Curl condition for a four-state Born-Oppenheimer system employing the Mathieu equation

When a group of four states forms a subspace of the Hilbert space, i.e., appears to be strongly coupled with each other but very weakly interacts with all other states of the entire space, it is possible to express the nonadiabatic coupling (NAC) elements either in terms of s or in terms of electronic basis function angles, namely, mixing angles presumably representing the same sub-Hilbert space. We demonstrate that those explicit forms of the NAC terms satisfy the curl conditions--the necessary requirements to ensure the adiabatic-diabatic transformation in order to remove the NAC terms (could be often singular also at specific point(s) or along a seam in the configuration space) in the adiabatic representation of nuclear SE and to obtain the diabatic one with smooth functional form of coupling terms among the electronic states. In order to formulate extended Born-Oppenheimer (EBO) equations [J. Chem. Phys. 2006, 124, 074101] for a group of four states, we show that there should exist a coordinate independent ratio of the gradients for each pair of ADT/mixing angles leading to zero curls and, thereafter, provide a brief discussion on its analytical validity. As a numerical justification, we consider the first four eigenfunctions of the Mathieu equation to demonstrate the interesting features of nonadiabatic coupling (NAC) elements, namely, the validity of curl conditions and the nature of curl equations around CIs.     

Sustainable Synthesis of α-Hydroxycarboxylic Acids by Manganese Catalyzed Acceptorless Dehydrogenative Coupling of Ethylene Glycol and Primary Alcohols**

Herein, we report a straightforward synthesis of valuable α-hydroxycarboxylic acid molecules via an acceptorless dehydrogenative coupling of ethylene glycol and primary alcohols. A bench-stable manganese complex catalyzed the reaction, which is scalable, with the product being isolated with high yields and selectivities under mild conditions. The protocol is environmentally benign, producing water and hydrogen gas as the only byproducts. Methanol can also be used as a C1 source for producing the platform molecule lactic acid, with a high turnover of >10⁴. The methodology was also used to functionalize alcohols derived from natural products and fatty acids. Furthermore, it was applied for synthesizing α-amino acid, α-thiocarboxylic acid, and several drugs and bioactive molecules, including endogenous metabolites, Danshensu, Enalapril, Lisinopril, and Rosmarinic acid. Preliminary mechanistic studies were performed to shed light on the mechanism involved in the reaction.     

Multifunctional nanostructures based on inorganic nanoparticles and oligothiophenes and their exploitation for cellular studies

The combination of materials that possess different properties (such as, for instance, fluorescence and magnetism) into one single object of nanoscale size represents an attractive challenge for biotechnology, especially for their potential relevance in biomedical applications. We report here the preparation of novel bifunctional conjugates based on the linkage of inorganic nanoparticles to organic oligothiophene fluorophores (OTFs). In comparison to the organic dyes commonly used in bioimaging and more similarly to colloidal quantum dots, OTFs have broad optical absorption spectra, and therefore OTF fluorophores emitting at different colors can be excited with a single excitation source, allowing for easier multiplexing analysis. In this work we show the preparation of OTF-nanoparticle conjugates based on gold and iron oxide nanoparticles and their characterization using different techniques such as gel electrophoresis, photoluminescence spectroscopy, dynamic light scattering, and so on. In addition, by performing an in vitro study on human tumor cells we show that OTF-nanoparticle conjugates emitting at different colors can be used for multiplexing detection. Also, in the case of iron oxide-OTF conjugates, once uptaken by the cells, we show that they preserve both their fluorescent and their magnetic properties.     

