Relativistic Density Functional Theory Research Articles

On the geometry dependence of the nuclear magnetic resonance chemical shift of mercury in thiolate complexes: A relativistic density functional theory study.

Thiolate containing mercury(II) complexes of the general formula [Hg(SR) ] have been of great interest since the toxicity of mercury was recognized. 199Hg nuclear magnetic resonance spectroscopy (NMR) is a powerful tool for characterization of mercury complexes. In this work, the Hg shielding constants in a series of [Hg(SR) ] complexes are therefore investigated computationally with particular emphasis on their geometry dependence. Geometry optimizations and NMR chemical shift calculations are performed at the density functional theory (DFT) level with both the zeroth-order regular approximation (ZORA) and four-component relativistic methods. The four exchange-correlation (XC) functionals PBE0, PBE, B3LYP, and BLYP are used in combination with either Dyall's Gaussian-type (GTO) or Slater-type orbitals (STOs) basis sets. Comparing ZORA and four-component calculations, one observes that the calculated shielding constants for a given molecular geometry have a constant difference of 1070 ppm. This confirms that ZORA is an acceptable relativistic method to compute NMR chemical shifts. The combinations of four-component/PBE0/v3z and ZORA/PBE0/QZ4P are applied to explore the geometry dependence of the isotropic shielding. For a given coordination number, the distance between mercury and sulfur is the key factor affecting the shielding constant, while changes in bond and dihedral angles and even different side groups have relatively little impact.

Bis(acyl)phosphide Complexes of U(III)/U(IV): A Case of a Hidden Redox-Active Ligand.

The recently reported tris(bis(2,4,6-triisopropylbenzoyl)-phosphide)uranium (UIII(trippBAP)3, 2) complex (Inorg. Chem. 2022, 61 (32), 12508-12517) demonstrated a silent 31P NMR spectrum. This complex was described as a U(III) complex with an organic radical ligand fragment. Moreover, the EPR spectrum of 2 was indicative of an organic radical in the ligand framework complexed to uranium, in contrast to that of UIV(mesBAP)4, 1. Herein, with the help of relativistic density functional theory (DFT) calculations, the electronic structures of 1, 2, and U(mesBAP)3 (4) are examined in an effort to understand the unusual 31P NMR spectrum of 2. Results indicate the reduction of the carbonyl bonds and delocalization of the electrons over the ligands, indicative of U → L backbonding. Additionally, the reduced acyl carbons are found to exist as ketyl radicals [O═C• -] that are responsible for the silent 31P NMR spectra of 2. These findings demonstrate the redox noninnocent nature of BAP- in 2 and 4, causing uranium to exist in a formal oxidation state of +4.

Exploring the bonding and extraction separation effects of N donor ligands with different skeletons on Am(III) and Eu(III)

