Large Relativistic Effects Research Articles

A method to capture the large relativistic and solvent effects on the UV-vis spectra of photo-activated metal complexes.

We have recently developed a method based on relativistic time-dependent density functional theory (TD-DFT) that allows the calculation of electronic spectra in solution (Creutzberg, Hedegård, J. Chem. Theory Comput.18, 2022, 3671). This method treats the solvent explicitly with a classical, polarizable embedding (PE) description. Furthermore, it employs the complex polarization propagator (CPP) formalism which allows calculations on complexes with a dense population of electronic states (such complexes are known to be problematic for conventional TD-DFT). Here, we employ this method to investigate both the dynamic and electronic effects of the solvent for the excited electronic states of trans-trans-trans-[Pt(N3)2(OH)2(NH3)2] in aqueous solution. This complex decomposes into species harmful to cancer cells under light irradiation. Thus, understanding its photo-physical properties may lead to a more efficient method to battle cancer. We quantify the effect of the underlying structure and dynamics by classical molecular mechanics simulations, refined with a subsequent DFT or semi-empirical optimization on a cluster. Moreover, we quantify the effect of employing different methods to set up the solvated system, e.g., how sensitive the results are to the method used for the refinement, and how large a solvent shell that is required. The electronic solvent effect is always included through a PE potential.

The partial waves of B^{*}_{2}(5747) and their contributions in strong decays

The relativistic Bethe–Salpeter method is adopted to study the OZI-allowed strong decays of the 2^+ state B^{*}_{2}(5747)^{0}, with emphasis on the relativistic corrections. We first study the partial waves in the wave functions used and find that there are P, D, and F partial waves in the B^{*}_{2}(5747)^{0} meson, with ratios of P/D/F=1:0.421:0.051. We also find that S/P/D=1:0.354:0.046 for B^*, and S/P=1:0.343 for the B meson. The large components of the D wave in B^{*}_{2}(5747)^{0} and the P wave in B^{(*)} mean that large relativistic effects exist in these states. Second, we calculate the strong decays, and the total decay width Gamma (B^{*}_{2}(5747)^{0})=25.9 MeV and the branching fraction Gamma (B^{*}_{2}(5747)^{0} rightarrow B^{*}pi ) / Gamma (B^{*}_{2}(5747)^{0} rightarrow Bpi )=0.96 obtained are consistent with experimental data. Third, we study the contributions of different partial waves in the initial and final wave functions, and find that the relativistic effects are about 15% and 11% for B^{*}_{2}(5747)^{0} rightarrow Bpi and B^{*}_{2}(5747)^{0} rightarrow B^{*}pi , respectively, which are much smaller than our expected effects, showing that the relativistic corrections cancel each other in these decays.

Bonding properties of molecular cerium oxides tuned by the 4f-block from ab initio perspective.

Probing chemical bonding in molecules containing lanthanide elements is of theoretical interest, yet it is computationally challenging because of the large valence space, relativistic effects, and considerable electron correlation. We report a high-level ab initio study that quantifies the many-body nature of Ce-O bonding with the coordination environment of the Ce center and particularly the roles of the 4f orbitals. The growing significance of the overlap between Ce 4f and O 2p orbitals with the increasing coordination of Ce atoms enhances Ce-O bond covalency and in return directs the molecular geometry. Upon partial reduction from neutral to anionic ceria, the excessive electrons populate the Ce-centered localized 4f orbital. The interplay between the admixture and localization of the 4f-block dually modulates bonding patterns of cerium oxide molecules, underlying the importance of many-body interactions between ligands and various lanthanide elements.

Exact-Two-Component Multiconfiguration Pair-Density Functional Theory

Molecules containing late-row elements exhibit large relativistic effects. To account for both relativistic effects and electron correlation in a computationally inexpensive way, we derived a formulation of multiconfiguration pair-density functional theory with the relativistic exact-two-component Hamiltonian (X2C-MC-PDFT). In this new method, relativistic effects are included during variational optimization of a reference wave function by exact-two-component complete active-space self-consistent-field (X2C-CASSCF) theory, followed by an energy evaluation using pair-density functional theory. Benchmark studies of excited-state and ground-state fine-structure splitting of atomic species show that X2C-MC-PDFT can significantly improve the X2C-CASSCF results by introducing additional state-specific electron correlation.

