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.

Compact stars with non-uniform relativistic polytrope.

This paper presents new relativistic composite polytropic models for compact stars by simultaneously solving Einstein field equations with the polytropic state equation to simulate the spherically symmetric, static matter distribution. Using a non-uniform polytropic index, we get the Tolman-Oppenheimer-Volkoff equation for the relativistic composite polytrope (CTOV). To analyze the star's structure, we numerically solve the CTOV equation and compute the Emden and mass functions for various relativistic parameters and polytropic indices appropriate for neutron stars. The calculation results show that, as the relativistic parameter approaches zero, we recover the well-known Lane-Emden equation from the Newtonian theory of polytropic stars; thus, testing the computational code by comparing composite Newtonian models to those in the literature yields good agreement. We compute composite relativistic models for the neutron star candidates Cen X-3, SAXJ1808.4-3658, and PSR J1614-22304. We compare the findings with various existing models in the literature. Based on the accepted models for PSR J1614-22304 and Cen X-3, the star's core radius is predicted to be between 50 and 60% percent of its total radius, while we found that the radius of the core of star SAXJ1808.4-3658 is around 30% of the total radius. Our findings show that the neutron star structure may be approximated by a composite relativistic polytrope, resulting in masses and radii that are quite consistent with observation.

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.

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.

Relativistic four-component MRCISD+Q calculations of the six lowest valence states of molecular [Formula: see text] anion including breit interactions.

CONTEXT AND RESULTS: This study aimed to obtain potential energy curves within a multireference 4-component relativistic method and to present spectroscopic constants (R[Formula: see text],[Formula: see text],[Formula: see text]x[Formula: see text],[Formula: see text]y[Formula: see text], D[Formula: see text], D[Formula: see text], B[Formula: see text],[Formula: see text],[Formula: see text],[Formula: see text] ), accurate extended Rydberg analytical form, and rovibrational levels for the 6 low-lying states of the I[Formula: see text] anion. For these states, some spectroscopic constants, rovibrational levels, and an accurate analytical form are presented for the first time in literature, and they are of interest for femtosecond and dynamics experiments of I[Formula: see text] as well as for electron attachment of I[Formula: see text]. This study suggests that the inclusion of relativistic and correlation effects treated at the MRCISD+Q level is needed to obtain reliable results, specially for D[Formula: see text]. COMPUTATIONAL AND THEORETICAL TECHNIQUES: The potential energy curves of the ground and the excited states of the molecular iodine anion (I[Formula: see text]) were investigated at multireference configuration interaction (MRCISD) with Davidson size-extensivity correction (denoted as +Q) within a fully relativistic four-component relativistic framework including Breit interaction.

Exploring 129Xe NMR parameters for structural investigation of biomolecules: relativistic, solvent, and thermal effects.

In recent years, the study of new probes has aroused great interest in the scientific community around the world. Therefore, in the present work, we present a potential candidate for a new spectroscopic probe, the Xe(CO)3(NNO) conjugated to 2-(4'-aminophenyl) benzothiazole complex, XeABT. For this proposal, chemical shift calculations at the DFT level were performed; thus, a factorial design was carried out in order to choose the best computational method. The best combination was the base function ZORA-def2-TZVP, with the functional PBE0 and considering the relativistic effects with the ZORA implementation. Our findings reveal that the 129Xe chemical shifts are affected by thermal and solvent effects, and considering an enzymatic environment, a significant decrease in δ(129Xe) values is observed, suggesting with the XeABT complex it may be a promising spectroscopic probe.

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.

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.

Influence of modelling disorder on Hirshfeld atom refinement results of an organo-gold(I) compound.

Details of the validation of disorder modelling with Hirshfeld atom refinement (HAR) for a previously investigated organo-gold(I) compound are presented here. The impact of refining disorder on HAR results is discussed using an analysis of the differences of dynamic structure factors. These dynamic structure factor differences are calculated from thermally smeared quantum mechanical electron densities based on wavefunctions that include or exclude electron correlation and relativistic effects. When disorder is modelled, the electron densities stem from a weighted superposition of two (or more) different conformers. Here this is shown to impact the relative importance of electron correlation and relativistic effect estimates expressed by the structure factor magnitudes. The role of disorder modelling is also compared with the effect of the treatment of hydrogen anisotropic displacement parameter (ADP) values and atomic anharmonicity of the gold atom. The analysis of ADP values of gold and disordered carbon atoms showed that the effect of disorder significantly altered carbon ADP values and did not influence those of the gold atom.

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.

Vibrational frequencies and intramolecular force constants for cisplatin: assessing the role of the platinum basis set and relativistic effects.

The role of platinum basis set (PTBS) and relativistic effects for predicting the vibrational frequencies and intramolecular force constants for cisplatin are discussed. Nonrelativistic and relativistic computational protocols were built at B3LYP/PTBS/jorge-DZP/C-PCM and B3LYP-DKH2/PTBS/jorge-DZP-DKH/C-PCM levels, respectively, where 19 distinct PTBS were tested. As expected, the structural parameters were not very sensitive to the PTBS, however, the inclusion of relativistic effects improves the description of the cisplatin structure. When it comes to the vibrational frequencies, the results show that the PTBS, and mainly the relativistic effects, are both important. Moreover, the PBE0 functional led to better results than B3LYP in the protocols PBE0/LANL2TZ(f)/jorge-DZP/C-PCM (P20) and PBE0-DKH2/Sapporo-DKH3-DZP-2012/jorge-DZP-DKH/C-PCM (P22), which provided a mean absolute deviation (MAD) of only 10.8 cm-1 and 9.5 cm-1, respectively, for vibrational frequencies, which are excellent choices to study Pt complexes. Finally, a discussion of the intramolecular force constants for cisplatin is carried out, with the calculated bond and angles force constants with P20 and P22 protocols being recommended for the parameterization of the force field of cisplatin.

