Flat Information Geometries in Black Hole Thermodynamics

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein–Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.Supported by VR.     

Functional calculus for non-commuting operators with real spectra via an iterated Cauchy formula

We define a smooth functional calculus for a non-commuting tuple of (unbounded) operators A_j on a Banach space with real spectra and resolvents with temperate growth, by means of an iterated Cauchy formula. The construction is also extended to tuples of more general operators allowing smooth functional calculii. We also discuss the relation to the case with commuting operators.     

QED interconnection effects on W momentum distributions at LEP 2

The process ${? e}^{+}{? e}^{-}?ghtarrow {? W}^{+}{? W}^{-}?ghtarrow {? f}_{1}{?erline {? f}}_{2}{? f}_{3}{?erline {? f}}_{4}$ contains charges in the initial, intermediate and final stages. This gives a rich selection of possible QED interconnection effects. Coulomb interaction is the simplest of these, and can thus be used to explore consequences. We study a number of experimental observables, with emphasis on those related to the W momentum distribution. Second-order Coulomb effects are shown to be practically negligible. The limited LEP 2 statistics will not allow detailed tests, so any theory uncertainty will be reflected in the systematic error on the W mass. Currently the uncertainty from this source may be as high as 20 MeV.     

Relativistic atomic natural orbital type basis sets for the alkaline and alkaline-earth atoms applied to the ground-state potentials for the corresponding dimers

New basis sets of the atomic natural orbital (ANO) type have been developed for the atoms Li–Fr and Be–Ra. The ANOs have been obtained from the average density matrix of the ground states and the lowest excited states of the atom, the positive ion, and the dimer at its equilibirium geometry. Scalar realtivisitc effects are included through the use of a Douglas–Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of the ground-state potentials for the dimers. Computed bond energies are accurate to within 0.05 eV for the alkaline dimers and 0.02 eV for the alkaline-earth dimers (except for Be₂).Acknowledgments.ensp;B.O.R. would like to express his gratitude to Prof. Jacopo Tomasi for all the inspiration that his scientific work has given him through the years and continues to do in particular through the work on solvent effects on molecular properties. This work has been supported by a grant from the Swedish Science Research Council, VR.Contribution to the Jacopo Tomasi Honorary Issue     

Ab initio calculations of vibronic activity in phosphorescence microwave double resonance spectra of p-dichlorobenzene

The phosphorescence spectrum of p-dichlorobenzene has been calculated using multiconfiguration self-consistent-field wave functions and the quadratic response technique. Attention has been paid to the intensity distribution of the singlet–triplet (³B_1u¹A_g) transition through a number of vibronic subbands. The second order spin–orbit coupling (SOC) contribution to the spin splitting of the ³B_1u (^3*) state is found to be almost negligible, and the calculations therefore provide a good estimate for the zero-field splitting (ZFS) parameters based only on the electron spin–spin coupling expectation values. Nuclear quadrupole resonance constants for the different Cl isotopes are also calculated to accomplish the ZFS assignment. The electric dipole activity of the spin sublevels in the triplet–singlet transitions to the ground-state vibrational levels is estimated by calculations of derivatives using distorted geometries which are shifted from the equilibrium position along different vibrational modes. A vibrational analysis of the phosphorescence spectrum, based on the SOC-induced mixing of the singlet and triplet states calculated along different vibrational modes, provides reasonable agreement with experimental data.Acknowledgment O. R.-P. would like to thank the European MOLPROP network for support. The authors thank Alexander Baev for fruitful discussions. This work was supported by the Swedish Royal Academy of Science (KVA).     

Molecular orbital interpretation of X-ray emission spectra of ClCN and ONCl

Ab initio as well as semi-empirical SCF MO calculations are presented for ClCN and ONCl. The relative intensities for Cl Kβ emission in the two molecules were calculated. The calculated spectra from the ab initio wavefunctions are in excellent agreement with experiments.     

Synthesis and Photophysical and Electrochemical Study of Tyrosine Covalently Linked to High‐Valent Copper(III) and Manganese(IV) Complexes

As bio‐inspired chemical model of the oxygen‐evolving complex (OEC) in photosystem II, a new tyrosine‐modified corrole ligand 3 and its high‐valent copper and manganese complexes 3a and 3b were synthesized and characterized. The copper complexes 1a and 2a of corrole 1 and 2 were also prepared for comparison. The emission property indicates that the emission of ligands 2 and 3 is located at 670 nm, but no emission is observed for their metal complexes due to its suppression by the metal center. The electrochemical study shows that 3a might dimerize at the first two reversible oxidations, a behavior which was not observed in the case of 1a and 2a . The corrolato manganese(IV) complex 3b shows one reversible reduction and one quasireversible oxidation at ?0.17 and 0.77 V vs. Ag/Ag⁺, respectively.     

Enantiomers of polarized alkenes: chromatographic enrichment and thermal interconversion

(+)- and (?)-$\text{1}$ as well as (+)- and (?)-$\text{2}$ were partially separated by liquid chromatography on triacetylcellulose; racemizations resulted in the barriers (Table 2) to rotation via planarized transition states.     

Investigations of reactions involved in flameless atomic absorption procedures : Part IV. A theoretical study of factors influencing the determination of aluminium

High-temperature equilibrium calculations are used to study potential interferences in the determination of aluminium by flameless a.a.s. The conditions for the formation of interfering aluminium compounds like AlO(g), Al₂O(g), Al₂O₃(s), AlOH(g), AlH(g), AlHO₂(g), AlS(g), AlN(g), AlN(s) and AlCl(g) have been calculated. The influence of kinetic parameters on the equilibrium calculations for the reactions involving carbon—oxygen and carbon—sulphur has been established by varying the input amount of carbon. The results indicate that even in the nanomole range the presence of elements like H, O, N, Cl and S may cause severe interferences during the atomization step (2300–2900 K)