Designing ligands for effective separation of actinide(III)/lanthanide(III) is one of the key issues in the treatment of spent nuclear fuel. However, due to the chemical similarity of trivalent actinides and lanthanides, their separation faces a great challenge in the reprocessing of spent nuclear fuel. Nitrogen donor extractants are considered as promising reagents for separation of trivalent actinides and lanthanides. To the best of our knowledge, the pre-organized structure of the ligand has a strong influence on the extraction separation capacity. In this work, we designed four N-donor ligands (L1 and L2 with pyridine and bipyridine skeletons, respectively, and L3 and L4 both with phenanthroline skeletons) with different pre-organized structures and investigated their selective extraction for Am(III) and Eu(III) by using scalar relativistic density functional theory (DFT). The absolute minimum ESP values of these ligands and the higher HOMO level suggest that the ligand L2 may have a stronger affinity for Am(III)/Eu(III) ions than other ligands. The three average bond lengths of each complex indicate that the Am(III) and Eu(III) ions have larger bond lengths with N2 atoms than with N1 atoms. Various theoretical approaches have been used to evaluate the properties of the four ligands as well as the coordination structures, bonding properties and thermodynamic properties of the complexes of the four ligands with Am(III) and Eu(III). The WBIs, QTAIM, NBO, DOS and EDA analysis indicate that the metal–ligand bonds are mainly ionic in character, the Am-N bond has more covalency than the Eu-N bond because the Am 5f orbitals are more involved in bonding with ligand than Eu 4f orbitals. According to the extended transition state and natural orbital chemical valence theory (ETS-NOCV) analysis, electrons are obviously transferred from the lone pair of the ligand N atom to the hybrid s, d and f orbitals of the metal ion. The thermodynamic results show that the four ligands can coordinate well with the Am and Eu ions, and also have suitable separation capacity for Am and Eu. Among the four ligands, the L2 and L3 ligands have the strongest coordination ability for metals and the best extraction separation effect for Am and Eu. It can be seen that the bridging skeleton of the ligand and the number of N atoms on the five-membered ring and also different organic solvents have obvious effects on the extraction and separation capacity of the ligand. This study provides a theoretical basis for the efficient separation of Am(III)/Eu(III) by adjusting the preorganization level of ligands, and provides a theoretical basis for the design and screening of ligands by preorganization.

Dirac-Coulomb-Breit Molecular Mean-Field Exact-Two-Component Relativistic Equation-of-Motion Coupled-Cluster Theory.

We present a relativistic equation-of-motion coupled-cluster with single and double excitation formalism within the exact two-component framework (X2C-EOM-CCSD), where both scalar relativistic effects and spin-orbit coupling are variationally included at the reference level. Three different molecular mean-field treatments of relativistic corrections, including the one-electron, Dirac-Coulomb, and Dirac-Coulomb-Breit Hamiltonian, are considered in this work. Benchmark calculations include atomic excitations and fine-structure splittings arising from spin-orbit coupling. Comparison with experimental values and relativistic time-dependent density functional theory is also carried out. The computation of the oscillator strength using the relativistic X2C-EOM-CCSD approach allows for studies of spin-orbit-driven processes, such as the spontaneous phosphorescence lifetime.

Weak Bimetal Coupling-Assisted MN4 Catalyst for Enhanced Carbon Dioxide Reduction Reaction.

The design of multimetal catalysts holds immense significance for efficient CO2 capture and its conversion into economically valuable chemicals. Herein, heterobimetallic catalysts (MiMo)L were exploited for the CO2 reduction reactions (CO2RR) using relativistic density functional theory (DFT). The octadentate Pacman-like polypyrrolic ligand (H4L) accommodates two metal ions (Mo, W, Nd, and U) inside (Mi) and outside (Mo) its month, rendering a weak bimetal coupling-assisted MN4 catalytically active site. Adsorption reactions have access to energetically stable coordination modes of -OCO, -OOC, and -(OCO)2, where the donor atom(s) are marked in bold. Among all of the species, (UiMoo)L releases the most energy. Along CO2RR, it favors to produce CO. The high-efficiency CO2 reduction is attributed to the size matching of U with the ligand mouth and the effective manipulation of the electron density of both ligand and bimetals. The mechanism in which heterobimetals synergetically capture and reduce CO2 has been postulated. This establishes a reference in elaborating on the complicated heterogeneous catalysis.

