Structures, internal rotor potentials, and thermochemical properties for a series of nitrocarbonyls, nitroolefins, corresponding nitrites, and their carbon centered radicals

Structures, enthalpy (Δ(f)H°(298)), entropy (S°(T)), and heat capacity (C(p)(T)) are determined for a series of nitrocarbonyls, nitroolefins, corresponding nitrites, and their carbon centered radicals using the density functional B3LYP and composite CBS-QB3 calculations. Enthalpies of formation (Δ(f)H°(298)) are determined at the B3LYP/6-31G(d,p), B3LYP/6-31+G(2d,2p), and composite CBS-QB3 levels using several work reactions for each species. Entropy (S) and heat capacity (C(p)(T)) values from vibration, translational, and external rotational contributions are calculated using the rigid-rotor-harmonic-oscillator approximation based on the vibration frequencies and structures obtained from the density functional studies. Contribution to Δ(f)H(T), S, and C(p)(T) from the analysis on the internal rotors is included. Recommended values for enthalpies of formation of the most stable conformers of nitroacetone cc(═o)cno2, acetonitrite cc(═o)ono, nitroacetate cc(═o)no2, and acetyl nitrite cc(═o)ono are -51.6 kcal mol(-1), -51.3 kcal mol(-1), -45.4 kcal mol(-1), and -58.2 kcal mol(-1), respectively. The calculated Δ(f)H°(298) for nitroethylene c═cno2 is 7.6 kcal mol(-1) and for vinyl nitrite c═cono is 7.2 kcal mol(-1). We also found an unusual phenomena: an intramolecular transfer reaction (isomerization) with a low barrier (3.6 kcal mol(-1)) in the acetyl nitrite. The NO of the nitrite (R-ONO) in CH(3)C(═O')ONO moves to the C═O' oxygen in a motion of a stretching frequency and then a shift to the carbonyl oxygen (marked as O' for illustration purposes).     

Thermochemical properties and bond dissociation energies of C3-C5 cycloalkyl hydroperoxides and peroxy radicals: cycloalkyl radical + (3)O2 reaction thermochemistry

Cyclic aliphatic hydrocarbons are major components in modern fuels; they can be present in the reactants, and they can be formed during the gas-phase oxidation processes. In combustion and thermal oxidation processes, these cyclics will form radicals that react with (3)O(2) to form peroxy radicals. In this study, density functional theory and higher level ab initio calculations are used to calculate thermochemical properties and bond dissociation energies of 3-5-membered cycloalkanes, corresponding hydroperoxides, hydroperoxycycloalkyl radicals, and cycloalkyl radicals that occur in these reaction systems. Geometries, vibration frequencies, and thermochemical properties, ΔH(f 298)°, are calculated with the B3LYP/6-31 g(d,p), B3LYP/6-31 g(2d,2p), composite CBS-QB3, and G3MP2B3 methods. Standard enthalpies of formation at 298 K are evaluated using isodesmic reaction schemes with several work reactions for each species. Group additivity contributions are developed, and application of group additivity with comparison to calculated values is illustrated. Entropy and heat capacities, S°(T) and C(p)°(T) (5 K ≤ T ≤ 5000), are determined using geometric parameters and frequencies from the B3LYP/6-31 g(d,p) calculations.     

Thermochemical properties, DeltafH degrees (298), S degrees (298), and Cp degrees (T), for n-butyl and n-pentyl hydroperoxides and the alkyl and peroxy radicals, transition states, and kinetics for intramolecular hydrogen shift reactions of the peroxy radicals

