Gas-Surface Scattering Processes from Machine Learning High … · High-Fidelity Potential Energy Surfaces for Gas Phase and Gas-Surface Scattering Processes from Machine Learning

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Perspective

High-Fidelity Potential Energy Surfaces for Gas Phase andGas-Surface Scattering Processes from Machine Learning

Bin Jiang, Jun Li, and Hua GuoJ. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.0c00989 • Publication Date (Web): 09 Jun 2020

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Submitted to JPCL, 3/25/2020, revised 4/23/2020

High-Fidelity Potential Energy Surfaces for Gas Phase and Gas-Surface Scattering Processes from Machine Learning

Bin Jiang,1,* Jun Li,2,* and Hua Guo3,*

1Hefei National Laboratory for Physical Science at the Microscale, Key Laboratory of Surface

and Interface Chemistry and Energy Catalysis of Anhui Higher Education Institutes, Department

of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026,

China

2School of Chemistry and Chemical Engineering and Chongqing Key Laboratory of Theoretical

and Computational Chemistry, Chongqing University, Chongqing 401331, China

3Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New

Mexico 87131, USA

*: corresponding authors, [email protected], [email protected], [email protected]

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Abstract

In this Perspective, we review recent advances in constructing high-fidelity potential

energy surfaces (PESs) from discrete ab initio points, using machine learning tools. Such PESs,

albeit with substantial initial investments, provide significantly higher efficiency than direct

dynamics methods and/or high accuracy at a level that is not affordable by on-the-fly approaches.

These PESs not only are a necessity for quantum dynamical studies due to delocalization of wave

packets, but also enable the study of low-probability and long-time events in (quasi-)classical

treatments. Our focus here is on inelastic and reactive scattering processes, which are more

challenging than bound systems because of the involvement of continua. Relevant applications

and developments for dynamical processes in both the gas phase and at gas-surface interfaces are

discussed.

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The concept of a potential energy surface (PES), first introduced by Born and Oppenheimer

(BO) through the separation of electronic and nuclear motions in molecular systems,1, 2 plays a

central role in physical chemistry. The PES establishes a relationship between a nuclear

configuration and the forces acting on nuclei, which governs nuclear dynamics leading to

molecular spectroscopy, energy transfer, and chemical reactivity. (Although electronic

degeneracies cause complications, the construct of PESs remains relevant, as discussed below).

The BO PES is appealing to chemists because nuclear dynamics can be intuitively related to its

topography. While it is not a measurable property, the PES is nonetheless an entity that

experimentalists seek to determine.3

Apart from diatomic systems, accurate determination of a global PES from first principles has

been a challenge until very recently.4-6 The difficulties were partly due to insufficient accuracy and

high costs of electronic structure theory. Thanks to more efficient quantum chemistry algorithms

and the dramatic increase in computing power, it is now possible to run ab initio calculations at

tens to hundreds of thousands configurations for reasonably large systems.7 Correlated

wavefunction based ab initio theory for molecular systems, such as coupled cluster8 and

configuration interaction theories,9 can now achieve chemical accuracy (1 kcal/mol) effectively

with uniform reliability in the dynamically relevant configuration space. For gas-solid interfaces,

such high-level ab initio methods are generally not available, but one can still rely on reasonably

accurate and highly efficient density functional theory (DFT).10 The bottleneck now becomes the

development of a faithful representation of the PES from a large number of discrete data points,

whose dimensionality is the number of nuclear degrees of freedom (DOFs) of the system.

A popular alternative to constructing PESs is direct dynamics, in which forces acting on nuclei

are computed on the fly in a (quasi-)classical treatment of nuclear dynamics.11, 12 Besides

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avoidance of constructing the PES, this approach has many other advantages, particularly for

exploring the potential landscape of a complex system. However, it can be computationally

expensive and extremely inefficient for rare and/or long-time events. To mitigate the high

computational costs, direct dynamics is often not run at the highest possible level of electronic

structure theory, compromising the reliability of calculated dynamics. Furthermore, this method is

very difficult to apply to quantum dynamics as a wave packet tends to delocalize. Hence, for

extensive dynamical studies, a high-fidelity PES based on ab initio points can provide significant

numerical savings over the on-the-fly calculations, even when the initial investment can be quite

substantial.

Pull Qoute inserted here: For extensive dynamical studies, a high-fidelity PES based on ab

initio points can provide significant numerical savings over the on-the-fly calculations.

In recent years, there have been keen and fast developing interests in developing high-

dimensional PESs using modern machine-learning (ML) methods.13 To this end, ML allows

accurate predictions of properties, such as PESs with a large number of nuclear DOFs, based on a

limited set of first principles data, such that new ab initio calculations are not needed. This is

possible because BO PESs are typically smooth functions of nuclear coordinates. There has been

tremendous progress in constructing interaction potentials for condensed phase materials as well

as large molecules using ML methods,14 which has enabled simulations of many properties that

were impossible to imagine only a few years ago. For these many-body problems, the key for ML-

based approaches is to express the PES in terms of atomic contributions because it can be readily

scaled to large systems with thousands of atoms.15-17 In this Perspective, we will instead focus on

molecular systems that involve dissociation continua, relevant to scattering and reactions. Such

systems are challenging in a different respect because scattering is highly sensitive to details of

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the PES. As a result, the PES is required to give a high-fidelity description of not only strongly

interacting regions, but also asymptotes that define the initial and final states of scattering.18, 19

While the aforementioned atomistic representation is viable,20-22 it might not be the most effective

for such problems. Due to space limitations, we will mostly focus on new and significant

developments since our review on this topic four years ago.23

Pull Quote inserted here: ML allows accurate predictions of properties, such as PESs with a

large number of nuclear DOFs, based on a limited set of first principles data, such that new ab

initio calculations are not needed.

It should be noted that there is no strict boundary between modern ML methods and

traditional interpolation/fitting approaches to represent PESs,6, 24-26 as none of them assumes a

physically derived functional form.13 While there has been a long history of using the simplest ML

technique, namely linear regression, in representing PESs,4, 5 the introduction of permutationally

invariant polynomials (PIPs) in terms of all internuclear distances by the Bowman group27, 28 led

to a powerful means to represent high-dimensional PESs with high fidelity. Indeed, the use of all

internuclear distances, despite their redundancy for systems with more than four atoms, greatly

simplified the coordinate system designed for different molecular geometries, thus enabling a

rubust fit of the global PES. Furthermore, they also streamlined the adaptation of permutation

symmetry in the system, which is of utmost importance in polyatomic molecules that contain

identical nuclei. The PIP representation also allows analytical expression for derivatives, which

can in turn be explicitly used in the fitting to improve the fitting quality.29 The readers are referred

to excellent reviews on the PIP method,6, 30 and some recent applications in relatively large reactive

systems.31, 32 In this Perspective, we will be focusing on two modern ML methods, namely neural

networks (NNs)13, 23, 33-36 and kernel-based regression13, 24, 37, 38 in constructing reactive PESs.

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An artificial NN consists of layers of interconnected mathematic functions mimicking

biological neurons.39 Theoretically, it provides an ultra-flexible form that is capable of

representing any multi-dimensional real analytical function with arbitrary precision. In a typical

NN-based approach, parameters in an NN are non-linearly optimized to minimize a cost function,

which can be written as a root-mean-square difference between the training data and NN output.

A key issue in this approach is the selection of points for the training set. Ideally, the distribution

of points should cover the dynamically relevant configuration space, but the number of points

should be as few as possible. The former is often achieved by running trajectories on the fly or on

primitive PESs to explore the configuration space. The latter can be accomplished by using

distance metrics and energy cutoffs to eliminate unnecessary points. More recently, there has been

strong interest in automated schemes in selecting the points.40-42

Unlike NNs, kernel-based regression approaches, such as Gaussian process (GP) regression,43

are non-parametric ML methods with no specific functional form. Indeed, GP is a probabilistic

model as a collection of prior normally distributed random functions characterized by its mean and

covariance functions, where the covariance or kernel function k(x, x′) describes the correlation

between the Gaussian distributions at two different configurations x and x′. According to Bayes’

theorem, the posterior probability distribution is also a Gaussian, whose mean and variance

correspond to the prediction and uncertainty at an unknown point, via maximizing the likelihood

of the GP model with the training data.

While the NN and GP methods are formally equivalent in some special cases,37 they both offer

advantages and disadvantages.44 For instance, GP explicitly provides uncertainty of the prediction

at an unknown configuration based on Bayesian estimation, but suffers from poor scalability due

to its interpolation nature. NNs, on the other hand, are capable of representing a much larger data

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set, thus finer details of a PES, with relatively high efficiency, but they typically require more ab

initio calculations. They are both able to learn energy and gradients simultaneously, which

significantly improves the fitting quality.45-47 Consequently, they are amenable to analytical

derivatives. These ML methods are generally superior to traditional interpolation methods, in

accuracy and/or efficiency. There have been some investigations on the comparison of different

ML methods in terms of their performance and computational costs.22, 48-50 However, the efficacy

of a ML method depends on the problem at hand, thus a comparison of applicability and efficiency

in one system might not be extendable to another system. Typically, ML methods excel in

interpolation, but often do poorly in extrapolation. No further details are given here for either the

NN or GP machinery, as they can be found in standard literature.

