Standard Statistical Thermodynamics Research Articles

Theoretical investigation on H abstraction reaction mechanisms and rate constants of sevoflurane with the OH radical

The H abstraction reaction mechanism for sevoflurane with an ·OH radical was investigated theoretically using dual levels B3LYP/6-311++G(d, p)//QCISD(T)/6-311G(d, p). Thermochemistry properties at 298.15–2000 K were analyzed with the standard statistical thermodynamics method. Three pathways P(1), P(2) and P(3) were found and corresponded to the H13, H14 and H15 abstractions reactions with the Gibbs free barriers of 54.86, 55.05 and 54.86 kJ mol−1, respectively. The corresponding rate constants for three pathways over a wide temperature range of 298.15–2000 K were calculated and the results are in good agreement with the experimental data.

Kinetics investigation of the hydrogen abstraction reaction between CH3SS and CN radicals.

The reaction mechanisms and rates for the H abstraction reactions between CH3SS and CN radicals in the gas phase were investigated with density functional theory (DFT) methods. The geometries, harmonic vibrational frequencies, and energies of all stationary points were obtained at B3PW91/6-311G(d,p) level of theory. Relationships between the reactants, intermediates, transition states and products were confirmed, with the frequency and the intrinsic reaction coordinate (IRC) analysis at the same theoretical level. High accurate energy information was provided by the G3(MP2) method combined with the standard statistical thermodynamics. Gibbs free energies at 298.15 K for all of the reaction steps were reported, and were used to describe the profile diagrams of the potential energy surface. The rate constants were evaluated with both the classical transition state theory and the canonical variational transition state theory, in which the small-curvature tunneling correction was included. A total number of 9 intermediates (IMs) and 17 transition states (TSs) were obtained. It is shown that IM1 is the most stable intermediate by the largest energy release, and the channel of CH3SS + CN → IM3 → TS10 → P1(CH2SS + HCN) is the dominant reaction with the lowest energy barrier of 144.7 kJ mol(-1). The fitted Arrhenius expressions of the calculated CVT/SCT rate constants for the rate-determining step of the favorable channel is k =7.73 × 10(6) T (1.40)exp(-14,423.8/T) s(-1) in the temperature range of 200-2000 K. The apparent activation energy E a(app.) for the main channel is -102.5 kJ mol(-1), which is comparable with the G3(MP2) energy barrier of -91.8 kJ mol(-1) of TS10 (relative to the reactants).

Thermodynamic study on the chemical vapor deposition of silicon nitride from the SiCl4–NH3–H2 system

The gas-phase reaction thermodynamics in the chemical vapor deposition (CVD) process of preparing silicon nitride with the precursors of SiCl4–NH3–H2 was investigated with a relatively complete set of 161 species, in which the thermochemistry data were calculated with accurate model chemistry at G3(MP2) and G3//B3LYP levels combined with standard statistical thermodynamics. The data include the heat capacities, entropies, enthalpies of formation, and Gibbs energies of formation. Two condensed phase, silicon nitride (Si3N4) and silicon (Si) were taken into consideration. Based on these data, the distribution of the equilibrium concentration of the 161 species was obtained with the principle of chemical equilibrium. It was concluded that Si3N4 could be produced at the initial temperature of 300K up to the temperature 1560K, and the ideal deposition ratio r=SiCl4/(SiCl4+NH3) for Si3N4 was found to be 0.5.

Thermodynamic study on the chemical vapor deposition of boron nitride from the BCl3–NH3–H2 system

The gas-phase reaction thermodynamics in the chemical vapor deposition (CVD) process of preparing boron nitride with the precursors of BCl3–NH3–H2 was investigated with a relatively complete set of 144 species, in which the thermochemistry data were calculated with accurate model chemistry at G3(MP2) and G3//B3LYP levels combined with standard statistical thermodynamics. The data include the heat capacities, entropies, enthalpies of formation, and Gibbs free energies of formation. Three different modifications of condensed phase boron nitride (hexagonal h-BN, cubic c-BN, and wurtzite w-BN) were taken into consideration. Based on these data, the distribution of the equilibrium concentration of the 144 species was obtained with the principle of chemical equilibrium. It was concluded that c-BN is formed at temperatures up to 1,800 K, h-BN is the most stable above this temperature, and w-BN is unstable under considerable conditions.

