Jan Hamaekers

The nano-branched structure of cementitious calcium–silicate–hydrate gel

Manipulation of concrete at the nanoscale is severely limited by the lack of precise knowledge on the nanostructure of calcium–silicate–hydrate gel, the main binding phase of cement-based materials. Here we report a computational description of C–S–H, which for the first time reconciles the existing structural and colloidal/gel-like models. Our molecular dynamic simulations predict the formation of a branched three-dimensional C–S–H solid network where the segmental branches (SB) are ∼3 × 3 × 6 nm-sized. The presented simulations account well for the features observed through Small Angle Neutron Scattering (SANS) experiments as well with various observations made by synchrotron X-ray, Nuclear Magnetic Resonance (NMR), and Inelastic Neutron Spectroscopy (INS) measurements and lead to a better understanding of the cementitious nanostructure formation and morphology.

Tensor Product Multiscale Many-Particle Spaces with Finite-Order Weights for the Electronic Schrödinger Equation

Abstract In this article we combine the favorable properties of efficient Gaussian type orbitals basis sets, which are applied with good success in conventional electronic structure methods, and tensor product multiscale bases, which provide guaranteed convergence rates and allow for adaptive resolution. To this end, we develop and study a new approach for the treatment of the electronic Schrödinger equation based on a modified adaptive sparse grid technique and a certain particle-wise decomposition with respect to one-particle functions obtained by a nonlinear rank-1 approximation. Here, we employ a multiscale Gaussian frame for the sparse grid spaces and we use Gaussian type orbitals to represent the rank-1 approximation. With this approach we are able to treat small atoms and molecules with up to six electrons.

Fast Discrete Fourier Transform on Generalized Sparse Grids

In this paper, we present an algorithm for trigonometric interpolation of multivariate functions on generalized sparse grids and study its application for the approximation of functions in periodic Sobolev spaces of dominating mixed smoothness. In particular, we derive estimates for the error and the cost. We construct interpolants with a computational cost complexity which is substantially lower than for the standard full grid case. The associated generalized sparse grid interpolants have the same approximation order as the standard full grid interpolants, provided that certain additional regularity assumptions on the considered functions are fulfilled. Numerical results validate our theoretical findings.

LC-GAP: Localized Coulomb Descriptors for the Gaussian Approximation Potential

We introduce a novel class of localized atomic environment representations based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system for generating atomic potentials through machine learning (ML). Tests on the QM7, QM7b and GDB9 biomolecular datasets demonstrate that potentials created with LC-GAP can successfully predict atomization energies for molecules larger than those used for training to chemical accuracy, and can (in the case of QM7b) also be used to predict a range of other atomic properties with accuracy in line with the recent literature. As the best-performing representation has only linear dimensionality in the number of atoms in a local atomic environment, this represents an improvement in both prediction accuracy and computational cost when compared to similar Coulomb matrix-based methods.

An Adaptive Multiscale Approach for Electronic Structure Methods

In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schrodinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the bond order dissection ANOVA approach introduced in [M. Griebel, J. Hamaekers, and F. Heber, Extraction of Quantifiable Information from Complex Systems, Springer, New York, pp. 211--235; F. Heber, Ph.D. thesis, Intitut fur Numerische Simulation, Rheinische Friedrich-Wilhelms-Universitat Bonn, 2014], with a hierarchy of basis sets of increasing order. Here, the energy is represented as a finite sum of contributions associated to subsets of nuclei and basis sets in a telescoping sum like fashion. Under the assumption of data locality of the electronic density (nearsightedness of electronic matter), the terms of this expansion decay rapidly and higher terms may be neglected. We further extend the approach in a dimension-adaptive fashion to generate quasi-optimal approximations, i.e., a specific tr...

ATK-ForceField: a new generation molecular dynamics software package

ATK-ForceField is a software package for atomistic simulations using classical interatomic potentials. It is implemented as a part of the Atomistix ToolKit (ATK), which is a Python programming environment that makes it easy to create and analyze both standard and highly customized simulations. This paper will focus on the atomic interaction potentials, molecular dynamics, and geometry optimization features of the software, however, many more advanced modeling features are available. The implementation details of these algorithms and their computational performance will be shown. We present three illustrative examples of the types of calculations that are possible with ATK-ForceField: modeling thermal transport properties in a silicon germanium crystal, vapor deposition of selenium molecules on a selenium surface, and a simulation of creep in a copper polycrystal.

A Bond Order Dissection ANOVA Approach for Efficient Electronic Structure Calculations

In this article, we present a new decomposition approach for the efficient approximate calculation of the electronic structure problem for molecules. It is based on a dimension-wise decomposition of the space the underlying Schrodinger equation lives in, i.e. \(\mathbb{R}^{3(M+N)}\), where M is the number of nuclei and N is the number of electrons. This decomposition is similar to the ANOVA-approach (analysis of variance) which is well-known in statistics. It represents the energy as a finite sum of contributions which depend on the positions of single nuclei, of pairs of nuclei, of triples of nuclei, and so on. Under the assumption of locality of electronic wave functions, the higher order terms in this expansion decay rapidly and may therefore be omitted. Furthermore, additional terms are eliminated according to the bonding structure of the molecule. This way, only the calculation of the electronic structure of local parts, i.e. small subsystems of the overall system, is necessary to approximate the total ground state energy. To determine the required subsystems, we employ molecular graph theory combined with molecular bonding knowledge. In principle, the local electronic subproblems may be approximately evaluated with whatever technique is appropriate, e.g. HF, CC, CI, or DFT. From these local energies, the total energy of the overall system is then approximately put together in a telescoping sum like fashion. Thus, if the size of the local subproblems is independent of the size of the overall molecular system, linear scaling is directly obtained. We discuss the details of our new approach and apply it to both, various small test systems and interferon alpha as an example of a large biomolecule.