# Computational discovery of new 2D materials using deep learning generative
models

Yuqi Song, Edirisuriya M. Dilanga Siriwardane, Yong Zhao
Department of Computer Science and Engineering
University of South Carolina
Columbia, SC 29201
&Jianjun Hu *
Department of Computer Science and Engineering
University of South Carolina
Columbia, SC 29201
<EMAIL_ADDRESS>

###### Abstract

Two dimensional (2D) materials have emerged as promising functional materials
with many applications such as semiconductors and photovoltaics because of
their unique optoelectronic properties. While several thousand 2D materials
have been screened in existing materials databases, discovering new 2D
materials remains to be challenging. Herein we propose a deep learning
generative model for composition generation combined with random forest based
2D materials classifier to discover new hypothetical 2D materials.
Furthermore, a template based element substitution structure prediction
approach is developed to predict the crystal structures of a subset of the
newly predicted hypothetical formulas, which allows us to confirm their
structure stability using DFT calculations. So far, we have discovered 267,489
new potential 2D materials compositions and confirmed twelve 2D/layered
materials by DFT formation energy calculation. Our results show that
generative machine learning models provide an effective way to explore the
vast chemical design space for new 2D materials discovery.

_K_ eywords 2D materials $\cdot$ generative adversarial network $\cdot$ random
forest $\cdot$ template based substitution

##  1 Introduction

Two dimensional materials such as graphene and hexagonal boron nitride have
the potential to create new electronics and technologies such as spintronics,
catalysis, and membranes owing to their exotic vibrational, electronic,
optical[1], magnetic, and topological behaviors[2, 3, 4, 5]. Using DFT based
screening, Mounet et al. [6] have found 1,825 compounds with requisite
geometric and bonding criteria that should make them relatively easy to
exfoliate and so produce novel 2D materials with potentially interesting
physical and electromagnetic properties. They discovered 56 ferromagnetic and
antiferromagnetic systems, including half-metals and half-semiconductors. This
greatly expands the list of predicted 2D materials and could fill the gaps in
the characteristics and properties of the likes of graphene, phosphorene, and
silicene. One can also expand the list of 2D materials by chemical
substitutions, alternative site decorations, crystal structure prediction and
so on[7]. Several screening approaches have been proposed to find 2D materials
from known layered bulk materials [8]. A simple criterion of comparing
experimental lattice constants and lattice constants mainly obtained from
Materials-Project (MP) density functional theory (DFT) calculation repository
is used to find potential 2D materials [8]: a relative difference between the
two lattice constants for a specific material is greater than or equal to 5%
is used to identify good candidates for 2D materials. Haastrup et al. [9]
developed the Computational 2D Materials Database (C2DB), which contains a
variety of structural, thermodynamic, elastic, electronic, magnetic, and
optical properties of around 1500 2D materials distributed over more than 30
different crystal structures. More recently, Zhou et al. [10] developed
2DMatPedia, an open computational database of 6351 two-dimensional materials
by screening all bulk materials in the database of Materials Project for
layered structures by a topology-based algorithm and theoretically exfoliating
them into monolayers. New 2D materials have also been generated by chemical
substitution of elements in known 2D materials by others from the same group
in the periodic table. These databases of experimental or hypothetical 2D
materials have made it possible for discovering novel function materials [11,
12, 13, 14, 15].

Despite these efforts, the scale of experimental and hypothetical 2D materials
is still limited. For example, computational generation of novel new materials
have been proposed in the name of inverse materials design [16], in which new
materials are to be searched to achieve a given specific function, most of
these methods involve a global optimization or search/sampling procedure to
explore the search space[17]. However, most of such inverse design research is
based on screening known materials. Suleyman Er et al. [18] proposed an
elemental substitution based approach and applied it to known 2D materials
structural prototypes to generate a large number of hypothetical 2D materials,
and then filtered those materials based on several criteria. They deposited
their predicted 2D materials in their V2DB database.

To expand the scope of 2D materials, we propose to design a generative deep
learning method to discover novel 2D materials in uncharted composition space.
Our approach is based on a high-accuracy composition based 2D materials
classifier, which is used to screen millions of hypothetical materials
compositions generated using our MatGAN, a generative adversarial network
(GAN) based model [19] that learns to generate chemically valid hypothetical
materials. Based on 2.65 million generated samples, we have identified 267,489
hypothetical 2D materials.

Our contributions can be summarized as follows:

  * •

We propose a composition based 2D materials classifier model which achieves
high prediction accuracy when trained with known 2D materials.

  * •

We combine the 2D materials classifier and the composition based generative
machine learning to discover new 2D materials, which greatly expand the space
of 2D materials.

  * •

we apply a template based element substitution based structure prediction
approach to get the structures of hypothetical 2D materials and verify them
using DFT formation energy calculations and phonon thermostability
verification.

