Learning to Use the Force: Fitting Repulsive Potentials in Density-Functional Tight-Binding with Gaussian Process Regression

2020 ◽  
Vol 16 (4) ◽  
pp. 2181-2191 ◽  
Author(s):  
Chiara Panosetti ◽  
Artur Engelmann ◽  
Lydia Nemec ◽  
Karsten Reuter ◽  
Johannes T. Margraf
Keyword(s):  
Gaussian Process ◽  
Density Functional ◽  
Tight Binding ◽  
Gaussian Process Regression ◽  
Repulsive Potentials

Learning to Use the Force: Fitting Repulsive Potentials in Density-Functional Tight-Binding with Gaussian Process Regression

2019 ◽  
Author(s):  
Chiara Panosetti ◽  
Artur Engelmann ◽  
Lydia Nemec ◽  
Karsten Reuter ◽  
Johannes T. Margraf
Keyword(s):  
Gaussian Process ◽  
Density Functional ◽  
Functional Form ◽  
Tight Binding ◽  
Gaussian Process Regression ◽  
Direct Access ◽  
Interatomic Potentials ◽  
Global Parameter ◽  
Repulsive Potentials ◽  
The Cost

The Density-Functional Tight Binding (DFTB) method is a popular semiempirical approximation to Density Functional Theory (DFT). In many cases, DFTB can provide comparable accuracy to DFT at a fraction of the cost, enabling simulations on length- and time-scales that are unfeasible with first principles DFT. At the same time (and in contrast to empirical interatomic potentials and force-fields), DFTB still offers direct access to electronic properties such as the band-structure. These advantages come at the cost of introducing empirical parameters to the method, leading to a reduced transferability compared to true first-principle approaches. Consequently, it would be very useful if the parameter-sets could be routinely adjusted for a given project. While fairly robust and transferable parameterization workflows exist for the electronic structure part of DFTB, the so-called repulsive potential Vrep poses a major challenge. In this paper we propose a machine-learning (ML) approach to fitting Vrep, using Gaussian Process Regression (GPR). The use of GPR circumvents the need for non-linear or global parameter optimization, while at the same time offering arbitrary flexibility in terms of the functional form. We also show that the proposed method can be applied to multiple elements at once, by fitting repulsive potentials for organic molecules containing carbon, hydrogen and oxygen. Overall, the new approach removes focus from the choice of functional form and parameterization procedure, in favour of a data-driven philosophy.

Learning to Use the Force: Fitting Repulsive Potentials in Density-Functional Tight-Binding with Gaussian Process Regression

2019 ◽  
Author(s):  
Chiara Panosetti ◽  
Artur Engelmann ◽  
Lydia Nemec ◽  
Karsten Reuter ◽  
Johannes T. Margraf
Keyword(s):  
Gaussian Process ◽  
Density Functional ◽  
Functional Form ◽  
Tight Binding ◽  
Gaussian Process Regression ◽  
Direct Access ◽  
Interatomic Potentials ◽  
Global Parameter ◽  
Repulsive Potentials ◽  
The Cost

The Density-Functional Tight Binding (DFTB) method is a popular semiempirical approximation to Density Functional Theory (DFT). In many cases, DFTB can provide comparable accuracy to DFT at a fraction of the cost, enabling simulations on length- and time-scales that are unfeasible with first principles DFT. At the same time (and in contrast to empirical interatomic potentials and force-fields), DFTB still offers direct access to electronic properties such as the band-structure. These advantages come at the cost of introducing empirical parameters to the method, leading to a reduced transferability compared to true first-principle approaches. Consequently, it would be very useful if the parameter-sets could be routinely adjusted for a given project. While fairly robust and transferable parameterization workflows exist for the electronic structure part of DFTB, the so-called repulsive potential Vrep poses a major challenge. In this paper we propose a machine-learning (ML) approach to fitting Vrep, using Gaussian Process Regression (GPR). The use of GPR circumvents the need for non-linear or global parameter optimization, while at the same time offering arbitrary flexibility in terms of the functional form. We also show that the proposed method can be applied to multiple elements at once, by fitting repulsive potentials for organic molecules containing carbon, hydrogen and oxygen. Overall, the new approach removes focus from the choice of functional form and parameterization procedure, in favour of a data-driven philosophy.

scholarly journals Generalized Density-Functional Tight-Binding Repulsive Potentials from Unsupervised Machine Learning

2018 ◽  
Vol 14 (5) ◽  
pp. 2341-2352 ◽  
Author(s):  
Julian J. Kranz ◽  
Maximilian Kubillus ◽  
Raghunathan Ramakrishnan ◽  
O. Anatole von Lilienfeld ◽  
Marcus Elstner
Keyword(s):  
Machine Learning ◽  
Density Functional ◽  
Tight Binding ◽  
Unsupervised Machine Learning ◽  
Repulsive Potentials

scholarly journals Density-Functional Tight-Binding Parameters for Bulk Zirconium: A Case Study for Repulsive Potentials

2021 ◽  
Vol 125 (10) ◽  
pp. 2184-2196
Author(s):  
Aulia Sukma Hutama ◽  
Chien-pin Chou ◽  
Yoshifumi Nishimura ◽  
Henryk A. Witek ◽  
Stephan Irle
Keyword(s):  
Density Functional ◽  
Tight Binding ◽  
Binding Parameters ◽  
Repulsive Potentials

