Ab initio Study of the Keto-Enol Equilibriumof Malonaldehyde

Summary.  The mechanism of the keto-enol tautomerism of malonaldehyde was studied by ab initio methods using 6-21G^** and 6-311G^** basis functions at the HF level. Two separate mechanisms were examined: through-space proton transfer in the ω-shaped form and through-space proton transfer in a sickle-shaped form obtained from the ω form by rotation. The transition state structure of the ω form is non-planar, whereas that of the sickle form is planar. The sickle form is connected with a 2^nd order saddle, indicating that there should exist a lower energy barrier, i.e. that the through-bond mechanism may be preferred. The calculated energy barriers of keto-enol tautomerism for the sickle form is twice as high as those for the omega form. Received January 18, 1999. Accepted (revised) August 4, 1999     

Löslichkeitsisotherme und Phasendiagramm des Systems Tm2O3-SeO2-H2O bei 100°C

Summary.  The selenites of thulium are used as starting substances to obtain the respective selenides which have valuable semiconductive properties. In analogy to the tellurites of the rare-earth elements, they can be applied as materials for the production of lasers. Bearing in mind the various recent usages of the lanthanides’ selenites (thulium in particular), the preparation and study of thulium selenites is considered to be a question of present interest. Therefore, a physico-chemical study of the system Tm₂O₃-SeO₂-H₂O at 100°C has been carried out.

Received December 19, 2000. Accepted (revised) April 10, 2001     

Unusual Reactions of (+)‐Car‐2‐ene and (+)‐Car‐3‐ene with Aldehydes on K10 Clay

The reactions of (+)‐car‐2‐ene ( 1 ) and (+)‐car‐3‐ene ( 2 ) with aldehydes in the presence of montmorillonite clay were studied for the first time (Schemes 3 and 5). The major products of these reactions are optically active, substituted hexahydroisobenzofurans, probably formed as a result of an attack of the protonated aldehyde at the cyclopropane ring. Quite unexpectedly, the products are cis‐configured at the ring‐fusion site; the fact was established by means of quantum‐chemical calculations and NMR data. It appeared that the behavior of the 2 : 3 mixture 1 / 2 in reactions with aldehydes in the presence of K10 clay differed substantially from the reactivities of the corresponding individual monoterpenes.     

The syn-oriented 2-OH provides a favorable proton transfer geometry in 1,2-diol monoester aminolysis: implications for the ribosome mechanism

A computational study of 1-formyl 1,2-ethanediol aminolysis predicts a stepwise mechanism involving syn-2-OH-assisted proton transfer. The syn-oriented 2-OH takes over the catalytic role of the external water or amine molecule previously observed in 2-deoxy ester aminolysis. It provides more favorable, that is, more linear, proton transfer geometry for the rate-limiting transition state resulting in an almost billion-fold rate acceleration of the overall reaction. These findings provide structural basis for explanation of the efficiency of the proton shuttling mechanism and imply double proton transfer catalysis by peptidyl tRNA A76 2'-OH as a possible catalytic strategy used by ribosome.     

Structure, stability, electronic and magnetic properties of Ni4 clusters containing impurity atoms

Using a gradient-corrected density functional method, we studied computationally how single impurity atoms affect the structure and the properties of a Ni4 cluster. H and O atoms coordinate at a Ni-Ni bond, inducing small changes to the structure of bare Ni4 which is essentially a tetrahedron. For a C impurity, we found three stable structures at a Ni4 cluster. In the most stable geometry, the carbon atom cleaves a Ni-Ni bond of Ni4, binding to all Ni atoms. Inclusion of the impurity atom leads to a partial oxidation of the metal atoms and, in the most stable structures, reduces the spin polarization of the cluster compared to bare Ni4. An H impurity interacts mainly with the Ni 4s orbitals, whereas the Ni 3d orbitals participate strongly in the bonding with O and C impurity atoms. For these impurity atoms, Ni 3d contributions dominate the character of the HOMO of the ligated cluster, in contrast to the HOMO of bare Ni4 where Ni 4s orbitals prevail. We also discuss a simple model which relates the effect of a H impurity on the magnetic state of metal clusters to the spin character (minority or majority) of the LUMO or HOMO of the bare metal cluster.     

High Frequency Resolvent Estimates for Perturbations by Large Long-range Magnetic Potentials and Applications to Dispersive Estimates

We prove optimal high-frequency resolvent estimates for self-adjoint operators of the form ${G=\left(i\nabla+b(x)\right)^2+V(x)}$ on ${L^2({\bf R}^n), n\ge 3}$ , where the magnetic potential b(x) and the electric potential V(x) are long-range and large. As an application, we prove dispersive estimates for the wave group ${{\rm e}^{it\sqrt{G}}}$ in the case n = 3 for potentials b(x), V(x) = O(|x|^?2-δ ) for ${|x|\gg 1}$ , where δ > 0.     

On the existence in a problem of the calculus of variations without convexity assumptions

Summary We obtain new sufficient conditions for the existence in a problem of the calculus of variations without convexity assumptions.     

Invariants of Isospectral Deformations and Spectral Rigidity

We introduce a notion of weak isospectrality for continuous deformations. Consider the Laplace–Beltrami operator on a compact Riemannian manifold with Robin boundary conditions. Given a Kronecker invariant torus Λ of the billiard ball map with a Diophantine vector of rotation we prove that certain integrals on Λ involving the function in the Robin boundary conditions remain constant under weak isospectral deformations. To this end we construct continuous families of quasimodes associated with Λ. We obtain also isospectral invariants of the Laplacian with a real-valued potential on a compact manifold for continuous deformations of the potential. These invariants are obtained from the first Birkhoff invariant of the microlocal monodromy operator associated to Λ. As an application we prove spectral rigidity of the Robin boundary conditions in the case of Liouville billiard tables of dimension two in the presence of a (?/2?)² group of symmetries.