Pull quote inserted here: GP explicitly provides uncertainty of the prediction at an unknown

configuration based on Bayesian estimation, but suffers from poor scalability due to its

interpolation nature. NNs, on the other hand, are capable of representing a much larger data set,

thus finer details of a PES, with relatively high efficiency, but they typically require more ab initio

calculations.

Comparing to condensed phase systems, molecules typically have much stronger directional

bonding. As a result, it is natural to use traditional structural descriptors, such as bond lengths and

angles, or internuclear distances, in constructing PESs for gas phase systems.4 They are also

preferred for ML representations of molecular PESs.6, 23, 30, 33, 35 For example, Zhang and coworkers

used internuclear distances in representing global NN PESs from high-level ab initio data to

achieve fitting errors within a few meV,51, 52 which is necessary for quantum scattering calculations

in polyatomic reactions.

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An important property of the BO PES is its invariance under the complete nuclear

permutation and inversion (CNPI) group.53 The PIPs provide a convenient way to adapt the

translation, inversion, as well as permutation symmetry in NN representation of PESs. In this PIP-

NN approach, permutation symmetry is enforced by using low-order PIPs in the input layer of an

NN.54 Different from the PIP approach in which symmetrized polynomials are used as the fitting

bases,6, 30 the PIP-NN method fits ab initio data using NNs in a space spanned by PIPs. As a result,

higher fidelity can be achieved with exact symmetry, but without modifications of NNs. It should

be noted that for systems with more than three atoms, PIPs with a higher order than the number of

internuclear distances are needed to avoid false permutations.55 This creates some redundancy, but

does not affect the fitting accuracy. Since our last review in 2016,23 this method has been

successfully applied to a wide range of reactive systems with up to seven atoms, including KRb +

KRb,56 Be+ + H2O,57 OH + SO,58 OH + O2,59 OH + H2O,60 O + C2H2,61 OH + HO2,62 N2 + HOC+,63

Cl + CH4,64 F + CH3OH,65 and Cl + CH3OH.66 The latter two cases involve fifteen DOFs, with

multiple reaction channels and rich dynamics. In Figure 1, the Cl + CH3OH PES is shown, which

contains two reaction channels to HCl + CH3O/CH2OH products.

Pull quote inserted here: The PIP-NN method fits ab initio data using NNs in a space spanned

by PIPs. As a result, higher fidelity can be achieved with exact symmetry, but without

modifications of NNs

In the PIP-NN approach, the number of PIPs increases quickly with the number of identical

nuclei in the system, thus lowering its efficiency. For instance, 1331 PIPs were used as the input

layer of an NN for fitting an OH + CH4 PES,67 which has five hydrogen atoms. As many of the

PIPs are redundant, it is advantageous to express PIPs in terms of non-redundant terms

corresponding to primary and secondary invariant polynomials.68 This can be achieved by

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decomposing any high-order PIPs into a product of two low-order polynomials with a remainder

invariant polynomial of the same order.28 Hence, one can use only non-redundant PIPs as the input

layer of NNs. For the H + H2S system, for example, only 9 non-redundant PIPs were used in the

PIP-NN PES for the three H nuclei, a significant reduction from 23 3th-order PIPs.69

When the system becomes more complicated, the decomposition may not be done completely.

Consequently, some redundancy remains in lower-order PIPs. It is known that all invariant

polynomials under a given symmetry group can be represented as polynomials in a finite

generating set of invariant polynomials.70 Although its form is not unique, there exists for a given

system a complete set of generating invariants, which can be determined using computer algebra

software like SINGULAR.71 Such an approach was first demonstrated by Opelka and Domcke,72

and investigated further by Zhang and coworkers.73 These generating invariants are denoted as

fundamental invariants (FIs) and the resulting NN fitting approach is called FI-NN.73 As the size

of the FIs is much smaller than that of PIPs, FI-NN is typically more efficient than PIP-NN,

resulting in a faster evaluation of the PES.36 The FI-NN method has been successfully applied to

several reactive systems.74-77

In some special cases, such as non-reactive scattering, full permutation symmetry is not

required. Without losing generality, a PES for a collection of weakly interacting subsystems can

be expressed as , where Vintra denotes the intramolecular PESs of subsystems and intra interV V V

Vinter represents the interaction among the constituent molecules. Because identical atoms among

different molecules are not exchanged in non-reactive events, there is little incentive to enforce the

permutation symmetry between them, as suggested by Truhlar, Bowman, and their coworkers.78,

79 Indeed, we have shown recently that a reduced set of PIPs can be used to adapt the permutation

symmetry in the intermolecular PIP-NN PESs.80 This reduced set of PIPs can be obtained by

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excluding all terms that are relevant only to the intramolecular subsystems, thus simplifying the

symmetry adaptation.

Even with all the improvements discussed above, it is still difficult to construct PESs for

systems with more than ten atoms and strong interactions, especially when there are many identical

atoms. To this end, the atomistic NN (AtNN) method of Behler and Parrinello15, 81 becomes more

attractive. As discussed in more detail below, AtNN expresses the PES as a sum of atomistic

contributions, each encoded by mapping functions that describe its local environment, which is

generally affected by other atoms within a specified cutoff radius. Each atomistic component of

the same element shares identical NN architecture and fitting parameters, naturally preserving

permutational invariance. Recent tests have demonstrated that the AtNN approach is capable of

describing global reactive PESs accurately, but it requires the determination of different NNs for

all atom types in the system. Furthermore, a large number of mapping functions and data points

are often needed to give an accurate description of the PES because of its strong anisotropy,

potentially slowing down the evaluation of the AtNN PES.20-22 In addition, long-range interactions,

especially for charged systems, are difficult to be described effectively by the AtNN approach.

In addition to NNs, kernel-based regression represents another class of ML methods. The use

of kernels in PES interpolation can be traced back to the reproducing kernel Hilbert spaces (RKHS)

method.24 Recently, GP regression has gained increasing popularity in developing PESs because

of several attractive features.82 This ML model was first introduced to construct force-fields83 and

high-dimensional atomistic PESs for condensed phase systems.16 It was also applied to represent

global PESs for calculating spectroscopic properties49, 50, 84-86 and reaction dynamics.87-92 In many

of these studies, GP regression has been shown to accurately and efficiently reproduce existing

PESs with often much fewer points than NNs,50, 87, 89, 92 which is now recognized as a distinct

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advantage of GP over other ML methods. Its prowess has also been demonstrated in constructing

accurate PESs from high level ab initio points for the S + H2 reaction88 and NaK + NaK collision.91

Another unique property of GP is that it provides the statistical uncertainty of a prediction, thus

offering an effective guide to add new data points. Known as “active learning” in the context of

ML, such algorithms based on the search of the maximum variance of the GP model have been

validated in a variety of systems.85, 89 Interestingly, Krems and coworkers proposed a GP model to

identify new data points by optimizing quantum dynamics results.92 This active learning strategy

is quite efficient, enabling GP PESs converged to the J = 0 reaction probability with only 30 points

for the H + H2 reaction and 290 points for the OH + H2 reaction. Another advantage is that

overfitting is generally not a concern in GP regression.50 A drawback of GP regression is its

relatively poor scaling of computational costs compared to NNs. Indeed, the numerical cost of

training and evaluating a GP model scales O(M3) and O(M), respectively, where M is the number

of points. It is therefore necessary to develop GP PESs with as few points as possible. Krems and

coworkers recently showed that both interpolation and extrapolation accuracy of a GP PES can be

significantly improved by increasing the complexity of kernels instead of increasing the number

of points.86 While most GP PESs discussed here are interpolated in terms of internal coordinates

of the system, the use of PIPs instead improves the description of permutation symmetry,49 in the

same spirit of the PIP-NN approach.

We note that there are significant efforts to apply ML methods to describe BO PESs for more

complex reactions.93-95 The resulting PESs, while extremely important, are typically not at the level

of accuracy as those discussed in this Perspective and thus not covered.

