Beyond Electrons: Correlation and Self-Energy in Multicomponent Density Functional Theory.

Post-Kohn-Sham methods are used to evaluate the ground-state correlation energy and the orbital self-energy of systems consisting of multiple flavors of different fermions. Starting from multicomponent density functional theory, suitable ways to arrive at the corresponding multicomponent random-phase approximation and the multicomponent Green's function G W ${GW}$ approximation, including relativistic effects, are outlined. Given the importance of both of this methods in the development of modern Kohn-Sham density functional approximations, this work will provide a foundation to design advanced multicomponent density functional approximations. Additionally, the G W ${GW}$ quasiparticle energies are needed to study light-matter interactions with the Bethe-Salpeter equation.

Chemical characterization of heavy actinides and light transactinides - Experimental achievements at JAEA.

The chemical characterization of the heaviest elements at the farthest reach of the periodic table (PT) and the classification of these elements in the PT are undoubtedly crucial and challenging subjects in chemical and physical sciences. The elucidation of the influence of relativistic effects on their outermost electronic configuration is also a critical and fascinating aspect. However, the heaviest elements with atomic numbers Z ≳ 100 must be produced at accelerators using nuclear reactions of heavy ions and target materials. Therefore, production rates for these elements are low, and their half-lives are as short as a few seconds to a few minutes; they are usually available in a quantity of only a few atoms at a time. Here, we review some highlighted studies on heavy actinide and light transactinide chemical characterization performed at the Japan Atomic Energy Agency tandem accelerator facility. We discuss briefly the prospects for future studies of the heaviest elements.

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.

Bismuth as a Z-Type Ligand: an Unsupported Pt-Bi Donor-Acceptor Interaction and its Umpolung by Reaction with H2.

Establishing unprecedented types of bonding interactions is one of the fundamental challenges in synthetic chemistry, paving the way to new (electronic) structures, physicochemical properties, and reactivity. In this context, unsupported element-element interactions are particularly noteworthy since they offer pristine scientific information about the newly identified structural motif. Here we report the synthesis, isolation, and full characterization of the heterobimetallic Bi / Pt compound [Pt(PCy3)2(BiMe2)(SbF6)] (1), bearing the first unsupported transition metal→bismuth donor/acceptor interaction as its key structural motif. 1 is surprisingly robust, its electronic spectra are interpreted in a fully relativistic approach, and it reveals an unprecedented reactivity towards H2.

Relativistic adapted Gaussian basis sets free of variational prolapse of small and medium size for cesium through radon.

Relativistic adapted Gaussian basis sets of small and medium sizes are presented in this study for all elements from cesium to radon, including some alternative electron configurations. Both basis sets are made free of variational prolapse, being developed by means of a polynomial version of the generator coordinate Dirac-Fock method. In addition, these sets were designed to be promptly used with two popular finite nuclear models, uniform sphere and Gaussian nuclei. The largest basis set errors found with the uniform sphere nucleus are 27.3 and 10.6 mHartree, respectively, for the small- and medium-size sets. The largest basis set errors obtained with the Gaussian nuclear model are smaller, reaching 23.2 and 7.1 mHartree for the small- and medium-size sets, respectively. Soon, these basis sets will be augmented with polarization functions to be properly used in molecular calculations.

Toward ICP-SIFT mass spectrometry and atomic cation ligation as a probe of relativistic effects-A personal journey.

The ICP-SIFT mass spectrometer at York University, a derivative of flowing afterglow (FA) and selected-ion flow tube (SIFT) mass spectrometers, has provided a powerful technique to measure the chemistry and kinetics of atomic cation-molecule reactions. Here, I focus on periodic trends in the kinetics of ligation reactions of atomic ions with small molecules. I examine trends in ammonia ligation kinetics across the first two rows of the atomic transition metal cations and their correlation with ligand bond enthalpies and ligand field stabilization energies. Also explored are trends down Groups 1 and 2 in the kinetics of noncovalent electrostatic ligand bonding and the tendency for s electron solvation of the atomic alkaline-earth cations with ammonia. Finally, I briefly review trends observed with 12 different ligands in the ligation rate down the periodic table with Group 9-12 transition atomic metal cations. These trends provide a compelling probe for the presence of relativistic effects that influence the strengths of the metal-ion ligand bonds that are formed. There is a clear third-row rate enhancement with Ir+ , Pt+ , Au+ , and Hg+ , the extent of which depends on the nature of the ligand. This large set of kinetic data provides an unprecedented broad perspective of relativistic effects in ligand bonding. With CS2 as a ligand, the third-row relativistic effect is apparent in the formation of both the first and the second ligand bond with the Groups 10 and 11 atomic cations as predicted by our quantum chemical calculations of ligation energies.

