A polymer dataset for accelerated property prediction and design

Emerging computation- and data-driven approaches are particularly useful for rationally designing materials with targeted properties. Generally, these approaches rely on identifying structure-property relationships by learning from a dataset of sufficiently large number of relevant materials. The learned information can then be used to predict the properties of materials not already in the dataset, thus accelerating the materials design. Herein, we develop a dataset of 1,073 polymers and related materials and make it available at http://khazana.uconn.edu/. This dataset is uniformly prepared using first-principles calculations with structures obtained either from other sources or by using structure search methods. Because the immediate target of this work is to assist the design of high dielectric constant polymers, it is initially designed to include the optimized structures, atomization energies, band gaps, and dielectric constants. It will be progressively expanded by accumulating new materials and including additional properties calculated for the optimized structures provided.


Workflow
The workflow in Fig. 1 summarizes the preparation of the polymer dataset. In the first step, crystal structures of polymers and related compounds were collected from various available sources, including the reported literature, the Crystallography Open Database (COD) 15 , and our structure prediction works [20][21][22][23][24][25][26] . Those obtained from structure prediction runs were subjected to a preliminary filter (described below), removing any obvious redundancy of identical structures. Then, the selected structures were optimized by DFT calculations, yielding the equilibrium structures and their atomization energies E at . The energy band gap E g was then calculated on a dense grid of k points while their dielectric constant ε, which is composed of an electronic part ε elec and an ionic part ε ion , was computed within the framework of density functional perturbation theory (DFPT) 33 . In the next step, the computational scheme and the calculated results were validated with available measured data, including the measured band gap E g , the dielectric constant ε and/or the infrared spectroscopy (IR) measurements. Those which do not agree with the available experimental data are subjected to further calculations at tighter convergence criteria of residual atomic force (see Technical Validation for more details), and if better agreement is not reached, these points are removed from the dataset. A post-filtering step was finally performed on the whole dataset, keeping only distinct data points. Relaxed structures of all the materials are finally converted into the crystallographic information format (cif) using the pymatgen library 34 . A note was also provided together with the dataset, indicating the convergence criteria of the datapoints reported herein.

Structure accumulation
Our dataset includes three primary subsets, each of them originating from a distinct source. Subset 1 consists of common polymers which have already been synthesized, resolved, and reported elsewhere. This set contains 34 polymers, listed in Table 1. Collecting polymer structures of this class is challenging because the reported data is widely scattered, and in case the information obtained is sufficient to reconstruct structures, this work has to be done manually and hence, substantially laborious. We further note that only for a few of them, measurement for band gap, dielectric constant, and/or infrared (IR) spectrum have been performed. This data was used for the validation step.
Subset 2 includes 314 new organic polymers (284 of them have been used in ref. 11) and 472 new organometallic polymers. Their structures were generated from a computation-driven strategy 19,20 which has been used to rationally design various classes of polymeric dielectrics 11,[20][21][22][23][24][25][26] . The starting point of this strategy is a pool of common polymer building blocks, which are either organic, e.g., -CH 2 -, -NH-, -CO-, -O-, -CS-, -C 6 H 4 -, and -C 4 H 2 S-, or inorganic (metal-containing) like -COO-Sn(CH 3 ) 2 -OCC-, -SnF 2 -, and -SnCl 2 -. The repeat unit of an organic polymer is then created by concatenating a given number of organic building blocks while that of an organometallic polymer contains at least one inorganic block linked with a chain of several CH 2 groups. Next, chains of the repeat units (illustrated in Fig. 2) are packed in low-energy crystal structures which are determined by Universal Structure Predictor: Evolutionary Xtallography (USPEX) 23,35 or minima-hopping (MH) 36,37 , two of the currently most powerful structure prediction methods. In brief, these methods allow for predicting the low-energy structures of a material as the local minima of the potential energy surface, constructed from DFT energy. The efficiency of these methods have been successfully demonstrated for many different materials classes [38][39][40][41] , including a large number of organic 20,23 and organometallic polymers [24][25][26] .
The material structures used to prepare subset 3 were collected from COD. Generally, materials provided by COD are not polymers, but a number of them are collected in this dataset as they are closely related to the examined polymers. Although collecting materials structures from this database is straightforward, we limited ourselves to only those whose cell volumes are not too large, i.e., roughly 1,500 Å 3 and below. This subset contains 253 molecular organic and organometallic crystals, 178 of them have recently been used in ref. 10 by some of us. Table 2 summarizes the contents of the polymer dataset, which contains both polymers (subset 1 and 2) and non-polymers (subset 3). In terms of chemistry, the included materials can be classified as either organic or organometallic, incorporating different metals in their backbone. The complete list of chemical elements that appear in this dataset is given in Table 3.

