Four-Component Relativistic Density-Functional Theory Calculations of Nuclear Spin–Rotation Constants: Relativistic Effects in p-Block Hydrides

Structural and Electronic Studies of Substituted m-Terphenyl Group 12 Complexes

The effects of para-substitution on the structural and electronic properties of four series of two-coordinate m-terphenyl Group 12 complexes (R-Ar^#)₂M (M = Zn, Cd, Hg; R = t-Bu 1–3, SiMe₃4–6, Cl 7–9, CF₃10–12, where R-Ar^# = 2,6-{2,6-Xyl}₂-4-R-C₆H₂ and 2,6-Xyl = 2,6-Me₂C₆H₃) have been investigated. X-ray crystallography shows little structural variation across the series, with no significant change in the C–M–C bond distances and angles. However, considerable electronic differences are revealed by heteronuclear nuclear magnetic resonance (NMR) spectroscopy; a linear correlation is observed between the ¹¹³Cd, ¹⁹⁹Hg, and ¹H (2,6-Xyl methyl protons) NMR chemical shifts of the para-substituted complexes and the Hammett constants for the R-substituents. Specifically, an upfield shift in the NMR signal is observed with increasingly electron-withdrawing R-substituents. Density functional theory (DFT) calculations are employed to attempt to rationalize these trends.

Relativistic study of parity-violating nuclear spin-rotation tensors

We present a four-component relativistic approach to describe the effects of the nuclear spin-dependent parity-violating (PV) weak nuclear forces on nuclear spin-rotation (NSR) tensors. The formalism is derived within the four-component polarization propagator theory based on the Dirac-Coulomb Hamiltonian. Such calculations are important for planning and interpretation of possible future experiments aimed at stringent tests of the standard model through the observation of PV effects in NSR spectroscopy. An exploratory application of this theory to the chiral molecules H₂X₂ (X = ¹⁷O, ³³S, ⁷⁷Se, ¹²⁵Te, and ²⁰⁹Po) illustrates the dramatic effect of relativity on these contributions. In particular, spin-free and spin-orbit effects are even of opposite signs for some dihedral angles, and the latter fully dominate for the heavier nuclei. Relativistic four-component calculations of isotropic nuclear spin-rotation constants, including parity-violating electroweak interactions, give frequency differences of up to 4.2 mHz between the H₂Po₂ enantiomers; on the nonrelativistic level of theory, this energy difference is 0.1 mHz only.

Structural and electronic studies of substituted m-terphenyl lithium complexes

Spectroscopic and computational investigation of the effects of para-substituted m-terphenyl lithium complexes reveals significant electronic differences at the metal centre.

Carbonyl compounds of Rh, Ir, and Mt: electronic structure, bonding and volatility

First bond dissociation energies and other properties have been predicted for carbonyl compounds of group-9 elements including those of element 109, Mt, from relativistic DFT and CC calculations. A remarkable Λ-shape of the trends is observed, caused by strong relativistic effects on the valence AOs of Mt.

Carbonyl compounds of Tc, Re, and Bh: Electronic structure, bonding, and volatility

Calculations of molecular properties of M(CO)₅ and MH(CO)₅, where M = Tc, Re, and Bh, and of the products of their decomposition, M(CO)₄ and MH(CO)₄, were performed using density functional theory and coupled-cluster methods implemented in the relativistic program suits such as ADF, DIRAC, and ReSpect. The calculated first M-CO bond dissociation energies (FBDEs) of Bh(CO)₅ and BhH(CO)₅ turned out to be significantly weaker than those of the corresponding Re homologs. The reason for that is the relativistic destabilization and expansion of the 6d AOs, responsible for weaker σ-forth and π-back donations in the Bh compounds. The relativistic FBDEs of M(CO)₅ have, therefore, a Λ-shape behavior in the row Tc-Re-Bh, while the non-relativistic values increase toward Bh. Using the results of the molecular calculations and a molecule-slab interaction model, adsorption enthalpies, ΔH _ads, of group-7 carbonyl hydrides on quartz and Teflon were estimated for future gas-phase chromatography experiments. It was found that BhH(CO)₅ should be almost as volatile as the homologs, although its interaction with the surfaces should be somewhat stronger than that of MH(CO)₅ (M = Tc and Re), while the M(CO)₄ (M = Tc, Re, and Bh) molecules should be non-volatile. It will, therefore, be difficult to distinguish between the group-7 MH(CO)₅ species by measuring their ΔH _ads on surfaces of Teflon and quartz with an error bar of ±4 kJ/mol. The trends in properties and ΔH _ads of group-7 carbonyl hydrides are similar to those of group-8 carbonyls of Ru, Os, and Hs.

