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Adaptive Resolution Molecular Dynamics Technique
M. Praprotnik, R. Cortes-Huerto, R. Potestio, L. Delle Site
in Handbook of Materials Modeling,Pages1443-1457,Springer International Publishing (2020);

Loss of Molecular Roughness upon Coarse-Graining Predicts the Artificially Accelerated Mobility of Coarse-Grained Molecular Simulation Models
M. K. Meinel, F. Müller-Plathe
J. Chem. Theor. Comput.16,1411 (2020);

Coarse-grained models include only the most important degrees of freedom to match certain target properties and thus reduce the computational costs. The dynamics of these models is usually accelerated compared to those of the parent atomistic models. We propose a new approach to predict this acceleration on the basis of the loss of geometric information upon coarse-graining. To this end, the molecular roughness difference is calculated by a numerical comparison of the molecular surfaces of both the atomistic and the coarse-grained systems. Seven homogeneous hydrocarbon liquids are coarse-grained using the structure-based iterative Boltzmann inversion. An acceleration factor is calculated as the ratio of diffusion coefficients of the coarse-grained and atomistic simulation. The molecular roughness difference and the acceleration factor of the seven test systems reach a very good linear correlation.

On the Energy Stable Approximation of Hamiltonian and Gradient Systems
Herbert Egger, Oliver Habrich, Vsevolod Shashkov
Computational Methods in Applied Mathematics21 (2),335-349 (2020);

Automated determination of hybrid particle-field parameters by machine learning
Morten Ledum, Sigbjørn Løland Bore, Michele Cascella
Molecular Physics118 (19-20),e1785571 (2020);

Characterizing Polymer Hydration Shell Compressibilities with the Small-System Method
Madhusmita Tripathy, Swaminath Bharadwaj, Shadrack Jabes B., Nico F. A. van der Vegt
Nanomaterials10 (8),1460 (2020);

On a Second-Order Multipoint Flux Mixed Finite Element Methods on Hybrid Meshes
Herbert Egger, Bogdan Radu
SIAM Journal on Numerical Analysis58 (3),1822-1844 (2020);

Hybrid particle-field molecular dynamics under constant pressure
Sigbjørn Løland Bore, Hima Bindu Kolli, Antonio De Nicola, Maksym Byshkin, Toshihiro Kawakatsu, Giuseppe Milano, Michele Cascella
The Journal of Chemical Physics152 (18),184908 (2020);

Chemotaxis on networks: Analysis and numerical approximation
Herbert Egger, Lukas Schöbel-Kröhn
ESAIM: Mathematical Modelling and Numerical Analysis54 (4),1339-1372 (2020);

Defects and defect engineering in Soft Matter
Amir Jangizehi, Friederike Schmid, Pol Besenius, Kurt Kremer, Sebastian Seiffert
Soft Matter16 (48),10809-10859 (2020);

A minimal Gō-model for rebuilding whole genome structures from haploid single-cell Hi-C data
S. Wettermann, M. Brems, J.T. Siebert, G.T. Vu, T.J. Stevens, P. Virnau
Computational Materials Science173,109178 (2020);

Structure Preserving Discretization of Allen–Cahn Type Problems Modeling the Motion of Phase Boundaries
Anke Böttcher, Herbert Egger
Vietnam Journal of Mathematics48 (4),847-863 (2020);

A mass-lumped mixed finite element method for acoustic wave propagation
H. Egger, B. Radu
Numerische Mathematik145 (2),239-269 (2020);

On the transport limit of singularly perturbed convection–diffusion problems on networks
Herbert Egger, Nora Philippi
Mathematical Methods in the Applied Sciences44 (6),5005-5020 (2020);

Quorum-sensing active particles with discontinuous motility
Andreas Fischer, Friederike Schmid, Thomas Speck
Physical Review E101 (1),012601 (2020);

We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There are, however, differences from the more conventional picture of liquid-gas coexistence based on a free energy, most notably the absence of a critical point. We corroborate our analytical predictions by numerical simulations of active particles under confinement and interacting through volume exclusion. Excellent quantitative agreement is reached through an effective translational diffusion coefficient. We finally show that an additional response to the chemical gradient direction is sufficient to induce vortex clusters. Our results pave the way to engineer motility responses in order to achieve aggregation and collective behavior even at unfavorable conditions.

