Entropy evaluation using the kinetic method: is it feasible?

The kinetic method is one of the most widely used experimental techniques for the measurement of thermochemical parameters by mass spectrometry. Recently it has been realized that it can also be used to determine reaction entropies, but the validity of this approach has not been established. This Perspective evaluates kinetic method plots in cases where there is a significant entropy difference between the competing fragmentation channels (i.e. between sample and reference compounds in the dissociating cluster ion). The concept underlying this study is to calculate mass spectra theoretically, based on known thermochemical parameters and as a function of experimental conditions. This can be done accurately using the RRKM-based MassKinetics software. The resulting mass spectra are then interpreted by the kinetic method, yielding DeltaH and DeltaS values. These values are, in turn, compared with the true values used to generate the calculated mass spectra. The results show that the reaction entropy difference between sample and reference has a very large influence on kinetic method plots. This should always be considered when studying energy-dependent mass spectra (using metastable ions or low- or high-energy collision-induced dissociation (CID)), even if only DeltaH is to be determined. Kinetic method plots are not strictly linear and this becomes a serious issue in the case of small molecules showing a large entropy effect. In such cases, results obtained at a low degree of excitation are more accurate. Energy and entropy effects can be evaluated in a relatively straightforward manner: first, the apparent Gibbs energy (DeltaG(app)) and effective temperature (T(eff)) are determined from kinetic method plots (intercept and slope, respectively), obtained from experiments using various degrees of excitation. Second, the resulting DeltaG(app) is plotted against T(eff), the slope yielding DeltaS while the intercept (extrapolation to zero temperature) yields DeltaH. This data evaluation yields more accurate results than alternative methods used in the literature. The resulting DeltaH values are fairly accurate, with errors, in most cases, <4 kJ mol(-1). On the other hand, DeltaS is systematically underestimated by 20-40%. Empirically scaling DeltaS values determined by the kinetic method by 1.35 results in a DeltaS value within 20% (or 10 J mol(-1) K(-1)) of the theoretical value.     

Theoretical study of thermal decomposition of azomethane

Summary.  Thermal one- and two-bond dissociation processes of cis- and trans-azomethane were studied by ab initio computation with DZP and TZ2P basis sets, using the d(N–C) bond lengths as the reaction coordinates. The geometries were optimized at the MP2 level, and the dissociation energies obtained exploiting a single-point, fourth-order M?ller–Plesset calculations [MP4SDTQ/TZ2P]. At this level of theory including zero-point energies, the trans-isomer is by 9.3 kcal/mol more stable than the cis-isomer. The results show that the energetically more favourable one-bond cleavage proceeds without transition state with the predicted bond dissociation energy D ₀ of 47.8 kcal/mol for trans-azomethane and 38.5 kcal/mol for cis-azomethane. With calculated barrier heights the unimolecular dissociation rate constants have been determined by means of the RRKM theory. The second-order saddle points localized for synchronous decomposition pathways lie 13 (trans)-23(cis) kcal/mol above the one-bond dissociation energies [MP2/DZP]. Received May 28, 1996/Final version received November 1, 1996 / Accepted November 1, 1996     

Collision cell pressure effect on CID spectra pattern using triple quadrupole instruments: a RRKM modeling

Control of the ion internal energy in mass spectrometry is needed to establish a workable mass spectral library. The purpose of this study is to understand and to compare the pressure effects on the collision‐induced dissociation (CID) spectrum pattern recorded using triple quadrupole instruments. The monoprotonated Leucine enkephalin [YGGFL, H⁺] was used as a thermometer molecule to calibrate the electrospray ionization (ESI) and the CID internal energies deposited on the molecular species and the time scale of ion decompositions. The survival yield and the ratio of a₄/b₄ fragment ions were mainly monitored. The energy uptake for the ESI source geometry used in our study has no impact on the CID spectrum fingerprint. The collision cell pressure for the [YGGFL, H⁺] has a major influence on the SY curves slope and on the experimental time scale. To demonstrate the pressure effect on internal energy distribution, three models (threshold, thermal and collisional) based on RRKM theory were built using the Masskinetics software. As a result, the limit of each model is discussed, and the investigation demonstrates that the thermal model, using truncated Maxwell‐Boltzmann internal energy distribution, is well‐suited for simulating the experimental data at high pressure widely used in the analytical conditions. Copyright © 2013 John Wiley & Sons, Ltd.     

