Accurate thermochemical properties for energetic materials applications. I. Heats of formation of nitrogen-containing heterocycles and energetic precursor molecules from electronic structure theory

The heats of formation of 1H-imidazole, 1H-1,2,4-trizazole, 1H-tetrazole, CH3NO2, CH3N3, CH3NH2, CH2CHNO2, HClO4, and phenol, as well as cations and anions derived from some of the molecules have been calculated using ab initio molecular orbital theory. These molecules are important as models for compounds used for energetic materials synthesis. The predicted heats of formation of the heterocycle-based compounds are in excellent agreement with available experimental values and those derived from proton affinities and deprotonation enthalpies to <1 kcal/mol. The predicted value for the tetrazolium cation differs substantially from the experimental value, likely due to uncertainty in the measurement. The heats of formation of the nitro and amino molecules, as well as phenol/phenolate, also are in good agreement with the experimental values (<1.5 kcal/mol). The heat of formation of CH3N3 is predicted to be 72.8 kcal/mol at 298 K with an estimated error bar of +/-1 kcal/mol on the basis of the agreement between the calculated and experimental values for DeltaH(f)(HN3). The heat of formation at 298 K of HClO4 is -0.4 kcal/mol, in very good agreement with the experimental value, as well as a W2 literature study. An extrapolation of the CCSD(T)/aug-cc-pV(Q,5) energies was required to obtain this agreement. This result suggests that very large basis sets (> or =aug-cc-pV5Z) may be needed to fully recover the valence correlation energy contribution in compounds containing elements with high formal oxidation states at the central atom. In addition tight d functions are needed for the geometry predictions. Douglas-Kroll-Hess (DKH) scalar relativistic corrections for HClO4 and ClO4- at the MP2 level with correlation-consistent DKH basis sets were predicted to be large, likely due to the high formal oxidation state at the Cl.     

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.     

Heats of formation of organic molecules by ab initio methods: Thiaalkanes

The bond energy scheme for calculating heats of formation of organic molecules from ab initio data (6–31G*) has been extended to include 24 compounds containing sulfur in the sulfide oxidation state. The rms deviation from the experimental values for these compounds is 0.54 kcal/mol, which is approximately experimental error.     

Heats of formation of organic molecules by Ab Initio calculations: Carboxylic acids and esters

A bond and group equivalent scheme that allows the calculation of heats of formation for carboxylic acids and esters from ab initio 6-31G* energies has been developed. For a group of 16 compounds, the rms error for the calculated heats of formation was 0.64 kcal/mol. Heats of formation have been predicted for an additional seven compounds for which the experimental values are either unknown or suspect. © 1992 by John Wiley & Sons, Inc.     

Comparison of SCC-DFTB and NDDO-based semiempirical molecular orbital methods for organic molecules

Extensive testing of the SCC-DFTB method has been performed, permitting direct comparison to data available for NDDO-based semiempirical methods. For 34 diverse isomerizations of neutral molecules containing the elements C, H, N, and O, the mean absolute errors (MAE) for the enthalpy changes are 2.7, 3.2, 5.0, 5.1, and 7.2 kcal/mol from PDDG/PM3, B3LYP/6-31G(d), PM3, SCC-DFTB, and AM1, respectively. A more comprehensive test was then performed by computing heats of formation for 622 neutral, closed-shell H, C, N, and O-containing molecules; the MAE of 5.8 kcal/mol for SCC-DFTB is intermediate between AM1 (6.8 kcal/mol) and PM3 (4.4 kcal/mol) and significantly higher than for PDDG/PM3 (3.2 kcal/mol). Similarly, SCC-DFTB is found to be less accurate for heats of formation of ions and radicals; however, it is more accurate for conformational energetics and intermolecular interaction energies, though none of the methods perform well for hydrogen bonds with strengths under ca. 7 kcal/mol. SCC-DFTB and the NDDO methods all reproduce MP2/cc-pVTZ molecular geometries with average errors for bond lengths, bond angles, and dihedral angles of only ca. 0.01 A, 1.5 degrees , and 3 degrees . Testing was also carried out for sulfur containing molecules; SCC-DFTB currently yields much less accurate heats of formation in this case than the NDDO-based methods due to the over-stabilization of molecules containing an SO bond.     

