The Computational Design of Two-Dimensional Materials

Daniel P. Miller, Adam Phillips, Herbert Ludowieg, Sarah Swihart, Jochen

Autschbach and Eva Zurek∗

Department of Chemistry, State University of New York at Buﬀalo, Buﬀalo, NY 14260-3000, USA

E-mail: ezurek@buﬀalo.edu

∗To whom correspondence should be addressed

1 Abstract

A computational laboratory experiment investigating molecular models for hexag-

onal boron-carbon-nitrogen sheets (h-BCN) was developed and employed in an upper-

level undergraduate chemistry course. Students used the Avogadro user interface for

molecular editing, and the WebMO interface for the quantum computational work-

ﬂow. Density functional theory calculations were carried out to compare the electronic

structures, relative energies, and other properties of mono-, di-, and tetrameric h-BCN

molecular models. Experimental precursor molecules and other analogous single-layer

2-dimensional (2D) materials were studied as well. These computations exempliﬁed

how electronic properties such as the band gaps of potentially useful 2D-materials can

be ﬁnely tuned by varying chemical structure.

Keywords: Computational Chemistry, Upper–Division Undergraduate, Nan- otechnology, Physical Chemistry, Quantum Chemistry, Molecular Modeling, Lab- oratory Instruction, Computer–Based Learning, Molecular Properties/Structure, Curriculum

2 Introduction

Recently, intense research activity has been directed towards materials that are a single layer thick and periodic in two dimensions (2D-materials),1–5 with a number of top-tier journals and funding solicitations6 dedicated to this area. Despite the fact that materials research is highly interdisciplinary, involving individuals with backgrounds in various branches of chemistry, engineering, and physics, many chemistry students are underexposed to materials related topics in their undergraduate studies. The main goal of this computational experiment is to teach students how to use the results of computations carried out on ﬁnite molecules to design theoretically, from the bottom up, novel materials with properties that are useful for applications in 2D-electronics devices. To supplement the chemistry curriculum at our university we have implemented a computational chemistry laboratory course at the upper undergraduate level, in which molecular modeling and various computational techniques are introduced and employed. The students enrolled in the course have a diverse set of backgrounds. Whereas most have been chemistry BS/BA majors, some have majored in medicinal chemistry, biological sciences, various branches of engineering, or physics. During the 2012-2019 timeframe 112 students have completed the course. We have therefore developed computational laboratory experiments that appeal to this broad spectrum of students, and four of them have been published in this journal.7–11 The steadily rising importance of computationally guided rational materials design inspired us to develop this new experiment. Some 2D-materials that have been studied intensely are graphene,12–15 hexagonal boron

16,17 18 19–21 nitride (h-BN), graphitic carbon nitride (g-C3N4), transition metal dichalcogenides, Xenes or Xanes,22–24 among many others. Examples of some of these are illustrated in Fig. 1. The computational 2D-materials database contains the structures and properties of ∼2000 materials with more than 30 diﬀerent crystal structure types.25,26 One of the main distin- guishing features of a 2D-material is its band gap, which is a measured optical or fundamental gap between its conduction and valence bands, because it dictates the materials’ potential

3 applications. Whereas graphene does not have a band gap (it is a semi-metal), the gap in the isoelectronic and isotypic h-BN is ∼6 eV.27 Neither material is useful in electronics devices, which would require band gaps in between these two extremes. In the past, ﬁrst principles calculations based upon density functional theory (DFT) have been used to predict 2D- materials comprised of main group atoms with a wide range of band gaps.28–31 Moreover, it has been speculated that because graphene and h-BN both possess a honeycomb structure, it may be possible to synthesize an analogous layered hexagonal material containing boron, carbon, and nitrogen (h-BCN) with a band gap that can be tuned to a desired value. Previ- ous studies have investigated h-BCN experimentally,32–37 and theoretically.38–42 Within this laboratory experiment, students explore this hypothesis by performing DFT calculations.

(a) (b)

(c)

(d) (e)

Figure 1: Examples of 2D-materials: (a) graphene, (b) h-BN, (c) a hypothetical h-BCN structure, (d) germanane, (e) MoS2. Car- bon/boron/nitrogen/hydrogen/germanium/sulfur/molybdenum atoms are colored black/pink/blue/white/purple/yellow/turquoise.

