Modeling 2D van der Waals Materials with Homonuclear Bonds of Main Group Cations

We survey a range of 2D van der Waals (vdW) layered materials that contain homonuclear bonds of main group elements, specifically Ga-Ga, In-In, Si-Si, Ge-Ge, and P-P, using first-principles density functional theory (DFT) methods. The covalent bonding and geometries present in these materials can stabilize oxidation states that differ from those found in conventional semiconductors composed of main group elements, such as Si, InP, and GaAs. Since 2D vdW materials did not gain widespread use until recently, many have been excluded from the first-principles test sets developed over a decade prior, where the focus was on determining the accuracy of potentials used in different modeling methods. In this study, we benchmark the set by exploring a range of modeling methods that include GGA and meta-GGA exchange-correlation functionals commonly used in first-principles DFT methods, as well as exact exchange introduced using HSE06 and PBE0. We investigate their effects on the ground-state structure, electronic band structure, and computational cost and report on this benchmarking data. Our test set of 2D vdW materials contains multiple structural types that span binary, ternary, and quaternary compositions, including ferroic ground states. We found that the vdW-corrected GGA is capable of accurately capturing lattice constants (within ±2% relative to available experimental data) across various 2D vdW materials in our test set, with relatively low computational cost and turn-key compatibility with the open-source code Quantum Espresso. Additionally, vdW-corrected GGA can reliably identify stable ferroelectric and ferromagnetic ground states, can be used to determine trends in electronic band structure, and serve as a starting point for predicting more accurate band gaps. The predicted electronic band structure and corresponding projected density of states (PDOS) are crucial for establishing the connection between microscopic properties and atomic or molecular orbitals, which can, in turn, be used to predict novel functional 2D vdW materials.