Alkyl radicals in atmospheric and combustion environments undergo a rapid association with molecular oxygen (3O2) to form an alkyl peroxy radical (ROO*). One important reaction of these peroxy radicals is the intramolecular H-shift (intramolecular abstraction) to form a hydroperoxide alkyl radical (R'*COOH), where the hydroperoxide alkyl radical may undergo chemical activation reaction with O2 and result in chain branching at moderate to low temperatures. The thermochemistry and trends in kinetic parameters for the hydrogen shift reactions from each carbon (4-8-member-ring TST's) in n-butyl and n-pentyl peroxy radicals (CCCCOO* and CCCCCOO*) are analyzed using density functional and ab initio calculation methods. Thermochemical properties, DeltafH degrees (298 K), C-H bond energies, S degrees (298 K), and Cp degrees (T) of saturated linear C4 and C5 aliphatic peroxides (ROOH), as well as the corresponding hydroperoxide alkyl radicals (R'*COOH), are determined. DeltafH degrees (298 K) are obtained from isodesmic reactions and the total energies of the CBS-QB3 and B3LYP computational methods. Contributions to the entropy and the heat capacity from translation, vibration, and external rotation are calculated using the rigid-rotor-harmonic-oscillator approximation based on the CBS-QB3 frequencies and structures. The results indicate that pre-exponential factors, A(T), decrease with the increase of the ring size (4-8-member-ring TS, H-atom included). The DeltaH for 4-, 5-, 6-, and 7-member rings in n-butyl (and n-pentyl) peroxy are 40.8 (40.8), 31.4 (31.5), 20.5 (20.0), 22.6-p (19.4) kcal mol(-1), respectively. The DeltaH for the 8-member ring in n-pentylperoxy is 23.8-p kcal mol(-1), All abstractions are from secondary (-CH2-) groups except those marked (-p), which are from primary sites. Enthalpy and barrier values from the B3LYP/6-311++G(2d,p) and BHandHLYP/6-311G(d,p) methods are compared with CBS-QB3 results. The B3LYP results show good agreement with the higher level CBS-QB3 calculation method; the BHandH barriers for the intramolecular peroxy H-shifts are not acceptable.     

The C-H and alpha(C-X) bond dissociation enthalpies of toluene, C6H5-CH2X (X = F, Cl), and their substituted derivatives: a DFT study

The homolytic C-H bond dissociation enthalpies (BDEs) of toluene and its para- and meta-substituted derivatives have been estimated by using the (RO)B3LYP/6-311++G(2df,2p)//(U)B3LYP/6-311G(d,p) procedure. The performance of two other hybrid functionals of DFT, namely, B3PWP91 and O3LYP, has also been evaluated using the same basis sets and molecules. Our computed results are compared with the available experimental values and are found to be in good agreement. The (RO)B3LYP and (RO)O3LYP procedures are found to produce reliable BDEs for the C-H bonds in toluene and the C-X (X = F, Cl) bond in alpha-substituted toluene (C6H5-CH2X) and their substituted derivatives. The substituent effect on the BDE values has been analyzed in terms of the ground-state effect and the radical effect. The effect of polarization of the C-H bond on the substituent effect is also analyzed. The BDE(C-H) and BDE(C-X) values for alpha-substituted (X = F and Cl) toluenes with a set of para substituents are presented for the first time.     

Protonation thermochemistry of selected hydroxy- and methoxycarbonyl molecules

The gas-phase basicities of a representative set of hydroxy- and methoxycarbonyl compounds (hydroxyacetone, 1, 3-hydroxybutanone, 2, 3-hydroxy-3-methylbutanone, 3, 1-hydroxy-2-butanone, 4, 4-hydroxy-2-butanone, 5, 5-hydroxy-2-pentanone, 6, methoxyacetone, 7, 3-methoxy-2-butanone, 8, 4-methoxy-2-butanone, 9, and 5-methoxy-2-pentanone, 10) were experimentally determined by the equilibrium method using Fourier transform ion cyclotron resonance and high-pressure mass spectrometry techniques. The latter method allows the measurement of proton transfer equilibrium constants at various temperatures and thus the estimate of both the proton affinities and the protonation entropies of the relevant species. Quantum chemical calculations at the G3 and the B3LYP/6-311+G(3df,2p)//6-31G(d) levels of theory were undertaken in order to find the most stable structures of the neutrals 1-10 and their protonated forms. Conformational and vibrational analyses have been done with the aim of obtaining a theoretical estimate of the protonation entropies.     

