Efficient Parallel All-Electron Four-Component Dirac–Kohn–Sham Program Using a Distributed Matrix Approach II

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. The accuracy and numerical stability of this new implementation, also using different auxiliary fitting basis sets, has been demonstrated on the simple NH₃-H₂O system, in comparison with a reference nonrelativistic implementation. The computational performance has been evaluated on a series of gold clusters (Au_n, with n = 2, 4, 8) embedded into an increasing number of water molecules (5, 10, 20, 40, and 80 water molecules). We found that the procedure scales approximately linearly both with the size of the frozen surrounding environment (consistent with the underpinnings of the FDE approach) and with the size of the active system (in line with the use of density fitting). Finally, we applied the code to a series of heavy (Rn) and super-heavy elements (Cn, Fl, Og) embedded in a C₆₀ cage to explore the confinement effect induced by C₆₀ on their electronic structure. We compare the results from our simulations, with respect to more-approximate models employed in the atomic physics literature. Our results indicate that the specific interactions described by FDE are able to improve upon the cruder approximations currently employed, and, thus, they provide a basis from which to generate more-realistic radial potentials for confined atoms.

Local Charge-Displacement Analysis: Targeting Local Charge-Flows in Complex Intermolecular Interactions

Charge-displacement (CD) analysis has recently proven to be a simple and powerful scheme for quantitatively analyzing the profile of the charge redistribution occurring upon intermolecular interactions along a given interaction axis. However, when two molecular fragments bind through complex interactions involving multiple concurrent charge flows, ordinary CD analysis is capable of providing only an averaged picture of the related charge-flow profiles and no detailed information on each of them. In this article, we combine CD analysis with a Hirshfeld partitioning of the molecular charge redistribution for a local analysis on focused portions of the molecule, allowing for a detailed characterization of one charge flow at a time. The resulting scheme - the local charge-displacement (LCD) analysis - is tested on the intriguing case of the dimethyl sulfide (DMS)-sulfur dioxide (SO2) complex, characterized by concurrent charge flows relating to a sulfur-sulfur homo-chalcogen interaction and a pair of hydrogen bonds. The LCD scheme is then applied to the analysis of multiple hydrogen bonding in the acetic acid dimer, of base-pairing interactions in DNA, and of ambifunctional hydrogen bonding in the ammonia-pyridine complex.

Charge-Flow Profiles along Curvilinear Paths: A Flexible Scheme for the Analysis of Charge Displacement upon Intermolecular Interactions

The Charge-Displacement (CD) analysis has proven to be a powerful tool for a quantitative characterization of the electron-density flow occurring upon chemical bonding along a suitably chosen interaction axis. In several classes of interesting intermolecular interactions, however, an interaction axis cannot be straightforwardly defined, and the CD analysis loses consistency and usefulness. In this article, we propose a general, flexible reformulation of the CD analysis capable of providing a quantitative view of the charge displacement along custom curvilinear paths. The new scheme naturally reduces to ordinary CD analysis if the path is chosen to be a straight line. An implementation based on a discrete sampling of the electron densities and a Voronoi space partitioning is described and shown in action on two test cases of a metal-carbonyl and a pyridine-ammonia complex.

Chemical bonding in cuprous complexes with simple nitriles: octet rule and resonance concepts versus quantitative charge-redistribution analysis

Resonance structures for six cuprous complexes with simple nitriles are interpreted by means of a quantitative analysis of charge redistribution upon copper-nitrile bonding.

How π back-donation quantitatively controls the CO stretching response in classical and non-classical metal carbonyl complexes

The CO stretching response upon coordination to a metal M to form [(L) n M(CO)] m complexes (L is an auxiliary ligand) is investigated in relation to the σ donation and π back-donation components of the M-CO bond and to the electrostatic effect exerted by the ligand-metal fragment. Our analysis encompasses over 30 carbonyls, in which the relative importance of donation, back-donation and electrostatics are varied either through the ligand in a series of [(L)Au(CO)]0/+ gold(i) complexes, or through the metal in a series of anionic, neutral and cationic homoleptic carbonyls. Charge-displacement analysis is used to obtain well-defined, consistent measures of σ donation and π back-donation charges, as well as to quantify the σ and π components of CO polarization. It is found that all complexes feature a comparable charge flow of σ symmetry (both in the M-CO bonding region and in the CO fragment itself), which is therefore largely uncorrelated to CO response. By contrast, π back-donation is exceptionally variable and is found to correlate tightly with the change in CO bond distance, with the shift in CO stretching frequency, and with the extent and direction (C → O or C ← O) of the CO π polarization. As a result, we conclusively show that π back-donation can be an important bond component also in non-classical carbonyls and we provide the framework in which the spectroscopic data on coordinated CO can be used to extract quantitative information on the π donor properties of metal-ligand moieties.

An ab Initio Benchmark and DFT Validation Study on Gold(I)-Catalyzed Hydroamination of Alkynes

High level ab initio calculations have been carried out on an archetypal gold(I)-catalyzed reaction: hydroamination of ethyne. We studied up to 12 structures of possible gold(I)-coordinated species modeling different intermediates potentially present in a catalytic cycle for the addition of a protic nucleophile to an alkyne. The benchmark is used to evaluate the performances of some popular density functionals for describing geometries and relative energies of stationary points along the reaction profile. Most functionals (including hybrid or meta-hybrid) give accurate structures but large nonsystematic errors (4-12 kcal/mol) along the reaction energy profile. The double hybrid functional B2PLYP outperforms all considered functionals and compares very nicely with our reference ab initio benchmark energies. Moreover, we present an assessment of the accuracy of commonly used approaches to include relativistic effects, such as relativistic effective potentials and a scalar ZORA Hamiltonian, by a comparison with the results obtained using a relativistic all-electron four-component Dirac-Kohn-Sham method. The contribution of nonscalar relativistic effects in gold(I)-catalyzed reactions, as we investigated here, is expected to be on the order of 1 kcal/mol.