##  2 Materials and Methods

###  2.1 2D materials discovery framework

The schematic diagram of our 2D materials discovery framework includes the
following four modules (Figure1): a GAN based hypothetical materials
generator, a composition based 2D materials classifier, a template based
structure predictor, and a DFT confirmation procedure. The hypothetical
materials generator is trained with known inorganic materials in the Materials
Project database to learn the composition rules of forming stable chemically
valid materials compositions. Then, we use the generative module to breed a
large number of hypothetical formulas (two million in our study). These
formulas are then subjected to chemical validity tests including charge
neutrality check and electronegativity check. After that, the remaining
samples will be screened by the 2D materials classifier using composition
alone. To verify the predicted 2D materials compositions, we apply template
based element substitution to generate their hypothetical structures for a
subset of 624 predicted 2D materials compositions. Using DFT calculations, the
stability of these structures is calculated to verify the existence of these
candidate 2D materials from which we identified twelve potentially stable
materials.

Figure 1: Framework for generation and prediction of 2D materials. It
comprises four components. The green part: a GAN based composition generation
module for breeding chemically valid materials. The blue part: a composition
based random forest 2D materials classifier. The orange part: a template based
element substitution structure predictor, as well as yellow part: DFT
validation.

###  2.2 Generative deep learning for hypothetical inorganic materials

In the material design research area, one core task is to explore chemical
space for searching new materials. In our previous work, a generative machine
learning model (MatGAN) [19] is designed to efficiently generate new
hypothetical inorganic materials composition based on generative adversarial
network (GAN) [20]. There are two main tasks of MatGAN: one is how to suitably
represent material composition; the other one is how to design the generative
adversarial network for generating new materials.

When exploring the representation of inorganic materials, we found that there
totally are 85 elements in ICSD dataset; and there are no more than 8 atoms
per element in any specific compound. Therefore, each material could be
represented as a sparse matrix M of dimension $8\times 85$ with 0/1 cell
values, where $M_{i,j}=1$ means the number of atoms of the element at column j
is $i+1$. Figure 2 shows the encoding matrix for PuP2H6CO8.

Figure 2: One hot representation of material composition PuP2H6CO8. Brown
color indicates the atom number of corresponding element in the specific
material.

The architecture of MatGAN is shown in Figure 3. In this generative
adversarial network training, a generator is trained from existing real
material representations to generate new samples. Meanwhile, the discriminator
tries to differentiate real samples from generated samples; as the feedback,
the discrimination loss is then used to guide the training of the generator
and the discriminator’s parameters to reduce this difference. These two
training processes are repeated until good performances of both the generator
and the discriminator are achieved. The loss function is shown in the
following equation:

$\operatorname{Loss}=-\operatorname{Dice}=-\frac{2|A\cap
B|}{|A|+|B|}\approx-\frac{2\times A\bullet
B}{\operatorname{Sum}(A)+\operatorname{Sum}(B)}$ (1)

where $A\cup B$ denotes the common elements of A and B, |g| represents the
number of elements in a matrix, • denotes dot product, Sum(g) is the sum of
all matrix elements. The dice coefficient essentially measures the overlap of
two matrix samples with values ranging from 0 to 1, and 1 indicating perfect
overlap.

We have generated 2,650,623 hypothetical materials compositions, and 1,940,209
of them satisfy both charge neutrality and electronegativity balance criteria.

Figure 3: Architecture of MatGAN. Generator (G) learns from known material
compositions to generate realistic samples while discriminator (D) learns to
determine whether a sample is a real one or generated one. Alternative
training of D and G will improve the performance of both G and D.

###  2.3 Composition based classifiers for predicting 2D materials

Predicting whether a material is 2D structure can be regarded as a binary
classification problem. Our goal is to screen unknown 2D materials from
MatGAN-generated materials by training a random forest classifier with
verified 2D and non-2D materials, and then predicting the probability of being
a 2D material of each new material.

Specifically, we employ the Random Forest (RF) [21] as the surrogate model for
predicting the 2D probability given a material’ Magpie composition features.
Magpie feature set[22] is calculated using the matminer library [23] which is
a Python-based platform that facilitates data-driven methods for analyzing and
predicting material properties by calculating a variety of descriptors from
material compositions or crystal structures. Magpie feature set summarizes 132
features about material composition information, such as atomic number in the
material, range of melting temperature, mean absolute deviation of valence.
Those 132 features of each material will be calculated and used in our random
forest model training.

RF is a kind of supervised bagging ensemble learning algorithm. The idea
behind random forests is to exploit the wisdom of the group. RF builds many
decision trees in a random way with low correlation among them. After building
the forest, when a new sample needs to be classified, each decision tree makes
a judgment separately to vote which category the sample belongs to. Random
forest improves the prediction accuracy without significantly increasing the
amount of computation, and it is relatively robust to unbalanced data.

