Quantitative computational thermochemistry of transition metal species

The correlation consistent Composite Approach (ccCA), which has been shown to achieve chemical accuracy (+/-1 kcal mol-1) for a large benchmark set of main group and s-block metal compounds, is used to compute enthalpies of formation for a set of 17 3d transition metal species. The training set includes a variety of metals, ligands, and bonding types. Using the correlation consistent basis sets for the 3d transition metals, we find that gas-phase enthalpies of formation can be efficiently calculated for inorganic and organometallic molecules with ccCA. However, until the reliability of gas-phase transition metal thermochemistry is improved, both experimentally and theoretically, a large experimental training set where uncertainties are near +/-1 kcal mol-1 (akin to commonly used main group benchmarking sets) remains an ambitious goal. For now, an average deviation of +/-3 kcal mol-1 appears to be the initial goal of "chemical accuracy" for ab initio transition metal model chemistries. The ccCA is also compared to a more robust but relatively expensive composite approach primarily utilizing large basis set coupled cluster computations. For a smaller training set of eight molecules, ccCA has a mean absolute deviation (MAD) of 3.4 kcal mol-1 versus the large basis set coupled-cluster-based model chemistry, which has a MAD of 3.1 kcal mol-1. However, the agreement for transition metal complexes is more system dependent than observed in previous benchmark studies of composite methods and main group compounds.     

The correlation consistent composite approach (ccCA): an alternative to the Gaussian-n methods

An alternative to the Gaussian-n (G1, G2, and G3) composite methods of computing molecular energies is proposed and is named the "correlation consistent composite approach" (ccCA, ccCA-CBS-1, ccCA-CBS-2). This approach uses the correlation consistent polarized valence (cc-pVXZ) basis sets. The G2-1 test set of 48 enthalpies of formation (DeltaHf), 38 adiabatic ionization potentials (IPs), 25 adiabatic electron affinities (EAs), and 8 adiabatic proton affinities (PAs) are computed using this approach, as well as the DeltaHf values of 30 more systems. Equilibrium molecular geometries and vibrational frequencies are obtained using B3LYP density functional theory. When applying the ccCA-CBS method with the cc-pVXZ series of basis sets augmented with diffuse functions, mean absolute deviations within the G2-1 test set compared to experiment are 1.33 kcal mol(-1) for DeltaHf,0.81 kcal mol(-1) for IPs, 1.02 kcal mol(-1) for EAs, and 1.51 kcal mol(-1) for PAs, without including the "high-level correction" (HLC) contained in the original Gn methods. Whereas the HLC originated in the Gaussian-1 method as an isogyric correction, it evolved into a fitted parameter that minimized the error of the composite methods, eliminating its physical meaning. Recomputing the G1 and G3 enthalpies of formation without the HLC reveals a systematic trend where most DeltaHf values are significantly higher than experimental values. By extrapolating electronic energies to the complete basis set (CBS) limit and adding G3-like corrections for the core-valence and infinite-order electron correlation effects, ccCA-CBS-2 often underestimates the experimental DeltaHf, especially for larger systems. This is desired as inclusion of relativistic and atomic spin-orbit effects subsequently improves theoretical DeltaHf values to give a 0.81 kcal mol(-1) mean absolute deviation with ccCA-CBS-2. The ccCA-CBS method is a viable "black box" method that can be used on systems with at least 10-15 heavy atoms.     