All discussion so far has been restricted to adiabatic PESs. When electronic degeneracies,

such as conical intersections (CIs),96, 97 are present, the adiabatic PESs contain cusps and the

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derivative coupling becomes singular at the CI seam. Under such circumstances, it is preferable to

represent the PESs and their couplings in a diabatic potential energy matrix (DPEM), in which the

diagonal potentials are coupled by the off-diagonal terms.98, 99 The elements of the DPEM are all

smooth functions of nuclear coordinates and thus amenable to ML representations. Furthermore,

it removes the intrinsic singularities at the degeneracy, rendering better behaved dynamics.100

Recently, NNs have been used to represent DPEMs for several systems.101-109 For example, Lenzen

et al. proposed an NN-based implementation for the X + CH4 HX + CH3 reactions using a

diabatization-by-ansatz approach. NNs were employed to represent both the diagonal and off-

diagonal elements of the DPEM, trained exclusively from adiabatic energies without derivative

couplings, where diabatization near a CI seam is determined from a symmetry-based ansatz.105

Permutation symmetry adds an extra layer of complexity in representing DPEMs. Depending

on the CNPI symmetry of each diabatic state, the diagonal and off-diagonal terms might belong to

different irreducible representations. For the 1,21A system of NH3, for example, the diagonal terms

are symmetric with respect to the permutation of H atoms, while the off-diagonal terms are

antisymmetric.110 These permutation symmetries can be enforced using an extension of the PIP-

NN method, in which the antisymmetric off-diagonal terms are represented as a PIP-NN multiplied

by an antisymmetric prefactor.103 A similar approach has been used in the NN-based simultaneous

diabatizing-fitting approach by Yarkony and coworkers,107-109 which generates the DPEM from

adiabatic energies, gradients and derivative couplings. The NN-based fits of DPEMs generally

have a higher fidelity than PIP-based ones. Very recently, Guan et al. demonstrated that this NN-

based approach can be extended to fitting of electronic properties such as dipole functions108 and

spin-orbit couplings,109 for which the diabatic representation is indispensable. Finally, we note in

passing that there is emerging interest in developing excited state PESs of more complicated

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systems from direct dynamics simulations.111-114 However, these efforts have so far been restricted

to semi-global adiabatic PESs at relatively low levels of theory without dissociation continua.

A gas-surface process differs from a gas-phase reaction in at least two aspects.115 First, the

molecule can interact with the surface at multiple sites. Second, the motion of surface atoms, and

sometimes electrons, allows energy exchange between the impinging molecule and the surface

during scattering and may significantly influence the reaction dynamics.116-119 As a result, PESs

for describing scattering at gas-surface interfaces are in general more complicated than their gas-

phase counterparts in terms of symmetry, dimensionality, and complexity. Furthermore, the

electronic structure characterization is almost exclusively given in DFT. Most non-NN-based first-

principles PESs used the corrugation reduction procedure (CRP),120 designed to reduce the strong

corrugation near the surface. They were however limited to describing diatomic scattering on static

surfaces with six molecular DOFs included, due to its interpolation nature. Higher-dimensional

PESs for gas-surface scattering/reaction from DFT calculations have emerged recently using NNs.

Interestingly, NNs have a long history in the development of molecule-surface PESs and

remain a formidable force in this arena. Indeed, the first ever NN-based PES was for CO adsorption

on frozen Ni(111).121 Many subsequent studies have focused on incorporating the periodicity of

the rigid surface into NNs. For example, Lorenz et al. first proposed a set of symmetry-adapted

coordinates as the input of the NN PES for H2 reactive scattering on rigid Pd(100),122 which were

later generalized by Reuter and coworkers using Fourier expansions of atomic Cartesian

coordinates on different crystal facets.123, 124 While the periodicity of rigid surfaces was taken into

account in these studies, the permutational invariance of the molecular DOFs was not rigorously

fulfilled. More recently, Zhang and coworkers developed high-fidelity NN PESs for diatomic and

polyatomic dissociation at rigid metal surfaces.125-130 These PESs were symmetrized by mapping

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the data points into a symmetry irreducible area on the surface surrounded by high-symmetry sites

and sorting the coordinates relevant to identical atoms. This approach could lead to discontinuous

derivatives at the boundary, which might affect energy conservation of classical trajectories.

We have extended the PIP-NN approach to gas-surface systems by incorporating both the

permutation symmetry of the molecule and surface periodicity.131 Differing from the gas-phase

counterpart, here the PIPs are crafted in terms of not only internuclear distances but also the

primitive Fourier expansions of atomic coordinates in the molecule on the periodic surface. These

PIPs were demonstrated to be essential in obtaining more accurate NN fits131 than the intuitive

symmetrization of the Fourier terms.123, 124 Since our review in 2016,23 the PIP-NN method has

been applied to several systems, including CO + Co(1120),132 NH3 + Ru(0001)133 and CH4 +

Ni(111),134 as well as a multi-channel reaction of CH3OH on Cu(111).135 We note in passing that

in gas-surface applications, the practical PIP-NN implementation is essentially the same as the FI-

NN method.73

These aforementioned methods represent the entire PES by a single NN and consider the

molecular DOFs only. They are difficult to include surface DOFs, which would increase the

dimensionality of the PES dramatically. As the condensed-phase characteristics of the substrate

becomes prominent in such problems, atomistic ML methods, which have revolutionized the

development of interaction potentials for condensed phase systems,13 are better suited. Taking the

example of AtNN, the PES is represented by a sum of energies of the constituent atoms in the

system. Each atomic type is represented by a distinct NN, which is trained to learn its local

environment in all possible configurations accessible by dynamics.15 Since all surface atoms with

the same elemental type share the same NN, this approach substantially reduces the complexity of

NNs and is naturally invariant under permutation of identical nuclei. The difficulties in

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representing a high-dimensional PES are thus converted to how to best encode the local

environmental information of each atom in the so-called mapping functions (or equivalently

descriptors136 or fingerprints137), being the input of NNs. The atomistic descriptors can be obtained

by, for example, the radial and angular atom centered symmetry functions (ACSFs) summing over

interactions between the central atom and neighboring atoms.15, 81 These ACSFs are relatively

short ranged so that only the local environment is encoded. Importantly, these descriptors are

invariant with respect to rotation, translation, and inversion, so that the corresponding AtNN PES

fulfills the required symmetry and/or periodicity of the systems across the gas and condensed

phases. For detailed implementation, the reader is referred to authoritative reviews by Behler.13, 14

The first application of the AtNN method to describe molecular scattering from a solid

surface was reported in 2017,138 trained from a data set generated from DFT direct dynamics. The

AtNN PESs for the HCl + Au(111) system, approximated with a periodic model that involves 60

DOFs, were shown to reproduce quantitatively not only the energy loss profile of scattered HCl

molecules,138 but also the dissociative sticking probabilities,139 obtained from direct dynamics

simulations, but with a ~105-fold speedup. Later, Zhang et al. extended the AtNN representation

to describe polyatomic (CO2) reactive scattering on Ni(100),47 trained with only ~10000 snapshots

selected from as few as 50 direct dynamics trajectories, taking advantage of simultaneous fitting

of both energies and forces. Likewise, Kroes and coworkers developed reactive AtNN PESs for

N2 on Ru(0001)140 and CH4 on Cu(111),141 which enabled efficient molecular dynamics

calculations of the dissociative sticking probability as low as ~10-5. In another example, an AtNN

PES for CO scattering from Au(111) was developed, which was instrumental for understanding

low-probability and long-time events such as trapping, as the molecule explores both

chemisorption and physisorption wells.142 More recently, AtNN PESs for the NO + Au(111)143

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and CO2 + Pt(111) (shown in Figure 2) systems144 have been developed, and they provided

unprecedented new physical insights into these important surface processes. These examples

demonstrate that the AtNN method is capable of constructing highly efficient and accurate high-

dimensional PES for scattering and reactions at metal surfaces including both molecular and

surface DOFs. A distinct advantage of analytical PESs is the ability to explore site specificity of

the reaction barrier, which offers a view of the “chemical shape” of the surface.144

Pull Qoute inserted here: The AtNN method is capable of constructing highly efficient and

accurate high-dimensional PES for scattering and reactions at metal surfaces including both

molecular and surface DOFs.

As discussed in Sec. III, the BO approximation breaks down when electronic states become

degenerate. Indeed, the coupling between moving nuclei and metallic electrons is ubiquitous

thanks to the vanishing band-gap in metallic systems,145 although its strength is system-dependent.

The continuous electronic states of a metal surface render the nonadiabatic dynamical calculations

much more challenging than those in the gas phase. Two approximate models have been

proposed.145, 146 One is the stochastic surface hopping model147 based on probabilistic electronic

transitions among multiple discretized states. Because of difficulties in computing excited state

PESs and derivative couplings in metallic systems, very few systems have been investigated using

this approach.148, 149 Even in these examples, very limited first-principles information on

nonadiabatic couplings is available, preventing the use of ML methods to represent the DPEM. An

alternative is the electronic friction model,150, 151 in which the effective nuclear-electron coupling

is ascribed to a friction force to capture the instantaneous response of slowly moved nuclei to fast

electronic motion,152 resulting in a generalized Langevin equation.150 In this model, an analytical

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representation of the electronic friction tensor (EFT), , becomes a prerequisite for efficient Λ𝑖𝑗

dynamics similations of nonadiabatic dissipation, reprsenting a relevant topic of this Perspective.

Within a simple local density friction approximation,153 the tensorial friction reduces to a

scalar property, i.e., atomic friction coefficients, which depend on the metal electron density at the

positions where the atoms are embedded. In practice, the electron density surface (EDS) of a metal

surface is formally equivalent to the PES of a single atom adsorbed on the same surface. As a

result, it is quite straightforward to construct the three-dimensional EDS when the surface is

frozen.153 The EDS depends on surface atom displacements as well, when the surface is moving.

