Spin−Orbit and Relativistic Effects on Structures and Stabilities of Group 17 Fluorides EF3 (E = I, At, and Element 117): Relativity Induced Stability for the D3h Structure of (117)F3

Relativity and the periodic table

The periodic table provides a deep unifying principle for understanding chemical behaviour by relating the properties of different elements. For those belonging to the fifth and earlier rows, the observations concerning these properties and their interrelationships acquired a sound theoretical basis by the understanding of electronic behaviour provided by non-relativistic quantum mechanics. However, for elements of high nuclear charge, such as occur in the sixth and higher rows of the periodic table, the systematic behaviour explained by non-relativistic quantum mechanics begins to fail. These problems are resolved by realizing that relativistic quantum mechanics is required in heavy elements where electrons velocities can reach significant fractions of the velocity of light. An essentially non-mathematical description of relativistic quantum mechanics explains how relativity modifies valence electron behaviour in heavy elements. The direct relativistic effect, arising from the relativistic increase of the electron mass with velocity, contracts orbitals of low angular momentum, increasing their binding energies. The indirect relativistic effect causes valence orbitals of high angular momentum to be more effectively screened as a result of the relativistic contraction of the core orbitals. In the alkali and alkaline earths, the s orbital contractions reverse the chemical trends on descending these groups, with heavy elements becoming less reactive. For valence d and f electrons, the indirect relativistic effect enhances the reductions in their binding energies on descending the periodic table. The d electrons in the heavier coinage metals thus become more chemically active, which causes these elements to exhibit higher oxidation states. The indirect effect on d orbitals causes the chemistries of the sixth-row transition elements to differ significantly from the very similar behaviours of the fourth and fifth-row transition series. The relativistic destabilization of f orbitals causes lanthanides to be chemically similar, forming mainly ionic compounds in oxidation state three, while allowing the earlier actinides to show a richer range of chemical behaviour with several higher oxidation states. For the 7p series of elements, relativity divides the non-relativistic p shell of three degenerate orbitals into one of much lower energy with the energies of the remaining two being substantially increased. These orbitals have angular shapes and spin distributions so different from those of the non-relativistic ones that the ability of the 7p elements to form covalent bonds is greatly inhibited. This article is part of the theme issue 'Mendeleev and the periodic table'.

Heteroatom and solvent effects on molecular properties of formaldehyde and thioformaldehyde symmetrically disubstituted with heterocyclic groups C4H3Y (where Y = O-Po)

In this work several molecular properties of symmetrically disubstituted formaldehyde and thioformaldehyde have been studied using a quantum chemistry approach based on density functional theory. Five-membered heteroaromatic rings containing a single group 16 heteroatom were taken into account as the substituents (i.e., furan-2-yl, thiophen-2-yl, selenophen-2-yl, tellurophen-2-yl, and the experimentally as yet unknown polonophen-2-yl). For the resulting ten formaldehyde and thioformaldehyde derivatives, the geometry, energetics, frontier molecular orbitals, dipole moment and polarizability of their molecules were examined in order to establish the effect of ring heteroatom on these properties. Furthermore, these properties were also determined for the molecules in three solvents of low polarity (benzene, chloroform, and dichloromethane) in order to expand our study to include solvent effects. The dipole moment and polarizability of the investigated molecules show regular variations when the ring heteroatom descends through group 16 and the solvent polarity grows. The heteroatom and/or solvent effects on the part of the studied properties are, however, more complex. An attempt is made to rationalize the observed variations in the molecular properties. The conformational behavior of the investigated molecules was also explored and the conformationally weighted values of dipole moment and polarizability are presented.

Graphical abstract

The bonding picture in hypervalent XF3 (X = Cl, Br, I, At) fluorides revisited with quantum chemical topology

