Feshbach resonances in the F + H2O → HF + OH reaction

Transiently trapped quantum states along the reaction coordinate in the transition-state region of a chemical reaction are normally called Feshbach resonances or dynamical resonances. Feshbach resonances trapped in the HF–OH interaction well have been discovered in an earlier photodetchment study of FH2O−; however, it is not clear whether these resonances are accessible by the F + H2O reaction. Here we report an accurate state-to-state quantum dynamics study of the F + H2O → HF + OH reaction on an accurate newly constructed potential energy surface. Pronounced oscillatory structures are observed in the total reaction probabilities, in particular at collision energies below 0.2 eV. Detailed analysis reveals that these oscillating structures originate from the Feshbach resonance states trapped in the hydrogen bond well on the HF(v′ = 2)-OH vibrationally adiabatic potentials, producing mainly HF(v′ = 1) product. Therefore, the resonances observed in the photodetchment study of FH2O− are accessible to the reaction.


A. Potential energy surface
The potential energy surface (PES) of F+H 2 O system was constructed using the all-electron spin restricted explicitly correlated singles and doubles coupled-cluster approach (AE-CCSD(T)), together with optimized correlation consistent triple-zeta basis set including RI and MP2 auxiliary sets (cc-pCVTZ-F12) 1 . The spin-orbit coupling (SO) energies were computed with the internally contracted multi-reference configuration interaction method with Davidson correction (iMRCI+Q) and the basis set of aug-cc-pVTZ, using multi-configurational SCF reference functions with 15 electrons in 10 active orbitals, followed by the Breit-Pauli Hamiltomian 2 . All these calculations were performed with the MOLPRO 2012.1 package 3 .
More than 24,000 points were used to construct the PES using the neural networks. These points, covering the asymptotic reactive channels of F+H 2 O, HF+HO, as well as interaction region, were selected iteratively by an effective scheme 4 which was proposed for high dimensional PES constructions. The 6 bond lengths are used for the input layer. The asymptotic channels and interaction region were fitted segmentally to improve the fitting accuracy and efficiency, and connected with smooth switch functions. The switch functions for each part are defined from the bond distances between F and H atoms as (with H atoms sorted to satisfy F−H1 ≤ F−H2 ):
The system Hamiltonian in the reactant Jacobi coordinates for a given total angular momentum tot can be written as ̂= − ℏ 2 2 2 2 + ( tot − 12 ) 2 2 2 + 1 2 2 1 1 2 + 2 2 2 2 2 2 + ( , 1 , 2 , 1 , 2 , ) where is the reduced mass of F and H 2 O, 1 is the reduced mass of H and OH, 2 is the reduced mass of OH. tot is the total angular momentum operator of the system; 12 is the rotational angular momentum operator of H 2 O; 2 is the rotational angular momentum operator of OH, and 1 = 12 − 2 is the orbital angular momentum operator of H 2 O. The reference Hamiltonian ℎ ( )( = 1,2) is defined as where ( ) is a diatomic potential.
The time-dependent wave function can be expanded in terms of the translational basis of R, the vibrational basis ( ), and the body-fixed (BF) rovibrational eigenfunction as The BF total angular momentum eigenfunctions can be defined as where is the parity of the system. ̅ (̂) is the Wigner rotation matrix, depending on Euler angles which rotate the space-fixed frame onto the body-fixed frame and are the eigenfunctions of 2 . 1 2 12 ̅ (̂1,̂2) is the angular momentum eigenfunction of 12 defined as 1 2 12 ̅ = ∑ ̅ 12 (̂1)√ 2 1 +1 4 < 2 1 0| 12 > 2 (̂2) where 2 are spherical harmonics. Note that the restriction (−1) + 1 + 2 + 12 = where ′ is the reduced mass of HF and OH, 1 ′ and 2 ′ are the reduced mass of HF and OH, 1 ′ and 2 ′ are the rotational angular momentum operator of HF and OH, which coupled to form 12 ′ .
The time-dependent wave function can be expanded as It should be pointed out here that the functional forms for the product arrangement basis (primed) are different from the one for the reagent arrangement basis (unprimed).
The BF total angular momentum eigenfunctions can be defined as (11)

C. PCB approach and numerical parameters
In the product coordinates based (PCB) approach 5,6 used here, we prepared an initial wave packet for H 2 O in the initial ground rovibrational state in the reactant Jacobi coordinates, and propagated it for 17000 a.u. from the asymptotic region to =6.0 bohrs. It is straightforward to carry out this propagation, because at that distance, only inelastic scattering process occurs. A coordinate transformation was then carried out to transfer the whole wave packet from the reactant coordinates to the product coordinates. After a continuous propagation for additional 80000 a.u. in the product coordinates, which beyond the range of the hydrogen bond well and strong interaction between HF and OH species, the converged reactive flux and state-to-state information can be obtained.
The wavefunction is propagated using the split-operator propagator. An L-shaped wavefunction expansion for ( ′ ) and 1 ( 1 ′ ) was used to reduce the size of the basis set. We carried out state-to-state calculations for the total angular momentum probabilities are only slightly different from the full 6D ones, indicating the OH bond is a good spectator for the reaction, and can be fixed in its initial vibrational state.
With two heavy atoms (F and O) involved and long-range dipole-dipole interactions in the exit channel, the computation is extremely expensive. To reduce the computational costs, the results in the main text are based on the PA5D calculations.
Since there are two equivalent product channels in the reaction, the reaction probabilities should be multiplied by a factor of 2, if compared with QCT results.