Application of the aperiodic defect model to a negatively charged monovacancy in phosphorene

Abstract

We apply the recently introduced aperiodic defect model (ADM) to a negatively charged monovacancy in a phosphorene monolayer. In contrast to conventional supercell approaches, the ADM treats a single defect embedded in the true non-defective crystalline mean field thereby avoiding spurious defect-defect interactions and the need for charge corrections. At the same time, it effectively reduces the calculation to a fragment, enabling the use of high-level molecular electronic-structure methods. Converging the Hartree-Fock and correlation contributions to the thermodynamic limit yields a benchmark CCSD(T)/POB-TZVP-rev2 formation energy of 0.91 eV for the negatively charged monovacancy in the (5|9) configuration. The excitation energy to the lowest singlet excited state of this defect at the EOM-CCSD/POB-TZVP-rev2 level is found to be 1.95 eV. Overall, the ADM provides a highly promising route towards quantitatively accurate and systematically improvable descriptions of defects in solids and on surfaces, bridging the gap between solid-state physics and molecular quantum chemistry.

Figures (4)

• Figure 1: Optimized structures of pristine phosphorene (a) and the negatively charged monovacancy in phosphorene within a $4\times3$ supercell (b). The structures of the pristine phosphorene (a) and of the negatively charged (5$|$9)-vacancy in phosphorene optimized within a 4$\times$3-supercell. The atoms belonging to the reconstructed 5- and 9-membered rings are highlighted in gray.
• Figure 2: Fragments used in the ADM calculations. Atoms forming the defect, i.e., those whose positions are explicitly changed, are marked in pink. These atoms, and their counterparts from the pristine structure, explicitly enter the summations over $K'$ and $K$ in Eqs. (\ref{['eq:defect_h']}) and (\ref{['eq:E_nuc_defect']}). Fragment atoms that remain in their positions but whose electrons are relaxed within the ADM are shown in blue. Atoms of the environment, whose electrons, represented by the respective WFs, are frozen and provide the embedding field, are shown in gold. The number of atoms in each fragment is indicated below the corresponding depiction.
• Figure 3: HF and correlation components of the defect formation energy as functions of the fragment size $N_{\rm at}$. The inset shows the HF formation energy plotted as a function of $1/N_{\rm at}^{2.8}$, along with the linear fit to extrapolate it to the thermodynamic limit.
• Figure 4: First excitation energy of the defect calculated using CIS, LADC(2), and EOM-CCSD methods, as well as the CIS excitation energy of pristine phosphorene computed both fully periodically and within the ADM.