The correlation-consistent composite approach: application to the G3/99 test set

The correlation-consistent composite approach (ccCA), an ab initio composite technique for computing atomic and molecular energies, recently has been shown to successfully reproduce experimental data for a number of systems. The ccCA is applied to the G3/99 test set, which includes 223 enthalpies of formation, 88 adiabatic ionization potentials, 58 adiabatic electron affinities, and 8 adiabatic proton affinities. Improvements on the original ccCA formalism include replacing the small basis set quadratic configuration interaction computation with a coupled cluster computation, employing a correction for scalar relativistic effects, utilizing the tight-d forms of the second-row correlation-consistent basis sets, and revisiting the basis set chosen for geometry optimization. With two types of complete basis set extrapolation of MP2 energies, ccCA results in an almost zero mean deviation for the G3/99 set (with a best value of -0.10 kcal mol(-1)), and a 0.96 kcal mol(-1) mean absolute deviation, which is equivalent to the accuracy of the G3X model chemistry. There are no optimized or empirical parameters included in the computation of ccCA energies. Except for a few systems to be discussed, ccCA performs as well as or better than Gn methods for most systems containing first-row atoms, while for systems containing second-row atoms, ccCA is an improvement over Gn model chemistries.     

A pseudopotential-based composite method: the relativistic pseudopotential correlation consistent composite approach for molecules containing 4d transition metals (Y-Cd)

The correlation consistent composite approach (ccCA) has proven to be an effective first-principles-based composite approach for main group and first-row transition metal species. By combining relativistic pseudopotentials and ccCA, accurate energetic and thermodynamic data for heavier elements, including transition metals, is obtainable. Relativistic pseudopotential ccCA (rp-ccCA) was formulated and tested on 25 molecules from the G3∕05 set that contain 4p elements (Ga-Kr). A 32.5% time savings was obtained using rp-ccCA, relative to ccCA employing all-electron basis sets. When implementing rp-ccCA to compute dissociation energies and enthalpies of formation for molecules from the 4p block, rp-ccCA results in a mean absolute deviation of 0.89 kcal?mol(-1) from experimental data. rp-ccCA was also applied to a set of 30 4d transition metal-containing molecules, ranging from diatomics to Mo(CO)(6), and enthalpies of formation for these species were obtained with a mean absolute deviation of 2.89 kcal mol(-1) in comparison to experimental data. Based on quality of the experimentally available enthalpies of formation, where the average value of reported experimental error bars is 3.43 kcal mol(-1), rp-ccCA is within transition metal chemical accuracy for the 4d molecule set. rp-ccCA is a pseudopotential-based composite method for transition metals and is shown to yield accurate thermodynamic results for molecules containing heavy elements Ga-Kr and Y-Cd.     

Accurate enthalpies of formation of alkali and alkaline earth metal oxides and hydroxides: assessment of the correlation consistent composite approach (ccCA)

Computing the enthalpies of formation for alkali metal and alkaline earth metal oxides (M(x)O) and hydroxides [M(OH)(n)] using the Gaussian-n (Gn) and Weismann-n (Wn) ab initio model chemistries is difficult due to an improper treatment of core-valence electron correlation effects. Using a new model chemistry called the correlation consistent Composite Approach (ccCA), enthalpies of formation were determined for eight different alkali/alkaline earth metal oxides and hydroxides. Unlike the Gn and Wn model chemistries, which must be modified to properly account for core-valence electron correlation, the standard implementations of the ccCA provide acceptable results, and all enthalpies of formation obtained with the ccCA are within the accepted range of recommended values.     

Prediction of hydrocarbon enthalpies of formation by various thermochemical schemes

