Hard-soft acid-base interactions of silylenes and germylenes

A detailed investigation of the electrophilic and nucleophilic character of singlet silylenes and germylenes, divalent compounds of silicon and germanium, respectively, substituted by first- and second-row elements is presented. In a first part, the Lewis acid properties of these compounds were studied through their complexation reaction with the Lewis bases NH3, PH3, and AsH3. The results indicate that this complexation is most favorable with the hardest base NH3, classifying these compounds as hard Lewis acids. This is confirmed by the linear correlation between the interaction energies and the value of the electrostatic potential, used as an approximation to the local hardness, near the empty p orbital of these compounds, indicating a charge-controlled interaction in the complex. Also the electrophilicity index, proposed by Parr et al., computed both at the global and the local level, correlates linearly with the complexation energies of the compounds with NH3. The Lewis base character of these silylenes has been investigated, through their interaction with the acids BH3 and AlH3. Also in this case, the electrostatic potential can be used to probe the reactivity of the compounds. It will finally be demonstrated that an increasing stability of the silylenes and germylenes is accompanied by an increase in their nucleophilicity and a decrease of the electrophilicity.     

The Mechanism of Biochemical NO-Sensing: Insights from Computational Chemistry

The binding of small gas molecules such as NO and CO plays a major role in the signaling routes of the human body. The sole NO-receptor in humans is soluble guanylyl cyclase (sGC) – a histidine-ligated heme protein, which, upon NO binding, activates a downstream signaling cascade. Impairment of NO-signaling is linked, among others, to cardiovascular and inflammatory diseases. In the present work, we use a combination of theoretical tools such as MD simulations, high-level quantum chemical calculations and hybrid QM/MM methods to address various aspects of NO binding and to elucidate the most likely reaction paths and the potential intermediates of the reaction. As a model system, the H-NOX protein from Shewanella oneidensis (So H-NOX) homologous to the NO-binding domain of sGC is used. The signaling route is predicted to involve NO binding to form a six-coordinate intermediate heme-NO complex, followed by relatively facile His decoordination yielding a five-coordinate adduct with NO on the distal side with possible isomerization to the proximal side through binding of a second NO and release of the first one. MD simulations show that the His sidechain can quite easily rotate outward into solvent, with this motion being accompanied in our simulations by shifts in helix positions that are consistent with this decoordination leading to significant conformational change in the protein.     

Paving Hessenberg varieties by affines

Regular nilpotent Hessenberg varieties form a family of subvarieties of the flag variety arising in the study of quantum cohomology, geometric representation theory, and numerical analysis. In this paper we construct a paving by affines of regular nilpotent Hessenberg varieties for all classical types, generalizing results of De Concini–Lusztig–Procesi and Kostant. This paving is in fact the intersection of a particular Bruhat decomposition with the Hessenberg variety. The nonempty cells of the paving and their dimensions are identified by combinatorial conditions on roots. We use the paving to prove these Hessenberg varieties have no odd-dimensional homology.      

Interaction of triols with formaldehyde and acetone: Experimental and theoretical study

Experimental and theoretical aspects of the condensation of glycerol and its homologs (1,2,3- and 1,2,4-butanetriols) with formaldehyde and acetone are studied under conditions of acid catalysis. Calculation of the thermodynamic parameters of the resulting products by the composite method CBS-QB3 shows that the six-membered heterocycles, the products of the interaction of triols with formaldehyde, are thermodynamically more stable than the five-membered acetals, while the reaction of the same triols with acetone is preferable for the formation of the five-membered acetals. This is due to the fact that the regioselectivity of the studied reactions is determined by the structural features and reactivity of the carbocations formed in a condensed medium during the course of the reaction. According to the theoretical data obtained experimentally, during the condensation of glycerol and 1,2,4-butanetriol with formaldehyde in the most stable form of the six-membered cyclic carbocation, intramolecular hydrogen bonding and anomeric stabilization due to the axially oriented hydroxyl group take place. As a result, cation 1b–1 is 1.2–1.6 kJ/mol more stable than its five-membered isomers ( 1a–1 and 1b–2 ). It leads to the predominant formation of 1,3-dioxane ( 3b ). However, upon condensation of butanetriol-1,2,3 with formaldehyde, the intermediate cation 4a–1 turns out to be significantly more stable than the other isomers due to the strong intramolecular hydrogen bond in the six-membered ring with the participation of the hydroxyl group of the substituent and the hydroxyl group of the cationic center, leading to the predominant formation of the dioxolane 6a .     