To this end, Jiang and coworkers have applied the AtNN model to accurately represent the EDS

of a movable Au(111) surface.143 More recently, EFT has been calculated by a first-order time-

dependent perturbation theory (TDPT) based on Kohn-Sham orbitals, fully accounting for the

electronic structure of the molecule-surface system.154-156 In such a case, the full tensorial

symmetry of EFT has to be taken into account, which is much more intricate than scalar properties

like potential energy and electron density. Specifically, EFT is not invariant but covariant under a

specific symmetry operation. Different NN representations for EFT of a diatomic molecule

scattering from a rigid surface have been developed independently by the Meyer group157 and Jiang

group.158 The molecule is either reoriented to a local reference frame or mapped to the symmetry

irreducible region of the surface, allowing one-to-one correspondence between the nuclear

configuration and the EFT that can be represented by NNs. However, by construction, neither

method is able to account for the influence of substrate structure and lattice motion on EFT. More

recently, Zhang and Jiang proposed to reconstruct the EFT form by manipulating the first and

second derivative matrices of multiple virtual outputs of atomistic NNs with respect to atomic

Cartesian coordinates.159 This strategy rigorously preserves positive semidefiniteness, directional

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property, and correct covariant symmetry of EFT. While this symmetrization scheme can work

with any atomistic ML methods, it was implemented with a physically inspired embedded atom

neural network (EANN) model developed by the same group.160 This EANN model uses atomic

density based descriptors, whose computational cost scales linearly with the number of

neighboring atoms, thus more efficient than the conventional ACSFs. Including both molecular

and surface DOFs, this tensorial representation for EFT will enable investigating adiabatic and

nonadiabatic energy dissipation during scattering and reactions at metal surfaces in a unified

framework.

It is clear from the discussion above that the emergence of ML methods has in the past few

years had a tremendous impact on high-fidelity development of PESs from first-principles data.

These PESs, often with high dimensionality, enabled dynamical calculations with unprecedented

accuracy and extraordinary efficiency, leading to new insights and discoveries. We note however

that the accuracy of ML PESs is ultimately limited by the level of electronic structure theory used

to generate the training set. Progress in that arena, possibly with ML, is expected to further improve

our ability to predict experimental observations.

There are already encouraging developments in extending ML approaches to construct

PESs for coupled electronic states in gas phase systems. To this end, DPEMs are the key, as their

elements are smooth functions of nuclear coordinates and thus amenable to ML methods. This

characteristic extends to other electronic properties, such as dipole moments, which can also be

accurately predicted using ML methods.109 However, stumbling blocks remain. For example, it is

well established that exact diabatization is unattainable for systems with more than two atoms.161

As a result, all diabatization schemes are approximate, and some might lead to unwanted effects.162

Numerically, the inclusion of derivative coupling and energy gradients in addition to energies leads

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to a very large data set, which potentially limits ML applications to relatively small systems. More

efficient approaches need to be found.

For gas-surface systems, we can envisage many possible improvements. For example, it

should be possible to train a single PES to describe the interaction of a molecule on different metal

facets, which will greatly improve our ability to understand the influence of defects on reactivity.

The currently ML approaches can be readily extended to describe a varying number of adsorbates

and surface atoms so as to investigate the influence of coverage and surface phonons on dynamics.

It is also interesting to apply ML approaches to more complex, such as the Eley-Rideal type,

surface reactions. Because DFT is not accurate enough in some cases,139, 163 higher level electronic

structure calculations are necessary, but they are limited by the number of points affordable. GP

regression may be more promising to tackle these systems as it requires much fewer points than

NNs.

As demonstrated in the ML fit of friction tensors, ML methods are expected to play a more

prominent role in representing vectorial and tensorial properties of molecular systems, such as

dipoles and polarizabilities. These properties are much harder to represent than scalar properties

because of their complicated covariances. Apart from the NN-based work described above,159 GP

has also been successfully applied.164 We expect more advances in this direction.

An ultimate question is whether it is possible to derive the PES directly from scattering

experiments. This inversion problem is very difficult because scattering attributes, such as

differential cross sections, are sensitively dependent on the details of the PES. Some efforts in this

direction has already been made,92 and more progress can be expected in the near future.

Finally, we note that rapid advances in ML methodology will certainly help to stimulate

new applications in developing PESs. State-of-the-art deep NNs based methods have been

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advanced to represent PESs165, 166 and some of them have been benchmarked in gas phase reactive

systems. For example, the latest continuous-filter convolutional neural networks model, known as

SchNet,165 has been applied to accurately refit global PESs of the H/Cl + H2 reactions and the

OCHCO+ and H2CO systems.167 It is interesting to explore whether these new ML methods,

designed to represent molecular properties of many systems, have better representability than

regular NNs and GP based methods for more complex multichannel reactions and/or involving

multi-conformers. The use of ML methods to describe long-range interactions also represents a

challenge, but kernel based methods have been shown to be effective.168 On the other hand, optimal

data selection strategies can be developed in the concept of “active learning”, with the ultimate

goal of sampling as few as possible points to generate an as accurate as possible ML PES. Other

ML concepts, e.g., classification and clustering,169 are able to assist more efficient geometric

recognition and partition in constructing PESs. More investigations in this direction are expected.

We also note in passing that several open-source ML packages containing the essential machinery

are available.29, 40, 46 Overall, we are extremely optimistic about the future of ML assisted

development of PESs for inelastic and reactive scattering.

Biographies

Bin Jiang is Professor of Chemical Physics at University of Science and

Technology of China. He received his PhD degree from Nanjing University and

worked with Prof. Hua Guo at University of New Mexico as a postdoctoral fellow.

His research interests focus on machine learning method development and applications to potential

energy surfaces across gas phase and gas-surface interfaces, as well as quantum/classical dynamics

of gas-surface reactions.

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Jun Li is Professor of Chemistry at Chongqing University, China. He received his

PhD degree from Sichuan University and worked with Prof. Hua Guo at University

of New Mexico as a postdoctoral fellow. His research interests include potential

energy surfaces, reaction kinetics and dynamics, for gas phase systems.

Hua Guo is Distinguished Professor at University of New Mexico. He received his

D.Phil. from Sussex University (UK) with the late Prof. John Murrell and did a

postdoc with Prof. George Schatz at Northwestern University. His research interests cover

mechanisms, dynamics, and kinetics of gas phase reactions, photochemistry, and surface reactions.

Acknowledgements:

B. J. was supported by National Key R&D Program of China (2017YFA0303500),

National Natural Science Foundation of China (91645202 and 21722306), and Anhui Initiative in

Quantum Information Technologies (AHY090200). J. L. was supported by National Natural

Science Foundation of China (21973009 and 21573027), Chongqing Municipal Natural Science

Foundation (cstc2019jcyj-msxmX0087), and Alexander von Humboldt Foundation (Humboldt

Fellowship for Experienced Researchers). H. G. thanks for support from National Science

Foundation (Grant No. CHE-1462109), Department of Energy (Grant No. DE-SC0015997) and

Department of Defense (Grant Nos. FA9550-18-1-0413 and W911NF-19-1-0283), and is grateful

for a Humboldt Research Award from the Alexander von Humboldt Foundation.

References:

1. Born, M.; Oppenheimer, R. Zur quantentheorie der molekeln, Ann. Phys. 1927, 84, 0457-0484.2. Born, M.; Huang, K. Dynamical Theory of Crystal Lattices. Clarendon: Oxford, 1954.3. Pan, H.; Wang, F.; Czakó, G.; Liu, K. Direct mapping of the angle-dependent barrier to reaction for Cl + CHD3 using polarized scattering data, Nat. Chem. 2017, 9, 1175-1180.