Resolution-of-identity accelerated relativistic two- and four-component electron dynamics approach to chiroptical spectroscopies

We present an implementation and application of electron dynamics based on real-time time-dependent density functional theory (RT-TDDFT) and relativistic 2-component X2C and 4-component Dirac-Coulomb (4c) Hamiltonians to the calculation of electron circular dichroism and optical rotatory dispersion spectra. In addition, the resolution-of-identity approximation for the Coulomb term (RI-J) is introduced into RT-TDDFT and formulated entirely in terms of complex quaternion algebra. The proposed methodology was assessed on the dimethylchalcogenirane series, C₄H₈X (X = O, S, Se, Te, Po, Lv), and the spectra obtained by non-relativistic and relativistic methods start to disagree for Se and Te, while dramatic differences are observed for Po and Lv. The X2C approach, even in its simplest one-particle form, reproduces the reference 4c results surprisingly well across the entire series while offering an 8-fold speed-up of the simulations. An overall acceleration of RT-TDDFT by means of X2C and RI-J increases with system size and approaches a factor of almost 25 when compared to the full 4c treatment, without compromising the accuracy of the final spectra. These results suggest that one-particle X2C electron dynamics with RI-J acceleration is an attractive method for the calculation of chiroptical spectra in the valence region.

Relativistic time-dependent density functional theories

The foundations, formalisms, technicalities, and practicalities of relativistic time-dependent density functional theories (R-TD-DFT) for spinor excited states of molecular systems containing heavy elements are critically reviewed.

Influence of the nuclear charge distribution and electron correlation effects on magnetic shieldings and spin-rotation tensors of linear molecules

The nuclear charge distribution effects (NChDE) on two response properties, the NMR magnetic shielding (σ) and the nuclear spin-rotation (SR) constants (M), are analyzed. We do it employing point-like and Gaussian-like models for describing the nuclear charge density of three linear molecules: HBr, HI and HAt. According to our results, both properties are sensitive to the NChDE. We show that the NChDE are almost completely relativistic, i.e., they nearly vanish in the non-relativistic limit of both properties. We calculated the NChDE on σ and M, and analyzed the differences between them in terms of a relativistic relation between these two properties. Using that relation we found that the electronic core mechanisms are the main ones for the NChDE on the shielding of nuclei of both, molecules and free atoms. The NChDE are smaller on SR constants than on shieldings. Nevertheless, within the relativistic polarization propagator formalism at the RPA level of approach they are very important for SR constants of nuclei in heavy-atom-containing compounds. Astatine in HAt has the largest influence: M_At = −9.95 kHz for a point-like model and −50.10 kHz for a Gaussian-like model. Correlation effects must be included and we do it using different DFT schemes. The PBE0 functional gives results that are closest to experiments for Br and I, though the LDA gives the closest for hydrogen. The value of the SR constant of At is reduced among 350 kHz and 500 kHz from its RPA value, when different and usual functionals are applied. Given that the NChDE on M and σ are mostly relativistic in their origin, these effects are also dependent on electron correlation. They have also a nonvanishing dependence with the Gaunt electron–electron interactions.

