Predicting the Electrochemical Properties of Lithium-Ion Battery

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C: Energy Conversion and Storage; Energy and Charge Transport

Predicting the Electrochemical Properties of Lithium Ion Battery Electrode Materials with Quantum Neural Network Algorithm Hwanho Choi, Kee-Sun Sohn, Myoungho Pyo, Kee-Choo Chung, and Hwangseo Park J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11335 • Publication Date (Web): 01 Feb 2019 Downloaded from http://pubs.acs.org on February 4, 2019

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The Journal of Physical Chemistry

Predicting the Electrochemical Properties of Lithium Ion Battery Electrode Materials with Quantum Neural Network Algorithm

Hwanho Choi†, Kee-Sun Sohn‡, Myoungho Pyo§, Kee-Choo Chung*†, and Hwangseo Park*†

†Department

of Bioscience and Biotechnology and ‡Department of Nanotechnology and

Advanced Materials Engineering, Sejong University, 209 Neungdong-ro, Kwangjin-gu, Seoul 05006, South Korea §Department

of Printed Electronics Engineering, Sunchon National University, Chonnam 540-742, South Korea

Author ORCID ID Hwanho Choi: 0000-0002-6204-0118 Kee-Sun Sohn: 0000-0002-7496-2283 Myoungho Pyo: 0000-0001-6411-7548 Kee-Choo Chung: 0000-0002-5210-8983 Hwangseo Park: 0000-0001-5806-2472

*Correspondence

may be addressed to either author.

Tel: +82-2-10-2963-1635 (KCC); +82-2-3408-3766 (HP) Fax: +82-2-3408-4334 (KCC); +82-2-3408-4334 (HP) E-mail: [email protected] (KCC); [email protected] (HP) 1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract

Discovery of new inorganic solid materials can be accelerated with the aid of a reliable computational tool for predicting the associated electrochemical properties. Hence, we propose a quantitative structure-property relationship model by combining the threedimensional (3D) quantum mechanical descriptors of materials and the artificial neural network algorithm, which is termed 3D-QANN model. 3D distribution of electrostatic potentials (ESPs) in the super cell of each inorganic solid material serves as the unique numerical descriptor to derive the 3D-QANN model. The optimized prediction model is then validated in terms of estimating the discharge energy density (D) and the capacity fading (Q) of lithium ion battery (LIB) cathode materials with layered structure. 3D-QANN model reveals good performance in predicting both D and Q values with high correlation with the corresponding experimental data. This indicates the suitability of the quantum mechanical ESP distribution as the numerical descriptor for LIB cathode materials. Due to the simplicity in model building and the high predictive capability, 3D-QANN model is anticipated to serve as a useful computational tool for estimating the electrochemical properties and accordingly for designing the new materials.

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Introduction As lithium ion batteries (LIBs) became prevalent in a variety of electronic and mechanical devices, it has been actively pursued to discover new electrode materials.1-14 Although a remarkable advancement has been made in the cell voltage and the charge-storage capacity, the current LIB technology remains insufficient to meet the need of innovative energy storage systems.15 Majority of efficient LIB electrode materials were identified via the trial and error of experimentation without the aid of appropriate computational methods. Although vast amounts of experimental data have accumulated regarding LIB cathode materials, the strong dependence of their electrochemical properties on the structural and compositional characteristics has rendered it difficult to establish a reliable computational model for designing the new materials. Nonetheless, quantum mechanical calculations based on density functional theory (DFT) have shed considerable light not only on elucidating the structureproperty relationship of LIB cathode materials but also on the discovery of new candidate compounds.16-19 Statistical data mining techniques have also proved useful in rationalizing the relationship between the structures and properties of inorganic solid materials as well as in reducing the computational cost for designing new materials.20 For example, a variety of numerical