密度泛函法计算C1-C14正构烃生成焓及C-C键裂解能

采用密度泛函理论(DFT)方法研究了费托石脑油裂解反应中涉及到C₁-C₁₄正构烃和自由基中间体的生成焓及其C-C键解离能(BDE)。 结果表明,在所有评价的密度泛函理论方法（B97-1、BB1K、B1B95、MPWB1K和MPW1B95）中,MPW1B95/6-311G(d,p)方法计算最精确。 以此方法为基准,进一步对高碳烃及其裂解产物的标准生成焓和C-C键解离能进行了预测。 与可得到的实验数据相比,MPW1B95/6-311G(d,p)方法预测的烃和自由基的平均生成焓分别为0.8和2.7 kJ/mol,C-C键解离能的平均绝对误差只有3.1 kJ/mol,表明此方法不仅可准确计算正构烃标准生成焓和C-C键解离能,而且还能正确预测C-C键解离能变化趋势。     

Computational study on the bond dissociation enthalpies in the enolic and ketonic forms of beta-diketones: their influence on metal-ligand bond enthalpies

A computational study on the thermodynamic properties of 13 beta-diketones is presented. The B3LYP//6-311+G(2d,2p)//B3LYP/6-31G(d) theoretical approach was employed to compute the O-H and C-H bond dissociation enthalpies and enthalpy of tautomerization and to estimate standard gas-phase enthalpies of formation for the radicals and for the parent molecules. The gas-phase enthalpies of formation for the neutral molecules are in excellent agreement with available experimental data, supporting the estimates made for the radicals. The latter are very important for the clarification of the thermochemistry of many beta-diketonato metal complexes previously reported in the literature. Importantly, when substituents R = -CHR' are attached to the beta-diketone's scaffold, C-H homolytic bond cleavage is always favored with respect to O-H bond scission.     

Homolytic C-H and N-H bond dissociation energies of strained organic compounds

High-level computations at G3, CBS-Q, and G3B3 levels were conducted, and good-quality C-H and N-H bond dissociation energies (BDEs) were obtained for a variety of saturated and unsaturated strained hydrocarbons and amines for the first time. From detailed NBO analyses, we found that the C-H BDEs of hydrocarbons are determined mainly by the hybridization of the parent compound, the hybridization of the radical, and the extent of spin delocalization of the radical. The ring strain has a significant effect on the C-H BDE because it forces the parent compound and radical to adopt certain undesirable hybridization. A structure-activity relationship equation (i.e., BDE (C-H) = 61.1-227.8 (p(parent)% - 0.75)(2) + 152.9 (p(radical)% - 1.00)(2) + 40.4 spin) was established, and it can predict the C-H BDEs of a variety of saturated and unsaturated strained hydrocarbons fairly well. For the C-H BDEs associated with the bridgehead carbons of the highly rigid strained compounds, we found that the strength of the C-H bond can also be predicted from the H-C-C bond angles of the bridgehead carbon. Finally, we found that N-H BDEs show less dependence on the ring strain than C-H BDEs.     

Thermochemical data and additivity group values for ten species of o-xylene low-temperature oxidation mechanism

