The Computational Design of Two-Dimensional Materials

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 hexagonal 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 ed- itor 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 stabil- ity, 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 gener- alized gradient approximation (PBE-GGA) and a 6-31G(d) basis set. Students built, opti- mized, 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

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