Rational Design of Metallylenes for Hydrogenation Reactions

AbstractThe hydrogenation of alkenes, alkynes, carbonyls, and imines by H2‐activated metallylenes (H3C−EH2−L, CELH2; E=Si, Ge, Sn and L=NMe2, PMe2) was studied using relativistic density functional theory at ZORA‐BP86/TZ2P. By means of activation strain and Kohn–Sham molecular orbital analyses, the physical factors underlying the trends in reactivity were identified and quantified. Firstly, the hydrogenation reactivity increases on descending Group 14, that is from silylenes (E=Si) to stannylenes (E=Sn). This reactivity trend originates primarily from a reduced energy required to break the bonds between the Group 14 atom and the hydrogen atoms because the strength of these bonds decreases from Si−H to Ge−H to Sn−H. Secondly, the reactivity decreases as the Group 15 ligand changes from nitrogen to phosphorus (L=NMe2, PMe2) which stems from the trigonal pyramidal PMe2 geometry compared to the trigonal planar NMe2 geometry. The latter can, therefore, effectively engage in stronger orbital interactions with the substrate than the former, due to a more efficient HOMO–LUMO orbital overlap. By combining our insights, we rationally designed an optimally tuned catalyst (Group 14 atom and ligand) considering the overall catalytic cycle involving H2 activation of the metallylene and subsequent hydrogenation.

Evaluation of picture change effects on fractional occupation number states in noble gas atoms

In the two-component relativistic density functional theory, the picture change error (PCE), which originates from insufficient transformation of operators, should be corrected. In this study, we examine the PCE in the fractional occupation number (FON) state based on the spin-free infinite-order two-component Hamiltonian. The PCE for the total and orbital energy changes is estimated with respect to the FON electrons of the highest occupied molecular orbital and 1s core orbital in noble gas atoms. PCE is significant in core orbitals in heavy elements but relatively small in light elements and valence orbitals. The delocalization error, which can be represented by the total energy deviation from the behavior of the exact energy, is overestimated by the lack of picture change correction of the two-electron operator and underestimated by that of the density operator. Corresponding to these results, the PCE influences the value of orbital energies and slope of orbital energy change to FON.

Inquiring 199Hg NMR Parameters by Combining Ab Initio Molecular Dynamics and Relativistic NMR Calculations.

Ab initio molecular dynamics (AIMD) sampling followed by relativistic density functional theory (DFT) 199Hg NMR calculations were performed for Hg organometallic complexes in water, dimethyl sulfoxide, and chloroform. The spin-orbit coupling, a relativistic effect, is a key factor for predicting δ(Hg) and 1J(Hg-C) accurately, in conjunction with a dynamic treatment of the systems. Good agreement between the theoretical and experimental results is reached by adopting implicit (based on a continuum model) and explicit (solvent molecules treated quantum mechanically) solvation models. Broader trends appearing in the experimental data available in the literature are reproduced by the calculations, and therefore, quantum chemistry is able to assist in the assignment and interpretation of 199Hg NMR data. Less pronounced trends, such as changes in the 199Hg chemical shift in different systems with the same atom types bound to Hg, are too weak to be predicted reliably by the current state-of-the-art theoretical methods based on AIMD sampling and relativistic DFT with hybrid functionals for NMR calculations.

Nuclear level density from relativistic density functional theory and combinatorial method

Nuclear level density is calculated with the combinatorial method based on the relativistic density functional theory including pairing correlations. The Strutinsky method is adopted to smooth the total state density in order to refine the prediction at low excitation energy. The impacts of pairing correlations and moments of inertia on the nuclear level density are discussed in detail. Taking Cd112 as an example, it is demonstrated that the nuclear level density based on the relativistic density functional PC-PK1 can reproduce the experimental data at the same level as or even better than the previous approaches.

Reactivity of Ts and At oxides and oxyhydrides with a gold surface from periodic DFT calculations.

Adsorption energies, Eads, of oxides and oxyhydrides of the superheavy element (SHEs) Ts and of its lighter homologue At on the gold surface are predicted on the basis of relativistic periodic density functional theory calculations via AMS BAND software. The following compounds were considered: MO, MO2, MOO, and MO(OH) (where M = At and Ts). The aim of this study is to support "one-atom-at-a-time" gas-phase chromatography experiments on reactivity/volatility of SHEs. The results obtained indicate that all the molecules investigated should interact fairly strongly with the gold surface, with those of Ts being more reactive than At ones. The similarity in the Eads values of all the considered At compounds would make it challenging to differentiate between them while measuring their adsorption enthalpies, given experimental uncertainty. However, the difference in Eads among Ts compounds is more pronounced, so that one should be able to differentiate between the species.