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descriptors to express the inorganic compounds were adopted to relate them with the electrochemical properties through the rigorous computational algorithms including partial least square regression, artificial neural network (ANN), support vector machine, similaritybased learning model, and confirmatory factor analysis.21-25 Despite the implementation of the sophisticated computational algorithms, the predictive accuracy has remained unsatisfactory due to the imperfection of the numerical descriptors that have to reflect the three dimensional (3D) structural features and simultaneously the electronic structures of materials in a unique fashion. As a reliable computational method combining the merits of ab initio quantum chemical calculations and the data mining algorithms, we propose an ANN-based prediction model by adopting the 3D distribution of electrostatic potentials (ESPs) as the unique compound descriptor, which is termed 3D-QANN model. With respect to the suitability of ESPs as the descriptor, their distribution on the van der Waals surface yielded good correlation with some physical properties of organic molecules.26 The ESP distribution is extended in this work to cope with all the 3D grid points defined in the super cell of inorganic solid materials. This modification seems to be necessary because the current research interest lies in the basic electrochemical properties rather than the intermolecular interactions. Quantum mechanical ESP descriptors are then processed with the ANN algorithm to construct the 3D-QANN

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model adequate for LIB cathode materials of layered structure. With respect to the electrochemical properties to be predicted, we focus our interest on the discharge energy density (D) and the capacity fading (Q) because of the rarity of precedent computational investigations. It is anticipated for the 3D-QANN model to serve as a useful computational tool for the discovery of efficient LIB cathode materials because of the simplicity in model building and the high predictive capability for D and Q values.

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Computational Methods Preparation of the dataset to establish and validate 3D-QANN model. A series of LIB cathode materials and their electrochemical data were collected to construct the 3D-QANN prediction model for D and Q values. Among a variety of electrode materials deposited in Inorganic Crystal Structure Database (ICSD), 30 structures with crystallographic formula of [LiM]3b[LiγMδ]3a[O2]6c (C2/m space group) were retrieved to prepare the reference dataset, which could be structurally and electrochemically characterized without ambiguity. All the compounds involving the structural defects and cationic/anionic dopants were excluded in this work because of the difficulty in performing ab initio quantum chemical calculations. Electrochemical data of inorganic solid materials depend on the physical and chemical conditions under which the measurements are carried out. Among the multiple D and Q data available in the literature, included in the reference dataset for generating the 3D-QANN model were those measured at room temperature, using carbonate-based solvents with hexafluorophosphate (PF6-) salts, and at the rates ranging from 10 to 50 mAg-1. The experimental D and Q values of individual LIB cathode materials that satisfied the above conditions were extracted from various scientific papers.1-3,6,27-50 To derive and validate the 3D-QANN model, the dataset was divided into the training and test set with the ratio of 23:7 because 70-80% of the dataset members were selected as the training set most widely in the

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literature.51,52 In both cases of D and Q predictions, the 5-fold external cross-validation was performed with the five training and test sets generated at random. Calculation of quantum mechanical ESP descriptors. All the atomic coordinates of 30 compounds were calculated from Wickoff positions available in the original X-ray crystallographic data. Instead of coping with the entire crystal structure, the super cell of each inorganic solid material was adopted as the simplified model system to calculate the unique numerical descriptor. All individual super cells containing a total of 192 cations/anions were embedded in the same 3D grid box of dimension 27.5  20.0  42.8 Å. The length, width, and height of the grid box were determined by adding the marginal distance of 7 Å along the three coordinate axes of the super cell. ESP values were then calculated at the all grid points distributed with the uniform spacing of 0.25 Å in the common grid box. To derive the ESP distribution of a compound in the super cell, we first calculated the determinantal wavefunction comprising the molecular orbitals optimized at the restricted Hartree-Fock level of theory. In these quantum chemical calculations, 6-31+G basis set and the local Gaussian basis set developed by Towler et al.53 were used for oxygen anions and metal cations, respectively. The next step involved the calculation of charge density () at all the grid points in the common grid box, which was given by multiplying the square of the determinantal wavefunction by electronic charge (e). This density distribution was in turn

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used to calculate the ESP value at the grid point r (V(r)) according to the following relation.