o-Xylene could be a good candidate to represent the family of aromatic hydrocarbons in a surrogate fuel. This study uses computational chemistry to calculate standard enthalpies of formation at 298 K, Δ(f)H°(298 K), standard entropies at 298 K, S°(298 K), and standard heat capacities C(p)°(T) over the temperature range 300 K to 1500 K for ten target species present in the low-temperature oxidation mechanism of o-xylene: o-xylene (1), 2-methylbenzyl radical (2), 2-methylbenzylperoxy radical (3), 2-methylbenzyl hydroperoxide (4), 2-(hydroperoxymethyl)benzyl radical (5), 2-(hydroperoxymethyl)benzaldehyde (6), 1-ethyl-2-methylbenzene (7), 2,3-dimethylphenol (8), 2-hydroxybenzaldehyde (9), and 3-hydroxybenzaldehyde (10). Δ(f)H°(298 K) values are weighted averages across the values calculated using five isodesmic reactions and five composite calculation methods: CBS-QB3, G3B3, G3MP2, G3, and G4. The uncertainty in Δ(f)H°(298 K) is also evaluated. S°(298 K) and C(p)°(T) values are calculated at B3LYP/6-311G(d,p) level of theory from molecular properties and statistical thermodynamics through evaluation of translational, rotational, vibrational, and electronic partition functions. S°(298 K) and C(p)°(300 K) values are evaluated using the rigid-rotor-harmonic-oscillator model. C(p)°(T) values at T ≥ 400 K are calculated by treating separately internal rotation contributions and translational, external rotational, vibrational, and electronic contributions. The thermochemical properties of six target species are used to develop six new additivity groups taking into account the interaction between two substituents in ortho (ORT/CH2OOH/ME, ORT/ET/ME, ORT/CHO/OH, ORT/CHO/CH2OOH) or meta (MET/CHO/OH) positions, and the interaction between three substituents (ME/ME/OH123) located one beside the other (positions numbered 1, 2, 3) for two- or three-substituted benzenic species. Two other additivity groups are also developed using the thermochemical properties of benzenic species taken from the literature: the C/CB/H2/OO and the CB/CO groups. These groups extend the capacities of the group additivity method to deal with substituted benzenic species.     

Computational methods in organic thermochemistry. 1. Hydrocarbon enthalpies and free energies of formation

Standard state enthalpies and free energies of formation can be computed with reasonable accuracy (usually within 4 and often 2 kJ/mol) using high level model chemistries. A comparison set of nearly 300 organic compounds ranging from 1 to 10 carbon atoms having a variety of functional groups for which enthalpy and free energy literature values are available has been examined using G2, G2MP2, G3, G3MP2, G3B3, G3MP2B3, CBS-QB3, and density functional (B3LYP/6-311+G(3df,2p)) model chemistries. G3 gives an average mean absolute deviation of 3.0 and 13.4 kJ/mol for the enthalpies and free energies, respectively, using the atomization method and 3.1 and 3.7 kJ/mol when bond separation reactions are employed. G3 and G3B3 are the most accurate overall; the related G3MP2 and G3MP2B3 are nearly as accurate and can compute larger molecules. CBS-QB3 was also found to be accurate but is more limited in the size of molecules that can be computed. The density functional energies were found to have large deviations from the literature values using either the atomization or the bond separation method. Regardless of the model employed, the free energies are increasingly underestimated by computation as the size of the molecule increases. A series of corrections applied to the aliphatic hydrocarbons is presented, which usually reduces the deviations to less than 4 kJ/mol regardless of the size of the molecule.     

Thermochemistry and kinetics of the 2-butanone-4-yl CH3C(=O)CH2CH2• + O2 reaction system

Thermochemistry and kinetic pathways on the 2-butanone-4-yl (CH₃C(=O)CH₂CH₂•) + O₂ reaction system are determined. Standard enthalpies, entropies, and heat capacities are evaluated using the G3MP2B3, G3, G3MP3, CBS-QB3 ab initio methods, and the B3LYP/6-311g(d,p) density functional calculation method. The CH₃C(=O)CH₂CH₂• radical + O₂ association reaction forms a chemically activated peroxy radical with 35 kcal mol⁻¹ excess of energy. The chemically activated adduct can undergo RO−O bond dissociation, rearrangement via intramolecular hydrogen transfer reactions to form hydroperoxide-alkyl radicals, or eliminate HO₂ and OH. The hydroperoxide-alkyl radical intermediates can undergo further reactions forming ketones, cyclic ethers, OH radicals, ketene, formaldehyde, or oxiranes. A relatively new path showing a low barrier and resulting in reactive product sets involves peroxy radical attack on a carbonyl carbon atom in a cyclic transition state structure. It is shown to be important in ketones when the cyclic transition state has five or more central atoms.     