Stabilization of Diborynes versus Destabilization of Diborenes by Coordination of Lewis Bases: Unravelling the Dichotomy.

We have quantum chemically investigated the boron-boron bonds in B2 , diborynes B2 L2 , and diborenes B2 H2 L2 (L=none, OH2 , NH3 ) using dispersion-corrected relativistic density functional theory at ZORA-BLYP-D3(BJ)/TZ2P. B2 has effectively a single B-B bond provided by two half π bonds, whereas B2 H2 has effectively a double B=B bond provided by two half π bonds and one σ 2p-2p bond. This different electronic structure causes B2 and B2 H2 to react differently to the addition of ligands. Thus, in B2 L2 , electron-donating ligands shorten and strengthen the boron-boron bond whereas, in B2 H2 L2 , they lengthen and weaken the boron-boron bond. The aforementioned variations in boron-boron bond length and strength become more pronounced as the Lewis basicity of the ligands L increases.

Understanding the Retro‐Cope Elimination Reaction of Linear Alkynes

AbstractThe bioorthogonal retro‐Cope elimination reaction of linear alkynes R3C−C≡C−X (R3 = combinations of H, MeO, F; X = H, F, Cl, Br, I) with N,N‐dimethylhydroxylamine was quantum chemically investigated using relativistic density functional theory at ZORA‐BP86/TZ2P. This novel reaction can be tuned through judicious substitution of the alkyne at both the terminal and propargylic position to render second‐order kinetics that rival and out‐compete strain‐promoted variants. Activation strain and quantitative molecular orbital analyses reveal that, both upon terminal or propargylic substitution of propyne, the main effect of substituting H for X is a lowering of the propyne LUMO which stabilizes the HOMO–LUMO interactions and thus the transition state. In the case of terminal substitution with larger halogens (X = Cl, Br, I), a secondary effect interferes: steric repulsion with these larger halogens is absorbed into a longer forming C⋯N bond leading to a more asynchronous reaction accompanied by less (not more) steric Pauli repulsion.

Heterocyclic Ligands with Different N/O Donor Modes for Am(III)/Eu(III) Separation: A Theoretical Perspective.

Excellent "CHON" compatible ligands based on a heterocyclic skeleton for the separation of trivalent actinides [An(III)] from lanthanides [Ln(III)] have been widely explored, the aim being spent nuclear fuel reprocessing. The combination mode of a soft/hard (N/O) donor upon the coordination chemistry of An(III) and Ln(III) should play a vital role with respect to the performance of ligands. As such, in this work, two typical experimentally available phenanthroline-derived tetradentate ligands, CyMe4-BTPhen (L1) and Et-Tol-DAPhen (L4), and two theoretically designed asymmetric tetradentate heterocyclic ligands, L2 and L3, with various N/O donors were investigated using scalar relativistic density functional theory. We have evaluated the electronic structures of L1-L4 and their coordination modes, bonding properties, and extraction reactions with Am(III) and Eu(III). We found that the Am/Eu-N interactions play a more important role in the orbital interactions between the ligand and Am(III)/Eu(III) ions. Compared with those of L1, the coordinated O atoms of L2 and L4 weaken the metal-N bonds. The Am(III)/Eu(III) selectivity follows the order L1 > L2 > L4 based on the change in Gibbs free energy, reflecting the fact that the Am(III)/Eu(III) selectivity of the ligand is affected by the number of coordinated N atoms. In addition, L3 displays the strongest binding ability for Am(III)/Eu(III) ions and the smallest Am(III)/Eu(III) selectivity among the four ligands, due to its structural preorganization. This work clarifies the influence of the number of coordinated N and O atoms of ligands on Am(III)/Eu(III) selectivity, which provides valuable fundamental information for the design of efficient ligands with N and O donors for An(III)/Ln(III) separation.

