Bridging the Gap between Direct Dynamics and Globally Accurate

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Bridge the Gap between Direct Dynamics and Globally Accurate Reactive Potential Energy Surface Using Neural Networks Yaolong Zhang, Xueyao Zhou, and Bin Jiang J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b00085 • Publication Date (Web): 25 Feb 2019 Downloaded from http://pubs.acs.org on February 26, 2019

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The Journal of Physical Chemistry Letters

Bridge the Gap between Direct Dynamics and Globally Accurate Reactive Potential Energy Surface Using Neural Networks Yaolong Zhang, Xueyao Zhou, Bin Jiang* Hefei National Laboratory for Physical Science at the Microscale, Department of Chemical Physics, Key Laboratory of Surface and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, University of Science and Technology of China, Hefei, Anhui 230026, China

*: corresponding author: [email protected]

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Abstract Direct dynamics simulations become increasingly popular in studying reaction dynamics for complex systems where analytical potential energy surfaces (PESs) are unavailable. Yet, the number and/or the propagation time of trajectories are often limited by high computational costs, and numerous energies and forces generated on-the-fly become wasted after simulations. We demonstrate here an example of reusing only a very small portion of existing direct dynamics data to reconstruct a ninety-dimensional globally accurate reactive PES describing the interaction of CO2 with a movable Ni(100) surface based on a machine learning approach. In addition to reproducing previous results with much better statistics, we predict scattering probabilities of CO2 at state-to-state level, which is extremely demanding for direct dynamics. We propose this unified way to investigate gaseous and gas-surface reactions of medium size, initiating with hundreds of preliminary direct dynamics trajectories, followed by low cost and high quality simulations on full-dimensional analytical PESs.

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Potential energy surfaces (PESs), as a natural consequence of the Born-Oppenheimer approximation, play a central role in understanding molecular spectroscopy, reaction dynamics, and energy/charge transfer processes at the microscopic level1. Intense efforts have been devoted to the accurate characterization of ab initio reactive PESs for small sized systems with less than ~10 atoms2-3. However, it becomes an increasingly challenging task to develop PESs for more extended systems with dozens to hundreds of atoms. Fortunately, the emergence of machine learning (ML) has offered a promising way to construct high-dimensional PESs4 and advanced this field quickly in recent years. Much attention has been paid to developing more efficient and transferable ML-based approaches in representing a big data set of a collection of molecules or materials5-12. Whereas for describing the detailed chemical reaction dynamics, it is essential to craft a globally accurate reactive PES that spans a large dynamically important configuration space involving bond formation/breaking, which additionally demands an efficient data sampling procedure. Such high-dimensional reactive PESs for high-dimensional systems have not been available until very recently13-15. An alternative way to overcome the obstacle of developing an explicit PES is exploring the reaction dynamics directly based on the energies and forces computed on-the-fly. This so-called Born Oppenheimer molecular dynamics (BOMD) or direct dynamics approach has become increasingly popular in studying both gas phase and gas-surface reactions. For example, Hase and coworkers have investigated the bimolecular nucleophilic substitution reactions in the gas phase by BOMD 3



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simulations at the hybrid density functional theory (DFT) level16-18. The BOMD method has also been pioneered by Groß, and later extended by many other groups to obtain statistically meaningful quantities in gas-surface reactions at the general gradient approximation based DFT level19-22, in which the surface atom motion and/or surface electron-hole pair excitation21,

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have been explicitly taken into account.

However, BOMD simulations are still quite expensive computationally and are often limited to a few hundred trajectories for a given initial condition and/or the simulation time of a few picoseconds, preventing the applicability to study more demanding long timescale and/or low probability channels. Perhaps more importantly, these energy and force information generated along BOMD trajectories, which potentially reflects the topography of the PES, are wasted after simulations. In this Letter, we aim to bridge direct dynamics and ML-based approaches to develop high-dimensional reactive PESs. To prove this concept, we report such a PES for describing the dissociative chemisorption of a polyatomic molecule on a movable metal surface, namely the CO2+Ni(100) system. Thanks to its importance in dry reforming of methane24 (CO2+CH4→2CO+2H2) and many other industrially catalytic reactions, the dissociation dynamics of CO2 on Ni(100) has been early explored by molecular beam experiments25, and more recently by various theoretical models including BOMD simulations26-29. Distinct from many earlier PESs14-15,

