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.

Topological data analysis of vortices in the magnetically-induced current density in LiH molecule.

A novel strategy for extracting axial (AV) and toroidal (TV) vortices in the magnetically-induced current density (MICD) in molecular systems is introduced, and its pilot application to LiH molecule is demonstrated. It exploits differences in the topologies of AV and TV cores and involves two key steps: selecting a scalar function that can describe vortex cores in MICD and its subsequent topological analysis. The scalar function of choice is ΩBα based on the velocity-gradient Ω method known in research on classical flows. The Topological Data Analysis (TDA) is then used to analyze the ΩBα scalar field. In particular, TDA robustly assigns distinct topological features of this field to different vortex types in LiH: AV to saddle-maximum separatrices which connect maxima to 2-saddles located on the domain's boundary, TV to a 1-cycle of the super-level sets of the input data. Both are extracted as the most persistent features of the topologically-simplified ΩBα scalar field.

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.

NMR shielding constants in group 15 trifluorides.

By combining large basis and complete basis set (CBS) extrapolations of the coupled-cluster equilibrium geometry results with rovibrational and relativistic corrections, we demonstrate that it is possible to achieve near-quantitative accuracy for the NMR shielding constants in three group 15 trifluorides - NF3, PF3 and AsF3. These systems provide a rich test set for the calculation of dynamic electron correlation effects on NMR shielding constants. Basis sets as large as aug-cc-pCV6Z were employed, together with coupled-cluster expansion up to CCSDT, at the CCSD(T)/aug-cc-pCVTZ optimised geometries. The results of this work serve to highlight the application of state-of-the-art theoretical techniques which can be employed to guide and supplement NMR experimentation. Combining chemical shifts (either from experiment or high-level calculations) has also enabled a revised reference 19F NMR shielding constant for gas phase CFCl3 to be determined.

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.

Strong enhancement of parity violation effects in chiral uranium compounds.

The effects of parity violation (PV) on the vibrational transitions of chiral uranium compounds of the type N≡UXYZ and N≡UHXY (X, Y, Z = F, Cl, Br, I) are analysed by means of exact two-component relativistic (X2C) Hartree-Fock and density functional calculations using NUFClI and NUHFI as representative examples. The PV contributions to the vibrational transitions were found to be in the Hz range, larger than for any of the earlier proposed chiral molecules. Thus, these systems are very promising candidates for future experimental PV measurements. A detailed comparison of the N≡UHFI and the N≡WHFI homologues reveals that subtle electronic structure effects, rather than exclusively a simple Z(5) scaling law, are the cause of the strong enhancement in PV contributions of the chiral uranium molecules.

A simple scheme for magnetic balance in four-component relativistic Kohn-Sham calculations of nuclear magnetic resonance shielding constants in a Gaussian basis.

We report the implementation of nuclear magnetic resonance (NMR) shielding tensors within the four-component relativistic Kohn-Sham density functional theory including non-collinear spin magnetization and employing London atomic orbitals to ensure gauge origin independent results, together with a new and efficient scheme for assuring correct balance between the large and small components of a molecular four-component spinor in the presence of an external magnetic field (simple magnetic balance). To test our formalism we have carried out calculations of NMR shielding tensors for the HX series (X = F, Cl, Br, I, At), the Xe atom, and the Xe dimer. The advantage of simple magnetic balance scheme combined with the use of London atomic orbitals is the fast convergence of results (when compared with restricted kinetic balance) and elimination of linear dependencies in the basis set (when compared to unrestricted kinetic balance). The effect of including spin magnetization in the description of NMR shielding tensor has been found important for hydrogen atoms in heavy HX molecules, causing an increase of isotropic values of 10%, but negligible for heavy atoms.

4-Component relativistic magnetically induced current density using London atomic orbitals.

We present the implementation and application of 4-component relativistic magnetically induced current density using London atomic orbitals for self-consistent field models. We obtain a magnetically balanced basis by a simple scheme where orbitals obtained by imposing restricted kinetic balance are extended by their unrestricted kinetic balance complement. The presented methodology makes it possible to analyze the concept of aromaticity based on the ring current criterion for closed-shell molecules across the periodic table and is independent of the choice of gauge origin. As a first illustration of the methodology we study plots of the magnetically induced current density and its divergence in the series C(5)H(5)E (E = CH, N, P, As, Sb, Bi) at the Kohn-Sham level, as well as integrated ring current susceptibilities, which we compare to previous results (R. Bast et al., Chem. Phys., 2009, 356, 187) obtained using a common gauge origin approach. We find that the current strength decreases monotonically along the series, but that all molecules qualify as aromatic according to the ring current criterion.