Page 21 of 31



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

22

4. Murrell, J. N.; Carter, S.; Farantos, S. C.; Huxley, P.; Varandas, A. J. C. Molecular Potential Energy Functions. Wiley: Chichester, 1984.5. Schatz, G. C. The analytical representation of electronic potential-energy surfaces, Rev. Mod. Phys. 1989, 61, 669-688.6. Qu, C.; Yu, Q.; Bowman, J. M. Permutationally invariant potential energy surfaces, Annu. Rev. Phys. Chem. 2018, 69, 151-175.7. Dawes, R.; Ndengué, S. A. Single- and multireference electronic structure calculations for constructing potential energy surfaces, Int. Rev. Phys. Chem. 2016, 35, 441-478.8. Bartlett, R. J.; Musiał, M. Coupled-cluster theory in quantum chemistry, Rev. Mod. Phys. 2007, 79, 291-352.9. Werner, H.-J. Matrix-formulated direct multiconfiguration self-consistent field and multiconfiguration reference configuration-interaction methods, Adv. Chem. Phys. 1987, 69, 1-62.10. Greeley, J.; Nørskov, J. K.; Mavrikakis, M. Electronic structure and catalysis on metal surfaces, Annu. Rev. Phys. Chem. 2002, 53, 319-348.11. Marx, D.; Hutter, J., Ab initio molecular dynamics: Basic theory and advance methods. In Modern Methods and Algorithms of Quantum Chemistry, Grotendorst, J., Ed. Cambridge University Press: Cambridge, 2009.12. Pratihar, S.; Ma, X.; Homayoon, Z.; Barnes, G. L.; Hase, W. L. Direct chemical dynamics simulations, J. Am. Chem. Soc. 2017, 139, 3570-3590.13. Behler, J. Perspective: Machine learning potentials for atomistic simulations, J. Chem. Phys. 2016, 145, 170901.14. Behler, J. First principles neural network potentials for reactive simulations of large molecular and condensed systems, Angew. Chem. Int. Ed. 2017, 56, 12828-12840.15. Behler, J.; Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces, Phys. Rev. Lett. 2007, 98, 146401.16. Bartók, A. P.; Payne, M. C.; Kondor, R.; Csányi, G. Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons, Phys. Rev. Lett. 2010, 104, 136403.17. Rupp, M.; Tkatchenko, A.; Müller, K.-R.; von Lilienfeld, O. A. Fast and accurate modeling of molecular atomization energies with machine learning, Phys. Rev. Lett. 2012, 108, 058301.18. Zhang, D. H.; Guo, H. Recent advances in quantum dynamics of bimolecular reactions, Annu. Rev. Phys. Chem. 2016, 67, 135-158.19. Jiang, B.; Yang, M.; Xie, D.; Guo, H. Quantum dynamics of polyatomic dissociative chemisorption on transition metal surfaces: Mode specificity and bond selectivity, Chem. Soc. Rev. 2016, 45, 3621-3640.20. Kolb, B.; Zhao, B.; Li, J.; Jiang, B.; Guo, H. Permutation invariant potential energy surfaces for polyatomic reactions using atomistic neural networks, J. Chem. Phys. 2016, 144, 224103.21. Lu, D.; Qi, J.; Yang, M.; Behler, J.; Song, H.; Li, J. Mode specific dynamics in the H2 + SH → H + H2S reaction, Phys. Chem. Chem. Phys. 2016, 18, 29113-29121.22. Li, J.; Song, K.; Behler, J. A critical comparison of neural network potentials for molecular reaction dynamics with exact permutation symmetry, Phys. Chem. Chem. Phys. 2019, 21, 9672-9682.23. Jiang, B.; Li, J.; Guo, H. Potential energy surfaces from high fidelity fitting of ab initio points: The permutation invariant polynomial-neural network approach, Int. Rev. Phys. Chem. 2016, 35, 479-506.24. Hollebeek, T.; Ho, T.-S.; Rabitz, H. Constructing multidimensional molecular potential energy surfaces from ab initio data, Annu. Rev. Phys. Chem. 1999, 50, 537-570.25. Collins, M. A. Molecular potential-energy surfaces for chemical reaction dynamics, Theo. Chem. Acc. 2002, 108, 313-324.26. Majumder, M.; Ndengué, A. S.; Dawes, R. Automated construction of potential energy surfaces, Mol. Phys. 2016, 114, 1-18.

Page 22 of 31



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

23

27. Jin, Z.; Braams, B. J.; Bowman, J. M. An ab initio based global potential energy surface describing CH5

+ → CH3+ + H2, J. Phys. Chem. A 2006, 110, 1569-1574.

28. Xie, Z.; Bowman, J. M. Permutationally invariant polynomial basis for molecular energy surface fitting via monomial symmetrization, J. Chem. Theo. Comput. 2010, 6, 26–34.29. Nandi, A.; Qu, C.; Bowman, J. M. Using gradients in permutationally invariant polynomial potential fitting: A demonstration for CH4 using as few as 100 configurations, J. Chem. Theo. Comput. 2019, 15, 2826-2835.30. Braams, B. J.; Bowman, J. M. Permutationally invariant potential energy surfaces in high dimensionality, Int. Rev. Phys. Chem. 2009, 28, 577–606.31. Kidwell, N. M.; Li, H.; Wang, X.; Bowman, J. M.; Lester, M. I. Unimolecular dissociation dynamics of vibrationally activated CH3CHOO Criegee intermediates to OH radical products, Nat. Chem. 2016, 8, 509-504.32. Nandi, A.; Qu, C.; Bowman, J. M. Full and fragmented permutationally invariant polynomial potential energy surfaces for trans and cis N-methyl acetamide and isomerization saddle points, J. Chem. Phys. 2019, 151, 084306.33. Raff, L. M.; Komanduri, R.; Hagan, M.; Bukkapatnam, S. T. S. Neural Networks in Chemical Reaction Dynamics. Oxford University Press: Oxford, 2012.34. Behler, J. Neural network potential-energy surfaces in chemistry: a tool for large-scale simulations, Phys. Chem. Chem. Phys. 2011, 13, 17930-17955.35. Manzhos, S.; Dawes, R.; Carrington Jr., T. Neural network-based approaches for building high dimensional and quantum dynamics-friendly potential energy surfaces, Int. J. Quant. Chem. 2015, 115, 1012–1020.36. Fu, B.; Zhang, D. H. Ab initio potential energy surfaces and quantum dynamics for polyatomic bimolecular reactions, J. Chem. Theo. Comput. 2018, 14, 2289-2303.37. Bartók, A. P.; Csányi, G. Gaussian approximation potentials: A brief tutorial introduction, Int. J. Quant. Chem. 2015, 115, 1051-1057.38. Popelier, P. L. A. QCTFF: On the construction of a novel protein force field, Int. J. Quant. Chem. 2015, 115, 1005-1011.39. Haykin, S. Neural Networks and Learning Machines: A Comprehensive Foundation. Prentice Hall,: Upper Saddle River, 2008.40. Abbott, A. S.; Turney, J. M.; Zhang, B.; Smith, D. G. A.; Altarawy, D.; Schaefer, H. F. PES-Learn: An open-source software package for the automated generation of machine learning models of molecular potential energy surfaces, J. Chem. Theo. Comput. 2019, 15, 4386-4398.41. Lin, Q.; Zhang, Y.; Zhao, B.; Jiang, B. Automatically growing global reactive neural network potential energy surfaces: A trajectory-free active learning strategy, J. Chem. Phys. 2020, 152, 154104.42. Győri, T.; Czakó, G. Automating the development of high-dimensional reactive potential energy surfaces with the ROBOSURFER program system, J. Chem. Theo. Comput. 2020, 16, 51-66.43. Rasmussen, C. E.; Williams, C. K. I. Gaussian Processes for Machine Learning. The MIT Press: Cambridge, MA, 2006.44. Zuo, Y.; Chen, C.; Li, X.; Deng, Z.; Chen, Y.; Behler, J.; Csányi, G.; Shapeev, A. V.; Thompson, A. P.; Wood, M. A., et al. Performance and cost assessment of machine learning interatomic potentials, J. Phys. Chem. A 2020, 124, 731-745.45. Pukrittayakamee, A.; Malshe, M.; Hagan, M.; Raff, L. M.; Narulkar, R.; Bukkapatnum, S.; Komanduri, R. Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks, J. Chem. Phys. 2009, 130, 134101.46. Unke, O. T.; Meuwly, M. PhysNet: A neural network for predicting energies, forces, dipole moments, and partial charges, J. Chem. Theo. Comput. 2019, 15, 3678-3693.

