Ionization of hydrogen and hydrogenic ions by antiprotons

Presented here is a description of the ionization of hydrogen and hydrogenic ions by antiproton-impact, based on very large scale numerical solutions of the time-dependent Schr\"odinger equation in three spatial dimensions and on analysis of the topology of the electronic eigenenergy surfaces in the plane of complex internuclear distance. Comparison is made with other theories and very recent measurements.Comment: RevTex document, 11 pages, 4 Postscript figures are available from the authors, in press Phys. Rev. Let

Calculation of the properties of the rotational bands of 155,157^{155,157}Gd

We reexamine the long-standing problem of the microscopic derivation of a particle-core coupling model. We base our research on the Klein-Kerman approach, as amended by D\"onau and Frauendorf. We describe the formalism to calculate energy spectra and transition strengths in some detail. We apply our formalism to the rotational nuclei $^{155,157}$Gd, where recent experimental data requires an explanation. We find no clear evidence of a need for Coriolis attenuation.Comment: 27 pages, 13 uuencoded postscript figures. Uses epsf.st

Magnetohydrodynamic equilibria of a cylindrical plasma with poloidal mass flow and arbitrary cross section shape

The equilibrium of a cylindrical plasma with purely poloidal mass flow and cross section of arbitrary shape is investigated within the framework of the ideal MHD theory. For the system under consideration it is shown that only incompressible flows are possible and, conscequently, the general two dimensional flow equilibrium equations reduce to a single second-order quasilinear partial differential equation for the poloidal magnetic flux function $\psi$, in which four profile functionals of $\psi$ appear. Apart from a singularity occuring when the modulus of Mach number associated with the Alfv\'en velocity for the poloidal magnetic field is unity, this equation is always elliptic and permits the construction of several classes of analytic solutions. Specific exact equlibria for a plasma confined within a perfectly conducting circular cylindrical boundary and having i) a flat current density and ii) a peaked current density are obtained and studied.Comment: Accepted to Plasma Physics & Controlled Fusion, 14 pages, revte

Predictive Models for the Free Energy of Hydrogen Bonded Complexes with Single and Cooperative Hydrogen Bonds

© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, WeinheimIn this work, we report QSPR modeling of the free energy ΔG of 1 : 1 hydrogen bond complexes of different H-bond acceptors and donors. The modeling was performed on a large and structurally diverse set of 3373 complexes featuring a single hydrogen bond, for which ΔG was measured at 298 K in CCl4. The models were prepared using Support Vector Machine and Multiple Linear Regression, with ISIDA fragment descriptors. The marked atoms strategy was applied at fragmentation stage, in order to capture the location of H-bond donor and acceptor centers. Different strategies of model validation have been suggested, including the targeted omission of individual H-bond acceptors and donors from the training set, in order to check whether the predictive ability of the model is not limited to the interpolation of H-bond strength between two already encountered partners. Successfully cross-validating individual models were combined into a consensus model, and challenged to predict external test sets of 629 and 12 complexes, in which donor and acceptor formed single and cooperative H-bonds, respectively. In all cases, SVM models outperform MLR. The SVM consensus model performs well both in 3-fold cross-validation (RMSE=1.50 kJ/mol), and on the external test sets containing complexes with single (RMSE=3.20 kJ/mol) and cooperative H-bonds (RMSE=1.63 kJ/mol)

Projective Hilbert space structures at exceptional points

A non-Hermitian complex symmetric 2x2 matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are Puiseux-expanded in terms of the root vectors at the EP. It is shown that the apparent contradiction between the two incompatible normalization conditions with finite and singular behavior in the EP-limit can be resolved by projectively extending the original Hilbert space. The complementary normalization conditions correspond then to two different affine charts of this enlarged projective Hilbert space. Geometric phase and phase jump behavior are analyzed and the usefulness of the phase rigidity as measure for the distance to EP configurations is demonstrated. Finally, EP-related aspects of PT-symmetrically extended Quantum Mechanics are discussed and a conjecture concerning the quantum brachistochrone problem is formulated.Comment: 20 pages; discussion extended, refs added; bug correcte

Non-Hermitian matrix description of the PT symmetric anharmonic oscillators

Schroedinger equation H \psi=E \psi with PT - symmetric differential operator H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at a>0. The proof of this non-variational construction is given. Our Taylor series form of \psi complements and completes the recent terminating solutions as obtained for certain couplings \delta at the less common negative a.Comment: 18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appea

Predictive Models for Halogen-bond Basicity of Binding Sites of Polyfunctional Molecules

© 2016 Wiley-VCH Verlag GmbH & Co. KGaA.Halogen bonding (XB) strength assesses the ability of an electron-enriched group to be involved in complexes with polarizable electrophilic halogenated or diatomic halogen molecules. Here, we report QSPR models of XB of particular relevance for an efficient screening of large sets of compounds. The basicity is described by pKBI2, the decimal logarithm of the experimental 1 : 1 (B :I2) complexation constant K of organic compounds (B) with diiodine (I2) as a reference halogen-bond donor in alkanes at 298K. Modeling involved ISIDA fragment descriptors, using SVM and MLR methods on a set of 598 organic compounds. Developed models were then challenged to make predictions for an external test set of 11 polyfunctional compounds for which unambiguous assignment of the measured effective complexation constant to specific groups out of the putative acceptor sites is not granted. At this stage, developed models were used to predict pKBI2 of all putative acceptor sites, followed by an estimation of the predicted effective complexation constant using the ChemEqui program. The best consensus models perform well both in cross-validation (root mean squared error RMSE=0.39-0.47logKBI2 units) and external predictions (RMSE=0.49). The SVM models are implemented on our website (http://infochim.u-strasbg.fr/webserv/VSEngine.html) together with the estimation of their applicability domain and an automatic detection of potential halogen-bond acceptor atoms

Adiabatic theory of Wannier threshold laws and ionization cross sections

The Wannier threshold law for three-particle fragmentation is reviewed. By integrating the Schroedinger equation along a path where the reaction coordinate R is complex, anharmonic corrections to the simple power law are obtained. These corrections are found to be non-analytic in the energy E, in contrast to the expected analytic dependence upon E

From Heisenberg matrix mechanics to EBK quantization: theory and first applications

Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there are, nevertheless, a number of previously unexploited aspects of this relationship that bear on the quantum-classical correspondence. In particular, we emphasize a quantum variational principle that implies the classical variational principle for invariant tori. We also expose the more indirect connection between commutation relations and quantization of action variables. With the help of several standard models with one or two degrees of freedom, we then illustrate how the methods of Heisenberg matrix mechanics described in this paper may be used to obtain quantum solutions with a modest increase in effort compared to semiclassical calculations. We also describe and apply a method for obtaining leading quantum corrections to EBK results. Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.