30,

which

required repeated human intervention in sampling data points wherever necessary, this ninety-dimensional reactive PES is constructed directly with only thousands of points selected exclusively from existing BOMD trajectories28 without further efforts 4


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of iterative sampling. This PES quantitatively reproduces the static and dynamic properties computed by DFT and enables us to predict state-to-state probabilities of a polyatomic molecule scattering off a metal surface for the first time. To represent the PES for the CO2/Ni(100) system, we adopt a modified version11 of atomistic neural network (AtNN) approach of Behler and Parrinello4, in which the total energy of the system (E) is represented as the sum of each atomic energy (e.g. Ej for the jth atom). Every atomic energy is described by an individual NN which takes an identical architecture for the same chemical element and has the chemical environment surrounding each atom as the input. The chemical environment is encoded in the so-called symmetry functions (SFs)4, 11, where the radial functions are the sum of two body terms, NZ

GiZ   exp[ -  (Rij - Rs ) 2 ] f c (Rij ) , j i

(1.)

and the angular functions are the sum of three body terms, N Z1 N Z2

Rij  Rik

j i k i

2

GiZ1 ,Z2  21   [1   cos(ijk )] exp[ (

Rs ) 2 ] f c ( Rij ) f c ( Rik ) ,

(2.)

where Rij and Rik correspond to the distances between the centered atom i and neighboring atoms j and k, ijk is the enclosed angle of atoms j, i, and k. η, Rs, ,  are parameters that determine the positions and widths of SFs. f c (Rij ) is a cutoff function that damps the inter-nuclear interaction smoothly to zero at the chosen cutoff distance (Rc) and thus truncates the environment locally4. It should be noted that SFs in Eqs. (1-2) are element dependent11, in which Z, Z1 and Z2 are the notations for chemical elements and NZ, N Z1 , and N Z2 represent the numbers of atoms of the corresponding types. Compared to the conventional SFs4, these modified ones are 5



able to distinguish the surrounding atoms with different types, providing a more sensitive characterization to the environment11. Whatever the fitting method used in the PES construction, a popular way of sampling data points is to run classical trajectories with an iteratively updated PES to supply points that best improve the current PES until its convergence with respect to the number of points and dynamical quantities31. This is unnecessary in our case as we have a large number of BOMD trajectories already. Indeed, 2200 trajectories for CO2 scattering on Ni(100) under various experimental conditions have been accumulated28, i.e. with the incidence energy (Ei) of 0.78 or 1.08 eV, nozzle temperature (TN) of 300 or 1000 K, and surface temperature (Ts) of 407 K. In these calculations, the Ni(100) surface was modeled by a four layers slab in a 3 × 3 unit cell where the top three layers containing 27 moveable Ni atoms. DFT energies and forces were calculated using Vienna Ab Initio Simulation Package (VASP)32-33, with the Perdew − Burke − Ernzerhof (PBE) functional34 and the projector augmented wave (PAW) method35. These trajectories include a huge number of data points (~2.5 million), which are supposed to sufficiently cover the configuration space that is dynamically important for molecular scattering and dissociation with a rolling surface. However, it is very difficult to deal with such a large amount of data with any ML-based method. It also unnecessary to do this as many data points are indeed quite close to some others in the coordinate space that contain redundant information of the PES. As a result, we shrank the size of data set on the basis of both structure and force similarities. 6


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According to a commonly used criterion for structure similarity, we added a new point with large coordinate-based generalized Euclidian distances (GLDs) with existing points indicating that this point is far from others already in the training data set36. However, we found that in some regions, e.g., nearby a stationary point, two similar configurations with a small GLD could have the atomic force vector pointing to opposite directions, representing a large force dissimilarity, as illustrated in Fig. S1. Consequently, the new point with small GLDs with existing data but with a large discrepancy in the atomic force vector was accepted. This scheme allowed us to locate data points mainly along different reaction pathways explored by the BOMD trajectories but avoid sampling many points the repulsive region with high energy and the asymptotic region with a flat energy curve. (see Fig. S1). More computational details on the AtNN training37, DFT calculations, and data sampling are given in the Supporting Information (SI). By adjusting the criterion of accepting useful configurations, we obtained several AtNN fits with a similar number (9000~10000) of data points, taken from a varying number of trajectories, ranging from 50 to 1050, respectively. All fits yielded quite small root mean square errors (RMSEs) with respect to the total energy (

Bridging the Gap between Direct Dynamics and Globally Accurate

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