Page 23 of 31



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

24

47. Zhang, Y.; Zhou, X.; Jiang, B. Bridging the gap between direct dynamics and globally accurate reactive potential energy surfaces using neural networks, J. Phys. Chem. Lett. 2019, 10, 1185-1191.48. Nguyen, T. T.; Székely, E.; Imbalzano, G.; Behler, J.; Csányi, G.; Ceriotti, M.; Götz, A. W.; Paesani, F. Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions, J. Chem. Phys. 2018, 148, 241725.49. Qu, C.; Yu, Q.; Van Hoozen, B. L.; Bowman, J. M.; Vargas-Hernández, R. A. Assessing Gaussian process regression and permutationally invariant polynomial approaches to represent high-dimensional potential energy surfaces, J. Chem. Theo. Comput. 2018, 14, 3381-3396.50. Kamath, A.; Vargas-Hernández, R. A.; Krems, R. V.; Carrington Jr., T.; Manzhos, S. Neural networks vs. Gaussian process regression for representing potential energy surfaces: A comparative study of fit quality and vibrational spectrum accuracy, J. Chem. Phys. 2018, 148, 241702.51. Chen, J.; Xu, X.; Xu, X.; Zhang, D. H. A global potential energy surface for the H2 + OH ↔ H2O + H reaction using neural networks, J. Chem. Phys. 2013, 138, 154301.52. Chen, J.; Xu, X.; Xu, X.; Zhang, D. H. Communication: An accurate global potential energy surface for the OH + CO → H + CO2 reaction using neural networks, J. Chem. Phys. 2013, 138, 221104.53. Bunker, P. R.; Jensen, P. Molecular Symmetry and Spectroscopy. NRC Research Press: Ottawa, 1998.54. Jiang, B.; Guo, H. Permutation invariant polynomial neural network approach to fitting potential energy surfaces, J. Chem. Phys. 2013, 139, 054112.55. Li, J.; Jiang, B.; Guo, H. Permutation invariant polynomial neural network approach to fitting potential energy surfaces. II. Four-atom systems, J. Chem. Phys. 2013, 139, 204103.56. Yang, D.; Zuo, J.; Huang, J.; Hu, X.; Dawes, R.; Xie, D.; Guo, H. A global full-dimensional potential energy surface for the K2Rb2 complex and its lifetime, J. Phys. Chem. Lett. 2020, 11, 2605-2610.57. Yang, T.; Li, A.; Chen, G. K.; Xie, C.; Suits, A. G.; Campbell, W. C.; Guo, H.; Hudson, E. R. Optical control of reactions between water and laser-cooled Be+ ions, J. Phys. Chem. Lett. 2018, 9, 3555-3560.58. Qin, J.; Liu, Y.; Lu, D.; Li, J. Theoretical study for the ground electronic state of the reaction OH + SO → H + SO2, J. Phys. Chem. A 2019, 123, 7218-7227.59. Hu, X.; Zuo, J.; Xie, C.; Dawes, R.; Guo, H.; Xie, D. An ab initio based full-dimensional potential energy surface for OH + O2 ⇄ HO3 and low-lying vibrational levels of HO3, Phys. Chem. Chem. Phys. 2019, 21, 13766-13775.60. Bai, M.; Lu, D.; Li, J. Quasi-classical trajectory studies on the full-dimensional accurate potential energy surface for the OH + H2O = H2O + OH reaction, Phys. Chem. Chem. Phys. 2017, 19, 17718-17725.61. Zuo, J.; Chen, Q.; Hu, X.; Guo, H.; Xie, D. Dissection of the multichannel reaction of acetylene with atomic oxygen: from the global potential energy surface to rate coefficients and branching dynamics, Phys. Chem. Chem. Phys. 2019, 21, 1408-1416.62. Liu, Y.; Bai, M.; Song, H.; Xie, D.; Li, J. Anomalous kinetics of the reaction between OH and HO2 on an accurate triplet state potential energy surface, Phys. Chem. Chem. Phys. 2019, 21, 12667-12675.63. Yao, Q.; Xie, C.; Guo, H. Competition between proton transfer and proton isomerization in the N2 + HOC+ reaction on an ab initio-based global potential energy surface, J. Phys. Chem. A 2019, 123, 5347-5355.64. Liu, Y.; Li, J. An accurate potential energy surface and ring polymer molecular dynamics study of the Cl + CH4 → HCl + CH3 reaction, Phys. Chem. Chem. Phys. 2020, 22, 344-353.65. Weichman, M. L.; DeVine, J. A.; Babin, M. C.; Li, J.; Guo, L.; Ma, J.; Guo, H.; Neumark, D. M. Feshbach resonances in the exit channel of the F + CH3OH → HF + CH3O reaction observed using transition-state spectroscopy, Nat. Chem. 2017, 9, 950-955.66. Lu, D.; Li, J.; Guo, H. Comprehensive dynamical investigations on the Cl + CH3OH → HCl + CH3O/CH2OH reaction: Validation of experiment and dynamical insights, CCS Chem. 2020, submitted.

Page 24 of 31



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

25

67. Li, J.; Guo, H. Communication: An accurate full 15 dimensional permutationally invariant potential energy surface for the OH + CH4 → H2O + CH3 reaction, J. Chem. Phys. 2015, 143, 221103.68. Hamermesh, M. Group Theory. Addison-Wesley: Reading, 1962.69. Lu, D.; Li, J. Full-dimensional global potential energy surfaces describing abstraction and exchange for the H + H2S reaction, J. Chem. Phys. 2016, 145, 014303.70. Weyl, H. The Classical Groups. Their Invariants and Representations. Princeton University Press: Princeton, 1946.71. Decker, W.; Greuel, G.-M.; Pfister, G.; Schonemann, H. Singular 4-1-2: A computer algebra system for polynomial computations, http://www.singular.uni-kl.de, 2019.72. Opalka, D.; Domcke, W. Interpolation of multi-sheeted multi-dimensional potential-energy surfaces via a linear optimization procedure, J. Chem. Phys. 2013, 138, 224103.73. Shao, K.; Chen, J.; Zhao, Z.; Zhang, D. H. Communication: Fitting potential energy surfaces with fundamental invariant neural network, J. Chem. Phys. 2016, 145, 071101.74. Lu, X.; Shao, K.; Fu, B.; Wang, X.; Zhang, D. H. An accurate full-dimensional potential energy surface and quasiclassical trajectory dynamics of the H + H2O2 two-channel reaction, Phys. Chem. Chem. Phys. 2018, 20, 23095-23105.75. Ping, L.; Zhu, Y.; Li, A.; Song, H.; Li, Y.; Yang, M. Dynamics and kinetics of the reaction OH + H2S → H2O + SH on an accurate potential energy surface, Phys. Chem. Chem. Phys. 2018, 20, 26315-26324.76. Fu, Y.-L.; Lu, X.; Han, Y.-C.; Fu, B.; Zhang, D. H.; Bowman, J. M. Collision-induced and complex-mediated roaming dynamics in the H + C2H4 → H2 + C2H3 reaction, Chem. Sci. 2020, 11, 2148-2154.77. Zhang, X.; Li, L.; Chen, J.; Liu, S.; Zhang, D. H. Feshbach resonances in the F + H2O → HF + OH reaction, Nat. Commun. 2020, 11, 223.78. Paukku, Y.; Yang, K. R.; Varga, Z.; Truhlar, D. G. Global ab initio ground-state potential energy surface of N4, J. Chem. Phys. 2013, 139, 044309.79. Qu, C.; Conte, R.; Houston, P. L.; Bowman, J. M. “Plug and play” full-dimensional ab initio potential energy and dipole moment surfaces and anharmonic vibrational analysis for CH4–H2O, Phys. Chem. Chem. Phys. 2015, 17, 8172-8181.80. Li, J.; Guo, H. Permutationally invariant fitting of intermolecular potential energy surfaces: A case study of the Ne-C2H2 system, J. Chem. Phys. 2015, 143, 214304.81. Behler, J. Atom-centered symmetry functions for constructing high-dimensional neural network potentials, J. Chem. Phys. 2011, 134, 074106.82. Krems, R. V. Bayesian machine learning for quantum molecular dynamics, Phys. Chem. Chem. Phys. 2019, 21, 13392-13410.83. Handley, C. M.; Hawe, G. I.; Kell, D. B.; Popelier, P. L. A. Optimal construction of a fast and accurate polarisable water potential based on multipole moments trained by machine learning, Phys. Chem. Chem. Phys. 2009, 11, 6365-6376.84. Dral, P. O.; Owens, A.; Yurchenko, S. N.; Thiel, W. Structure-based sampling and self-correcting machine learning for accurate calculations of potential energy surfaces and vibrational levels, J. Chem. Phys. 2017, 146, 244108.85. Uteva, E.; Graham, R. S.; Wilkinson, R. D.; Wheatley, R. J. Active learning in Gaussian process interpolation of potential energy surfaces, J. Chem. Phys. 2018, 149, 174114.86. Dai, J.; Krems, R. V. Interpolation and extrapolation of global potential energy surfaces for polyatomic systems by Gaussian processes with composite kernels, J. Chem. Theo. Comput. 2020, 16, 1386-1395.87. Cui, J.; Krems, R. V. Efficient non-parametric fitting of potential energy surfaces for polyatomic molecules with Gaussian processes, J. Phys. B 2016, 49, 224001.88. Kolb, B.; Marshall, P.; Zhao, B.; Jiang, B.; Guo, H. Representing global reactive potential energy surfaces using Gaussian processes, J. Phys. Chem. A 2017, 121, 2552-2557.

