Core Excitations of Uranyl in Cs2UO2Cl4 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. We showcase this approach for the uranium M4- and L3-edges and oxygen K-edge of the uranyl tetrachloride (UO2Cl42-) unit as found in a host Cs2UO2Cl4 crystal. We have found that the 4c-DR-TD-DFT simulations yield excitation spectra that very closely match the experiment for the uranium M4-edge and the oxygen K-edge, with good agreement for the broad experimental spectra for the L3-edge. By decomposing the complex polarizability in terms of its components, we have been able to correlate our results with angle-resolved spectra. We have observed that for all edges, but in particular the uranium M4-edge, an embedded model in which the chloride ligands are replaced by an embedding potential reproduces rather well the spectral profile obtained for UO2Cl42-. Our results underscore the importance of the equatorial ligands to simulating core spectra at both uranium and oxygen edges.

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. In the current work, we thereby focus on exact two-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 the starting point, but it 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.

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.; J. Chem. Phys. 2015, 142, 154116]. In the current paper, we extend our recent formulation of the real-time time-dependent Kohn-Sham method based on localized basis set functions and developed within the Psi4NumPy framework 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 employed this new implementation to investigate the stability of the time-propagation procedure, which is based on an efficient predictor/corrector second-order midpoint Magnus propagator employing an exact diagonalization, in combination with the FDE scheme. 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 the 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 a strong external field inducing nonlinear effects. Preliminary results are reported for high harmonic generation (HHG) of a water molecule embedded in a small water cluster. The effect of the embedding potential is evident in the HHG spectrum reducing the number of the well-resolved high harmonics at high energy with respect to the free water. This is consistent with a shift toward lower ionization energy passing from an isolated water molecule to a small water cluster. The computational burden for the propagation step increases approximately linearly with the size of the surrounding frozen environment. Furthermore, we have also shown that the updating frequency of the embedding potential may be significantly reduced, much less than one per time step, without jeopardizing the accuracy of the transition energies.

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 PuO2, PuO3, and PuO2(OH)2, 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 PuO3 and PuO2(OH2). We benchmark this approach by comparing it to relativistic coupled cluster calculations for the ground, ionized, and excited states of PuO2. Our results allow us to predict enthalpies of formation ΔfH⊖(298.15 K) of PuO2, PuO3, and PuO2(OH)2 to be -449.5 ± 8.8, -553.2 ± 27.5, and -1012.6 ± 38.1 kJ mol-1, respectively, which confirm the predominance of plutonium dioxide but also reveal the existence of plutonium trioxide in the gaseous phase under oxidative conditions, though the partial pressures of PuO3 and PuO2(OH)2 are nonetheless always rather low under a wet atmosphere. Our calculations also permit us to reassess prior results for PuO2, establishing that the ground state of the PuO2 molecule is mainly of 5Σg+ character, as well as to confirm the experimental value for the adiabatic ionization energy of PuO2.

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. We have applied this method to the halogen monoxide (XO, X = Cl, Br, I, At, Ts) species, in order to assess the quality of a few other recent EOM-CCSD implementations, where spin-orbit coupling contribution has been approximated in different degrees. Besides, we have also studied various excited states of CH2IBr, CH2I2, and I 3 - (as well as single electron attachment and detachment electronic states of the same species) where comparison has been made with a closely related multi-reference coupled-cluster method, namely, Intermediate Hamiltonian Fock Space Coupled-Cluster singles and doubles theory.

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. Furthermore, owing to the quantum mechanical treatment of both solute and solvent electron binding energies of semiquantitative quality are also obtained for (bulk) water as by-products of the calculations for the halogens (in droplets).