Accurate Thermochemistry and Kinetics of Molecules with Coupled Motions
Detailed reaction mechanisms are essential for modeling of energy and chemical engineering applications. This holds for fuel design applications as ingnition and combustion processes, but also for networks in polymerization. Often, the parameters of the fundamental chemical mechanisms are not experimentally accessible; nevertheless, they can be computed quantum-mechanically. Therefore one needs to model the electrons in the molecules on the one hand and the nuclei on the other.Copyright: © LTT
Nuclei move often in a complex coupled manner (cf. Figure of methanol dimer ). While methods describing the electrons are very accurate, modeling of the nuclear degrees of freedom turn out to be the bottleneck for the overall accuracy. Widely used models for nuclear motion (like the rigid-rotor harmonic-oscillator approximation) fail to describe coupled motions. Goal of this project is therefore a highly accurate computation of such coupled (and anharmonic) motions at the quantum-mechanical level. By using internal coordinates and some properties of the Jacobian , we develop a software that not only computes small systems with benchmark accuracy but also contains approximations for larger systems of technical interest, like biofuels  or solvents .
One such software is our Configuration Integral Monte Carlo Integration (CIMCI) algorithm . Rather than following the traditional approach of calculating an approximate model for nuclear motion from very few, high-accuracy energy calculations, CIMCI performs an exact numerical integration with a coarse-but-fast electronic model, like a force field, tight-binding method, or machine learning potential. Fully coupled handling of all nuclear degrees of freedom in this way produces substantial accuracy gains for some systems, even when force field-based CIMCI results are compared against coupled cluster-based results from other methods.
Another software developed by our group, TAMkinTools, focuses on molecular torsions and is an extension of the python package TAMkin. Using our code, the energy curve of torsions can be modeled more accurately and numerically stable, what we proved for the solvents mentioned above . Currently, we investigate the use of machine-learning methods for further improvements of the potentials.
Relevante Publications of our group
 Muhammad Umer and Kai Leonhard, Ab Initio Calculations of Thermochemical Properties of Methanol Clusters, The Journal of Physical Chemistry A, 2013, volume 117, issue 7, pages 1569-1582.
 Wassja A. Kopp and Kai Leonhard, General formulation of rovibrational kinetic energy operators and matrix elements in internal bond-angle coordinates using factorized Jacobians, The Journal of Chemical Physics, 2016, volume 145, issue 23, page 234102.
 Leif C. Kröger, Malte Döntgen, Dzmitry Firaha, Wassja A. Kopp and Kai Leonhard, Ab initio kinetics predictions for H-atom abstraction from diethoxymethane by hydrogen, methyl, and ethyl radicals and the subsequent unimolecular reactions, Proceedings of the Combustion Institute, 2019, volume 37, issue 1, pages 275-282.
 Hannes C. Gottschalk et al., The furan microsolvation blind challenge for quantum chemical methods: First steps, The Journal of Chemical Physics, 2018, volume 148, issue 1, page 014301.
 Gabriel Rath, Wassja A. Kopp and Kai Leonhard, Coupled Anharmonic Thermochemistry from Stratified Monte Carlo Integration, Journal of Chemical Information and Modeling, 2021, volume 61, issue 12, pages 5853-5870.
 Wassja A. Kopp, Matthias L. Mödden, Narasimhan Viswanathan, Gabriel Rath, and Kai Leonhard, Improved modeling of anharmonicity for furan microsolvation, Physical Chemistry Chemical Physics, 2023, volume 25, issue 16, pages 11316-11323.
Our research area on molecules with coupled motions comprises currently three projects that are operated by three researchers:
- In the project "Ab initio Thermochemistry and Kinetics of Molecules with Coupled Large-Amplitude Motions", funded by DFG in project number 403683184, the mathematical foundations of exact and approximate operators are expored and implemented into a software.
- In the project "High-accuracy ab initio rate constants for key reactions in bio-hybrid fuel combustion“, funded by the Cluster of Excellence 2186 "Fuel Science Center", ID 390919832, the description of reaction coordinates (and the orthogonal degrees of freedom in transition states) is investigated.
- In the finished project "Large amplitude motions (Work Package 4)", funded by the European Commission in EID "AutoChemo" with number 814143, semi-classical phase-space integration is used to determine strongly coupled degrees of freedom. The project focuses on the reduction of the coupled space and of the computational effort.