The hydrogen abstraction reaction mechanism and rate constants from 200 K to 2000 K between sevoflurane and chlorine atom: A theoretical investigation

The H abstraction reaction mechanisms between sevoflurane and Cl atom were investigated with DFT method. The geometries of all the species were optimized at wB97XD/6-311++G(d,p) level. Thermochemistry properties were calculated with the accurate model chemistry method G3MP2 combined with the standard statistical thermodynamics. Gibbs free energies were used for analyzing reaction pathways. Three pathways correspond to the H9, H11 and H10 reactions with the barriers of 55.01, 32.50 and 32.50kJ·mol−1, respectively. The rate constants for all the pathways over a wide temperature range of 200–2000K were calculated, and the result is in good agreement with the experimental values.

Thermodynamics investigation of the gas-phase reactions in the chemical vapor deposition of silicon borides with BCl3–SiCl4–H2 precursors

The gas-phase reaction thermodynamics in the chemical vapor deposition (CVD) process of preparing silicon borides with the precursors of BCl3–SiCl4–H2 is investigated with a relatively complete set of 220 species, in which the thermochemistry data are calculated with accurate model chemistry at G3(MP2) and G3//B3LYP levels combined with standard statistical thermodynamics. The data include the heat capacities, entropies, enthalpies of formation, and Gibbs free energies of formation. Based on these data, the distribution of the equilibrium concentration of the 220 species is obtained with the principle of chemical equilibrium. BHCl2, SiHCl3, and BH2Cl are found to be the crucial intermediates. This work provides fundamental data for analyzing the thermochemistry of the CVD process of the BCl3–SiCl4–H2 system, which is instructive to optimize the input precursors and temperatures for controlling the composition of the condensed phase B, SiB6, and SiB14.

A theoretical investigation on the proton transfer tautomerization mechanisms of 2-thioxanthine within microsolvent and long range solvent

A relative complete study on the mechanisms of the proton transfer reactions of 2-thioxanthine was carried out with density functional theory. The models were designed with monohydrated and dihydrated microsolvent catalyses either with or without the presence of water solvent considered with the polarized continuum model (PCM). A total number of 114 complexes and 67 transition states were found with the B3LYP/6-311+G** calculations. The energies were refined with both B3LYP/aug-cc-pVTZ and PCM-B3LYP/aug-cc-pVTZ methods. The activation energies were reported with respect to the Gibbs free energies obtained in conjunction with the standard statistical thermodynamics. Possible reaction pathways were confirmed with the intrinsic reaction coordinates. Pathways via C8 atom on the imidazole ring, via the bridged C4 and C5 atoms between pyrimidine and imidazole rings and via N, O and S atom on the pyrimidine ring were examined. The results show that the most feasible pathway is the proton transfers within the long range solvent surrounding via the N, O and S atoms in the pyrimidine ring with di-hydrated catalysis: N(7)H + 2H2O → IM89 → IM90 → P13 + 2H2O → IM91 → IM92 → P6 + 2H2O → IM71 → IM72 → P7 + 2H2O → IM107 → IM108 → P18 + 2H2O → IM111 → IM112 → P19 + 2H2O → IM113 → IM114 → P17 + 2H2O → IM105 → IM106 → N(9)H + 2H2O that has the highest energy barrier of 44.0 kJ mol(-1) in the transition of IM89 to IM90 via TS54. The small energy barrier is in good agreement with the experimental observation that 2-TX tautomerizes at room temperature in water. In the aqueous phase, the most stable intermediate is found to be IM21 [N(7)H + 2H2O] and the possible co-existing species are the monohydrated IM1, IM9, IM39 and IM46, and the di-hydrated IM5, IM8, IM13, IM16, IM81, IM89, IM90, IM91 and IM106 complexes that have a relative concentration larger than 10(-6) (1 ppm) with respect to IM21.

