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.
Background & Summary
A central tenet of data-driven materials discovery is that if the volume of accumulated or available data is sufficiently large, and if it can be mined properly with suitable data-driven techniques, the process of designing a new material could be more efficient and rational1,
Within this context, it is worth noting that the recent rational development of nearly a hundred novel polymeric dielectrics for capacitive or electrostatic energy storage19,
This contribution describes a dataset of 1,073 polymers and related materials as the first step aiming at the rational design of polymers by data-driven approaches. The dataset reported herein, referred to as ‘‘polymer dataset’’ for convenience, was prepared at a uniform and consistent level of first-principles DFT computations. Since our initial goal is to assist the design of high dielectric constant polymers for energy storage, the polymer dataset supplies the equilibrium (relaxed) structures of the materials associated with relevant calculated properties, including the atomization energy εat, the dielectric constant ε and the energy band gap Eg. The initial structures used for the preparation were collected either from other available sources or, quite often, from computational structure searches. This dataset, which is available at http://khazana.uconn.edu/, can readily be expanded in multiple ways, i.e., new properties can be calculated from the provided equilibrium structures, and new materials with relevant calculated properties can also be progressively added. Furthermore, it may also serve as a playground for data-mining.
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 works20,
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 strategy19,20 which has been used to rationally design various classes of polymeric dielectrics11,20,
For each structure prediction run, the lowest-energy structure and those within 200 meV per atom above it were collected. The number of structures within this energy window is material-dependent, ranging from several to several dozens. Because many of them are just slightly different by small perturbations in the atomic arrangement, a preliminary filtering step was used to remove this redundancy. In particular, we used a clustering algorithm (hierarchical) to group those which are different by less than 5 meV per atom in εat and less than 0.1 eV in Eg, keeping the representative structures. Only those with polymeric motifs, when visually confirmed, are selected for the next steps. In the predicted polymer structures, especially for those of organometallic polymers, these polymeric chains are not necessarily isolated, i.e., inter-chain bonds may occur in various fashions24,
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 Å3 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.
The computed data reported in our dataset was prepared with density functional theory (DFT)31,32 calculations, using the projector augmented-wave (PAW) formalism42 as implemented in Vienna Ab initio Simulation Package (vasp)43,
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 mesh51 of a given spacing parameter hk in the reciprocal space was used. For the geometry optimization and dielectric constant calculations, hk=0.25 Å−1 while the band gap calculations have been performed on a finer Γ-centered mesh with hk=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 Eg was then carried out on top of the equilibrium structures. Because Eg 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 functional53,54 with an expectation that the calculated result would become much closer to the true material band gap. Both EgGGA and EgHSE06, 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.
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 Eg, less than 5 meV per atom in εat, and less than 0.1 in both εelec and εion, are clustered. At this point, the number of clustered points is not large, and all of them were inspected visually, keeping only distinct materials.
The complete dataset of 1,073 polymers and related materials can be downloaded as a tarball from Dryad Repository (Data Citation 1: Dryad Digital Repository http://dx.doi.org/10.5061/dryad.5ht3n) 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: NoMaD Repository http://dx.doi.org/10.17172/NOMAD/2016.01.27-1).
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
# Source: VSharma_etal:NatCommun.5.4845(2014)
# Class: organic_polymer_crystal
# Label: Polyimide
# Structure prediction method used: USPEX
# Number of atoms: 32
# Number of atom types: 4
# Atom types: C H O N
# Dielectric constant, electronic: 3.71475E+00
# Dielectric constant, ionic: 1.54812E+00
# Dielectric constant, total: 5.26287E+00
# Band gap at the GGA level (eV): 2.05350E+00
# Band gap at the HSE06 level (eV): 3.30140E+00
# Atomization energy (eV/atom): -6.46371E+00
# Volume of the unit cell (A^3): 2.79303E+02
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 , , and , 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 Eg and ε. Within the recent effort of developing polymers for high-energy-density applications19,
Figure 3a clearly indicates a limit of the form between and Eg, which is applicable for both organic and organometallic classes of materials. We note that this behavior has also been reported elsewhere10,19. 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 developed24,
Among the materials properties reported in the present dataset, the atomization energy is physically relevant and has always been used as a standard method for examining the thermodynamic stability of various classes of materials, including inorganic crystals38,
We now consider the calculations of the dielectric constants, namely and . Overall, the theoretical foundations and the implementations for calculating and are well developed and tested, leading to rather accurate results. Within the DFT-based perturbative approach, is computed via the response to the external field perturbations while 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 . To linear order, the electronic contribution of the dielectric tensor is given by where Pα 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 ωm,q=0 at the Brillouin zone center (q=0) while the mode oscillator strength Smαβ is determined through the Born effective charge Zs,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., .
Equation 2 implies that at the limit of ω→0, is rather sensitive to the numerical accuracy of ωm,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 by56 where em,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 Im 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 materials57,58. We show in Figure 4c–f the IR spectra calculated for four polymers, including orthohombic polyethylene, orthohombic polyoxymethylene, poly(dimethyltin glutarate)24, and polythiourea20, 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.
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 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/.
Huan, T. D. NoMaD Repository http://dx.doi.org/10.17172/NOMAD/2016.01.27-1 (2016)
The present work was supported by Multidisciplinary University Research Initiative (MURI) grant from the Office of Naval Research under Award No. N00014-10-1-0944. G.P. acknowledges the support provided by U.S. Department of Energy through the LANL/LDRD Program's Director's postdoctoral fellowship. A.M.K. would like to thank Turab Lookman at Los Alamos National Laboratory for providing access to computational resources. Computational work was made possible through XSEDE computational resource allocation number TG-DMR080058N59.
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