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http://www.singular.uni-kl.de

26

89. Guan, Y.; Yang, S.; Zhang, D. H. Construction of reactive potential energy surfaces with Gaussian process regression: active data selection, Mole. Phys. 2017, 116, 823-834.90. Laude, G.; Calderini, D.; Tew, D. P.; Richardson, J. O. Ab initio instanton rate theory made efficient using Gaussian process regression, Faraday Discuss. 2018, 212, 237-258.91. Christianen, A.; Karman, T.; Vargas-Hernández, R. A.; Groenenboom, G. C.; Krems, R. V. Six-dimensional potential energy surface for NaK–NaK collisions: Gaussian process representation with correct asymptotic form, J. Chem. Phys. 2019, 150, 064106.92. Vargas-Hernández, R. A.; Guan, Y.; Zhang, D. H.; Krems, R. V. Bayesian optimization for the inverse scattering problem in quantum reaction dynamics, New J. Phys. 2019, 21, 022001.93. Gastegger, M.; Marquetand, P. High-dimensional neural network potentials for organic reactions and an improved training algorithm, J. Chem. Theo. Comput. 2015, 11, 2187-2198.94. Smith, J. S.; Isayev, O.; Roitberg, A. E. ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost, Chem. Sci. 2017, 8, 3192-3203.95. Rivero, U.; Unke, O. T.; Meuwly, M.; Willitsch, S. Reactive atomistic simulations of Diels-Alder reactions: The importance of molecular rotations, J. Chem. Phys. 2019, 151, 104301.96. Yarkony, D. R. Diabolical conical intersections, Rev. Mod. Phys. 1996, 68, 985-1013.97. Domcke, W.; Yarkony, D. R.; Köppel, H., Conical Intersections: Electronic Structure, Dynamics and Spectroscopy. World Scientific: Singapore, 2004.98. Köppel, H.; Domcke, W.; Cederbaum, L. S. Multimode molecular dynamics beyond the Born-Oppenheimer approximation, Adv. Chem. Phys. 1984, 57, 59-246.99. Yarkony, D. R.; Xie, C.; Zhu, X.; Wang, Y.; Malbon, C. L.; Guo, H. Diabatic and adiabatic representations: Electronic structure caveats, Comput. Theo. Chem. 2019, 1152, 41-52.100. Guo, H.; Yarkony, D. R. Accurate nonadiabatic dynamics, Phys. Chem. Chem. Phys. 2016, 18, 26335-26352.101. Lenzen, T.; Manthe, U. Neural network based coupled diabatic potential energy surfaces for reactive scattering, J. Chem. Phys. 2017, 147, 084105.102. Guan, Y.; Fu, B.; Zhang, D. H. Construction of diabatic energy surfaces for LiFH with artificial neural networks, J. Chem. Phys. 2017, 147, 224307.103. Xie, C.; Zhu, X.; Yarkony, D. R.; Guo, H. Permutation invariant polynomial neural network approach to fitting potential energy surfaces. IV. Coupled diabatic potential energy matrices, J. Chem. Phys. 2018, 149, 144107.104. Williams, D. M. G.; Eisfeld, W. Neural network diabatization: A new ansatz for accurate high-dimensional coupled potential energy surfaces, J. Chem. Phys. 2018, 149, 204106.105. Lenzen, T.; Eisfeld, W.; Manthe, U. Vibronically and spin-orbit coupled diabatic potentials for X(2P) + CH4 → HX + CH3 reactions: Neural network potentials for X = Cl, J. Chem. Phys. 2019, 150, 244115.106. Guan, Y.; Zhang, D. H.; Guo, H.; Yarkony, D. R. Representation of coupled adiabatic potential energy surfaces using neural network based quasi-diabatic Hamiltonians: 1,2 2A′ states of LiFH, Phys. Chem. Chem. Phys. 2019, 21, 14205-14213.107. Guan, Y.; Guo, H.; Yarkony, D. R. Neural network based quasi-diabatic Hamiltonians with symmetry adaptation and a correct description of conical intersections, J. Chem. Phys. 2019, 150, 214101.108. Guan, Y.; Guo, H.; Yarkony, D. R. Extending the representation of multistate coupled potential energy surfaces to include properties operators using neural networks: Application to the 1,21A states of ammonia, J. Chem. Theo. Comput. 2020, 16, 302-313.109. Guan, Y.; Yarkony, D. R. Accurate neural network representation of the ab initio determined spin–orbit Interaction in the diabatic representation including the effects of conical intersections, J. Phys. Chem. Lett. 2020, 11, 1848-1858.

Page 26 of 31



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

27

110. Zhu, X.; Ma, J.; Yarkony, D. R.; Guo, H. Computational determination of the Ã state absorption spectrum of NH3 and of ND3 using a new quasi-diabatic representation of the X̃ and Ã states and full six-dimensional quantum dynamics, J. Chem. Phys. 2012, 136, 234301.111. Hu, D.; Xie, Y.; Li, X.; Li, L.; Lan, Z. Inclusion of machine learning kernel ridge regression potential energy surfaces in on-the-fly nonadiabatic molecular dynamics simulation, J. Phys. Chem. Lett. 2018, 9, 2725-2732.112. Dral, P. O.; Barbatti, M.; Thiel, W. Nonadiabatic excited-state dynamics with machine learning, J. Phys. Chem. Lett. 2018, 9, 5660-5663.113. Chen, W.-K.; Liu, X.-Y.; Fang, W.-H.; Dral, P. O.; Cui, G. Deep learning for nonadiabatic excited-state dynamics, J. Phys. Chem. Lett. 2018, 9, 6702-6708.114. Westermayr, J.; Gastegger, M.; Menger, M. F. S. J.; Mai, S.; González, L.; Marquetand, P. Machine learning enables long time scale molecular photodynamics simulations, Chem. Sci. 2019, 10, 8100-8107.115. Jiang, B.; Guo, H. Dynamics in reactions on metal surfaces: A theoretical perspective, J. Chem. Phys. 2019, 150, 180901.116. Golibrzuch, K.; Bartels, N.; Auerbach, D. J.; Wodtke, A. M. The dynamics of molecular interactions and chemical reactions at metal surfaces: Testing the foundations of theory, Annu. Rev. Phys. Chem. 2015, 66, 399-425.117. Guo, H.; Farjamnia, A.; Jackson, B. Effects of lattice motion on dissociative chemisorption: Toward a rigorous comparison of theory with molecular beam experiments, J. Phys. Chem. Lett. 2016, 7, 4576-4584.118. Alducin, M.; Díez Muiño, R.; Juaristi, J. I. Non-adiabatic effects in elementary reaction processes at metal surfaces, Prog. Surf. Sci. 2017, 92, 317-340.119. Rittmeyer, S. P.; Bukas, V. J.; Reuter, K. Energy dissipation at metal surfaces, Adv. Phys. X 2018, 3, 1381574.120. Busnengo, H. F.; Salin, A.; Dong, W. Representation of the 6D potential energy surface for a diatomic molecule near a solid surface, J. Chem. Phys. 2000, 112, 7641-7651.121. Blank, T. B.; Brown, S. D.; Calhoun, A. W.; Doren, D. J. Neural-network models of potential-energy surfaces, J. Chem. Phys. 1995, 103, 4129-4137.122. Lorenz, S.; Groß, A.; Scheffler, M. Representing high-dimensional potential-energy surfaces for reactions at surfaces by neural networks, Chem. Phys. Lett. 2004, 395, 210-215.123. Behler, J.; Lorenz, S.; Reuter, K. Representing molecule-surface interactions with symmetry-adapted neural networks, J. Chem. Phys. 2007, 127, 014705.124. Bukas, V. J.; Meyer, J.; Alducin, M.; Reuter, K. Ready, set and no action: A static perspective on potential energy surfaces commonly used in gas-surface dynamics, Z. Phys. Chem. 2013, 227, 1523-1542.125. Liu, T.; Fu, B.; Zhang, D. H. Six-dimensional potential energy surface of the dissociative chemisorption of HCl on Au(111) using neural networks, Sci. China: Chem. 2014, 57, 147-155.126. Liu, T.; Zhang, Z.; Fu, B.; Yang, X.; Zhang, D. H. A seven-dimensional quantum dynamics study of the dissociative chemisorption of H2O on Cu(111): effects of azimuthal angles and azimuthal angle-averaging, Chem. Sci. 2016, 7, 1840-1845 127. Zhang, Z.; Liu, T.; Fu, B.; Yang, X.; Zhang, D. H. First-principles quantum dynamical theory for the dissociative chemisorption of H2O on rigid Cu(111), Nat. Comm. 2016, 7, 11953.128. Liu, T.; Chen, J.; Zhang, Z.; Shen, X.; Fu, B.; Zhang, D. H. Water dissociating on rigid Ni(100): A quantum dynamics study on a full-dimensional potential energy surface, J. Chem. Phys. 2018, 148, 144705.129. Shen, X.; Zhang, Z.; Zhang, D. H. CH4 dissociation on Ni(111): a quantum dynamics study of lattice thermal motion, Phys. Chem. Chem. Phys. 2015, 17, 25499-25504.