From scalar to polar active matter: Connecting simulations with mean-field theory
Ashreya Jayaram, Andreas Fischer, Thomas Speck
Physical Review E101 (2), (2020);

We study numerically the phase behavior of self-propelled elliptical particles interacting through the “hard” repulsive Gay-Berne potential at infinite Péclet number. Changing a single parameter, the aspect ratio, allows us to continuously go from discoid active Brownian particles to elongated polar rods. Discoids show phase separation, which changes to a cluster state of polar domains, which then form polar bands as the aspect ratio is increased. From the simulations, we identify and extract the two effective parameters entering the mean-field description: the force imbalance coefficient and the effective coupling to the local polarization. These two coefficients are sufficient to obtain a complete and consistent picture, unifying the paradigms of scalar and polar active matter.

Semiautomatic construction of lattice Boltzmann models
Dominic Spiller, Burkhard Dünweg
Physical Review E101 (4), (2020);

Skyrmion Lattice Phases in Thin Film Multilayer
Jakub Zázvorka, Florian Dittrich, Yuqing Ge, Nico Kerber, Klaus Raab, Thomas Winkler, Kai Litzius, Martin Veis, Peter Virnau, Mathias Kläui
Advanced Functional Materials30 (46),2004037 (2020);

Can Soft Models Describe Polymer Knots?
Jianrui Zhang, Hendrik Meyer, Peter Virnau, Kostas Ch. Daoulas
Macromolecules53 (23),10475-10486 (2020);

Application of the 2PT model to understanding entropy change in molecular coarse-graining
Marvin P. Bernhardt, Marco Dallavalle, Nico F. A. Van der Vegt
Soft Materials18 (2-3),274-289 (2020);

Statistical theory of helical turbulence
B. Deußen, D. Dierkes, and M. Oberlack
Physics of Fluids32 (6),065109 (2020);

A statistical theory for homogeneous helical turbulence is developed under the condition of strong symmetry. The latter describes reflectional symmetry in planes through and normal to the helical unit vector eξ, which can be achieved by demanding that the mean velocity is zero. The two-point velocity correlation, the pressure–velocity correlation, and the two-point triple correlation are expressed by scalar functions in the helical unit vector system. By introducing the continuity equation for the correlations, the number of unknown functions can be reduced to such an extent that ultimately, a single scalar transport equation remains. Furthermore, a two-point Poisson equation is derived to express the pressure–velocity correlation in terms of the triple correlation. From the two-point version of the transport equation, the single-point limit is derived. Using the single-point equation, it can be shown that all velocity components are generally non-zero. Therefore, it is concluded that the phenomenon of vortex stretching is present in the helical coordinate system. Finally, the theory of axisymmetric turbulence is derived as a limiting case of helical turbulence to show consistency with former work.

Coarse-grained conformational surface hopping: Methodology and transferability
Joseph F. Rudzinski and Tristan Bereau
Journal of Chemical Physics153,214110 (2020);
URL: https://doi.org/10.1063/5.0031249

Coarse-grained (CG) conformational surface hopping (SH) adapts the concept of multisurface dynamics, initially developed to describe electronic transitions in chemical reactions, to accurately describe classical molecular dynamics at a reduced level. The SH scheme couples distinct conformational basins (states), each described by its own force field (surface), resulting in a significant improvement of the approximation to the many-body potential of mean force [T. Bereau and J. F. Rudzinski, Phys. Rev. Lett. 121, 256002 (2018)]. The present study first describes CG SH in more detail, through both a toy model and a three-bead model of hexane. We further extend the methodology to non-bonded interactions and report its impact on liquid properties. Finally, we investigate the transferability of the surfaces to distinct systems and thermodynamic state points, through a simple tuning of the state probabilities. In particular, applications to variations in temperature and chemical composition show good agreement with reference atomistic calculations, introducing a promising “weak-transferability regime,” where CG force fields can be shared across thermodynamic and chemical neighborhoods.

