Thermochemistry Of Radicals Research Articles

Subgraph Isomorphic Decision Tree to Predict Radical Thermochemistry with Bounded Uncertainty Estimation.

Detailed chemical kinetic models offer valuable mechanistic insights into industrial applications. Automatic generation of reliable kinetic models requires fast and accurate radical thermochemistry estimation. Kineticists often prefer hydrogen bond increment (HBI) corrections from a closed-shell molecule to the corresponding radical for their interpretability, physical meaning, and facilitation of error cancellation as a relative quantity. Tree estimators, used due to limited data, currently rely on expert knowledge and manual construction, posing challenges in maintenance and improvement. In this work, we extend the subgraph isomorphic decision tree (SIDT) algorithm originally developed for rate estimation to estimate HBI corrections. We introduce a physics-aware splitting criterion, explore a bounded weighted uncertainty estimation method, and evaluate aleatoric uncertainty-based and model variance reduction-based prepruning methods. Moreover, we compile a data set of thermochemical parameters for 2210 radicals involving C, O, N, and H based on quantum chemical calculations from recently published works. We leverage the collected data set to train the SIDT model. Compared to existing empirical tree estimators, the SIDT model (1) offers an automatic approach to generating and extending the tree estimator for thermochemistry, (2) has better accuracy and R2, (3) provides significantly more realistic uncertainty estimates, and (4) has a tree structure much more advantageous in descent speed. Overall, the SIDT estimator marks a great leap in kinetic modeling, offering more precise, reliable, and scalable predictions for radical thermochemistry.

Dissociative Photoionization of the C7H8 Isomers Cycloheptatriene and Toluene: Looking at Two Sides of the Same Coin Simultaneously.

The dissociation of energy-selected 1,3,5-cycloheptatriene (CHT) and toluene (Tol) cations was investigated by imaging photoelectron photoion coincidence spectroscopy. In the measured energy ranges of 10.30-11.75 eV for CHT and 11.45-12.55 eV for Tol, only the hydrogen atom loss channels open up, leading to C7H7+ from both molecular ions, which are both metastable at the H-loss threshold. Quantum chemical calculations showed that an interconversion of the molecular ions happens below the dissociation threshold. Therefore, a single statistical model was constructed to describe both systems simultaneously. We determined 0 K appearance energies for the tropylium (Tr+) and benzyl (Bz+) fragment ions from CHT to be 9.520 ± 0.060 and 9.738 ± 0.082 eV and that from Tol to be 10.978 ± 0.063 and 11.196 ± 0.080 eV, respectively. Using the experimentally determined benzyl ion appearance energy, its 0 K heat of formation was calculated to be 937.9 ± 7.7 kJ mol-1. Finally, on the basis of this value and the recently determined benzyl ionization energy, we point out discrepancies concerning the benzyl radical thermochemistry.

Thermochemistry of radicals formed by hydrogen abstraction from 1-butanol, 2-methyl-1-propanol, and butanal

We calculate the standard state entropy, heat capacity, enthalpy, and Gibbs free energy for 13 radicals important for the combustion chemistry of biofuels. These thermochemical quantities are calculated from recently proposed methods for calculating partition functions of complex molecules by taking into account their multiple conformational structures and torsional anharmonicity. The radicals considered in this study are those obtained by hydrogen abstraction from 1-butanol, 2-methyl-1-propanol, and butanal. Electronic structure calculations for all conformers of the radicals were carried out using both density functional theory and explicitly correlated coupled cluster theory with quasipertubative inclusion of connected triple excitations. The heat capacity and entropy results are compared with sparsely available group additivity data, and trends in enthalpy and free energy as a function of radical center are discussed for the isomeric radicals.