Long-bonding and bonding nature in noble gas insertion compounds MNgBY of transition metal-boron bond

The nature of inert gas bonding has always been an important topic. The bonds of noble gases cover the entire range of chemical bonds, from the weakest van der Waals forces, to non-covalent interactions, and to covalent bonds. Two types of methods were used to investigate the properties of chemical bonds in the inert gas inserted compound MNgBY with the transition metal M = Cu/Ag/Au and substituents Y = O/S/NH, one based on orbital analysis and the other based on electron density analysis. The NBO/NRT analysis shows that in these compounds there exists long-bonding striding the noble gas between the transitional metal and boron, similar to the noble gas insertion compounds HNgX of hydrohalide, and so a three-center four-electron bond exists among the M-Ng-B part. The electron density analyses show that the M-Ng bond between the metal Cu/Ag/Au and noble gas and the Ng-B bond in the Cu/Ag compounds are partial covalent but the Ng-B bond in Au compounds is a typical covalent bond. The large relativistic effects of Au cause the bonds in Au compounds shorter and stronger than the bonds in Ag/Cu compounds. The properties of the M-Ng and Ng-B bonds are not affected by substituents Y, but the bond lengths are sensitive to substituents.

Temperature-dependent lattice dynamics in iridium

The characterization of simple elemental systems is key to benchmarking first-principles modeling of electronic and vibrational behaviors of materials. A large body of literature has been built for most elemental systems in the periodic table. However, surprisingly little neutron work has been performed to probe the vibrational properties of iridium, likely due to its large neutron absorption cross section. Nonetheless, iridium is of significant scientific and technological interest due to large relativistic electron effects and electron-phonon coupling, particularly in strongly correlated iridate compounds. Here, we report temperature-dependent inelastic neutron scattering measurements of the vibrational properties of iridium, from which we extract key thermodynamic properties. To overcome the challenge of the large neutron absorption of iridium, we developed a simple postprocessing correction procedure. The measured densities of phonon states compare well with quasiharmonic density functional theory calculations, although the obtained experimental phonon Gr\uneisen parameters are much larger than expected, reaching as high as $\ensuremath{\gamma}=4.5$, indicating substantial anharmonicity.

Relativistic structural characterization of molybdenum and tungsten disulfide materials

AbstractThe advent of two‐dimensional transition metal dichalcogenides has triggered an interest in exploring a new class of high‐performance materials with intriguing physicochemical attributes. Molybdenum and tungsten disulfides have attracted significant attention due to surface excitons and trions and the large spin‐orbit effects of these compounds. Moreover, WS2 is especially intriguing due to large relativistic effects, which result in bound excitons at the edge and biexciton formation in the bilayers. Hence, we present a relativistic topological model for the characterization of these two types of metal disulfides. We have employed relativistically weighted graph‐theoretical methods for obtaining structural descriptors of these compounds through the inclusion of different shapes on the boundaries and employing the topological cut techniques.

All-electron fully relativistic Kohn-Sham theory for solids based on the Dirac-Coulomb Hamiltonian and Gaussian-type functions

We present the first full-potential method that solves the fully relativistic 4-component Dirac-Kohn-Sham equation for materials in the solid state within the framework of atom-centered Gaussian-type orbitals (GTOs). Our GTO-based method treats one-, two-, and three-dimensional periodic systems on an equal footing, and allows for a seamless transition to the methodology commonly used in studies of molecules with heavy elements. The scalar relativistic effects and spin-orbit interaction are handled variationally. The full description of the electron-nuclear potential in the core region of heavy nuclei is straightforward due to the local nature of the GTOs and does not pose any computational difficulties. We show how the time-reversal symmetry and a quaternion algebra-based formalism can be exploited to significantly reduce the increased methodological complexity and computational cost associated with multiple wave-function components coupled by the spin-orbit interaction. We provide a description of how to employ the matrix form of the multipole expansion and an iterative renormalization procedure to evaluate the conditionally convergent lattice sums arising for periodic systems. We investigate the problem of inverse variational collapse that arises if the Dirac operator containing a repulsive periodic potential is expressed in a basis containing diffuse functions, and suggest a possible solution. We demonstrate the validity of the method on silver halide crystals with large relativistic effects, and two-dimensional honeycomb structures (silicene and germanene) exhibiting the spin-orbit-driven quantum spin Hall effect. Our results are well-converged with respect to the basis limit using standard bases developed for molecular calculations, and indicate that the rule of removing basis functions with small exponents should not be applied when transferring the molecular basis to solids.