Vapour Pressure Isotope Effect on Evaporation from Pure Organic Phases - a PIMD Approach

2020 ◽  
Author(s):  
Luis Vasquez ◽  
Agnieszka Dybala-Defratyka
Keyword(s):  
Path Integral ◽  
Vapour Pressure ◽  
Density Functional ◽  
Isotope Effects ◽  
Tight Binding ◽  
Decomposition Analysis ◽  
Energy Decomposition Analysis ◽  
Special Importance ◽  
Non Covalent Interactions ◽  
Covalent Interactions

<p></p><p>Very often in order to understand physical and chemical processes taking place among several phases fractionation of naturally abundant isotopes is monitored. Its measurement can be accompanied by theoretical determination to provide a more insightful interpretation of observed phenomena. Predictions are challenging due to the complexity of the effects involved in fractionation such as solvent effects and non-covalent interactions governing the behavior of the system which results in the necessity of using large models of those systems. This is sometimes a bottleneck and limits the theoretical description to only a few methods.<br> In this work vapour pressure isotope effects on evaporation from various organic solvents (ethanol, bromobenzene, dibromomethane, and trichloromethane) in the pure phase are estimated by combining force field or self-consistent charge density-functional tight-binding (SCC-DFTB) atomistic simulations with path integral principle. Furthermore, the recently developed Suzuki-Chin path integral is tested. In general, isotope effects are predicted qualitatively for most of the cases, however, the distinction between position-specific isotope effects observed for ethanol was only reproduced by SCC-DFTB, which indicates the importance of using non-harmonic bond approximations.<br> Energy decomposition analysis performed using the symmetry-adapted perturbation theory (SAPT) revealed sometimes quite substantial differences in interaction energy depending on whether the studied system was treated classically or quantum mechanically. Those observed differences might be the source of different magnitudes of isotope effects predicted using these two different levels of theory which is of special importance for the systems governed by non-covalent interactions.</p><br><p></p>

Quasi-Barrierless Submolecular Motion in Mechanically Interlocked Carbon Nanotubes

2020 ◽  
Author(s):  
Julia Villalva ◽  
Belén Nieto-Ortega ◽  
Manuel Melle-Franco ◽  
Emilio Pérez
Keyword(s):  
Density Functional ◽  
Close Contact ◽  
Tight Binding ◽  
Energetic Cost ◽  
Molecular Fragments ◽  
Activation Barriers ◽  
Flat Surfaces ◽  
Different Types ◽  
Atomically Flat ◽  
Derivatives Of

The motion of molecular fragments in close contact with atomically flat surfaces is still not fully understood. Does a more favourable interaction imply a larger barrier towards motion even if there are no obvious minima? Here, we use mechanically interlocked rotaxane-type derivatives of SWNTs (MINTs) featuring four different types of macrocycles with significantly different affinities for the SWNT thread as models to study this problem. Using molecular dynamics, we find that there is no direct correlation between the interaction energy of the macrocycle with the SWNT and its ability to move along or around it. Density functional tight-binding calculations reveal small (<2.5 Kcal·mol-1) activation barriers, the height of which correlates with the commensurability of the aromatic moieties in the macrocycle with the SWNT. Our results show that macrocycles in MINTs rotate and translate freely around and along SWNTs at room temperature, with an energetic cost lower than the rotation around the C−C bond in ethane.<br>

Exchange Spin Coupling from Gaussian Process Regression

2020 ◽  
Author(s):  
Marc Philipp Bahlke ◽  
Natnael Mogos ◽  
Jonny Proppe ◽  
Carmen Herrmann
Keyword(s):  
Machine Learning ◽  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Molecular Magnets ◽  
Molecular Structures ◽  
Spin Coupling ◽  
Structure Property ◽  
Data Set ◽  
Uncertainty Estimates

Heisenberg exchange spin coupling between metal centers is essential for describing and understanding the electronic structure of many molecular catalysts, metalloenzymes, and molecular magnets for potential application in information technology. We explore the machine-learnability of exchange spin coupling, which has not been studied yet. We employ Gaussian process regression since it can potentially deal with small training sets (as likely associated with the rather complex molecular structures required for exploring spin coupling) and since it provides uncertainty estimates (“error bars”) along with predicted values. We compare a range of descriptors and kernels for 257 small dicopper complexes and find that a simple descriptor based on chemical intuition, consisting only of copper-bridge angles and copper-copper distances, clearly outperforms several more sophisticated descriptors when it comes to extrapolating towards larger experimentally relevant complexes. Exchange spin coupling is similarly easy to learn as the polarizability, while learning dipole moments is much harder. The strength of the sophisticated descriptors lies in their ability to linearize structure-property relationships, to the point that a simple linear ridge regression performs just as well as the kernel-based machine-learning model for our small dicopper data set. The superior extrapolation performance of the simple descriptor is unique to exchange spin coupling, reinforcing the crucial role of choosing a suitable descriptor, and highlighting the interesting question of the role of chemical intuition vs. systematic or automated selection of features for machine learning in chemistry and material science.

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