An attempt on the calculation of relativistic potential energy curves: Noble gas difluorides

Total energy SCF calculations were performed for noble gas difluorides in a relativistic procedure and compared with analogous non-relativistic calculations. The discrete variational method with numerical basis functions was used. Rather smooth potential energy curves could be obtained. The theoretical Kr-F and Xe-F bond distances were calculated to be 3.5 a.u. and 3.6 a.u. which should be compared with the experimental values of 3.54 a.u. and 3.7 a.u. Although the dissociation energies are off by a factor of about five it was found that ArF₂ may be a stable molecule. Theoretical ionization energies for the outer levels reproduce the experimental values for KrF₂ and XeF₂ to within 2 eV.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

Triangulations and moduli spaces of Riemann surfaces with group actions

Summary We study that subset of the moduli space of stable genusg,g>1, Riemann surfaces which consists of such stable Riemann surfaces on which a given finite groupF acts. We show first that this subset is compact. It turns out that, for general finite groupsF, the above subset is not connected. We show, however, that for ℤ₂ actions this subsetis connected. Finally, we show that even in the moduli space ofsmooth genusg Riemann surfaces, the subset of those Riemann surfaces on which ℤ₂ actsis connected. In view of deliberations of Klein ([8]), this was somewhat surprising. These results are based on new coordinates for moduli spaces. These coordinates are obtained by certainregular triangulations of Riemann surfaces. These triangulations play an important role also elsewhere, for instance in approximating eigenfunctions of the Laplace operator numerically. This work has been supported by the European Communities Science Plan Project No SCI^*-CT91 (TSTS) “Computational Methods in the Theory of Riemann Surfaces and Algebraic Curves,” by Academy of Finland and by the Swiss National Science Foundation Grant 20-34099.92. We thank M. C. Petrus for providing excellent motivation for this work. This article was processed by the author using the LATEX style filecljourl from Springer-Verlag.     

Zur Kenntnis der Chemie der Metallcarbonyle und der Cyanokomplexe in flüssigem Ammoniak. XXXII. Über die Reaktionen von η5-C5H5Mo(CO)3CH3 und η5-C5H5Fe(CO)2CH3 mit flüssigem Ammoniak

The Chemistry of Metal Carbonyls and Cyano Complexes in Liquid Ammonia. XXXII. On the Reaction of η⁵-C₅H₅Mo(CO)₃CH₃ and η⁵-C₅H₅Fe(CO)₂CH₃ with Liquid Ammonia η⁵-C₅H₅Mo(CO)₃CH₃ reacts with liquid NH₃ to give η⁵-C₅H₅Mo(CO)₂(NH₃)H and acetamide: In contrast, η⁵-C₅H₅Fe(CO)₂CH₃ undergoes a carbonyl insertion to give the acetyl complex η⁵-C₅H₅Fe(CO)(NH₃)COCH₃: The NH₃ ligand in η⁵-C₅H₅Fe(CO)(NH₃)COCH₃ can be substituted by pyridine.     

Calculation of binary magnetic properties and potential energy curve in xenon dimer: second virial coefficient of (129)Xe nuclear shielding

Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order M?ller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.     

Polymerization of methyl methacrylate in the presence of iron(II) complex with tetradentate nitrogen ligands under conditions of atom transfer radical polymerization

Four tetradentate nitrogen ligands, viz. dichloro{[N,N^′-diphenyl-N,N^′-di(quinoline-2-methyl)]-1,2-ethylene diamine} (1), {[N,N^′-dioctyl-N,N^′-di(quinoline-2-methyl)]-1,2-ethylene diamine} (2), {[N,N^′-dibenzyl-N,N^′-di(quinoline-2-methyl)]-1,2-ethylene diamine} (3), and (1R,2R)-(−)-N,N^′-di(quinoline-2-methyl) di-iminocyclohexane (4), were investigated as novel complexing ligands in iron-mediated atom transfer radical polymerization (ATRP) of methyl methacrylate where ethyl-2-bromoisobutyrate was the initiator in o-xylene at 90 °C. With ligands 1 and 2 the experimental molecular weights increased gradually with monomer conversion. High to moderate conversions (87%, 43%) were obtained in relatively short times (90 min for 1 and 30 min for 2), which indicates an efficient catalyst system, but after these times a dramatic increase in viscosity of the polymerization medium led to loss of control. It is noteworthy that polymerization proceeded in a controlled manner with ligand 1, which has two rather bulky substituents on the N-atom. Such bulky ligands did not work for a copper-based system, where they led to excessive terminations or other side reactions. When the bulkiness of the substituents was significantly increased, as in ligand 3, a decrease in polymerization rate and loss of control occurred. Ligand 4 was less efficient than the other ligands, probably because the ethylene bridge was replaced by cyclohexane bridge.     