Calculation of electron scattering on atomic silver

We report on the application of the relativistic convergent close-coupling method to electron scattering from silver atoms. Differential and integrated cross sections are presented for elastic scattering and excitation to a number of low-lying excited states for energies ranging from 0.1 to 200 eV. The total and ionisation cross sections and elastic spin asymmetry parameters are also presented, and we find potentially large relativistic effects for elastic scattering at low energies. The results are compared with experiments where available, and somewhat variable agreement is found.

Theoretical hyperfine structures of F19 i and O17 i

Multiconfiguration Hartree-Fock (MCHF) and multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations are performed for the $2p^{5}~^{2}P^{o}$, $2p^4(^{3}P)3s~^{4}P$, $2p^4(^{3}P)3s~^{2}P$ and $2p^4(^{3}P)3p~^{4}S^o$ states of $^{19}$F~I to determine their hyperfine constants. Several computing strategies are considered to investigate electron correlation and relativistic effects. High-order correlation contributions are included in MCHF calculations based on single and double multireference (SD-MR) expansions. The largest components of the single reference MCHF wave functions are selected to define the MR sets. In this scheme, relativistic corrections are evaluated in the Breit-Pauli approximation. A similar strategy is used for the calculation of MCDHF relativistic wave functions and hyperfine parameters. While correlation and relativistic corrections are found to be rather small for the ground state, we highlight large relativistic effects on the hyperfine constant $A_{3/2}$ of $2p^4(^{3}P)3p~^{4}S^o$ and, to a lesser extent, on $A_{1/2}$ of $2p^4(^{3}P)3s~^{4}P$. As expected for such a light system, electron correlation effects dominate over relativity in the calculation of the hyperfine interaction of all other levels considered. We also revisit the hyperfine constants of $2p^3(^{4}S)3s~^{5}S^{o}$ and $2p^3(^{4}S)3p~^{5}P$ in $^{17}$O using similar strategies. The results are found to be in excellent agreement with experiment.

Femtosecond X-ray solution scattering reveals that bond formation mechanism of a gold trimer complex is independent of excitation wavelength.

The [Au(CN)2−]3 trimer in water experiences a strong van der Waals interaction between the d10 gold atoms due to large relativistic effect and can serve as an excellent model system to study the bond formation process in real time. The trimer in the ground state (S0) exists as a bent structure without the covalent bond between the gold atoms, and upon the laser excitation, one electron in the antibonding orbital goes to the bonding orbital, thereby inducing the formation of a covalent bond between gold atoms. This process has been studied by various time-resolved techniques, and most of the interpretation on the structure and dynamics converge except that the structure of the first intermediate (S1) has been debated due to different interpretations between femtosecond optical spectroscopy and femtosecond X-ray solution scattering. Recently, the excitation wavelength of 267 nm employed in our previous scattering experiment was suggested as the culprit for misinterpretation. Here, we revisited this issue by performing femtosecond X-ray solution scattering with 310 nm excitation and compared the results with our previous study employing 267 nm excitation. The data show that a linear S1 structure is formed within 500 fs regardless of excitation wavelength and the structural dynamics observed at both excitation wavelengths are identical to each other within experimental errors.

Nonlinear effects of general relativity from multiscale structure

When do the nonlinear effects of general relativity matter in astrophysical situations? They are obviously relevant for very compact sources of the gravitational field, such as neutron stars or black holes. In this paper I discuss another, less obvious situation, in which large relativistic effects may arise due to a complicated, multiscale structure of the matter distribution. I present an exact solution with an inhomogeneous energy density distribution in the form of a hierarchy of nested voids and overdensities of various sizes, extending from the homogeneity scale down to arbitrary small scales. I show that although each of the voids and overdensities seems to be very weakly relativistic, and thus easy to describe using the linearized general relativity, the solution taken as a whole lies in fact in the nonlinear regime. Its nonlinear properties are most easily seen when we compare the ADM mass of the solution and the integral of the local mass density: the difference between them, i.e. the relativistic mass deficit, can be significant provided that the inhomogeneities extend to sufficiently small scales. The non-additivity of masses implies a large backreaction effect, i.e. significant discrepancy between the averaged, large-scale effective stress–energy tensor and the naive average of the local energy density. I show that this is a general relativistic effect arising due to the inhomogeneous, multiscale structure. I also discuss the relevance of the results in cosmology and relativistic astrophysics.

