Reactivity of Ts and At oxides and oxyhydrides with a gold surface from periodic DFT calculations.

Adsorption energies, Eads, of oxides and oxyhydrides of the superheavy element (SHEs) Ts and of its lighter homologue At on the gold surface are predicted on the basis of relativistic periodic density functional theory calculations via AMS BAND software. The following compounds were considered: MO, MO2, MOO, and MO(OH) (where M = At and Ts). The aim of this study is to support "one-atom-at-a-time" gas-phase chromatography experiments on reactivity/volatility of SHEs. The results obtained indicate that all the molecules investigated should interact fairly strongly with the gold surface, with those of Ts being more reactive than At ones. The similarity in the Eads values of all the considered At compounds would make it challenging to differentiate between them while measuring their adsorption enthalpies, given experimental uncertainty. However, the difference in Eads among Ts compounds is more pronounced, so that one should be able to differentiate between the species.

Relativistic Coupled-Cluster Calculations of Spectroscopic Properties of Copernicium and Flerovium Monoxides.

Calculations of spectroscopic properties of the CnO and FlO molecules are performed using ab initio all-electron 4c- and 2c-relativistic coupled-cluster approaches with single, double, and perturbative triple excitations. The corresponding calculation for HgO is also accomplished for comparison with the published data. The dependence of the results on the parameters of the basis set and approximations used is investigated in detail. The overall relative uncertainties of the recommended values on the level of 1-2 % are reached. The calculated spectroscopic constants are indicative of the following trend in the reactivity of the oxides HgO>FlO>CnO. This is confirmed by the trend in the adsorption energies, Eads , of these molecules on the surfaces of gold, quartz, and Teflon. The predicted rather low Eads values for the latter case should guarantee their delivery from the recoil chamber to the chemistry set up in gas-phase experiments.

A theoretical study of the adsorption behavior of superheavy 7p-elements and their compounds on a surface of gold in comparison with their lighter homologs.

Adsorption energies, Eads, of the 7th row superheavy elements (SHEs) Lv through Og, as well as of the homologous species of the 6th row elements Po through Rn on a gold surface are predicted on the basis of relativistic periodic density functional theory calculations via SCM BAND software. Since some of the elements can also form compounds such as hydrides and oxyhydrides under experimental conditions, the Eads values of the MH (M = Bi/Mc, Po/Lv, At/Ts and Rn/Og) and MOH (M = At/Ts and Rn/Og) molecules on a gold surface were also calculated. The aim of this study is to support "one-atom-at-a-time" gas-phase chromatography experiments on the reactivity/volatility of SHEs. The obtained results show that, in agreement with earlier predictions using somewhat different approaches and with experimental results on Hg, Cn and Rn, the adsorption strength of the elements on the Au(111) surface should follow the sequence: Hg > Fl > Og > Cn ≫ Rn, with the Eads values of less than 100 kJ mol-1. The other elements and their compounds under consideration should adsorb much more strongly on the gold surface with Eads values above 160 kJ mol-1, which should make them indistinguishable with respect to Eads in the chromatography column kept at room temperature and lower. However, with the further detector development, investigations of the chemical properties of these short-lived and less volatile SHEs and their compounds at high temperatures should be possible.

Mechanochemical Conversion of Aromatic Amines to Aryl Trifluoromethyl Ethers.

Increased interest in the trifluoromethoxy group in organic synthesis and medicinal chemistry has induced a demand for new, selective, general, and faster methods applicable to natural products and highly functionalized compounds at a later stage of hit-to-lead campaigns. Applying pyrylium tetrafluoroborate, we have developed a mechanochemical protocol to selectively substitute the aromatic amino group with the OCF3 functionality. The scope of our method includes 31 examples of ring-substituted anilines, including amides and sulfonamides. Expected SNAr products were obtained in excellent yields. The presented concise method opens a pathway to new chemical spaces for the pharmaceutical industry.

Reactivity of Group 13 Elements Tl and Element 113, Nh, and of Their Hydroxides with Respect to Various Quartz Surfaces from Periodic Relativistic DFT Calculations.

