Unimolecular Reaction of Methyl Isocyanide to Acetonitrile: A High-Level Theoretical Study

Abstract

A combination of high-level coupled-cluster calculations and two-dimensional master equation approaches based on semiclassical transition state theory is used to reinvestigate the classic prototype unimolecular isomerization of methyl isocyanide (CHNC) to acetonitrile (CHCN). The activation energy, reaction enthalpy, and fundamental vibrational frequencies calculated from first-principles agree well with experimental results. In addition, the calculated thermal rate constants adequately reproduce those of experiment over a large range of temperature and pressure in the falloff region, where experimental results are available, and are generally consistent with statistical chemical kinetics theory (such as Rice-Ramsperger-Kassel-Marcus (RRKM) and transition state theory (TST)).

Pressure-Dependent Rate Constant Caused by Tunneling Effects: OH + HNO3 as an Example

“…These data are then used as input to the two-dimensional master equation (2DME), which depends on both internal energy and total angular momentum, to obtain thermal rate constants (as well as product yields) as a function of both temperature and pressure. Algorithms for solution of the 2DME were previously reported elsewhere − and are briefly summarized in the Supporting Information.…”

Pragmatic Solution for a Fully E,J-Resolved Master Equation

“…Very recently, Hase and co-workers have restudied this reaction using trajectory calculations based on the density functional theory (DFT) based potential energy surface (PES) and again drawn the same conclusion. This reaction has also recently been investigated using the high accuracy extrapolated ab initio thermochemistry (HEAT) method for the potential energy surface (PES) in combination with Miller’s semiclassical transition state theory (SCTST) and the fixed- J 2DME method alluded to the previous section . We have been able to replicate Rabinovitch’s falloff curves using either a collision efficiency of 0.7 with the modified strong collision model or an average down energy transferred per collision of ca.…”

“…Nowadays, 1DME methods are routinely used and found to work fairly well for a broad range of reaction systems that have multiple intermediates and multiple products. A second “dimension”the effects of angular momentum (i.e., centrifugal corrections)is also sometimes included in 1DME approaches through an indirect approximation ,,,,, or calculated as an expectation value. − For some reaction pathways where there is a significant change of rotational constants along the reaction coordinate (for example, breaking a single bond C–H of CH 4 to form CH 3 + H), a proper treatment of total angular momentum in computing E , J -resolved microcanonical rate constants as well as in the master equation becomes desirable.…”

“…In previous papers, − to simplify solution of the 2DME problem, we have proposed the use of the fixed- J approximation where total angular momentum quantum number ( J ) has been kept unchanged in collisions of a bath gas and an energized molecule. − On the basis of this assumption, solution of 2DME is reduced to a number of independent 1DMEs, which are relatively straightforward to be solved. This pragmatic model has three important advantages over the usual 1DME approach: (i) the effects of angular momentum are explicitly included in computing microcanonical rate constants k ( E , J ) (although not in the context of an E , J -resolved collisional transfer probability distribution function P ( E 1 , J | E 2 , J ) = P ( E 1 | E 2 ) J ); pressure-dependent rate constants are then calculated as expectation values; (ii) this fixed- J 2DME model can be applied to any (thermally or chemically activated) reactions having multiple wells and multiple product channels (its range of applicability is the same as that for a 1DME treatment); and (iii) since each particular angular momentum quantum number ( J x ) is completely uncoupled to the other J y , the fixed- J algorithm is easily done in parallel on any high-performance computing system.…”

Mechanism and kinetics of the reaction CH3 + CH3CHO: Ab initio semiclassical transition state theory study

“…[ 47,48 ] An efficient, practical algorithm to compute microcanonical and canonical SCTST rate constants of larger systems is described by Nguyen et al [ 49 ] and utilized thoroughly for chemical reactions. [ 49–53 ]…”