Accurate Thermochemistry of Hydrocarbon Radicals via an Extended Generalized Bond Separation Reaction Scheme

Detailed knowledge of hydrocarbon radical thermochemistry is critical for understanding diverse chemical phenomena, ranging from combustion processes to organic reaction mechanisms. Unfortunately, experimental thermochemical data for many radical species tend to have large errors or are lacking entirely. Here we develop procedures for deriving high-quality thermochemical data for hydrocarbon radicals by extending Wheeler et al.'s "generalized bond separation reaction" (GBSR) scheme (J. Am. Chem. Soc., 2009, 131, 2547). Moreover, we show that the existing definition of hyperhomodesmotic reactions is flawed. This is because transformation reactions, in which one molecule each from the predefined sets of products and reactants can be converted to a different product and reactant molecule, are currently allowed. This problem is corrected via a refined definition of hyperhomodesmotic reactions in which there are equal numbers of carbon-carbon bond types inclusive of carbon hybridization and number of hydrogens attached. Ab initio and density functional theory (DFT) computations using the expanded GBSRs are applied to a newly derived test set of 27 hydrocarbon radicals (HCR27). Greatly reduced errors in computed reaction enthalpies are seen for hyperhomodesmotic and other highly balanced reactions classes, which benefit from increased matching of hybridization and bonding requirements. The best performing DFT methods for hyperhomodesmotic reactions, M06-2X and B97-dDsC, give average deviations from benchmark computations of only 0.31 and 0.44 (±0.90 and ±1.56 at the 95% confidence level) kcal/mol, respectively, over the test set. By exploiting the high degree of error cancellation provided by hyperhomodesmotic reactions, accurate thermochemical data for hydrocarbon radicals (e.g., enthalpies of formation) can be computed using relatively inexpensive computational methods.

Modeling the Gas‐Phase Thermochemistry of Organosulfur Compounds

Key to understanding the involvement of organosulfur compounds in a variety of radical chemistries, such as atmospheric chemistry, polymerization, pyrolysis, and so forth, is knowledge of their thermochemical properties. For organosulfur compounds and radicals, thermochemical data are, however, much less well documented than for hydrocarbons. The traditional recourse to the Benson group additivity method offers no solace since only a very limited number of group additivity values (GAVs) is available. In this work, CBS-QB3 calculations augmented with 1D hindered rotor corrections for 122 organosulfur compounds and 45 organosulfur radicals were used to derive 93 Benson group additivity values, 18 ring-strain corrections, 2 non-nearest-neighbor interactions, and 3 resonance corrections for standard enthalpies of formation, standard molar entropies, and heat capacities for organosulfur compounds and organosulfur radicals. The reported GAVs are consistent with previously reported GAVs for hydrocarbons and hydrocarbon radicals and include 77 contributions, among which 26 radical contributions, which, to the best of our knowledge, have not been reported before. The GAVs allow one to estimate the standard enthalpies of formation at 298 K, the standard entropies at 298 K, and standard heat capacities in the temperature range 300-1500 K for a large set of organosulfur compounds, that is, thiols, thioketons, polysulfides, alkylsulfides, thials, dithioates, and cyclic sulfur compounds. For a validation set of 26 organosulfur compounds, the mean absolute deviation between experimental and group additively modeled enthalpies of formation amounts to 1.9 kJ mol(-1). For an additional set of 14 organosulfur compounds, it was shown that the mean absolute deviations between calculated and group additively modeled standard entropies and heat capacities are restricted to 4 and 2 J mol(-1) K(-1), respectively. As an alternative to Benson GAVs, 26 new hydrogen-bond increments are reported, which can also be useful for the prediction of radical thermochemistry.

Thermochemistry of Radicals and Molecules Relevant to Atmospheric Chemistry: Determination of Group Additivity Values using G3//B3LYP Theory

Thermochemistry of radicals is not as extensively tabulated as that of stable molecular species, even when group additivity schemes are applied. When these radicals contain oxygen or nitrogen atoms, the availability of radical groups is even more limited. Many oxygen- and nitrogen-containing radicals and molecules are present in the atmosphere, and thermochemistry is a valuable component of the development of atmospheric models with predictive capabilities. This paper presents quantum chemical calculations using G3//B3LYP that have been performed to obtain heats of formation, entropies, and heat capacities as a function of the temperature of radicals and molecules from which group additivity values were obtained. Isodesmic and homodesmotic reactions were used to obtain improved estimates of the heats of formation. Thermodynamic property estimates were corrected to account for internal rotations. A total of 323 molecules were studied from which a total of 122 different groups, 21 gauche and cis corrections, and 5 secondary corrections were regressed.