Adsorption properties of group 13 element Tl and the superheavy element Nh, as well of their hydroxides on various modified quartz surfaces, are predicted on the basis of relativistic periodic DFT calculations using the BAND software. The obtained adsorption energies, Eads, of the MOH (M = Tl and Nh) molecules are indicative of the relatively strong interaction of the hydroxides with all the considered quartz surfaces. In contrast, adsorption of the Tl and Nh atoms was found to be significantly weaker. The adsorption strength of both M and MOH (M = Tl and Nh) was shown to increase with the dehydroxylation of the quartz surface. Very good agreement is reached between the calculated Eads(TlOH) of 133 kJ/mol on the fully hydroxylated quartz surface and of 157 kJ/mol on the partially dehydroxylated quartz surface on the one hand and experimental adsorption enthalpies, -ΔHads, of 134/137 ± 5 kJ/mol (at ∼300 °C) and 158 ± 3 kJ/mol (at ∼500 °C), respectively, on the other hand. Thus, we suggest that all the experimental ΔHads values for Tl should be assigned to the adsorption/desorption of the TlOH molecule. For NhOH, its adsorption properties on various quartz surfaces should be very similar to those of TlOH, with slightly smaller Eads values. Adsorption of the Nh atom should, however, be much weaker than that of the Tl atom due to stronger spin-orbit effects in Nh.

Reactivity of the Superheavy Element 115, Mc, and Its Lighter Homologue, Bi, with Respect to Gold and Hydroxylated Quartz Surfaces from Periodic Relativistic DFT Calculations: A Comparison with Element 113, Nh.

Adsorption energies (Eads) of the superheavy element (SHE) Mc, its lighter homologue (Bi), as well as of another superheavy element Nh and some lighter homologues of SHEs on gold and hydroxylated quartz surfaces are predicted via periodic relativistic density functional theory calculations. The aim of this study is to support "one-atom-at-a-time" gas-phase chromatography experiments that are examining the reactivity and volatility of Mc. The obtained Eads values of the Bi and Mc atoms on the Au(111) surface are >200 kJ/mol. On the hydroxylated quartz surface, Mc should adsorb with a minimal energy of 58 kJ/mol. On both types of surfaces, Eads(Mc) should be ∼100 kJ/mol smaller than Eads(Bi) due to strong relativistic effects on its valence 7p electrons. A comparison with other SHEs under investigation shows that Mc should adsorb on gold more strongly than Cn, Nh, and Fl, while on quartz, Mc should adsorb like Nh, with both of them absorbing more strongly than volatile Cn and Fl. The highest reactivity of Mc in the row of the 7p elements is caused by the largest orbital and relativistic destabilization and expansion of the 7p3/2 atomic orbital. Using the calculated Eads, the distribution of the Nh and Mc events in the gas-phase chromatography column with quartz and gold-plated detectors is predicted via Monte Carlo simulations. As a result, Mc atoms should be almost 100% adsorbed in the first section of the chromatography column on quartz, while a few atoms of Nh can reach the second part of the column with gold-plated detectors.

Systematic study and uncertainty evaluation of P, T-odd molecular enhancement factors in BaF.

A measurement of the magnitude of the electric dipole moment of the electron (eEDM) larger than that predicted by the Standard Model (SM) of particle physics is expected to have a huge impact on the search for physics beyond the SM. Polar diatomic molecules containing heavy elements experience enhanced sensitivity to parity (P) and time-reversal (T)-violating phenomena, such as the eEDM and the scalar-pseudoscalar (S-PS) interaction between the nucleons and the electrons, and are thus promising candidates for measurements. The NL-eEDM collaboration is preparing an experiment to measure the eEDM and S-PS interaction in a slow beam of cold BaF molecules [P. Aggarwal et al., Eur. Phys. J. D 72, 197 (2018)]. Accurate knowledge of the electronic structure parameters, Wd and Ws, connecting the eEDM and the S-PS interaction to the measurable energy shifts is crucial for the interpretation of these measurements. In this work, we use the finite field relativistic coupled cluster approach to calculate the Wd and Ws parameters in the ground state of the BaF molecule. Special attention was paid to providing a reliable theoretical uncertainty estimate based on investigations of the basis set, electron correlation, relativistic effects, and geometry. Our recommended values of the two parameters, including conservative uncertainty estimates, are 3.13 ±0.12×1024Hzecm for Wd and 8.29 ± 0.12 kHz for Ws.

Hyperfine Structure Constants on the Relativistic Coupled Cluster Level with Associated Uncertainties.

Accurate predictions of hyperfine structure (HFS) constants are important in many areas of chemistry and physics, from the determination of nuclear electric and magnetic moments to benchmarking of new theoretical methods. We present a detailed investigation of the performance of the relativistic coupled cluster method for calculating HFS constants within the finite-field scheme. The two selected test systems are 133Cs and 137BaF. Special attention has been paid to construct a theoretical uncertainty estimate based on investigations on basis set, electron correlation and relativistic effects. The largest contribution to the uncertainty estimate comes from higher order correlation contributions. Our conservative uncertainty estimate for the calculated HFS constants is ∼5.5%, while the actual deviation of our results from experimental values is <1% in all cases.

