The periodic table and the physics that drives it

As the International Year of the Periodic Table came to an end in 2019, the authors reflect on the chemistry and physics that drive the periodic table of the elements. This includes aspects of periodic trends, relativistic electronic-structure theory, nuclear-structure theory and the astrophysical origin of the elements. Mendeleev's introduction of the periodic table of elements is one of the most important milestones in the history of chemistry, as it brought order into the known chemical and physical behaviour of the elements. The periodic table can be seen as parallel to the Standard Model in particle physics, in which the elementary particles known today can be ordered according to their intrinsic properties. The underlying fundamental theory to describe the interactions between particles comes from quantum theory or, more specifically, from quantum field theory and its inherent symmetries. In the periodic table, the elements are placed into a certain period and group based on electronic configurations that originate from the Pauli and Aufbau principles for the electrons surrounding a positively charged nucleus. This order enables us to approximately predict the chemical and physical properties of elements. Apparent anomalies can arise from relativistic effects, partial-screening phenomena (of type lanthanide contraction) and the compact size of the first shell of everyl-value. Further, ambiguities in electron configurations and the breakdown of assigning a dominant configuration, owing to configuration mixing and dense spectra for the heaviest elements in the periodic table. For the short-lived transactinides, the nuclear stability becomes an important factor in chemical studies. Nuclear stability, decay rates, spectra and reaction cross sections are also important for predicting the astrophysical origin of the elements, including the production of the heavy elements beyond iron in supernova explosions or neutron-star mergers. In this Perspective, we critically analyse the periodic table of elements and the current status of theoretical predictions and origins for the heaviest elements, which combine both quantum chemistry and physics.Peer reviewe

Homogeneous Gold Catalysis through Relativistic Effects: Addition of Water to Propyne

In the catalytic addition of water to propyne the Au(III) catalyst is not stable under non-relativistic conditions and dissociates into a Au(I) compound and Cl2. This implies that one link in the chain of events in the catalytic cycle is broken and relativity may well be seen as the reason why Au(III) compounds are effective catalysts.Comment: 12 pages, 3 figures, 1 tabl

The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r^4) scaling

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI) tensor and the two-particle excitation amplitudes used in the parametric reduced density matrix (pRDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r4), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the traditional pRDM algorithm, somewhere between that of CCSD and CCSD(T).Comment: 11 pages, 1 figur

The convergence of the ab-initio many-body expansion for the cohesive energy of solid mercury

A many-body expansion for mercury clusters of the form E = \sum_{i<j}\Delta \epsilon_{ij} + \sum_{i<j<k}\Delta \epsilon_{ijk} + ... \quad, does not converge smoothly with increasing cluster size towards the solid state. Even for smaller cluster sizes (up to n=6), where van der Waals forces still dominate, one observes bad convergence behaviour. For solid mercury the convergence of the many-body expansion can dramatically be improved by an incremental procedure within an embedded cluster approach. Here one adds the coupled cluster many-body electron correlation contributions of the embedded cluster to the bulk HF energy. In this way we obtain a cohesive energy (not corrected for zero-point vibration) of 0.79 eV in perfect agreement with the experimental value.Comment: 10 pages, 3 figures, accepted PR

Identification of the slow E3 transition 136mCs -> 136Cs with conversion electrons

We performed at ISOLDE the spectroscopy of the decay of the 8- isomer in 136Cs by and conversion-electron detection. For the first time the excitation energy of the isomer and the multipolarity of its decay have been measured. The half-life of the isomeric state was remeasured to T1/2 = 17.5(2) s. This isomer decays via a very slow 518 keV E3 transition to the ground state. In addition to this, a much weaker decay branch via a 413 keV M4 and a subsequent 105 keV E2 transition has been found. Thus we have found a new level at 105 keV with spin 4+ between the isomeric and the ground state. The results are discussed in comparison to shell model calculations.Comment: Phys. Rev. C accepted for publicatio

Verification of a Central Pacemaker in Brain Stem by Phase-Coupling Analysis Between HR Interval- and BOLD-Oscillations in the 0.10–0.15 Hz Frequency Band

