Relativistic effects in chemistry

Relativistic effects become apparent when the velocity of the electron is arbitrarily close to the speed of light (137 au) without actually attaining it (in heavy atoms of elements at the end of Mendeleev's Periodic Table). At the orbital level, the relativistic effect is apparent in the radial contraction of penetrating s and p shells, expansion of nonpenetrating d and f shells, and the spin-orbit splitting of p-, d-, and f-shells. The appearance of a relativistic effect is indicated in the variation in the electronic configurations of the atoms in the Periodic Table, the appearance of new types of closed electron shells (6s_1/2 ², 6p_1/2 ², 7s_1/2 ², 5d_3/2 ⁴), the stabilization of unstable oxidation states of heavy elements, the characteristic variation in the ionization enthalpies of heavy atoms, their electron affinity, hydration energies, redox potentials, and optical electronegativities. In the spectra of coordination compounds, a relativistic effect is observed when comparing the position of the charge transfer bands in analogous compounds, the parameters characterizing the ligand field strength (10Dq), the interatomic distances and angles in compounds of heavy elements. A relativistic effect is also apparent in the ability of heavy metals to form clusters and superclusters. Relativistic corrections also affect other properties of heavy metal compounds (force constants, dipole moments, biological activity, etc.).Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 31, No. 3, pp. 181–199, May–June, 1995.     

Tuning Molecular Electron Affinities against Atomic Electronegativities by Spatial Expansion of a π-System

2,1,3-Benzochalcogenadiazoles C₆R₄N₂E ( E / R ; E=S, Se, Te; R=H, F, Cl, Br, I) and C₆H₂R₂N₂E ( E / R’ ; E=S, Se, Te; R=Br, I) are 10π-electron hetarenes. By CV/EPR measurements, DFT calculations, and QTAIM and ELI-D analyses, it is shown that their molecular electron affinities (EAs) increase with decreasing Allen electronegativities and electron affinities of the E and non-hydrogen R (except Cl) atoms. DFT calculations for E / R +e⋅⁻→[E/R]⋅⁻ electron capture reveal negative ΔG values numerically increasing with increasing atomic numbers of the E and R atoms; positive ΔS has a minor influence. It is suggested that the EA increase is caused by more effective charge/spin delocalization in the radical anions of heavier derivatives due to contributions from diffuse (a real-space expanded) p-AOs of the heavier E and R atoms; and that this counterintuitive effect might be of the general character.     

Relativistic effects on inversion barriers of pyramidal group 15 hydrides

Quantum chemistry is an important tool for determining general molecular properties, although relativistic corrections are usually required for systems containing heavy and super heavy elements. Non‐relativistic along with relativistic two‐ and four‐component electronic structure calculations done with the CCSD‐T method and the new RPF‐4Z basis set have therefore been applied for determining inversion barriers, corresponding to the change from a pyramidal (C_3v) ground‐state structure to the trigonal planar (D_3h) transition state, TS, of group 15 hydrides, XH₃ (X= N, P, As, Sb, and Bi). The ground‐state structure of the McH₃ molecule, which contains the super heavy element Moscovium, is also predicted as pyramidal (C_3v), with an atomization energy of 90.8 kcal mol⁻¹. However, although non‐relativistic calculations still provided a D_3h planar TS for McH₃, four‐component relativistic calculations based on single‐reference wave functions are unable to elucidate the definitive TS geometry in this case. Hence, the results show that relativistic effects are crucial for this barrier determination in those hydrides containing Bi and Mc. Moreover, while the scalar relativistic effects predominate, increasing barrier heights by as much as 17.6 kcal mol⁻¹ (32%) in BiH₃, the spin‐orbit coupling cannot be disregarded in those hydrides containing the heaviest group 15 elements, decreasing the barrier by 2.5 kcal mol⁻¹ (4.5%) in this same molecule.     

“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 ¹H, ¹³C, and ¹⁵N 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.     