Hypervalent XF₃ (X = Cl, Br, I, At) fluorides exhibit T-shaped C_2V equilibrium structures with the heavier of them, AtF₃ , also revealing an almost isoenergetic planar D_3h structure. Factors explaining this behavior based on simple "chemical intuition" are currently missing. In this work, we combine non-relativistic (ClF₃ ), scalar-relativistic and two-component (X = Br - At) density functional theory calculations, and bonding analyses based on the electron localization function and the quantum theory of atoms in molecules. Typical signatures of charge-shift bonding have been identified at the bent T-shaped structures of ClF₃ and BrF₃ , while the bonds of the other structures exhibit a dominant ionic character. With the aim of explaining the D_3h structure of AtF₃ , we extend the multipole expansion analysis to the framework of two-component single-reference calculations. This methodological advance enables us to rationalize the relative stability of the T-shaped C_2v and the planar D_3h structures: the Coulomb repulsions between the two lone-pairs of the central atom and between each lone-pair and each fluorine ligand are found significantly larger at the D_3h structures than at the C_2v ones for X = Cl - I, but not with X = At. This comes with the increasing stabilization, along the XF₃ series, of the planar D_3h structure with respect to the global T-shaped C_2v minima. Hence, we show that the careful use of principles that are at the heart of the valence shell electron pair repulsion model provides reasonable justifications for stable planar D_3h structures in AX₃ E₂ systems. © 2017 Wiley Periodicals, Inc.

Structures and stabilities of group 17 fluorides EF3 (E = I, At, and element 117) with spin-orbit coupling

In this work, a recently developed CCSD(T) approach with spin-orbit coupling (SOC) as well as density functional theory (DFT) using various exchange-correlation (XC) functionals are employed to investigate structures and stabilities of group 17 fluorides EF(3) (E = I, At, and element 117). These molecules are predicted to have bent T-shaped C(2v) structures according to the second-order Jahn-Teller (SOJT) effects or the valance shell electron pair repulsion (VSEPR) theory. For IF(3) and (117)F(3), our results are consistent with previous SOC-DFT calculations. However, different XC functionals provide different results for AtF(3) and our SOC-CCSD(T) calculations show that both the C(2v) and D(3h) structures are minima on the potential energy surface and the C(2v) structure is the global minimum for AtF(3). The performance of XC functionals on structures and stabilities of IF(3) and AtF(3) is found to depend on the fraction of the Hartree-Fock exchange (HFX) included in the XC functionals and the M06-2X functional with 54% of HFX providing results that agree best with CCSD(T) results. In addition, although both the C(2v) and D(3h) structures are minima for AtF(3), the energy barrier between them is only 8 kJ mol(-1) for the C(2v) structure and 0.05 kJ mol(-1) for the D(3h) structure. This indicates that the D(3h) structure could not possibly be observed experimentally and AtF(3) can convert easily between the three C(2v) structures. The SOJT term is shown to be reduced by electron correlation for IF(3) and AtF(3). On the other hand, although SOC decreases the energy difference between the C(2v) and D(3h) structures and reduces the deviation of the C(2v) structure from the D(3h) structure, it decreases the frequency of the bond bending mode, which may indicate that SOC actually increases the SOJT term. This could be related to mixing of spin-singlet E' states to low-energy spin-triplet states due to SOC.

Relativistic effects in chemistry: more common than you thought

Relativistic effects can strongly influence the chemical and physical properties of heavy elements and their compounds. This influence has been noted in inorganic chemistry textbooks for a couple of decades. This review provides both traditional and new examples of these effects, including the special properties of gold, lead-acid and mercury batteries, the shapes of gold and thallium clusters, heavy-atom shifts in NMR, topological insulators, and certain specific heats.

Bonding analysis using localized relativistic orbitals: Water, the ultrarelativistic case and the heavy homologues H2X (X=Te, Po, eka-Po)

We report the implementation of Pipek-Mezey [J. Chem. Phys. 90, 4916 (1989)] localization of molecular orbitals in the framework of a four-component relativistic molecular electronic structure theory. We have used an exponential parametrization of orbital rotations which allows the use of unconstrained optimization techniques. We demonstrate the strong basis set dependence of the Pipek-Mezey localization criterion and how it can be eliminated. We have employed localization in conjunction with projection analysis to study the bonding in the water molecule and its heavy homologues. We demonstrate that in localized orbitals the repulsion between hydrogens in the water molecule is dominated by electrostatic rather than exchange interactions and that freezing the oxygen 2s orbital blocks polarization of this orbital rather than hybridization. We also point out that the bond angle of the water molecule cannot be rationalized from the potential energy alone due to the force term of the molecular virial theorem that comes into play at nonequilibrium geometries and which turns out to be crucial in order to correctly reproduce the minimum of the total energy surface. In order to rapidly assess the possible relativistic effects we have carried out the geometry optimizations of the water molecule at various reduced speed of light with and without spin-orbit interaction. At intermediate speeds, the bond angle is reduced to around 90 degrees , as is known experimentally for H(2)S and heavier homologues, although our model of ultrarelativistic water by construction does not allow any contribution from d orbitals to bonding. At low speeds of light the water molecule becomes linear which is in apparent agreement with the valence shell electron pair repulsion (VSEPR) model since the oxygen 2s12 and 2p12 orbitals both become chemically inert. However, we show that linearity is brought about by the relativistic stabilization of the (n + 1)s orbital, the same mechanism that leads to an electron affinity for eka-radon. Actual calculations on the series H2X (X = Te, Po, eka-Po) show the spin-orbit effects for the heavier species that can be rationalized by the interplay between SO-induced bond lengthening and charge transfer. Finally, we demonstrate that although both the VSEPR and the more recent ligand close packing model are presented as orbital-free models, they are sensitive to orbital input. For the series H2X (X = O, S, Se, Te) the ligand radius of the hydrogen can be obtained from the covalent radius of the central atom by the simple relation r(lig)(H) = 0.67r(cov)(X) + 27 (in picometers).