In the data preparation stage, we first collect known 2D and non-2D materials,
as well as MatGAN generated new materials. Then, we calculate the Magpie
features for all of them. In training the random forest model, known 2D
materials and non-2D materials are treated as positive and negative samples to
train the RF classifier with 10-fold cross-validation. The RF hyper-parameters
are tuned to achieve good prediction performance with detailed settings
explained in Section 3.2.2. Afterward, the trained RF model is utilized to
predict the labels and probability scores of 2D for generated hypothetical new
materials.

###  2.4 Template based structure prediction

Although we have predicted the 2D probability scores of the hypothetical new
materials generated by our MATGAN algorithm and the candidates with their
probability scores greater than 95% are likely to be 2D materials, it is not
enough to verify their existence by DFT calculation of their formation energy
or phonon calculation based stability check. However, crystal structure
prediction of complex compositions using current ab initio crystal structure
prediction algorithms are not feasible [24]. To address this issue, we propose
to use the template based or element substitution based structure prediction
method, which is shown in Figure 4.

Firstly, for each predicted 2D formula, we use the Crystal Structure
Prediction Network (CRYSPNet) [25] tool to predict its space group that the
formula most likely belongs to. This method consists of many neural network
models to predict the material’s space group, Bravais lattice, and lattice
constants. As CRYSPNet only needs chemical composition information as input,
we use it to estimate the top 3 potential space groups for each new
hypothetical 2D material.

Next, we try to find similar template materials from known 2D materials in the
2dMatpedia database. Specifically, For each new 2D formula with three
potential space groups, we search the target 2D material that has the same
number of elements and the same space group. However, one formula may lead to
many potential target 2D material template. To identify the most similar
template material, we use Element Movers Distance (ElMD) [26] to calculate and
sort the similarity between the candidate material and potential template
materials. ElMD is a similarity measure for chemical compositions, which is
measured by the minimal amount of work taken to transform one distribution of
elements to another along the modified Pettifor scale.

Finally, we select the top 10 most similar known 2D materials as the structure
templates according to the ElMD values. New 2D material’s structures could be
then predicted by one to one element substitution from those pairs. For
example, as shown in Figure 4, the structure of XY is predicted from the
structure of AB by using X to replace A (gray atom) and Y to replace B (yellow
atom).

Figure 4: The framework of template based structure prediction. The main parts
are: predicting new formula’s space group; finding candidate template formulas
according to the same element number and the same space group; calculating and
sorting ElMD between the new formula and template formulas; selecting top n
templates to do element substitution to get the new formula’s structure.

###  2.5 DFT calculation for verification

The density functional theory (DFT) calculations were performed based on the
Vienna ab initio simulation package (VASP) [27, 28, 29, 30]. The electron-ion
interactions were considered by using the projected augmented wave (PAW)
method [31, 32]. The energy cutoff value was set as 500 eV. The generalized
gradient approximation (GGA) based on the Perdew-Burke-Ernzerhof (PBE)
pseudopotentials [33, 34] represented the exchange-correlation potentials. The
energy convergence criterion was set as 10-7 eV, while the force convergence
criterion of the ionic steps was considered as 10-2 eV/Å. The
$\Gamma$-centered Monkhorst-Pack $k$-meshes were considered to perform the
Brillouin zone integration for the unit cells. Formation energy per atom of a
material were calculated based on Eq.2. Here, $E[\mathrm{Material}]$ is the
total energy per unit formula of corresponding material, $E[A_{i}]$ is the
energy of $i^{\mathrm{th}}$ element of the material and N indicates the total
number of atoms in a unit formula of the material.

$E_{\mathrm{form}}=\frac{1}{N}(E[\mathrm{Material}]-\sum_{i}E[A_{i}])$ (2)

##  3 Experiments

###  3.1 2D materials Dataset

All the 2D materials are collected from 2DMatPedia[10], an open computational
database of two-dimensional materials, which is constructed by a topology
based screening algorithm and element substitutions. There are 6,351 2D
materials in total, they are regarded as positive training samples in our
work. We also collect all existing materials from the materials project
database with 126,356 materials in total. After removing known 2D materials,
there are 115,498 negative samples. We use the MatGAN model to generate
2,650,264 new materials as candidates for 2D materials prediction.

Table 1: Datasets  Dataset | Amount | Role
---|---|---
2dMaterials | 6,351 | positive training sample
MaterialProject | 126,356 | negative training sample (exclude 2D materials)
ICSD_2M | 2,650,624 | potential new material
V2DB | 294,077 | comparative dataset

###  3.2 Results

####  3.2.1 Generation of candidate inorganic materials

Trained with 291,840 inorganic materials compositions in Material Project
database, a generative deep learning model (MATGAN) is used to generate
2,650,623 new compositions, and then charge neutrality and balanced
electronegativity are used to screen out 1,947,792 formulas, among which
1,940,209 are not in the training set. In order to better display the
generated materials distribution information, we draw a histogram based on the
element number, and another line chart to show the frequencies of 112
elements.