First Principles Based Group Additive Values for the Gas Phase Standard Entropy and Heat Capacity of Hydrocarbons and Hydrocarbon Radicals

In this work a complete and consistent set of 95 Benson group additive values (GAVs) for standard entropies S(o) and heat capacities C(p)(o) of hydrocarbons and hydrocarbon radicals is presented. These GAVs include 46 groups, among which 25 radical groups, which, to the best of our knowledge, have not been reported before. The GAVs have been determined from a set of B3LYP/6-311G(d,p) ideal gas statistical thermodynamics values for 265 species, consistently with previously reported GAVs for standard enthalpies of formation. One-dimensional hindered rotor corrections for all internal rotations are included. The computational methodology has been compared to experimental entropies (298 K) for 39 species, with a mean absolute deviation (MAD) between experiment and calculation of 1.2 J mol(-1) K(-1), and to 46 experimental heat capacities (298 K) with a resulting MAD = 1.8 J mol(-1) K(-1). The constructed database allowed evaluation of corrections on S(o) and C(p)(o) for non-nearest-neighbor effects, which have not been determined previously. The group additive model predicts the S(o) and C(p)(o) within approximately 5 J mol(-1) K(-1) of the ab initio values for 11 of the 14 molecules of the test set, corresponding to an acceptable maximal deviation of a factor of 1.6 on the equilibrium coefficient. The obtained GAVs can be applied for the prediction of S(o) and C(p)(o) for a wide range of hydrocarbons and hydrocarbon radicals. The constructed database also allowed determination of a large set of hydrogen bond increments, which can be useful for the prediction of radical thermochemistry.

Thermochemistry of aqueous hydroxyl radical from advances in photoacoustic calorimetry and ab initio continuum solvation theory.

Photoacoustic signals from dilute ( approximately 30 mM) solutions of H2O2 were measured over the temperature range from 10 to 45 degrees C to obtain the reaction enthalpy and volume change for H2O2(aq) --> 2 OH(aq) from which we ultimately determined DeltafG degrees , DeltafH degrees and partial molal volume, v degrees , of OH (aq). We find DeltarH = 46.8 +/- 1.4 kcal/mol, which is 4 kcal/mol smaller than the gas-phase bond energy, and DeltaVr = 6.5 +/- 0.4 mL/mol. The v degrees for OH in water is 14.4 +/- 0.4 mL/ml: smaller than the v degrees of water. Using ab intio continuum theory, the hydration free energy is calculated to be -3.9 +/- 0.3 kcal/mol (for standard states in number density concentration units) by a novel approach devised to capture in the definition of the solute cavity the strength and specific interactions of the solute with a water solvent molecule. The shape of the cavity is defined by "rolling" a three-dimensional electron density isocontour of water on the ab initio water-OH minimum interaction surface. The value of the contour is selected to reproduce the volume of OH in water. We obtain for OH(aq): DeltafH degrees = -0.2 +/- 1.4 and DeltafG degrees = 5.8 +/- 0.4 kcal/mol that are in agreement with literature values. The results provide confidence in the pulsed PAC technique for measuring aqueous thermochemistry of radicals and open the way to obtaining thermochemistry for most radicals that can be formed by reaction of OH with aqueous substrates while advancing the field of continuum solvation theory toward ab initio-defined solute cavities.

G3-RAD and G3X-RAD: Modified Gaussian-3 (G3) and Gaussian-3X (G3X) procedures for radical thermochemistry

