From an Icosahedron to a Plane: Flattening Dodecaiodo‐dodecaborate by Successive Stripping of Iodine

It has been shown by electrospray ionization–ion‐trap mass spectrometry that B₁₂I₁₂^2? converts to an intact B₁₂ cluster as a result of successive stripping of single iodine radicals or ions. Herein, the structure and stability of all intermediate B₁₂I_n^? species (n=11 to 1) determined by means of first‐principles calculations are reported. The initial predominant loss of an iodine radical occurs most probably via the triplet state of B₁₂I₁₂^2?, and the reaction path for loss of an iodide ion from the singlet state crosses that from the triplet state. Experimentally, the boron clusters resulting from B₁₂I₁₂^2? through loss of either iodide or iodine occur at the same excitation energy in the ion trap. It is shown that the icosahedral B₁₂ unit commonly observed in dodecaborate compounds is destabilized while losing iodine. The boron framework opens to nonicosahedral structures with five to seven iodine atoms left. The temperature of the ions has a considerable influence on the relative stability near the opening of the clusters. The most stable structures with five to seven iodine atoms are neither planar nor icosahedral.     

A Comparison of Two Variational Methods

A discussion is given of the relation between the maximum functionaltheorem and Schwinger's variational principle, and it is shownthat the bound given by Schwinger's principle is better thanor the same as that given by the maximum functional theorem.     

Further Gurtin-type Variational Principles for Linear Initial Value Problems

Following the variational principles for linear initial valueproblems associated with the wave and heat conduction equationsdiscussed by Gurtin and Leitmann and using time convolutionsit is shown that general variational principles exist for theseproblems with sources on the boundaries and within the regionunder consideration.     

Modified Locally One Dimensional Methods for Parabolic Partial Differential Equations in Two Space Variables

In this note we consider the locally one dimensional methodas discussed in Gourlay & Mitchell (1969, 1972) and indicatehow this scheme can be used to solve accurately a parabolicpartial differential equation in two space variables.     

Noncovalent Bifunctional Organocatalysts: Powerful Tools for Contiguous Quaternary‐Tertiary Stereogenic Carbon Formation,Scope, and Origin of Enantioselectivity

Relying on the assembly of commercially available catalyst building blocks, highly stereocontrolled quaternary carbon (all carbon substituted) formation has been achieved with unmatched substrate diversity. For example, the in situ assembly of a tricomponent catalyst system allows α‐branched aldehyde addition to nitroalkene or maleimide electrophiles (Michael products), while addition to an α‐iminoester affords Mannich reaction products. Very good yields are observed and for fifteen of the eighteen examples 96–99 % ee is observed. Using racemic α‐branched aldehydes, two contiguous (quaternary–tertiary) stereogenic centers can be formed in high diastereo‐ and enantiomeric excess (eight examples) via an efficient in situ dynamic kinetic resolution, solving a known shortcoming for maleimide electrophiles in particular. The method is of practical value, requiring only 1.2 equiv of the aldehyde, a 5.0 mol % loading of each catalyst component, for example, O‐tBu‐L ‐threonine (O‐tBu‐L ‐Thr), sulfamide, DMAP or O‐tBu‐L ‐Thr, KOH, and room temperature reactions. As a highlight, the first demonstration of ethylisovaleraldehyde ( 7 ) addition is disclosed, providing the most congested quaternary stereogenic carbon containing succinimide product ( 8 ) known to date. Finally, mechanistic insight, via DFT calculations, support a noncovalent assembly of the catalyst components into a bifunctional catalyst, correctly predict two levels of product stereoselectivity, and suggest the origin of the tricomponent catalyst system’s exceptionality: an alternative hydrogen bond motif for the donor‐acceptor pair than currently suggested for non‐assembled catalysts.