Diabatic ordering of vibrational normal modes in reaction valley studies

Abstract

Diabatic ordering of the normal model of a reaction complex along the reaction path has several advantages with regard to adiabatic ordering. The method is based on rotations of the vibrational normal modes at one point, s, of the reaction path to maximize overlap with the vibrational modes at a neighboring point. Global rotations precede the rotations of degenerate modes so that changes in the direction of the reaction path and changes in the force constant matrix, which represent the two major effects for changes in mode ordering, can be separated. Overlap criteria identify resolved and unresolved avoided crossings of normal modes of the same symmetry. Diabatic mode ordering (DMO) can be used to resolve the latter by reducing the step size, thus guaranteeing correct ordering of normal modes in dependence of s. DMO is generally applicable to properties of the reaction complex that depend on s such as normal mode frequencies, orbital energies, the energy of excited states, etc. Additional applications are possible using a generalized reaction path vector, which may describe the change in atom masses, geometrical parameters, and/or the force constant matrix. In this way, the vibrational spectra of isotopomers can be investigated or the vibrational frequencies of different molecules correlated. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1282–1294, 1997

Relating normal vibrational modes to local vibrational modes with the help of an adiabatic connection scheme

“…(28) requires resolving all avoided crossings, which is handled by applying the diabatic mode ordering (DMO) algorithm of Konkoli, Kraka, and Cremer. 63 The DMO algorithm is based on overlap between the vibrational mode vectors of consecutive λ-steps rather than symmetry criteria (therefore the characterization as being diabatic 40 ). By decreasing the step-length λ to 0.01 or even smaller, DMO can correctly resolve any avoided crossing of vibrational eigenstates for increasing λ.…”

Reaction mechanism – explored with the unified reaction valley approach

“…[129][130][131][132][133] However, the depth of mechanistic information provided by the RPH was not fully exploited in a systematic way, until Kraka, Cremer, and co-workers started to transform the RPH approach into an advanced mechanistic tool, coined as the Unified Reaction Valley approach URVA. [108][109][110]134…”