Tilt-induced charge localisation in phosphide antiperovskite photovoltaics

Antiperovskites are a rich family of compounds with applications in battery cathodes, superconductors, solid-state lighting, and catalysis. Recently, a novel series of antimonide phosphide antiperovskites (A 3SbP, where A = Ca, Sr Ba) were proposed as candidate photovoltaic absorbers due to their ideal band gaps, small effective masses and strong optical absorption. In this work, we explore this series of compounds in more detail using relativistic hybrid density functional theory. We reveal that the proposed cubic structures are dynamically unstable and instead identify a tilted orthorhombic Pnma phase as the ground state. Tilting is shown to induce charge localisation that widens the band gap and increases the effective masses. Despite this, we demonstrate that the predicted maximum photovoltaic efficiencies remain high (24%–31% for 200 nm thin films) by bringing the band gaps into the ideal range for a solar absorber. Finally, we assess the band alignment of the series and suggest hole and electron contact materials for efficient photovoltaic devices.

Tipping the Balance Between the bcc and fcc Phase Within the Alkali and Coinage Metal Groups.

Why the Group 1 elements crystallize in the body-centered cubic (bcc) structure, and the iso-electronic Group 11 elements in the face-centered cubic (fcc) structure, remains a mystery. Here we show that a delicate interplay between many-body effects, vibrational contributions and dispersion interactions obtained from relativistic density functional theory offers an answer to this long-standing controversy. It also sheds light on the Periodic Table of Crystal Structures. A smooth diffusionless transition through cuboidal lattices gives a detailed insight into the bcc→fcc phase transition for the Groups 1 and 11 elements.

Einflüsse auf die Balance zwischen bcc‐ und fcc‐Phasenstabilitäten von Alkali‐ und Münzmetallen

AbstractBisher war es ein Rätsel, weshalb die Elemente der Gruppe 1 in der kubisch‐raumzentrierten (bcc) und die iso‐elektronischen Elemente der Gruppe 11 in der kubisch‐flächenzentrierten Struktur (fcc) kristallisieren. In dieser Untersuchung auf Grundlage von relativistischer Dichtefunktionaltheorie wird demonstriert, wie ein komplexes Zusammenspiel zwischen Mehrteilcheneffekten, Schwingungsenergiebeiträgen und Dispersionswechselwirkungen eine Antwort auf diese langjährige Kontroverse liefert und dabei gleichzeitig zum Verständnis des Periodensystems der Kristallstrukturen beiträgt. Ein sanfter, diffusionloser Übergang durch kuboidale Gitterstrukturen hindurch bietet detaillierte Einblicke in den bcc→fcc Phasenübergang für die Elemente der Gruppen 1 und 11.

Nuclear chiral rotation within Relativistic Configuration-interaction Density functional theory

The Relativistic Configuration-interaction Density functional (ReCD) theory that combines the advantages of large-scale configuration-interaction shell model and relativistic density functional theory is extended to study nuclear chiral rotation. The energy spectra and transition probabilities of the chiral doublet bands are reproduced satisfactorily without any free parameters. By analyzing the probability amplitudes of the wavefunctions, the significant roles of configuration mixing and four quasiparticle states to the chiral doublets are revealed. The evolution from chiral vibration to static chirality is clearly illustrated by the K plot and azimuthal plot. The present investigation provides both microscopic and quantal descriptions for nuclear chirality for the first time and demonstrates the robustness of chiral geometry against the configuration mixing as well as the four quasiparticle states.

Blueshift in Trifurcated Hydrogen Bonds: A Tradeoff between Tetrel Bonding and Steric Repulsion.