Dodecatwistarene Imides with Zigzag-Twisted Conformation for Organic Electronics

1D nonplanar graphene nanoribbons generally have three possible conformers: helical, zigzag, and mixed conformations. Now, a kind of 1D nonplanar graphene nanoribbon, namely dodecatwistarene imides featuring twelve linearly fused benzene rings, was obtained by bottom-up synthesis of palladium-catalyzed Stille coupling and C−H activation. Single-crystal X-ray diffraction analyses revealed that it displays a zigzag-twisted conformation caused by steric hindrance between imide groups and neighboring annulated benzene rings with the pendulum angle of 53°. This conformation is very stable and could not convert into other conformations even when heated up to 250 °C for 6 h. Despite of the highly twisted topology, organic field-effect transistor based on it exhibits electron mobility up to 1.5 cm² V⁻¹ s⁻¹ after annealing.     

meso‐Tetrakis[4‐(heptyloxy)phenyl]porphyrin

The core of the novel title centrosymmetric porphyrin derivative, C₇₂H₈₆N₄O₄, with long flexible hexyloxy substituents, is almost planar, which is anticipated to facilitate π‐electron delocalization and lead to a significant deviation between the planes of the benzene rings and the molecular plane. The two N‐bound H atoms on the pyrrole rings are disordered and the occupancy factors refined to a ratio of 0.28 (2):0.72 (2).     

A Topological Data Analysis perspective on noncovalent interactions in relativistic calculations

Topological Data Analysis (TDA) is a powerful mathematical theory, largely unexplored in theoretical chemistry. In this work we demonstrate how TDA provides new insights into topological features of electron densities and reduced density gradients, by investigating the effects of relativity on the bonding of the Au₄-S-C₆H₄-S′-Au′₄ molecule. Whereas recent analyses of this species carried out with the Quantum Theory of Atoms-In-Molecules (a previous study) concluded, from the emergence of new topological features in the electron density, that relativistic effects yielded noncovalent interactions between gold and hydrogen atoms, we show from their low persistence values (which decrease with increased basis set size) these features are not significant. Further analysis of the reduced density gradient confirms no relativity-induced noncovalent interactions in Au₄-S-C₆H₄-S′-Au′₄. We argue TDA should be integrated into electronic structure analysis methods, and be considered as a basis for the development of new topology-based approaches.     

Structure-parameter and force-field refinement for lead dihalide molecules

Conclusions It has been shown for PbF₂ that one can process electron-diffraction data for molecules containing heavy atoms on the basis of atomic scattering amplitudes calculated with a relativistic approximation for the atomic electron density. The errors in calculating the atomicscattering amplitudes explain the previous discrepancies in the observed values for the Pb-Cl amplitudes in PbCl₂ derived in two independent researches. The differences between those values are now not so considerable, and they may be explained as due to experimental error or to the processing of the measurements in Hungary for most of the scattering angles having been performed without the relativistic corrections to the electron density.Our mean-square vibration amplitudes and the measured frequencies can be used with our semiempirical relationships for the force constants to determine the potential-energy parameters for those molecules and to estimate the vibrational frequencies for PbI₂, which have not been measured.I am indebted to Professor V. P. Spiridonov and staff at the vapor electron-diffraction laboratory at Moscow University for providing the observed values for the reduced molecular component of the scattering intensities for lead dihalides and for valuable comments in discussion on the draft.High-Temperature Institute, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No. 1, pp. 54–59, January–February, 1991.     

Quantum electrodynamic effects in atomic structure

Summary In high-Z atoms, quantum electrodynamic (QED) corrections are an important component in the theoretical prediction of atomic energy levels. The main QED effects in electronic atoms are the one-electron self-energy and vacuum-polarization corrections which are well known. At the next level of precision, estimates of the effect of electron interactions on the self energy and higher-order effects in two exchanged photon corrections are necessary. These corrections can be evaluated within the framework of QED in the bound interaction picture. For high-Z few-electron atoms, this approach provides a rapidly converging series in 1/Z for the corrections, which is the generalization of the well-known relativistic 1/Z expansion methods. This paper describes recent work on the effect of electron interactions on the self energy. The QED effects are particularly important for the theory for lithiumlike uranium where an accurate measurement of the Lamb shift has been made, as well as for numerous other cases where systematic differences appear between theory that does not include these QED effects and experiment.     

Contributions to the Chemistry of Silicon-Sulfur Compounds. 65 synthesis,crystal and molecular structure of cyclo-tetrakis[tri-tert-butoxysilanethiolatogold(I)], [(t-C4H9O)3SiSAu]4, the first example of an Au4S4 ring System

The preparation of the first silanethiolate complex of gold, cyclo-tetrakis[tri-tert-butoxysilanethiolatogold(I)] from tri-tert-butoxysilanethiol and tetrachloroauric acid is described. The compound forms colorless orthorhombic crystals, and the molecular structure was determined at 200 K by single crystal X-ray diffraction. At 187 K, a possible, reversible phase transition is observed. The center of the molecule is a distinctly folded eight-membered Au₄S₄ ring of alternating three-fold coordinated sulfur and two-fold coordinated gold atoms. The relevant bond lengths and angles are: Au? S 228.4 and 229.6 pm, Si? S 216.9 pm, S? Au? S 178.8° and 178.3°, Au? S? Au 90.3°, Si? S? Au 103.7° and 101.9°. The gold atoms are separated by 324.8 pm.     