Figure 5: Generated materials distribution information.

The distribution of generated materials based on element numbers is shown in
Figure 5. The number of 2-element, 3-element, 4-element, >=5=element are 1217,
18946, 36827, 78639, respectively. There are two reasons to explain why binary
materials account for the least proportion: one is the diversity of the
combination of two elements is much less than that of five elements. The other
is many binary materials have already been discovered. The generated 2-element
materials play an important role in subsequent research because most known 2D
materials are binary materials.

Figure 6 shows the frequency distribution of 112 elements ordered by atomic
number in three datasets: generated ICSD-2M candidate materials by MatGAN, the
published 2D material dataset and the predicted 2D materials. From these three
curves, we can see that the top 5 crests positions basically overlap, the
number ranges are 7-9, 15-17, 32-35, 50-53, and 80-83. It proves that the
space of candidate materials generated by MatGAN is consistent with the real
2D materials. Furthermore, it provides a solid candidate range for the
following 2D new material prediction.

Figure 6: Element frequency distribution. The abscissa represents 112 chemical
elements arranged according to the atomic number from hydrogen (H) to
Copernicium (Cn), vertical axis indicates the frequency of each element. The
red curve denotes the distribution information of 2dMaterials dataset. The
green curve shows our generated candidate materials. The blue line represents
our predicted 2D materials.

####  3.2.2 Performance of the 2D materials classifier

The hyper-parameter configuration for training 2D random forest classifier is
set as follows: we set the maximum tree depth to be 20 and the number of
decision trees as 250. There are 6351 2D material samples and 15,959 non-2D
samples. In order to mitigate the imbalanced positive and negative samples, we
randomly select 1.5 times the number of positive samples as negative samples.
Besides, the class weight parameter is set to be balanced. With these settings
tuned per feature iteration, we train the RF 2D materials prediction models
and evaluate their performance. Our algorithm is implemented using the Scikit-
Learn library in Python 3.6.

To evaluate the prediction performance of our model, precision, recall,
accuracy, F1 score, and receiver operating characteristic area under the curve
ROC are used as performance metrics. ROC is plotted with TPR and FPR as the
vertical and horizontal axes under different threshold settings.

$TPR=\frac{TP}{TP+FN}$ (3)

$FPR=\frac{FP}{FP+TN}$ (4)

The accuracy, precision, recall, and F1-measure of the RF classifier with 10
fold cross-validation is 88.97%, 88.98%, 88.96%, and 88.96%. Figure 7(a) shows
the ROC curve of the classifier with an AUC score reaching 96%.

We also use a series of thresholds to differentiate 2D and non-2D materials to
evaluate the performance of the RF classifier, as shown in Figure 7(b). The
abscissa represents the the predicted probability threshold to declare a 2D
materials when its probability is higher than this threshold value; the y
coordinate indicates the corresponding false-positive rate. As the threshold
increases, the higher the probability score is required to be judged as a 2D
material leading to lower false-positive rate.

(a) ROC curve of the 2D materials RF classifier

(b) False-positive curve of the 2D materials RF classifier.

Figure 7: performance of random forest classifier.

####  3.2.3 Finding new 2D materials using our framework

To identify interesting hypothetical new 2D materials, we applied our RF-based
2D materials classifiation model to screen the 2.6 million hypothetical
materials generated by our Generative Adversarial Network (GAN) based on new
materials composition generator [19]. After predicting the probability of each
candidate belonging to 2D materials, we sort them by the probability scores.
The statistics of the predicted 2D materials with different probability
thresholds are shown in Table2. With a stringent probability threshold of
0.95, our algorithm has identified 1,485 hypothetical 2D material formulas
with 266 binary, 361 ternary, 327 quartenary candidates. When the threshold is
lowered to 0.9, the number of candidate 2D formulas increases to 5,034 or to
18,451 with threshold of 0.8.