Proton transfer tautomerization mechanisms of 2-thioxanthine

Mechanisms of the intramolecular proton transfer reactions of 2-thioxanthine in the gas phase were investigated with ab initio methods. Geometries of the reactants, transition states, intermediates and products were optimized with B3LYP/6-311+G(d,p). Reaction pathways were confirmed with the intrinsic reaction coordinates. Thermochemistry properties were calculated with the accurate model chemistry method of G3MP2 combined with the standard statistical thermodynamics. Reaction paths were analyzed with respect to the Gibbs free energies. Three paths of the proton transfers in the imidazole ring were discussed in detail, nine necessary energy barriers of the proton transfers in the pyrimidine ring were examined and the tautomerizations between the thiol–enol and keto–thione isomers were investigated. The results show that the highest energy barrier for the imidazole associated paths are 209.9, 306.2 and 224.9kJ/mol, corresponding to a C8 sp3-type hybrid intermediate, a C8 carbene type intermediate and two intermediates of tetrahedral carbons C(4) and C(5). The necessary energy barriers of the pyrimidine ring associated reactions are within 218.3–295.0kJ/mol. The reactions in producing thiol–enol and keto–thiol isomers need smaller energy barriers.

Enthalpies of Formation of DNA and RNA Nucleobases from G3X Theory

The Gaussian-3X (G3X) method has been used to calculate accurate values of the gas-phase enthalpies of formation of all five DNA and RNA nucleobases: thymine, adenine, cytosine, guanine, and uracil, whose experimental gas-phase study is a difficult problem because of the low vapor pressures. Only for uracil, the published experimental value agrees well with the theoretical one. However, the revision of available experimental data on enthalpies of formation for compounds in the solid phase and enthalpies of sublimation allowed us to recommend a set of self-consistent thermochemical data for thymine, adenine, and cytosine, which lead to good agreement between experimental and theoretical gas-phase enthalpies of formation. To obtain more reliable values of enthalpy of sublimation at 298.15 K, the heat capacity values of gaseous compounds were calculated by standard statistical thermodynamics formulas using molecular parameters determined from B3LYP/6-31G(2df,p) calculations. The following values are recommen...

Revision of standard molar enthalpies of formation of glycine and l-alanine in the gaseous phase on the basis of theoretical calculations

The standard molar enthalpies of formation of urea, glycine, and l-alanine in the gaseous phase at 298.15 K were calculated by the high-level Gaussian-3X method. The agreement with the available experimental data is very good for urea and glycine and, thus, supports the high accuracy of calculated values. A significant discrepancy between theoretical and experimental enthalpy of formation values for l-alanine provides a reason to reconsider the experimental data previously used to derive the standard molar enthalpy of formation of l-alanine in the gaseous phase at 298.15 K. To obtain a more reliable value of enthalpy of sublimation at 298.15 K, the heat capacity values of gaseous l-alanine were calculated by standard statistical thermodynamics formulae using molecular parameters determined from B3LYP/cc-pVTZ calculations. With the obtained value of C p ,m ∘ ( l-alanine, g, 298.15 K) = 112.6 ± 4.0 J · K −1 · mol −1 the original published experimental values of enthalpy of sublimation of l-alanine were readjusted to the reference temperature: Δ cr g H m ( l-alanine, 298.15 K) = 135.2 ± 2.0 kJ · mol −1. This value, together with the experimental enthalpy of formation of solid l-alanine, Δ f H m ∘ ( l-alanine, cr, 298.15 K) = −560.0 ± 1.0 kJ · mol −1 [S.N. Ngauv, R. Sabbah, M. Laffitte, Thermochim. Acta 20 (1977) 371–380; I. Contineanu, D.I. Marchidan, Rev. Roum. Chim. 29 (1984) 43–48], gives a new value for the enthalpy of formation of l-alanine in the gaseous phase, Δ f H m ∘ ( l-alanine, g, 298.15 K) = −424.8 ± 2.0 kJ · mol −1, which is in good agreement with our theoretical G3X result, −427.6 ± 4.0 kJ · mol −1. The same procedure for glycine allowed us to improve the literature value of the enthalpy of formation for this compound, Δ f H m ∘ (glycine, g, 298.15 K) = −393.7 ± 1.5 kJ · mol −1. As a result a set of self-consistent thermochemical data for glycine and l-alanine is proposed.

