Local Excitations of a Charged Nitrogen Vacancy in Diamond with Multireference Density Matrix Embedding Theory

Abstract

We investigate the negatively charged nitrogen-vacancy center in diamond using periodic density matrix embedding theory (pDMET). To describe the strongly correlated excited states of this system, the complete active space self-consistent field (CASSCF) followed by n-electron valence state second-order perturbation theory (NEVPT2) was used as impurity solver. Since the NEVPT2-DMET energies show a linear dependence on the inverse of the size of the embedding subspace, we performed an extrapolation of the excitation energies to the non-embedding limit using linear regression. The extrapolated NEVPT2-DMET first triplet-triplet excitation energy is 2.31 eV and that for the optically inactive singlet-singlet transition is 1.02 eV, both in agreement with the experimentally observed vertical excitation energies of ~2.18 eV and ~1.26 eV, respectively. This is the first application of pDMET to a charged periodic system and the first investigation of the NV- defect using NEVPT2 for periodic supercell models.

Quantum Vibronic Effects on the Excitation Energies of the Nitrogen-Vacancy Center in Diamond

“…We note that being spin-forbidden, VEEs of the singlet excited states from the triplet ground state cannot be measured directly, but they can be deduced from the experimental zero-phonon lines (ZPLs) and VEEs for the 3 A 2 → 1 E and 1 A 1 → 1 E transitions and the difference in energy between states 3 E and 1 A 1 . 21 The computed VEEs for the lower branch of the 1 E and 3 E states agree remarkably well with those obtained from experiments; a slight (0.06 eV) difference for the latter is acceptable, considering that TDDFT includes only singly excited Slater determinants. Our results show that is it crucial to include quantum vibronic effects on energy levels when comparing to experiments.…”

“…On the basis of the Allen−Heine−Cardona (AHC) theory, 23,24 first-principles calculations of the quantum vibronic effects in solids have been carried out in the literature with both perturbative 25−29 and nonperturbative methods, 30−34 and all methods used, so far, provided phonon renormalizations of only TDDFT (PBE) 47 0.512 1.336 2.089 TDDFT (DDH) 47 0.681 1.973 2.372 QDET 47 0.479 1.317 2.162 CASSCF 18 0.34 1.41 1.93 DMET 21 0.50 1.56 2.31 GW+BSE 17 0.40 0.99 2.32 QMC 22 0.81−1.06 2.13−2.37 2.37−2.54 Exp. 48−52 0.50−0.59 b 1.76−1.85 b 2.18 48 Exp.…”

“…b Extrapolated to the infinite supercell limit based on the calculations on C 62 N and C 214 N supercells (see Table S3). c Not directly measured; obtained from the measured ZPL/VEE's of 3 A 2 → 3 E and 1 A 1 → 1 E and the energy difference between states 3 E and 1 A 1 (see ref 21). order of a hundred millielectronvolts) due to quantum vibronic effects of the ground state.…”

Optical Properties of Neutral F Centers in Bulk MgO with Density Matrix Embedding

“…These methods involve mapping the infinite bulk system onto an impurity model embedded within a bath. [19][20][21][22][23] By partitioning the full system into smaller fragments, these techniques address the computational complexity associated with extended systems featuring localized correlation. The fragment with the region of interest is treated with an expensive yet accurate method and is embedded in the rest of the system termed as the environment, which is solved at a low cost, mean field level of theory.…”