V (r ) 

ZA  A r

R A



 (r )dr  r r

(1)

Here, ZA and RA denote the charge and the position of nucleus A, respectively, while r represents the electron coordinates. Basically, the ESP values reflect the charge distribution around a compound generated by its nuclei and electrons. The usefulness of ESP distribution has recently been appreciated in predicting the complexation pattern between Li+ ion and LIB cathode materials.54 Because the ESP values could be calculated everywhere in the common grid box, the descriptor of each LIB cathode material was constructed in the form of K-dimensional vector comprising the ESP values at the predefined K grid points. Because both geometrical and electronic structural features are taken into account, 3D distribution of ESP would have the advantage over classical 1D and 2D descriptors in terms of the correlation with the electrochemical properties of materials. The preparation of fully quantum mechanical 3D descriptors was facilitated by the advancement in graphics processing unit (GPU) architectures, which rendered it possible for the large super cell of inorganic solid materials to be handled with ab initio quantum chemical calculations. Because the common 3D grid box contained a vast number of grid points to discriminate 8


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the structurally similar LIB cathode materials, it was necessary to reduce the dimensionality of ESP descriptors to make them adequate for ANN modeling. This could be accomplished with principal component analysis (PCA) algorithm that has been widely employed to extract the principle components from complex numerical data.55 Finally, the reduced ESP vectors served as the numerical descriptors of LIB cathode materials to estimate their D and Q values through the ANN algorithm. Optimization of 3D-QANN prediction model. 3D-QANN model aimed to quantitatively predict the relationship between the ESP descriptors of inorganic solid materials and their electrochemical properties based on the ANN algorithm. Open-source ANN libraries were collected and linked to optimize the 3D-QANN prediction model in the feed-forward fashion with the backpropagation of error network.56 As depicted in Figure 1, the whole network consisted of input, hidden, and output layers. The reduced ESP vectors of the training-set compounds constituted the neurons in the input layer. All the input neurons ( Iˆ k ’s) were combined after multiplying the weighting factors (wki’s) to produce the new neurons ( Hˆ i ’s) in the hidden layer. These intermediate neurons were then hybridized to the single output neuron ( Oˆ ) whose vector elements (Oj’s) corresponded to the predicted D or Q values of N compounds in the training set.

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 N  Hˆ i  sgm  w ki Iˆ k     k 1 



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  and Oˆ  sgm   w ij Hˆ i  M

 i 1



(2)

Here, sgm(x) is the sigmoidal function defined by (1+e-x)-1. The output neuron can thus be related with the input vectors as follows.

 M  N  Oˆ  sgm  w ij sgm  w ki Iˆ k       k 1   i 1





(3)

Figure 1. Schematic representation of N  M  1 neural network adopted to optimize the 3DQANN model. Column I, H, and O represent the input, hidden, and output layer, respectively. The neurons in the three layers are mutually associated with weight matrices wki and wij.

All the weighting factors in eq 3 had to be determined to construct the 3D-QANN prediction model. This parameterization was carried out with the gradient-based minimization 10


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of the error hypersurface (E) defined by the sum of the squares of the differences between the experimental (Xj) and the predicted (Oj) electrochemical data of N compounds in the training set.

N

E

 X

j

Oj

2

(4)

j 1

In this work, nine intermediate neurons were introduced in the hidden layer to bridge 23 input neurons and the single output neuron. Preliminary to the operation of 23  9  1 neural network, all the experimental data were adjusted to range from 0 to 1 to match up with the sigmoidal function required for relating the ESP descriptors with the output neuron. Accordingly, the experimental D data were provided in the unit of Wh g-1 while the Q values reported in the unit of % loss per charge/discharge cycle were converted to (1-logQ)/3. Thus, the original D and the normalized Q (Qnor) values served as the baselines to optimize the respective 3D-QANN prediction models. The weighting parameters became convergent with the E values of 0.0002 and 0.0004 during the operation of ANN algorithms for predicting D and

Qnor

data

of

LIB

cathode

11


materials,

respectively.