The correlation consistent composite approach (ccCA) has been used to compute the enthalpies of formation (ΔH_f′s) for 60 closed‐shell, neutral hydrocarbon molecules selected from an established set (Cioslowski et al., J. Chem. Phys. 2000 , 113, 9377). This set of thermodynamic values includes ΔH_f's for hydrocarbons that span a range of molecular sizes, degrees of aromaticity, and geometrical configurations, and, as such, provides a rigorous assessment of ccCA's applicability to a variety of hydrocarbons. The ΔH_f's were calculated via atomization energies, isodesmic reactions, and hypohomodesmotic reactions. In addition, for 12 of the aromatic molecules in the set that are larger than benzene, the energies of ring‐conserved isodesmic reactions were used to calculate the ΔH_f′s. Using an atomization energy approach to determine the ΔH_f′s, the lowest mean absolute deviation (MAD) from experiment achieved by ccCA for the 60 hydrocarbons was 1.10 kcal mol^?1. The use of the mixed Gaussian/inverse exponential complete basis set extrapolation scheme (ccCA‐P) in conjunction with hypohomodesmotic reaction energies resulted in a MAD of 0.87 kcal mol^?1. This value is compared with MADs of 1.17, 1.18, and 1.28 kcal mol^?1 obtained via the Gaussian‐4 (G4), Gaussian‐3 (G3), and Gaussian‐3(MP2) [G3(MP2)] methods, respectively (using the hypohomodesmotic reactions). © 2012 Wiley Periodicals, Inc.     

Enthalpies of formation, bond dissociation energies, and molecular structures of the n-aldehydes (acetaldehyde, propanal, butanal, pentanal, hexanal, and heptanal) and their radicals

Aldehydes are important intermediates and products in a variety of combustion and gas-phase oxidation processes, such as in low-temperature combustion, in the atmosphere, and in interstellar media. Despite their importance, the enthalpies of formation and bond dissociation energies (BDEs) for the aldehydes are not accurately known. We have determined enthalpies of formation for acetaldehyde, propanal, and butanal from thermodynamic cycles, using experimentally measured reaction and formation enthalpies. All enthalpy values used for reference molecules and reactions were first verified to be accurate to within around 1 kcal mol-1 using high-level ab initio calculations. Enthalpies of formation were found to be -39.72 +/- 0.16 kcal mol-1 for acetaldehyde, -45.18 +/- 1.1 kcal mol-1 for propanal, and -49.27 +/- 0.16 kcal mol-1 for butanal. Enthalpies of formation for these three aldehydes, as well as for pentanal, hexanal, and heptanal, were calculated using the G3, G3B3, and CBS-APNO theoretical methods, in conjunction with bond-isodesmic work reactions. On the basis of the results of our thermodynamic cycles, theoretical calculations using isodesmic work reactions, and existing experimental measurements, we suggest that the best available formation enthalpies for the aldehydes acetaldehyde, propanal, butanal, pentanal, hexanal, and heptanal are -39.72, -45.18, -50.0, -54.61, -59.37, and -64.2 kcal mol-1, respectively. Our calculations also identify that the literature enthalpy of formation of crotonaldehyde is in error by as much as 1 kcal mol-1, and we suggest a value of -25.1 kcal mol-1, which we calculate using isodesmic work reactions. Bond energies for each of the bonds in the aldehydes up to pentanal were calculated at the CBS-APNO level. Analysis of the BDEs reveals the R-CH(2)CH=O to be the weakest bond in all aldehydes larger than acetaldehyde, due to formation of the resonantly stabilized vinoxy radical (vinyloxy radical/formyl methyl radical). It is proposed that the vinoxy radical as well as the more commonly considered formyl and acetyl radicals are important products of aldehyde combustion and oxidation, and the reaction pathways of the vinoxy, formyl, and acetyl radicals are discussed. Group additivity values for the carbon-oxygen-hydrogen groups common to the aldehydes are also determined. Internal rotor profiles and electrostatic potential surfaces are used to study the dipole induced dipole-dipole interaction in the synperiplanar conformation of propanal. It is proposed that the loss of this dipole-dipole interaction in RC(.-)HCH(2)CH=O radicals causes a ca. 1-2 kcal mol-1 decrease in the aldehyde C-H and C-C bond energies corresponding to RC(.-)HCH(2)CH=O radical formation.     