Adversarial reverse mapping of equilibrated condensed-phase molecular structures
Marc Stieffenhofer, Michael Wand, Tristan Bereau
Machine Learning: Science and Technology1,045014 (2020);

A tight and consistent link between resolutions is crucial to further expand the impact of multiscale modeling for complex materials. We herein tackle the generation of condensed molecular structures as a refinement—backmapping—of a coarse-grained (CG) structure. Traditional schemes start from a rough coarse-to-fine mapping and perform further energy minimization and molecular dynamics simulations to equilibrate the system. In this study we introduce DeepBackmap: A deep neural network based approach to directly predict equilibrated molecular structures for condensed-phase systems. We use generative adversarial networks to learn the Boltzmann distribution from training data and realize reverse mapping by using the CG structure as a conditional input. We apply our method to a challenging condensed-phase polymeric system. We observe that the model trained in a melt has remarkable transferability to the crystalline phase. The combination of data-driven and physics-based aspects of our architecture help reach temperature transferability with only limited training data.

Compression-induced anti-nematic order in glassy and semicrystalline polymers
Sara Jabbari-Farouji, Damien Vandembroucq
Soft Matter16 (1),102-106 (2020);

Emergent pattern formation of active magnetic suspensions in an external field
Fabian R Koessel, Sara Jabbari-Farouji
New Journal of Physics22 (10),103007 (2020);

Role of image charges in ionic liquid confined between metallic interfaces
Samuel Ntim, Marialore Sulpizi
Physical Chemistry Chemical Physics22 (19),10786-10791 (2020);

Structure and Dynamics of Solid/Liquid Interfaces
Marie‐Pierre Gaigeot Marialore Sulpizi
Surface and Interface Science: Volume 7: Liquid and Biological InterfacesVolume 7 (Chapter 50),143-193 (2020);

Surface Charges at the CaF 2 /Water Interface Allow Very Fast Intermolecular Vibrational‐Energy Transfer
Dominika Lesnicki, Zhen Zhang, Mischa Bonn, Marialore Sulpizi, Ellen H. G. Backus
Angewandte Chemie International Edition59 (31),13116-13121 (2020);

Oberflächenladungen an der CaF 2 ‐Wasser‐Grenzfläche erlauben eine sehr schnelle intermolekulare Übertragung von Schwingungsenergie
Dominika Lesnicki, Zhen Zhang, Mischa Bonn, Marialore Sulpizi, Ellen H. G. Backus
Angewandte Chemie132 (31),13217-13222 (2020);

Dynamic Self-Consistent Field Approach for Studying Kinetic Processes in Multiblock Copolymer Melts
Friederike Schmid, Bing Li
Polymers12 (10),2205 (2020);
URL: https://www.mdpi.com/2073-4360/12/10/2205

The self-consistent field theory is a popular and highly successful theoretical framework for studying equilibrium (co)polymer systems at the mesoscopic level. Dynamic density functionals allow one to use this framework for studying dynamical processes in the diffusive, non-inertial regime. The central quantity in these approaches is the mobility function, which describes the effect of chain connectivity on the nonlocal response of monomers to thermodynamic driving fields. In a recent study, one of us and coworkers have developed a method to systematically construct mobility functions from reference fine-grained simulations. Here we focus on melts of linear chains in the Rouse regime and show how the mobility functions can be calculated semi-analytically for multiblock copolymers with arbitrary sequences without resorting to simulations. In this context, an accurate approximate expression for the single-chain dynamic structure factor is derived. Several limiting regimes are discussed. Then we apply the resulting density functional theory to study ordering processes in a two-length scale block copolymer system after instantaneous quenches into the ordered phase. Different dynamical regimes in the ordering process are identified: at early times, the ordering on short scales dominates; at late times, the ordering on larger scales takes over. For large quench depths, the system does not necessarily relax into the true equilibrium state. Our density functional approach could be used for the computer-assisted design of quenching protocols in order to create novel nonequilibrium materials

Convergence of finite volume schemes for the Euler equations via dissipative measure--valued solutions
E. Feireisl, M. Lukáčová-Medvid’ová, H. Mizerová
Found Comput Math 20,923-966 (2020);

The Cauchy problem for the complete Euler system is in general ill-posed in the class of admissible (entropy producing) weak solutions. This suggests that there might be sequences of approximate solutions that develop fine-scale oscillations. Accordingly, the concept of measure-valued solution that captures possible oscillations is more suitable for analysis. We study the convergence of a class of entropy stable finite volume schemes for the barotropic and complete compressible Euler equations in the multidimensional case. We establish suitable stability and consistency estimates and show that the Young measure generated by numerical solutions represents a dissipative measure-valued solution of the Euler system. Here dissipative means that a suitable form of the second law of thermodynamics is incorporated in the definition of the measure-valued solutions. In particular, using the recently established weak-strong uniqueness principle, we show that the numerical solutions converge pointwise to the regular solution of the limit systems at least on the lifespan of the latter.

