Understanding and Calibrating Density-Functional-Theory Calculations Describing the Energy and Spectroscopy of Defect Sites in Hexagonal Boron Nitride

Abstract

Defect states in 2D materials present many possible uses but both experimental and computational characterization of their spectroscopic properties is difficult. We provide and compare results from 13 DFT and ab initio computational methods for up to 25 excited states of a paradigm system, the V N C B defect in hexagonal boron nitride (h-BN). Studied include include: (i) potentially catastrophic effects for computational methods arising from the multi-reference nature of the closed-shell and open-shell states of the defect, which intrinsically involves broken chemical bonds, (ii) differing results from DFT and time-dependent DFT (TDDFT) calculations, (iii) comparison of cluster models to periodic-slab models of the defect, (iv) the starkly differing effects of nuclear relaxation on the various electronic states as broken bonds try to heal that control the widths of photoabsorption and photoemission spectra, (v) the effect of zero-point energy and entropy on free-energy differences, (vi) defect-localized and conduction/valence band transition natures, and (vii) strategies needed to ensure that the lowest-energy state of a defect can be computationally identified. Averaged state-energy differences of 0.3 eV are found between CCSD(T) and MRCI energies, with thermal effects on free energies sometimes also being of this order. However, DFT-based methods can perform very poorly. Simple generalized-gradient functionals like PBE fail at the most basic level and should never be applied to defect states. Hybrid functionals like HSE06 work very well for excitations within the triplet manifold of the defect, with an accuracy equivalent to or perhaps exceeding the accuracy of the ab initio methods used. However, HSE06 underestimates triplet state energies by on average 0.7 eV compared to closed-shell singlet states, while open-shell singlet states are predicted to be too low in energy by 1.0 eV. This leads to miss-assignment of the ground state of the V N C B defect. Long-range corrected functionals like CAM-B3LYP are shown to work much better and to represent the current entry level for DFT calculations on defects. As significant differences between cluster and periodic-slab models are also found, the widespread implementation of such functionals in periodic codes is in urgent need.

Defect states in hexagonal boron nitride: Assignments of observed properties and prediction of properties relevant to quantum computation

“…Since the exact reproduction of experimental gap by adjustment of alpha parameter does not guarantee the accurate prediction of defect levels, in the present study we stick with the standard value of alpha parameter of 0.25 for HSE06. The accuracy of defect levels is ensured by calibrating the individual levels against ab initio CCSD(T), EOMCCSD, CASPT2, and MRCI calculations for a model compound [32].…”

“…However, recent calibration of this procedure for one h-BN defect against ab initio and time-dependent DFT (TDDFT) calculations indicates that the relative energies of different openshell states are realistically predicted but in general these states are predicted to be 1 eV too low in energy compared to closed-shell singlet states [32]. Corrections for this effect are applied using state-specific values for V N C B (see later in Fig.…”

“…Indeed, such calculations have been helpful in the identification of point defects in different semiconductors by comparing the experimental and calculated hyperfine constants [27][28][29][30][31]. However, the nature of many ground or excited states relevant to defects and their applications are such that DFT methods deliver results of widely varying accuracy [32], meaning that great care must always be taken when this method is applied. A summary of results comparing DFT calculations to high-level ab initio calculations for a model defect in h-BN, V N C B, concludes that DFT is reliable for the triplet-state manifold but underestimates the stability of closed-shell singlet states by around 0.5 eV and overestimates the stability of open-shell singlet states by around 0.5 eV [32], meaning that open-shell singlet states are predicted to be too low in energy by of order 1.0 eV compared to closed-shell singlet states.…”

“…However, the nature of many ground or excited states relevant to defects and their applications are such that DFT methods deliver results of widely varying accuracy [32], meaning that great care must always be taken when this method is applied. A summary of results comparing DFT calculations to high-level ab initio calculations for a model defect in h-BN, V N C B, concludes that DFT is reliable for the triplet-state manifold but underestimates the stability of closed-shell singlet states by around 0.5 eV and overestimates the stability of open-shell singlet states by around 0.5 eV [32], meaning that open-shell singlet states are predicted to be too low in energy by of order 1.0 eV compared to closed-shell singlet states. In the context of this work, these errors indicate that DFT should properly describe the magnetic properties of states but the nature of the ground state may not be correctly predicted.…”

“…In the context of this work, these errors indicate that DFT should properly describe the magnetic properties of states but the nature of the ground state may not be correctly predicted. Further, we have also considered the effects of zero-point energy correction and free-energy corrections at 298 K [32], finding sizeable changes in relative state energies of up to 0.25 eV, but corrections of this magnitude remain small compared to effects of interest herein and so are neglected.…”