Explicit definition of the reaction coordinate for the Jackels?Gu?Truhlar projection technique to compute harmonic vibrational frequencies along the intrinsic reaction path

Abstract

It is shown that the Jackels–Gu–Truhlar projection technique for computing harmonic frequencies along the intrinsic reaction path is equivalent to use of a new, enormously broad family of the so-called hyperplanar-vibrational-surface (HVS) reaction coordinates, namely, for any arbitrarily chosen set of internal variables σ, the appropriate HVS reaction coordinate, sσ, is implicitly defined via the requirement that it remains constant on any so-called orthogonal-to-path hyperplane in the coordinate space spanned by variables σ. It is proven that sσ defined in such a way satisfies the local Hofacker–Marcus conditions and therefore there is no linear term in a Taylor expansion of the potential in terms of vibrational coordinates Qσ. Since the transformation from Qσ and sσ to σ is explicitly defined, one can use a standard technique to account for potential anharmonicities along the reaction path.