Relativistic and quantum electrodynamics effects on NMR shielding tensors of TlX (X = H, F, Cl, Br, I, At) molecules.

The results of relativistic calculations of nuclear magnetic resonance shielding tensors (σ) for the thallium monocation (Tl+), thallium hydride (TlH), and thallium halides (TlF, TlCl, TlBr, TlI, and TlAt) are presented as obtained within a four-component polarization propagator formalism and a two-component linear response approach within the zeroth-order regular approximation. In addition to a detailed analysis of relativistic effects performed in this work, some quantum electrodynamical (QED) effects on those nuclear magnetic resonance shieldings and other small contributions are estimated. A strong dependence of σ(Tl) on the bonding partner is found, together with a very weak dependence of QED effects with them. In order to explain the trends observed, the excitation patterns associated with relativistic ee (or paramagnetic-like) and pp (or diamagnetic-like) contributions to σ are analyzed. For this purpose, the electronic spin-free and spin-dependent contributions are separated within the two-component zeroth-order regular approximation, and the influence of spin-orbit coupling on involved molecular orbitals is studied, which allows for a thorough understanding of the underlying mechanisms.

Opportunities for fundamental physics research with radioactive molecules.

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

Quasi-relativistic approach to analytical gradients of parity violating potentials.

An analytic gradient approach for the computation of derivatives of parity-violating (PV) potentials with respect to displacements of the nuclei in chiral molecules is described and implemented within a quasirelativistic mean-field framework. Calculated PV potential gradients are utilized for estimating PV frequency splittings between enantiomers in rotational and vibrational spectra of four chiral polyhalomethanes, i.e., CHBrClF, CHClFI, CHBrFI, and CHAtFI. Values calculated within the single-mode approximation for frequency shifts agree well with previously reported theoretical values. The influence of non-separable anharmonic effects (multi-mode effects) on vibrational frequency shifts, which are readily accessible with the present analytic derivative approach, is estimated for the C-F stretching fundamental of all four molecules and computed for each of the fundamentals in CHBrClF and CHAtFI. Multi-mode effects are found to be significant, in particular, for C-F stretching modes, being for some modes and cases of similar size as the single-mode contribution.

Relativistic and QED corrections to one-bond indirect nuclear spin-spin couplings in X2 2+ and X3 2+ ions (X = Zn, Cd, Hg).

The indirect spin-spin coupling tensor, J, between mercury nuclei in systems containing this element can be of the order of a few kHz and one of the largest measured. We analyzed the physics behind the electronic mechanisms that contribute to the one- and two-bond couplings nJHg-Hg (n = 1, 2). For doing so, we performed calculations for J-couplings in the ionized X2 2+ and X3 2+ linear molecules (X = Zn, Cd, Hg) within polarization propagator theory using the random phase approximation and the pure zeroth-order approximation with Dirac-Hartree-Fock and Dirac-Kohn-Sham orbitals, both at four-component and zeroth-order regular approximation levels. We show that the "paramagnetic-like" mechanism contributes more than 99.98% to the total isotropic value of the coupling tensor. By analyzing the molecular and atomic orbitals involved in the total value of the response function, we find that the s-type valence atomic orbitals have a predominant role in the description of the coupling. This fact allows us to develop an effective model from which quantum electrodynamics (QED) effects on J-couplings in the aforementioned ions can be estimated. Those effects were found to be within the interval (0.7; 1.7)% of the total relativistic effect on isotropic one-bond 1J coupling, though ranging those corrections between the interval (-0.4; -0.2)% in Zn-containing ions, to (-1.2; -0.8)% in Hg-containing ions, of the total isotropic coupling constant in the studied systems. The estimated QED corrections show a visible dependence on the nuclear charge Z of each atom X in the form of a power-law proportional to ZX 5.

Chiral Molecules as Sensitive Probes for Direct Detection of P-Odd Cosmic Fields.

Potential advantages of chiral molecules for a sensitive search for parity violating cosmic fields are highlighted. Such fields are invoked in different models for cold dark matter or in the Lorentz-invariance violating standard model extensions and thus are signatures of physics beyond the standard model. The sensitivity of a 20-year-old experiment with the molecule CHBrClF to pseudovector cosmic fields as characterized by the parameter |b_{0}^{e}| is estimated to be O(10^{-12} GeV) employing ab initio calculations. This allows us to project the sensitivity of future experiments with favorable choices of chiral heavy-elemental molecular probes to be O(10^{-17} GeV), which will be an improvement of the present best limits by at least two orders of magnitude.

Toolbox approach for quasi-relativistic calculation of molecular properties for precision tests of fundamental physics.

A generally applicable approach for the calculation of relativistic properties described by one-electron operators within a two-component wave function approach is presented. The formalism is explicitly evaluated for the example of quasirelativistic wave functions obtained within the zeroth order regular approximation (ZORA). The wide applicability of the scheme is demonstrated for the calculation of parity (P) and time-reversal (T ) symmetry violating properties, which are important for searches of physics beyond the standard model of particle physics. The quality of the ZORA results is shown exemplarily for the molecules RaF and TlF by comparison with data from four-component calculations as far as available. Finally, the applicability of RaF in experiments that search for P,T-violation not only in the electronic but also in the quark sector is demonstrated.

Synthesis and Characterization of [Br3 ][MF6 ] (M=Sb, Ir), as well as Quantum Chemical Study of [Br3 ]+ Structure, Chemical Bonding, and Relativistic Effects Compared with [XBr2 ]+ (X=Br, I, At, Ts) and [TsZ2 ]+ (Z=F, Cl, Br, I, At, Ts).

[Br3 ][SbF6 ] and [Br3 ][IrF6 ] were synthesized by interaction of BrF3 with Sb2 O3 or iridium metal, respectively. The former compound crystallizes in the orthorhombic space group Pbcn (No. 60) with a=11.9269(7), b=11.5370(7), c=12.0640(6) Å, V=1660.01(16) Å3 , Z=8 at 100 K. The latter compound crystallizes in the triclinic space group P 1 ‾ (No. 2) with a=5.4686(5), b=7.6861(8), c=9.9830(9) Å, α=85.320(8), ß=82.060(7), γ=78.466(7)°, V=406.56(7) Å3 , Z=2 at 100 K. Both compounds contain the cation [Br3 ]+ , which has a bent structure and is coordinated by octahedron-like anions [MF6 ]- (M=Sb, Ir). Experimentally obtained cell parameters, bond lengths, and angles are confirmed by solid-state DFT calculations, which differ from the experimental values by less than 2 %. Relativistic effects on the structure of the tribromonium(1+) cation are studied computationally and found to be small. For the heaviest analogues containing At and Ts, however, pronounced relativistic effects are found, which lead to a linear structure of the polyhalogen cation.

Zeroth order regular approximation approach to electric dipole moment interactions of the electron.

A quasi-relativistic two-component approach for an efficient calculation of P,T-odd interactions caused by a permanent electric dipole moment of the electron (eEDM) is presented. The approach uses a (two-component) complex generalized Hartree-Fock and a complex generalized Kohn-Sham scheme within the zeroth order regular approximation. In applications to select heavy-elemental polar diatomic molecular radicals, which are promising candidates for an eEDM experiment, the method is compared to relativistic four-component electron-correlation calculations and confirms values for the effective electric field acting on the unpaired electron for RaF, BaF, YbF, and HgF. The calculations show that purely relativistic effects, involving only the lower component of the Dirac bi-spinor, are well described by treating only the upper component explicitly.