-shell YbF and YbF species, respectively.

Implementation of Relativistic Coupled Cluster Theory for Massively Parallel GPU-Accelerated Computing Architectures.

In this paper, we report reimplementation of the core algorithms of relativistic coupled cluster theory aimed at modern heterogeneous high-performance computational infrastructures. The code is designed for 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 the electronic structure are included from the outset.

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- (CHI, HX, and X, X = Cl-At) and xenon-containing (Xe, XeF) species. Our results show that the X2C molecular mean-field approach [Sikkema, J.

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 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, M.; 2015, 142, 154116].

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.

Accurate Predictions of Volatile Plutonium Thermodynamic Properties.

The ability to predict the nature and amounts of plutonium emissions in industrial accidents, such as in solvent fires at PUREX nuclear reprocessing facilities, is a key concern of nuclear safety agencies. In accident conditions and in the presence of oxygen and water vapor, plutonium is expected to form the three major volatile species PuO, PuO, and PuO(OH), for which the thermodynamic data necessary for predictions (enthalpies of formation and heat capacities) presently show either large uncertainties or are lacking. In this work we aim to alleviate such shortcomings by obtaining the aforementioned data via relativistic correlated electronic structure calculations employing the multi-state complete active space with second-order perturbation theory (MS-CASPT2) with a state-interaction RASSI spin-orbit coupling approach, which is able to describe the multireference character of the ground-state wave functions of PuO and PuO(OH).

Predictive Simulations of Ionization Energies of Solvated Halide Ions with Relativistic Embedded Equation of Motion Coupled Cluster Theory.

A subsystem approach for obtaining electron binding energies in the valence region is presented and applied to the case of halide ions (X^{-},X=F-At) in water. This approach is based on electronic structure calculations combining the relativistic equation-of-motion coupled cluster method for electron detachment and density functional theory via the frozen density embedding approach, using structures from classical molecular dynamics with polarizable force fields for discrete systems (in our study, droplets containing the anion and 50 water molecules). Our results indicate that one can accurately capture both the large solvent effect observed for the halides and the splitting of their ionization signals due to the increasingly large spin-orbit coupling of the p_{3/2}-p_{1/2} manifold across the series, at an affordable computational cost.

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.

We report in this paper an implementation of a 4-component relativistic Hamiltonian based Equation-of-Motion Coupled-Cluster with singles and doubles (EOM-CCSD) theory for the calculation of ionization potential, electron affinity, and excitation energy. In this work, we utilize the previously developed double group symmetry-based generalized tensor contraction scheme and also extend it in order to carry out tensor contractions involving non-totally symmetric and odd-ranked tensors. Several approximated spin-free and two-component Hamiltonians can also be accessed in this implementation.

On the calculation of second-order magnetic properties using subsystem approaches in a relativistic framework.

We report an implementation of nuclear magnetic resonance (NMR) shielding (σ), isotope-independent indirect spin-spin coupling (K) and the magnetizability (ξ) tensors in a frozen density embedding scheme using the four-component (4c) relativistic Dirac-Coulomb (DC) Hamiltonian and non-collinear spin density functional theory. The formalism takes into account the magnetic balance between the large and the small components of molecular spinors and assures the gauge-origin independence of the NMR shielding and magnetizability results. This implementation has been applied to hydrogen-bonded HXHOH complexes (X = Se, Te, Po) and compared with supermolecular calculations and with an approach based on the integration of the magnetically induced current density vector.

On the multi-reference nature of plutonium oxides: PuO, PuO, PuO and PuO(OH).

Actinide-containing complexes present formidable challenges for electronic structure methods due to the large number of degenerate or quasi-degenerate electronic states arising from partially occupied 5f and 6d shells. Conventional multi-reference methods can treat active spaces that are often at the upper limit of what is required for a proper treatment of species with complex electronic structures, leaving no room for verifying their suitability. In this work we address the issue of properly defining the active spaces in such calculations, and introduce a protocol to determine optimal active spaces based on the use of the Density Matrix Renormalization Group algorithm and concepts of quantum information theory.

Structural, dynamical, and transport properties of the hydrated halides: How do At(-) bulk properties compare with those of the other halides, from F(-) to I(-)?

The properties of halides from the lightest, fluoride (F(-)), to the heaviest, astatide (At(-)), have been studied in water using a polarizable force-field approach based on molecular dynamics (MD) simulations at the 10 ns scale. The selected force-field explicitly treats the cooperativity within the halide-water hydrogen bond networks. The force-field parameters have been adjusted to ab initio data on anion/water clusters computed at the relativistic Möller-Plesset second-order perturbation theory level of theory.

Effective bond orders from two-step spin-orbit coupling approaches: the I2, At2, IO(+), and AtO(+) case studies.

The nature of chemical bonds in heavy main-group diatomics is discussed from the viewpoint of effective bond orders, which are computed from spin-orbit wave functions resulting from spin-orbit configuration interaction calculations. The reliability of the relativistic correlated wave functions obtained in such two-step spin-orbit coupling frameworks is assessed by benchmark studies of the spectroscopic constants with respect to either experimental data, or state-of-the-art fully relativistic correlated calculations. The I2, At2, IO(+), and AtO(+) species are considered, and differences and similarities between the astatine and iodine elements are highlighted.

Communication: Relativistic Fock-space coupled cluster study of small building blocks of larger uranium complexes.

We present a study of the electronic structure of the [UO2](+), [UO2](2 +), [UO2](3 +), NUO, [NUO](+), [NUO](2 +), [NUN](-), NUN, and [NUN](+) molecules with the intermediate Hamiltonian Fock-space coupled cluster method. The accuracy of mean-field approaches based on the eXact-2-Component Hamiltonian to incorporate spin-orbit coupling and Gaunt interactions are compared to results obtained with the Dirac-Coulomb Hamiltonian. Furthermore, we assess the reliability of calculations employing approximate density functionals in describing electronic spectra and quantities useful in rationalizing Uranium (VI) species reactivity (hardness, electronegativity, and electrophilicity).

Electronic structure investigation of the evanescent AtO(+) ion.

The electronic structure of the XO and XO(+) (X = I, At) species, as well that of a AtO(+)-H2O complex have been investigated using relativistic wave-function theory and density functional theory (DFT)-based approximations (DFAs). The n-electron valence state perturbation method with the perturbative inclusion of spin-orbit coupling including spin-orbit polarization effects (SO-NEVPT2) was shown to yield transition energies within 0.1 eV of the reference four-component intermediate Fock-space coupled cluster (DC-IHFSCCSD) method at a significantly lower computational cost and can therefore be used as a benchmark to more approximate approaches in the case of larger molecular systems.

Solvatochromic shifts from coupled-cluster theory embedded in density functional theory.

Building on the framework recently reported for determining general response properties for frozen-density embedding [S. Höfener, A. S.