To demonstrate how the newly predicted 2D materials are distributed in the
composition space, we apply t-sne dimension reduction tool [35] to map the
Magpie features of the 6351 2D materials in the 2Dmatpedia database and the
predicted 2D materials, and then plot their distribution in Figure 8. In
Figure 8(a), We apply the same dimension reduction transformation to both the
training set and the newly predicted 2D materials and visualize their
distribution where red points are training samples, and blue points are the
1485 predicted 2D materials with the highest probability scores. Similarly,
top 20,0000 predicted 2D materials are drawn as blue points in Figure 8(b)
together with known 2D materials used for training. We found that in Figure
8(a) the majority of blue points are located in the dense red point areas in
the bottom left corner (which can be seen also from Figure 8(c)), indicating
that our predicted 2D materials have similar composition distribution with
regard to known 2D materials. Figure 8(b) further confirms this composition
distribution match, in which we find that the blue points in general only
appear in areas with red points. The areas with sparse red points also contain
few blue points. Figure 8(c) shows the distribution of 20,000 hypothetical 2D
materials in the V2DB dataset against to the known 2D materials. It is found
these candidate 2D materials have different composition distribution as regard
to the known 2D materials: many yellow points appear in areas without red
points. Quite many yellow points reach out of the boundary defined by the red
points. For better comparison, top 6000 predicted samples by our method and
the V2DB are drawn in Figure 8(d) together with 6351 known 2D materials. It
can be seen that the majority of the overlapped blue and yellow points (117 as
shown in Table3) are located in the lower-left corner, which means there are
new 2D materials that are jointly predicted by both methods.

To screen out top candidate materials, we use the Roost algorithm [36] for
formation energy prediction, which is a graph network based machine learning
model for materials property prediction using only composition information.
After predicting the formation energies of all candidates, we draw a histogram
of formation energy distribution, as shown in Figure 6. Furthermore, we filter
out those with probability scores greater than 0.95 and then sort them by the
formation energy in ascending order and pick the top 40 candidates with 2, 3,
and 4 elements respectively. The results are in Table 4. In our supplementary
file, we have listed 1000 top hypothetical 2D materials with high 2D
probability scores and low predicted formation energies.

Furthermore, we analyze the 2DMatPedia dataset, 2-element materials occupy
65%, 3-element materials, and 4-element materials account for 25% and 9%,
therefore, from the perspective of the probability distribution, our
prediction is meaningful. We also find that the predicted 2D probabilities of
2-element materials are in general higher than those of 3-element materials
and 4-element materials, corresponding to the fact that the majority of known
2D materials (65%) are binary materials. We also count the number of our
predicted new 2D materials with 2D probability greater than 0.5 that overlap
with those in V2DB and 117 hypothetical 2D materials are found to be predicted
by both methods. Table 3 shows the overlapped candidate 2D materials in five
parts according to their 2D probability scores. It is found the overlapped
materials with 2D probability greater than 0.8 account for nearly 50% of all
overlapped candidates.

Table 2: Statistics of predicted 2D materials  2D Probability | # of Predicted new 2D formula | # 2 element | # 3 element | # 4 element | # >= 5 element
---|---|---|---|---|---
0.95 | 1,485 | 266 | 861 | 327 | 31
0.9 | 5,034 | 439 | 2,617 | 1,695 | 283
0.8 | 18,451 | 729 | 8,123 | 7,316 | 2,283
0.7 | 48,592 | 942 | 16,827 | 21,430 | 9,393
0.6 | 119,489 | 1,146 | 28,172 | 51,998 | 38,173
0.5 | 267,489 | 1,340 | 40,382 | 99,943 | 125,824