KiSThelP: A program to predict thermodynamic properties and rate constants from quantum chemistry results†

Kinetic and Statistical Thermodynamical Package (KiSThelP) is a cross‐platform free open‐source program developed to estimate molecular and reaction properties from electronic structure data. To date, three computational chemistry software formats are supported (Gaussian, GAMESS, and NWChem). Some key features are: gas‐phase molecular thermodynamic properties (offering hindered rotor treatment), thermal equilibrium constants, transition state theory rate coefficients (transition state theory (TST), variational transition state theory (VTST)) including one‐dimensional (1D) tunnelling effects (Wigner, and Eckart) and Rice‐Ramsperger‐Kassel‐Marcus (RRKM) rate constants, for elementary reactions with well‐defined barriers. KiSThelP is intended as a working tool both for the general public and also for more expert users. It provides graphical front‐end capabilities designed to facilitate calculations and interpreting results. KiSThelP enables to change input data and simulation parameters directly through the graphical user interface and to visually probe how it affects results. Users can access results in the form of graphs and tables. The graphical tool offers customizing of 2D plots, exporting images and data files. These features make this program also well‐suited to support and enhance students learning and can serve as a very attractive courseware, taking the teaching content directly from results in molecular and kinetic modelling. © 2013 Wiley Periodicals, Inc.     

Comparison of the activation time effects and the internal energy distributions for the CID,PQD and HCD excitation modes

Reproducibility among different types of excitation modes is a major bottleneck in the field of tandem mass spectrometry library development in metabolomics. In this study, we specifically evaluated the influence of collision voltage and activation time parameters on tandem mass spectrometry spectra for various excitation modes [collision‐induced dissociation (CID), pulsed Q dissociation (PQD) and higher‐energy collision dissociation (HCD)] of Orbitrap‐based instruments. For this purpose, internal energy deposition was probed using an approach based on Rice–Rampserger–Kassel–Marcus modeling with three thermometer compounds of different degree of freedom (69, 228 and 420) and a thermal model. This model treats consecutively the activation and decomposition steps, and the survival precursor ion populations are characterized by truncated Maxwell–Boltzmann internal energy distributions. This study demonstrates that the activation time has a significant impact on MS/MS spectra using the CID and PQD modes. The proposed model seems suitable to describe the multiple collision regime in the PQD and HCD modes. Linear relationships between mean internal energy and collision voltage are shown for the latter modes and the three thermometer molecules. These results suggest that a calibration based on the collision voltage should provide reproducible for PQD, HCD to be compared with CID in tandem in space instruments. However, an important signal loss is observed in PQD excitation mode whatever the mass of the studied compounds, which may affect not only parent ions but also fragment ions depending on the fragmentation parameters. A calibration approach for the CID mode based on the variation of activation time parameter is more appropriate than one based on collision voltage. In fact, the activation time parameter in CID induces a modification of the collisional regime and thus helps control the orientation of the fragmentation pathways (competitive or consecutive dissociations). Copyright © 2014 John Wiley & Sons, Ltd.     

Density functional theory and RRKM calculations of decompositions of the metastable E‐2,4‐pentadienal molecular ions

The potential energy profiles for the fragmentations that lead to [C₅H₅O]⁺ and [C₄H₆]^+? ions from the molecular ions [C₅H₆O]^+? of E‐2,4‐pentadienal were obtained from calculations at the UB3LYP/6‐311G + + (3df,3pd)//UB3LYP/6‐31G(d,p) level of theory. Kinetic barriers and harmonic frequencies obtained by the density functional method were then employed in Rice–Ramsperger–Kassel–Marcus calculations of individual rate coefficients for a large number of reaction steps. The pre‐equilibrium and rate‐controlling step approximations were applied to different regions of the complex potential energy surface, allowing the overall rate of decomposition to be calculated and discriminated between three rival pathways: C? H bond cleavage, decarbonylation and cyclization. These processes should have to compete for an equilibrated mixture of four conformers of the E‐2,4‐pentadienal ions. The direct dissociation, however, can only become important in the high‐energy regime. In contrast, loss of CO and cyclization are observable processes in the metastable kinetic window. The former involves a slow 1,2‐hydrogen shift from the carbonyl group that is immediately followed by the formation of an ion‐neutral complex which, in turn, decomposes rapidly to the s‐trans‐1,3‐butadiene ion [C₄H₆]^+?. The predominating metastable channel is the second one, that is, a multi‐step ring closure which starts with a rate‐limiting cis—trans isomerization. This process yields a mixture of interconverting pyran ions that dissociates to the pyrylium ions [C₅H₅O]⁺. These results can be used to rationalize the CID mass spectrum of E‐2,4‐pentadienal in a low‐energy regime. Copyright © 2010 John Wiley & Sons, Ltd.     