The origin of slow intrinsic oscillations in resting states of functional magnetic resonance imaging (fMRI) signals is still a matter of debate. The present study aims to test the hypothesis that slow blood oxygenation level-dependent (BOLD) oscillations with frequency components greater than 0.10 Hz result from a central neural pacemaker located in the brain stem. We predict that a central oscillator modulates cardiac beatto- beat interval (RRI) fluctuations rapidly, with only a short neural lag around 0.3 s. Spontaneous BOLD fluctuations in the brain stem, however, are considerably delayed due to the hemodynamic response time of about 2–3 s. In order to test these predictions, we analyzed the time delay between slow RRI oscillations from thorax and BOLD oscillations in the brain stem by calculating the phase locking value (PLV). Our findings show a significant time delay of 2.2 0.2 s between RRI and BOLD signals in 12 out of 23 (50%) participants in axial slices of the pons/brain stem. Adding the neural lag of 0.3 s to the observed lag of 2.2 s we obtain 2.5 s, which is the time between neural activity increase and BOLD increase, termed neuro-BOLD coupling. Note, this time window for neuro-BOLD coupling in awake humans is surprisingly of similar size as in awake head-fixed adult mice (Mateo et al., 2017)

First identification of large electric monopole strength in well-deformed rare earth nuclei

Excited states in the well-deformed rare earth isotopes $^{154}$Sm and $^{166}$Er were populated via ``safe'' Coulomb excitation at the Munich MLL Tandem accelerator. Conversion electrons were registered in a cooled Si(Li) detector in conjunction with a magnetic transport and filter system, the Mini-Orange spectrometer. For the first excited $0^+$ state in $^{154}$Sm at 1099 keV a large value of the monopole strength for the transition to the ground state of $\rho^2(\text{E0}; 0^+_2 \to 0^+_\text{g}) = 96(42)\cdot 10^{-3}$ could be extracted. This confirms the interpretation of the lowest excited $0^+$ state in $^{154}$Sm as the collective $\beta$-vibrational excitation of the ground state. In $^{166}$Er the measured large electric monopole strength of $\rho^2(\text{E0}; 0^+_4 \to 0^+_1) = 127(60)\cdot 10^{-3}$ clearly identifies the $0_4^+$ state at 1934 keV to be the $\beta$-vibrational excitation of the ground state.Comment: submitted to Physics Letters

High resolution spectroscopy of methyltrioxorhenium: towards the observation of parity violation in chiral molecules

Originating from the weak interaction, parity violation in chiral molecules has been considered as a possible origin of the biohomochirality. It was predicted in 1974 but has never been observed so far. Parity violation should lead to a very tiny frequency difference in the rovibrational spectra of the enantiomers of a chiral molecule. We have proposed to observe this predicted frequency difference using the two photon Ramsey fringes technique on a supersonic beam. Promising candidates for this experiment are chiral oxorhenium complexes, which present a large effect, can be synthesized in large quantity and enantiopure form, and can be seeded in a molecular beam. As a first step towards our objective, a detailed spectroscopic study of methyltrioxorhenium (MTO) has been undertaken. It is an ideal test molecule as the achiral parent molecule of chiral candidates for the parity violation experiment. For the 187Re MTO isotopologue, a combined analysis of Fourier transform microwave and infrared spectra as well as ultra-high resolution CO2 laser absorption spectra enabled the assignment of 28 rotational lines and 71 rovibrational lines, some of them with a resolved hyperfine structure. A set of spectroscopic parameters in the ground and first excited state, including hyperfine structure constants, was obtained for the antisymmetric Re=O stretching mode of this molecule. This result validates the experimental approach to be followed once a chiral derivative of MTO will be synthesized, and shows the benefit of the combination of several spectroscopic techniques in different spectral regions, with different set-ups and resolutions. First high resolution spectra of jet-cooled MTO, obtained on the set-up being developed for the observation of molecular parity violation, are shown, which constitutes a major step towards the targeted objective.Comment: 20 pages, 6 figure