Harmonic Rate Constants Research Articles

Theoretical study of the anharmonic effect on the main reactions in the combustion mechanism of methanol

The harmonic and anharmonic rate constants, kinetic and thermodynamic parameters of the important reactions of the combustion mechanism of CH3OH are calculated from 300 K to 4000 K. Furthermore, the effect of pressure and tunneling effect are considered in this paper. The calculations indicate that the bimolecular reaction exhibits a particularly obvious anharmonic effect than the unimolecular reaction. The calculated anharmonic rate constants are more in line with other theoretical or experimental results. In summary, these calculations complement the basic database of methanol, thereby improving the accuracy of the combustion reaction mechanism.

Theoretical studies and anharmonic effect analysis on the reaction mechanism of 3-methyl-1-butanol with OH radical

The mechanism of hydrogen abstraction in the reaction of 3-methyl-1-butanol with an OH radical was investigated by quantum chemical calculations. The total reaction consists of five channels (R1–R5), with channel R3 having the lowest energy barrier (5.4 kcal·mol−1) and channel R4 having the highest energy barrier (13.2 kcal·mol−1). All channels are exothermic reactions with lower energy barriers. Thermodynamic parameters, including constant pressure molar heat capacity CPo, enthalpy of formation ΔfHo, and entropy So, for all reactants and products, were researched using the CBS-QB3 level across a temperature scale of 298–5000 K. The harmonic and anharmonic rate constants of all reaction channels were calculated at the CCSD(T)/6-311++G(d,p) level for a temperature range of 223–4000 K. Throughout the temperature range, except for R2, the harmonic rate constant of all reaction channels is consistently higher than the anharmonic one, and it can be seen from the results that the anharmonic effect is significant and cannot be ignored. Meanwhile, the polynomial coefficients a1–a7 for the thermodynamic parameters and the polynomial coefficients A, n, and E for the kinetic parameters were fitted using the principle of least squares.

Research on the possible combustion reaction of C4H4 and its anharmonic effect

The reactions of C4H4 with free radicals and inorganic substances are the significant part in miniaturizing combustion mechanisms. 35 reactions are studied in these reaction processes in the temperature range of 300 K to 4000 K. The harmonic rate constants are larger than the anharmonic rate constants in most cases and the anharmonic effect in these reactions shouldn't be ignored. Especially, the experimental data is closer to the anharmonic rate constant at high temperature, and the negative temperature coefficient appears in anharmonic rate constant and in the experiments. Finally, the kinetic parameters and the thermodynamic parameters are calculated.

Calculation of the anharmonic effect on hydrogen abstraction in the combustion mechanism of n‐propylbenzene

AbstractThis paper presents a comprehensive investigation of the hydrogen abstraction reactions of ‐propylbenzene during the combustion process, encompassing 14 reaction systems. The harmonic and anharmonic reaction rate constants were computed over a temperature range of 300–4000 K and the paper derived kinetic and thermodynamic parameters for these reactions. The findings indicate that, in the majority of the reactions, the harmonic reaction rate constants consistently exceed the anharmonic ones, particularly in the high‐temperature regime, showcasing a significant disparity between the two. However, it is important to acknowledge the presence of certain differences, such as the presence of a negative temperature coefficient in R12. The study demonstrates the notable influence of anharmonic effects while validating the feasibility of the YL (Yao and Lin) method and these results provide reliable data for the engine combustion reaction mechanism construction.

Theoretical study of the oxidation mechanisms of excited P4Ox (x = 1–3) and the anharmonic effect on the main reactions

The combustion mechanisms of excited P4OX(x = 1–3) have been systematically investigated using the transition state and Rice-Ramsperger-Kassel-Marcus theories. The anharmonic and harmonic rate constants are calculated using the Yao and Lin method for the main reactions in the oxidation mechanisms of excited P4OX (x = 1–3). The parameters of thermodynamic are also given. Generally speaking, the B-P4O is the main presence relative to the T-P4O and C-P4O. For the bimolecular reaction, the anharmonic effect is particularly obvious than the unimolecular reaction in the whole temperature range. For most of the reaction, the anharmonic effect is quite significant and cannot be neglected.