Results and Discussion Figure 2 illustrates the super cell structures of two LIB cathode materials (LiCoO2 and LiNi0.8Co0.1Mn0.08Al0.02O2) with layered structure. It is characteristic of inorganic solid materials that the constituent atoms and ions occupy the fixed positions in the whole crystal structure. This is hardly true of organic molecules that have various translational, rotational, and conformational degrees of freedom. The motional flexibilities of organic molecules make it difficult to determine the optimal atomic coordinates of one molecule with respect to the others in the dataset. This leads to what is called the alignment problem that has been regarded as the bottleneck restricting the accuracy of statistical prediction methods for organic molecules.57,58 Such a critical problem becomes trivial in the case of structurally related inorganic crystalline solids due to the positional restraints, which offers the better opportunity to derive an accurate structure-property relationship model.

Figure 2. Super cell structures of (a) LiCoO2 and (b) LiNi0.8Co0.1Mn0.08Al0.02O2. 12


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Using the ESP distributions of 30 LIB cathode materials as individual descriptors, 3DQANN models were optimized and assessed through the 5-fold external cross-validation using the five training and test sets divided randomly at the ratio of 23 to 7. With respect to the electrochemical properties to be estimated, we focused our interest on the D and Q values of LIB cathode materials because precedent computational studies were relatively rare as compared to those on cell voltage, voltage profile, thermal stability, and ionic mobility.16 Table 1 lists the D and Q values of 30 compounds calculated with the best 3D-QANN model in the 5-fold external cross-validation in comparison with the experimental counterparts. The predicted D values of seven test-set compounds are in reasonably good agreement with the experimental data with only 12.7% of average error. The reliability of D prediction may be confirmed by the root-mean-square error (RMSE) of 0.065, which corresponds to 13.6% of the D value averaged over the test-set compounds. The accuracy of 3D-QANN model in D prediction is comparable to that of the previous deterministic method optimized and tested with four compounds,59 in which the RMSE values ranged from 0.122 to 0.176. However, the former seems to be more rigorous than the latter at least in the statistical sense because much more LIB electrode materials were involved in model building and validation.

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Table 1. Calculated D (in Wh g-1) and Q (in % loss per charge/discharge cycle) values of 30 LIB cathode materials in comparison with the corresponding experimental data. Asterisk indicates the compound in the test set. % error and RMSE values are calculated with respect to the experimental data for the seven compounds in the test set. compound

