scholarly journals Active Machine Learning for Chemical Dynamics Simulations. I. Estimating the Energy Gradient

2021 ◽  
Author(s):  
Kazuumi Fujioka ◽  
Yuheng Luo ◽  
Rui Sun
Keyword(s):  
Machine Learning ◽  
Ab Initio ◽  
Density Functional ◽  
Computational Cost ◽  
Basis Sets ◽  
Intrinsic Reaction Coordinate ◽  
Chemical Systems ◽  
Energy Gradient ◽  
Gradient Calculation ◽  
Dynamics Simulations

Ab initio molecular dymamics (AIMD) simulation studies are a direct way to visualize chemical reactions and help elucidate non-statistical dynamics that does not follow the intrinsic reaction coordinate. However, due to the enormous amount of the ab initio energy gradient calculations needed for AIMD, it has been largely restrained to limited sampling and low level of theory (i.e., density functional theory with small basis sets). To overcome this issue, a number of machine learning (ML) methods have been employed to predict the energy gradient of the system of interest. In this manuscript, we outline the theoretical foundations of a novel ML method which trains from a varying set of atomic positions and their energy gradients, called interpolating moving ridge regression (IMRR), and directly predicts the energy gradient of a new set of atomic positions. Several key theoretical findings are presented regarding the inputs used to train IMRR and the predicted energy gradient. A hyperparameter used to guide IMRR is rigorously examined as well. The method is then applied to three bimolecular reactions studied with AIMD, including HBr+ + CO2, H2S + CH, and C4H2 + CH, to demonstrate IMRR’s performance on different chemical systems of different sizes. This manuscript also compares the computational cost of the energy gradient calculation with IMRR vs. ab initio, and the results highlight IMRR as a viable option to greatly increase the efficiency of AIMD.

scholarly journals Active Machine Learning for Chemical Dynamics Simulations. I. Estimating the Energy Gradient

2021 ◽  
Author(s):  
Kazuumi Fujioka ◽  
Rui Sun
Keyword(s):  
Machine Learning ◽  
Ab Initio ◽  
Density Functional ◽  
Computational Cost ◽  
Basis Sets ◽  
Intrinsic Reaction Coordinate ◽  
Chemical Systems ◽  
Energy Gradient ◽  
Gradient Calculation ◽  
Dynamics Simulations

Ab initio molecular dymamics (AIMD) simulation studies are a direct way to visualize chemical reactions and help elucidate non-statistical dynamics that does not follow the intrinsic reaction coordinate. However, due to the enormous amount of the ab initio energy gradient calculations needed for AIMD, it has been largely restrained to limited sampling and low level of theory (i.e., density functional theory with small basis sets). To overcome this issue, a number of machine learning (ML) methods have been employed to predict the energy gradient of the system of interest. In this manuscript, we outline the theoretical foundations of a novel ML method which trains from a varying set of atomic positions and their energy gradients, called interpolating moving ridge regression (IMRR), and directly predicts the energy gradient of a new set of atomic positions. Several key theoretical findings are presented regarding the inputs used to train IMRR and the predicted energy gradient. A hyperparameter used to guide IMRR is rigorously examined as well. The method is then applied to three bimolecular reactions studied with AIMD, including HBr+ + CO2, H2S + CH, and C4H2 + CH, to demonstrate IMRR’s performance on different chemical systems of different sizes. This manuscript also compares the computational cost of the energy gradient calculation with IMRR vs. ab initio, and the results highlight IMRR as a viable option to greatly increase the efficiency of AIMD.

scholarly journals Active Machine Learning for Chemical Dynamics Simulations. I. Estimating the Energy Gradient

2021 ◽  
Author(s):  
Kazuumi Fujioka ◽  
Rui Sun
Keyword(s):  
Machine Learning ◽  
Ab Initio ◽  
Density Functional ◽  
Computational Cost ◽  
Basis Sets ◽  
Intrinsic Reaction Coordinate ◽  
Chemical Systems ◽  
Energy Gradient ◽  
Gradient Calculation ◽  
Dynamics Simulations

