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

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 (N 2 V 0, N 2 V −, and N 3 V 0 ) 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 C 21 H 28, C 35 H 36, and C 51 H 52 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 (N 2 V) or broken (N 3 V) C−C bond and nonbonding combinations of nitrogen lone pairs as donors, with the C−C antibonding molecular orbital (MO) in N 2 V 0, broken C−C bond in N 3 V 0, 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 N 3 V 0 (2 2 A 1 and 1 2 E excited states). The first optically active excitation in the N 2 V 0 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 N 2 V − system, the lowest excitation to the 1 2 A 1 state is predicted to occur from the singly occupied antibonding b 1 MO to the empty diffuse a 1 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 N 3 V 0, 2 2 A 1, and 1 2 E 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.