Heats of formation of organic molecules calculated from ab initio theory and a group equivalent scheme: Alkenes

A bond and group equivalent scheme that allows the calculation of heats of formation of alkenes from ab initio 6-31G* energies has been developed. For a group of 26 compounds, the root mean square (rms) error for the calculated heat of formation was 0.78 kcal/mol. Heats of formation have been predicted for an additional nine compounds for which the experimental values are either unknown or suspect. The heats of hydrogenation of barrelene and related compounds are discussed. © 1994 by John Wiley & Sons, Inc.     

Improved semiempirical heats of formation through the use of bond and group equivalents

Deficiencies in energetics obtained using the common semiempirical methods, AM1, PM3, and MNDO, may partly be traced to the use of pseudoatomic equivalents for conversion of molecular energies to heats of formation at 298 K. We present an alternative scheme based on the use of bond and group equivalents. Values for the 61 bond and group equivalents necessary for treatment of molecules containing the common organic elements, hydrogen, carbon, nitrogen, and oxygen have been derived. For a set of 583 neutral, closed-shell molecules mean absolute errors in AM1, PM3, and MNDO heats of formation are reduced from 6.6, 4.2, and 8.2 kcal/mol to 2.3, 2.2, and 3.0 kcal/mol, respectively. Several systematic problems are overcome in the present scheme including relative stabilities of branched hydrocarbons, energetics of conjugated systems, heats of formation of long chain hydrocarbons, and enthalpies of molecules containing multiple heteroatoms. Although the approach is restricted to molecules with well-defined functional groups, the equivalents are easy to incorporate and are chemically relevant. This revised procedure allows semiempirical methods to be used for far more reliable evaluations of heats of reactions. Estimates are made of the errors inherent in these semiempirical formalisms, arising from integral approximations and the neglect of explicit treatment of electron correlation effects, while excluding those from inadequate parameterization.     

2-氯丁烷、1,2=二氯丁烷气态生成焓的测量

用转动氧弹燃烧热量计测量了298.15K时2-氯丁烷和1,2-二氯丁烷的标准液态燃烧反应内能变化值,得到了它们的标准所态生成焓值,并进一步考查了二氯取代地氯代烷烃气态生成焓值的影响量.     

Heats of formation of beryllium, boron, aluminum, and silicon re-examined by means of W4 theory

Benchmark total atomization energies (TAE0 values) were obtained, by means of our recent W4 theory [Karton, A.; Rabinowitz, E.; Martin, J. M. L.; Ruscic, B. J. Chem. Phys. 2006, 125, 144108], for the molecules Be2, BeF2, BeCl2, BH, BF, BH3, BHF2, B2H6, BF3, AlF, AlF3, AlCl3, SiH4, Si2H6, and SiF4. We were then able to deduce "semi-experimental" heats of formation for the elements beryllium, boron, aluminum, and silicon by combining the calculated TAE0 values with experimental heats of formation obtained from reactions that do not involve the species Be(g), B(g), Al(g), and Si(g). The elemental heats of formation are fundamental thermochemical quantities that are required whenever a molecular heat of formation has to be derived from a calculated binding energy. Our recommended DeltaH degrees f,0 [A(g)] values are Be 76.4+/-0.6 kcal/mol, B 135.1+/-0.2 kcal/mol, Al 80.2+/-0.4 kcal/mol, and Si 107.2+/-0.2 kcal/mol. (The corresponding values at 298.15 K are 77.4, 136.3, 80.8, and 108.2 kcal/mol, respectively.) The Be value is identical to the CODATA recommendation (but with half of the uncertainty), while the B, Al, and Si values represent substantial revisions from established earlier reference data. The revised B and Si values are in agreement with earlier semi-ab initio derivations but carry much smaller uncertainties.     

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.     