Ab initio molecular dymamics (AIMD) simulation studies are a direct way to visualize chemical reactions and help elucidate non-statistical dynamics that does not follow the intrinsic reaction coordinate. However, due to the enormous amount of the ab initio energy gradient calculations needed for AIMD, it has been largely restrained to limited sampling and low level of theory (i.e., density functional theory with small basis sets). To overcome this issue, a number of machine learning (ML) methods have been employed to predict the energy gradient of the system of interest. In this manuscript, we outline the theoretical foundations of a novel ML method which trains from a varying set of atomic positions and their energy gradients, called interpolating moving ridge regression (IMRR), and directly predicts the energy gradient of a new set of atomic positions. Several key theoretical findings are presented regarding the inputs used to train IMRR and the predicted energy gradient. A hyperparameter used to guide IMRR is rigorously examined as well. The method is then applied to three bimolecular reactions studied with AIMD, including HBr+ + CO2, H2S + CH, and C4H2 + CH, to demonstrate IMRR’s performance on different chemical systems of different sizes. This manuscript also compares the computational cost of the energy gradient calculation with IMRR vs. ab initio, and the results highlight IMRR as a viable option to greatly increase the efficiency of AIMD.

scholarly journals Machine Learning Accurate Exchange and Correlation Functionals of the Electronic Density

2019 ◽  
Author(s):  
Sebastian Dick ◽  
Marivi Fernandez-Serra
Keyword(s):  
Machine Learning ◽  
Density Functional ◽  
Computational Cost ◽  
Atomic Scale ◽  
Training Data ◽  
Supervised Machine Learning ◽  
Electronic Density ◽  
Standard Formalism ◽  
Dynamics Simulations ◽  
Exchange And Correlation

Density Functional Theory (DFT) is the standard formalism to study the electronic structure of matter<br>at the atomic scale. The balance between accuracy and computational cost that<br>DFT-based simulations provide allows researchers to understand the structural and dynamical properties of increasingly large and complex systems at the quantum mechanical level.<br>In Kohn-Sham DFT, this balance depends on the choice of exchange and correlation functional, which only exists<br>in approximate form. Increasing the non-locality of this functional and climbing the figurative Jacob's ladder of DFT, one can systematically reduce the amount of approximation involved and thus approach the exact functional. Doing this, however, comes at the price of increased computational cost, and so, for extensive systems, the predominant methods of choice can still be found within the lower-rung approximations. <br>Here we propose a framework to create highly accurate density functionals by using supervised machine learning, termed NeuralXC. These machine-learned functionals are designed to lift the accuracy of local and semilocal functionals to that provided by more accurate methods while maintaining their efficiency. We show that the functionals learn a meaningful representation of the physical information contained in the training data, making them transferable across systems. We further demonstrate how a functional optimized on water can reproduce experimental results when used in molecular dynamics simulations. Finally, we discuss the effects that our method has on self-consistent electron densities by comparing these densities to benchmark coupled-cluster results.

scholarly journals Methanol Carbonylation over Acid Mordenite: Insights from Ab Initio Molecular Dynamics and Machine Learning Thermodynamic Perturbation Theory

2021 ◽  
Author(s):  
Monika Gešvandtnerová ◽  
Dario Rocca ◽  
Tomas Bucko
Keyword(s):  
Machine Learning ◽  
Molecular Dynamics ◽  
Perturbation Theory ◽  
Ab Initio ◽  
Molecular Dynamics Simulations ◽  
Density Functional ◽  
Ab Initio Molecular Dynamics ◽  
Thermodynamic Perturbation Theory ◽  
Dynamics Simulations ◽  
Thermodynamic Perturbation