The DIRAC code for relativistic molecular calculations.

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

Properties and Reactivity of Hydroxides of Group 13 Elements In, Tl, and Nh from Molecular and Periodic DFT Calculations.

Adsorption energies, Eads, of gaseous hydroxides of In, Tl, and the superheavy element Nh on surfaces of Teflon and gold are predicted using molecular and periodic relativistic DFT calculations. The ambition of the work is to assist related "one atom at a time" gas-phase chromatography experiments on the volatility of NhOH. The obtained low values of Eads(MOH), where M = In, Tl, Nh, on Teflon should guarantee easy transportation of the molecules through the Teflon capillaries from the accelerator to the chemistry setup. Straightforward band-structure DFT calculations using the revPBE-D3(BJ) functional have given an Eads(MOH) value of 161.4 kJ/mol on the Au(111) surface, being indicative of significant molecule-surface interaction. The MOH-gold surface binding is shown to take place via the oxygen atom of the hydroxide, with the oxygen-gold charge density transfer increasing from InOH to NhOH. The trend in Eads(MOH) is shown to be InOH < TlOH < NhOH, caused by increasing molecular dipole moments and decreasing stability of the hydroxides in this row. A trend in Eads of the atoms of these elements on gold is, however, opposite, In > Tl > Nh, caused by the increasing relativistic contraction and stabilization of the np1/2 AO with Z. These opposite trends in Eads(MOH) and Eads(M) in group 13 lead to almost equal Eads(Nh) and Eads(NhOH) values, making identification of Nh, as a type of species, difficult by measuring its adsorption enthalpy on gold.

Hexacarbonyls of Mo, W, and Sg: Metal-CO Bonding Revisited.

Calculations of the first bond dissociation energies (FBDEs) and other molecular properties of M(CO)6, where M = Mo, W, and Sg, have been performed using a variety of nonrelativistic and relativistic methods, such as ZORA-DFT, X2c+AMFI-CCSD(T), and Dirac-Coulomb density functional theory. The aim of the study is to assist experiments on the measurements of the FBDE of Sg(CO)6. We have found that, different from the results published earlier, the metal-CO bond in Sg(CO)6 should be weaker than that in W(CO)6. A comparison of the relativistic and nonrelativistic FBDE values, as well as molecular orbital and vibrational frequency analyses within both the nonrelativistic and relativistic approaches, have shown that this is a relativistic, predominantly scalar, effect causing weaker d(M) → π(CO) back-bonding in Sg(CO)6 than in the lighter homologues. Good agreement between the calculated FBDEs in this work and the experimental FBDEs for the Mo and W compounds gives credit to the present FBDE of Sg(CO)6, which should serve as guidance for ongoing experiments.

Reactivity of superheavy elements Cn and Fl and of their oxides in comparison with homologous species of Hg and Pb, respectively, towards gold and hydroxylated quartz surfaces.

Adsorption energies, Eads, and other properties of atoms and oxides of the superheavy elements (SHEs) Cn and Fl, as well as of the homologous species of Hg and Pb, on Au(111) and fully hydroxylated quartz surfaces are predicted on the basis of 2c-DFT calculations and a periodic slab model using BAND software. The ambition of the work is to interpret the outcome of "one-atom-at-a-time" gas-phase chromatography experiments on the reactivity/volatility of SHEs. The present results with an improved (dispersion corrected) exchange-correlation functional show that, in agreement with our earlier predictions and experimental results on Pb, Hg and Cn, the sequence of the Eads values of the atoms on the gold surface should be Pb ≫ Hg > Fl > Cn, with rather moderate Eads values smaller than 90 kJ mol-1 (except for that for Pb). Oxides of Hg, Cn and Fl should be much more reactive with the gold surface than the corresponding atoms, with Eads values of about 200 kJ mol-1. A striking difference in the geometry of the deposited oxides was found between group 12 and group 14. An analysis of the Eads values for M and MO (M = Hg/Cn and Pb/Fl) on the hydroxylated α-quartz surface enables one to conclude that atoms of Hg, Cn and Fl should not interact with such a surface at room temperature, while Pb should adsorb on it. Oxides of these elements, on the contrary, should strongly adsorb on quartz with Eads ≥ 100 kJ mol-1. The present theoretical data agree with the experimental results on the elemental species of Hg, Cn and Fl.