Thermochemistry of methyl and ethyl nitro, RNO2, and nitrite, RONO, organic compounds

Computational quantum theory is employed to determine the thermochemical properties of n-alkyl nitro and nitrite compounds: methyl and ethyl nitrites, CH3ONO and C2H5ONO, plus nitromethane and nitroethane, CH3NO2 and C2H5NO2, at 298.15 K using multilevel G3, CBS-QB3, and CBS-APNO composite methods employing both atomization and isodesmic reaction analysis. Structures and enthalpies of the corresponding aci-tautomers are also determined. The enthalpies of formation for the most stable conformers of methyl and ethyl nitrites at 298 K are determined to be -15.64 +/- 0.10 kcal mol-1 (-65.44 +/- 0.42 kJ mol-1) and -23.58 +/- 0.12 kcal mol-1 (-98.32 +/- 0.58 kJ mol-1), respectively. DeltafHo(298 K) of nitroalkanes are correspondingly evaluated at -17.67 +/- 0.27 kcal mol-1 (-74.1 +/- 1.12 kJ mol-1) and -25.06 +/- 0.07 kcal mol-1 (-121.2 +/- 0.29 kJ mol-1) for CH3NO2 and C2H5NO2. Enthalpies of formation for the aci-tautomers are calculated as -3.45 +/- 0.44 kcal mol-1 (-14.43 +/- 0.11 kJ mol-1) for aci-nitromethane and -14.25 +/- 0.44 kcal mol-1 (-59.95 +/- 1.84 kJ mol-1) for the aci-nitroethane isomers, respectively. Data are evaluated against experimental and computational values in the literature with recommendations. A set of thermal correction parameters to atomic (H, C, N, O) enthalpies at 0 K is developed, to enable a direct calculation of species enthalpy of formation at 298.15 K, using atomization reaction and computation outputs.     

Heats of formation of boron hydride anions and dianions and their ammonium salts [BnHmy-][NH4+]y with y=1-2

Thermochemical parameters of the closo boron hydride BnHn2- dianions, with n=5-12, the B3H8- and B11H14- anions, and the B5H9 and B10H14 neutral species were predicted by high-level ab initio electronic structure calculations. Total atomization energies obtained from coupled-cluster CCSD(T)/complete basis set (CBS) extrapolated energies, plus additional corrections were used to predict the heats of formation of the simplest BnHmy- species in the gas phase in kcal/mol at 298 K: DeltaHf(B3H8-)=-23.1+/-1.0; DeltaHf(B5H52-)=119.4+/-1.5; DeltaHf(B6H62-)=64.1+/-1.5; and DeltaHf(B5H9)=24.1+/-1.5. The heats of formation of the larger species were evaluated by the G3 method from hydrogenation reactions (values at 298 K, in kcal/mol with estimated error bars of+/-3 kcal/mol): DeltaHf(B7H72-)=51.8; DeltaHf(B8H82-)=46.1; DeltaHf(B9H92-)=24.4; DeltaHf(B10H102-)=-12.5; DeltaHf(B11H112-)=-11.8; DeltaHf(B12H122-)=-86.3; DeltaHf(B11H14-)=-57.3; and DeltaHf(B10H14)=18.7. A linear correlation between atomization energies of the dianions and energies of the BH units was found. The heats of formation of the ammonium salts of the anions and dianions were predicted using lattice energies (UL) calculated from an empirical expression based on ionic volumes. The UL values (0 K) of the BnHn2- dianions range from 319 to 372 kcal/mol. The values of UL for the B3H8- and B11H14- anions are 113 and 135 kcal/mol, respectively. The calculated lattice energies and gas-phase heats of formation of the constituent ions were used to predict the heats of formation of the ammonium crystal salts [BnHmy-][NH4+]y. These results were used to evaluate the thermodynamics of the H2 release reactions from the ammonium hydro-borate salts.     