Twist‐dependent stacking energy of base‐pair steps in B‐DNA geometry: A density functional theory approach

Stacking energy of all the 10 unique DNA base‐pair steps (bp step) are calculated using density functional theory within the ultrasoft pseudopotential plane wave method and local density approximation for the exchange‐correlation functional. We have studied the dependence of stacking energy on twist angle, an aspect found difficult to explain using classical theory. We have found that the twist angle for different bp steps at stacking energy minimum matches extremely well with the values of average twist obtained from B‐DNA crystal structure data. This indicates that the use of a proper quantum chemical method to calculate the π‐π electronic interactions may explain stacking energy without incorporating hydrophobic interaction through solvent or effect of backbone through pseudobond. From the twist angle‐dependent stacking energy profile, we have also generated the probability distributions of twist for all the bp steps and calculated the variance of the distribution. Our calculated variances show similar trend to that of the experimental data for which sufficient numbers of data are available. The TA, AT, and CG doublets show large variances among the 10 possible bp steps, indicating their maximum flexibility. This might be the case of unusual deformation observed at the TATA‐box while binding to TBP protein. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

[1+1+1] Cyclotrimerization for the Synthesis of Cyclopropanes

The synthesis of small rings by functionalization of C(sp³)?H bonds remains a great challenge. We report for the first time a copper‐catalyzed [1+1+1] cyclotrimerization of acetophenone derivatives under mild reaction conditions. The reaction has a broad scope for the stereoselective synthesis of cyclopropanes by trimerization of acetophenone. The developed transformation is based on an extraordinary copper‐catalyzed cascade process that allows saturated carbocycles to be obtained for the first time by cyclotrimerization through functionalization of C(sp³)?H bonds. The cascade of sixfold C(sp³)?H bond functionalization allows the synthesis of cyclopropanes in a highly stereoselective approach.     

Cobalt(II)-(dpyo)-dicarboxylate networks: unique H-bonded assembly and rare bridging mode of dpyo in one of them [dpyo = 4,4'-dipyridyl N,N'-dioxide

Polymeric networks, {[Co(dpyo)(ox)]}(n) (1), {[Co(dpyo)(fum)(H(2)O)(2)]}(n) (1) and {[Co(dpyo)(tp)(H(2)O)(2)] x [Co(H(2)O)(6)] x (tp) x (H(2)O)}(n) (3) [ox = oxalate dianion, fum = fumarate dianion, tp = terephthalate dianion and dpyo = 4,4'-dipyridyl N,N'-dioxide] have been synthesized and characterized by single crystal X-ray diffraction analyses. The structural determination reveals 1 and 2 are covalent bonded 2D networks of 4,4 topology and of these, complex 2 undergoes a H-bonding scheme resulting in a 3D supramolecular architecture. Complex 3 is a 1D coordination polymer built up by almost collinear hexacoordinated Co(ii), doubly bridged by a tp carboxylate group and a dpyo oxygen, which in combination with lattice [Co(H(2)O)(6)](2+), tp and water molecules shows an unprecedented 3D supramolecular network through H-bonding. In the polymer the dpyo shows novel mu-4,4 bridging mode towards the cobalt ion. Low temperature magnetic interaction reveals antiferromagnetic coupling in all of the complexes.     

Dipyridyl bridged coordination polymers of Cu(II): Synthesis,crystal structure and magnetic study

Two coordination polymers, [Cu(bpp)(H₂O)₂(ClO₄)₂]_n (1) and {[Cu(bpds)₂(ClO₄)₂] · 1.5(H₂O)}_n (2) [bpp, 1,3-bis(4-pyridyl)propane and bpds, 4,4′-bipyridyl disulfide] have been synthesized and characterized by X-ray single crystal diffraction study and magnetic measurement. Both the coordination polymers display 1D chains with perchlorate anions acting as pendant ligands. In 1 undulated polymers are built by Cu(H₂O)₂(ClO₄)₂ units connected by single bpp and in complex 2 Cu(ClO₄)₂ fragments are linked by pairs of bpds ligands to form a double-stranded chain. The crystal packing evidences polymers of 1 involved in weak H-bonding interactions leading to a 3D supramolecular network. Magnetic study reveals weak antiferromagnetic interactions in both complexes.     

Rational Landen transformations on

The Landen transformation preserves the value of an elliptic integral, and its iteration produces the classical arithmetic-geometric mean AGM. We present analogous transformations for rational functions integrated over the whole real line.