PDDG/PM3 and PDDG/MNDO: improved semiempirical methods

Two new semiempirical methods employing a Pairwise Distance Directed Gaussian modification have been developed: PDDG/PM3 and PDDG/MNDO; they are easily implemented in existing software, and yield heats of formation for compounds containing C, H, N, and O atoms with significantly improved accuracy over the standard NDDO schemes, PM5, PM3, AM1, and MNDO. The PDDG/PM3 results for heats of formation also show substantial improvement over density functional theory with large basis sets. The PDDG modifications consist of a single function, which is added to the existing pairwise core repulsion functions within PM3 and MNDO, a reparameterized semiempirical parameter set, and modified computation of the energy of formation of a gaseous atom. The PDDG addition introduces functional group information via pairwise atomic interactions using only atom-based parameters. For 622 diverse molecules containing C, H, N, and O atoms, mean absolute errors in calculated heats of formation are reduced from 4.4 to 3.2 kcal/mol and from 8.4 to 5.2 kcal/mol using the PDDG modified versions of PM3 and MNDO over the standard versions, respectively. Several specific problems are overcome, including the relative stability of hydrocarbon isomers, and energetics of small rings and molecules containing multiple heteroatoms. The internal consistency of PDDG energies is also significantly improved, enabling more reliable analysis of isomerization energies and trends across series of molecules; PDDG isomerization energies show significant improvement over B3LYP/6-31G* results. Comparison of heats of formation, ionization potentials, dipole moments, isomer, and conformer energetics, intermolecular interaction energies, activation energies, and molecular geometries from the PDDG techniques is made to experimental data and values from other semiempirical and ab initio methods.     

Nonlocal density functional calculation of gas phase heats of formation

A general procedure is presented for computing the gas phase heats of formation of a wide variety of organic compounds. ΔE for the formation of the molecule from its elements at 0 K is obtained from density functional calculations (Gaussian 92/DFT) for optimized geometries. This result is converted to ΔH at 298 K by assuming ideal behavior and adding the translational, rotational, and vibrational energies. Additive correction terms corresponding to the various coordination states of the carbons, nitrogens, and oxygens were developed using a database of 54 compounds. The experimental ΔH values of these compounds are then reproduced with an average absolute error of 3 kcal/mol and a standard deviation of 4 kcal/mol. For a group of 10 test cases that were not part of the database, the average absolute error is 3.5 kcal/mol and the standard deviation is 4.1 kcal/mol. © 1995 by John Wiley & Sons, Inc.     

Quantum monte carlo study of heats of formation and bond dissociation energies of small hydrocarbons

A quantum Monte Carlo (QMC) benchmark study of heats of formation at 298 K and bond dissociation energies (BDEs) of 22 small hydrocarbons is reported. Diffusion Monte Carlo (DMC) results, obtained using a simple product trial wavefunctions consisting of a single determinant and correlation function, are compared to experiment and to other theory including a version of complete basis set theory (CBS‐Q) and density functional theory (DFT) with the B3LYP functional. For heats of formation, the findings are a mean absolute deviation from experiment of 1.2 kcal/mol for CBS‐Q, 2.0 kcal/mol for B3LYP, and 2.2 kcal/mol for DMC. The mean absolute deviation of 31 BDEs is 2.0 kcal/mol for CBS‐Q, 4.2 kcal/mol for B3LYP, and 2.5 kcal/mol for DMC. These findings are for 17 BDEs of closed‐shell molecules that have mean absolute deviations from experiment of 1.7 kcal/mol (CBS‐Q), 4.0 kcal/mol (B3LYP), and 2.2 kcal/mol (DMC). The corresponding results for the 14 BDEs of open‐shell molecules studied are 2.4 kcal/mol (CBS‐Q), 4.3 kcal/mol (B3LYP), and 2.9 kcal/mol (DMC). The DMC results provide a baseline from which improvement using multideterminant trial functions can be measured. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 583–592, 2005     

Extension of the PDDG/PM3 and PDDG/MNDO semiempirical molecular orbital methods to the halogens