REACTION THERMODYNAMICS IN CHEMICAL VAPOR DEPOSITION OF BORON CARBIDES WITH BCl3–C3H6 (PROPENE)-H2 PRECURSORS

The gas phase reaction thermodynamics in the chemical vapor deposition (CVD) process of preparing boron carbides via the precursors of BCl 3– C 3 H 6(propene)– H 2 is investigated with a set of 325 gaseous species, in which the data for 135 species are evaluated in this work. The thermochemistry data are calculated with accurate model chemistry at G3(MP2) and G3//B3LYP levels. The concentration distribution of all of the 325 species is obtained with the principle of chemical equilibrium. The thermochemistry data include the heat capacities, entropies, enthalpies of formation, and Gibbs free energies of formation. The heat capacities and entropies at temperatures in 298.15–2000 K are evaluated with the standard statistical thermodynamics. The Gibbs free energies of formation in 298.15–2000 K are calculated with the classical thermodynamics based on the developed heat capacities and entropies. By including the crystal B 4 C , C (graphite), and B , the results for an example of the 3:1:2 precursors of BCl 3: C 3 H 6: H 2 show that the crystal B 4 C can be produced at temperatures higher than 700 K while the graphite has a higher molar value and can be produced at lower temperatures. It is also examined that the production of graphite can be controlled by changing the ratio of the injected reactants or pressure. It is interesting that BHCl 2, BCH 3 Cl 2, BH 2 Cl , and B 2 Cl 4 are found to be the most effective species in the CVD process, which is similar to those in the BCl 3– CH 4– H 2 system. The results predicted in this work are consistent with the experiments.

Thermodynamics of the gas-phase reactions in chemical vapor deposition of silicon carbide with methyltrichlorosilane precursor

The gas-phase reaction thermodynamics in the chemical vapor deposition system of preparing silicon carbide via methyltrichlorosilane pyrolysis is investigated with a relatively complete set of 226 species, in which the thermodynamic data of 163 species are evaluated in this work with accurate model chemistry G3(MP2) and G3//B3LYP calculations combined with standard statistical thermodynamics. The data include heat capacity (C ,m θ ), entropy (S m θ ), enthalpy of formation (Δf H m θ ) and Gibbs free energy of formation (Δf G m θ ). All the results are consistent with the available reliable experiments. Based on these thermodynamic data, the equilibrium concentration distribution of the 226 possible species in 300–2,000 K is evaluated with the chemical equilibrium principle under a typical experimental condition. It is shown that the theoretical results are in very good agreement with the experiments. We conclude that the present work is instructive for experiments with different conditions.

Thermodynamic properties of the most stable gaseous small silicon-carbon clusters in their ground states

The most stable structures of gaseous Si m C n (3 ⩽ n+m ⩽ 6) clusters in their ground electronic states are determined with the high level electronic correlation method QCISD(T)/g3large. Thermodynamic properties on heat capacity (C Θ ), entropy (S Θ ), Gibbs energy function (−[G Θ −H Θ(T r )]/T) and enthalpy function (H Θ−H Θ(T r )) are predicted with standard statistical thermodynamics using the structure parameters and vibrational frequencies obtained with B3PW91/6-31G(d) method combined with the electronic excitation energies determined with time dependent density functional (TD DFT) method at B3PW91/6-31G(d) level. The electronic energies are calculated with the accurate model chemistry method at G3(QCI) level of theory and the Δ f H Θ (0 K), Δ f H Θ (298.15 K) and Δ f G Θ (298.15 K) values are predicted. The heat capacities C Θ (T) as a function of temperature within 298.15-2000 K are fitted into analytical equations. The thermodynamic functions at higher temperatures are determined classically by using these equations. Most of the results obtained in this work are consistent with the available experiments.

Thermodynamic investigation of the gas-phase reactions in the chemical vapor deposition of boron carbide with BCl 3–CH 4–H 2 precursors

A relatively complete set of thermochemical data involving 154 species in the gas-phase chemical vapour deposition (CVD) reactions in preparing boron carbides via the precursors of BCl 3–CH 4–H 2 is obtained with high accurate model chemistry calculations. The data include the heat capacities, entropies, enthalpies of formation and Gibbs free energies of formation. The heat capacities and entropies at temperatures in 100–2000 K are evaluated with the standard statistical thermodynamics. The distribution of the equilibrium concentration of the 154 species is obtained with the principle of chemical equilibrium. By including the crystal B 4C, C(graphite) and B, the results for an example of the 5:1:5 precursors of BCl 3:CH 4:H 2 show that the crystal B 4C can be produced at temperatures higher than 760 K, while the graphite can also be produced at temperatures higher than 820 K. However, the production of graphite can be controlled by changing the ratio of the inject reactants. In the CVD process, BHCl 2, BCH 3Cl 2, BH 2Cl and B 2Cl 4 are found to be the most effective species. The results obtained in this work are consistent with the available experiments and the work is instructive for experiments with different conditions (ratio of the inject reactants, pressure and temperature).

