The Computational Design of Two-Dimensional Materials | Journal of

Laboratory Experiment Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX

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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, New York 14260-3000, United States

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S Supporting Information *

ABSTRACT: A computational laboratory experiment investigating molecular models for hexagonal boron−carbon−nitrogen sheets (hBCN) 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 workflow. 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 twodimensional (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, Nanotechnology, Physical Chemistry, Quantum Chemistry, Molecular Modeling, Laboratory Instruction, Computer-Based Learning, Molecular Properties/Structure, Curriculum

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INTRODUCTION

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 nitride (h-BN),16,17 graphitic carbon nitride (g-C3N4),18 transition metal dichalcogenides,19−21 and Xenes or Xanes,22−24 among many others. Examples are illustrated in Figure 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 distinguishing 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 applications. Whereas graphene does not have a band gap (it is a semimetal), 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 hypothesized 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 (hBCN) with a band gap that can be tuned to a desired value. Previous studies have investigated h-BCN experimentally32−37

Recently, intense research activity has been directed toward 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 may be 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 diverse 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 time frame, 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, and a computational exercise on solid state systems, have been published in this journal.7−11 The steadily rising importance of computationally © XXXX American Chemical Society and Division of Chemical Education, Inc.

Received: May 24, 2019 Revised: July 17, 2019

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DOI: 10.1021/acs.jchemed.9b00485 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Laboratory 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 technical aspects of first-principles calculations. This allows students to focus on topics that are interesting to them and is relevant to 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 presentation of ∼15 min 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 12 in 2018 and 8 in 2019. To assess if the laboratory improved the learning process of the students, the class of 2019 was given a prelab quiz and a postlab assessment (both provided in the Supporting Information). In the long answer portion of the prelab 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 postlab assessment, students were asked if they wanted to change or expand upon their initial hypotheses on the basis of the results of their calculations. Most students were able to make informed hypotheses, and in the postlab assessment, they supported their initial hypotheses with the results of their calculations. Along with the questions on the postlab assessment, students were asked to fill out a survey 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.

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

and theoretically.38−42 Within this laboratory experiment, students explore this hypothesis by performing DFT calculations.

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LABORATORY COURSE SETUP 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 web-based interface to computational chemistry packages. For this particular experiment, the Gaussian 16 46 program was employed. WebMO provides support for Gamess, Gaussian, MolPro, Mopac 7 and 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 5 h 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 prelab lecture that introduces the specific experiment being performed. Students take a short quiz to ensure that they have read the laboratory manual and paid attention to the introductory lecture, before they are allowed to start the experiment.

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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 provided in the laboratory manual (see the Supporting Information). 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 toward 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. The experimentally measured band gap is typically underestimated by the HOMO-LUMO gap from GGA functionals, and more reliable estimates can be obtained using a hybrid functional such as the one commonly known as B3LYP86 or B




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 Figure 1. For example, Figure 1d illustrates the most stable chair conformation of germanane, but other single-layer GeH structures are known29 or can be imagined.

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HAZARDS There are no hazards involved with this computational laboratory experiment. RESULTS A recent study36 suggested that it might be possible to synthesize h-BCN starting from the precursor molecule bis-BN cyclohexane, B2N2C2H12.88 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 bisBN 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 intramolecular dihydrogen bond is formed between two hydrogen atoms on adjacent monomers, one of which is protic and the other of 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

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 au.

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. 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 Supporting Information). B−N bonded dimers are the most stable, and C−N bonded dimers are the least stable, with the 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. Figure 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 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

Table 1. Typical Student Data Calculated for the Eight hBCN Dimers (PBE Functional, 6-31G(d) Basis)a,bc Dimer

Dihydrogen Bond Type

Erel (kcal/mol)

ΔEF (kcal/mol)

HOMO−LUMO (eV)

B−N B−N C−C C−B C−C C−B C−N C−N h-BN

B−H···H−N C−H···H−N B−H···H−N B−H···H−N B−H···H−B N−H···H−N B−H···H−N B−H···H−B B−H···H−N

0.0 1.2 2.1 4.9 7.1 7.4 15.8 17.6

112.2 113.3 114.2 116.9 119.0 119.4 127.4 129.2

1.94 1.92 1.53 1.85 1.41 1.75 1.84 1.79 5.12

a

The dihydrogen bond type, energies relative to the most stable dimer (Erel), formation energy from the h-BN and benzene dimers (ΔEF), and HOMO−LUMO gaps. bSelect data is also provided for the h-BN dimer. cFinite basis set error corrections were not considered.

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 Figure 2a, 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 Figure 2b, results in unfavorable dihydrogen interactions and adopts a 21° dihedral angle. Isosurfaces of the frontier MOs are also provided in this C




may be possible to construct multiple tetramers with the same number of C−C bonds and similar properties.

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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 is used to carry out geometry optimizations as well as molecular orbital and vibrational frequency calculations for molecular precursors to h-BCN and 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 toward 2D periodicity as well as by tuning the molecular structure. Students who performed the lab subsequently expressed interest in working with cuttingedge 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.

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.

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 Supporting Information). The lowest energy B−N bonded dimer can be used to construct tetramers. Students are asked to optimize four different tetramers on the basis of 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 Figure 4, which plots typical results for their relative energies

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.9b00485.

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The laboratory manual and a powerpoint introduction to the lab, a grading rubric, prelab quiz and postlab assessment, as well as Cartesian coordinates, electronic energies of the optimized structures, and computed Raman spectra for two dimers (ZIP)

AUTHOR INFORMATION

Corresponding Author

*E-mail: ezurek@buffalo.edu. ORCID

Daniel P. Miller: 0000-0003-1507-2667 Adam Phillips: 0000-0002-5742-6817 Jochen Autschbach: 0000-0001-9392-877X Eva Zurek: 0000-0003-0738-867X Notes

The authors declare no competing financial interest.

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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 Supporting Information) contain one C−C bond. The HOMO−LUMO gap of the h-BN tetramer is also provided.

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 CHE1560881 for financial support. We thank the Center of Computational Research (CCR)47 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.

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 D



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