A finite volume scheme for the Euler system inspired by the two velocities approach
E. Feireisl, M. Lukacova-Medvidova, H. Mizerova
Num. Math. 144 (89-132), (2020);

We propose a new finite volume scheme for the Euler system of gas dynamics motivated by the model proposed by H. Brenner. Numerical viscosity imposed through upwinding acts on the velocity field rather than on the convected quantities. The resulting numerical method enjoys the crucial properties of the Euler system, in particular positivity of the approximate density and pressure and the minimal entropy principle. In addition, the approximate solutions generate a dissipative measure-valued solutions of the limit system. In particular, the numerical solutions converge to the smooth solution of the system as long as the latter exists.

K-convergence as a new tool in numerical analysis
E.Feireisl, M. Lukacova-Medvidova, H. Mizerova
IMA J. Num. Anal. 40,2227–2255 (2020);

We adapt the concept of K-convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise convergence of numerical solutions in the case when solutions of the limit continuous problem possess minimal regularity. We apply the abstract theory to a finite volume method for the isentropic Euler system describing the motion of a compressible inviscid fluid. The result can be seen as a nonlinear version of the fundamental Lax equivalence theorem.

On the convergence of a finite volume method for the Navier–Stokes–Fourier system
E.Feireisl, M. Lukacova-Medvidova, H. Mizerova, B. She
IMA J. Num. Anal. , (2020);
C5 Project

We study convergence of a finite volume scheme for the Navier-Stokes-Fourier system describing the motion of compressible viscous and heat conducting fluids. The numerical flux uses upwinding with an additional numerical diffusion of order O(h^{ε+1}), 0<ε<1. The approximate solutions are piecewise constant functions with respect to the underlying mesh. We show that any uniformly bounded sequence of numerical solutions converges unconditionally to the solution of the Navier-Stokes-Fourier system. In particular, the existence of the solution to the Navier-Stokes-Fourier system is not a priori assumed.

How Alcoholic Disinfectants Affect Coronavirus Model Membranes: Membrane Fluidity, Permeability, and Disintegration
Hossein Eslami, Shubhadip Das, Tianhang Zhou, and Florian Müller-Plathe
J. Phys. Chem. B124 (46),10374–10385 (2020);
URL: https://pubs.acs.org/doi/abs/10.1021/acs.jpcb.0c08296

Atomistic molecular dynamics simulations have been carried out with a view to investigating the stability of the SARS-CoV-2 exterior membrane with respect to two common disinfectants, namely, aqueous solutions of ethanol and n-propanol. We used dipalmitoylphosphatidylcholine (DPPC) as a model membrane material and did simulations on both gel and liquid crystalline phases of membrane surrounded by aqueous solutions of varying alcohol concentrations (up to 17.5 mol %). While a moderate effect of alcohol on the gel phase of membrane is observed, its liquid crystalline phase is shown to be influenced dramatically by either alcohol. Our results show that aqueous solutions of only 5 and 10 mol % alcohol already have significant weakening effects on the membrane. The effects of n-propanol are always stronger than those of ethanol. The membrane changes its structure, when exposed to disinfectant solutions; uptake of alcohol causes it to swell laterally but to shrink vertically. At the same time, the orientational order of lipid tails decreases significantly. Metadynamics and grand-canonical ensemble simulations were done to calculate the free-energy profiles for permeation of alcohol and alcohol/water solubility in the DPPC. We found that the free-energy barrier to permeation of the DPPC liquid crystalline phase by all permeants is significantly lowered by alcohol uptake. At a disinfectant concentration of 10 mol %, it becomes insignificant enough to allow almost free passage of the disinfectant to the inside of the virus to cause damage there. It should be noted that the disinfectant also causes the barrier for water permeation to drop. Furthermore, the shrinking of the membrane thickness shortens the gap needed to be crossed by penetrants from outside the virus into its core. The lateral swelling also increases the average distance between head groups, which is a secondary barrier to membrane penetration, and hence further increases the penetration by disinfectants. At alcohol concentrations in the disinfectant solution above 15 mol %, we reliably observe disintegration of the DPPC membrane in its liquid crystalline phase.