4 Laboratory Course Set-Up

The experiments are conducted in a technology classroom where each student has access to a personal computer. Molecules are built and visualized using the open–source molecular editor and visualizer Avogadro,43,44 and computations are carried out using WebMO,45 which is a free web-based interface to computational chemistry packages. For this particular experiment, the Gaussian ’1646 program was employed. WebMO provides support for Gamess, Gaussian, MolPro, Mopac 7 & 20XX, NWChem, Orca, PQS 3.3, PSI 4, QChem, Tinker, PWSCF (Quantum Espresso), and VASP. This lab can therefore be adapted to use one of the other supported molecular quantum chemistry packages if Gaussian is not available. The computational nodes used for this course are maintained and administered by the University at Buffalo’s Center for Computational Research (CCR).47 A separate computation job queue was devoted to this class in order to ensure a fast turnaround of the computations. Each semester the students perform a total of four computational experiments, covering a wide range of topics,7–11,48 and two five-hour laboratory periods are allotted for each experiment. Because WebMO is used to manage the computations and visualize the results, the students can and do also work from their homes. At the beginning of each laboratory session, the instructor gives an introductory lecture about topics relevant to quantum chemistry (e.g. accuracy and precision in quantum chemistry,49 different levels of theory, basis sets, the orbital approximation,50 modeling the chemical environment), followed by a pre-lab lecture that introduces the specific experiment being performed. Students take a short quiz, whose purpose is to ensure that they have read the laboratory manual and paid attention to the introductory lecture, before they are allowed to start the experiment. In addition to the mandatory experiments, students are required to design an independent computational project in consultation with the instructor. They may choose an experiment that has already been published in this journal (e.g. Refs.51–84), design a project that is relevant to research projects they have carried out in experimental groups, or explore tech- nical aspects of first principles calculations. This allows students to focus on topics that are

5 interesting to them, and fosters their diverse backgrounds. Students are required to submit an abstract of the proposed project in advance. The abstract is revised until the instructor decides that it is feasible, ensuring that time is not wasted on projects that are impractical. In addition to the abstract and laboratory write-ups, the students give an oral presenta- tion of ∼15 minutes on their independent project. Many students enjoyed the independent project because it gave them an opportunity to focus on their interests and be creative. The number of students that carried out this particular experiment was twelve in 2018, and eight in 2019. To assess if the laboratory improved the learning process of the students, the class of 2019 was given a pre-lab quiz, and a post-lab assessment (both provided in the Supporting Information, SI). In the long answer portion of the pre-lab quiz, the students were asked to make hypotheses on how the structures of the dimers affected their stability, and on the effect of the presence of C-C bonds in the tetramers on the magnitude of their HOMO-LUMO gaps. In the post-lab assessment students were asked if they wanted to change or expand upon their initial hypotheses based on the results of their calculations. Generally speaking, most students were able to make informed hypotheses, and in the post- lab assessment they supported their initial hypotheses with the results of their calculations. Along with the questions on the post-lab assessment, students were asked to fill out a sur- vey in which six of the seven students in attendance reported a positive improvement in their understanding of the key objectives provided in the lab manual, suggesting that the pedagogical goals were achieved.

Experiment

The computations were carried out using DFT with the Perdew-Burke-Ernzerhof85 generalized gradient approximation (PBE-GGA) and a 6-31G(d) basis set. Students built, optimized, and calculated the electronic structure of mono-, di-, and tetrameric h-BCN molecular analogues (as well as some experimental precursors) according to the detailed instructions

6 provided in the laboratory manual (see SI). The successive increase in the system size (from monomer to tetramer) increases the potential combinatorial structures and also illustrates finite size effects and the trends towards periodicity, as is evidenced by a decreasing gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which is used to approximate the band gap. Students draw conclusions regarding stability, preferred structural motifs, electronic structure, and spectroscopic properties of the hypothetical materials, guided by the questions in the manual. The instructor emphasizes the power of these modeling methods for predicting trends in compounds and materials that cannot yet be synthesized. It is well known that the experimentally measured band gap is underestimated by GGA functionals, and more reliable estimates can be obtained using a hybrid functional such as B3LYP86 or PBE0.87 Depending upon the computational resources available the instructor may want to employ these hybrid functionals, or investigate the effect of the basis set or functional on the results vs. the CPU time consumed. The experiment described below could also potentially be adapted to other 2D-materials, some of which are shown in Fig. 1. For example, Fig. 1(d) illustrates the most stable chair conformation of germanane, but other single layer GeH structures are known,29 or can be imagined.