The origin and the size of both, electron correlation and nuclear charge distribution on shieldings and spin-rotations of heavy-atom containing linear molecules are shown. The analysis is performed on the relativistic and non relativistic regimes.

Exploring the potential energy surface of small lead clusters using the gradient embedded genetic algorithm and an adequate treatment of relativistic effects

Theoretical inclusion of relativistic effects (scalar and spin–orbit) play a crucial role to assure an adequate structural assignment on lead clusters.

Relativistic Calculations of Nuclear Magnetic Resonance Parameters

Relativistic effects are important for the accurate evaluation of the observables of nuclear magnetic resonance (NMR) spectroscopy, the nuclear magnetic shielding and the indirect spin–spin coupling tensors. Some of the most notable relativistic effects, in particular for light elements in the vicinity of heavy nuclei, are due to spin–orbit effects, an effect difficult to evaluate when starting from a non-relativistic wavefunction. Two- and four-component relativistic methods include spin–orbit effects variationally, and the recent improvements in the computational efficiency of these methods open new opportunities for accurate calculations of NMR parameters also for molecules with heavy elements. We here present an overview of the different approximations that have been introduced for calculating relativistic effects with two- and four-component methods and how these methods can be used to calculate the NMR parameters. We will also give some examples of systems that have been studied computationally with two- and four-component relativistic methods and discuss the importance of relativistic effects on the shielding and indirect spin–spin coupling constants.

NMR absolute shielding scale and nuclear magnetic dipole moment of 207Pb

A new absolute shielding scale is proposed for ²⁰⁷Pb nuclear magnetic resonance (NMR) spectroscopy.

Theoretical analysis of NMR shieldings in XSe and XTe (X = Si, Ge, Sn and Pb): the spin-rotation constant saga

How the electronic contribution to the spin-rotation constant is close to the paramagnetic contribution of the NMR absolute shielding constant?

Big picture of relativistic molecular quantum mechanics

Any quantum mechanical calculation on electronic structure ought to choose first an appropriate Hamiltonian H and then an Ansatz for parameterizing the wave function Ψ, from which the desired energy/property E(λ) can finally be calculated. Therefore, the very first question is: what is the most accurate many-electron Hamiltonian H? It is shown that such a Hamiltonian i.e. effective quantum electrodynamics (eQED) Hamiltonian, can be obtained naturally by incorporating properly the charge conjugation symmetry when normal ordering the second quantized fermion operators. Taking this eQED Hamiltonian as the basis, various approximate relativistic many-electron Hamiltonians can be obtained based entirely on physical arguments. All these Hamiltonians together form a complete and continuous ‘Hamiltonian ladder’, from which one can pick up the right one according to the target physics and accuracy. As for the many-electron wave function Ψ, the most intriguing questions are as follows. (i) How to do relativistic explicit correlation? (ii) How to handle strong correlation? Both general principles and practical strategies are outlined here to handle these issues. Among the electronic properties E(λ) that sample the electronic wave function nearby the nuclear region, nuclear magnetic resonance (NMR) shielding and nuclear spin-rotation (NSR) coupling constant are especially challenging: they require body-fixed molecular Hamiltonians that treat both the electrons and nuclei as relativistic quantum particles. Nevertheless, they have been formulated rigorously. In particular, a very robust ‘relativistic mapping’ between the two properties has been established, which can translate experimentally measured NSR coupling constants to very accurate absolute NMR shielding scales that otherwise cannot be obtained experimentally. Since the most general and fundamental issues pertinent to all the three components of the quantum mechanical equation HΨ = EΨ (i.e. Hamiltonian H, wave function Ψ, and energy/property E(λ)) have fully been understood, the big picture of relativistic molecular quantum mechanics can now be regarded as established.

Structure, solvent, and relativistic effects on the NMR chemical shifts in square-planar transition-metal complexes: assessment of DFT approaches

The role of various factors (geometry, solvent, relativistic treatment, functional) influencing the relativistic NMR chemical shift calculations for square-planar transition-metal complexes.