Comparison of Force Fields on the Basis of Various Model Approaches—How To Design the Best Model for the [CnMIM][NTf2] Family of Ionic Liquids

In this contribution, we present two new united‐atom force fields (UA‐FFs) for 1‐alkyl‐3‐methylimidazolium bis(trifluoromethylsulfonyl)imide [C_nMIM][NTf₂] (n=1, 2, 4, 6, 8) ionic liquids (ILs). One is parametrized manually, and the other is developed with the gradient‐based optimization workflow (GROW). By doing so, we wanted to perform a hard test to determine how researchers could benefit from semiautomated optimization procedures. As with our already published all‐atom force field (AA‐FF) for [C_nMIM][NTf₂] (T. Köddermann, D. Paschek, R. Ludwig, ChemPhysChem­ 2007, 8, 2464 ), the new force fields were derived to fit experimental densities, self‐diffusion coefficients, and NMR rotational correlation times for the IL cation and for water molecules dissolved in [C₂MIM][NTf₂]. In the manual force field, the alkyl chains of the cation and the CF₃ groups of the anion were treated as united atoms. In the GROW force field, only the alkyl chains of the cation were united. All other parts of the structures of the ions remained unchanged to prevent any loss of physical information. Structural, dynamic, and thermodynamic properties such as viscosity, cation rotational correlation times, and heats of vaporization calculated with the new force fields were compared with values simulated with the previous AA‐FF and the experimental data. All simulated properties were in excellent agreement with the experimental values. Altogether, the UA‐FFs are slightly superior for speed‐up reasons. The UA‐FF speeds up the simulation by about 100 % and reduces the demanded disk space by about 78 %. More importantly, real time and efforts to generate force fields could be significantly reduced by utilizing GROW. The real time for the GROW parametrization in this work was 2 months. Manual parametrization, in contrast, may take up to 12 months, and this is, therefore, a significant increase in speed, though it is difficult to estimate the duration of manual parametrization.     

On the self-similar solution to the Euler equations for an incompressible fluid in three dimensions

The equations for a self-similar solution to an inviscid incompressible fluid are mapped into an integral equation that hopefully can be solved by iteration. It is argued that the exponents of the similarity are ruled by Kelvin's theorem of conservation of circulation. The end result is an iteration with a nonlinear term entering a kernel given by a 3D integral for a swirling flow, likely within reach of present-day computational power. Because of the slow decay of the similarity solution at large distances, its kinetic energy diverges, and some mathematical results excluding non-trivial solutions of the Euler equations in the self-similar case do not apply.     

Synthesis of Pure Silica MWW Zeolite in Fluoride Medium by Using an Imidazolium-Based Long Dication

As the spacer length in 1,2-dimethylimidazolium-based dications increases beyond a specific point (six methylene units), they fail in structure-directing towards STW zeolites in any synthetic conditions. These dications can instead produce, under fluoride concentrated conditions, either *BEA [in the case of the eight-methylene-unit structure-directing agent (SDA)] or MWW (ten methylene units) zeolites. For any length of the dication, the default zeolite (MTW) is a relatively dense zeolite containing a unidimensional channel, whereas the zeolite demanding most specificity (STW, *BEA or MWW) is more porous, affording a larger concentration of the dication to be occluded. This work provides the first reported fluoride synthesis of pure silica MWW zeolites. Charge balance of the organic dications in this zeolite was achieved by combining “structural” silanolates, regular “connectivity defects” and occluded fluoride. Molecular mechanics calculations showed a perfect fit of the decamethylenebis(dimethylimidazolium) dication in the sinusoidal intralayer pore system of MWW. The calculations showed also that the dication is able to stabilize the interlayer space without disturbing the hydrogen-bonding system that holds the layers together in the as-made material. The ¹⁹F magic-angle spinning (MAS) NMR presented two distinct resonances at −71 and −83 ppm, which, on the basis of DFT calculations, we tentatively assigned to fluoride occluded in [4⁶6²] and [4¹5²6²] cages of the MWW structure, respectively. The same DFT study determines a different chemical shift of one methyl ¹³C nuclear magnetic resonance according to the imidazolium ring residing in the sinusoidal channels or in the large cup cavities, thus explaining an experimentally observed splitting of that resonance.     

On the use of surfaces of section in the N-body ring problem

In the N-body ring problem, we investigate the motion of a massless body interacting with N bodies of equal masses at the vertices of a regular polygon that rotates around a central mass. In this paper, we analyze the use of different surfaces of section in the numerical exploration of the escape in the N-body ring problem in order to get some conclusions about the geometry of the basins of escape in the corresponding configuration spaces.     

Geometric derivation of the microscopic stress: A covariant central force decomposition

We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle–Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving–Kirkwood–Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.