We have quantum chemically investigated the origin of the atypical blueshift of the H-C bond stretching frequency in the hydrogen-bonded complex X- •••H3 C-Y (X, Y=F, Cl, Br, I), as compared to the corresponding redshift occurring in Cl- •••H3 N and Cl- •••H3 C-H, using relativistic density functional theory (DFT) at ZORA-BLYP-D3(BJ)/QZ4P. Previously, this blueshift was attributed, among others, to the contraction of the H-C bonds as the H3 C moiety becomes less pyramidal. Herein, we provide quantitative evidence that, instead, the blueshift arises from a direct and strong X- •••C interaction of the HOMO of A- with the backside lobe on carbon of the low-lying C-Y antibonding σ* LUMO of the H3 C-Y fragment. This X- •••C bond, in essence a tetrel bond, pushes the H atoms towards a shorter H-C distance and makes the H3 C moiety more planar. The blueshift may, therefore, serve as a diagnostic for tetrel bonding.

Relativistic DFT Calculations of Cadmium and Selenium Solid-State NMR Spectra of CdSe Nanocrystal Surfaces.

Solid-state NMR spectra have been used to probe the structure of CdSe nanocrystals and propose detailed models of their surface structures. Density functional theory (DFT)-optimized cluster models that represent probable molecular structures of carboxylate-coordinated surface sites have been proposed. However, to the best of our knowledge, 113Cd and 77Se chemical shifts have not been calculated for these surface models. We performed relativistic DFT calculations of cadmium and selenium magnetic shielding tensors on model compounds with previously measured solid-state NMR spectra with (i) the four-component Dirac-Kohn-Sham (DKS) Hamiltonian and (ii) the scalar and (iii) spin-orbit levels within the ZORA Hamiltonian. Molecular clusters with Cd and Se sites in varying bonding environments were used to model CdSe (100) and CdSe(111) surfaces capped with carboxylic acid ligands. Our calculations identify the observed 113Cd isotropic chemical shifts δ(iso) of -465, -318, and -146 ppm arising from CdSeO3, CdSe2O2, and CdSe3O surface groups, respectively, with very good agreement with experimental measurements. The 113Cd chemical shifts linearly decrease with the number of O-neighbors. The calculated spans (δ11 - δ33) encompass the experimental values for CdSe3O and CdSe2O2 clusters but are slightly larger than the measured value for CdSeO3 clusters. Relativistic DFT calculations predicted a one-bond 113Cd-77Se scalar coupling of 258 Hz, which is in good agreement with the experimental values of 250 Hz. With a dense coverage of carboxylic acid ligands, the CdSe (100) surface shows a distribution of Cd-Se bond lengths and J-couplings. Relativistic DFT simulations thus aid in interpretation of NMR spectra of CdSe nanocrystals and related nanomaterials.

Novel Computational Chemistry Infrastructure for Simulating Astatide in Water: From Basis Sets to Force Fields Using Particle Swarm Optimization.

Using the example of astatine, the heaviest naturally occurring halogen whose isotope At-211 has promising medical applications, we propose a new infrastructure for large-scale computational models of heavy elements with strong relativistic effects. In particular, we focus on developing an accurate force field for At- in water based on reliable relativistic density functional theory (DFT) calculations. To ensure the reliability of such calculations, we design novel basis sets for relativistic DFT, via the particle swarm optimization algorithm to optimize the coefficients of the new basis sets and the polarization-consistent basis set idea's extension to heavy elements to eliminate the basis set error from DFT calculations. The resulting basis sets enable the well-grounded evaluation of relativistic DFT against "gold-standard" CCSD(T) results. Accounting for strong relativistic effects, including spin-orbit interaction, via our redesigned infrastructure, we elucidate a noticeable dissimilarity between At- and I- in halide-water force field parameters, radial distribution functions, diffusion coefficients, and hydration energies. This work establishes the framework for the systematic development of polarization-consistent basis sets for relativistic DFT and accurate force fields for molecular dynamics simulations to be used in large-scale models of complex molecular systems with elements from the bottom of the periodic table, including actinides and even superheavy elements.