Analysis of parity violation in chiral molecules.

In order to guide the experimental search for parity violation in molecular systems, in part motivated by the possible link to biomolecular homochirality, we present a detailed analysis in a relativistic framework of the mechanism behind the tiny energy difference between enantiomers induced by the weak force. A decomposition of the molecular expectation value into atomic contributions reveals that the effect can be thought of as arising from a specific mixing of valence s(1/2) and p(1/2) orbitals on a single center induced by a chiral molecular field. The intra-atomic nature of the effect is further illustrated by visualization of the electron chirality density and suggests that a simple model for parity violation in molecules may be constructed by combining pre-calculated atomic quantities with simple bonding models. A 2-component relativistic computational procedure is proposed which bridges the relativistic and non-relativistic approaches to the calculation of parity violation in chiral molecules and allows us to explore the single-center theorem in a variational setting.

The molecular mean-field approach for correlated relativistic calculations.

A new approach for relativistic correlated electron structure calculations is proposed by which a transformation to a two-spinor basis is carried out after solving the four-component relativistic Hartree-Fock equations. The method is shown to be more accurate than approaches that apply an a priori transformation to a two-spinor basis. We also demonstrate how the two-component relativistic calculations with properly transformed two-electron interaction can be simulated at the four-component level by projection techniques, thus allowing an assessment of errors introduced by more approximate schemes.

Gauge origin independent calculations of nuclear magnetic shieldings in relativistic four-component theory.

The use of perturbation-dependent London atomic orbitals, also called gauge including atomic orbitals, has proven efficient for calculations of NMR shielding constants and other magnetic properties in the nonrelativistic framework. In this paper, the theory of London atomic orbitals for NMR shieldings is extended to the four-component relativistic framework and our implementation is described. The relevance of London atomic orbitals in four-component calculations as well as computational aspects are illustrated with test calculations on hydrogen iodide. We find that the use of London atomic orbitals is an efficient method for reliable calculations of NMR shielding constants with standard basis sets, also for four-component calculations with spin-orbit coupling effects included in the wave function optimization. Furthermore, we find that it is important that the small component basis functions fulfill the magnetic balance for accurate description of the diamagnetic shielding and that the role of London atomic orbitals in the relativistic domain is to provide atomic magnetic balance even in the molecular case, thus greatly improving basis set convergence. The Sternheim approximation, which calculates the diamagnetic contribution as an expectation value, leads to significant errors and is not recommended.

An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation.

The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.

Relativistic effects in the intermolecular interaction-induced nuclear magnetic resonance parameters of xenon dimer.

Relativistic effects on the (129)Xe nuclear magnetic resonance shielding and (131)Xe nuclear quadrupole coupling (NQC) tensors are examined in the weakly bound Xe(2) system at different levels of theory including the relativistic four-component Dirac-Hartree-Fock (DHF) method. The intermolecular interaction-induced binary chemical shift delta, the anisotropy of the shielding tensor Deltasigma, and the NQC constant along the internuclear axis chi( parallel) are calculated as a function of the internuclear distance. DHF shielding calculations are carried out using gauge-including atomic orbitals. For comparison, the full leading-order one-electron Breit-Pauli perturbation theory (BPPT) is applied using a common gauge origin. Electron correlation effects are studied at the nonrelativistic (NR) coupled-cluster singles and doubles with perturbational triples [CCSD(T)] level of theory. The fully relativistic second-order Moller-Plesset many-body perturbation (DMP2) theory is used to examine the cross coupling between correlation and relativity on NQC. The same is investigated for delta and Deltasigma by BPPT with a density functional theory model. A semiquantitative agreement between the BPPT and DHF binary property curves is obtained for delta and Deltasigma in Xe(2). For these properties, the currently most complete theoretical description is obtained by a piecewise approximation where the uncorrelated relativistic DHF results obtained close to the basis-set limit are corrected, on the one hand, for NR correlation effects and, on the other hand, for the BPPT-based cross coupling of relativity and correlation. For chi( parallel), the fully relativistic DMP2 results obtain a correction for NR correlation effects beyond MP2. The computed temperature dependence of the second virial coefficient of the (129)Xe nuclear shielding is compared to experiment in Xe gas. Our best results, obtained with the piecewise approximation for the binary chemical shift combined with the previously published state of the art theoretical potential energy curve for Xe(2), are in excellent agreement with the experiment for the first time.