Calculation of the anharmonic effect on the main reactions referring to ethylbenzene combustion mechanism

AbstractAbout 11 reactions related to ethylbenzene are studied in this paper using transition state theory. The YL method proposed by Yao and Lin is utilized to calculate the anharmonic and the harmonic rate constants in these reaction processes in the temperature range of 300–4,000 K, energy diagram and the temperature dependence of the rate coefficients are also presented. The calculations indicate that the harmonic rate constants are larger than the anharmonic rate constants in most cases. Especially, there is a temperature junction between the high and low relationship between the anharmonic and harmonic rate constants in several reactions. Furthermore, the calculated values are in good agreement with other theoretical ones within the allowable error. Finally, the kinetic parameters and the thermodynamic parameters are calculated. To sum up, it can be concluded that the anharmonic effect in these reactions is very significant and cannot be ignored.

Calculation of anharmonic effect on the reactions of small sulfur‐containing molecules with NO/NO2 in combustion

AbstractNitrogen oxides and sulfur oxides are the main pollutants that destroy the atmosphere, the emission and control of which have received wide attention. Notably, the interactions between nitrogen species and sulfur species occur extensively in combustion and the atmosphere. This article summarizes the 12 reactions of small sulfur‐containing molecules with NO/NO2 in combustion. The reaction rate constants of the 12 reactions at the temperature ranging from 300 to 4,000 K are calculated according to YL (Yao‐Lin) method and TS (transition state) theory. The results show that there is a large difference between the anharmonic and the harmonic rate constants for many reactions, especially at high temperature. In particular, the calculated values of the reactions S + NO2 → SO + NO, N + SO2 → SO + NO, and SH + NO2 → HSO + NO are in good agreement with other theoretical or experimental ones. Finally, the kinetic and thermodynamic parameters are calculated according to the anharmonic and harmonic rate constants as well as the least square methods. All these indicate that the anharmonic effect cannot be ignored and YL method is feasible.

Theoretical calculations and anahrmonic effect analysis for the conversion of nitrogen radical in burning reaction

AbstractThe purpose of this research is that clearly comprehends the conversion and reaction mechanism of N radical in burning reaction. The harmonic and anharmonic rate constants of the related reactions were calculated by the transition state (TS) theory and Yao and Lin (YL) method. And the kinetic and thermodynamic parameters considering anharmonic and harmonic factor were fitted respectively. In conclusion, the anharmonic effect cannot be ignored on the reaction process of N radical conversion. Besides, the simulation by CHEMKIN will be carried out by the fitted results in the future work. Therefore, the calculation can provide theoretical basis for the further research of the N‐related reactions, such as on the aspect of the removal of NOx.

Ab initio calculations and the anharmonic effect of the combustion mechanism of PxOy(x = 1,2 and y = 1–5) system

This paper provides results of the rate constants about several main reactions in the combustion mechanism of the PxOy(x = 1, 2 and y = 1–5) system. The harmonic and anharmonic rate constants of the primary reaction related to phosphorus combustion mechanisms are calculated by RRKM method and the TS theory. The thermodynamic and kinetics parameters are also given. It turns out that there is a junction occurs between the anharmonic and harmonic rate constant for some bimolecular reactions. Generally speaking, the harmonic rate constant is higher than the anharmonic rate constant at high temperatures. Moreover, the anharmonic effect is more evident with the increasing temperature, which cannot be ignored.

Calculation of anharmonic effect of the reactions related to NO2 in fuel combustion mechanism

According to the existing combustion mechanisms, the main reactions related to NO2 have been investigated in this research. Based on the transition state theory, the YL method proposed by Yao and Lin is utilized to obtain both the anharmonic and harmonic rate constants in a canonical system, respectively. The anharmonic effect of these reactions is also examined by comparing the anharmonic rate constant with the harmonic rate constant. The calculations indicate that there is a junction between the anharmonic and harmonic rate constants, and the anharmonic rate is lower than the harmonic one at high temperature. The results show that the anharmonic effect is significant and cannot be ignored, especially at high temperature. Finally, inspired by the least square idea, the kinetics and thermodynamic parameters of reaction mechanism involving NO2 are also given in fuel combustion processes.

