Microwave-assisted organic synthesis: scale-up of palladium-catalyzed aminations using single-mode and multi-mode microwave equipment

Batch wise scale-up of Buchwald-Hartwig aminations under microwave irradiation has been investigated for the first time. Multi-mode (microSYNTH and MARS) (several vessels irradiated in parallel per batch) as well as single-mode (Discover) (one vessel irradiated per batch) platforms can be successfully used for this purpose with trifluoromethylbenzene (benzotrifluoride: BTF) as amination solvent. The obtained yields indicate a direct scalability in BTF for all the studied aminations. The Voyager equipment (based on a Discover platform) is the most convenient system since it allows an automatic continuous batch wise production without the necessity to manually load and unload reaction vessels.     

Corrélation électronique et effets de base dans l'étude de la liaison hydrogène: le dimère mixte ammoniac-eau

Résumé L'énergie de la liaison hydrogène N...H-O dans le dimère ammoniac — eau a été calculée par la méthode LCAO-MO, à l'aide d'une base minimale d'orbitales de Slater dont les exposants sont déterminés variationnellement dans les monomères isolés. Les orbitales moléculaires occupées et virtuelles ont été déterminées par un calcul SCF classique; la corrélation électronique a été introduite par un calcul de perturbation du second ordre utilisant différentes bases d'orbitales moléculaires équivalentes. L'énergie de liaison du dimère est de 7,66 kcal/mole à l'étape SCF et de 9,65 kcal/mole après correction du second ordre. Ce dernier résultat est donné par un jeu d'orbitales moléculaires équivalentes obtenues par projection des orbitales canoniques des monomères dans l'espace des orbitales du dimère. Les valeurs précédentes sont réduites à 3,96 kcal/mole à l'étape SCF et à 4,63 kcal/mole au second ordre, si l'on tient compte de l'élargissement de base provenant de la proximité des monomères dans le dimère.

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Electron correlation and basis effects in the theory of hydrogen bonds: The mixed dimer ammonia-water

The energy of the hydrogen bond N...H-O in the dimer (NH₃, H₂O) has been computed by the LCAO-MO method, using a minimal set of Slater-type orbitals optimized for the isolated monomers. The doubly occupied and virtual orbitals have been determined by the standard SCF technique, and electron correlation has been introduced by a complete second-order perturbation calculation, using different sets of equivalent MO's. The bonding energy is found to be equal to 7.66 kcal/mol at the SCF step and to 9.65 kcal/mol after second order corrections. The latter value is given by a set of equivalent MO's obtained by projecting the canonical MO's of the monomers into the space of the dimer MO's. The preceding values are reduced to 3.96 kcal/mol at the SCF step and to 4.63 kcal/mol at the second-order, if the basis extension arising from the vicinity of the two monomers inside the dimer is taken into account.

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Zusammenfassung Mit Hilfe der LCAO-MO-Methode wurde die Energie der N...H-O-Wasserstoffbrücke im Dimeren (NH₃, H₂O) berechnet. Es wurde dazu ein minimaler, für die isolierten Monomeren optimierter Basissatz von Slater-Orbitalen benutzt. Die doppelt besetzten und die virtuellen Orbitale sind mit Standard-SCF-Techniken bestimmt worden, die Elektronenkorrelation wurde durch eine Störungsrechnung zweiter Ordnung unter Benutzung von anderen SÄtzen Äquivalenter Orbitale eingeführt. Mit der SCF-Rechnung erhielt man eine Bindungsenergie von 7,66 kcal/mol und nach Berücksichtigung der Störung zweiter Ordnung von 9,65 kcal/mol. Der letztgenannte Wert wird aus einem Satz Äquivalenter Orbitale erhalten, die durch Projektion der kanonischen Orbitale der Monomeren in den Raum der MO's der Dimeren entstehen. Diese beiden Werte werden zu 3,96 kcal/mol im SCF-Schritt und zu 4,63 kcal/mol in der zweiten Ordnung reduziert, wenn die Basiserweiterung, die durch die AnnÄherung der beiden Monomeren im Dimeren zustande kommt, in Betracht gezogen wird.

     

NMR kinetic investigations of the photochemical and thermal reactions of a photochromic chromene

The photochromic behavior of 2,2-di(4-fluorophenyl)-6-methoxy-2H-1-chromene has been investigated by 19F NMR spectroscopy. Photocoloration under UV irradiation at low temperature led to the formation of three interconverting photoisomers including two merocyanines and an unprecedented allenyl-phenol isomer. Photobleaching with visible light, which was known to lead to reversion to the initial closed chromene, was shown to increase allenyl-phenol concentration. Thermal relaxation of the preirradiated system was also studied at various temperatures. In each case (UV and visible irradiations, thermal isomerization), the kinetics of each of the four species was monitored. Numerical analysis of concentration vs time profiles enabled us to unequivocally establish the global mechanism occurring in each of the experimental conditions and to interpret the specific reactivity of each photoisomer. It has been shown that, among the 12 possible isomerization processes, only some paths were active. For the first time, it has been possible to determine their corresponding thermal activation parameters and photochemical quantum yield ratios.     

Ultrashort self-similar periodic waves and similaritons in an inhomogeneous optical medium with an external source and modulated coefficients

Nonlinear Dynamics - In this paper, we use the similarity transformation to reduce the generalized higher-order nonlinear Schrödinger equation with space- and time-modulated coefficients...     

Carré d’unn-vecteur dans unE n

A _n being an-vector of a vectorial spaceE _n we calculate (A _n)² which is equal to 1 or −1.      

Almost automorphic solutions of semilinear evolution equations

We are concerned with the semilinear differential equation in a Banach space ,

where generates an exponentially stable -semigroup and is a function of the form . Under appropriate conditions on and , and using the Schauder fixed point theorem, we prove the existence of an almost automorphic mild solution to the above equation.

     

Produit d’inversions elliptiques ou hyperboliques

Let x and y be orthogonal coordinates of a point M (u = ax + iby or ax + ɛ by) of a plane where as x′ and y′ are orthogonal coordinates of a point M′(V = ax′ + iby′ or ax′ + ɛ by′) inverse of M in the elliptic hyperbolic inversion (k and k′ positive) designating the conjugate of v while i and ɛ are Clifford numbers such that i² = −1 and ɛ² = 1 (a and b are real). O is the origin of axises. Ox is the axis of inversions. We study particularly the product of two inversions.