Deep Learning Method to Accelerate Discovery of Hybrid Polymer-Graphene Composites

Interfacial encoded properties of polymer adlayers adsorbed on the graphene (GE) and silicon dioxide (SiO2) have been constituted a scaffold for the creation of new materials. The holistic understanding of nanoscale intermolecular interaction of 1D/2D polymer assemblies on substrate is the key to bottom-up design of molecular devices. We develop an integrated multidisciplinary approach based on electronic structure computation [density functional theory (DFT)] and big data mining [machine learning (ML)] in parallel with neural network (NN) and statistical analysis (SA) to design hybrid polymers from assembly on substrate. Here we demonstrate that interfacial pressure and structural deformation of polymer network adsorbed on GE and SiO2 offer unique directions for the fabrication of 1D/2D polymers using only a small number of simple molecular building blocks. Our findings serve as the platform for designing a wide range of typical inorganic heterostructures, involving noncovalent intermolecular interaction observed in many nanoscale electronic devices.


Data generation
As we have previously observed that molecular adsorption on graphene layers can tune the electronic and mechanical properties of substrate by structural deformation, charge transfer and orbital mixing [21][22][23] , interfacial properties of polymer adsorbed on graphene layers offer the best starting point. Herein, we demonstrate a exclusive approach to predicting hybrid organic-inorganic nanomaterials via leveraging advanced computational techniques including ab initio quantum mechanical computation based on density functional theory (DFT), statistical analysis techniques such as machine learning (ML), and neural network (NN) methods rooted in intelligent data mining ( Figure S1). The selection of simulation tools for materials screening must be guided by clearly defined objectives in terms of the electronic properties of polymer network interface that are desired for the target technology.
The adsorption of a 1D and 2D CPs/GE (SiO 2 ) as semiconductor heterostructures introduce significant variations of the electronic properties of substrate through structural deformation and orbital mixing, creating new class of materials with specific electronic surface states, which is unattainable in conventional semiconductors 24 .
To compare the electronic properties induced by 1D and 2D polymer adsorbed on two substrates, we calculate various interfacial properties via DFT calculations. The dataset for 244 material motifs of 4-blocks such as unitcells shown in Figs. 1, S4, S5, S13, S22 was gained by DFT quantum computation. We consider to the building blocks (BB) of the following seven possibilities: CH 2 , SiF 2 , SiCl 2 , GeF 2 , GeCl 2 , SnF 2 , and SnCl 2 . These BB set to be CH 2 , leading to polyethylene (PE), a common polymeric insulator. The Group IV halides introduced in a base polymer such as PE involve the beneficial effects on various properties.

