Heavy‐Atom Quantum Tunnelling in Spin Crossovers of Nitrenes**

Abstract

We simulate two recent matrix-isolation experiments at cryogenic temperatures, in which a nitrene undergoes spin crossover from its triplet state to a singlet state via quantum tunnelling. We detail the failure of the commonly applied weak-coupling method (based on a linear approximation of the potentials) in describing these deep-tunnelling reactions. The more rigorous approach of semiclassical golden-rule instanton theory in conjunction with double-hybrid density-functional theory and multireference perturbation theory does, however, provide rate constants and kinetic isotope effects in good agreement with experiment. In addition, these calculations locate the optimal tunnelling pathways, which provide a molecular picture of the reaction mechanism. The reactions involve substantial heavy-atom quantum tunnelling of carbon, nitrogen and oxygen atoms, which unexpectedly even continues to play a role at room temperature.

Transfer Learning for Affordable and High-Quality Tunneling Splittings from Instanton Calculations

“…A typically used shortcut is to optimize the instanton using a LL ab initio method, for example, DFT or MP2, and then compute the CCSD­(T) properties along the path to correct the action S /ℏ. Such a hybrid approach was assessed using the PhysNet MP2 PES to optimize the instanton, whereas the action S /ℏ was calculated on the TL ext PES. ,,, The results are summarized in Table and illustrate that although the hybrid approach is, in this case, able to infer the correct value for S /ℏ, the TL approach additionally improves Φ. Using eq with the action as determined by the hybrid approach ( S /ℏ = 5.7401) and the fluctuation factor determined on the PhysNet MP2 PES (Φ = 42.7705) yields Δ H ∼ 31.5 cm –1 , which overestimates the value of 25.1 cm –1 from TL ext .…”

Simultaneous Tunneling Control in Conformer-Specific Reactions

“…The heavy-atom tunneling reaction of s- 3 2 to 3 was previously demonstrated to occur through crossing triplet to singlet surfaces. 41 , 50 Our previous computations at the M06-2X/6-311++G(d,p) level found the corresponding minimum-energy crossing point ( MECP ) at 12.1 kcal mol –1 , 41 whereas Heller and Richardson’s most recent computations at the MRMP(10,10)/TZVP//B2-PLYP/def2-TZVPD level found it at 10.5 kcal mol –1 . 50 Then, they used the state-of-the-art semiclassical golden-rule instanton theory and obtained tunneling rate constants [∼8 × 10 –3 s –1 ; τ 1/2 ∼ 1.5 min] in good quantitative agreement with the experiment.…”

“… 41 , 50 Our previous computations at the M06-2X/6-311++G(d,p) level found the corresponding minimum-energy crossing point ( MECP ) at 12.1 kcal mol –1 , 41 whereas Heller and Richardson’s most recent computations at the MRMP(10,10)/TZVP//B2-PLYP/def2-TZVPD level found it at 10.5 kcal mol –1 . 50 Then, they used the state-of-the-art semiclassical golden-rule instanton theory and obtained tunneling rate constants [∼8 × 10 –3 s –1 ; τ 1/2 ∼ 1.5 min] in good quantitative agreement with the experiment. Here, the B3LYP/6-311+G(2d,p) MECP energy (or the barrier height defined as the energy difference between the MECP and s- 3 2 ) was found at 9.8 kcal mol –1 , in good agreement with the value of the high-cost MRMP//B2-PLYP computations.…”

Transfer learning for affordable and high quality tunneling splittings from instanton calculations

“…Such a hybrid approach was assessed using the PhysNet MP2 PES to optimize the instanton and then calculate the action S/ on the TL ext PES. 11,12,50,51 The results are summarized in Table 4 and illustrate that although the hybrid approach is, in this case, able to infer the correct value for S/ , the TL approach additionally improves Φ. Using Equation 1with the action as determined by the hybrid approach (S/ = 5.7401) and the fluctuation factor determined on the PhysNet MP2 PES (Φ = 42.7705) yields ∆ H ∼ 31.5 cm −1 which overestimates the value of 25.1 cm −1 from TL ext .…”