Toward Understanding the Bonding Character in Complexes of Coinage Metals with Lone-Pair Ligands. CCSD(T) and DFT Computations

We present CCSD(T) interaction energies and the bonding analysis for complexes of Cu, Ag, and Au with the lone-pair ligands H2O, OF2, OMe2, NH3, NF3, NMe3, H2S, SF2, SMe2, PH3, PF3, PCl3, and PMe3 (ML complexes). Both electron correlation and relativistic effects are crucial in the bonding of all complexes. AuPH3, AuPF3, and AuPCl3 (AuPX3) complexes exhibit particularly large relativistic effects, 30-46 kJ/mol. Upon neglecting relativistic effects, the Au-P bonds almost vanish aside from weak long-range van der Waals interactions. Highest binding energies are computed for complexes with Au, followed by Cu and Ag. For all coinage metals the strongest interactions are computed for PX3 ligands followed by SX2 and NX3 OX2 ligands. Upon methylation the interaction energy rises significantly. Metal-thiol complexes, particularly AuSCH3, form a separate class. Exceptional stability of gold complexes is due to large relativistic enhancement of the electron affinity of Au. Along with the electron affinity of a metal, we link the pattern of interaction energies in ML complexes with ionization potentials (IPs) of ligands. Strong interaction with P containing ligands is attributed to their lower IP and the lone pair → metal electron donation accompanied with the back-donation characteristic for P containing ligand. Energy data are accompanied with the natural bond orbital analysis. Computationally less demanding DFT computations with the PBE0 functional provide correct pattern of interaction energies when compared with benchmark CCSD(T) results.

Unusual Thermal Decomposition of AgIISO4 Yielding AgI2S2O7: Bending Hammond’s Rule

“It could be said that among the coinage metals (Cu, Ag, Au), only silver is normal . (...) gold is anomalous due to large relativistic effects. Copper is anomalous as it has a nodeless and therefore very compact d shell, with strong electron–electron repulsion (...)”. The “normality” of elemental silver, is reflected in the prevalence of its monovalent oxidation state, +1 (as expected for a Group 11 element), which also has severe consequences for its second oxidation state—it renders Ag an extremely powerful oxidizer. The standard redox potential for the Ag/Ag redox pair equals +1.98 V versus NHE and it is surpassed only by those of FC/F , F2/2F , ClC/Cl and OHC/OH . Thus Ag is stabilized in connections with fluoride ligands, whereas its oxo and aza compounds are rare and are quite unstable thermodynamically and thermally. Here we investigate in detail the thermal decomposition of recently synthesized Ag sulfate, AgSO4. [4] The activation energy for decomposition turns out to be substantial ( 127 kJmol ) rendering this compound metastable at ambient (p, T) conditions. We show, based on literature about thermal decomposition for over 50 different sulfates and oxo-sulfates (see the Supporting Information), that solely AgSO4 s low-temperature thermal decomposition is associated with the reduction of a metal cation (“reductive decomposition”). We consider the reaction pathway for decomposition and we point out structural links between AgSO4 and crystalline product of its decomposition, AgSO3.5 Ag2S2O7. Ag sulfate was reported to decompose thermally in a single step while yielding Ag disulfate and releasing O2 [Eq. (1)]:

Ab initio study of NMR shielding constants and spin-rotation constants in N, P and As diatomic molecules

Ab initio calculations of NMR shielding constants and spin-rotation constants of six diatomic molecules XY where X, Y = N, P or As are described. We analyse the dependence of the results on the description of the correlation effects and their convergence with the extension of the basis set. Our best results, obtained at the CCSD(T)/cc-pV5Zs,p-unc level, appear to be sufficiently accurate for the smaller diatomics—N 2, PN and P 2; for the AsN, AsP and As 2 molecules large relativistic effects should be taken into account. Moreover, relativistic four-component density functional calculations of NMR shielding constants for the latter molecules demonstrate that the relativistic corrections cannot be determined at the Hartree–Fock level. The computed spin-rotation constants for PN and AsP can be compared with experimental data, the differences between theory and experiment are below 2% for PN and ≈10% for AsP.

