Determination of kinetic properties in unimolecular dissociation of complex systems from graph theory based analysis of an ensemble of reactive trajectories

Abstract

In this paper we report how graph-theory can be used to analyze an ensemble of independent molecular trajectories which can react during the simulation time-length and obtain structural and kinetic information. The method is totally general and here is applied to the prototypical case of gas phase fragmentation of protonated cyclo-di-glycine. The methodology allows to analyze the whole set of trajectories in an automatic computer-based way without the need of visual inspection, but getting all the needed information. In particular, we not only determine the appearance of different products and intermediates, but we can characterize the corresponding kinetics. The use of colored-graph and canonical labeling allows the correct characterization of the chemical species involved. In the present case, the simulations consist of an ensemble of unimolecular fragmentation trajectories at constant energy, such that from the rate constants at different energies the threshold energy can also be obtained for both global and specific pathways. This approach allows the characterization of ion-molecule complexes, likely through a roaming mechanism, by properly taking into account the elusive nature of such species. Finally, it is possible to obtain directly the theoretical mass spectrum of the fragmenting species if the reacting system is an ion, as in the specific example.

Quantum versus Classical Unimolecular Fragmentation Rate Constants and Activation Energies at Finite Temperature from Direct Dynamics Simulations

“…From the ensemble of trajectories and associated reaction times it is thus possible to reconstruct the number of trajectories which are in the reactant state at each time frame. If the resulting curve follows a single exponential decay (as it was generally observed in previous studies 18,20,21,[57][58][59] ) then we can directly obtain τ and thus k.…”

“…Note that it was recently shown that the rate constant obtained in such a way converges more rapidly with the number of trajectories compared to those obtained by the flux approach. 59 Each trajectory is considered to be converted to products when a given threshold distance is passed. Trajectories are then immediately stopped, so that they don't allow for recrossing, as in the main assumption of transition state theory.…”

Do Stereochemical Effects Overcome a Charge-Induced Perturbation in Isolated Protonated Cyclo(Tyr-Tyr)?

“…Protonated cyclic dipeptides have been the subject of several studies as possible intermediates in the fragmentation of peptides. − A comparison between collision-induced dissociation (CID) experiments and chemical dynamics simulations showed that the fragmentation processes of the amide CO protonated systems do not depend much on chirality, in contrast to those that are protonated on the side chain of a basic residue. − Protonation modifies the balance between the different conformers of biomolecules . For cyclic dipeptides based on Tyr, Phe, or Pro residues, the proton is located on the amide CO and does not influence its conformation much.…”

How change in chirality prevents β-amyloid type interaction in a protonated cyclic dipeptide dimer

“…As a result, protonation of cyclic dipeptides usually happens on the amide CO, which results in the limited effect of chirality on their collision-induced dissociation (CID) efficiency. 45–47 Histidine-containing peptides stand out by the basic nature of the His residue, which is protonated on the imidazole ring. 48 This peculiar protonation site makes histidine very sensitive to solvation.…”