Probing the activated complex of the F + NH3 reaction via a dipole-bound state

Experimental characterization of the transition state poses a significant challenge due to its fleeting nature. Negative ion photodetachment offers a unique tool for probing transition states and their vicinity. However, this approach is usually limited to Franck-Condon regions. For example, high-lying Feshbach resonances with an excited HF stretching mode (vHF = 2-4) were recently identified in the transition-state region of the F + NH3 → HF + NH2 reaction through photo-detaching FNH3− anions, but the direct photodetachment failed to observe the lower-lying vHF = 0,1 resonances and bound states due apparently to negligible Franck-Condon factors. Indeed, these weak transitions can be resonantly enhanced via a dipole-bound state (DBS) formed between an electron and the polar FNH3 species. In this study, we unveil a series of Feshbach resonances and bound states along the F + NH3 reaction path via a DBS by combining high-resolution photoelectron spectroscopy with high-level quantum dynamical computations. This study presents an approach for probing the activated complex in a reaction by negative ion photodetachment through a DBS.


Quantum dynamics calculations
The quantum dynamics calculations were carried out within a seven-dimensional model.Supplementary Fig. 1 shows the nine-dimensional diatom-triatom (AB-CDE) Jacobi coordinates employed in this work.
Under the approximation of fixing the two non-reactive NH bond lengths, the full-dimensional Hamiltonian is reduced to a seven-dimensional one, as shown in the main text.
The parity e adapted wavefunction of the system was expanded in terms of body-fixed (BF) rovibrational basis functions: where  ( () represents the translational sine basis function along the translational coordinate R,  ) # ( $ ) denotes the vibrational basis function along r1, which is defined as the eigenfunction of the onedimensional (1D) reference Hamiltonian, ℎ 1 = − and  % ,  $ is rotational angular momentum of AB, and  is coupled by  $ and  %' . *+ !!"! "# in Eq. (S1) is the parity-adapted eigenfunction of the total angular momentum operator ( ; 121 = 0), and is expressed as where  +," !!"! denotes the Wigner rotation matrix.M and K the projections of the total angular momentum on the space-fixed and BF z axes, respectively.The BF z axis was defined to be along with the coordinate is the eigenfunction of  ; , which is defined as and where  is the projection of  $ on the BF z axis R and  is the projection of  ' on r2.yjm denotes the spherical harmonics.The angular bases must satisfy the condition (−1) * # 6: % 6* & 6!6! !"! = 0 for  = 0 in Eq. (S2).
The initial wave packet | = ⟩ was obtained by diagonalizing the seven-dimensional Hamiltonian on the anion PES, in which the parallel ARPACK software package 1 was utilized.The anion ground rovibrational state was then placed vertically on the neural PES and propagated in the Chebyshev order domain 2 : where

G (
, where  A is the starting point of the damping function and  <AD is the maximum of the corresponding grid.
The energy spectrum was calculated from the Chebyshev autocorrelation function  > = ⟨ 3 | > ⟩: where  >,3 denotes the Kronecker delta and the Chebyshev angle is given by  = ( −  6 )/ 4 .In addition, the raw spectrum was broadened by including a window function, exp (− %  % ), in Eq. (S6) to mimic the finite experimental resolution.
The wavefunction at the energy E was computed by The numerical parameters used in the calculations are provided in Supplementary Table 2.All the parameters were carefully checked to give converged results.
and two nodes along R for peaks 0d-0f, respectively, and one, two, three and four nodes for peaks 0g-0j, respectively.Peaks 0d-0f were thus assigned with v8 = 0, 1, and 2, respectively and peaks 0g-0j with v8 = 1, 2, 3, and 4, respectively.Supplementary Figure 2a shows 2D cuts of the wavefunctions along different angular coordinates.For peaks 0a-0c, there is no node along the angular coordinates and these peaks were assigned with v6 = 0.For peaks 0d-0f, there exists one node along the coordinate φ2, indicating the excitation of modes related to the out-of-plane motion.According to the normal mode analysis, only the modes, v6 and v7, are associated with the out-of-plane motion.The two modes are both formed by the coupling of the pseudo-rotational mode of HF with the out-of-plane wagging of NH2, with the corresponding harmonic frequencies being 829 and 318 cm -1 , respectively.Considering the energy gap between peaks 0a and 0d is 565 cm -1 (and similarly from peak 0b to 0e and from 0c and 0f), peaks 0d-0f were assigned with v6 = 1.The assignments of peaks 0g-0j are somewhat tentative.It appears that there exist two nodes along the coordinate θ2 except peak 0i and one peak along the coordinate φ2.These peaks were assigned with v6 = 2 in combination with the energy gap.Supplementary Table 1 lists the assignments of all these peaks based on the nodal structures of the wavefunctions and energies.

Peaks 1a-1f
As shown in Fig. 4 in the main text, there exists one mode along the coordinate r1 for peaks 1a-1f.These peaks were hence assigned with vHF = 1.The wave functions of peaks 1a and 1b display zero and one node along R, respectively, and thus the two peaks were assigned with v8 = 0 and 1, respectively.Similarly, peaks 1c-1e were assigned with v8 = 0, 1 and 2 and peak 1f with v8 = 0.The two cuts of the wavefunctions along the different angular coordinates are plotted in Supplementary Figure 2b.Clearly, there is no node along the angular coordinates for peaks 1a and 1b and the two peaks were assigned with v6 = 0.There exists one node along the coordinate φ2 for peaks 1c-1e and the three peaks were assigned with v6 = 1 in combination with the energy gap.In turn, peak 1f was assigned with v6 = 2.

S14
Supplementary Table 4.The extra 6s6p diffusive functions added to the standard aug-cc-pVTZ basis sets in an even-tempered manner for N, H, and F atoms for the DBS calculations.The data listed here are in the Gaussian format.The exponents ak were generated using the equation ak+1 = a0e k , k = 1-6.a0 was obtained from the same type functions with the smallest exponent in the aug-cc-pVTZ basis sets, and e was the ratio of the smallest two exponents.

'
and | 3 ⟩ = | = ⟩.To evaluate the action of the Hamiltonian onto the wave packet, the Hamiltonian needs to be normalized to the range [-1, 1] as  Q ?@A:&B = ( Q −  6 )/ 4 to avoid the divergence of the Chebyshev propagator.Here the spectral medium and half-width of the discretized Hamiltonian were calculated by  ± = ( <AD ±  <=( )/2 with Hmin and Hmax being the spectral extrema 3 .The action of the Hamiltonian matrix onto the wave packet was efficiently evaluated by transforming the wave packet between the finite basis representation and discrete variable representation4 . is a damping function to enforce outgoing boundary conditions, which was defined as () =  4EF 121 is the total angular momentum of the system and set to zero in the simulation.The composite index j denotes the rotational bases ( $ ,  % ,  ' ,  %' , ) , in which  ' represents the rotational angular momentum of DE and  % the orbital angular momentum of atom C with respect to DE,  %' is coupled by  '