Supramolecular Packing Drives Morphological Transitions of Charged Surfactant Micelles
Ken Schäfer, Hima Bindu Kolli, Mikkel Killingmoe Christensen, Sigbjørn Løland Bore, Gregor Diezemann, Jürgen Gauss, Giuseppe Milano, Reidar Lund, Michele Cascella
Angewandte Chemie International Edition59 (42),18591-18598 (2020);

The shape and size of self-assembled structures upon local organization of their molecular building blocks are hard to predict in the presence of long-range interactions. Combin- ing small-angle X-ray/neutron scattering data, theoretical modelling, and computer simulations, sodium dodecyl sulfate (SDS), over a broad range of concentrations and ionic strengths, was investigated. Computer simulations indicate that micellar shape changes are associated with different binding of the counterions. By employing a toy model based on point charges on a surface, and comparing it to experiments and simulations, it is demonstrated that the observed morphological changes are caused by symmetry breaking of the irreducible building blocks, with the formation of transient surfactant dimers mediated by the counterions that promote the stabili- zation of cylindrical instead of spherical micelles. The present model is of general applicability and can be extended to all systems controlled by the presence of mobile charges.

Force-dependent folding pathways in mechanically interlocked calixarene dimers via atomistic force quench simulations
Ken Schäfer, Gregor Diezemann
Molecular Physics118 (19-20),e1743886 (2020);

Single-molecule force spectroscopy and molecular simulations are well-established techniques to study the mechanical unfolding of supramolecular complexes in various fields of biomolecular physics. In the present study, we investigate the details of the force-dependent folding transition of a well-studied model system, a calix[4]arene catenane dimer, using atomistic force quench simu- lations. This protocol allows us to reach a range of much smaller forces than possible with the more common force ramp simulations where the force is changed with a constant velocity. We find that the folding pathway changes its character as a function of external force. For small forces (on the order of 50 pN), the folding transition occurs via the transition to a metastable intermediate structure in about 30% of the simulations. We characterise the structure of this intermediate and demonstrate its relevance by considering the averaged potential of mean force of the system as a function of a well-defined reaction coordinate. When the force increases, the importance of the intermediate diminishes and for high external forces (500 pN), our results can be interpreted in terms of a simple two-state model, that has also been used in earlier simulations on the same system.

Why Do Elastin-Like Polypeptides Possibly Have Different Solvation Behaviors in Water–Ethanol and Water–Urea Mixtures?
Yani Zhao, Manjesh K. Singh, Kurt Kremer, Robinson Cortes-Huerto, Debashish Mukherji
Macromolecules53 (6),2101-2110 (2020);

Investigating the Conformational Ensembles of Intrinsically Disordered Proteins with a Simple Physics-Based Model
Yani Zhao, Robinson Cortes-Huerto, Kurt Kremer, Joseph F. Rudzinski
The Journal of Physical Chemistry B124 (20),4097-4113 (2020);

Open-boundary Hamiltonian adaptive resolution. From grand canonical to non-equilibrium molecular dynamics simulations
Maziar Heidari, Kurt Kremer, Ramin Golestanian, Raffaello Potestio, Robinson Cortes-Huerto
The Journal of Chemical Physics152 (19),194104 (2020);

Bottom-up Construction of Dynamic Density Functional Theories for Inhomogeneous Polymer Systems from Microscopic Simulations
Sriteja Mantha, Shuanhu Qi, Friederike Schmid
Macromolecules53 (9),3409-3423 (2020);

We propose and compare different strategies to constructdynamic density functional theories (DDFTs) for inhomogeneouspolymer systems close to equilibrium from microscopic simulationtrajectories. We focus on the systematic construction of the mobilitycoefficient,Λ(r,r′), which relates the thermodynamic driving force onmonomers at positionr′to the motion of monomers at positionr.Afirstapproach based on the Green−Kubo formalism turns out to beimpractical because of a severe plateau problem. Instead, we propose toextract the mobility coefficient from an effective characteristic relaxationtime of the single chain dynamic structure factor. To test our approach, we study the kinetics of ordering and disordering in diblockcopolymer melts. The DDFT results are in very good agreement with the data from correspondingfine-grained simulations

Using Copolymers to Design Tunable Stimuli-Reponsive Brushes
Shuanhu Qi, Leonid I. Klushin, Alexander M. Skvortsov, Friederike Schmid
Macromolecules53 (13),5326-5336 (2020);