The new semiempirical methods, PDDG/PM3 and PDDG/MNDO, have been parameterized for halogens. For comparison, the original MNDO and PM3 were also reoptimized for the halogens using the same training set; these modified methods are referred to as MNDO' and PM3'. For 442 halogen-containing molecules, the smallest mean absolute error (MAE) in heats of formation is obtained with PDDG/PM3 (5.6 kcal/mol), followed by PM3' (6.1 kcal/mol), PDDG/MNDO (6.6 kcal/mol), PM3 (8.1 kcal/mol), MNDO' (8.5 kcal/mol), AM1 (11.1 kcal/mol), and MNDO (14.0 kcal/mol). For normal-valent halogen-containing molecules, the PDDG methods also provide improved heats of formation over MNDO/d. Hypervalent compounds were not included in the training set and improvements over the standard NDDO methods with sp basis sets were not obtained. For small haloalkanes, the PDDG methods yield more accurate heats of formation than are obtained from density functional theory (DFT) with the B3LYP and B3PW91 functionals using large basis sets. PDDG/PM3 and PM3' also give improved binding energies over the standard NDDO methods for complexes involving halide anions, and they are competitive with B3LYP/6-311++G(d,p) results including thermal corrections. Among the semiempirical methods studied, PDDG/PM3 also generates the best agreement with high-level ab initio G2 and CCSD(T) intrinsic activation energies for S(N)2 reactions involving methyl halides and halide anions. Finally, the MAEs in ionization potentials, dipole moments, and molecular geometries show that the parameter sets for the PDDG and reoptimized NDDO methods reduce the MAEs in heats of formation without compromising the other important QM observables.     

Optimization of parameters for semiempirical methods II. Applications

MNDO/AM1-type parameters for twelve elements have been optimized using a newly developed method for optimizing parameters for semiempirical methods. With the new method, MNDO-PM3, the average difference between the predicted heats of formation and experimental values for 657 compounds is 7.8 kcal/mol, and for 106 hypervalent compounds, 13.6 kcal/mol. For MNDO the equivalent differences are 13.9 and 75.8 kcal/mol, while those for AM1, in which MNDO parameters are used for aluminum, phosphorus, and sulfur, are 12.7 and 83.1 kcal/mol, respectively. Average errors for ionization potentials, bond angles, and dipole moments are intermediate between those for MNDO and AM1, while errors in bond lengths are slightly reduced.     

Computational study on the mechanisms and energetics of trimethylindium reactions with H2O and H2S

The reactions of trimethylindium (TMIn) with H2O and H2S are relevant to the chemical vapor deposition of indium oxide and indium sulfide thin films. The mechanisms and energetics of these reactions in the gas phase have been investigated by density functional theory and ab initio calculations using the CCSD(T)/[6-31G(d,p)+Lanl2dz]//B3LYP/[6-31G(d,p)+Lanl2dz] and CCSD(T)/[6-31G(d,p)+Lanl2dz] //MP2/[6-31G(d,p)+Lanl2dz] methods. The results of both methods are in good agreement for the optimized geometries and relative energies. When TMIn reacts with H2O and H2S, initial molecular complexes [(CH3)3In:OH2 (R1)] and [(CH3)3In:SH2 (R2)] are formed with 12.6 and 3.9 kcal/mol binding energies. Elimination of a CH4 molecule from each complex occurs with a similar energy barrier at TS1 (19.9 kcal/mol) and at TS3 (22.1 kcal/mol), respectively, giving stable intermediates (CH3)2InOH and (CH3)2InSH. The elimination of the second CH4 molecule from these intermediate products, however, has to overcome very high and much different barriers of 66.1 and 53.2 kcal/mol, respectively. In the case of DMIn with H2O and H2S reactions, formation of both InO and InS is exothermic by 3.1 and 30.8 kcal/mol respectively. On the basis of the predicted heats of formation of R1 and R2 at 0 K and -20.1 and 43.6 kcal/mol, the heats of formation of (CH3)2InOH, (CH3)2InSH, CH3InO, CH3InS, InO, and InS are estimated to be -20.6, 31.8, and 29.0 and 48.4, 35.5, and 58.5 kcal/mol, respectively. The values for InO and InS are in good agreement with available experimental data. A similar study on the reactions of (CH3)2In with H2O and H2S has been carried out; in these reactions CH3InOH and CH3InSH were found to be the key intermediate products.     

