A New Type of Stereoselectivity in Baeyer–Villiger Reactions: Access to E- and Z-Olefins

A new concept for accessing configurationally defined trisubstituted olefins has been developed. Starting from a common ketone precursor of the type 4-ethylidenecyclohexanone, Baeyer–Villiger monooxygenases are employed as catalysts in diastereoselective Baeyer–Villiger reactions leading to the corresponding E- or Z-configurated lactones. Wild-type cyclohexanone monooxygenase (CHMO) as catalyst delivers the E-isomers and a directed evolution mutant the opposite Z-isomers. Subsequent transition metal-catalyzed chemical transformations of a key product containing a vinyl bromide moiety provide a variety of different trisubstituted E- or Z-olefins. A model based on QM/MM sheds light on the origin of this unusual type of diastereoselectivity. In contrast to this biocatalytic approach, traditional Baeyer–Villiger reagents such as m-CPBA fail to show any selectivity, 1:1 mixtures of E- and Z-olefins being formed

Charge migration engineered by localisation: electron-nuclear dynamics in polyenes and glycine

We demonstrate that charge migration can be ‘engineered’ in arbitrary molecular systems if a single localised orbital – that diabatically follows nuclear displacements – is ionised. Specifically, we describe the use of natural bonding orbitals in Complete Active Space Configuration Interaction (CASCI) calculations to form cationic states with localised charge, providing consistently well-defined initial conditions across a zero point energy vibrational ensemble of molecular geometries. In Ehrenfest dynamics simulations following localised ionisation of -electrons in model polyenes (hexatriene and decapentaene) and -electrons in glycine, oscillatory charge migration can be observed for several femtoseconds before dephasing. Including nuclear motion leads to slower dephasing compared to fixed-geometry electron-only dynamics results. For future work, we discuss the possibility of designing laser pulses that would lead to charge migration that is experimentally observable, based on the proposed diabatic orbital approach

Synthesis of a PID-controller of a trim robust control system of an autonomous underwater vehicle

Autonomous underwater vehicles are often used for performing scientific, emergency or other types of missions under harsh conditions and environments, which can have non-stable, variable parameters. So, the problem of developing autonomous underwater vehicle motion control systems, capable of operating properly in random environments, is highly relevant. The paper is dedicated to the synthesis of a PID-controller of a trim robust control system, capable of keeping an underwater vehicle stable during a translation at different angles of attack. In order to synthesize the PID-controller, two problems were solved: a new method of synthesizing a robust controller was developed and a mathematical model of an underwater vehicle motion process was derived. The newly developed mathematical model structure is simpler than others due to acceptance of some of the system parameters as interval ones. The synthesis method is based on a system poles allocation approach and allows providing the necessary transient process quality in a considered system

Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality constraints. A number of optimization problems in applications can be stated in this form, examples being the entropy-linear programming, the ridge regression, the elastic net, the regularized optimal transport, etc. We extend the Fast Gradient Method applied to the dual problem in order to make it primal-dual so that it allows not only to solve the dual problem, but also to construct nearly optimal and nearly feasible solution of the primal problem. We also prove a theorem about the convergence rate for the proposed algorithm in terms of the objective function and the linear constraints infeasibility.Comment: Submitted for DOOR 201

Counting and computing regions of DD-decomposition: algebro-geometric approach

New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families of polynomial and matrices is given. For the case of two parametric family more sharp estimate is proven. Theoretic results are supported by various numerical simulations that show higher precision of presented methods with respect to traditional ones. The presented methods are inherently global and could be applied for studying $D$-decomposition for the space of parameters as a whole instead of some prescribed regions. For symbolic computations the Maple v.14 software and its package RegularChains are used.Comment: 16 pages, 8 figure

The Pure Virtual Braid Group Is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of such a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies corrected, reflecting suggestions made by the referee of the published version of the pape

Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

A non-linear conjugate gradient optimization scheme is used to obtain excitation energies within the Random Phase Approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size, N, is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular- orbital-free algorithm is found to be robust and computationally efficient providing a first step toward a large-scale, reduced complexity calculation of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent Density Functional theory.Comment: 9 pages, 7 figure

Quantum Mechanical/Molecular Mechanical Study on the Enantioselectivity of the Enzymatic Baeyer–Villiger Reaction of 4-Hydroxycyclohexanone

We report a combined quantum mechanical/molecular mechanical (QM/MM) study of the effect of mutations of the Phe434 residue in the active site of cyclohexanone monooxygenase (CHMO) on its enantioselectivity toward 4-hydroxycyclohexanone. In terms of our previously established model of the enzymatic Baeyer–Villiger reaction, enantioselectivity is governed by the preference toward the equatorial ((S)-selectivity) or axial ((R)-selectivity) conformation of the substituent at the C4 carbon atom of the cyclohexanone ring in the Criegee intermediate and the subsequent rate-limiting transition state for migration (TS2). We assess the enantiopreference by locating all relevant TS2 structures at the QM/MM level. In the wild-type enzyme we find that the axial conformation is energetically slightly more stable, thus leading to a small excess of (R)-product. In the Phe434Ser mutant, there is a hydrogen bond between the serine side chain and the equatorial substrate hydroxyl group that is retained during the whole reaction, and hence there is pronounced reverse (S)-enantioselectivity. Another mutant, Phe434Ile, is shown to preserve and enhance the (R)-selectivity. All these findings are in accordance with experiment. The QM/MM calculations allow us to explain the effect of point mutations on CHMO enantioselectivity for the first time at the molecular level by an analysis of the specific interactions between substrate and active-site environment in the TS2 structures that satisfy the basic stereoelectronic requirement of anti-periplanarity for the migrating σ-bond

Projection methods in conic optimization

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear conic optimization, and applications in polynomial optimization. This is a presentation of the material of several recent research articles; we aim here at clarifying the ideas, presenting them in a general framework, and pointing out important techniques