Oliver T. Unke

Toolkit for the Construction of Reproducing Kernel-Based Representations of Data: Application to Multidimensional Potential Energy Surfaces

In the early days of computation, slow processor speeds limited the amount of data that could be generated and used for scientific purposes. In the age of big data, the limiting factor usually is the method with which large amounts of data are analyzed and useful information is extracted. A typical example from chemistry are high-level ab initio calculations for small systems, which have nowadays become feasible even if energies at many different geometries are required. Molecular dynamics simulations often require several thousand distinct trajectories to be run. Under such circumstances suitable analytical representations of potential energy surfaces (PESs) based on ab initio calculations are required to propagate the dynamics at an acceptable cost. In this work we introduce a toolkit which allows the automatic construction of multidimensional PESs from gridded ab initio data based on reproducing kernel Hilbert space (RKHS) theory. The resulting representations require no tuning of parameters and allow energy and force evaluations at ab initio quality at the same cost as empirical force fields. Although the toolkit is primarily intended for constructing multidimensional potential energy surfaces for molecular systems, it can also be used for general machine learning purposes. The software is published under the MIT license and can be downloaded, modified, and used in other projects for free.

Collision-induced rotational excitation in N2+(2Σg+,v=0)–Ar: Comparison of computations and experiment

The collisional dynamics of N2 (+)((2)Σg (+)) cations with Ar atoms is studied using quasi-classical simulations. N2 (+)-Ar is a proxy to study cooling of molecular ions and interesting in its own right for molecule-to-atom charge transfer reactions. An accurate potential energy surface (PES) is constructed from a reproducing kernel Hilbert space (RKHS) interpolation based on high-level ab initio data. The global PES including the asymptotics is fully treated within the realm of RKHS. From several ten thousand trajectories, the final state distribution of the rotational quantum number of N2 (+) after collision with Ar is determined. Contrary to the interpretation of previous experiments which indicate that up to 98% of collisions are elastic and conserve the quantum state, the present simulations find a considerably larger number of inelastic collisions which supports more recent findings.

Minimal distributed charges: Multipolar quality at the cost of point charge electrostatics

Most empirical force fields use atom-centered point charges (PCs) to represent the electrostatic potential (ESP) around molecules. While such PC models are computationally efficient, they are unable to capture anisotropic electronic features, such as σ holes or lone pairs. These features are better described using atomic multipole (MTP) moments, which significantly improve the quality of the resulting ESP. However, the improvement comes at the expense of a considerably increased computational complexity and cost for calculating the interaction energies and forces. In the present work, a novel minimal distributed charge model (MDCM) based on off-centered point charges is presented and the quality of the resulting ESP is compared to the performance of MTPs and atom-centered PC models for several test molecules. All three models are fitted using the same algorithm based on differential evolution, which is available as a Fortran90 program from the authors upon request. We show that the MDCM is capable of approximating the reference ab initio ESP with an accuracy as good as, or better than, MTPs without the need for computationally expensive higher order multipoles. Further it is demonstrated that the MDCM is numerically stable in molecular dynamics simulations and is able to reproduce electrostatic interaction energies and thermodynamic quantities with the same accuracy as MTPs at reduced computational cost.

A reactive, scalable, and transferable model for molecular energies from a neural network approach based on local information

Despite the ever-increasing computer power, accurate ab initio calculations for large systems (thousands to millions of atoms) remain infeasible. Instead, approximate empirical energy functions are used. Most current approaches are either transferable between different chemical systems, but not particularly accurate, or they are fine-tuned to a specific application. In this work, a data-driven method to construct a potential energy surface based on neural networks is presented. Since the total energy is decomposed into local atomic contributions, the evaluation is easily parallelizable and scales linearly with system size. With prediction errors below 0.5 kcal mol-1 for both unknown molecules and configurations, the method is accurate across chemical and configurational space, which is demonstrated by applying it to datasets from nonreactive and reactive molecular dynamics simulations and a diverse database of equilibrium structures. The possibility to use small molecules as reference data to predict larger structures is also explored. Since the descriptor only uses local information, high-level ab initio methods, which are computationally too expensive for large molecules, become feasible for generating the necessary reference data used to train the neural network.

Nonadiabatic effects in electronic and nuclear dynamics

Due to their very nature, ultrafast phenomena are often accompanied by the occurrence of nonadiabatic effects. From a theoretical perspective, the treatment of nonadiabatic processes makes it necessary to go beyond the (quasi) static picture provided by the time-independent Schrödinger equation within the Born-Oppenheimer approximation and to find ways to tackle instead the full time-dependent electronic and nuclear quantum problem. In this review, we give an overview of different nonadiabatic processes that manifest themselves in electronic and nuclear dynamics ranging from the nonadiabatic phenomena taking place during tunnel ionization of atoms in strong laser fields to the radiationless relaxation through conical intersections and the nonadiabatic coupling of vibrational modes and discuss the computational approaches that have been developed to describe such phenomena. These methods range from the full solution of the combined nuclear-electronic quantum problem to a hierarchy of semiclassical approaches and even purely classical frameworks. The power of these simulation tools is illustrated by representative applications and the direct confrontation with experimental measurements performed in the National Centre of Competence for Molecular Ultrafast Science and Technology.

Migration of small ligands in globins: Xe diffusion in truncated hemoglobin N

In heme proteins, the efficient transport of ligands such as NO or O2 to the binding site is achieved via ligand migration networks. A quantitative assessment of ligand diffusion in these networks is thus essential for a better understanding of the function of these proteins. For this, Xe migration in truncated hemoglobin N (trHbN) of Mycobacterium Tuberculosis was studied using molecular dynamics simulations. Transitions between pockets of the migration network and intra-pocket relaxation occur on similar time scales (10 ps and 20 ps), consistent with low free energy barriers (1-2 kcal/mol). Depending on the pocket from where Xe enters a particular transition, the conformation of the side chains lining the transition region differs which highlights the coupling between ligand and protein degrees of freedom. Furthermore, comparison of transition probabilities shows that Xe migration in trHbN is a non-Markovian process. Memory effects arise due to protein rearrangements and coupled dynamics as Xe moves through it.

Molecular Oxygen Formation in Interstellar Ices Does Not Require Tunneling

The formation of molecular oxygen in and on amorphous ice in the interstellar medium requires oxygen diffusion to take place. Recent experiments suggest that this process involves quantum tunneling of the oxygen atoms at sufficiently low temperatures. Fitting experimental diffusion rates between 6 and 25 K to an expression that accounts for the roughness of the surface yields excellent agreement. The molecular dynamics of adsorbed oxygen is characterized by rapid intrasite dynamics, followed by intersite transitions over distances of ∼10 Å. Explicit simulations using a realistic free-energy surface for oxygen diffusion on amorphous ice down to 10 K show that quantum tunneling is not required for mobility of adsorbed oxygen. This is confirmed by comparing quantum and classical simulations using the same free-energy surface. The ratio of diffusional and desorption energy Edif/ Edes = 275/1082 ≈ 0.3 is at the lower end of typically used values but is still consistent with the assumptions made in models for interstellar chemistry.