<div>In this work we present a detailed \textit{ab initio} study of the carbonylation reaction of methoxy groups in the zeolite mordenite, as it is the rate determining step in a series of elementary reactions leading to ethanol. </div><div>For the first time we employ full molecular dynamics simulations to evaluate free energies of activation for the reactions in side pockets and main channels. Results show that the reaction in the side pocket is preferred and, when dispersion interactions are taken into account, this preference becomes even stronger. This conclusion is confirmed using multiple levels of density functional theory approximations with (PBE-D2, PBE-MBD, and vdW-DF2-B86R) or without (PBE, HSE06) dispersion corrections. These calculations, that in principle would require several demanding molecular dynamics simulations, were made possible at a minimal computational cost by using a newly developed approach that combines thermodynamic perturbation theory with machine learning.</div>

scholarly journals Machine Learning a Highly Accurate Exchange and Correlation Functional of the Electronic Density

2019 ◽  
Author(s):  
Sebastian Dick ◽  
Marivi Fernandez-Serra
Keyword(s):  
Machine Learning ◽  
Density Functional ◽  
Computational Cost ◽  
Atomic Scale ◽  
Training Data ◽  
Supervised Machine Learning ◽  
Electronic Density ◽  
Standard Formalism ◽  
Dynamics Simulations ◽  
Exchange And Correlation

Density Functional Theory (DFT) is the standard formalism to study the electronic structure of matter<br>at the atomic scale. The balance between accuracy and computational cost that<br>DFT-based simulations provide allows researchers to understand the structural and dynamical properties of increasingly large and complex systems at the quantum mechanical level.<br>In Kohn-Sham DFT, this balance depends on the choice of exchange and correlation functional, which only exists<br>in approximate form. Increasing the non-locality of this functional and climbing the figurative Jacob's ladder of DFT, one can systematically reduce the amount of approximation involved and thus approach the exact functional. Doing this, however, comes at the price of increased computational cost, and so, for extensive systems, the predominant methods of choice can still be found within the lower-rung approximations. <br>Here we propose a framework to create highly accurate density functionals by using supervised machine learning, termed NeuralXC. These machine-learned functionals are designed to lift the accuracy of local and semilocal functionals to that provided by more accurate methods while maintaining their efficiency. We show that the functionals learn a meaningful representation of the physical information contained in the training data, making them transferable across systems. We further demonstrate how a functional optimized on water can reproduce experimental results when used in molecular dynamics simulations. Finally, we discuss the effects that our method has on self-consistent electron densities by comparing these densities to benchmark coupled-cluster results.

scholarly journals Methanol Carbonylation over Acid Mordenite: Insights from Ab Initio Molecular Dynamics and Machine Learning Thermodynamic Perturbation Theory

2021 ◽  
Author(s):  
Monika Gešvandtnerová ◽  
Dario Rocca ◽  
Tomas Bucko
Keyword(s):  
Machine Learning ◽  
Molecular Dynamics ◽  
Perturbation Theory ◽  
Ab Initio ◽  
Molecular Dynamics Simulations ◽  
Density Functional ◽  
Ab Initio Molecular Dynamics ◽  
Thermodynamic Perturbation Theory ◽  
Dynamics Simulations ◽  
Thermodynamic Perturbation

<div>In this work we present a detailed \textit{ab initio} study of the carbonylation reaction of methoxy groups in the zeolite mordenite, as it is the rate determining step in a series of elementary reactions leading to ethanol. </div><div>For the first time we employ full molecular dynamics simulations to evaluate free energies of activation for the reactions in side pockets and main channels. Results show that the reaction in the side pocket is preferred and, when dispersion interactions are taken into account, this preference becomes even stronger. This conclusion is confirmed using multiple levels of density functional theory approximations with (PBE-D2, PBE-MBD, and vdW-DF2-B86R) or without (PBE, HSE06) dispersion corrections. These calculations, that in principle would require several demanding molecular dynamics simulations, were made possible at a minimal computational cost by using a newly developed approach that combines thermodynamic perturbation theory with machine learning.</div>