Results

A recent study36 suggested that it might be possible to synthesize h-BCN starting from the

88 precursor molecule bis-BN cyclohexane, B2N2C2H12. Accordingly, the students considered the dehydrogenation reaction (B2N2C2H12 → B2N2C2H6+3H2), which was endothermic by ∼46 kcal/mol. Vibrational frequency calculations showed that the resulting bis-BN benzene molecule is a local minimum suggesting it may be kinetically stable. Next, dimers were constructed from the bis-BN benzene molecule by forming a single bond between one atom in each heterocycle (and removing a hydrogen from each). Dimers were formed through C-C, C- B, C-N, and B-N bonds. A stabilizing intermolecular dihydrogen bond is formed between two

7 hydrogen atoms on adjacent monomers, one which is protic and the other which is hydridic, − e.g. B-Hδ ··· Hδ+-N.89,90 For each dimer, rotamers exist about the newly formed bond, which are characterized by the nature of the stabilizing or destabilizing dihydrogen bonding hydrogens (see Table 1). Eight h-BCN dimers are constructed with the initial unoptimized geometries all having the two rings in the same plane. After optimization, most of the dimers are twisted out of the plane, while some remain flat due to favorable vs. unfavorable dihydrogen interactions. For example, the more stable C-C bound dimer, shown in Fig. 2(a), allows for the formation of stabilizing dihydrogen interactions (B-H−0.04 · ··H+0.34-N), and results in a flat molecule. Conversely, the rotamer of this C-C dimer, shown in Fig. 2(b), results in unfavorable dihydrogen interactions, and adopts a 21◦ dihedral angle. Isosurfaces of the frontier MOs are also provided in this figure. Note the π character of the orbitals, the increased number of nodes in the LUMO as compared to the HOMO, and the fact that the MOs of the two rotamers are related by a rotation about the C-C bond.

HOMO LUMO (a)

(b)

Figure 2: Frontier molecular orbital isosurfaces computed for (a) the lowest energy C-C bound dimer with stabilizing N-Hδ+ · ··Hδ−-B interactions, and (b) the highest energy C-C bound dimer with destabilizing N-Hδ+ ···Hδ+-N and H-Bδ− ···Hδ−-B interactions. The HOMO is shown in red/blue and the LUMO is displayed in yellow/green, isovalue 0.05 a.u.

Table 1 provides typical student data for the type of dihydrogen interactions present, relative energies, formation energies (from dimers of benzene and h-BN) and HOMO-LUMO gaps for each of the eight h-BCN dimers (optimized coordinates are provided in the SI). B-N bonded dimers are the most stable, and C-N bonded dimers are the least stable, with the

8 Table 1: Typical student data calculated for the eight h-BCN dimers (PBE functional, G-31G(d) basis): the dihydrogen bond type, energies relative to the most stable dimer (Erel), formation energy from the h-BN and benzene dimers (∆EF), and HOMO-LUMO gaps. Select data is also provided for the h-BN dimer.

Dimer Dihydrogen Bond Type Erel (kcal/mol) ∆EF (kcal/mol) HOMO-LUMO (eV) B-N B-H···H-N 0.0 112.2 1.94 B-N C-H···H-N 1.2 113.3 1.92 C-C B-H···H-N 2.1 114.2 1.53 C-B B-H···H-N 4.9 116.9 1.85 C-C B-H···H-B 7.1 119.0 1.41 C-B N-H···H-N 7.4 119.4 1.75 C-N B-H···H-N 15.8 127.4 1.84 C-N B-H···H-B 17.6 129.2 1.79 h-BN B-H···H-N - - 5.12

dihydrogen interaction dictating which rotamer is preferred. C-C and C-B bonded dimers are intermediate to these two extremes, and their relative stability is primarily determined by the dihydrogen interactions. The formation of the dimers from benzene and h-BN is endothermic, suggesting it must be catalyzed and can only occur at high temperatures. However, vibrational frequency calculations confirm the dimers are local minima. Students are asked to visualize the partial charges on each atom type and to use this information to justify why certain geometries are flat, whereas others are twisted. They find that the HOMO-LUMO gap is primarily dependent upon the bond between the two monomers, with B-N > C-N ≈ C-B > C-C. All of the HOMO-LUMO gaps are lower than that of an h-BN dimer, whose gap is close to that of a 2D h-BN sheet. Students are asked to generate the IR spectra of the three lowest energy dimers. Fig. 3 shows the computed spectra for the most stable C-C and B-N bound dimers with the major peaks assigned to the corresponding vibrational modes. Making these assignments can be performed via the visualization software in the WebMO interface, and one can use the results to explain how these species could, hypothetically, be distinguished if they are ever synthesized. The B-N dimer has increased intensity in the C-H stretching bands as it contains more of these bonds relative to the C-C dimer, and reduced intensity in the B-H and N-H stretching bands because these hydrogen atoms are removed to form this dimer. For the lowest energy C-C bonded dimer, a number of the highest frequency modes are nearly

