Selfadjointness of Integral and Matrix Operators

Criteria for selfadjointness of integral operators, includingmatrix operators, based on our earlier domination results areestablished. The range of applicability is elucidated by carefullychosen examples, not covered by previously known criteria.     

Equations of motion from field equations and a gauge-invariant variational principle for the motion of charged particles

New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is proposed. It differs from the standard, gauge-dependent, first-order Lagrangian by boundary terms only. A new method of deriving equations of motion from field equations is developed. When applied to classical electrodynamics, this method enables us to obtain unambiguously the above, second-order Lagrangian from the general energy-momentum conservation principle.     

On unstable and unoptimal prediction

We consider the notion of prediction functions (or predictors) studied before in the context of randomness and stochasticity by Ko, and later by Ambos‐Spies and others. Predictor is a total computable function which tries to predict bits of some infinite binary sequence. The prediction error is defined as the limit of the number of incorrect answers divided by the number of answers given so far. We discuss indefiniteness of prediction errors for weak 1‐generics and show that this phenomenon affects certain c.e. sequences as well. On the other hand, a notion of optimal predictor is considered. It is shown that there is a sequence for which increasingly better predictors exist but for which no predictor is optimal.     

On the fundamental theorem of algebra for polynomial equations over real composition algebras

A topological proof is given that real compositions algebras of finite dimension greater than one are algebraically closed under polynomial equations with a tame tail.     

Probing the Origin of Adaptive Aromaticity in 16-Valence-Electron Metallapentalenes

Species with adaptive aromaticity are aromatic in the ground and lowest-lying triplet excited states and they have normally intermediate singlet-triplet gaps. Few examples of compounds with adaptive aromaticity are known to date, including 16-valence-electron (16e) metallapentalenes. A sweeping search could be conducted to discover new members of this group, but efficient designs with an explicit strategy would facilitate the quest for new members of this elusive family. Density functional theory calculations and aromaticity evaluations have been performed to reveal the nature of triplet-state aromaticity in 16e metallapentalenes. Our results show that coordination of strong σ- or π-donor ligands helps achieving adaptive aromaticity of 16e metallapentalenes by means of a spin delocalization mechanism. These results have important implications for understanding the unusual properties of the organometallic adaptive aromatics, leading the way to efficient design of new compounds with tunable singlet-triplet gaps.     

New Cyclic Dimers of Cholic Acid

Two new cyclic dimers of cholic acid were obtained in the reaction of 3-O-acetyl methyl cholate with oxalyl chloride. The oxalates bound the cholate subunits side-to-side as a result of acylation of 7 and 12 OH groups in the substrate. The selective deprotection of hydroxy groups at C-3 and C-24 proved to be rather difficult and led to various products depending on the reaction conditions.     

Simultaneous quantification of Echinacea species, Flos Lonicerae, Radix Scutellaria and Fructus Forsythiae combinations by rapid resolution liquid chromatography

Echinacea angustifolia and E. purpurea are commonly used in North America for their anti-bacterial effects. Flos Lonicerae, Radix Scutellaria and Fructus Forsythiae are traditional Chinese medicinal herbs commonly used for the treatment of complaints such as pneumonia, acute upper respiratory tract infection, and acute bronchitis. A reproducible, simple, and reliable rapid resolution liquid chromatographic (RRLC) method has been developed to analyze extracts of products formulated containing E. angustifolia, E. purpurea, Flos Lonicerae, Radix Scutellariae and Fructus Forsythiae simultaneously in one run in less than 6 minutes. The method uses a C18-HST column, a mobile phase consisting of 0.1% aqueous phosphoric acid solution and acetonitrile, and UV detection at 327 nm and 229 nm. A stability test was performed that revealed that chlorogenic acid is more stable in acidic pH, and hence it is best to keep the extract of E. augustifolia, E. purpurea, Flos Lonicerae, Radix Scutellariae and Fructus Forsythiae in mild acidic conditions at approximately pH 5.     

Can we trust docking results? Evaluation of seven commonly used programs on PDBbind database

Docking is one of the most commonly used techniques in drug design. It is used for both identifying correct poses of a ligand in the binding site of a protein as well as for the estimation of the strength of protein–ligand interaction. Because millions of compounds must be screened, before a suitable target for biological testing can be identified, all calculations should be done in a reasonable time frame. Thus, all programs currently in use exploit empirically based algorithms, avoiding systematic search of the conformational space. Similarly, the scoring is done using simple equations, which makes it possible to speed up the entire process. Therefore, docking results have to be verified by subsequent in vitro studies. The purpose of our work was to evaluate seven popular docking programs (Surflex, LigandFit, Glide, GOLD, FlexX, eHiTS, and AutoDock) on the extensive dataset composed of 1300 protein–ligands complexes from PDBbind 2007 database, where experimentally measured binding affinity values were also available. We compared independently the ability of proper posing [according to Root mean square deviation (or Root mean square distance) of predicted conformations versus the corresponding native one] and scoring (by calculating the correlation between docking score and ligand binding strength). To our knowledge, it is the first large‐scale docking evaluation that covers both aspects of docking programs, that is, predicting ligand conformation and calculating the strength of its binding. More than 1000 protein–ligand pairs cover a wide range of different protein families and inhibitor classes. Our results clearly showed that the ligand binding conformation could be identified in most cases by using the existing software, yet we still observed the lack of universal scoring function for all types of molecules and protein families. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Modeling the electronic structures of the ground and excited states of the ytterbium atom and the ytterbium dimer: A modern quantum chemistry perspective

We present a comprehensive theoretical study of the electronic structures of the Yb atom and the Yb₂ molecule, respectively, focusing on their ground and lowest-lying electronically excited states. Our study includes various state-of-the-art quantum chemistry methods such as CCSD, CCSD(T), CASPT2 (including spin-orbit coupling), and EOM-CCSD as well as some recently developed pCCD-based approaches and their extensions to target excited states. Specifically, we scan the lowest-lying potential energy surfaces of the Yb₂ dimer and provide a reliable benchmark set of spectroscopic parameters including optimal bond lengths, vibrational frequencies, potential energy depths, and adiabatic excitation energies. Our in-depth analysis unravels the complex nature of the electronic spectrum of Yb₂, which is difficult to model accurately by any conventional quantum chemistry method. Finally, we scrutinize the bi-excited character of the first excited state and its evolution along the potential energy surface.