Theoretical Study of Mechanisms, Thermodynamics, and Kinetics of the Decomposition of Gas-Phase α-HMX (Octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine)

We present a theoretical study of the decomposition mechanism of gas-phase α-HMX. Four distinct channels were studied using the B3LYP/cc-pVDZ level of theory. These are as follows: (i) HMX first loses an NO2 to form HMR which further breaks a C−N bond to form a chain structure and then later loses three methylenenitramines (MN, H2CNNO2) successively; (ii) the chain structure forms a 10-member ring via a rung closure step before undergoing further decomposition; (iii) HMX first eliminates an HONO, then loses two MN, and eliminates an HONO successively; (iv) HMX eliminates two HONO successively, then loses an MN, and finally eliminates an HONO. The rate constants of each elementary reaction have been calculated using the transition-state theory. The thermodynamics properties were also calculated for the stable species by employing a standard statistical thermodynamics method. Channel i was found to be the preferred decomposition pathway on the basis of the analysis of rate constants of the elementary reactions.

A model of spontaneous generation of population inversion in open quantum systems

Mathematical theorems by Davies justify, upon a specific choice of the scaling parameter, the weak-coupling relaxation theory. We use this exact mathematics again but with another, equally admissible and physically motivated, scaling parameter beyond regime of the weak system–bath coupling. This allows us to study very specific particle vs. surroundings correlations of a type known from, e.g., molecular biology. A model utilizing these correlations is suggested and solved using the above rigorous mathematics here. It yields successive spontaneous excitation of a particle at positive bath temperatures to finite number of excited states, with even dominating asymptotic population of the highest one, challenging thus standard statistical thermodynamics. Model assumptions are shortly discussed but no approximate steps are involved.

Twilight of a Dogma of Statistical Thermodynamics

In very specific situations, processes are possible where particles get transferred from one subsystem to another one, even uphill in energy and at the cost of thermal energy of the bath only. This means that expected grandcanonical equilibrium is not achieved in the course of the time development what imposes limitations on so far supposed universal validity of the standard statistical thermodynamics.

Comparison of Standard Statistical Thermodynamics with Generalized Statistical Thermodynamics Results for Ising Chain

In this study, the internal energy and the specific heat of the one-dimensional Ising model obtained in the frame of the generalized statistical thermodynamics by Andrade, were somewhat extended and compared with the internal energy and the specific heat which were calculated in the standard (conventional) statistical thermodynamics. In the q —> 1 case, approaching of the generalized internal energy and the specific heat to the standard well-known results, were illustrated by numerical applications. In addition to these, N >1 case was also investigated. PACS numbers: 05.20.—y, 05.50.+q

Effect of Finite Ion Size on the “Overbeek Correction” to the Sogami−Ise Interaction Potential between Macroions of Like Charge

The Sogami−Ise (SI) interaction potential has a “long range attraction” tail that is not present in the DLVO potential. Overbeek suggested that an “error” was present in the SI theory and that the inclusion of the solvent contribution eliminated the source of this long range attraction. The model used by Overbeek assumed that the macroions, by virtue of being fixed in their equilibrium positions, did not contribute to the electrical free energy of the solution. It is shown herein that the “Overbeek correction” is not rigorously zero for arbitrary polyion concentrations, as it must be in order to eliminate the Gibbs minimum for actual experimental conditions. It is shown herein on the basis of standard statistical thermodynamics expressions that the presence of a minimum in the pairwise Gibbs electrical free energy occurs for all screened Coulombic expressions for the Helmholtz electrical free energy, and therefore the correction term of Overbeek is in error. It is concluded that the concepts of screened C...

Oxygen deficiency and superconducting properties of Ba-Y-Cu oxide compounds

Abstract Orthorhombic-tetragonal phase relation of YBa 2 Cu 3 O 7−δ has been determined by applying standard statistical thermodynamics. The resultant phase relation can explain the difference between the boundary value δ determined in situ by increasing temperature at a constant oxygen pressure and that determined at room temperature for quenched samples. It is shown that the orthorhombic-tetragonal phase boundry at room temperature extends to much higher δ value, i.e. 0.8, than hitherto expected. The sample heated to tetragonal region can transform to orthorhombic during the quenching process if δ is smaller than 0.8. From the resistivity data of the quenched and annealed samples, we imply that the role of Cu-O one-dimensional chain on the superconductivity is minor.