Enthalpies of formation of gas-phase N3, N3-, N5+, and N5- from Ab initio molecular orbital theory, stability predictions for N5(+)N3(-) and N5(+)N5(-), and experimental evidence for the instability of N5(+)N3(-)

Ab initio molecular orbital theory has been used to calculate accurate enthalpies of formation and adiabatic electron affinities or ionization potentials for N3, N3-, N5+, and N5- from total atomization energies. The calculated heats of formation of the gas-phase molecules/ions at 0 K are DeltaHf(N3(2Pi)) = 109.2, DeltaHf(N3-(1sigma+)) = 47.4, DeltaHf(N5-(1A1')) = 62.3, and DeltaHf(N5+(1A1)) = 353.3 kcal/mol with an estimated error bar of +/-1 kcal/mol. For comparison purposes, the error in the calculated bond energy for N2 is 0.72 kcal/mol. Born-Haber cycle calculations, using estimated lattice energies and the adiabatic ionization potentials of the anions and electron affinities of the cations, enable reliable stability predictions for the hypothetical N5(+)N3(-) and N5(+)N5(-) salts. The calculations show that neither salt can be stabilized and that both should decompose spontaneously into N3 radicals and N2. This conclusion was experimentally confirmed for the N5(+)N3(-) salt by low-temperature metathetical reactions between N5SbF6 and alkali metal azides in different solvents, resulting in violent reactions with spontaneous nitrogen evolution. It is emphasized that one needs to use adiabatic ionization potentials and electron affinities instead of vertical potentials and affinities for salt stability predictions when the formed radicals are not vibrationally stable. This is the case for the N5 radicals where the energy difference between vertical and adiabatic potentials amounts to about 100 kcal/mol per N5.     

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.     

Reliable predictions of the thermochemistry of boron-nitrogen hydrogen storage compounds: BxNxHy, x = 2, 3

Thermochemical data calculated using ab initio molecular orbital theory are reported for 16 BxNxHy compounds with x = 2, 3 and y > or = 2x. Accurate gas-phase heats of formation were obtained using coupled cluster with single and double excitations and perturbative triples (CCSD(T)) valence electron calculations extrapolated to the complete basis set (CBS) limit with additional corrections including core/valence, scalar relativistic, and spin-orbit corrections to predict the atomization energies and scaled harmonic frequencies to correct for zero point and thermal energies and estimate entropies. Computationally cheaper calculations were also performed using the G3MP2 and G3B3 variants of the Gaussian 03 method, as well as density functional theory (DFT) using the B3LYP functional. The G3MP2 heats of formation are too positive by up to approximately 6 kcal/mol as compared with CCSD(T)/CBS values. The more expensive G3B3 method predicts heats of formation that are too negative as compared with the CCSD(T)/CBS values by up to 3-4 kcal/mol. DFT using the B3LYP functional and 6-311+G** basis set predict isodesmic reaction energies to within a few kcal/mol compared with the CCSD(T)/CBS method so isodesmic reactions involving BN compounds and the analogous hydrocarbons can be used to estimate heats of formation. Heats of formation of c-B3N3H12 and c-B3N3H6 are -95.5 and -115.5 kcal/mol at 298 K, respectively, using our best calculated CCSD(T)/CBS approach. The experimental value for c-B3N3H6 appears to be approximately 7 kcal/mol too negative. Enthalpies, entropies, and free energies are calculated for many dehydrocoupling and dehydrogenation reactions that convert BNH6 to alicyclic and cyclic oligomers and H2(g). Generally, the reactions are highly exothermic and exergonic as well because of the release of 1 or more equivalents of H2(g). For c-B3N3H12 and c-B3N3H6, available experimental data for sublimation and vaporization lead to estimates of their condensed phase 298 K heats of formation: DeltaHf degrees [c-B3N3H12(s)] = -124 kcal/mol and DeltaHf degrees [c-B3N3H6(l)] = -123 kcal/mol. The reaction thermochemistries for the dehydrocoupling of BNH6(s) to c-B3N3H12(s) and the dehydrogenation of c-B3N3H12(s) to c-B3N3H6(l) are much less exothermic compared with the gas-phase reactions due to intermolecular forces which decrease in the order BNH6 > cyclo-B3N3H12 > cyclo-B3N3H6. The condensed phase reaction free energies are less negative compared with the gas-phase reactions but are still too favorable for BNH6 to be regenerated from either c-B3N3H12 or c-B3N3H6 by just an overpressure of H2.     

