Characterization of the conformational probability of N-acetyl-phenylalanyl-NH2 by RHF, DFT, and MP2 computation and AIM analyses, confirmed by jet-cooled infrared data

Computational and experimental determinations were carried out in parallel on the conformational probability of N-Acetyl-Phenylalanine-NH2 (NAPA). Ab initio computations were completed at the BLYP/6-311G(df,p), B3LYP/6-31G(d), B3LYP/6-31G(d,p), and B3LYP/6-31+G(d) levels of theory, labeled L/61fp, B/6, B/6p, and B/6+, respectively. Three experimentally identified conformers were compared with theoretical data, confirming their identities as the betaLanti, gammaLgauche+, and gammaLgauche- (BACKBONESIDECHAIN) conformers. Evidence comes from matching experimental and theoretical data for all three constituent N-H stretches of NAPA, with a Delta(Experimental-Theoretical) = approximately 1-3 cm(-1), approximately 0-5 cm(-1), and approximately 1-6 cm(-1), at the L/61fp and B/6+ levels, respectively. Corrected-ZPE relative energies were computed to be 0.14, 0.00, 0.26 and 0.00, 0.67, 0.57 (kcal*mol(-1)) for the betaLanti, gammaLgauche+, and gamma(Lgauche- conformers, respectively, at the L/61fp and B/6+ levels, respectively. The MP2/6-31+G(d) level of theory was subsequently found to give similar relative energies. Characterization of the intramolecular interactions responsible for red and blue shifting of the N-H stretches showed the existence of the following intramolecular interactions: C=O[i]- - -HN[i], (Ar[i])-Cgamma- - -HN[i+1], (Ar[i])-Cdelta-H- - -O=C[i-1] for betaLanti; C=O[i-1]- - -HN[i+1], (Ar[i])-Cgamma- - -HN[i+1], (Ar[i])-C-H- - -O=C[i] for gammaLgauche+; and C=O[i-1]- - -HN[i+1] for gammaLgauche-. Each of these interactions were further investigated and subsequently characterized by orbital population and Atoms-In-Molecules (AIM) analyses, with the identity of overlap and bond critical points (BCP) serving as 'scoring criteria', respectively. Experimental and theoretical carbonyl stretches were also compared and showed good agreement, adding further strength to the synergy between experiment and theory.     

The excluded volume of hard sphero-zonotopes

Excluded volume effects can account for most ordering transitions in simple liquids and liquid crystals. Starting with the work of Onsager, this has been demonstrated in the case of liquid crystals for a number of simple convex bodies, e.g. sphero-cylinders, for which the orientation-dependent pair-excluded volume could be written down analytically. However, in recent years, experiments and simulations have been reported on ordering transitions in suspensions of more complex convex colloids. For these systems, theoretical understanding is hampered by the fact that no analytical expressions for the pair-excluded volume were available. Here we show that it is possible to obtain explicit expressions for the pair-excluded volume of a much larger class of convex bodies: the so-called sphero-zonotopes. These bodies are obtained by ‘padding’ a special class of convex polytopes with a blanket of uniform thickness. The resultant family of particles encompasses a wide range of shapes that have been considered as models for fluid and liquid crystalline behaviour e.g. spheres, cubes, sphero-cylinders, sphero-platelets. We discuss two explicit examples: sphero-cuboids, the 3D core generalization of the sphero-cylinder and the sphero-platelet, and hexagonal prisms that are models for the recently synthesized colloidal gibbsite platelets. Employing the fact that a cylinder is a zonoid, i.e. the limit of a sequence of right regular prisms, we are able to compute the excluded volume of the ‘true’ sphero-cylinder, a uniformly padded cylinder, of which the oblate-spherocylinder is a known example. Our approach en passant provides a relatively elementary rederivation of Onsager's classical result on cylinders.     

A truncation/recoupling method for eigenvalues and eigenvectors ideal for parallel computation

Summary We review a new truncation/recoupling method to obtain eigenvalues and eigenvectors of anF-mode vibrational Hamiltonian. In particular we focus on the block diagonalization aspects of the method which are ideal for massive parallelization, and we demonstrate this using H₂O₂ as an example. We then present vibrational energies for non-rotating HO₂ and HCN, which illustrate several key advantages of this method.     

Dynamics and Stability of Bose-Einstein Condensates: The Nonlinear Schrödinger Equation with Periodic Potential

Summary. The cubic nonlinear Schr?dinger equation with a lattice potential is used to model a periodic dilute-gas Bose-Einstein condensate. Both two- and three-dimensional condensates are considered, for atomic species with either repulsive or attractive interactions. A family of exact solutions and corresponding potential is presented in terms of elliptic functions. The dynamical stability of these exact solutions is examined using both analytical and numerical methods. For condensates with repulsive atomic interactions, all stable, trivial-phase solutions are off-set from the zero level. For condensates with attractive atomic interactions, no stable solutions are found, in contrast to the one-dimensional case [8].     

Finite dimensional approximation of Riemannian path space geometry

In this paper, we construct a finite dimensional approximation for the geometry on the path space over a compact Riemannian manifold. This approximation allows to construct the horizontal lift of the Ornstein-Uhlenbeck process on the path space through the Markovian connection. We also prove a representation formula for the heat semigroup on (adapted) vector fields as well as a commutation formula for its derivative.     

PHOTOCHEMICAL BEHAVIOR OF BACTERIORHODOPSIN IMMOBILIZED IN NaCl PELLETS

Abstract— Some photochemical reactions of bacteriorhodopsin (BR) embedded in NaCl pellets (BR-NaCI) in the visible region are described here. BR in these preparations is a mixture of two classes of species: a drastically blue-shifted form and the unchanged purple pigment. Depending on the illumination history of the BR before being immobilized, both kinds of BR could be demonstrated in light-adapted (LA) and dark-adapted (DA) forms, but light adaptation was not possible once the pellets were made. Analogously to BR suspensions, the light-adapted blue-shifted BRexhibited an a/l-trans type photocycle, but the thermal steps were greatly slowed down (time constants 1 to 5 min). The parent species absorb at 506 nm. The DA blue-shifted BR exhibited absorption changes resolved into two photoreactions, one all-(rans- like (as in LA-BR) and another, 13-cw like, whose decay rate is also greatly slowed down (recovery time several hours). The parent species of the 13-cis like cycle absorb at 480 nm. That pigment fraction in the pellets whose absorption was not blue-shifted, also exhibited similar photoreactions to BR in suspension, but with an overall turnover rate only one order of magnitude slower. From a previous report (Lazarev and Terpugov, Biochim. Biophys. Acta 590 ,324–338,1980) and this one, it appears that the very slow photocycles in NaCl-BR of low moisture content originate from blue-shifted chromophores rather than from unchanged BR.