Accurate Prediction of Core Properties for Chiral Molecules using Pseudo Potentials

Pseudo potentials (PPs) constitute perhaps the most common way to treat relativity, often in a formally non-relativistic framework, and reduce the electronic structure to the chemically relevant part. The drawback is that orbitals obtained in this picture (called pseudo orbitals (POs)) show a reduced nodal structure and altered amplitude in the vicinity of the nucleus, when compared to the corresponding molecular orbitals (MOs). Thus expectation values of operators localized in the spatial core region that are calculated with POs, deviate significantly from the same expectation values calculated with all-electron (AE) MOs. This study describes the reconstruction of AE MOs from POs, with a focus on POs generated by energy consistent pseudo Hamiltonians. The method reintroduces the nodal structure into the POs, thus providing an inexpensive and easily implementable method that allows to use nonrelativistic, efficiently calculated POs for good estimates of expectation values of core-like properties. The discussion of the method proceeds in two parts: Firstly, the reconstruction scheme is developed for atomic cases. Secondly, the scheme is discussed in the context of MO reconstruction and successfully applied to numerous numerical examples. Starting from the equations of the state-averaged multi-configuration self- consistent field method, used for the generation of energy consistent pseudo potentials, the electronic spectrum of the many-electron Hamiltonian is linked to the spectrum of the effective one-electron Fock operator by means of various models systems. This relation and the Topp–Hopfield–Kramers theorem, are used to show the shape-consistency of energy-consistent POs for atomic systems. Shape-consistency describes POs that follow distinct AOs exactly outside a core-radius r_core . In the cases presented here, shape-consistency holds to a high degree and it follows that in atomic systems every PO has one distinct partner in the set of AOs. The overlap integral between these two orbitals is close to one, as it is determined mainly by the spatial orbital parts outside r_core . Expanding, e.g., a 5s PO in occupied AOs, the 5s AOs will have the highest contribution. The POs itself contains contributions from high-energy unoccupied AOs as well (e.g. 15s), which damp the nodal structure of the POs near the nucleus. Consequently, neglecting contributions from unoccupied orbitals in a projection of the POs reintroduces the nodal structure. This approach is not directly suitable for the reconstruction of MOs, as they often need to be expanded in a full set of AOs at each atomic center, including all unoccupied orbitals, to properly account for the electron density distribution in the molecule. However, it is shown that the occupied MOs are well described by occupied and low-energy unoccupied AOs only and a mapping of the POs onto a basis containing only these orbitals reconstructs the nodal structure of the MO. The approach uses only standard integrals available in most quantum chemistry programs. The computational cost of these integrals scales with N^2 , where N is the number of basis functions. The most time consuming step is a Gram-Schmidt orthogonalization, which scales in this implementation with MN^2 , M being the number of reconstructed orbitals. The reconstruction method is subsequently tested: Valence orbitals of atomic, closed-shell systems were reconstructed numerically exactly. The influence of numerical parameters is investigated using the molecule BaF . It is shown that the method is basis set dependent: One has to ensure that the PO basis can be expanded exactly in the basis of AOs. Violating this rule of thumb may degrade the quality of reconstructed orbitals. Additionally, the representation of MOs by a linear combination of occupied and unoccupied AOs is investigated. For the exemplary systems, the shells included in the fitting procedure of the PP were sufficient. Reconstruction of the alkaline earth monofluorides showed that periodic trends can be reconstructed as well. Scaling of hyperfine structure parameters with increasing atomic number is discussed. For hydrogenic atoms, the scaling should be linear, whereas small deviations from the linear behavior were observed for molecules. The scaling laws computed from reconstructed and reference orbitals were almost identical. In this context, the failure of commonly used relativistic enhancement factors beyond atomic number 100 is discussed. Applicability of the method is also tested on parity violating properties for which the main contribution is generated by the valence orbitals near the nucleus. Symmetry-independence of the method is shown by successful reconstruction of orbitals of the tetrahedral PbCl_4 and chiral NWHClF. The reliable reconstruction of chemical trends is shown with the help of the NWHClF derivatives NWHBrF and NWHFI. The study of chiral compounds as, e.g., NWHClF and its group 17 derivatives, which have been proposed as paradigm for the detection of parity-violation in chiral molecules, remains of great importance. Especially the direct determination of absolute configuration of chiral centers is still non-trivial. The author contributed to this field with a self-written molecular dynamics (MD) program to simulate Coulomb explosions and thus to provide an insight especially into the early explosion stages directly after an instantaneous multi-ionization of the molecule CHBrClF, comparable to experiments using the Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) technique. An algorithm for the determination of the investigated molecule’s absolute configuration from time-of-flight data and detection locations of molecular fragments is included in the program. The program was used to generate experiment-equivalent data which allowed for the first time the investigation of non-racemic mixtures by the analysis routines of the experiment. The MD program includes harmonic and anharmonic bond potentials. A charge-exchange model can model partial charges in early phases of the Coulomb explosion. Furthermore, Born–Oppenheimer MD simulations and statistical models are used to explain the relative abundance of products belonging to competing reaction channels, as obtained by photoion coincidence measurements. Additionally, qualitative statements about reaction branching ratios are made by comparing the partition functions of involved degrees of freedom. Analytic equations for partition functions of simple models are used to provide a simple formula allowing fast estimates of reaction branching ratios