Are calculated enthalpies of formation sometimes more reliable than experimental? A test on alkyl substituted benzoic acids

Energies of 20 alkyl-substituted benzoic acids were calculated at the levels B3LYP/6-311+G(d,p)//B3LYP/6-311+G(d,p) and MP2/6-311+G(d,p)//MP2/6-311+G(d,p); the pertinent enthalpies at 298 K were calculated at the same levels. Comparison with experimental enthalpies of formation Delta(f)H degrees (g)(298) was carried out in terms of isodesmic reactions, that is, in the relative values. Of the four calculated quantities, the DFT enthalpies yielded best correlation with the standard deviation of 2.1 kJ mol(-1), near to the experimental uncertainty; the DFT energies are only slightly worse and the MP2 enthalpies or energies much worse. However, the DFT method overestimated systematically the substituent effects and had to be calibrated. Comparison with the experimental gas-phase acidities was less telling and the fit was worse because both methods overestimated the substituent effects. Extending the base in selected examples did not give better results. Although the systematic deviations are evidently due to the imperfections of the theoretical models, individual big deviations should be attributed to experimental errors or to the abnormal behavior of certain compounds at the experimental conditions. From this point of view, three examples of the so-called long-range effect claimed in the case of different benzoic acid derivatives, always for substituents in the meta position, must be refused as unproven because the experimental energies were not confirmed by calculations.     

The shape of gaseous n-butylbenzene: assessment of computational methods and comparison with experiments

Conformational landscape of neutral and ionized n-butylbenzene has been examined. Geometries have been optimized at the B3LYP/6-31G(d), B3LYP/6-31+G(d,p), B3LYP-D/6-31+G(d,p), B2PLYP/6-31+G(d,p), B2PLYP-D/6-31+G(d,p), B97-D/6-31+G(d,p), and M06-2X/6-31+G(d,p) levels. This study is complemented by energy computations using 6-311++G(3df,2p) basis set and CBS-QB3 and G3MP2B3 composite methods to obtain accurate relative enthalpies. Five distinguishable conformers have been identified for both the neutral and ionized systems. Comparison with experimentally determined rotational constants shows that the best geometrical parameters are provided by B3LYP-D and M06-2X functionals, which include an explicit treatment of dispersion effects. Composite G3MP2B3 and CBS-QB3 methods, and B2PLYP-D, B3LYP-D, B97-D, and M06-2X functionals, provide comparable relative energies for the two sets of neutral and ionized conformers of butyl benzene. An exception is noted however for conformer V(+) the stability of which being overestimated by the B3LYP-D and B97-D functionals. The better stability of neutral conformers I, III, and IV, and of cation I(+) , demonstrated by our computations, is in perfect agreement with conclusions based on micro wave, fluorescence, and multiphoton ionization experiments.     

CH and Chalogen bond dissociation energies for fluorinated and chlorinated methane evaluated with hybrid B3LYP density functional theory methods and their comparison with experimental data and the CBS-Q ab initio computational approach

The CH and Chalogen bond dissociation energies (BDEs) were computed with the hybrid B3LYP/6-311 + G(2d,2p) theory model for chlorinated and fluorinated methane. All computed values were substantially lower (5–10 kcal mol⁻¹) than the experimental values. To obtain better agreement, a correlation factor was introduced. When this factor was applied, excellent agreement between the B3LYP/6-311 + G(2d,2p) computed energies and the experimental BDEs was observed. On the other hand, the CBS-Q ab initio computational approach generated BDEs which are in good agreement with experimental values without a correction factor.     