Anharmonic Effect in CH3CH2C(=O)OCH2CH3 Decomposition

In this paper, using the B3LYP functional and CCSD(T) method with 6-311++G** basis set, the harmonic and anharmonic rate constants in the unimolecular dissociation of ethyl propanoate have been calculated using Rice–Ramsperger–Kassel–Marcus theory. The anharmonic rate constants of the title reaction have also been examined, the comparison shows that, the anharmonic effect especially in the case of high total energies and temperature for channels 3 to 6 is significant, so that the anharmonic effect cannot be neglected for unimolecular dissociation reaction of CH3CH2C(=O)OCH2CH3 both in microcanonical and canonical systems.

Anharmonic effect of the rate constant of the reactions of CH3SCH2OO system in high-temperature combustion

The study mainly focuses on the anharmonic effect of the reactions of CH3SCH2OO system. The geometries of the reactants and the transition states are optimized with Gaussian 09. The barrier heights are calculated with the energy of the reactants and the transition states. The RRKM theory is utilized to calculate the anharmonic and harmonic rate constants of the reactions. The anharmonic effect of these reactions can be clearly demonstrated by our results. Generally speaking, in the study, for most reactions, the rate constants increase with the temperature in the canonical case and the total energy in the microcanonical case, and the anharmonic effect of these reactions is significant and should not be neglected in high-temperature combustion. In CH3SCH2OO system, CH3SCH2OO → CH2SCH2OOH → CH2S + CH2O + OH is the main reaction channel. After a series of calculations, the anharmonic effect is remarkable, especially in high-temperature combustion. By analyzing other meaningful reactions that followed that channel above, the anharmonic effect of these reactions is generally obvious enough, especially for those reactions whose barrier heights are relatively low.

Anharmonic Effect of N‐Propyl Peroxy Dissociation

The anharmonic and harmonic dissociation rate constants of alkylperoxy (RO2) in different pathways, as well as those for the reactions of the n‐propyl peroxy radical, were calculated using the Rice–Ramsperger–Kassel–Marcus (RRKM) theory. When the temperature/total energy increased, the rate constants of the different pathways varied independently, causing changes in the dominating/leading products. Anharmonic rate constants were larger than harmonic rate constants, and their difference increased with increasing temperature/energy. Therefore, the anharmonic effect cannot be neglected. The rate‐determining steps of CH3CH2CH2OO dissociation are discussed. Then the anharmonic effect was found clearly for CH3CH2CH2OO dissociation, especially for the hydroperoxyalkyl radical (QOOH) dissociation. At low temperature, the rate constants were similar to those found from experiment, which indicated the RRKM theory was suitable for calculating the dissociation rates of RO2 species.

Anharmonic Effect of the Unimolecular Dissociation of HFCO and DFCO

AbstractThe unimolecular reactions of HFCO and DFCO have been studied by RRKM theory. The harmonic and anharmonic rate constants of the HFCO and DFCO decompositions have been calculated. The harmonic and anharmonic rate constants increase with the increasing temperatures and total energies both in the canonical and microcanonical systems. The comparison shows that the rate constants of DFCO decomposition are lower than that of the HFCO decomposition. The anharmonic effect and isotope effect have also been investigated. It has been found that the anharmonic effect and isotope effect are not significant either in the canonical or microcanonical system for all the reactions.

Calculation of anharmonic effects for the unimolecular dissociation of CH3OOH and its deuterated species CD3OOD using the Rice–Ramsperger–Kassel–Marcus theory

Anharmonic and harmonic rate constants for the unimolecular dissociation of CH3OOH and CD3OOD were calculated using the Rice–Ramsperger–Kassel–Marcus (RRKM) theory at the MP2/6-311++G(3df,3pd) level of theory. The anharmonic effect of the reactions was investigated. Comparison of results for the decompositions of CH3OOH and CD3OOD shows that the direct bond dissociation channel, CH3(D3) O + OH (D), is the most dominant reaction. The anharmonic effect plays an important role in the unimolecular dissociation of both CH3OOH and CD3OOD. For channels CH3(D3) O + OH (D) and CH3(D3) + H (D) O2, the anharmonic effect of the unimolecular dissociation of CD3OOD is more pronounced than that of the unimolecular dissociation of CH3OOH. For channel H2(D2) CO + H2(D2) O, the anharmonic effect of the unimolecular dissociation of CH3OOH is more pronounced than that of the unimolecular dissociation of CD3OOD. The isotope effect is more distinct in the anharmonic oscillator model.