Anharmonic Effect of the Unimolecular Isomerization/Decomposition of Benzyne

The anharmonic and harmonic rate constants were calculated for the unimolecular decomposition of o‐benzyne, the isomerization of o‐benzyne to m‐benzyne, the isomerization of m‐benzyne to p‐benzyne and unimolecular decomposition of p‐benzyne by using the Rice–Ramsperger–Kassel–Marcus (RRKM) theory respectively, in the canonical and microcanonical systems. The geometry and the vibrational frequencies were calculated by MP2 and B3LYP methods with 6‐311G(d,p) basis set and the barrier energies were corrected using CBS‐QB3 theory. The anharmonic effect on the reactions was also examined. Comparison of results for the decompositions of benzyne indicate that both in microcanonical and canonical cases, the anharmonic effect on the decomposition of the o‐C₆H₄ and p‐C₆H₄ are significant, while the anharmonic effect on the two isomerizations are not pronounced.     

甲基肼自由基在高温燃烧分解反应下的非谐振效应

In this work, the harmonic and anharmonic rate constants of the decomposition reaction of monomethylhydrazine (MMH) radicals have been calculated by using transition state (TS) and Rice-Ramsperger-Kassel-Marcus (RRKM) theories with either MP2 or B3LYP method at 6-311++G (3df, 2p) basis set, respectively. The reaction mechanism and anharmonic effect of the MMH radicals are studied in detail and both of the harmonic and anharmonic rate constants increase sharply with increasing temperature in the canonical system. In the microcanonical system, these constants also show sharp increase with the energies. Overall, the anharmonic effect becomes more pronounced with the increasing temperature or energy in the canonical and microcanonical systems, respectively. These results indicate that the anharmonic effect of the decomposition reaction of MMH radicals is quite significant and cannot be ignored.     

High level ab initio,DFT, and RRKM calculations for the unimolecular decomposition reaction of ethylamine

Mechanisms for the decomposition reaction of ethylamine, CH₃CH₂NH₂, were investigated using ab initio, DFT, and RRKM calculations. Optimized geometries of reactants, transition states, intermediates, and products were determined at HF, MP2, and B3LYP levels of theory using the 6-31G(d) and 6-31+G(d) basis sets. Single point energies were also determined at G3MP2B3 and G3B3 levels of theory. Thermodynamic properties, activation energies, enthalpies and Gibbs energies of activation were calculated for each reaction pathway investigated. Intrinsic reaction coordinate (IRC) analysis was performed to characterize the transition states on the potential energy surface. The conformational change and planarity of the ethylamine moiety along with the twist angle of the amino group about the CN axis are examined. Four pathways for the decomposition reaction of ethylamine were studied. All pathways involve a 1,2-elimination reaction and 1,3-proton shift to produce ethene, ethanimine, ethenamine, and methanimine. All pathways are single-step mechanisms. Elimination of the NH₃ dominates the decomposition behavior up to 1200 K whereas after this temperature, secession of the C–N gradually holds more importance. While pathways signifying departures of NH₃ and NH₂ exhibit pressure-dependent behavior, branching ratios for these two channels are generally not influenced by variation in pressure higher than the atmospheric pressure.     

The anharmonic effect study of coupled Morse oscillators for the unimolecular reaction

The importance of anharmonic effect in dissociation of molecular systems especially clusters has been noted. In this paper, we shall study the effect of coupled anharmonic oscillator of the standard bilinear form (SBF) Morse oscillator (MO) potential on unimolecular reaction. We shall use the systematic theoretical approach, YL method, proposed by Yao and Lin (YAO L, et. al. J Phys Chem A, 2007, 111(29): 6722-6729), which can evaluate anharmonic effects on the rate constants based on the transition state theory. In treating the anharmonic effect with the Morse oscillator potential on unimolecular reactions under collision-free conditions by using the RRKM (Rice-Ramsperger-Kassel-Marcus) theory, the in-verse Laplace transformation of the partition functions was used to obtain the total amount of state and density of state by using the first-order and the second-order approximations of the saddle-point method. To demonstrate the anharmonic effect of the SBF Morse model, we choose some model systems and a real reaction as examples.