Computational study of the reactions of SiH3X (X=H, Cl, Br, I) with HCN

Ab initio calculations were carried out for the reactions of silane and halosilanes (SiH3X, X=H, Cl, Br, I) with HCN. Geometries of the reactants, transition states, intermediates and products were optimized at HF, MP2, and B3LYP levels of theory using the 6-31G(d) and 6-31G(d,p) basis sets. Energies were also obtained using G3MP2 and G3B3 levels of theory. Intrinsic reaction coordinate (IRC) calculations were performed to characterize the transition states on the potential energy surface. It was found that HCN can react with silane and halosilanes via three different mechanisms. One involves HX elimination by a one-step pathway producing SiH3CN. The second mechanism consists of H2 elimination, producing SiH2XCN via a one-step pathway or three multiple-step pathways. The third mechanism involves dissociation of SiH3X to various products, which can then react with HCN. Activation energies, enthalpies, and free energies of activation along with the thermodynamic properties (DeltaE, DeltaH, and DeltaG) of each reaction pathway were calculated. The reaction of SiH3X with HCN produce different products depending on substituent X. We have found that the standard 6-31G(d) bromine basis set gave results which were in better agreement with the G3MP2 results than for the Binning-Curtiss basis set. Computed heats of formation (DeltaHf) for SiH3CN, SiH3NC, SiH2ClCN, SiH2BrCN, SiH2ICN, SiHCl, SiHBr, and SiHI were found to be 133.5, 150.8, -34.4, 23.6, 102.4, 48.7, 127.1, and 179.8 kJ mol-1, respectively. From enthalpies calculated at G3MP2, we predict that the DeltaHf for SiH2 to be 262.8 kJ mol-1 compared to the experimental value of 273.8+/-4.2 kJ mol-1.     

Enthalpy of the gas-phase CO2 + Mg reaction from ab initio total energies

Various highly accurate ab initio composite methods of Gaussian-n (G1, G2, G3), their variations (G2(MP2), G3(MP2), G3//B3LYP, G3(MP2)//B3LYP), and complete basis set (CBS-Q, CBS-Q//B3LYP) series of models were applied to compute reaction enthalpies of the ground-state reaction of CO2 with Mg. All model chemistries predict highly endothermic reactions, with DeltaH(298) = 63.6-69.7 kcal x mol(-1). The difference between the calculated reaction enthalpies and the experimental value, evaluated with recommended experimental standard enthalpies of formation for products and reactants, is more than 20 kcal x mol(-1) for all methods. This difference originates in the incorrect experimental enthalpy of formation of gaseous MgO given in thermochemical databases. When the theoretical formation enthalpy for MgO calculated by a particular method is used, the deviation is reduced to 1.3 kcal x mol(-1). The performance of the methodologies used to calculate the heat of this particular reaction and the enthalpy of formation of MgO are discussed.     

Quantum chemical study of the structure and thermochemistry of the five-membered nitrogen-containing heterocycles and their anions and radicals

