Master equation modeling of water dissociation in small ionic water clusters: Ag+(H2O) n , n = 4-6

Abstract

We model temperature-dependent blackbody infrared radiative dissociation (BIRD) rate coefficients of Ag⁺(H₂O) _n , n = 4-6, a system with loosely bound water molecules. We employ a master equation modeling (MEM) approach with consideration of absorption and emission of blackbody radiation, comparing single and multiple-well descriptions. The unimolecular dissociation rate coefficients are obtained using the Rice-Ramsperger-Kassel-Marcus (RRKM) theory, employing two approaches to model the sum of states in the transition state, the rigid activated complex (RAC) and the phase space limit (PSL) approach. A genetic algorithm is used to find structures of low-lying isomers for the kinetic modeling. We show that the multiple-well MEM approach with PSL RRKM in the All Wells and Transition States Are Relevant (AWATAR) variant provides a reliable description of Ag⁺(H₂O) _n BIRD, in agreement with previously published experimental data. Higher-lying isomers contribute significantly to the overall dissociation rate coefficient, underlying the importance of the multiple-well ansatz in which all isomers are treated on the same footing.

Fig. 1. Optimized structures of Ag⁺(H₂O)_n, n = 3–6, at the B3LYP/aug-cc-pVTZ-PP level of theory. The electronic energy in kJ mol⁻¹ relative to the lowest energy structure of each size has been evaluated using a single-point calculation at the CCSD(T)-F12A/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ-PP level and is zero-point corrected.

Fig. 2. Arrhenius plots for Ag⁺(H₂O)_n, n = 4–6, comparing experimental results (black points) to linear fits of the rate coefficients as obtained from MEM within the AWATAR approach (orange) and single-well approach (blue and red dashed lines). The dotted black lines were obtained by fitting the activation energy and IR intensity within the AWATAR approach to the experimental data. For clarity, only linear fits of rate coefficients calculated in the range of 280 to 320 K are included in the plot.

Fig. 3. Population of the energy levels of all isomers included in MEM at the stationary point P_i(t_inf) for Ag⁺(H₂O)_n, n = 4–6, at 280 K in the AWATAR approach.

Fig. 4. Arrhenius plots for n = 4, 5, and 6 using the AWATAR and single-well (SW) approach within loose transition state approximation. The MEM rate coefficients as fitted to the experiment have been used. The dotted lines represent the linear fits using a classical Arrhenius equation and the solid lines indicate the fits using the modified Arrhenius equation. For the fits, the AWATAR data has been used; the SW data is only shown for comparison. A curvature with χ = 12.5, 18.3, 17.1 for n = 4, 5, 6, respectively, can be observed.

Fig. 5. Population of the energy levels of all isomers included in MEM at the stationary point P_i(t_inf) at different temperatures T for Ag⁺(H₂O)₅ in the AWATAR approach. Activation energies and scaling factors are given in Table 1. The dashed lines indicate the sum of the population for all isomers in the AWATAR approach, and the dotted lines the population for the loose TS SW approach.