Exploring speciation and reactivity with machine learning and molecular dynamics

Methods

A combination of different quantum chemical software was employed: Gaussian 16 and xTB/CREST. Gaussian was used for the optimization of stationary points such as intermediates and transition states as well as for Born-Oppenheimer molecular dynamics (BOMD) at the DFT level. The xTB package was used to conduct molecular dynamics simulations with explicit solvation. While a BOMD approach using DFT is our preferred approach for molecular dynamics in gas phase, solvation can only be accounted for implicitly (by means of solvation models). Involving explicit solvent molecules would require simulation times of hundreds of picoseconds to observe solvent motion and reactive events. Although computationally affordable for up to 5 ps (up to 80 atoms), BOMD becomes unfeasible for longer simulation times. However, the xTB package utilizes a rapid semi-empirical method that is capable to dynamically study systems up to 1000 atoms. Therefore, using xTB gives the unique opportunity to study mechanisms dynamically in solution at reasonable accuracy, even for larger systems. CREST is part of the xTB program package and allows sampling the best conformation for a structure. This is of particular importance for the larger metal complexes, which possess increased degrees of freedom.

Results

Subproject 1 is focused on dynamic aspects of reaction mechanisms using the nucleophilic aromatic substitution reaction as an example. Subproject 2 aims at utilizing machine learning to solve speciation problems of nickel catalysts that are of relevance for carbon dioxide activation.

(1) Stepwise vs concerted mechanism in nucleophilic aromatic substitution
Previously we investigated the competition between stepwise and concerted mechanisms in the nucleophilic aromatic substitution of arenes. Employing both static DFT and molecular dynamics, our investigation suggested that the lifespan of the intermediate σ-complex associated with the stepwise mechanism is frequently short and at times comparable to that of a transition state, thereby posing a challenge to the conventional comprehension of these reactions. In this project, we focused on a subset of nucleophilic aromatic substitutions with fluoride as the leaving group and the methoxide anion as the nucleophile. The rationale behind this focus stems from the observation that this particular combination showed a nuanced interplay of stepwise and concerted mechanisms, depending on the nature of the substrate. From a combinatorically constructed chemical space, substrates for further investigation were chosen by calculating their electron affinity, a method proven effective in literature to distinguish between concerted and stepwise mechanisms. To broaden our initial dynamic assessment employing xTB with explicit solvation, we extended our investigation by conducting an additional 50 trajectories per reaction. This step was taken to mitigate the influence of potential statistical fluctuations in measured lifetimes. To validate our prior results obtained with semi-empirical xTB, we also conducted additional BOMD simulations at the DFT level.

(2) Nickel catalysts for CO₂ insertion
As part of our prior work, we were able to show using DFT calculations that Ni^(I) complexes are superior to their Ni^(II) analogues in the context of CO₂ insertion into Ni-C bonds. The stability of the key intermediate L-Ni^(I)-R is generally affected by the employed ligand (L) and the residue that CO₂ is inserted to (R). In this project we aim to identify stable species, that can facilitate CO₂ insertion, using an unsupervised machine learning workflow. Our initial focus was on the ligand (L) and due to their prevalence in the literature we concentrated on bidentate phosphine ligands. Calculations were performed for a variety of metal-ligand species of different oxidation and ligation state as well as different nuclearity, incorporating conformational sampling via xTB and subsequent identification of optimal conformers through DFT. Descriptors for the unsupervised machine learning were then extracted. To establish a comprehensive ligand database, we further expanded our scope for a selection of monodentate phosphines, and nitrogen-based ligands. Regarding the organic moiety (R), we observed that most clustering approaches led to splits based on the R group into aliphatic and aromatic groups. Consequently, we decided to initially focus on aromatic R.

Discussion

For subproject 1 our findings reaffirmed the observation of short intermediate lifetimes. Notably, this phenomenon was found to be disconnected from the free energy profile obtained by static DFT, therefore highlighting the importance of molecular dynamics. The nuanced disparity prompted a deeper exploration and analysis. In our commitment to methodological rigor, we are now evaluating different DFT methods, adding an extra layer of verification to ensure the validity of our observation. In subproject 2 we tested different machine learning models, employing different methods for feature selection, which will now be further evaluated.

Additional Project Information

DFG classification: 301-02 Organic Molecular Chemistry
Software: CREST, Gaussian16
Cluster: CLAIX