Recently, a new design for switch sensors has been proposed that exploits a conformational transition of end-grafted minority adsorption-active homopolymers in a monodisperse polymer brush [Klushin et al. Phys. Rev. Lett.2014, 113, 068303]. The transition is sharp and first-order type if the minority chain is longer than the brush chains. However, the intrinsic nature of the system imposes a constraint on the relation between the sharpness of the transition and the height of the free energy barrier controlling the transition kinetics: The sharper the transition, the slower the transition time. Here we demonstrate that adopting diblock copolymers with the adsorption-active block anchored at the substrate as the minority chains allows a much more flexible control of the three main characteristics of the transition, i.e., the transition point, its sharpness, and the barrier height. In particular, the barrier height can be greatly reduced without compromising the sharpness. We develop an analytical theory that predicts the relevant characteristics of the transition and verify it with SCF calculations and Monte Carlo simulations. We also demonstrate that from a thermodynamic point of view the transition characteristics of a diblock copolymer are equivalent to those of the active block alone in a modified brush with the same grafting density and reduced length.

Supramolecular Packing Drives Morphological Transitions of Charged Surfactant Micelles
Ken Schäfer, Hima Bindu Kolli, Mikkel Killingmoe Christensen, Sigbjørn Løland Bore, Gregor Diezemann, Jürgen Gauss, Giuseppe Milano, Reidar Lund, Michele Cascella
Angewandte Chemie International Edition, (2020);

The shape and size of self‐assembled structures upon local organization of their molecular building blocks are hard to predict in the presence of long‐range interactions. Combining small‐angle X‐ray/neutron scattering data, theoretical modelling, and computer simulations, sodium dodecyl sulfate (SDS), over a broad range of concentrations and ionic strengths, was investigated. Computer simulations indicate that micellar shape changes are associated with different binding of the counterions. By employing a toy model based on point charges on a surface, and comparing it to experiments and simulations, it is demonstrated that the observed morphological changes are caused by symmetry breaking of the irreducible building blocks, with the formation of transient surfactant dimers mediated by the counterions that promote the stabilization of cylindrical instead of spherical micelles. The present model is of general applicability and can be extended to all systems controlled by the presence of mobile charges.

Kernel-Based Machine Learning for Efficient Simulations of Molecular Liquids
Christoph Scherer, René Scheid, Denis Andrienko, Tristan Bereau
Journal of Chemical Theory and Computation16 (5),3194-3204 (2020);

The Grignard Reaction – Unraveling a Chemical Puzzle
Raphael Mathias Peltzer, Jürgen Gauss, Odile Eisenstein, Michele Cascella
Journal of the American Chemical Society142 (6),2984-2994 (2020);

More than 100 years since its discovery, the mechanism of the Grignard reaction remains unresolved. Ambiguities arise from the concomitant presence of multiple organomagnesium species and the competing mechanisms involving either nucleophilic addition or the formation of radical intermediates. To shed light on this topic, quantum-chemical calculations and ab initio molecular dynamics simulations are used to study the reaction of CH3MgCl in tetrahydrofuran with acetaldehyde and fluorenone as prototypical reagents. All organomagnesium species coexisting in solution due to the Schlenk equilibrium are found to be competent reagents for the nucleophilic pathway. The range of activation energies displayed by all of these compounds is relatively small. The most reactive species are a dinuclear Mg complex in which the substrate and the nucleophile initially bind to different Mg centers and the mononuclear dimethyl magnesium. The radical reaction, which requires the homolytic cleavage of the Mg–CH3 bond, cannot occur unless a substrate with a low-lying π*(CO) orbital coordinates the Mg center. This rationalizes why a radical mechanism is detected only in the presence of substrates with a low reduction potential. This feature, in turn, does not necessarily favor the nucleophilic addition, as shown for the reaction with fluorenone. The solvent needs to be considered as a reactant for both the nucleophilic and the radical reactions, and its dynamics is essential for representing the energy profile. The similar reactivity of several species in fast equilibrium implies that the reaction does not occur via a single process but by an ensemble of parallel reactions.

A generalized Newton iteration for computing the solution of the inverse Henderson problem
Fabrice Delbary, Martin Hanke, Dmitry Ivanizki
Inverse Problems in Science and Engineering,1-25 (2020);


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