Relativistic effects and primordial non-Gaussianity in the galaxy bias

When dealing with observables, one needs to generalize the bias relation between the observed galaxy fluctuation field to the underlying matter distribution in a gauge-invariant way. We provide such relation at second-order in perturbation theory adopting the local Eulerian bias model and starting from the observationally motivated uniform-redshift gauge. Our computation includes the presence of primordial non-Gaussianity. We show that large scale-dependent relativistic effects in the Eulerian bias arise independently from the presence of some primordial non-Gaussianity. Furthermore, the Eulerian bias inherits from the primordial non-Gaussianity not only a scale-dependence, but also a modulation with the angle of observation when sources with different biases are correlated.

Amalgamating at the molecular level. A study of the strong closed-shell Au(i)⋯Hg(ii) interaction

Complex {[Hg(C(6)F(5))(2)][Au(C(6)F(5))(PMe(3))](2)}(n)2 displays unsupported Au(I)···Hg(II) and Au(I)···Au(I) interactions. Its crystal structure displays a polymeric -(Au-Hg-Au-Au-Hg-Au)(n)- disposition. Ab initio calculations show very strong Au(I)···Hg(II) and Au(I)···Au(I) closed-shell interactions of -73.3 kJ mol(-1) and -57.0 kJ mol(-1), respectively, which have a dispersive (van der Waals) nature and are strengthened by large relativistic effects (>20%).

ChemInform Abstract: Relativistic Effects and the Chemistry of Gold

In atoms of high nuclear charge (Z), as a consequence of a relativistic effect, the s electrons of an atom become more bound and their orbitals smaller than if this effect were absent. Simultaneously, the d (and f ) electrons are less bound because of this effect, which scales roughly as Z2. Gold exhibits a large relativistic effect. This accounts for gold being more resistant to oxidation than silver. It also accounts for higher oxidation states being more accessible in gold than in silver. These effects are illustrated by some fluorine chemistry of gold and silver.

Fully Relativistic, Comparative Investigation of Gold and Platinum Alkyne Complexes of Relevance for the Catalysis of Nucleophilic Additions to Alkynes.

For a range of additions to alkynes gold is known to exhibit a much higher catalytic activity than a corresponding platinum compound. In order to approach the origin of this behavior we first investigate the propyne activation by the gold and platinum catalysts AuCl3 and PtCl2(H2O) where both metals possess a d(8) electron configuration and where the catalysts exhibit similar steric effects. Propyne serves as a representative for alkynes. Fully relativistic ab initio calculations of these alkyne-catalyst complexes are presented at the Dirac-Hartree-Fock self-consistent field (DHF-SCF), density functional theory (DFT/B3LYP), and Green's function (GF) level in order to properly account for the large relativistic effects of gold and platinum. For the alkyne/catalyst complexes both the perpendicular and in-plane conformations were studied as these possess very similar ground state energies and may easily transform into each other. Strongly varying orbital populations together with sizable energetic and structural differences of the frontier orbitals are found and can be considered as a major source of the differing catalytic activity. These mainly comprise vanishing LUMO densities at the carbon centers in the platinum complex together with increased LUMO energies making a nucleophilic attack harder than in the gold compound. As Green's function calculations show, DFT/B3LYP seems to overestimate correlation contributions leading to an unphysical energetic lowering of many unoccupied orbitals.

Relativistic hartree-fock compton profiles

Theoretical analysis and computer codes have been developed for calculating Compton profiles from numerical nonrelativistic and relativistic Hartree–Fock wave functions. Calculations are performed in uranium and results for nonrelativistic and relativistic electron densities, momentum distributions, and Compton profiles for individual orbitals are presented and compared. Large relativistic effects on the Compton profiles of the s and p orbitals are observed, even for orbitals with large principal quantum numbers. The 7s J (O) relativistic value lies 15.2% below the nonrelativistic Hartree–Fock value. The total uranium profile is decreased by 6.60% at the center when a relativistic wave function is used. Cited profile results for other atoms indicate that relativistic calculations may be necessary for atoms of xenon or for even smaller atoms.