Theoretical study on N 2+, P 2+, As 2+, NP +, NAs +, and PAs +: Hyperfine coupling constants for [formula omitted], and electron-spin g-factors for [formula omitted] and 1,2 2Σ + ( XY+) states

Abstract

ESR parameters are reported for N 2 +, P 2 +, As 2 +, NP +, NAs +, and PAs + radicals. Hyperfine coupling constants ( A iso, A dip) are given for the lowest-lying 2 Σ g + / 2 Σ + state of each ion (which is the ground state in the three nitrides but the first excited state in others). A iso/ A dip are calculated with ab initio and density functional theory methods. The A dip ( X)’s for 1 2Σ + (2 σ 23 σ1 π 4) show that the 3 σ(2 σ g ) singly occupied MOs have large p ( X)-character (45–50%). All A iso ( X) and A dip ( X) are positive, except for A iso(P)/ A iso(As) ≈ −200 MHz in NP + and NAs +. Electron-spin g-shifts, calculated with multireference CI methods via sum-over-states expansions, are studied for several 2Σ + states—two for XY + (1,2 2Σ +) and three for X 2 + ( 1 2 Σ g + / 1 , 2 2 Σ u + ) . They are negative for 1 2 Σ g + / 1 2 Σ + ( 2 σ 2 3 σ 1 π 4 ) , increasing in magnitude from 2700 to 15 600 to 17 500 to 36 200 to 103 000 ppm for N 2 + → NP + → P 2 + → PAs + → As 2 +, as expected due to the parallel rise in 2Σ +– 2Π spin–orbit mixing. NAs + has an anomalously large |Δ g ⊥ (1 2Σ +)| of 153 000 ppm, due to a small Δ E vert (1 2Π) = 0.27 eV. At equilibrium, 1 2 Σ u + / 2 2 Σ + are described mainly by a three-open-shell configuration leading to positive Δ g ⊥’s (800–77 000 ppm). Only for N 2 + is 1 2 Σ u + a one-open-shell state, with a negative Δ g ⊥ (−6000 ppm). Thus, according to Curl’s equation, the spin–rotation coupling constant γ is always positive for 1 2 Σ g + / 1 2 Σ + ( σ 2 σ π 4 ) but positive or negative for 1 2 Σ u + / 2 2 Σ + , depending on whether its composition is σσ 2 π 4 or σ 2 σπ 3 π ∗ (one- versus three-open-shells). Our findings rationalize why the experimental γ (2 2Σ +) of NP + is vanishingly small: a mixed composition σσ 2 π 4 + σ 2 σπ 3 π ∗ at R e (2 2Σ +) results in the mutual cancellation of second-order contributions. Spin–orbit ( α el) and orbital ( β el) parameters describing 2Σ +– 2Π perturbations are provided. The calculated ESR and γ values compare well with experimental numbers as far as available.