NMR shielding constants in PH3, absolute shielding scale, and the nuclear magnetic moment of 31P.

Ab initio values of the absolute shielding constants of phosphorus and hydrogen in PH(3) were determined, and their accuracy is discussed. In particular, we analyzed the relativistic corrections to nuclear magnetic resonance (NMR) shielding constants, comparing the constants computed using the four-component Dirac-Hartree-Fock approach, the four-component density functional theory (DFT), and the Breit-Pauli perturbation theory (BPPT) with nonrelativistic Hartree-Fock or DFT reference functions. For the equilibrium geometry, we obtained σ(P) = 624.309 ppm and σ(H) = 29.761 ppm. Resonance frequencies of both nuclei were measured in gas-phase NMR experiments, and the results were extrapolated to zero density to provide the frequency ratio for an isolated PH(3) molecule. This ratio, together with the computed shielding constants, was used to determine a new value of the nuclear magnetic dipole moment of (31)P: µ(P) = 1.1309246(50) µ(N).

Spin-spin coupling constants transmitted through Ir-H...H-N dihydrogen bonds.

Relativity matters: Calculations of NMR shielding tensors and spin-spin coupling constants transmitted through Ir-H...H-N dihydrogen bonds are presented. The picture shows one of the simplified models employed. It is shown that the spin-orbit relativistic effects influence the NMR shielding constants far more than the spin-spin coupling constants.We present calculations of NMR shielding tensors and spin-spin coupling constants transmitted through Ir-H...H-N dihydrogen bonds. For this purpose, three six-coordinated complexes of iridium have been selected as models of heavy metal complexes and their NMR properties have been calculated within the DFT-ZORA (density functional theory zeroth-order regular approximation) methodology. The influence of intramolecular interactions between hydrogen atoms from IrH(3) and NH(2) groups (including both single dihydrogen bonding and bifurcated hydrogen bonding) on the NMR properties is discussed and the results are compared with the experimental observations. In complexes where dihydrogen bonding occurs, the calculated value of "through-space" (1h)J(H(a)H(b)) is in the range 1.6-7.9 Hz [depending on the model, but with R(H(a)-H(b))<2.0 A], while the experimental values are 2-5 Hz for similar H(a)--H(b) distances. The (2h)J(NH) coupling is also sizeable, ranging from approximately -5.1 Hz for dihydrogen bonds of 2 A up to -7.1 Hz for very short (1.6 A) dihydrogen bonds, and should therefore be experimentally accessible when using (15)N-labelled compounds. The dihydrogen-bond transmitted spin-spin coupling constants (1h)J(HH) and (2h)J(NH) and the shielding tensor of the H(a) atom are the most sensitive probes of the H(a)-H(b) distance, which potentially makes them attractive tools to determine the structure of molecules. The main conclusions are qualitatively similar to those drawn from nonrelativistic calculations in small inorganic complexes, and the spin-orbit relativistic effects influence the NMR shielding constants far more than the spin-spin coupling constants.

Theoretical investigation on the linear and nonlinear susceptibilities of urea crystal.

The linear and second-order nonlinear susceptibilities of the urea crystal have been evaluated by applying the supermolecule approach. Calculations performed at the time-dependent Hartree-Fock (TDHF) level using the Austin model (AM1) semiempirical Hamiltonian have first demonstrated the almost additive character of the essential polarizability and first hyperpolarizability components. In fact, the only exception concerns the chi(cc) ((1)) component when stacking urea molecules along the c axis, i.e., the axis of the hydrogen bonds. This behavior has been confirmed by ab initio calculations on small clusters. The macroscopic quantities have then been determined by adopting the multiplicative scheme and by correcting the TDHF/AM1 values for missing electron correlation by means of density functional theory and coupled cluster method. The reliability of the multiplicative scheme was demonstrated for clusters as large as 3ax3bx3c. While the electron correlation correction factors are similar for a single molecule and different small clusters, the global performance of the scheme differs for the linear and nonlinear responses. For the second-order nonlinear susceptibility, our predictions are in good agreement with experiment, while for the linear susceptibility and the associated refractive index, our predictions underestimate the experimental values. The limitations of our approach may be attributed to its inability to account for more subtle cooperative effects, like those associated with a network of hydrogen bonds. Together with other works, the supermolecule calculations confirm that the sign of chi(abc) ((2)) is negative, contrary to an estimate from band structure calculation.