Tautomerism of pyrimidines and purines in the gas phase and in low-temperature matrices,and some biological implications

Infrared spectra in the NH, OH, and C?O stretching regions are reviewed for various methylated and halogenated 2(4)-oxopyrimidines and uracils, as well as other nucleic acid derivatives, in the vapor phase and in low-temperature matrices. The 2-oxopyrimidines are predominantly in the enol form both in the vapor phase and in low-temperature matrices. By contrast, the 4-oxopyrimidines exhibit comparable populations of the keto and enol forms, with K_T ≈ 1–2, and a difference in chemical binding energy between the two forms in the gaseous phase of the order of 1–2 kcal/mol. The observed tautomeric equilibria in the gas phase point to the need for a drastic revision of interpretations of theoretical methods, and simultaneously provide the appropriate quantitative data necessary for testing the results of quantum mechanical calculations. In sharp contrast to other heterocyclic systems, several of the bases found in natural nucleic acids were found to exist predominantly in the keto or amino forms, as in the solution phase. In particular, uracils exist predominantly in the keto form. This has made possible, for this class of compounds, to evaluate the heats of sublimation and vaporization, and to relate these data to hydrogen bonding and stacking interactions in the condensed phases. Examples are presented of base analogs which do exhibit appreciable tautomerism in solution. Some biological implications of the foregoing are presented in relation to the types of heterocyclic bases found in natural nucleic acids, and to concepts of spontaneous and induced mutagenesis.     

Computational study of reaction pathways for the formation of indium nitride from trimethylindium with HN3: comparison of the reaction with NH3 and that on TiO2 rutile (110) surface

The reactions of trimethylindium (TMIn) with HN3 and NH3 are relevant to the chemical vapor deposition of indium nitride thin film. The mechanisms and energetics of these reactions in the gas phase have been investigated by density functional theory and ab initio calculations using the CCSD(T)/Lanl2dz//B3LYP/Lanl2dz and CCSD(T)/Lanl2dz//MP2/Lanl2dz methods. The results of both methods are in good agreement for the optimized geometries and relative energies. These results suggest that the reaction with HN3 forms a new stable product, dimethylindiumnitride, CH3-In=N-CH3 via another stable In(CH3)2N3 (dimethylindium azide, DMInA) intermediate. DMInA may undergo unimolecular decomposition to form CH3InNCH3 by two main possible pathways: (1) a stepwise decomposition process through N2 elimination followed by CH3 migration from In to the remaining N atom and (2) a concerted process involving the concurrent CH3 migration and N2 elimination directly giving N2+CH3InNCH3. The reaction of TMIn with NH3 forms a most stable product DMInNH2 following the initial association and CH4-elimination reaction. The required energy barrier for the elimination of the second CH4 molecule from DMInNH2 is 74.2 kcal/mol. Using these reactions, we predict the heats of formation at 0 K for all the products and finally for InN which is 123+/-1 kcal/mol predicted by the two methods. The gas-phase reaction of HN3 with TMIn is compared with that occurring on rutile TiO2 (110). The most noticeable difference is the high endothermicity of the gas-phase reaction for InN production (53 kcal/mol) and the contrasting large exothermicity (195 kcal/mol) released by the low-barrier Langmuir-Hinshelwood type processes following the adsorption of TMIn and HN3 on the surface producing a horizontally adsorbed InN(a), Ti-NIn-O(a), and other products, CH4(g)+N2(g)+2CH3O(a) [J. Phys. Chem. B 2006, 110, 2263].     

Molecular mechanics (MM3) calculations on conjugated hydrocarbons

The MM3 molecular mechanics program has been extended to conjugated systems. A VESCF method is applied to the pi-system to calculate bond orders, from which various stretching and torsional parameters are obtained. The procedure gives somewhat better results than the analogous MM2 calculations. It has been applied to a study of 81 compounds of aromatic and other conjugated hydrocarbons, as well as 45 alkenes and unconjugated polyenes. The structures calculated are generally in good agreement with experiment, and the heats of formation of these compounds can be calculated with a rms value of 0.62 kcal/mol, which may be compared with the average experimental error of 0.61 kcal/mol. In addition, vibrational frequencies for five representative conjugated model structures are calculated, with an rms value of 46 cm^?1, and from these, other properties such as entropy can be calculated.