Electronic structure calculations of small Al n (n=2–8) clusters

The electronic states of small Al _n (n=2–8) clusters have been calculated with a relativistic ab-initio MO-LCAO Dirac-Fock-Slater method using numerical atomic DFS wave-functions. The excitation energies were obtained from a ground state calculation of neutral clusters, and in addition from negative clusters charged by half an electron in order to account for part of the relaxation. These energies are compared with experimental photo-electron spectra.     

The remote effect of vicinal large groups on the anomeric equilibrium: 2-methoxy-cis- and -trans-5,6-dimethyltetrahydropyrans

The anomeric equilibrium of 2-methoxy-trans-5,6-dimethyltetrahydropyran was found to have an enhanced fraction of axial methoxyl compared to 2-methoxy-4- or 6-methyltetrahydropyran. The 2-methoxy-cis-5,6-dimethyltetrahydropyran did not. The enhanced anomeric effect is attributed to a steric repulsion between the trans vicinal Me groups. A similar effect is postulated for methyl glucoside and glucose pentaacetate.     

The vane method and kinetic modeling: shear rheology of nanofibrillated cellulose suspensions

We conduct rheological characterization of nanofibrillated cellulose (NFC) suspensions, a highly non-Newtonian complex fluid, at several concentrations. Special care is taken to cope with the prevalent problems of time scale issues, wall depletion and confinement effects. We do this by combining the wide-gap vane geometry, extremely long measurement times, and modeling. We take into account the wide-gap related stress heterogeneity by extending upon mainstream methods and apply a gap correction. Furthermore, we rationalize the experimental data through a simple viscous structural model. With these tools we find that, owing to the small size of the particles subjected to Brownian motion, the NFC suspensions exhibit a critical shear rate, where the flow curve experiences a turning point. This makes the steady state of these suspensions at low shear rates non-unique. To optimize various mixing and pumping applications, such history dependent tendency of NFC suspensions to shear band needs to be taken into account.     

On applicability of PCA,voxel-wise variance normalization and dimensionality assumptions for sliding temporal window sICA in resting-state fMRI

Subject-level resting-state fMRI (RS-fMRI) spatial independent component analysis (sICA) may provide new ways to analyze the data when performed in the sliding time window. However, whether principal component analysis (PCA) and voxel-wise variance normalization (VN) are applicable pre-processing procedures in the sliding-window context, as they are for regular sICA, has not been addressed so far. Also model order selection requires further studies concerning sliding-window sICA. In this paper we have addressed these concerns. First, we compared PCA-retained subspaces concerning overlapping parts of consecutive temporal windows to answer whether in-window PCA and VN can confound comparisons between sICA analyses in consecutive windows. Second, we compared the PCA subspaces between windowed and full data to assess expected comparability between windowed and full-data sICA results. Third, temporal evolution of dimensionality estimates in RS-fMRI data sets was monitored to identify potential challenges in model order selection in a sliding-window sICA context. Our results illustrate that in-window VN can be safely used, in-window PCA is applicable with most window widths and that comparisons between windowed and full data should not be performed from a subspace similarity point of view. In addition, our studies on dimensionality estimates demonstrated that there are sustained, periodic and very case-specific changes in signal-to-noise ratio within RS-fMRI data sets. Consequently, dimensionality estimation is needed for well-founded model order determination in the sliding-window case. The observed periodic changes correspond to a frequency band of ≤ 0.1 Hz, which is commonly associated with brain activity in RS-fMRI and become on average most pronounced at window widths of 80 and 60 time points (144 and 108 s, respectively). Wider windows provided only slightly better comparability between consecutive windows, and 60 time point or shorter windows also provided the best comparability with full-data results. Further studies are needed to determine the cause for dimensionality variations.