The G3-RAD, G3X-RAD, G3(MP2)-RAD, and G3X(MP2)-RAD, procedures, designed particularly for the prediction of reliable thermochemistry for free radicals, are formulated and their performance assessed using the G2/97 test set. The principal features of the RAD procedures include (a) the use of B3-LYP geometries and vibrational frequencies (in place of UHF and UMP2), including the scaling of vibrational frequencies so as to reproduce ZPVEs, (b) the use of URCCSD(T) [in place of UQCISD(T)] as the highest-level correlation procedure, and (c) the use of RMP (in place of UMP) to approximate basis-set-extension effects. G3-RAD and G3X-RAD are found to perform well overall with mean absolute deviations (MADs) from experiment of 3.96 and 3.65 kJ mol−1, respectively, compared with 4.26 and 4.02 kJ mol−1 for standard G3 and G3X. G3-RAD and G3X-RAD successfully predict heats of formation with MADs of 3.68 and 3.11 kJ mol−1, respectively (compared with 3.93 and 3.60 kJ mol−1 for standard G3 and G3X), and perform particularly well for radicals with MADs of 2.59 and 2.50 kJ mol−1, respectively (compared with 3.51 and 3.18 kJ mol−1 for standard G3 and G3X). The G3(MP2)-RAD and G3X(MP2)-RAD procedures give acceptable overall performance with mean absolute deviations from experiment of 5.17 and 4.92 kJ mol−1, respectively, compared with 5.44 and 5.23 kJ mol−1 for standard G3(MP2) and G3X(MP2). G3(MP2)-RAD and G3X(MP2)-RAD give improved performance over their standard counterparts for heats of formation (MADs=4.73 and 4.44 kJ mol−1, respectively, versus 4.94 and 4.64 kJ mol−1). G3(MP2)-RAD shows similar performance to G3(MP2) for radical heats of formation (MAD=5.10 versus 5.15 kJ mol−1) while G3X(MP2)-RAD performs significantly better than G3X(MP2) (MAD=4.67 versus 5.19 kJ mol−1).

Erratum: “An assessment of theoretical procedures for the calculation of reliable free radical thermochemistry: A recommended new procedure” [J. Chem. Phys. 108, 604 (1998)

First Page

An assessment of theoretical procedures for the calculation of reliable free radical thermochemistry: A recommended new procedure

The ability to predict reliable thermochemical properties of molecules and ions has led to an ever increasing application of ab initio molecular orbital theory. Methods such as G2 theory have been shown to generally give accurate heats of formation (ΔfH) for closed-shell molecules and ions. Open-shell systems have been less thoroughly examined to date and the present paper attempts to redress this situation through a detailed assessment of the performance of a variety of levels of theory in calculating ΔfH values for free radicals. Representatives of three families of theoretical procedures have been studied: the infinite basis set extrapolation techniques of Martin, the CBS procedures of Petersson et al., and the G2 methods of Pople et al. Among the specific influences investigated are choice of geometry, zero-point vibrational energy, high level electron correlation treatment and basis set size. We recommend a new procedure called CBS-RAD for the treatment of free radicals. CBS-RAD is a modification of the CBS-Q method in which the geometry and zero-point energies are obtained at the QCISD/6-31G(d) level, and coupled-cluster theory is used in place of quadratic configuration interaction in single-point energy calculations. We find that for free radicals with low spin contamination G2 theory also performs adequately, but as 〈S2〉 increases the results of G2 calculations can become increasingly unsatisfactory. The recommended CBS-RAD procedure should yield more reliable results over a broader range of free radicals.

Radical thermochemistry and organic reactions

Abstract

New approaches to free radical thermochemistry

A variety of unusual techniques have been used to measure thermodynamic propeties of free radicals and heats of the reactions in which they participate. These include a radical buffer EPR technique, the appearance energy method, photoacoustic spectroscopy, and electrochemical detection of free radicals. The methods can be applied to systems involving organometallic and high molecular weight materials which are normally inaccessible to conventional, gas phase techniques.

Entropies and heat capacities of free radicals

AbstractMethods are presented for rapidly estimating the entropies and heat capacities of free radicals from the known S0 and C of structurally similar compounds. The methods consist of estimating the differences due to changes in mass, vibration frequencies, spin, symmetry, and changes in rotational barriers. Tables of contributions to S0 and C by different frequencies over the temperature range 300–1500°K are presented to facilitate the tabulation of the above differences. Conjugated radicals, such as benzyl and allyl, are included. It is shown that the greatest uncertainties in the estimates arise from uncertainties in the barriers to rotation in the radicals.The results are applied to kinetic data on the pyrolysis of branched hydrocarbons and the reverse reactions of radical recombination. Major discrepancies exist in these data which can be nearly reconciled by postulating improbably high rotational barriers of 8 kcal for CH3 rotation in isopropyl and t‐butyl radicals.It is shown that radical thermochemistry can be fitted into group schemes and tables of groups values are given for the rapid estimation of ΔH, S0, and C for different organic radicals, including those containing sulfur, oxygen, and nitrogen.