Molecular structure and internal rotation potential of perfluoro (2,4-dimethyl-3-oxa-2,4-diazapentane), (CF3)2N–O–N(CF3)2

Ab initio quantum chemical calculation were performed on R₂N–O–NR₂ type (R=H, F, CH₃ and CF₃) molecules, using the HF, B3LYP and MP2/6-31G* levels of theory. The equilibrium structures and the internal rotation potentials have been determined. Three stable conformers were found for R=H, F and CH₃ while only two in case of R=CF₃. The rotation potential energy curves do not change significantly upon fluorination. The calculations suggests that in the ED measurement of the title compound the NC and NO bond length might have been interchanged.     

Representation stability of the cohomology of Springer varieties and some combinatorial consequences

Journal of Algebraic Combinatorics - A sequence of $$S_n$$ -representations $$\{V_n\}$$ is said to be uniformly representation stable if the decomposition of $$V_n = \bigoplus _{\mu } c_{\mu ,n}...     

The nonmonotonic concentration dependence of the mean activity coefficient of electrolytes is a result of a balance between solvation and ion-ion correlations

We propose a simple model to explain the nonmonotonic concentration dependence of the mean activity coefficient of simple electrolytes without using any adjustable parameters. The primitive model of electrolytes is used to describe the interaction between ions computed by the adaptive grand canonical Monte Carlo method. For the dielectric constant of the electrolyte, we use experimental concentration dependent values. This is included through a solvation term in our treatment to describe the interaction between ions and water that changes as the dielectric constant changes with concentration. This term is computed by a Born-treatment fitted to experimental hydration energies. Our results for LiCl, NaCl, KCl, CsCl, NaBr, NaI, MgCl(2), CaCl(2), SrCl(2), and BaCl(2) demonstrate that the principal reason of the nonmonotonic behavior of the activity coefficient is a balance between the solvation and ion-ion correlation terms. This conclusion differs from previous studies that assumed that it is the balance of hard sphere repulsion and electrostatic attraction that produces the nonmonotonic behavior. Our results indicate that the earlier assumption that solvation can be taken into account by a larger, "solvated" ionic radius should be reconsidered. To explain second order effects (such as dependence on ionic size), we conclude that explicit water models are needed.     

Cyclodextrin knowledgebase a web-based service managing CD-ligand complexation data

Cyclodextrins are cyclic oligosaccharides that are able to form water-soluble inclusion complexes with small molecules. Because of their complexing ability, they are widely applied in food, pharmaceutical and chemical industries. In this paper we describe the development of a free web-service, Cyclodextrin KnowledgeBase: (http://www.cyclodextrin.net). The database contains four modules: the Publication, Interaction, Chirality and Analysis Modules. In the Publication Module, almost 50,000 publication details are collected that can be retrieved by text search. In the Interaction and Chirality Modules relevant literature data on cyclodextrin complexation and chiral recognition are collected that can be retrieved by both text and structural searches. Moreover, in the Analysis Module, the geometries of small molecule-cyclodextrin complexes can be predicted using molecular docking tools in order to explore the structures and interaction energies of the inclusion complexes. Complex geometry prediction is made possible by the built-in database of 95 cyclodextrin derivatives, where the 3D structures as well as the partial charges are calculated and stored for further utilization. The use of the database is demonstrated by several examples.     

Exponents for -stable ideals

Let be a simple algebraic group over the complex numbers containing a Borel subgroup . Given a -stable ideal in the nilradical of the Lie algebra of , we define natural numbers which we call ideal exponents. We then propose two conjectures where these exponents arise, proving these conjectures in types and some other types.

When , we recover the usual exponents of by Kostant (1959), and one of our conjectures reduces to a well-known factorization of the Poincaré polynomial of the Weyl group. The other conjecture reduces to a well-known result of Arnold-Brieskorn on the factorization of the characteristic polynomial of the corresponding Coxeter hyperplane arrangement.