Numerical calculations
The computed data reported in our dataset was prepared with density functional theory (DFT) 31,32 calculations, using the projector augmented-wave (PAW) formalism 42 as implemented in Vienna Ab initio Simulation Package (vasp) [43][44][45][46] . The default accuracy level of our calculations is``Accurate'', specified by setting PREC = Accurate in all the runs with vasp. The basis set includes all the plane waves with kinetic energies up to 400 eV, as recommended by vasp manual for this level of accuracy. PAW datasets of version 5.2, which were used to describe the ion-electron interactions, are also summarized in Table 3. The van der Waals dispersion interactions, known 47 to be important in stabilizing soft materials dominated by non-bonding interactions like polymers 48 , were estimated with the non-local density functional vdW-DF2 (ref. 49). The generalized gradient approximation (GGA) functional associated with vdW-DF2, i.e., refitted Perdew-Wang 86 (rPW86) 50 , was used for the exchange-correlation (XC) energies.
Because the examined material structures are significantly different in terms of the cell shape, the sampling procedure of their Brillouin zones must be handled appropriately. For each structure, a Monkhorst-Pack k-point mesh 51 of a given spacing parameter h k in the reciprocal space was used. For the geometry optimization and dielectric constant calculations, h k = 0.25 Å − 1 while the band gap calculations have been performed on a finer Γ-centered mesh with h k = 0.20 Å − 1 . We further set the lower limit for the Monkhorst-Pack mesh dimensionality, that is, the number of grid points along any reciprocal axis is no less than 3, regardless of how short the reciprocal lattice dimension along this axis is.
During the relaxation step, we optimized both the cell and the atomic degrees of freedom of the materials structures until atomic forces are smaller than 0.01 eV Å − 1 . Calculations for band gap E g was then carried out on top of the equilibrium structures. Because E g is typically underestimated with a GGA XC functional like rPW86 (ref. 52), this important physical property has also been calculated with the hybrid Heyd-Scuseria-Ernzerhof (HSE06) XC functional 53,54 with an expectation that the calculated result would become much closer to the true material band gap. Both E GGA g and E HSE06 g , the band gap calculated at the GGA-rPW86 and HSE06 levels of theory, are provided in all the entries of the dataset (see File format for more details). Finally, the dielectric constant ε of these structures was calculated within the DFPT formalism as implemented in vasp package. Calculations of this type involve the determination of the lattice vibrational spectra at Γ, the center of the Brillouin zone. This information is also used to compute the IR spectra of some structures for the purpose of validation.

Post-filtering
Given that the sources of the polymer dataset reported herein are diversified, any clear duplicate and/or redundancy should be identified and removed. Because the preliminary filtering step was performed only on subset 2 based on their DFT energy and band gap estimated during the structure prediction runs with a limited accuracy, an additional filtering step was performed on the whole dataset. Within this step, all cases with the same chemical composition but different by less than 0.1 eV in E g , less than 5 meV per atom in E at , and less than 0.1 in both ε elec and ε ion , are clustered. At this point, the number of clustered points is not large, and all of them were inspected visually, keeping only distinct materials.

Data Records
The complete dataset of 1,073 polymers and related materials can be downloaded as a tarball from Dryad Repository (Data Citation 1) or can be accessed via http://khazana.uconn.edu/ (all the records with ID from 0001 to 1073). All 4,292 DFT runs of the entire dataset (for each structure, there are 4 runs, including relax, dielectric, GGA band gap, and HSE06 band gap) are hosted by NoMaD Repository (Data Citation 2).

File format
All the information reported in the dataset for a given material is stored in a file, named as 0001.cif, where a cardinal number (0001 in this example) is used for the identification of the entry in the dataset. The first part of a file of this type is devoted to the optimized structure in the standard cif format which is compatible with majority of visualization software. Other information, including the calculated properties, is provided as the comments lines in the second part of the file as follow   While most of the keywords are clear, we used Source to provide the origin of the material structure and Class to refer to the class of materials which can either be ''organic polymer crystal'', ''organometallic polymer crystal'', ''organic molecular crystal'', or ''organometallic molecular crystal''. Keyword Label was used to provide more detailed information on the material, which can be the common name of the material if it is available, the ID of the record obtained from COD, or the repeat unit of the polymer structure predicted.