Final-state QED Multipole Radiation in Antenna Parton Showers

We present a formalism for a fully coherent QED parton shower. The complete multipole structure of photonic radiation is incorporated in a single branching kernel. The regular on-shell 2 to 3 kinematic picture is kept intact by dividing the radiative phase space into sectors, allowing for a definition of the ordering variable that is similar to QCD antenna showers. A modified version of the Sudakov veto algorithm is discussed that increases performance at the cost of the introduction of weighted events. Due to the absence of a soft singularity, the formalism for photon splitting is very similar to the QCD analogon of gluon splitting. However, since no color structure is available to guide the selection of a spectator, a weighted selection procedure from all available spectators is introduced.Comment: 33 pages, 12 figures. Added subsection 4.3 and some comments and references per reviewer request. Version accepted by JHE

Clues for flavor from rare lepton and quark decays

Flavor symmetries successfully explain lepton and quark masses and mixings yet it is usually hard to distinguish different models that predict the same mixing angles. Further experimental input could be available, if the agents of flavor breaking are sufficiently low in mass and detectable or if new physics with non-trivial flavor charges is sufficiently low in mass and detectable. The recent hint for lepton-nonuniversality in the ratio of branching fractions $B \to K \mu \mu$ over $B \to K e e$, $R_K$, suggests the latter, at least for indirect detection via rare decays. We demonstrate the discriminating power of the rare decay data on flavor model building taking into account viable leptonic mixings and show how correlations with other observables exist in leptoquark models. We give expectations for branching ratios $B \to K \ell \ell^\prime, B_{(s)} \to \ell \ell^\prime$ and $\ell \to \ell^\prime \gamma$, and Higgs decays $h \to \ell \ell^\prime$.Comment: 23 pages plus references and appendices, 1 figure; v2: comment on mu to e conversion and references added, conclusions unchanged; v3: footnote 3 added, typos fixe

Baryon Number Violating Scalar Diquarks at the LHC

Baryon number violating (BNV) processes are heavily constrained by experiments searching for nucleon decay and neutron-antineutron oscillations. If the baryon number violation occurs via the third generation quarks, however, we may be able to avoid the nucleon stability constraints, thus making such BNV interactions accessible at the LHC. In this paper we study a specific class of BNV extensions of the standard model (SM) involving diquark and leptoquark scalars. After an introduction to these models we study one promising extension in detail, being interested in particles with mass of O(TeV). We calculate limits on the masses and couplings from neutron-antineutron oscillations and dineutron decay for couplings to first and third generation quarks. We explore the possible consequences of such a model on the matter-antimatter asymmetry. We shall see that for models which break the global baryon minus lepton number symmetry, (B-L), the most stringent constraints come from the need to preserve a matter-antimatter asymmetry. That is, the BNV interaction cannot be introduced if it would remove the matter-antimatter asymmetry independent of baryogenesis mechanism and temperature. Finally, we examine the phenomenology of such models at colliders such as the LHC.Comment: 10 pages, 9 figures. v2: references added, some typos corrected. v3: some small corrections to match published version, no change in conclusion

Is it the boundaries or disorder that dominates electron transport in semiconductor `billiards'?

Semiconductor billiards are often considered as ideal systems for studying dynamical chaos in the quantum mechanical limit. In the traditional picture, once the electron's mean free path, as determined by the mobility, becomes larger than the device, disorder is negligible and electron trajectories are shaped by specular reflection from the billiard walls alone. Experimental insight into the electron dynamics is normally obtained by magnetoconductance measurements. A number of recent experimental studies have shown these measurements to be largely independent of the billiards exact shape, and highly dependent on sample-to-sample variations in disorder. In this paper, we discuss these more recent findings within the full historical context of work on semiconductor billiards, and offer strong evidence that small-angle scattering at the sub-100 nm length-scale dominates transport in these devices, with important implications for the role these devices can play for experimental tests of ideas in quantum chaos.Comment: Submitted to Fortschritte der Physik for special issue on Quantum Physics with Non-Hermitian Operator