9 N-H C-H stretch stretch

concerted wagging

B-H concerted stretch stretching/wagging C-C

Intensity (arbitrary units) B-N

3500 3000 2500 2000 1500 1000 500 0 Energy (cm-1) Figure 3: Computed vibrational (IR) spectra for the most stable C-C and B-N bound dimers with the major peaks assigned to the corresponding vibrational modes.

20 (a) 15

10 (kcal/mol) rel

E 5

0 2C-C 1C-C(a) 1C-C(b) 0C-C 5 (b) 4

1 HOMO-LUMO (eV) HOMO-LUMO

0 2C-C 1C-C(a) 1C-C(b) 0C-C h-BN Figure 4: (a) The relative energies, and (b) HOMO-LUMO gaps of the h-BCN tetramers vs. the number of C-C bonds they contain. Two diﬀerent h-BCN tetramers (coordinates are given in the SI) contain one C-C bond. The HOMO-LUMO gap of the h-BN tetramer is also provided.

10 degenerate but one has no intensity, whereas the other one is quite intense. By visualizing the corresponding vibrational modes, which are N-H stretches, one can rationalize this in terms of symmetry. The symmetric stretches do not change the molecular dipole moment and are therefore IR inactive. As an additional exercise, the Raman spectra may be computed to confirm that these symmetric stretches are indeed Raman active (instructions and computed spectra are provided in the SI). The lowest energy B-N bonded dimer can be used to construct tetramers. Students are asked to optimize four different tetramers based on this dimer, which can be distinguished by the number of C-C bonds present, and calculate their molecular orbitals. Introducing C-C bonds to these systems tends to stabilize the tetramers as shown in Fig. 4, which plots typical results for their relative energies and HOMO-LUMO gaps. The number of C-C bonds also affects the electronic structure, suggesting that the band gap can be finely tuned, if the structure can be precisely controlled. The instructor can choose to only consider one of the two potential species containing a single C-C bond (1 C-C(a) or 1 C-C(b)); data for both are provided here to illustrate that it may be possible to construct multiple tetramers with the same number of C-C bonds, and similar properties.

Hazards

There are no hazards involved with this computational laboratory experiment.

Conclusions

A computational laboratory experiment that investigates ﬁnite molecular models of 2D- periodic materials has been developed and carried out in an upper-level undergraduate chemistry laboratory course. Namely, a novel hexagonal material containing boron, carbon and nitrogen (hexagonal BCN, or h-BCN) is investigated. The predicted small band gap would make it an ideal material for electronics applications. Density functional theory

11 is used to carry out geometry optimizations, as well as molecular orbital and vibrational frequency calculations for molecular precursors to h-BCN, as well as mono-, di-, and tetrameric h-BCN models. Insights are gained regarding the fundamental stability of the h-BCN material, unique dihydrogen bonding eﬀects that inﬂuence the stability of the dimers, and how the electronic structure changes with increasing system size towards 2D-periodicity and by tuning the molecular structure. Students who performed the lab subsequently expressed interest in working with cutting-edge materials that have potentially useful electronics applications. We believe this is a valuable addition to an undergraduate chemistry curriculum looking to incorporate a laboratory experiment in computational materials science.

Acknowledgments

D.P.M. thanks the Chemistry Department at the University at Buffalo, SUNY, for a Silbert Fellowship (2017-2018), and the NSF-HRD 1345163 for funding. E.Z. acknowledges the NSF (DMR-1827815), and J.A. acknowledges NSF grant CHE-1560881 for financial support. We thank the Center of Computational Research (CCR),47 and its employees at the University at Buffalo, SUNY, for computational support. D.P.M. thanks Charlie Sykes, Colin Murphy, Shih-Yuan Liu, James Hooper, Sumit Beniwal, and Axel Enders for their collaboration on related BCN-based systems, which inspired this work.

Supporting Information Available:

The laboratory manual and a powerpoint introduction to the lab, a grading rubric, pre-lab quiz and post-lab assessment, as well as Cartesian coordinates and electronic energies of the optimized structures, and computed Raman spectra for two dimers. This material is available free of charge via the Internet at http://pubs.acs.org.

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