(a) New 2D materials (Probability > 0.95) vs. known ones

(b) 20,000 2D materials in the whole MP composition space

(c) 20,000 2D materials in the V2DB

(d) 6,000 2D materials in MP and V2DB vs. known ones

Figure 8: Distribution of the new and old 2D materials using t-sne visualization. Red ones are known 2D materials, blue ones are our predicted 2D materials while yellow ones are predicted 2D materials from V2DB. Figure (a) shows 1485 points with the highest 2D probability scores. (b) and (c) display distribution of 20,000 predicted samples from our model and from V2DB respectively. For better visual comparison, 6,000 predicted 2D materials from our model and from V2DB are shown together in (d). Figure 9: Formation energy distribution of predicted 2D materials. Table 3: Predicted hypothetical 2D materials that overlap with V2DB Formula | Probability | Formula | Probability | Formula | Probability | Formula | Probability | Formula | Probability
---|---|---|---|---|---|---|---|---|---
| >0.9 |  | >0.8 |  | >0.7 |  | >0.6 |  | >0.5
AgS | 0.9999 | ZrClS | 0.8997 | TiSeCl | 0.7913 | VISe | 0.6879 | NiF | 0.5998
AlS | 0.9982 | AlIS | 0.8926 | ZrSeF | 0.7900 | NiSeCl | 0.6830 | ZrTeN | 0.5993
ScI | 0.9840 | VClF | 0.8917 | SbSeO | 0.7856 | CoBrF | 0.6797 | MnSeS | 0.5872
InTeS | 0.9753 | FeClS | 0.8909 | ZrTeSe | 0.7802 | NiSF | 0.6794 | SrSF | 0.5840
SnTeSe | 0.9748 | PbTeS | 0.8884 | MnBr | 0.7793 | RhSeS | 0.6759 | YSeS | 0.5709
SnTeS | 0.9737 | GeSF | 0.8852 | MnIS | 0.7782 | CoTeS | 0.6740 | NbSeO | 0.5669
PbTeSe | 0.9465 | BiSF | 0.8830 | CuTeO | 0.7647 | CrSeO | 0.6732 | CoF | 0.5638
SbSeF | 0.9421 | TiClF | 0.8800 | CoCl | 0.7602 | CoSF | 0.6714 | NbTeO | 0.5636
SbClS | 0.9418 | ZnBrS | 0.8777 | GeSO | 0.7588 | RhTeS | 0.6710 | TaSO | 0.5604
GeClS | 0.9409 | MnClS | 0.8757 | ZnSF | 0.7579 | MnBrN | 0.6697 | TaTeS | 0.5506
AsClS | 0.9374 | SnSeO | 0.8727 | ZnSO | 0.7579 | AlSeO | 0.6609 | NiSO | 0.5474
SbSF | 0.9224 | ZnClS | 0.8725 | AgSO | 0.7557 | PbTeO | 0.6540 | NiSeO | 0.5419
NbSe | 0.9221 | AgIS | 0.8670 | CuSeF | 0.7546 | MnSeO | 0.6473 | YTeS | 0.5249
AlSeS | 0.9197 | PbSeO | 0.8535 | MnSF | 0.7518 | VSeS | 0.6451 | TiSeN | 0.5186
SnSO | 0.9181 | AsSF | 0.8532 | MnSeF | 0.7466 | NbSeF | 0.6367 | SrClS | 0.5120
BiTeS | 0.9102 | AgTeS | 0.8524 | AsSO | 0.7422 | RuTeS | 0.6310 |  |
AlTeS | 0.9060 | PbSO | 0.8494 | AgSeO | 0.7406 | TaSeO | 0.6217 |  |
|  | YClS | 0.8471 | ZrSeS | 0.7392 | FeSeF | 0.6190 |  |
|  | BiTeF | 0.8462 | CoClF | 0.7362 | TaTeSe | 0.6077 |  |
|  | NiClS | 0.8457 | PdFO | 0.7319 | CrTeO | 0.6066 |  |
|  | YTeF | 0.8457 | ZrTeO | 0.7317 | ZrSeN | 0.6014 |  |
|  | CoClS | 0.8433 | MnI | 0.7312 |  |  |  |
|  | VClS | 0.8397 | CuSF | 0.7245 |  |  |  |
|  | VSF | 0.8395 | AlSO | 0.7239 |  |  |  |
|  | AlTeCl | 0.8285 | TiTeS | 0.7230 |  |  |  |
|  | NiBr | 0.8254 | NiClO | 0.7077 |  |  |  |
|  | SbSeS | 0.8220 | NiTeCl | 0.7056 |  |  |  |
|  | AgSeS | 0.8217 | NbSO | 0.7005 |  |  |  |
|  | BiSO | 0.8201 |  |  |  |  |  |
|  | ZnClF | 0.8176 |  |  |  |  |  |
|  | TiSeF | 0.8155 |  |  |  |  |  |
|  | MnCl | 0.8077 |  |  |  |  |  |
|  | FeI | 0.8074 |  |  |  |  |  |
|  | AlSeF | 0.8017 |  |  |  |  |  |
|  | AlTeF | 0.8015 |  |  |  |  |  |
|  | CoI | 0.8002 |  |  |  |  |  |
Table 4: Hypothetical 2D materials sorted by predicted formation energy(only top 120 are listed here) 2 Elements | 3 Elements | 4 Elements
---|---|---
Formula | Probability |  | Formation