Dexp

Dcalc

Qexp

Qcalc

reference #

LiCoO2

0.543

0.508

0.510

0.337

27

LiNi1/3Mn1/3Co1/3O2

0.672

0.677

0.050

0.042

28

3

LiNi0.5Mn0.5O2

0.861

0.826

0.780

0.762

29

4

Li0.98Ni1.02O2

0.643

0.656

1.949

2.418

30

5*

Li0.94Ni0.90Mg0.16O2

0.422

0.335

6.031

6.446

30

6

LiFe0.15Co0.85O2

0.370

0.434

5.419

6.446

31

7

LiNi1/6Mn1/6Co2/3O2

0.616

0.603

0.490

0.476

1

8

LiAl0.25Ni0.75O2

0.563

0.566

0.170

0.113

32

9

LiNi0.8Co0.1Mn0.08Al 0.02O2

0.695

0.696

0.130

0.124

33

10*

LiNi0.8Co0.1Mn0.08Mg0.02O2

0.711

0.826

0.110

0.102

33

11

Li0.981Ni0.769Ti0.05Co0.2O2

0.743

0.776

0.310

0.257

34

12

Li0.963Ni0.737Ti0.10Co0.2O2

0.705

0.764

0.210

0.175

34

13

Li0.86V0.8O2

0.295

0.271

0.680

0.749

35

14

LiMn0.6Cr0.4O2

0.599

0.488

0.820

1.049

36

15*

Li1.25Mn0.5Cr0.25O2

0.445

0.420

0.110

0.076

37

16

LiNi0.5Mn0.4Ti0.1O2

0.630

0.635

0.020

0.042

38

17

Li1.24Ni0.07Co0.14Mn0.55O2

0.905

0.826

0.190

0.176

2

18*

LiNi1/3Mn1/3Fe1/3O2

0.353

0.420

0.160

0.163

3

19

LiNi0.5Co0.5O2

0.701

0.671

0.220

0.131

39

20

LiNi0.5Co0.4Al0.1O2

0.716

0.731

0.052

0.050

39

21

Li1.06Ni0.47Mn0.47O2

0.696

0.671

0.050

0.047

40

22

LiCo0.75Al0.25O2

0.446

0.439

5.629

6.446

41, 42

23

Li1.17Ni0.4Co0.08Mn0.33Zr0.02O2

0.468

0.535

0.500

0.515

43

24

Li0.91Na0.015Mn0.82O2

0.252

0.271

1.140

1.351

44

25*

LiNi0.4Mn0.5Mg0.1O2

0.508

0.460

2.269

1.702

45

26

LiCo0.95B0.05O2

0.466

0.481

0.450

0.419

46

27

Li1.02Ni0.88Ti0.1O2

0.351

0.406

1.739

1.702

47

28*

LiFeO2

0.240

0.271

0.760

1.134

6, 48

29

LiNi0.475Mn0.475Al0.05O2

0.762

0.764

0.060

0.076

49

30

LiNi0.98Ga0.02O2

0.735

0.747

0.050

0.056

50

# 1 2*

chemical formula

average % error

12.1

19.6

RMSE

0.065

0.301

14


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Although LIB electrodes with layered structure can yield high discharge capacity at high cell voltages, practical applications have often been hampered due to a rapid fade in capacity during the charge/discharge cycles. With respect to the degradation of LIB performance, various mathematical modeling techniques have been proposed to elucidate successfully the time evolutions of the capacity at varying temperatures.60-62 Although these previous studies provided a rationale for optimizing the charge and discharge protocols of LIB, it remained difficult to figure out the fluctuation of Q values with structural and compositional changes. To promote the discovery of new efficient LIB cathode materials, therefore, it is necessary to develop a computational tool for estimating the Q values with accuracy. Nonetheless, the development of a relevant computational method has lagged behind the mechanistic investigations on the capacity fade.63,64 This motivated the establishment of 3D-QANN model for predicting the Q values of LIB cathode materials. As listed in Table 1, the average error and RMSE amount to 19.6% and 0.301, respectively, when the Q values are estimated with the optimized 3D-QANN model. Related with the lower accuracy than in D prediction, it is noteworthy that the experimental data are unavailable for the intermediate Q values between 2.3 and 5.4 (Table 1). This can be invoked to explain the reduced performance because it is difficult for the weighting parameters to be fully optimized with the incomplete dataset. To the best of our knowledge, however, 3D-

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QANN prediction model provides the first example of computational application to account quantitatively for the differential Q values among various electrode materials. The reliability of 3D-QANN model was further assessed in terms of the correlation with the experimental data. Figure 3 shows the linear correlation diagrams between the experimental and calculated D values of 30 LIB cathode materials. The best and the worst prediction results produced in the 5-fold external cross-validation are presented together for strictness in proving the accuracy. The results of all five fits are provided in Supporting Information along with the elements of training and test set in each fold. 3D-QANN models were optimized well with good convergence irrespective of the components in the training set. Accurate prediction results are expected because the squared linear correlation coefficient for the training set (R2train) exceeded 0.920 in all five cases.