Energetic differences between the five- and six-membered ring hydrocarbons: strain energies in the parent and radical molecules

The C-H bond dissociation enthalpies (BDEs) for the five- and six-membered ring alkanes, alkenes, and dienes were investigated and discussed in terms of conventional strain energies (SEs). New determinations are reported for cyclopentane and cyclohexane by time-resolved photoacoustic calorimetry and quantum chemistry methods. The C-H BDEs for the alkenes yielding the alkyl radicals cyclopenten-4-yl and cyclohexen-4-yl and the alpha-C-H BDE in cyclopentene were also calculated. The s-homodesmotic model was used to determine SEs for both the parent molecules and the radicals. When the appropriate s-homodesmotic model is chosen, the obtained SEs are in good agreement with the ones derived from group additivity schemes. The different BDEs in the title molecules are explained by the calculated SEs in the parent molecules and their radicals: (1) BDEs leading to alkyl radicals are ca. 10 kJ mol (-1) lower in cyclopentane and cyclopentene than in cyclohexane and cyclohexene, due to a smaller eclipsing strain in the five-membered radicals relative to the parent molecules (six-membered hydrocarbons and their radicals are essentially strain free). (2) C-H BDEs in cyclopentene and cyclohexene leading to the allyl radicals are similar because cyclopenten-3-yl has almost as much strain as its parent molecule, due to a synperiplanar configuration. (3) The C-H BDE in 1,3-cyclopentadiene is 27 kJ mol (-1) higher than in 1,4-cyclohexadiene due to the stabilizing effect of the conjugated double bond in 1,3-cyclopentadiene and not to a destabilization of the cyclopentadienyl radical. The chemical insight afforded by group additivity methods in choosing the correct model for SE estimation is highlighted.     

Computational methods to calculate accurate activation and reaction energies of 1,3-dipolar cycloadditions of 24 1,3-dipoles

Theoretical calculations were performed on the 1,3-dipolar cycloaddition reactions of 24 1,3-dipoles with ethylene and acetylene. The 24 1,3-dipoles are of the formula X≡Y(+)-Z(-) (where X is HC or N, Y is N, and Z is CH(2), NH, or O) or X═Y(+)-Z(-) (where X and Z are CH(2), NH, or O and Y is NH, O, or S). The high-accuracy G3B3 method was employed as the reference. CBS-QB3, CCSD(T)//B3LYP, SCS-MP2//B3LYP, B3LYP, M06-2X, and B97-D methods were benchmarked to assess their accuracies and to determine an accurate method that is practical for large systems. Several basis sets were also evaluated. Compared to the G3B3 method, CBS-QB3 and CCSD(T)/maug-cc-pV(T+d)Z//B3LYP methods give similar results for both activation and reaction enthalpies (mean average deviation, MAD, < 1.5 kcal/mol). SCS-MP2//B3LYP and M06-2X give small errors for the activation enthalpies (MAD < 1.5 kcal/mol), while B3LYP has MAD = 2.3 kcal/mol. SCS-MP2//B3LYP and B3LYP give the reasonable reaction enthalpies (MAD < 5.0 kcal/mol). The B3LYP functional also gives good results for most 1,3-dipoles (MAD = 1.9 kcal/mol for 17 common 1,3-dipoles), but the activation and reaction enthalpies for ozone and sulfur dioxide are difficult to calculate by any of the density functional methods.     

Gas-phase acidity, bond dissociation energy and enthalpy of formation of fluorine-substituted benzenes: A theoretical study

A variety of theoretical methods have been used to study the gas-phase acidity of benzene and its eleven fluorine-substituted derivatives: fluorobenzene, three isomers of difluorobenezene, three isomers of trifluorobenzene, three isomers of tetrafluorobenzene and 1,2,3,4,5-pentafluorobenzene. The high-level ab initio methods, G3//B3-LYP and CBS-QB3, are shown to reproduce experimental data to within an average of 1.9 and 1.4 kcal mol⁻¹, respectively. Of the lower-cost methods studied, M05-2X and MP2 showed the best overall performance with mean absolute deviations of just 1.2 and 1.1 kcal mol⁻¹, respectively. The effect of substitution and position on the acidity of the protons in the various compounds are studied and the structure-reactivity trends in these heterolytic C-H bond dissociation energies (BDEs) are compared with the corresponding homolytic C-H BDEs for the same species.     

