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Keywords
Transition point prediction in a multicomponent lattice Boltzmann model: Forcing scheme dependencies
(2018)
In an effort to assist researchers in choosing basis sets for quantum mechanical modeling of molecules (i.e. balancing calculation cost versus desired accuracy), we present a systematic study on the accuracy of computed conformational relative energies and their geometries in comparison to MP2/CBS and MP2/AV5Z data, respectively. In order to do so, we introduce a new nomenclature to unambiguously indicate how a CBS extrapolation was computed. Nineteen minima and transition states of buta-1,3-diene, propan-2-ol and the water dimer were optimized using forty-five different basis sets. Specifically, this includes one Pople (i.e. 6-31G(d)), eight Dunning (i.e. VXZ and AVXZ, X=2-5), twenty-five Jensen (i.e. pc-n, pcseg-n, aug-pcseg-n, pcSseg-n and aug-pcSseg-n, n=0-4) and nine Karlsruhe (e.g. def2-SV(P), def2-QZVPPD) basis sets. The molecules were chosen to represent both common and electronically diverse molecular systems. In comparison to MP2/CBS relative energies computed using the largest Jensen basis sets (i.e. n=2,3,4), the use of smaller sizes (n=0,1,2 and n=1,2,3) provides results that are within 0.11--0.24 and 0.09-0.16 kcal/mol. To practically guide researchers in their basis set choice, an equation is introduced that ranks basis sets based on a user-defined balance between their accuracy and calculation cost. Furthermore, we explain why the aug-pcseg-2, def2-TZVPPD and def2-TZVP basis sets are very suitable choices to balance speed and accuracy.
The influence of interaction details on the thermal diffusion in binary Lennard-Jones liquids
(2001)
Structural and Dynamical Properties of Polystyrene Determined by Coarse-Graining MD Simulations
(2007)
We present results from a detailed study of a new, optimized coarse-grained (CG) model of polystyrene (PS) and compare it with a recently published one (Harmandaris et al., Macromolecules 2006, 39, 6708). We will explain in detail, what led us to a different mapping scheme and put that into the general framework, with special emphasis on the aspect of time mapping. The new model is tested against the structural and dynamic properties of PS, resulting from atomistic simulations.
Stably stratified Taylor–Green vortex simulations are performed by lattice Boltzmann methods (LBM) and compared to other recent works using Navier–Stokes solvers. The density variation is modeled with a separate distribution function in addition to the particle distribution function modeling the flow physics. Different stencils, forcing schemes, and collision models are tested and assessed. The overall agreement of the lattice Boltzmann solutions with reference solutions from other works is very good, even when no explicit subgrid model is used, but the quality depends on the LBM setup. Although the LBM forcing scheme is not decisive for the quality of the solution, the choice of the collision model and of the stencil are crucial for adequate solutions in underresolved conditions. The LBM simulations confirm the suppression of vertical flow motion for decreasing initial Froude numbers. To gain further insight into buoyancy effects, energy decay, dissipation rates, and flux coefficients are evaluated using the LBM model for various Froude numbers.
Molecular modeling is an important subdomain in the field of computational modeling, regarding both scientific and industrial applications. This is because computer simulations on a molecular level are a virtuous instrument to study the impact of microscopic on macroscopic phenomena. Accurate molecular models are indispensable for such simulations in order to predict physical target observables, like density, pressure, diffusion coefficients or energetic properties, quantitatively over a wide range of temperatures. Thereby, molecular interactions are described mathematically by force fields. The mathematical description includes parameters for both intramolecular and intermolecular interactions. While intramolecular force field parameters can be determined by quantum mechanics, the parameterization of the intermolecular part is often tedious. Recently, an empirical procedure, based on the minimization of a loss function between simulated and experimental physical properties, was published by the authors. Thereby, efficient gradient-based numerical optimization algorithms were used. However, empirical force field optimization is inhibited by the two following central issues appearing in molecular simulations: firstly, they are extremely time-consuming, even on modern and high-performance computer clusters, and secondly, simulation data is affected by statistical noise. The latter provokes the fact that an accurate computation of gradients or Hessians is nearly impossible close to a local or global minimum, mainly because the loss function is flat. Therefore, the question arises of whether to apply a derivative-free method approximating the loss function by an appropriate model function. In this paper, a new Sparse Grid-based Optimization Workflow (SpaGrOW) is presented, which accomplishes this task robustly and, at the same time, keeps the number of time-consuming simulations relatively small. This is achieved by an efficient sampling procedure for the approximation based on sparse grids, which is described in full detail: in order to counteract the fact that sparse grids are fully occupied on their boundaries, a mathematical transformation is applied to generate homogeneous Dirichlet boundary conditions. As the main drawback of sparse grids methods is the assumption that the function to be modeled exhibits certain smoothness properties, it has to be approximated by smooth functions first. Radial basis functions turned out to be very suitable to solve this task. The smoothing procedure and the subsequent interpolation on sparse grids are performed within sufficiently large compact trust regions of the parameter space. It is shown and explained how the combination of the three ingredients leads to a new efficient derivative-free algorithm, which has the additional advantage that it is capable of reducing the overall number of simulations by a factor of about two in comparison to gradient-based optimization methods. At the same time, the robustness with respect to statistical noise is maintained. This assertion is proven by both theoretical considerations and practical evaluations for molecular simulations on chemical example substances.
The elucidation of conformations and relative potential energies (rPEs) of small molecules has a long history across a diverse range of fields. Periodically, it is helpful to revisit what conformations have been investigated and to provide a consistent theoretical framework for which clear comparisons can be made. In this paper, we compute the minima, first- and second-order saddle points, and torsion-coupled surfaces for methanol, ethanol, propan-2-ol, and propanol using consistent high-level MP2 and CCSD(T) methods. While for certain molecules more rigorous methods were employed, the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pV5Z theory level was used throughout to provide relative energies of all minima and first-order saddle points. The rPE surfaces were uniformly computed at the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ level. To the best of our knowledge, this represents the most extensive study for alcohols of this kind, revealing some new aspects. Especially for propanol, we report several new conformations that were previously not investigated. Moreover, two metrics are included in our analysis that quantify how the selected surfaces are similar to one another and hence improve our understanding of the relationship between these alcohols.
This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows. In contrast to other LBM for compressible flows, the vertices are organized in cells, and interpolation polynomials up to fourth order are used to attain the off-vertex distribution function values. Differing from the recently introduced Particles on Demand (PoD) method , the method operates in a static, non-moving reference frame. Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance. The SLLBM solver allows for an independent time step size due to the integration along characteristics and for the use of unusual velocity sets, like the D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.
This work introduces a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows (with or without discontinuities). It makes use of a cell-wise representation of the simulation domain and utilizes interpolation polynomials up to fourth order to conduct the streaming step. The SLLBM solver allows for an independent time step size due to the absence of a time integrator and for the use of unusual velocity sets, like a D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the proposed model are shown in diverse example simulations of a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.