Recombination of N Atoms in a Manifold of Electronic States Simulated by Time-Reversed Nonadiabatic Photodissociation Dynamics of N2

Abstract

Following a single photon VUV absorption, the N₂ molecule dissociates into distinct channels leading to N atoms of different reactivities. The optically accessible singlets are bound, and dissociation occurs through spin-orbit induced transfer to the triplets. There is a forest of coupled electronic states, and we here aim to trace a path along the nonadiabatic couplings toward a particular exit channel. To achieve this, we apply a time-reversed quantum dynamical approach that corresponds to a dissociation running back. It begins with an atom-atom relative motion in a particular product channel. Starting with a Gaussian wave packet at the dissociation region of N₂ and propagating it backward in time, one can see the population transferring among the triplets due to a strong nonadiabatic interaction between these states. Simultaneously, the optically active singlets get populated because of spin-orbit coupling to the triplets. Thus, backward propagation traces the nonradiative association of nitrogen atoms.

Scheme 1. Spin–Orbit Couplings between the Electronic States of N₂ Included in the Hamiltonian

Singlet ¹Σ_u⁺ states are coupled to triplet ³Σ_u^– and ³Π_u (1st order coupling), the triplets ³Σ_u^– and ³Π_u are coupled to one another and to quintet ⁵Π_u (2nd order coupling). The magnetic quantum number for each electronic state, m_S, is indicated in parentheses. The different columns are for different spin multiplicities.

Figure 1

(A) Potential energy curves of the optically accessible singlet ¹Σ_u⁺ (in black), one ³Σ_u^–, four ³Π_u, and one ⁵Π_u adiabatic electronic states of N₂ as functions of the internuclear distance R. Different electronic states are color coded as shown in the figure. The computed potentials are shifted in energy by 850 cm^–1 to be in agreement with high resolution spectra as reported in. The arrows indicate two dissociation channels to N(⁴S_3/2) + N(²D_J) (channel I, blue) and N(⁴S_3/2) + N(²P_J) (channel II, orange). (B) Nonadiabatic coupling terms among singlet ¹Σ_u⁺ states (top panel in B) and triplet ³Π_u states (bottom panel in B). (C) Spin–orbit coupling terms between triplet ³Π_u states and 1¹Σ_u⁺ states (top panel in C) and 2¹Σ_u⁺ states (bottom panel in C).

Figure 2

Backward propagation all the way to the singlets. (A, B) Population of triplet ³Π_u states along the grid at early time (t = 200 fs) after an initial 1³Π_u (A, top row) or, independently, a2³Π_u (B, top row) state of the same total energy (E = 113,551 cm^–1) and the same width in energy (σ_E = 90 cm^–1) start moving back to the region of interactions. Singlet ¹Σ_u⁺ states (A and B, bottom rows) become populated due to slow spin–orbit induced transfer from the triplets. (C, D) Population redistribution of triplet ³Π_u (top rows) and ¹Σ_u⁺ singlet states (bottom rows) during time-reversed propagation at longer time (t = 1000 fs) evolve to a very similar triplet and singlet components. Panels E–H show a corresponding example for the total energy of 114,538 cm^–1.

Figure 3

Branching fraction into N(⁴S_3/2) + N(²P_J) (channel II) computed with backward propagation (red sticks) versus experimental data of Song et al. (black open circles). The dynamics at the energies of 113,551 and 114,538 cm^–1 that have a rather different branching ratio are shown in detail in Figure 2.