Active Learning Accelerates Ab Initio Molecular Dynamics on Pericyclic Reactive Energy Surfaces

2020 ◽  
Author(s):  
Shi Jun Ang ◽  
Wujie Wang ◽  
Daniel Schwalbe-Koda ◽  
Simon Axelrod ◽  
Rafael Gomez-Bombarelli
Keyword(s):  
Molecular Dynamics ◽  
Potential Energy ◽  
Transition State ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Energy Surface ◽  
Computational Cost ◽  
Reactive Trajectories ◽  
Dynamics Simulations ◽  
Energy Surfaces

<div>Modeling dynamical effects in chemical reactions, such as post-transition state bifurcation, requires <i>ab initio</i> molecular dynamics simulations due to the breakdown of simpler static models like transition state theory. However, these simulations tend to be restricted to lower-accuracy electronic structure methods and scarce sampling because of their high computational cost. Here, we report the use of statistical learning to accelerate reactive molecular dynamics simulations by combining high-throughput ab initio calculations, graph-convolution interatomic potentials and active learning. This pipeline was demonstrated on an ambimodal trispericyclic reaction involving 8,8-dicyanoheptafulvene and 6,6-dimethylfulvene. With a dataset size of approximately</div><div>31,000 M062X/def2-SVP quantum mechanical calculations, the computational cost of exploring the reactive potential energy surface was reduced by an order of magnitude. Thousands of virtually costless picosecond-long reactive trajectories suggest that post-transition state bifurcation plays a minor role for the reaction in vacuum. Furthermore, a transfer-learning strategy effectively upgraded the potential energy surface to higher</div><div>levels of theory ((SMD-)M06-2X/def2-TZVPD in vacuum and three other solvents, as well as the more accurate DLPNO-DSD-PBEP86 D3BJ/def2-TZVPD) using about 10% additional calculations for each surface. Since the larger basis set and the dynamic correlation capture intramolecular non-covalent interactions more accurately, they uncover longer lifetimes for the charge-separated intermediate on the more accurate potential energy surfaces. The character of the intermediate switches from entropic to thermodynamic upon including implicit solvation effects, with lifetimes increasing with solvent polarity. Analysis of 2,000 reactive trajectories on the chloroform PES shows a qualitative agreement with the experimentally-reported periselectivity for this reaction. This overall approach is broadly applicable and opens a door to the study of dynamical effects in larger, previously-intractable reactive systems.</div>

BAND NN: A Deep Learning Framework For Energy Prediction and Geometry Optimization of Organic Small Molecules

2019 ◽  
Author(s):  
Siddhartha Laghuvarapu ◽  
Yashaswi Pathak ◽  
U. Deva Priyakumar
Keyword(s):  
Machine Learning ◽  
Density Functional ◽  
Computational Cost ◽  
Geometry Optimization ◽  
Dft Methods ◽  
Energy Prediction ◽  
Machine Learning Model ◽  
Equilibrium Structures ◽  
High Level ◽  
Non Equilibrium

Recent advances in artificial intelligence along with development of large datasets of energies calculated using quantum mechanical (QM)/density functional theory (DFT) methods have enabled prediction of accurate molecular energies at reasonably low computational cost. However, machine learning models that have been reported so far requires the atomic positions obtained from geometry optimizations using high level QM/DFT methods as input in order to predict the energies, and do not allow for geometry optimization. In this paper, a transferable and molecule-size independent machine learning model (BAND NN) based on a chemically intuitive representation inspired by molecular mechanics force fields is presented. The model predicts the atomization energies of equilibrium and non-equilibrium structures as sum of energy contributions from bonds (B), angles (A), nonbonds (N) and dihedrals (D) at remarkable accuracy. The robustness of the proposed model is further validated by calculations that span over the conformational, configurational and reaction space. The transferability of this model on systems larger than the ones in the dataset is demonstrated by performing calculations on select large molecules. Importantly, employing the BAND NN model, it is possible to perform geometry optimizations starting from non-equilibrium structures along with predicting their energies.

