Depleted uranium hexafluoride (UF_{6}), a stockpiled byproduct of the nuclear fuel cycle, reacts readily with atmospheric humidity, but the mechanism is poorly understood. Here we compare several potential initiation steps at a consistent level of theory, generating underlying structures and vibrational modes using hybrid density functional theory (DFT) and computing relative energies of stationary points with double-hybrid (DH) DFT. A benchmark comparison is performed to assess the quality of DH-DFT data using reference energy differences obtained using a complete-basis-limit coupled-cluster (CC) composite method. The associated large-basis CC computations were enabled by a new general-purpose pseudopotential capability implemented as part of this work. Dispersion-corrected parameter-free DH-DFT methods, namely PBE0-DH-D3(BJ) and PBE-QIDH-D3(BJ), provided mean unsigned errors within chemical accuracy (1 kcal mol^{-1}) for a set of barrier heights corresponding to the most energetically favorable initiation steps. The hydrolysis mechanism is found to proceed via intermolecular hydrogen transfer within van der Waals complexes involving UF_{6}, UF_{5}OH, and UOF_{4}, in agreement with previous studies, followed by the formation of a previously unappreciated dihydroxide intermediate, UF_{4}(OH)_{2}. The dihydroxide is predicted to form under both kinetic and thermodynamic control, and, unlike the alternate pathway leading to the UO_{2}F_{2} monomer, its reaction energy is exothermic, in agreement with observation. Finally, harmonic and anharmonic vibrational simulations are performed to reinterpret literature infrared spectroscopy in light of this newly identified species.

We have extended the computational singular perturbation (CSP) method to differential algebraic equation (DAE) systems and demonstrated its application in a heterogeneous-catalysis problem. The extended method obtains the CSP basis vectors for DAEs from a reduced Jacobian matrix that takes the algebraic constraints into account. We use a canonical problem in heterogeneous catalysis, the transient continuous stirred tank reactor (T-CSTR), for illustration. The T-CSTR problem is modelled fundamentally as an ordinary differential equation (ODE) system, but it can be transformed to a DAE system if one approximates typically fast surface processes using algebraic constraints for the surface species. We demonstrate the application of CSP analysis for both ODE and DAE constructions of a T-CSTR problem, illustrating the dynamical response of the system in each case. We also highlight the utility of the analysis in commenting on the quality of any particular DAE approximation built using the quasi-steady state approximation (QSSA), relative to the ODE reference case.