Quantum Chemical Modeling of Photoabsorption Properties of Two- and Three-Nitrogen Vacancy Point Defects in Diamond

Abstract

Quantum chemical calculations of the geometric and electronic structures and vertical transition energies for several low-lying excited states of the neutral and negatively charged vacancy-related point defects in diamond containing two and three nitrogen atoms (N2V0, N2V−, and N3V0) have been performed employing various theoretical methods (time-dependent density functional theory, equation-of-motion coupled cluster, and multireference perturbation theory) and different basis sets and using C21H28, C35H36, and C51H52 finite model clusters. In the ground states, the vacancy-related atoms are found to be shifted away from the vacancy center by ∼0.1 Å, whereas the positions of atoms from the second layer around the vacancy remain nearly unchanged, indicating a local character of geometry relaxation due to defects. The lowest excited states are formed with participation of the stretched (N2V) or broken (N3V) C−C bond and nonbonding combinations of nitrogen lone pairs as donors, with the C−C antibonding molecular orbital (MO) in N2V0, broken C−C bond in N3V0, and diffuse vacancy-related MOs serving as acceptors. Normally, the first excited states have a valence character, but the diffuse states are rather close in energy, especially for N3V0 (22A1 and 12E excited states). The first optically active excitation in the N2V0 defect with the calculated energy of ∼2.6 eV (in close agreement with the experiment) is formed by the electronic transition from the stretched C−C bond to the antibonding C−C MO, with an additional contribution from the combination of nitrogen lone pairs. For the negatively charged N2V− system, the lowest excitation to the 12A1 state is predicted to occur from the singly occupied antibonding b1 MO to the empty diffuse a1 orbital, but the CASPT2 calculated excitation energy, ∼0.9 eV, underestimates the experimental zero phonon line observed at 1.26 eV. The lowest excited states of N3V0, 22A1, and 12E correspond to transitions from the singly occupied MO (SOMO) to the diffuse lowest vacant orbital and from the nonbonding combination of nitrogen lone pairs to SOMO, respectively, and have similar energies of about 3.1−3.3 eV, in agreement with the experimental photoabsorption band maximum at ∼3 eV.