Geometry optimization based on Gaussian process regression (GPR) was extended to internal coordinates. We used delocalized internal coordinates composed of distances and several types of angles and compared two methods of including them. In both cases, the GPR surrogate surface is trained on geometries in internal coordinates. In one case, it predicts the gradient in Cartesian coordinates and in the other, in internal coordinates. We tested both methods on a set of 30 small molecules and one larger Rh complex taken from the study of a catalytic mechanism. The former method is slightly more efficient, while the latter method is somewhat more robust. Both methods reduce the number of required optimization steps compared to GPR in Cartesian coordinates or the standard L-BFGS optimizer. We found it advantageous to use automatically adjusted hyperparameters to optimize them.
Atom probe tomography allows us to measure the three-dimensional composition of materials with up to atomic resolution by evaporating the material using high electric fields. Initially developed for metals, it is increasingly used for covalently bound structures. To aid the interpretation of the obtained fragmentation pattern, we modeled the fragmentation and desorption of self-assembled monolayers of thiolate molecules on a gold surface in strong electrostatic fields using density functional theory. We used a cluster model and a periodic model of amino-undecanethiolate, NH 2 (CH 2 ) 11 S, and fluoro-decanethiolate, CF 3 (CF 2 ) 7 (CH 2 ) 2 S. In the former molecule, the fragment CH 2 NH 2 + was found to evaporate at fields of 5.4−7.7 V/nm. It was followed by different hydrocarbon fragments. Fluorodecanethiolate evaporates CF 3 + at fields of 5.7−6.7 V/nm in the cluster model and at 15.4−23.1 V/nm in the periodic model, followed by CF 2 + and C 2 F 4 2+ . Detailed analysis of the electronic structure during the evaporation process revealed a stepwise accumulation of the charge in the head groups exposed to the strongest fields, followed by dissociation of covalent bonds. These observations will facilitate the analysis of atom probe experiments of covalently bound structures.
The positions of grid points for representing a multidimensional potential energy surface (PES) have a non-negligible impact on its accuracy and the associated computational effort for its generation. Six different positioning schemes were studied for PESs represented by n-mode expansions as needed for the accurate calculation of anharmonic vibrational frequencies by means of vibrational configuration interaction theory. A static approach, which has successfully been used in many applications, and five adaptive schemes based on Gaussian process regression have been investigated with respect to the number of necessary grid points and the accuracy of the fundamental modes for a small set of test molecules. A comparison with a related, more sophisticated, and consistent approach by Christiansen et al. is provided. The impact of the positions of the ab initio grid points is discussed for multilevel PESs, for which the computational effort of the individual electronic structure calculations decreases for increasing orders of the n-mode expansion. As a result of that, the ultimate goal is not the maximal reduction of grid points but rather the computational cost, which is not directly related.
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