---
Energy
Formula | Probability |  | Formation
---
Energy
Formula | Probability |  | Formation
---
Energy
ZrF3 | 0.9876 | -3.8661 | ScYF3 | 0.9760 | -3.3429 | NbMoCl5S2 | 0.9757 | -1.5188
YF2 | 0.9880 | -3.7549 | NbMoF6 | 0.9720 | -3.0069 | CrNbMoCl8 | 0.9638 | -1.4547
TaF4 | 0.9990 | -3.4457 | ZnTaF5 | 0.9755 | -2.9848 | CrNbRuCl8 | 0.9598 | -1.3912
SiF3 | 0.9607 | -3.3363 | NbRuF7 | 0.9665 | -2.7521 | NbRuCl5S2 | 0.9753 | -1.3857
ZrF2 | 0.9997 | -3.1413 | InSnF5 | 0.9519 | -2.7437 | NbRuCl4S2 | 0.9712 | -1.3826
ScF | 0.9760 | -2.7647 | TaIrF7 | 0.9794 | -2.7379 | NbRuCl6S | 0.9673 | -1.3719
YF | 0.9640 | -2.747 | NbRuF6 | 0.9708 | -2.7165 | NbRuCl6S2 | 0.9633 | -1.3688
GeF3 | 0.9705 | -2.6997 | TaWO5 | 0.9732 | -2.6845 | CrMoCl5S | 0.9517 | -1.3163
NbF2 | 0.9671 | -2.5717 | ScYCl6 | 0.9677 | -2.6222 | NbMoRuCl6 | 0.9676 | -1.2988
YCl2 | 0.9919 | -2.4657 | NbMoO5 | 0.9816 | -2.6101 | Ga3AsCl6S2 | 0.9514 | -1.2548
ZrF | 0.9720 | -2.4356 | TaWF5 | 0.9760 | -2.5844 | InSn3SeCl6 | 0.9513 | -1.2127
WF3 | 0.9999 | -2.4182 | TaIrF5 | 0.9511 | -2.5832 | SnSbAsCl8 | 0.9593 | -1.205
TaF2 | 0.9880 | -2.4126 | ScYCl4 | 0.9679 | -2.527 | MoRuCl5S2 | 0.9633 | -1.171
AlF | 0.9999 | -2.4107 | YZrCl6 | 0.9598 | -2.4481 | Sn2AsCl6S | 0.9550 | -1.1705
ScCl2 | 0.9799 | -2.338 | ScZrCl6 | 0.9518 | -2.3783 | InSn3Cl4S2 | 0.9907 | -1.1704
GaF | 0.9995 | -2.0765 | MoRuF6 | 0.9708 | -2.352 | MoRuCl6S2 | 0.9633 | -1.1499
FB | 0.9880 | -2.0746 | TaOsF5 | 0.9640 | -2.3308 | Sb2BrAsCl8 | 0.9671 | -1.1406
F3C | 0.9800 | -2.0634 | ScTiCl4 | 0.9600 | -2.2386 | InSnCl2S2 | 0.9745 | -1.1381
InF | 0.9880 | -1.9397 | VTc2F7 | 0.9661 | -2.2366 | InSnCl4S2 | 0.9709 | -1.1229
Tc2O5 | 0.9650 | -1.9029 | VZrCl6 | 0.9560 | -1.9388 | SnSbAsCl4 | 0.9514 | -1.1043
ErBr3 | 0.9674 | -1.8561 | YLaBr6 | 0.9547 | -1.9262 | Sn2AsCl4S | 0.9628 | -1.0983
OsF3 | 0.9837 | -1.7279 | TbDyBr6 | 0.9729 | -1.8741 | Sn2AsCl8S2 | 0.9627 | -1.0955
NbCl3 | 0.9959 | -1.7273 | TiVCl6 | 0.9519 | -1.8074 | Sn3SeCl6S2 | 0.9509 | -1.0928
S2O5 | 0.9859 | -1.7237 | Nb3Cl8S | 0.9919 | -1.7429 | Sn2AsCl7S2 | 0.9587 | -1.0901
NbCl2 | 0.9799 | -1.7137 | NbCl2S | 0.9599 | -1.6969 | SnPb2Br2Cl2 | 0.9573 | -1.0892
OB | 0.9600 | -1.7046 | AlClS | 0.9596 | -1.6887 | Sn2AsCl6S2 | 0.959 | -1.0838
TaCl2 | 0.9950 | -1.6658 | TaRe2F6 | 0.9640 | -1.6724 | InSn2Cl2S2 | 0.9755 | -1.0789
RuF2 | 0.9864 | -1.5312 | CrNbCl7 | 0.9677 | -1.6054 | Sn2As2Cl6S | 0.9511 | -1.0705
SF | 0.9798 | -1.4954 | CrNbCl6 | 0.9758 | -1.602 | InSnClS2 | 0.9820 | -1.0414
MnCl3 | 0.9997 | -1.4641 | CrNbCl8 | 0.9637 | -1.5821 | Sn2AsCl4S2 | 0.9628 | -1.0387
CrCl4 | 0.9838 | -1.4529 | TiYBr6 | 0.9538 | -1.5738 | CuRuAgCl6 | 0.9629 | -1.0133
SeF | 0.9795 | -1.436 | SnPbCl6 | 0.9577 | -1.5723 | Sn2AsCl6S3 | 0.9587 | -1.011
O3C2 | 0.992 | -1.3673 | VMnCl4 | 0.96 | -1.5719 | Sn2SeCl6S2 | 0.9509 | -1.0109
GeCl3 | 0.9988 | -1.3663 | CrNbCl5 | 0.9598 | -1.5622 | Sn2SeCl5S2 | 0.9549 | -1.0048
YS3 | 0.9618 | -1.3661 | Te2SO5 | 0.9508 | -1.5303 | AsGeCl6S | 0.9590 | -1.0045
V2S3 | 0.9661 | -1.3311 | InSnCl6 | 0.9795 | -1.5166 | AsGe2Cl6S2 | 0.9636 | -0.9982
TiCl | 0.9599 | -1.3269 | SnTlCl5 | 0.9507 | -1.5121 | Sn2As2Cl6S3 | 0.9547 | -0.9832
HoS3 | 0.9755 | -1.3082 | TaWCl6 | 0.9794 | -1.5067 | Sn2SeCl4S2 | 0.9549 | -0.9821
SmS3 | 0.9555 | -1.3041 | NbMoCl6 | 0.9839 | -1.5054 | Sn2AsCl6S4 | 0.9590 | -0.977
YI2 | 0.9999 | -1.2846 | Cl6SSi2 | 0.9877 | -1.5012 | SnPb2Se2Cl2 | 0.9538 | -0.9457