Bonding and 13 C-NMR properties of coinage metal tris(ethylene) and tris(norbornene) complexes: Evaluation of the role of relativistic effects from DFT calculations.

The π-complexes of cationic coinage metal ions (Cu(I), Ag(I), Au(I)) provide useful experimental support for understanding fundamental characteristics of bonding and 13 C-NMR patterns of the group 11 triad. Here, we account for the role of relativistic effects on olefin-coinage metal ion interaction for cationic, homoleptic tris-ethylene, and tris-norbornene complexes, [M(η2 -C2 H4 )3 ]+ and [M(η2 -C7 H10 )3 ]+ (M = Cu, Ag, Au), as representative case of studies. The M-(CC) bond strength in the cationic, tris-ethylene complexes is affected sizably for Au and to a lesser extent for Ag and Cu (48.6%, 16.7%, and 4.3%, respectively), owing to the influence on the different stabilizing terms accounting for the interaction energy in the formation of coinage metal cation-π complexes. The bonding elements provided by olefin → M σ-donation and olefin ← M π-backbonding are consequently affected, leading to a lesser covalent interaction going down in the triad if the relativistic effects are ignored. Analysis of the 13 C-NMR tensors provides further understanding of the observed experimental values, where the degree of backbonding charge donation to π2 *-olefin orbital is the main influence on the observed high-field shifts in comparison to the free olefin. This donation is larger for ethylene complexes and lower for norbornene counterparts. However, the bonding energy in the later complexes is slightly stabilized given by the enhancement in the electrostatic character of the interaction. Thus, the theoretical evaluation of metal-alkene bonds, and other metal-bonding situations, benefits from the incorporation of relativistic effects even in lighter counterparts, which have an increasing role going down in the group.

Relativistic adapted Gaussian basis sets free of variational prolapse of small and medium size for hydrogen through xenon.

Two new relativistic adapted Gaussian basis sets of small and medium size are presented for all elements from Hydrogen through Xenon. These sets are free of variational prolapse and were developed with the polynomial generator coordinate Dirac-Fock method to be used with two finite nuclear models, uniform sphere and Gaussian. The largest basis set errors for electronic configurations from the Aufbau principle are around 10.0 and 4.7 mHartree for the small- and medium-size sets, respectively, which is in accordance with the accuracy level expected in each case. Hence, to our knowledge, these are the smallest prolapse free basis sets developed for these elements.

Evidence for genuine hydrogen bonding in gold(I) complexes.

The ability of gold to act as proton acceptor and participate in hydrogen bonding remains an open question. Here, we report the synthesis and characterization of cationic gold(I) complexes featuring ditopic phosphine-ammonium (P,NH+) ligands. In addition to the presence of short Au∙∙∙H contacts in the solid state, the presence of Au∙∙∙H-N hydrogen bonds was inferred by NMR and IR spectroscopies. The bonding situation was extensively analyzed computationally. All features were consistent with the presence of three-center four-electron attractive interactions combining electrostatic and orbital components. The role of relativistic effects was examined, and the analysis is extended to other recently described gold(I) complexes.

Quantum chemical calculations of 77 Se and 125 Te nuclear magnetic resonance spectral parameters and their structural applications.

An accurate quantum chemical (QC) modeling of 77 Se and 125 Te nuclear magnetic resonance (NMR) spectra is deeply involved in the NMR structural assignment for selenium and tellurium compounds that are of utmost importance both in organic and inorganic chemistry nowadays due to their huge application potential in many fields, like biology, medicine, and metallurgy. The main interest of this review is focused on the progress in QC computations of 77 Se and 125 Te NMR chemical shifts and indirect spin-spin coupling constants involving these nuclei. Different computational methodologies that have been used to simulate the NMR spectra of selenium and tellurium compounds since the middle of the 1990s are discussed with a strong emphasis on their accuracy. A special accent is placed on the calculations resorting to the relativistic methodologies, because taking into account the relativistic effects appreciably influences the precision of NMR calculations of selenium and, especially, tellurium compounds. Stereochemical applications of quantum chemical calculations of 77 Se and 125 Te NMR parameters are discussed so as to exemplify the importance of integrated approach of experimental and computational NMR techniques.

Chirality and Relativistic Effects in Os3(CO)12.