Figure 3. (a) The best and (b) the worst linear correlation diagram between the experimental and calculated D values of LIB cathode materials in training (black) and test set (red). 16


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All the prediction models optimized with varying training sets appear to be efficient to the extent that the squared linear correlation coefficient for the test set (R2test) ranges from 0.861 to 0.930. These good correlations are consistent with the low % error and RMSE (Table 1). To further validate the 3D-QANN model in estimating the D values of LIB cathode materials, we also calculated the external predictivity parameter (r2pred) that has been widely adopted to quantify the accuracies of various computational prediction methods.65 In general, a statistical model is considered predictive when the r2pred value exceeds 0.6.66 The r2pred values for varying training and test sets range from 0.817 to 0.905, which are comparable to those yielded in estimating the biological activities of small organic molecules with sophisticated quantum mechanical descriptors.67,68 The achievement of such a high predictive capability implies that the distribution of quantum mechanical ESPs in the super cell would be appropriate as a numerical descriptor for estimating the D values of LIB cathode materials. The good performance of 3D-QANN method also exemplifies the possibility of predicting the electrochemical properties of inorganic crystalline solids using the local electronic structure of the repetition unit. We next turn to assessing the correlation of the calculated Qnor values of LIB cathode materials with the corresponding experimental data. The best and the worst correlation diagrams are compared in Figure 4. All the results of the 5-fold external cross-validation are

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provided in Supporting Information along with the elements of training and test set in each fold. As in D predictions, 3D-QANN models were optimized well with 23 training-set compounds, yielding the R2train values larger than 0.947. The estimated Qnor values of seven compounds in the test set compare reasonably well with the experimental data with the R2test values of 0.983 and 0.853 for the best and the worst fit, respectively. The r2pred values exceed 0.766 and reach 0.978, the range of which becomes broader than that in the prediction of D values (Figure 3). Judging from the extent of correlation with the experimental data, Qnor values of LIB cathode materials can be predicted with the 3D-QANN model as precisely as the physical properties of small organic molecules that were derived from the all-atom level simulations of macroscopic systems.69,70 This supports the reliability of 3D-QANN model in predicting the electrochemical properties of inorganic solid materials.

Figure 4. (a) The best and (b) the worst linear correlation diagram between the experimental and calculated Qnor values of LIB cathode materials in training (black) and test set (red). 18


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Noting that the non-uniform distribution of Q values in the dataset (Table 1) became even more equitable by the normalization to (1-logQ)/3, we examined if the original Q values could also be estimated with the 3D-QANN model as accurately as the Qnor values. As shown in Figure 5, R2test and r2pred values of the worst 3D-QANN model decrease and increase a little bit to 0.838 and 0.792, respectively, due to the reconversion of Qnor to Q while those of the best fit remain almost invariant. It is thus confirmed that the normalization of Q data has trivial effect on the validation results for predictive capability. In both the best and the worst fit, the largest deviation is recorded at the Q values near the intermediate region in which experimental data are unavailable. In this regard, the performance of 3D-QANN model is expected to be enhanced further upon the availability of LIB cathode materials with the intermediate Q values.

Figure 5. (a) The best and (b) the worst linear correlation diagram between the experimental and calculated Q values of LIB cathode materials in training (black) and test set (red). 19



The experimental identification of new LIB electrodes may be impractical because of the difficulty in exploring the multivariate chemical space involving the atom type, oxidation state, and atomic composition. Furthermore, each candidate material should be screened through a complicated multistep process to measure a variety of electrochemical properties such as safety, cell voltage, ion mobility, capacity, and capacity fading. High-throughput computational techniques have accordingly emerged as an alternative to experimental screening, which was promoted by the advancement in both computing facilities and the theoretical modeling method for solid materials.71 Judging from the high predictive capability and the simplicity in model building, 3D-QANN method is anticipated to serve as a useful computational screening tool for candidate electrolyte materials. 3D-QANN model would also have the advantage over the atomistic simulation methods in terms of the computational cost because only a single point energy calculation on the super cell is required for each candidate material. Due to the structural rigidity, inorganic solid materials are more tractable for computational modeling than flexible organic molecules. Nonetheless, it is still a formidable take to investigate the former with data mining methods because the infinitely large system size makes it difficult to calculate the numerical descriptors of individual compounds. This is the reason why we simplified the structure of the entire crystalline solid to the repetition unit