Anion⋅⋅⋅Anion Interactions Involving σ-Holes of Perrhenate,Pertechnetate and Permanganate Anions

In this communication experimental and theoretical results are reported affording strong evidence that interactions between electron rich atoms and the metal of tetroxide anions of group 7 elements are a new case of attractive and σ-hole interactions. Single crystal X-ray analyses, molecular electrostatic potentials, quantum theory of atoms-in-molecules, and noncovalent interaction plot analyses show that in crystalline permanganate and perrhenate salts the metal in Mn/ReO₄⁻ anion can act as electron acceptors, the oxygen of another Mn/ReO₄⁻ anion can act as the donor and supramolecular anionic dimers or polymers are formed. The name matere bond (MaB) is proposed to categorize these noncovalent interactions and to differentiate them from the classical metal-ligand coordination bond.     

Enhanced electron transfer between gold nanoparticles and horseradish peroxidase reconstituted onto alkanethiol-modified hemin

Robust molecular bioelectronic devices require a programmable and efficient electronic communication between biological molecules and electrodes. With proteins it is often compromised by their uncontrollable assembly on electrodes that does not provide neither uniform nor efficient electron flow between proteins and electrodes. Here, horseradish peroxidase reconstituted onto C₁₁-alkanethiol-conjugated hemin and self-assembled onto the gold nanoparticle (NP)-modified electrodes via the exposed alkanethiol tail exhibits enhanced electron transfer (ET), proceeding via the gold NP relay with the ET rate constant approaching 115 s^− 1 vs. 14 s^− 1 shown on bare gold, by this offering an advanced controllable design of interfaces for bioelectronic devices based on heme-containing enzymes with a non-covalently bound heme.     

Relativistic all-electron molecular Hartree-Fock-Dirac-(Breit) calculations on CH4, SiH4, GeH4, SnH4, PbH4

Summary Results and details of molecular Fock-Dirac-(Breit) calculations on CH₄, SiH₄, GeH₄, SnH₄, and PbH₄ obtained with the MOLFDIR© program package are presented and compared with other calculations and experimental results. The relativistic ground state energies (including the Breit interaction) of the atoms C, Si, Ge, Sn, and Pb, necessary for reference purposes, have been calculated using a small relativistic CI. One of our findings is that for the heavier systems perturbation theory over-estimates the relativistic bond length contraction. The Breit interaction has only a small effect on the bond lengths.     

Structural influence of transition metal (Sc,Y, and Lu) atoms inside gold nanoparticles

We theoretically investigated the influences of dopant transition metal atoms on structures and stability of gold nanoparticles. The optimized structures of Au₃M and Au₃M in an Au₃₂ cage (M = Au, Sc, Y, and Lu) obtained using relativistic density functional theory, show different configurations. Substitutions of one Au atom in the Au₄ cluster by only one M atom cause the Au₃M clusters to form equilateral triangles where M atoms prefer the central position, which is different from the original rhombus structure of a pure Au₄ cluster. All Au₃M nanoparticles, however, assume stable tetrahedral configurations in the Au₃₂ cage. Analysis of electronic structures indicates that the equilateral triangle Au₃M nanoparticles have higher chemical stability, in other words, lower reactivity than Au₃M@Au₃₂, while interaction energies between M and Au atoms in the Au₃M are smaller than those in Au₃M@Au₃₂. Different amounts of charge transfer and orbital hybridizations between the Au and M cause the change of the chemical stability and interaction energies. Our results indicate the potential manipulation of gold nanoparticle reactivity by metal substitution.     