The energy and structural parameters were obtained for all forms of the carbonyl complex of osmium Os3(CO)12 with D3h and D3 symmetries using density functional theory (DFT) methods. The calculations took into account various levels of relativistic effects, including those associated with nonconservation of spatial parity. It was shown that the ground state of Os3(CO)12 corresponds to the D3 symmetry and thus may be characterized either as left-twisted (D3S) or right-twisted (D3R). The D3S↔D3R transitions occur through the D3h transition state with an activation barrier of ~10-14 kJ/mol. Parity violation energy difference (PVED) between D3S and D3R states equals to ~5 × 10-10 kJ/mol. An unusual three-center exchange interaction was found inside the {Os3} fragment. It was found that the cooperative effects of the mutual influence of osmium atoms suppress the chirality of the electron system in the cluster.

Exclusively Relativistic: Periodic Trends in the Melting and Boiling Points of Group†12.

First-principles simulations can advance our understanding of phase transitions but are often too costly for the heavier elements, which require a relativistic treatment. Addressing this challenge, we recently composed an indirect approach: A precise incremental calculation of absolute Gibbs energies for the solid and liquid with a relativistic Hamiltonian that enables an accurate determination of melting and boiling points (MPs and BPs). Here, we apply this approach to the Group 12 elements Zn, Cd, Hg, and Cn, whose MPs and BPs we calculate with a mean absolute deviation of only 5 % and 1 %, respectively, while we confirm the previously predicted liquid aggregate state of Cn. At a non-relativistic level of theory, we obtain surprisingly similar MPs and BPs of 650±30 K and 1250±20 K, suggesting that periodic trends in this group are exclusively relativistic in nature. Ultimately, we discuss these results and their implication for Groups 11 and 14.

Experimental and Theoretical Evidence of Spin-Orbit Heavy Atom on the Light Atom 1 H†NMR Chemical Shifts Induced through H⋠⋠⋠I- Hydrogen Bond.

Spin-orbit (SO) heavy-atom on the light-atom (SO-HALA) effect is the largest relativistic effect caused by a heavy atom on its light-atom neighbors, leading, for example, to unexpected NMR chemical shifts of 1 H, 13 C, and 15 N nuclei. In this study, a combined experimental and theoretical evidence for the SO-HALA effect transmitted through hydrogen bond is presented. Solid-state NMR data for a series of 4-dimethylaminopyridine salts containing I- , Br- and Cl- counter ions were obtained experimentally and by theoretical calculations. A comparison of the experimental chemical shifts with those calculated by a standard DFT methodology without the SO contribution to the chemical shifts revealed a remarkable error of the calculated proton chemical shift of a hydrogen atom that is in close contact with the iodide anion. The addition of the relativistic SO correction in the calculations significantly improves overall agreement with the experiment and confirms the propagation of the SO-HALA effect through hydrogen bonds.

On the Interplay between Charge-Shift Bonding and Halogen Bonding.

The nature of halogen-bond interactions has been analysed from the perspective of the astatine element, which is potentially the strongest halogen-bond donor. Relativistic quantum calculations on complexes formed between halide anions and a series of Y3 C-X (Y=F to X, X=I, At) halogen-bond donors disclosed unexpected trends, e. g., At3 C-At revealing a weaker donating ability than I3 C-I despite a stronger polarizability. All the observed peculiarities have their origin in a specific component of C-Y bonds: the charge-shift bonding. Descriptors of the Quantum Chemical Topology show that the halogen-bond strength can be quantitatively anticipated from the magnitude of charge-shift bonding operating in Y3 C-X. The charge-shift mechanism weakens the ability of the halogen atom X to engage in halogen bonds. This outcome provides rationales for outlier halogen-bond complexes, which are at variance with the consensus that the halogen-bond strength scales with the polarizability of the halogen atom.

Correlated ab initio calculations of one-bond 31 P77 Se and 31 P125 Te spin-spin coupling constants in a series of PSe and PTe systems accounting for relativistic effects (part 2).

Synthetic chalcogen-phosphorus chemistry permanently makes new challenges to computational Nuclear Magnetic Resonance (NMR) spectroscopy, which has proven to be a powerful tool of structural analysis of chalcogen-phosphorus compounds. This paper reports on the calculations of one-bond 31 P77 Se and 31 P125 Te NMR spin-spin coupling constants (SSCCs) in the series of phosphine selenides and tellurides. The applicability of the combined computational approach to the one-bond 31 P77 Se and 31 P125 Te SSCCs, incorporating the composite nonrelativistic scheme, built of high-accuracy correlated SOPPA (CC2) and Coupled Cluster Single and Double (CCSD) methods and the Density Functional Theory (DFT) relativistic corrections (four-component level), was examined against the experiment and another scheme based on the four-component relativistic DFT method. A special J-oriented basis set (acv3z-J) for selenium and tellurium atoms, developed previously by the authors, was used throughout the NMR calculations in this work at the first time. The proposed computational methodologies (combined and 'pure') provided a reasonable accuracy for 31 P77 Se and 31 P125 Te SSCCs against experimental data, characterizing by the mean absolute percentage errors of about 4% and 1%, and 12% and 8% for selenium and tellurium species, respectively. The present study reports typical relativistic corrections to 77 Se31 P and 125 Te31 P SSCCs, calculated within the four-component DFT formalism for a broad series of tertiary phosphine selenides and tellurides with different substituents at phosphorus.