The nitrogen-containing heterocycles are of interest as high-energy-density materials for use as propellants and explosives, while the pyrolysis of these compounds is also important in understanding the evolution of unwanted NO and NO2 (NOx) from organic fuels such as coal and biomass. We have used ab initio and density functional methods to study the molecular structures and thermochemical properties of the five-membered nitrogen-containing heterocycles and their anions and radicals corresponding to respective heterolytic and homolytic loss of a hydrogen atom from either a nitrogen or carbon site. Many of these thermochemical properties have not previously been measured, especially for the heterocycles containing three and four nitrogen atoms. Using the theoretical methods CBS-APNO, G3, and G3B3, we calculate enthalpies of formation of 26.5, 42.4, 31.9, 63.7, 46.8, 81.0, and 79.0 kcal mol-1 for pyrrole, pyrazole, imidazole, 1,2,3-triazole, 1,2,4-triazole, 1H-tetrazole, and 2H-tetrazole. A correlation is developed between the number of nitrogen atoms in a heterocycle and its enthalpy, and we extrapolate this relationship to predict the enthalpy of formation of pentazole. N-H BDEs in the heterocycles typically increase with the number of nitrogen atoms in the molecule, while C-H BDEs are similar in all of the studied heterocycles, at around 120 kcal mol-1. In all cases the N-H BDEs are weaker than the C-H BDEs, suggesting abstraction of the N-H hydrogen atom is more likely. Deprotonation enthalpies and free energies reveal that the N-H protons become more acidic with increasing number of nitrogen atoms in the heterocycle. C-H protons are less acidic than N-H protons by ca. 49 kcal mol-1, or ca. 35 kcal mol-1 when adjacent to the NH group. Trends in N-H and C-H acidities can be qualitatively explained by electrostatic effects and electron affinities. From its use as a reference species in our calculations, we identify that the experimental enthalpy of pyrimidine (1,3-diazine) may be in error by ca. 1-3 kcal mol-1, and we recommend an enthalpy of formation of 44.8 +/- 1.0 kcal mol-1.     

Theoretical study of the enthalpies of formation for C40H56 carotenes

Theoretical study of the enthalpies of formation (DeltaHf) for polyenes up to nine ethylene units and for several C40H56 carotenes including beta-carotene, alpha-carotene, lycopene, and prolycopene is presented. For polyenes and small branched alkenes, we used G2, G3, and G3MP2B3 theories, and the DeltaHf values were evaluated with the atomization, isodesmic bond separation, and homodesmic schemes. The applicability of six DFT functionals were evaluated by comparing their predictions with those obtained using G3 theory within the atomization scheme. Additivity approaches, including atom equivalents and group equivalents using DFT and semiempirical theories, were explored. We found that group equivalents associated with isodesmic reactions are able to provide the most accurate predictions within the test set. The predictions from the six functionals are in good agreement with the G3 results. Among them, B3LYP performs the best, with an average absolute deviation of only 0.30 kcal/mol. The application of DFT in the prediction for the DeltaHf value of C40H56 carotenes is promising.     

Accurate heats of formation of the "Arduengo-type" carbene and various adducts including H2 from ab initio molecular orbital theory

The heats of formation of saturated and unsaturated diaminocarbenes (imadazol(in)-2-ylidenes) have been calculated by using high levels of ab initio electronic structure theory. The calculations were done at the coupled cluster level through noniterative triple excitations with augmented correlation consistent basis sets up through quadruple. In addition, four other corrections were applied to the frozen core atomization energies: (1) a zero point vibrational correction; (2) a core/valence correlation correction; (3) a scalar relativistic correction; (4) a first-order atomic spin-orbit correction. The value of DeltaHf( 298) for the unsaturated carbene 1 is calculated to be 56.4 kcal/mol. The value of DeltaHf( 298) for the unsaturated triplet carbene (3)1 is calculated to be 142.8 kcal/mol, giving a singlet-triplet splitting of 86.4 kcal/mol. Addition of a proton to 1 forms 3 with DeltaHf( 298)(3) = 171.6 kcal/mol with a proton affinity for 1 of 250.5 kcal/mol at 298 K. Addition of a hydrogen atom to 1 forms 4 with DeltaHf( 298)(4) = 72.7 kcal/mol and a C-H bond energy of 35.8 kcal/mol at 298 K. Addition of H- to 1 gives 5 with DeltaHf( 298)(5) = 81.2 kcal/mol and 5 is not stable with respect to loss of an electron to form 4. Addition of H2 to the carbene center forms 6 with DeltaHf( 298)(6) = 41.5 kcal/mol and a heat of hydrogenation at 298 K of -14.9 kcal/mol. The value of DeltaHf( 298) for the saturated carbene 7 (obtained by adding H2 to the C=C bond of 1) is 47.4 kcal/mol. Hydrogenation of 7 to form the fully saturated imidazolidine, 8, gives DeltaHf( 298)(8) = 14.8 kcal/mol and a heat of hydrogenation at 298 K of -32.6 kcal/mol. The estimated error bars for the calculated heats of formation are +/-1.0 kcal/mol.     