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(super cell) as illustrated in Figure 2. Although such a cluster approximation may be inappropriate to elucidate the bulk phenomena of solid materials, it has often served as a good model system for estimating the physical properties associated with the local electronic structure.72 In this regard, the ESP distribution in the super cell seems to be a proper numerical descriptor to represent the crystalline LIB cathode materials as evidenced by the good correlations between the experimental and computational results for both D and Q values. Besides the electrode materials, the applicability of 3D-QANN method may be extended to other inorganic crystalline solids once the physical properties of interest become available for structurally similar compounds. The structural and positional restraints in inorganic solid materials are also meritorious in the context that D and Q values can be estimated with reasonable accuracy using only 23 compounds in the training set. This is remarkable because a few hundreds of members are usually required in the training set to derive a reliable quantitative structure-property relationship model for organic molecules.73 3D-QANN method is thus likely to work for the inorganic solid materials more efficiently than the flexible organic molecules. The experimental D and Q values of the newly synthesized LIB cathode materials are expected to be predictable with 3D-QANN method if they are included in the range of the reference dataset. Despite the reasonably high accuracy, the performance of 3D-QANN

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method needs to be further enhanced for practical applicability. We note, for example, that the errors in predicting the D value of compound 5 and the Q value of 25 amount to 20.6% and 25.0% even in the best model, respectively (Table 1). Most probably, a large portion of the error stems from the approximation of an infinite crystalline solid to the super cell, which was inevitable to calculate the numerical descriptor. A significant improvement of the predictive accuracy is therefore anticipated if one would apply the periodic boundary condition (PBC) to mimic the infinite system more closely than the simple cluster model. The outperformance of the PBC approach has been appreciated in elucidating the band structures of crystalline solids with ab initio quantum chemical calculations.74 Our future work will be focused on the enhancement of the predictive capability of 3D-QANN model within the PBC framework.

Conclusions We proposed a reliable computational method for estimating the electrochemical properties of inorganic solid materials using the ESP distribution in the super cell as the unique numerical descriptor. The performance of this 3D-QANN model was validated with the experimental data for the D and Q values of LIB cathode materials adopting the layered structure. High predictive capabilities were achieved with the 3D-QANN model in both cases in terms of varying statistical validation parameters. This indicates that 3D distribution of

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quantum mechanical ESPs in the super cell would be appropriate as a unique numerical descriptor for LIB cathode materials. The predictive accuracy of 3D-QANN seems to be enhanced further upon the availability of experimental Q data between 2.3 and 5.4, and the effective computational method to compute the ESP distributions of LIB cathode materials with the structural defects and cationic/anionic dopants. Due to the high predictive capability and the straightforwardness in model building, 3D-QANN method is expected to serve as a useful computational tool for predicting the physical properties of inorganic crystalline solids and accordingly for designing new materials.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Linear correlation diagrams of the calculated D, Qnor, and Q values of 30 LIB cathode materials with respect to the corresponding experimental data in the 5-fold external cross-validation. The members of the training and test set are indicated in each fold.

Author Contributions This paper was written by contributions from all the authors. All the authors have approved the final version of the manuscript.

Notes 23



The authors declare no competing financial interest.

Acknowledgements This work was supported by the financial supports from Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1D1A1B07051166), from BioNano Health-Guard Research Center of Global Frontier Project (H-GUARD_2014M3A6B2060507), and from Creative Materials Discovery Program (2015M3D1A1069705).

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Predicting the Electrochemical Properties of Lithium-Ion Battery

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