Excimer and Exciplex Formation in Gold(I) Complexes Preconditioned by Aurophilic Interactions.

Excimers and exciplexes are defined as assemblies of atoms or molecules A/A' where interatomic/intermolecular bonding appears only in excited states such as [A2 ]* (for excimers) and [AA']* (for exciplexes). Their formation has become widely known because of their role in gas-phase laser technologies, but their significance in general chemistry terms has been given little attention. Recent investigations in gold chemistry have opened up a new field of excimer and exciplex chemistry that relies largely on the preorganization of gold(I) compounds (electronic configuration AuI (5d10 )) through aurophilic contacts. In the corresponding excimers, a new type of Au⋅⋅⋅Au bonding arises, with bond energies and lengths approaching those of ground-state Au-Au bonds between metal atoms in the Au0 (5d10 6s1 ) and AuII (5d9 ) configurations. Excimer formation gives rise to a broad range of photophysical effects, for which some of the relaxation dynamics have recently been clarified. Excimers have also been shown to play an important role in photoredox binuclear gold catalysis.

Synthesis and Structures of Stable PtII and PtIV Alkylidenes: Evidence for π-Bonding and Relativistic Stabilization.

Isolable cationic PtII and PtIV alkylidenes, proposed intermediates in catalytic organic transformations, are reported. The bonding in these species was probed by experimental, structural, spectroscopic, electrochemical and computational methods, providing direct evidence for π-bonding, the often-theorized relativistic stabilization of these species, and the influence of oxidation state.

"Through-Space" Relativistic Effects on NMR Chemical Shifts of Pyridinium Halide Ionic Liquids.

We have investigated, using two-component relativistic density functional theory (DFT) at ZORA-SO-BP86 and ZORA-SO-PBE0 level, the occurrence of relativistic effects on the 1 H, 13 C, and 15 N NMR chemical shifts of 1-methylpyridinium halides [MP][X] and 1-butyl-3-methylpyridinium trihalides [BMP][X3 ] ionic liquids (ILs) (X=Cl, Br, I) as a result of a non-covalent interaction with the heavy anions. Our results indicate a sizeable deshielding effect in ion pairs when the anion is I- and I3- . A smaller, though nonzero, effect is observed also with bromine while chlorine based anions do not produce an appreciable relativistic shift. The chemical shift of the carbon atoms of the aromatic ring shows an inverse halogen dependence that has been rationalized based on the little C-2s orbital contribution to the σ-type interaction between the cation and anion. This is the first detailed account and systematic theoretical investigation of a relativistic heavy atom effect on the NMR chemical shifts of light atoms in the absence of covalent bonds. Our work paves the way and suggests the direction for an experimental investigation of such elusive signatures of ion pairing in ILs.

Relativistic Effects on NMR Parameters of Halogen-Bonded Complexes.

Relativistic effects are found to be important for the estimation of NMR parameters in halogen-bonded complexes, mainly when they involve the heavier elements, iodine and astatine. A detailed study of 60 binary complexes formed between dihalogen molecules (XY with X, Y = F, Cl, Br, I and At) and four Lewis bases (NH3, H2O, PH3 and SH2) was carried out at the MP2/aug-cc-pVTZ/aug-cc-pVTZ-PP computational level to show the extent of these effects. The NMR parameters (shielding and nuclear quadrupolar coupling constants) were computed using the relativistic Hamiltonian ZORA and compared to the values obtained with a non-relativistic Hamiltonian. The results show a mixture of the importance of the relativistic corrections as both the size of the halogen atom and the proximity of this atom to the basic site of the Lewis base increase.

Proof of Concept for Hydrogen Bonding to Gold, Au⋠⋠⋠H-X.

Convincing and consistent evidence for the existence of hydrogen bonding to gold has been obtained. An ammonium or pyridinium group has been shown to be an efficient hydrogen bond donor unit for gold(I) coordination centers, and the assembly leads to the structural pattern typical for standard hydrogen bonds. This constitutes the first rigorous, scrutinizing, and comprehensive study of hydrogen bonds to a metal atom, with gold being an ideal model element because of relativistic effects.