####  3.2.4 Structure prediction and verification

To verify the predicted 2D materials, we picked 1485 predicted material
formulas with the highest probability scores and try to use the template based
structure prediction method to find their structures. For 101 materials, we
have found the templates of known layered materials or 2D materials in the
2DMatPedia database. We then predict the space group of our predicted 2D
materials and choose the templates with the same or similar space groups. We
then apply element substitution to get their structures. Some of the predicted
2D materials structures are shown in Figure10. In total, 101 predicted
materials with structures have been obtained. We then applied DFT relaxation
to 17 of these structures and calculate their formation energies. In total we
found 12 hypothetical materials with negative formation energy as shown in
Table 5. We found they are all binary materials with space group numbers
ranging from 11 to 166. The structures of four of these materials are shown in
Figure10, all showing layered structures as expected.

To further verify whether these hypothetical materials can really exist, we
applied DFT first principle calculation to compute the formation energies per
atom for 12 2D-layered materials as shown in Table 5. The materials with high
formation energies like TaF4 (-2.8048 eV/atom) and WF3 (-2.2548 eV/atom)
implies that the proposed method in this research is able to discover 2D
layered materials which are highly thermodynamically stable against the parent
compounds of their elements.

Table 5: Hypothetical 2D materials with DFT verified formation energies in eV/atom Formula | FormationEnergy | SpaceGroup | Formula | FormationEnergy | SpaceGroup
---|---|---|---|---|---
TaF4 | -2.8048 | P$2$/c [15] | YI2 | -1.2603 | C2/m [12]
WF3 | -2.2548 | P$2_{1}$/c [14] | YS3 | -1.1584 | P$2_{1}$/c [14]
YCl2 | -1.7472 | C2/m [12] | V2S3 | -0.9071 | C2/m [12]
MnCl3 | -1.4512 | R$\overline{3}$m[166] | MnBr3 | -0.6306 | R3m[166]
S2O5 | -1.4447 | P$2_{1}$/m [11] | AgCl2 | -0.5711 | Pmmn [59]
FB | -1.3800 | P$2_{1}$/c [14] | SeSi | -0.1462 | P$\overline{3}$m1 [164]

(a) 2D material YI2 by element substitution with formation energy -1.26 eV

(b) 2D materials MnCl3 by element substitution with formation energy -1.45 eV

(c) 2D material V2S3 by element substitution with formation energy -0.907 eV

(d) 2D materials WF3 by element substitution with formation energy -2.255 eV

Figure 10: Selected structures of the discovered new 2D materials with DFT
validation

##  4 Conclusion

We propose a generative inverse design approach for finding hypothetical new
2D materials. It includes a GAN based composition generation model for
generating chemically valid materials formulas, a composition based random
forest 2D materials classifier, a template based element substitution
structure predictor, and DFT verification. Using this pipeline, we have
generated 1485 hypothetical 2D materials with probability scores greater 95%.
We computationally verified 12 materials are 2D materials using DFT formation
energy calculation and validation two materials’ thermostability using DFT
phonon calculation. These new hypothetical materials can be used to guide the
screening of 2D materials for special functions using materials property
prediction models. The experiments demonstrate the effectiveness of the
proposed approach for discovering new 2D materials and can be used as a
complement of the prototype based element substitution based generation
approach.

##  5 Contribution

Conceptualization, J.H.; methodology, J.H., Y.S.; software, Y.S.; validation,
Y.S., D.S. and J.H.; investigation,J.H., Y.S., D.S., and Y.Z.; resources,
J.H.; data curation, J.H., Y.S. and Y.Z.; writing–original draft preparation,
J.H. and Y.S., E.S., and Y.Z.; writing–review and editing, J.H, Y.S.;
visualization, Y.S.; supervision, J.H.; funding acquisition, J.H.

##  6 Acknowledgement

Research reported in this work was supported in part by NSF under grant and
1940099 and 1905775. The views, perspective, and content do not necessarily
represent the official views of the SC EPSCoR Program nor those of the NSF.

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