Page 27 of 31



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

28

130. Shen, X.; Chen, J.; Zhang, Z.; Shao, K.; Zhang, D. H. Methane dissociation on Ni(111): A fifteen-dimensional potential energy surface using neural network method, J. Chem. Phys. 2015, 143, 144701.131. Jiang, B.; Guo, H. Permutation invariant polynomial neural network approach to fitting potential energy surfaces. III. Molecule-surface interactions, J. Chem. Phys. 2014, 141, 034109.132. Hu, X.; Zhou, Y.; Jiang, B.; Guo, H.; Xie, D. Dynamics of carbon monoxide dissociation on Co(11-20), Phys. Chem. Chem. Phys. 2017, 19, 12826-12837.133. Hu, X.; Yang, M.; Xie, D.; Guo, H. Vibrational enhancement in the dynamics of ammonia dissociative chemisorption on Ru(0001), J. Chem. Phys. 2018, 149, 044703.134. Zhou, X.; Nattino, F.; Zhang, Y.; Chen, J.; Kroes, G.-J.; Guo, H.; Jiang, B. Dissociative chemisorption of methane on Ni(111) using a chemically accurate fifteen dimensional potential energy surface, Phys. Chem. Chem. Phys. 2017, 19, 30540-30550.135. Chen, J.; Zhou, X.; Zhang, Y.; Jiang, B. Vibrational control of selective bond cleavage in dissociative chemisorption of methanol on Cu(111), Nat. Commun. 2018, 9, 4039.136. Bartók, A. P.; Kondor, R.; Csányi, G. On representing chemical environments, Phys. Rev. B 2013, 87, 184115.137. Zhu, L.; Amsler, M.; Fuhrer, T.; Schaefer, B.; Faraji, S.; Rostami, S.; Ghasemi, S. A.; Sadeghi, A.; Grauzinyte, M.; Wolverton, C., et al. A fingerprint based metric for measuring similarities of crystalline structures, J. Chem. Phys. 2016, 144, 034203.138. Kolb, B.; Luo, X.; Zhou, X.; Jiang, B.; Guo, H. High-dimensional atomistic neural network potentials for molecule–surface interactions: HCl scattering from Au(111), J. Phys. Chem. Lett. 2017, 8, 666-672.139. Liu, Q.; Zhou, X.; Zhou, L.; Zhang, Y.; Luo, X.; Guo, H.; Jiang, B. Constructing high-dimensional neural network potential energy surfaces for gas–surface scattering and reactions, J. Phys. Chem. C 2018, 122, 1761-1769.140. Shakouri, K.; Behler, J.; Meyer, J.; Kroes, G.-J. Accurate neural network description of surface phonons in reactive gas–surface dynamics: N2 + Ru(0001), J. Phys. Chem. Lett. 2017, 8, 2131-2136.141. Gerrits, N.; Shakouri, K.; Behler, J.; Kroes, G.-J. Accurate probabilities for highly activated reaction of polyatomic molecules on surfaces using a high-dimensional neural network potential: CHD3 + Cu(111), J. Phys. Chem. Lett. 2019, 10, 1763-1768.142. Huang, M.; Zhou, X.; Zhang, Y.; Zhou, L.; Alducin, M.; Jiang, B.; Guo, H. Adiabatic and nonadiabatic energy dissipation during scattering of vibrationally excited CO from Au(111), Phys. Rev. B 2019, 100, 201407.143. Yin, R.; Zhang, Y.; Jiang, B. Strong vibrational relaxation of NO scattered from Au(111): Importance of the adiabatic potential energy surface, J. Phys. Chem. Lett. 2019, 10, 5969-5974.144. del Cueto, M.; Zhou, X.; Zhou, L.; Zhang, Y.; Jiang, B.; Guo, H. New perspectives on CO2–Pt(111) interaction with a high-dimensional neural network potential energy surface, J. Phys. Chem. C 2020, 124, 5174-5181.145. Tully, J. C. Perspective: Nonadiabatic dynamics theory, J. Chem. Phys. 2012, 137, 22A301.146. Guo, H.; Saalfrank, P.; Seideman, T. Theory of photoinduced surface reactions of admolecules, Prog. Surf. Sci. 1999, 62, 239-303.147. Tully, J. C. Molecular dynamics with electronic transitions, J. Chem. Phys. 1990, 93, 1061-1071.148. Shenvi, N.; Roy, S.; Tully, J. C. Nonadiabatic dynamics at metal surfaces: Independent-electron surface hopping, J. Chem. Phys. 2009, 130, 174107.149. Carbogno, C.; Behler, J.; Reuter, K.; Groß, A. Signatures of nonadiabatic O2 dissociation at Al(111): First-principles fewest-switches study, Phys. Rev. B 2010, 81, 035410.150. Head-Gordon, M.; Tully, J. C. Molecular dynamics with electronic frictions, J. Chem. Phys. 1995, 103, 10137-10145.

Page 28 of 31



123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

29

151. Dou, W.; Subotnik, J. E. Perspective: How to understand electronic friction, J. Chem. Phys. 2018, 148, 230901.152. Persson, B. N. J.; Persson, M. Vibrational lifetime for CO adsorbed on Cu(100), Solid State Commun. 1980, 36, 175-179.153. Juaristi, J. I.; Alducin, M.; Díez Muiño, R.; Busnengo, H. F.; Salin, A. Role of electron-hole pair excitations in the dissociative adsorption of diatomic molecules on metal surfaces, Phys. Rev. Lett. 2008, 100, 116102.154. Maurer, R. J.; Jiang, B.; Guo, H.; Tully, J. C. Mode specific electronic friction in dissociative chemisorption on metal surfaces: H2 on Ag(111), Phys. Rev. Lett. 2017, 118, 256001.155. Spiering, P.; Meyer, J. Testing electronic friction models: Vibrational de-excitation in scattering of H2 and D2 from Cu(111), J. Phys. Chem. Lett. 2018, 9, 1803-1808.156. Maurer, R. J.; Zhang, Y.; Guo, H.; Jiang, B. Hot electron effects during reactive scattering of H2 from Ag(111): assessing the sensitivity to initial conditions, coupling magnitude, and electronic temperature, Faraday Disc. 2019, 214, 105-121.157. Spiering, P.; Shakouri, K.; Behler, J.; Kroes, G.-J.; Meyer, J. Orbital-dependent electronic friction significantly affects the description of reactive scattering of N2 from Ru(0001), J. Phys. Chem. Lett. 2019, 10, 2957-2962.158. Zhang, Y.; Maurer, R. J.; Guo, H.; Jiang, B. Hot-electron effects during reactive scattering of H2 from Ag(111): the interplay between mode-specific electronic friction and the potential energy landscape, Chem. Sci. 2019, 10, 1089-1097.159. Zhang, Y.; Maurer, R. J.; Jiang, B. Symmetry-adapted high dimensional neural network representation of electronic friction tensor of adsorbates on metals, J. Phys. Chem. C 2020, 124, 186-195.160. Zhang, Y.; Hu, C.; Jiang, B. Embedded atom neural network potentials: Efficient and accurate machine learning with a physically inspired representation, J. Phys. Chem. Lett. 2019, 10, 4962-4967.161. Baer, M. Beyond Born-Oppenheimer: Electronic Nonadiabatic Coupling Terms and Conical Intersections. Wiley: New Jersey, 2006.162. Zhu, X.; Yarkony, D. R. On the construction of property based diabatizations: Diabolical singular points, J. Phys. Chem. A 2015, 119, 12383-12391.163. Yin, R.; Zhang, Y.; Libisch, F.; Carter, E. A.; Guo, H.; Jiang, B. Dissociative chemisorption of O2 on Al(111): Dynamics on a correlated vave-function-based potential energy surface, J. Phys. Chem. Lett. 2018, 9, 3271-3277.164. Grisafi, A.; Wilkins, D. M.; Csányi, G.; Ceriotti, M. Symmetry-adapted machine learning for tensorial properties of atomistic systems, Phys. Rev. Lett. 2018, 120, 036002.165. Schütt, K. T.; Sauceda, H. E.; Kindermans, P. J.; Tkatchenko, A.; Müller, K. R. SchNet – A deep learning architecture for molecules and materials, J. Chem. Phys. 2018, 148, 241722.166. Han, J.; Zhang, L.; Car, R.; E, W. Deep potential: A general representation of a many-body potential energy surface, Commun. Comput. Phys. 2018, 23, 629-639.167. Brorsen, K. R. Reproducing global potential energy surfaces with continuous-filter convolutional neural networks, J. Chem. Phys. 2019, 150, 204104.168. Unke, O. T.; Meuwly, M. Toolkit for the construction of reproducing kernel-based representations of data: Application to multidimensional potential energy surfaces, J. Chem. Info. Model. 2017, 57, 1923-1931.169. Guan, Y.; Yang, S.; Zhang, D. H. Application of clustering algorithms to partitioning configuration space in fitting reactive potential energy surfaces, J. Phys. Chem. A 2018, 122, 3140-3147.

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Figure 1. Contour plots of the 15 dimensional PIP-NN PES for the Cl + CH3OH → HCl + CH3O reaction (a) along RHCl and RHO, and for the Cl + CH3OH → HCl + CH2OH reaction (b) along RHCl and RCH. All other coordinates are optimized.

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Figure 2. Contour plots of the 90 dimensional AtNN PES for CO* + O* CO2* CO2 reaction on Pt(111) along the CO2 reaction path in the vicinity of the reactive and non-reactive transition states. The first layer of the Pt surface and the reminder of the CO2 coordinates were optimized. Reproduced from Ref. 144 with permission.

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Gas-Surface Scattering Processes from Machine Learning High … · High-Fidelity Potential Energy Surfaces for Gas Phase and Gas-Surface Scattering Processes from Machine Learning