Calculation of anharmonic effects in the unimolecular dissociation of M2+(H2O)2 (M = Be, Mg, and Ca)

The anharmonic and harmonic rate constants of the unimolecular dissociation of M2+(H2O)2 (M = Be, Mg, and Ca) were calculated using the Rice–Ramsperger–Kassel–Marcus theory. The anharmonic effects of the reactions were investigated. The results show that the energy barrier of the dissociation of Be2+(H2O)2 is 68.47 kcal/mol, and the anharmonic (T4000K = 4.28×108 s−1) and harmonic (T4000K = 4.22×108 s−1) rate constants were close in value in both the canonical and microcanonical systems. The energy barriers of the two steps for the dissociation, Mg2+(H2O)2 → MgOH++H3O+, were 37.41 and 11.39 kcal/mol, and those for the dissociation, Ca2+(H2O)2 → CaOH++H3O+, were 21.15 and 26.42 kcal/mol. The anharmonic effect of the two reactions is significant and cannot be neglected in both the canonical and microcanonical systems. The comparison also shows that the rate constants of the dissociation of Ca2+(H2O)2 have the maximum values, while those of Be2+(H2O)2 have the minimum values in the three reactions; however, the anharmonic effect also shows the similar trend in the comparison.

Anharmonic Effect of the Unimolecular Isomerization/Decomposition of Benzyne

AbstractThe 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.

Anharmonic effect of the unimolecular dissociation of CH3COOH

Anharmonic and harmonic rate constants of the reactions have been calculated with the Rice–Ramsperger–Kassel–Marcus theory, and the anharmonic results are higher than the harmonic ones. The anharmonic effect and isotopic effect on the decomposition reactions have also been examined. The anharmonic effect in all the four reactions is obvious, especially at the high temperatures or energies. Relatively, the anharmonic effect on the reaction trans-acetic acid → TS2 radical is the least obvious among the four reactions. In the microcanonical system, the difference of the rate constants between the deuterated results and the non-deuterated results is not negligible; in other words, the isotopic effect is obvious in all the four reactions. Among these reactions, three of the deuterated results (d, d3 and d4) have a big difference.

Anharmonic Effect of the Unimolecular Dissociation of Ethyl Radical

AbstractThe anharmonic and harmonic rate constants have been calculated for the unimolecular dissociation of ethyl radical using the method proposed by Yao and Lin (YL method) at both B3LYP/6‐311++G** and MP2/6‐311++G** levels. The different rate constants indicate that the results obtained from B3LYP and MP2 method are very close. The anharmonic and tunneling effect of the title reaction has also been examined. The comparison shows that, both in microcanonical and canonical systems, the anharmonic rate constants are higher than those for harmonic cases, especially in the case of high total energies and temperatures, which indicates that anharmonic effect of the unimolecular dissociation of ethyl into C2H4 and H is so significant that cannot be neglected. The tunneling effect is very small for the decomposition of C2H5 radical.

Anharmonic effect of the unimolecular dissociation of CF3CX2O (X=F, H) Radicals

The C-C bond scission of the three fluorinated ethoxy radicals CF3CF2O, CF3CFHO, CF3CH2O has been investigated using YL (Yao and Lin) method. Anharmonic and harmonic rate constants have been calculated for the reactions. In the canonical system of the three reactions at 1 atm pressure, the anharmonic (k1) and harmonic (k2) rate constants of the unimolecular decomposition reactions are k1 (300K)=6.35×10 6 s -1 and k2 (300K) =7.05×10 6 s -1 for CF3CF2O radical, k1 (300K) =3.79×10 3 s -1 and k2 (300K)=3.88×10 3 s -1 for