Thermochemical properties for n‐propyl,iso‐propyl,and tert‐butyl nitroalkanes,alkyl nitrites,and their carbon‐centered radicals

Density functional theory (DFT) based calculations are performed on a series of alkyl nitrites and nitroalkanes representing large‐scale primary, secondary, and tertiary nitro compounds and their radicals resulting from the loss of their skeletal hydrogen atoms. Geometries, vibration frequencies, and thermochemical properties [S°(T) and C°_p(T) (10 K ? T ? 5000 K)] are calculated at the B3LYP/6‐31G(d,p) DFT level. Δ_fH°₂₉₈ values are from B3LYP/6‐31G(d,p), B3LYP/6‐31+G(2d,2p), and the composite CBS‐QB3 levels. Potential energy barriers for the internal rotations have been computed at the B3LYP/6‐31G(d,p) level of theory, and the lower barrier contributions are incorporated into entropy and heat capacity data. The standard enthalpies of formation at 298 K are evaluated using isodesmic reaction schemes with several work reactions for each species. Recommended values derived from the most stable conformers of respective nitro‐ and nitrite isomers include ?30.57 and ?28.44 kcal mol^?1 for n‐propane‐, ?33.89 and ?32.32 kcal mol^?1 for iso‐propane‐, ?42.78 and ?41.36 kcal mol^?1 for tert‐butane‐nitro compounds and nitrites, respectively. Entropy and heat capacity values are also reported for the lower homologues: nitromethane, nitroethane, and corresponding nitrites. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 181–199, 2010     

Accurate prediction of thermodynamic properties of alkyl peroxides by combining density functional theory calculation with least-square calibration

Owing to the significance in kinetic modeling of the oxidation and combustion mechanisms of hydrocarbons, a fast and relatively accurate method was developed for the prediction of Delta(f)H(298)(o) of alkyl peroxides. By this method, a raw Delta(f)H(298)(o) value was calculated from the optimized geometry and vibration frequencies at B3LYP/6-31G(d,p) level and then an accurate Delta(f)H(298)(o) value was obtained by a least-square procedure. The least-square procedure is a six-parameter linear equation and is validated by a leave-one out technique, giving a cross-validation squared correlation coefficient q(2) of 0.97 and a squared correlation coefficient of 0.98 for the final model. Calculated results demonstrated that the least-square calibration leads to a remarkable reduction of error and to the accurate Delta(f)H(298)(o) values within the chemical accuracy of 8 kJ mol(-1) except (CH(3))(2)CHCH(2)CH(2)CH(2)OOH which has an error of 8.69 kJ mol(-1). Comparison of the results by CBS-Q, CBS-QB3, G2, and G3 revealed that B3LYP/6-31G(d,p) in combination with a least-square calibration is reliable in the accurate prediction of the standard enthalpies of formation for alkyl peroxides. Standard entropies at 298 K and heat capacities in the temperature range of 300-1500 K for alkyl peroxides were also calculated using the rigid rotor-harmonic oscillator approximation.     

Investigation of the use of B3LYP zero-point energies and geometries in the calculation of enthalpies of formation

The use of B3LYP/6–31G^* zero-point energies and geometries in the calculation of enthalpies of formation has been investigated for the enlarged G2 test set of 148 molecules [J. Chem. Phys. 106 (1997) 1063]. A scale factor of 0.96 for the B3LYP zero-point energies gives an average absolute deviation nearly the same as scaled HF/6–31G^* zero-point energies for G2, G2(MP2), and B3LYP/6–311 + G(3df,2p) enthalpies. A scale factor of 0.98, which has been recommended in some studies, increases the average absolute deviation by about 0.2 kcal/mol. Geometries from B3LYP/6–31G^* are found to do as well as MP2/6–31G^* geometries in the calculation of the enthalpies of formation.