On-demand interface properties and prediction
Some physical interfacial properties of adsorption of 1D CPs/GE such as adsorption energy (E ads ), the net Mulliken charges, structural deformation, energy gap, interfacial pressure (P = i,j F i,j A , where F i;j is the force on polymer ith atom due to graphene jth atom and A is GE area) and dipole moment are considered to acquire from DFT calculation.
When a polymer and graphene or SiO 2 are brought together, a host of phenomena can occur at their interfaces. The calculated band gap opening for 1D CPs/GE is around 0.5-2 eV (Figures S9, S10, S11, S12) and for 1D CPs/SiO 2 (Figures S16, S17, S20, S21), indicating that different functional groups and arrangement in these networks may introduce a symmetry breaking of the π-states near Fermi energy 25 . This suggestion is supported by the resulting band structure (Supplementary Information 4) where our calculated band gap openings agree with previous works 21, 23 where a small charge transfer and states mixing of the adsorbate with GE provokes a small band gap opening by breaking the local symmetry of band states of GE. The major effect at an interface is breaking the symmetry, which leads to a modification of the electronic and structural properties. A modification   (Table S2) support this local mixing of states. In semiconductor heterostructures, (see SI 2,4,5) this phenomenon has been exploited in a wealth of devices ranging from p-n junctions and Schottky diodes to high-mobility transistors based on 2D electron gases (2DEGs) 24 .
To probe the electronic states and states mixing in our system, we obtained the simulated scanning tunneling microscopy (STM) images for the adsorption of CPs/GE (SiO 2 ), plotted in Figures S7, S8, S18, S19, which give a perspective of the influence of CPs on substrates. Computing a STM image could reveal subtle information on the variation of electronic properties and extra electronic states; red protrusions are related to negative charge accumulation on the polymer moiety, consistent with Mulliken charge analysis presented in Tables S2, S3.
The DFT results of 1D CPs/GE (SiO 2 ) provide the necessary inputs for predicting new materials by ML (Figs. 2, S14I), and for NN interpretation by self-organization, Figs. 2, S14II. Figures 2, S14I show the agreement between trained data acquired by ML and test set data for six interfacial properties. The NN can cluster ML data into different classes topologically, providing insight into the correlation and similarity of interfacial interactions and a useful tool for creating classifications. NN qualitatively show a weight plane for each of the six input interfacial properties (Figs. 3, S14II), connecting each input to each of the 576 neurons in the 24 × 24 hexagonal grid (vector of dimension sizes [24 24] for clustering of data). Darker colors represent larger weights. If two inputs have similar weight planes (i.e. their color gradients may be the same or in reverse) they are highly correlated. For instance in Fig. 3 the adsorption energy and energy gap have reverse gradient color, then highly correlated.
Correlation diagrams as shown in Figs. 3, S14II offer a pathway to design novel materials with on-demand chemical-physical properties. One of the unique features of van der Waals (vdW) assembly of 2D crystals technology is the possibility of trapping molecules, which experience pressures as high as 1 GPa 26 . Here we demonstrate this interfacial pressure by adsorption of inorganic molecules and reveal its effect on the structural and conformational changes.
The correlation between pressure and other interfacial properties for CP/GE is key to predict new materials, which will be discussed shortly. Figure 4 demonstrates correlation of vdW hetero-structure pressure with several interfaces features of inorganic molecules adsorbed on GE. For instance, a search for a chain polymer adsorbed on GE with large pressure and charge transfer as shown by green circle in Fig. 5a, would lead to those systems at Fig. 5b i.e, systems with one Si at the starting point of chain and CH 2 at the middle of chain (for polymer/SiO 2 features see SI 2,5).
Finally, we predict new materials by using 8-block trained data obtained from 4-block trained data. We consider eight building blocks drawn from extension of the 4-block structures, such as: CH 2 SiF 2 SnF 2 GeF 2  www.nature.com/scientificreports/ CH 2 SiCl 2 SnCl 2 GeCl 2 , and their permutations. At first step, we compare DFT results of 8-block structures as test data with learning prediction and then for expanding our data into a family of 1D-chain polymers with 8-block repeat units (~ 60,000 data [244*244]), we employed the augmentation learning methodology to data sampling of huge number of possible cases. Determination of properties of 8-block trained data then followed by the estimation of Pearson's correlation coefficient for each pair of interfacial properties.

On-demand polymer design
To this end, while an excellent agreement between the ML training data of 4-block polymers and the DFT results for some interfacial properties is existing, the real application of this prediction paradigm establishes a platform for exploring a much greater systems than is practically possible using DFT computations (or experimentation). For instance, a search for high-mobility transistors via correlation map of Fig. 5h suggests a semiconductor with large band gap as shown by the purple circle in this Figure (in the case CPs/GE). The triangular map (Fig. 5d) confirms systems of contiguous SnF 2 GeF 2 SiCl 2 , indicating darker colors (see highlighted candidates by orange colors in Table S2). Moreover, a search for semiconductor heterostructures applicable in perovskite solar cells [27][28][29] , p-n junction and diodes require a system with high charge transfers between adsorbate and substrate. The top parts of panel (c) of Figure S15 (red circle) in the case of CPs/SiO 2 are good candidate to satisfy this purpose. As matched in the correlation map (the triangle in Figure S15), these are systems that contain 2 or more contiguous GeF 2 SnF 2 units as highlighted by orange color in Table S3, but with some fraction of CH 2 . Theses correlation diagrams can aid to extract the proper candidate from data, which can dictate material behavior such as Hume-Rothery-like semi-empirical rules. Moreover, Fig. 5e,f capture an inverse relationship between the adsorption energy and charge transfer with pressure (histogram of pressure in Fig. 5j). Figure 5h shows a direct relationship between band gap and pressure for 8-block 1D CPs, consistent with correlation matrix of CPs/GE in Fig. 4, which is for 4-block structures. These behaviors for adsorption energy (Fig. 5e), charge transfer (Fig. 5f), electrical dipole moment (Fig. 5g) band gap (Fig. 5h) and structural deformation (Fig. 5i) are quite familiar to the semiconductor community 30 .
The ML might offer new hypotheses and a step toward the creation of successful hybrid nanomaterials. Moreover, NN and CM between different interfacial properties of 1D polymer adsorption on graphene suggest that correlation between van der Waals pressure and other characters plays a key role to accelerate material discovery (as recently van der Waals pressure created new phase of materials 23,26 ), in line with experimental  Moreover, correlation matrix of 2D systems ( Figure S24) reveals that both electrical dipole moment and energy gap correlates with other interfacial properties as well. Our findings suggest that for 2D polymers, investigation of their adsorption on graphene and specifically the behavior of energy gap or dipole moment relative to electronic properties ( Figure S25) could be used as to predict novel materials.