Simulations of 129Xe NMR chemical shift of atomic xenon dissolved in liquid benzene

The isotropic ¹²⁹Xe NMR chemical shift of atomic Xe dissolved in liquid benzene was simulated by combining classical molecular dynamics and quantum chemical calculations of ¹²⁹Xe nuclear magnetic shielding. Snapshots from the molecular dynamics trajectory of xenon atom in a periodic box of benzene molecules were used for the quantum chemical calculations of isotropic ¹²⁹Xe chemical shift using nonrelativistic density functional theory as well as relativistic Breit?CPauli perturbation corrections. Thus, the correlation and relativistic effects as well as the temperature and dynamics effects could be included in the calculations. Theoretical results are in a very good agreement with the experimental data. The most of the experimentally observed isotropic ¹²⁹Xe shift was recovered in the nonrelativistic dynamical region, while the relativistic effects explain of about 8% of the total ¹²⁹Xe chemical shift.     

A novel two‐dimensional zinc(II) coordination polymer with 6‐mercaptonicotinic acid

The novel title Zn^II coordination polymer, poly[bis(μ‐6‐thioxo‐1,6‐dihydropyridine‐3‐carboxylato‐κ²S:O)zinc(II)], [Zn(C₆H₄NO₂S)₂]_n, consists of two crystallographically independent zinc centers and two 6‐mercaptonicotinate (Hmna⁻) ligands. Each Zn^II atom is four‐coordinated and lies at the center of a distorted tetrahedral ZnS₂O₂ coordination polyhedron, bridged by four Hmna⁻ ligands to form a two‐dimensional (4,4)‐network. Each Hmna⁻ ion acts as a bridging bidentate ligand, coordinating to two Zn^II atoms through the S atom and a carboxyl O atom. The metal centers reside on twofold rotation axes. The coordination mode of the S atoms and N—H...O hydrogen‐bonding interactions between the protonated N atoms and the uncoordinated carboxyl O atoms give the extended structure a wavelike form.     

铁脂质体/水分配系数测定及影响因素考察

基于PAF-301分子模型通过Li 掺杂或B取代等模式设计了几种新型多孔芳香骨架(PAFs)材料, 采用量子力学和分子力学方法对新材料的储氢性能进行研究. 由量子力学计算得到了不同分子片段与H₂之间的结合能, 并结合DDEC方法计算了各分子片段的原子电荷分布. 利用巨正则蒙特卡洛(GCMC)模拟方法计算了77和298 K下H₂在不同PAFs材料中的吸附平衡性质. 结果表明, H₂直接与苯环的结合能较低, 但掺杂Li 原子能够提高H₂与六元环的结合能, 同时Li 原子体现出较高的正电性质, B原子取代苯环中的两个C原子后, 使得原有C原子电负性增强; 77 K下PAF-301Li 具有最高的储氢性能, 而PAF-C₄B₂H₄-Li₂-Si 和PAF-C₄B₂H₄-Li₂-Ge体现出较好的常温储氢性能, 各种材料的常温储氢性能远低于其低温储氢性能. 通过77 K下H₂在PAFs材料中的等位能面分布和吸附平衡质心密度分布对H₂在PAFs 材料中的优先吸附位置进行分析, 发现在PAF-301 和PAF-301Li 骨架中, 由于中心能量较低的等位能区域范围较宽, H₂在其中存在四个明显的吸附高密度分布区域, 而其它三种PAFs晶胞中心能量较低的等位能区域范围较窄, 使得H₂在其中只存在两个明显的吸附高密度分布区域.     

Cooperativity and Anticooperativity in Ion-Water Interactions: Implications for the Aqueous Solvation of Ions

Non-additive effects in hydrogen bonds (HB) take place as a consequence of electronic charge transfers. Therefore, it is natural to expect cooperativity and anticooperativity in ion-water interactions. Nevertheless, investigations on this matter are scarce. This paper addresses the interactions of (i) the cations Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, and Ca²⁺ together with (ii) the anions F⁻, Cl⁻, Br⁻, NO₃⁻ and SO₄²⁻ with water clusters (H₂O)_n, n=1–8, and the effects of these ions on the HBs within the complete molecular adducts. We used quantum chemical topology tools, specifically the quantum theory of atoms in molecules and the interacting quantum atoms energy partition to investigate non-additive effects among the interactions studied herein. Our results show a decrease on the interaction energy between ions and the first neighbouring water molecules with an increment of the coordination number. We also found strong cooperative effects in the interplay between HBs and ion-dipole interactions within the studied systems. Such cooperativity affects considerably the interactions among ions with their first and second solvation shells in aqueous environments. Overall, we believe this article provides valuable information about how ion-dipole contacts interact with each other and how they relate to other interactions, such as HBs, in the framework of non-additive effects in aqueous media.