Combined experimental and computational study of the thermochemistry of the fluoroaniline isomers

The standard (p degrees = 0.1 MPa) molar enthalpies of formation in the condensed phase of all the fluoroanilines, with the exception of the 2,3,5-trifluoroaniline compound, were derived from the standard molar energies of combustion in oxygen at T = 298.15 K, measured by rotating bomb combustion calorimetry. Calvet high-temperature vacuum sublimation experiments were performed to measure their enthalpies of vaporization or sublimation. These experiments allowed the determination of the standard molar enthalpies of formation in the gaseous phase and at T = 298.15 K. These values are also compared with estimates based on G3MP2B3 and BP86/6-31+G(d) computations, which have been extended also to the fluoroaniline that was not studied experimentally. The results are in close agreement with a mean deviation of approximately 3 kJ.mol-1. The largest difference between experimental and G3MP2B3 values is found for the pentafluoroaniline (-7.0 kJ.mol-1). For the three monofluoroanilines, the composite approach has been used also to compute gas-phase acidities, electron and proton affinities, ionization enthalpies and N-H bond dissociation enthalpies. The computed values compare well with available experimental results supporting the new computed data.     

Polyfunctional methodology for improved DFT thermochemical predictions

Statistical error distributions for enthalpies of formation as predicted by 18 different density functionals have been analyzed using a test set of 675 molecules. Systematic errors, dependent on the number of valence electrons, have been identified for some functionals. A simple empirical correction makes a significant improvement in the prediction error for these single functionals. Linear combinations of enthalpy estimates from different density functionals are identified that exploit the error correlations among the functionals and allow for further improvements in the accuracy of thermodynamic predictions. A good compromise between accuracy and computational efforts is achieved by the BLUE (best linear unbiased estimator) combination of three functionals, B3LYP, BLYP, and VSXC (polyfunctional 3 or PF3). The PF3 method has a mean absolute deviation (MAD) from experiment of 2.4 kcal/mol on the G3 set of 271 molecules. This can be compared to the MAD of 4.9 kcal/mol for B3LYP and 1.2 kcal/mol for the more costly G3 method. On the larger set of 675 molecules, the MAD for PF3 is 3.0 kcal/mol. Opportunities for further improvements in the accuracy of this method are discussed.     

Performance of the correlation consistent composite approach for transition states: a comparison to G3B theory

The correlation consistent composite approach (ccCA) was applied to the prediction of reaction barrier heights (i.e., transition state energy relative to reactants and products) for a standard benchmark set of reactions comprised of both hydrogen transfer reactions and nonhydrogen transfer reactions (i.e., heavy-atom transfer, SN2, and unimolecular reactions). The ccCA method was compared against G3B for the same set of reactions. Error metrics indicate that ccCA achieves "chemical accuracy" with a mean unsigned error (MUE) of 0.89 kcal/mol with respect to the benchmark data for barrier heights; G3B has a mean unsigned error of 1.94 kcal/mol. Further, the greater accuracy of ccCA for predicted reaction barriers is compared to other benchmarked literature methods, including density functional (BB1K, MUE=1.16 kcal/mol) and wavefunction-based [QCISD(T), MUE=1.10 kcal/mol] methods.