Summary
This paper highlights integrated computational studies of physics phenomena at interfaces for polymer group IV adsorbed on GE (SiO 2 ), where non-intuitive interfacial interaction exists due to specific electronic surface states combined with quantum phenomena. We proposed a classified framework, in which the discovery of new materials accelerates by investigating electronic properties of adsorption of 1D and 2D polymers on GE and SiO 2 using first principles DFT, statistical analysis of big data, NN and ML analytical tools. The structural deformations of the polymers affect the modulation of electronic properties (charge transfer, band gap, adsorption energy, dipole moment) of GE and SiO 2 . Our findings show that the correlation between van der Waals pressure and other interfacial properties for CP/GE and the correlation between of structural deformation and  www.nature.com/scientificreports/ other interfacial properties for CP/SiO 2 (see SI for more details) play a major role on the prediction of materials. For instance, a search for p-n junction and diodes heterostructures such as polymers of group IV adsorbed on graphene (SiO 2 ) leads to systems that contain 2 or more contiguous GeF 2 SnF 2 units with an overall fraction of CH 2 (based on our computational results). Finally, our demonstration of emergent computational approach that uses NN, ML and CM algorithms trained on DFT big and deep data illustrates a path for developing new materials with exclusive physical and chemical properties that would be difficult to achieve through experimental set up. Such an approach could ultimately lead to the development of artificial materials for the creation of synthetic living materials as well as self-assembly networks for nanoengineering sciences.    www.nature.com/scientificreports/ Methods DFT study. To study the structural properties of polymer adsorbed on GE and SiO 2 , we have used the periodic density functional theory (DFT) technique that employs localized atomic orbital basis functions implication in SIESTA packages 32 . The dispersion corrected and vdW function (vdW-DF) is used for the exchange correlation term as described by Roman-Perez and Soler 33 , in conjunction with a basis set of double-ζ polarized 34 .
To include nonlinearity and transferability of core corrections, we used relativistic norm-conserving Troullier-Martins pseudopotentials for carbon, fluorine, chlorine, hydrogen, tin, silicon, oxygen atoms. The Brillouin zone (BZ) sampling is performed within the Monkhorst-Pack 35 by a fine grid of 12 × 12 × 1 to produce an accurate band structure. Optimization convergence criteria for the total energy were set to less than 10 -5 eV, with the self-consistent field (SCF) cycle set to 10 -5 Ryd and ≤ 0.01 eV/Å for forces 36,36 . The Mulliken method was used for charge transfer analysis, which is based on the linear combination of atomic and molecular orbitals to provide a means of estimating partial atomic charges.
To study and compare the variation of electronic properties induced by 1D and 2D polymer adsorbed on two substrates, we consider eight possible functional polymers for adsorption on GE. We have investigated different functional network structures shown in Figs. 1, S13, S22, S23. It is worth to note that we modeled these structures by repeating the unitcell in periodic boundary condition for both chain polymer and substrate simultaneously. Figures 1, S13 show the unit cells used to model the chain polymer on GE and SiO 2 network. The former system contains 54 atoms, comprised of 14 chain polymer for the adsorbate and 40 carbon atoms for GE and 50 atoms for SiO 2. In the case of 2D polymer system (Figures S22, S23) the model contains 78 atoms, comprised of 18 atoms for the 2D-polymer and 60 C atoms for GE. The interfacial electronic properties of these 2D polymers are plotted in Figures S26, S27, S28.
Kernel ridge regression. We apply the ML algorithm, kernel ridge regression (KRR) to our 1D and 2D polymer adsorbed on GE and SiO 2 . As we mentioned, the initial dataset was created using DFT with polymer building blocks of 4 atoms. We took 33 basis set for both 1D CPs/GE and CPs./SiO 2 , as shown in Fig. 5b 11 row*3 column), with 8 building blocks (BB1,…,BB8), which are different combination of SiF 2 , SiCl 2 , SnF 2 , SnCl 2 , GeF 2 , GeCl 2 , CH 2 and with total number 33*8 = 244 samples (for more details see Table S1).