An Anomalous Bond Angle in (116)H2. Theoretical Evidence for Supervalent Hybridization

The electronic structure and geometry of the superheavy group VI molecule (116)H(2) are examined and compared to those of the lighter group analogues H(2)O-PoH(2). The spin-orbit interaction is found to lengthen the (116)-H bond and more importantly lead to a modest but significant H-(116)-H bond angle increase. It is suggested that the latter is the result of a rehybridization of the valence 7p orbitals with a "supervalent" 8s orbital of element 116.

One-photon mass-analyzed threshold ionization spectroscopy of CH2BrI: Extensive bending progression, reduced steric effect, and spin-orbit effect in the cation

One-photon mass-analyzed threshold ionization (MATI) spectrum of CH2BrI was obtained using coherent vacuum-ultraviolet radiation generated by four-wave difference-frequency mixing in Kr. Unlike CH2ClI investigated previously, a very extensive bending (Br-C-I) progression was observed. Vibrational frequencies of CH2BrI+ were measured from the spectra and the vibrational assignments were made by utilizing frequencies calculated by the density-functional-theory (DFT) method using relativistic effective core potentials with and without the spin-orbit terms. A noticeable spin-orbit effect on the vibrational frequencies was observed from the DFT calculations, even though its influence was not so dramatic as in CH2ClI+. A simple explanation based on the bonding characteristics of the molecular orbitals involved in the ionization is presented to account for the above differences between the MATI spectra of CH2BrI and CH2ClI. The 0-0 band of the CH2BrI spectrum could be identified through the use of combined data from calculations and experiments. The adiabatic ionization energy determined from the position of this band was 9.5944+/-0.0006 eV, which was significantly smaller than the vertical ionization energy reported previously.

Vibrational assignment and Franck-Condon analysis of the mass-analyzed threshold ionization (MATI) spectrum of CH2ClI: the effect of strong spin-orbit interaction

Detailed analysis of the one-photon mass-analyzed threshold ionization (MATI) spectrum of CH(2)ClI is presented. This includes the determination of the ionization energy of CH(2)ClI, complete vibrational assignments, and quantum-chemical calculations at the spin-orbit density-functional-theory (SODFT) level with various basis sets. Relativistic effective core potentials with effective spin-orbit operators can be used in SODFT calculations to treat the spin-orbit term on an equal footing with other relativistic effects and electron correlations. The comparison of calculated and experimental vibrational frequencies indicate that the spin-orbit effects are essential for the reasonable description of the CH(2)ClI(+) cation. Geometrical parameters and thus the molecular shape of the cation are greatly influenced by the spin-orbit effects even for the ground state. Calculated geometrical parameters deviate substantially for different basis sets or effective core potentials. In an effort to derive the exact geometrical parameters for this cation, SODFT geometries were further improved utilizing Franck-Condon fit of the MATI spectral pattern. This empirical fitting produced the well-converged set of geometrical parameters that are quite insensitive to the choice of SODFT calculations. The C-I bond length and the Cl-C-I bond angle show large deviations among different SODFT calculations, but the empirical spectral fitting yields 2.191 +/- 0.003 Angstroms for the C-I bond length and 107.09 +/- 0.09 degrees for the Cl-C-I angle. Those fitted geometrical parameters along with the experimental vibrational frequencies could serve as a useful reference in calibrating relativistic quantum-chemical methods for radicals.