Microcanonical analysis of the kinetic method. The meaning of the “apparent entropy”

Abstract

A rigorous analysis of the kinetic method is carried out using Rice-Ramsperger-KasselMarcus (RRKM) theory of microcanonical statistical unimolecular dissociation rates. The model employs a kinetics treatment appropriate for metastable ion dissociation. Protonbound alkoxide dimer anions are used as model systems, with realistic vibrational and rotational parameters calculated by ab initio methods for the cluster ion and transition states leading to the competitive dissociation channels. The numerical simulations show that the kinetic method plots of ln(I 2 /I 1 ) versus ⌬⌬H are nearly linear but can exhibit significant curvature. The apparent entropy obtained in the extended kinetic method is not approximately equal to the thermodynamic entropy difference for dissociation, ⌬⌬S(T), or for activation, ⌬⌬S ‡ (T), either at the effective temperature or at any fixed equilibrium temperature. Instead, the apparent entropy term can be related to the ratio of the microcanonical sum of states of the dissociation transition states for the kinetically selected internal energy of the dissociating ions. (J Am Soc Mass Spectrom 2002, 13, 435-452)

Stereochemical effects during [M-H]− dissociations of epimeric 11-OH-17β-estradiols and distant electronic effects of substituents at C(11) position on gas phase acidity

“…It is well established that the effective temperature depends on the amplitude degree of excitation, the time-scale window of the dissociation processes, and a number of other parameters [43,44]. The measurements of proline basicity, performed by our group [47], underline the advantage of the combination of experimental results obtained with an ion trap and triple quadrupole instruments.…”

“…This approach is based on the eq 2 with GA T eff app ͑A 0 , A i ͒ ϭ ⌬H°a cid ͑A 0 ͒ Ϫ T eff ⌬⌬S°a cid ͑A 0 , A i ͒ (T eff : effective temperature in K [42][43][44]; R: Boltzmann constant ϳ 8.31 J mol Ϫ1 K Ϫ1 , and GA T eff app : apparent gas-phase acidity in kJ mol Ϫ1 [45]. In this regard, it should be noted that the A i references require similar chemical and physicochemical properties with each other and a ⌬H°a cid (A i ) ϳ [⌬H°a cid (A 0 ) Ϯ 10] kJ mol Ϫ1 [44].…”

“…In this regard, it should be noted that the A i references require similar chemical and physicochemical properties with each other and a ⌬H°a cid (A i ) ϳ [⌬H°a cid (A 0 ) Ϯ 10] kJ mol Ϫ1 [44]. Under these experimental conditions and in the used energy range, the ⌬⌬S°a cid value is considered as constant and the plot of ln(k i /k 0 ) versus ⌬H°a cid (A i ) yields a linear dependence.…”

“…The slope and the x-intercept of this curve are Ϫ1/RT eff and GA T eff app , respectively. In the case of the extended method, this experiment is performed under variable CID conditions allowing to change the effective temperature (fictitious value, which describes the behavior of ions dissociating in the time window of analyzer with non-thermal internal energy distribution) [42][43][44]. Finally, the relation of GA T eff app versus T eff yields a linear dependence that allows an estimation of ⌬H°a cid (A 0 ) and Ϫ⌬⌬S°(A 0 , A i ) corresponding to the y-intercept and the slope, respectively.…”

Determination of the gas-phase acidities of cysteine-polyalanine peptides using the extended kinetic method

“…The effective temperature is an empirical parameter that depends on several experimental variables and properties of the proton-bound dimers [15][16][17][18][19][20]. The term ⌬(⌬S) is the difference of the activation entropies between the two competing dissociation channels, ⌬S (with k) -⌬S (with k i ).…”