We used ML algorithm based on KRR and probabilistic models for classification of datasete 37 . From a mathematical point of view with a regression task, we seek a function or model P, mapping an input vector x onto the corresponding property such as adsorption energy, charge transfer, etc. The ML algorithm is defined as a minimization problem of the form 38 : where the first term "l" is loss function, describing empirical risk, which determines the quality of the function P Tra . In our case study, we apply the squared loss function of l P Tra x i ′ , P DFT ( where P Tra is the training property label vector and P DFT is the interfacial property by DFT calculation. The second term is a regularization term, which determines the complexity or roughness of function P Tra . The interplay between these two terms relates to all functions P Tra predicting outputs i.e. interfacial properties from input x. At each of n discrete compositions, the variable x i indicate different structures of building block (BB1,…,BB8), present in the Figs. 1, S13, S22 (i.e., the domain of x i extends over the set of non-equivalent structure types that can occur at ith BB such as x 1 is BB1 sample, x 2 is BB2 sample, …, x 8 is BB8). We have a multiclass classification with k classes (every class related to one interfacial property, we have 6 different classes include 6 interfacial properties), and the feature from class k is modeled by an independent Gaussian with mean μ k and variance σ k 2 (likelihood procedure). Linear regression functions are generalized by KRR toward nonlinear functions, using a kernel function k x, x ′ to do it in one operation. One commonly used kernel is Gaussian kernel (k x, x 38 , facilitating treat of nonlinear problems by mapping into infinite-dimensional feature space, which σ is obtained by training data on the system. KRR uses the weights α i as quadratic constraints and solves the nonlinear regression model 38 : . After solving the minimization problem, the solution α = (K + I) −1 P DFT will acquired, where P DFT is the DFT label vector and K is the kernel matrix. The regularization parameter is a hyperparameter and kernel dependent parameters 39,40 .
The ML approach is based on establishing high quality prediction models, which are measured by the prediction error bar on new data. To separate the data set into training and a test set, we construct the average loss over the test set 38 : Equation (3) approximately determines the generalization error to build test set data. www.nature.com/scientificreports/ In a learning machine method, we need both optimizing the loss function regard to the model parameters, and choosing the hyper parameters accurately to tune the optimization problem. Herein, we used the established five-fold cross-validation 38 procedure to select the hyper parameters.
Neural network (NN). One of the major NN applications is the clustering data, involving grouping data into related subdivisions. The workflow for NN process has the following steps: (i) collect data, (ii) create the network, (iii) configure the network, (iv) initialize the weights and biases, (v) train the network, (vi) post-training analysis (validate the network), and (vii) use the network 41 . In a NN simulation method, three functional operations take place (for more details see Figure S3). Self-organizing map classifies vectors dataset and consists of a competitive layer ( Figure S3b). The input weigth vector of competitive layer IW i,j is made by the negative distance between input vector P and the weight vectors and adding the biases b. If input vector P equals the neuron's weight vector, all biases become zero. 2D topology network of neurons in a competitive layer distribute themselves to form a representation of input vectors 41 . The || ndist || box in Figure S3b, accepts IW i,j (input weight matrix), and produces a S i elements vector of weight matrix. The competitive transfer function returns neuron output of zero for net input vector except for the winner.
The NN simulation is trained with the self-organized algorithm 41 , using clustering process to categorize NN according to relative topology or pattern similarity. To simplify the data, one set data clustering map before further analysis.

Correlation matrix (CM). The correlation between different interfacial properties acquired by DFT and
ML play a key role in predicting large library of polymers. We plotted the correlation matrix for different properties in Figs. 4, S13 for 1D-chain polymer/GE and /SiO 2 . This correlation matrix between interfacial properties serves a full loop in the design cycles for materials discovery. To calculate the correlation matrix, we employ the most commonly method; Pearson correlation = (x−m x )(y−m y ) (x−m x ) 2 (y−m y ) 2 , where x,y are two arrays of length n, and m x , m y are the means of x and y variables. Pearson correlation depends on the distribution of data and compute a linear dependency between two properties (x,y).
In this paper, we focus on the description of interfacial properties of polymer adsorbed on GE and SiO 2 to discover novel polymers. We start from electronic structure calculation by using first principles DFT calculations, and then we employ ML methodology to train DFT data. Then we use statistical analysis to correlate different features to guide designing accurate polymer structures.

Data availability
The datasets generated during the current study are available from the corresponding authors upon reasonable request.