Graphical summary of the dataset
To graphically summarize the polymer dataset, we visualize it in the property space. Because the band gap and the dielectric constant are the primary properties reported by this dataset, three plots, namely E HSE06 g -ε elec , E HSE06 g -ε ion , and E HSE06 g -ε, were compiled and shown in Fig. 3. Materials from different classes are shown in different colors to clarify the role of the polymer chemical composition in controlling E g and ε. Within the recent effort of developing polymers for high-energy-density applications [19][20][21][22][23][24][25][26] , such plots are useful for identifying promising candidates, i.e., those which have high dielectric constant while maintaining sufficient band gap (E g ≥ 3 eV). Figure 3a clearly indicates a limit of the form ε elec $ 1=E g between ε elec and E g , which is applicable for both organic and organometallic classes of materials. We note that this behavior has also been reported elsewhere 10,19 . Figure 3c, on the other hand, demonstrates that the classes of organic and organometalic polymers and molecular crystals occupy different regions in the property space. At a given value of band gap, the organometallic polymers are generally much higher than the organic polymers in terms of the dielectric constant. While a fairly large number of organometallic polymers were already developed [24][25][26] , this observation suggests that there remains significant room for manipulating the dielectric constant of the organometallic polymers.

Technical Validation
Among the materials properties reported in the present dataset, the atomization energy E at is physically relevant and has always been used as a standard method for examining the thermodynamic stability of various classes of materials, including inorganic crystals [38][39][40][41] and polymers [19][20][21][22][23][24][25][26] . While the band gap E GGA g calculated at the GGA level of DFT is not ready to be compared with the measured data due to the aforementioned well-known underestimation 52 , E HSE06 g (the band gap calculated with the HSE06 XC functional) is expected to be rather close to the true band. We show in Fig. 4a E HSE06 g of 11 polymers for which the band gap has been measured experimentally. The calculated band gap seems to agree pretty well with the measured data with a numerical discrepancy of about 20% and below.
We now consider the calculations of the dielectric constants, namely ε elec and ε ion . Overall, the theoretical foundations and the implementations for calculating ε elec and ε ion are well developed and tested, leading to rather accurate results. Within the DFT-based perturbative approach, ε elec is computed via the response to the external field perturbations while ε ion is evaluated through the phonon frequencies at the Γ point of the Brillouin zone. To be precise, the dielectric response of a crystalline insulator to an external electric field E is given in terms of a frequency-dependent tensor ε αβ ðωÞ. To linear order, the electronic contribution of the dielectric tensor is given by where P α is the component along the α direction of the induced polarization P. On the other hand, the ionic part of the dielectric tensor is determined as In this expression, Ω is the volume of the simulation cell, appearing as a normalization factor. The sum is taken over the index m of the phonon normal modes, which assumes the frequency ω m,q = 0 at the Brillouin zone center (q = 0) while the mode oscillator strength S mαβ is determined through the Born effective charge Z s,αβ * of the atom s. For an isotropic material, the dielectric constant of the practical interest is taken to be the average value of its diagonal elements at the static limit, i.e., ε ¼ 1 3 P α ½ε αα ðω-0Þ.  Equation 2 implies that at the limit of ω → 0, ε αβ ion ðωÞ is rather sensitive to the numerical accuracy of ω m,q = 0 , which, in turn, suggests highly equilibrated materials structures for the DFPT calculations. As mentioned in the Workflow Section, if the calculated dielectric constant ε of a polymer is different from its measured data (this information is available for just a limited number polymers in subset 1 and 2) by more than 20%, the structures are further optimized until the residual atomic forces are smaller than 0.001 eV Å − 1 . Only those with calculated dielectric constant within 20% of the experimental data [shown in Fig. 4b] are kept.
Within our dataset, the IR spectrum was measured for some materials. From the computational side, this material characteristic can also be calculated rather accurately from the byproducts of the dielectric constant calculations with DFPT. In particular, the intensities of the infrared-active modes are given by 56 where e m,sβ is the β component of the normalized vibrational eigenvector of the mode m at the atom s. Obviously, all of the necessary quantities needed to calculate I m according to Equation 3 can be obtained within the DFPT-based computational scheme of ε, thus requiring essentially no computational overhead. This approach has widely been used in characterizing various classes of materials 57,58 . We show in Figure 4c-f the IR spectra calculated for four polymers, including orthohombic polyethylene, orthohombic polyoxymethylene, poly(dimethyltin glutarate) 24 , and polythiourea 20 , each of them is compared with the corresponding measured IR spectrum. The excellent agreement between the calculated and the measured IR spectra can be regarded as a supportive validation of the computational scheme based on DFT calculations used for this polymer dataset.

Usage Notes
This dataset, which includes a variety of known and new organic and organometallic polymers and related materials, has been consistently prepared using first-principles calculations. While the HSE06 band gap E HSE06 g is believed to be fairly close to the true band gap of the materials, the GGA-rPW86 band gap is also reported for completeness and for further possible analysis. The reported atomization energy and the dielectric constants are also expected to be accurate.
The polymer dataset is one among many recently developed datasets which can be used for designing materials by various data-driven approaches. To be specific, this dataset is expected to be useful in the development of polymers for energy storage and electronics applications. Moving forward, the development of this dataset will be continuously validated and updated, and the most recent version can be accessed at repository http://khazana.uconn.edu/.