Quantum-Chemical Ab Initio Calculations on Inda- and Thallabenzene (C5H5In and C5H5Tl) and their Structural Isomers η5-C5H5In and η5-C5H5Tl

2018 ◽  
Vol 71 (3) ◽  
pp. 102
Author(s):  
Emma Persoon ◽  
Yuekui Wang ◽  
Gerhard Raabe
Keyword(s):  
Ab Initio ◽  
Quantum Chemical ◽  
Density Functional ◽  
Single Point ◽  
Normal Modes ◽  
Dft Method ◽  
Basis Sets ◽  
Triplet States ◽  
Structural Isomers ◽  
Td Dft

Quantum-chemical ab initio, time-independent, as well as time-dependent density functional theory (TD-DFT) calculations were performed on the so far elusive heterocycles inda- and thallabenzene (C5H5In and C5H5Tl), employing several different methods (MP2, CISD, CCSD, CCSD(T), BD, BD(T), QCISD, QCISD(T), CASSCF, DFT/B3LYP), effective core potentials, and different basis sets. While calculations on the MP2 level predict the ground states of the title compounds to be singlets with the first triplet states between 13 and 15 kcal mol−1 higher in energy, single point calculations with the QCISD(T), CCSD(T), and BD(T) methods at CCSD-optimized structures result in energy differences between the singlet and the triplet states in the range between 0.3 and 2.1 kcal mol−1 in favour of the triplet states. According to a CASSCF(8,8) calculation the triplets are also more stable by about 2.5–2.9 kcal mol−1. Calculations were also performed for the C5v-symmetric η5 structural isomers (cyclopentadienylindium, CpIn, and cyclopentadienylthallium, CpTl, Cp = C5H5) of the title compounds. At the highest level of theory employed in this study, C5H5In is between 79 and 88 kcal mol−1 higher in energy than CpIn, while this energy difference is even larger for thallabenzene where C5H5Tl is energetically between 94 and 102 kcal mol−1 above CpTl. In addition we report on the UV/vis spectra calculated with a TD-DFT method as well as on the spectra of the normal modes of C5H5In and C5H5Tl. Both types of spectra might facilitate identification of the title compounds eventually formed in photolysis or pyrolysis experiments.

scholarly journals Investigating Tunneling Controlled Chemical Reactions Through Ab-Initio Ring Polymer Molecular Dynamics

2021 ◽  
Author(s):  
Xinyang Li ◽  
Pengfei Huo
Keyword(s):  
Molecular Dynamics ◽  
Ab Initio ◽  
Chemical Reaction ◽  
Quantum Tunneling ◽  
Quantum Dynamics ◽  
Density Functional ◽  
Molecular System ◽  
Ring Polymer ◽  
Ring Polymer Molecular Dynamics ◽  
Dynamics Simulations

<div>We use the ab-initio ring polymer molecular dynamics (RPMD) approach to investigate tunneling controlled reactions in methylhydroxycarbene. Nuclear tunneling effects enable molecules to overcome the barriers which can not be overcome classically. Under low-temperature conditions, intrinsic quantum tunneling effects canfacilitate the chemical reaction in a pathway that is neither favored thermodynamically nor kinetically. This</div><div>behavior is referred to as the tunneling controlled chemical reaction and regarded as the third paradigm of chemical</div><div>reaction controls. In this work, we use the ab-initio RPMD approach to incorporate the tunneling effects in our quantum dynamics simulations. The reaction kinetics of two competitive reaction pathways at various temperatures are investigated with the Kohn-Sham density functional theory (KS-DFT) on-the-fly molecular dynamics simulations and the ring polymer quantization of the nuclei. The reaction rate constants obtained here agree extremely well with the experimentally measured rates. We demonstrate the feasibility of using ab-initio RPMD rate calculations in a realistic molecular system, and provide an interesting and important example for future investigations on reaction mechanisms dominated by quantum tunneling effects.</div>

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