Fully relativistic study of polyatomic closed shell E121X3 (X = F, Cl, Br) molecules: effects of Gaunt interaction, relativistic effects and advantages of an exact-two component (X2C) hamiltonian.

In this study, all electron relativistic calculations with 4-component Dirac-Coulomb-Breit (DCB), 4-component Dirac-Coulomb (DC), Dyall's spin-free Dirac-Coulomb (SFDC), exact two-component (X2C) and Levy-Leblond non-relativistic hamiltonians calculations were performed in polyatomic closed shell E121X3 (X = F, Cl, Br) within density functional theory (DFT) with hybrid functional B3LYP, where E121 is the superheavy element (SHE) with Z = 121. The aims of this study were to investigate relativistic effects in polyatomic E121X3 (X = F, Cl, Br) and verify the importance of Gaunt effects. The results demonstrate that although the effect of Gaunt interaction is small on change equilibrium bond lengths and bonding, it is important to obtain reliable vibrational frequencies. Moreover, it is possible to use the X2C spin-free hamiltonian to lower computational costs in a fully relativistic investigation of polyatomics including the SHE of the 8th period. Finally, a comparison between electron localization function (ELF) analysis and Mulliken population analysis suggests bonding similarity between LaBr3 and E121Br3. Graphical Abstract Relativistic 4-Component calculations suggest bond similarity between LaBr3 and E121Br3.

Relativistic Hirshfeld atom refinement of an organo-gold(I) compound.

The main goal of this study is the validation of relativistic Hirshfeld atom refinement (HAR) as implemented in Tonto for high-resolution X-ray diffraction datasets of an organo-gold(I) compound. The influence of the relativistic effects on statistical parameters, geometries and electron density properties was analyzed and compared with the influence of electron correlation and anharmonic atomic motions. Recent work in this field has indicated the importance of relativistic effects in the static electron density distribution of organo-mercury compounds. This study confirms that differences in electron density due to relativistic effects are also of significant magnitude for organo-gold compounds. Relativistic effects dominate not only the core region of the gold atom, but also influence the electron density in the valence and bonding region, which has measurable consequences for the HAR refinement model parameters. To study the effects of anharmonic motion on the electron density distribution, dynamic electron density difference maps were constructed. Unlike relativistic and electron correlation effects, the effects of anharmonic nuclear motion are mostly observed in the core area of the gold atom.

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.

ZORA all-electron double zeta basis sets for the elements from H to Xe: application in atomic and molecular property calculations.

From the segmented all-electron basis set of double zeta valence quality plus polarization functions (DZP) for the elements from H to Xe, the zeroth-order regular approximation (ZORA) is used to generate a DZP-ZORA basis set, i.e., the contraction coefficients of the DZP set are re-optimized using the minimum ZORA energy criterion. To properly describe electrons distant from the nuclei, a diffuse function is added to each atomic symmetry (s, p, d, and f). The later basis set is designated as DZP-ZORA augmented. To test the effectiveness of the basis sets developed in this work, calculations of ionization energies and mean dipole polarizabilities of some elements are performed using the ZORA-CCSD(T) method. At the same level of theory, bond lengths, dissociation energies, and harmonic vibrational frequencies of some diatoms are also reported. Comparison with experimental data and recommended values available in the literature is made. Except for polarizability, scalar relativistic effects are estimated for the other properties. The performances of the ZORA and second-order Douglas-Kroll-Hess Hamiltonians are evaluated.

Relativistic four-component MRCISD+Q calculations of the six lowest valence states of molecular F[Formula: see text] anion including Breit interactions.

In this study, the potential energy curves of the ground and the excited states of molecular fluorine anion (F[Formula: see text]) were investigated at multireference configuration interaction (MRCISD) with Davidson size-extensivity correction (denoted as +Q) within fully relativistic four-component relativistic framework including Breit interaction. Spectroscopic constants (Re, ωe, ωexe, ωeye, De,D0,Be, αe, ße, γe ), accurate extended Rydberg analytical form and rovibrational levels for ground state X:[Formula: see text] are presented, as well as spectroscopic constants for non dissociative excited states. For most states these spectroscopic constants are presented for the first time in literature and they are of interest for experimental studies, specially regarding electron attachment of F2. Results suggest that inclusion of relativistic effects at 4-component level and correlation effects treated at MRCISD+Q level are needed to obtain reliable results, which we report for X:[Formula: see text] ground state's Re, ωe and De the values of 1.999 Å, 391 cm- 1 and 1.22 eV, respectively.

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.

HgH2 meets relativistic quantum crystallography. How to teach relativity to a non-relativistic wavefunction.

The capability of X-ray constrained wavefunction (XCW) fitting to introduce relativistic effects into a non-relativistic wavefunction is tested. It is quantified how much of the reference relativistic effects can be absorbed in the non-relativistic XCW calculation when fitted against relativistic structure factors of a model HgH2 molecule. Scaling of the structure-factor sets to improve the agreement statistics is found to introduce a significant systematic error into the XCW fitting of relativistic effects.