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. We describe the approach that we have implemented to this end in a dedicated code, PyEmbed, currently part of a Python scripting framework. We discuss how it has facilitated the development of quantum-chemical subsystem and embedding methods and highlight several applications that have been enabled by PyEmbed, including wave-function theory (WFT) in density-functional theory (DFT) embedding schemes mixing non-relativistic and relativistic electronic structure methods, real-time time-dependent DFT-in-DFT approaches, the density-based many-body expansion, and workflows including real-space data analysis and visualization. Our approach demonstrates, in particular, the merits of exchanging (complex) grid-based data and, in general, the potential of modular software development in quantum chemistry, which hinges upon libraries that facilitate interoperability.

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.

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 HXHOH2 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. A comparison with the approximate zeroth-order regular approximation (ZORA) Hamiltonian indicates non-negligible differences in σ and K in the HPoHOH2 complex, and calls for a thorough comparison of ZORA and DC Hamiltonians in the description of environment effects on NMR parameters for molecular systems with heavy elements.

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. These wavefunction calculations indicate that the ground state for the AtO(+) and AtO(+)-H2O systems is the Ω = 0(+) component of the (3)Σ(-) LS state, which is quite well separated (by ≃0.5 eV) from the Ω = 1 components of the same state and from the Ω = 2 state related to the (1)Δ LS state (by ≃1 eV). Time-dependent DFT calculations, on the other hand, place the Ω = 1 below the Ω = 0(+) component with the spurious stabilization of the former increasing as one increases the amount of Hartree-Fock exchange in the DFAs, while those employing the Tamm-Dancoff approximation and DFAs not including Hartree-Fock exchange yield transition energies in good agreement with SO-NEVPT2 or DC-IHFSCCSD for the lower-lying states. These results indicate the ingredients necessary for devising a DFA-based computational protocol applicable to the study of the properties of large AtO(+) clusters so that it may (at least) qualitatively reproduce reliable reference (SO-NEVPT2) calculations.

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 I2 molecule; (b) indirect spin-spin coupling constants for benchmark systems such as the hydrogen halides (HX, X = F-I) as well the H2Se-H2O dimer as a prototypical system containing hydrogen bonds; and (c) optical rotations at the sodium D line for hydrogen peroxide analogues (H2Y2, 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. Comparing standard CC response theory with the flavor based upon the equation of motion formalism, we find that for valence properties such as polarizabilities, the two frameworks yield very similar results across the periodic table as found elsewhere in the literature; for properties that probe the core region, such as spin-spin couplings, on the other hand, we show a progressive differentiation between the two as relativistic effects become more important. Our results also suggest that as one goes down the periodic table, it may become increasingly difficult to measure pure optical rotation at the sodium D line due to the appearance of absorbing states.

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.