Evaluation of MINDO/3 calculated structures. II. Branching errors in alkanes and cycloalkanes

MINDO/3 calculations have been carried out for a series of branched chain alkanes in order to assess effects of branching on calculated geometries and heats of formation (ΔH_f). With vicinal branching, MINDO/3 calculates the central C? C bond to be too long. Bond angles are also found to be distorted. Errors in calculated heats of formation are large when geminal branching is present and significant with vicinal branching. Branching error corrections for ΔH_f have been derived and applied to a separate series of branched acyclic and cyclic compounds. For the test sample, application of the branching error corrections gave calculated structures of acyclic branched hydrocarbons with heats of formation having an average absolute error of 1.3 kcal/mole rather than 17.3 kcal/mole before correction. Cyclic branched hydrocarbons are shown to be less well corrected. Calculations of heats of reaction have also been carried out for some isomerization and cyclization reactions using the MINDO/3 and MNDO methods. It is clear from the comparisons that MNDO calculations give less severe errors for highly branched compounds but the errors are still substantial. For prediction of heats of reaction, the error-corrected calculations are shown to be superior to the “raw” calculations obtained by MINDO/3 or MNDO.     

Mindo/3 and mndo calculations of closed- and open-shell cations containing C,H, N,and O

Heats of formation of 119 closed- and open-shell carbocations calculated by the semiempirical quantum chemical methods MINDO/3 and MNDO are reported and compared with experimental data. With proper consideration of failures in specific areas, both methods can be used for the thermodynamics of carbocations containing C, H, N, and O. MINDO/3 predicts unrealistic values for nitrogen containing cations with nitrogen multiple bonds and is not suited for closed-shell cations containing oxygen. Saturated acyclic hydrocarbon radical cations often are computed with abnormally long CC bonds by MNDO. Otherwise, the standard deviation of the two methods is not very different, being in the range of ±13 kcal/mol. MINDO/3 tends to overestimate the cation stabilities, whereas MNDO calculates cations usually too high in energy. Some of the errors which were found in the calculations of the ions are related to the computed values for the parent neutral structures, but others are not.     

MINDO-SCF-MO-berechnung der cis-trans-isomerisierung von N-methyl- und N-phenylazomethin

MINDO/2-SCF-MO calculations for the ground state properties of N-methyl- and N-phenyl-azomethin have been carried out. The calculated rotation barrier for the methyl group in N-methyl-azomethin was 0·8 kcal/mol, the eclipsed conformation being most stable. The calculated rotation barrier about the CN bond in the protonated methylazomethin was 27·9 kcal/mol. MINDO/1-SCF-MO treatment for the N-inversion barrier of the unprotonated species yielded 13·00 kcal/mol. Similar MINDO/2 calculations for N-phenylazomethin yielded 4·0 kcal/mol for the rotation barrier of the phenyl ring around the CN= bond, the perpendicular conformation of the ring to the CNC plane being most stable. For the corresponding N protonated derivative the value 27·3 kcal/mol was calculated for the rotation barrier around the CN bond. MINDO/1 treatment yielded an inversion barrier of 14·0 kcal/mol for N-phenylazomethin.     

The heat of formation of C2F4

The CCSD(T) atomization energies are extrapolated to the complete basis set limit, and are corrected for zero-point energy, spin–orbit, core-valence, and scalar relativistic effects. Our best heats of formation at 298 K for CF₄ and C₂F₄ are −223.1±1.1 and −160.5±1.5 kcal/mol, respectively. The CF₄ value is in excellent agreement with experiment (−223.04±0.18 kcal/mol), while the C₂F₄ result suggests that the experimental value (−157.6±0.6 kcal/mol) has a larger error than believed. Our value for C₂F₄ also shows that the G3 value has the expected error of ±2 kcal/mol.     

Extension of MNDO to d orbitals: Parameters and results for the halogens

A recently proposed extension of the MNDO formalism to d orbitals has been parameterized for the halogens CI, Br, and I. Extensive test calculations indicate slight consistent improvements for normalvalent molecules and dramatic improvements for hypervalent molecules, in comparison with established MNDO -type methods without d orbitals. The mean absolute errors in calculated heats of formation are 3.9 kcal/mol for 155 normalvalent compounds and 2.8 kcal/mol for 23 hypervalent compounds. The predicted structures of the hypervalent molecules are qualitatively correct, with a mean absolute error of 2° in 19 bond angles.     

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.     

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.     

硝酸酯化合物生成热的分子轨道研究

用MINDO/3, MNDO和AM1三种SCF-MO方法, 在全优化分子几何构型的基础上, 系统地计算研究了32个硝酸酯化合物的生成热, 与实验值相比, MNDO计算结果偏大很多; MINDO/3计算值与凝聚相实验值符合较好, 由于克服了MNDO法过高地估算原子之间Van der Waals核排斥能的缺点, AM1法给出了较满意的结果: 与七个气态实验值之间存在良好的线性关系(相关系数为0.992), 其间的平均绝对差值和平均差值分别只有10.28和-1.01kJ/mol。     

Semiempirical implementation of strictly localized geminals for analysis of molecular electronic structure

Approximate electronic trial wave function taken as the antisymmetrized product of strictly localized geminals (APSLG) is implemented for semiempirical analysis of molecular electronic structure of “organic” compounds and for calculations of their heats of formation. This resulted in an O(N)‐scaling method. Using the MINDO/3 form of the semiempirical Hamiltonian with reparameterized β_AB values in combination with the APSLG form of the wave function yields the computational procedure BF'98. Calculations on the heats formation and the equilibrium geometries for a wide range of molecules show that the APSLG‐MINDO/3 approach is more favorable than its self‐consistent field‐based counterpart. Also, the APSLG formalism allows to interpret molecular electronic wave function in chemically sensible terms. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 752–764, 2001     

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.     

Application of the computationally efficient self-consistent-charge density-functional tight-binding method to magnesium-containing molecules

The geometric properties, ionization potentials, heats of formation, incremental binding energies, and protonation energies for up to 75 magnesium-containing compounds have been studied using the self-consistent-charge density-functional tight-binding method (SCC-DFTB), the complete-basis set (CBS-QB3) method, traditional B3LYP density-functional theory, and a number of modern semiempirical methods such as Austin Model 1 (AM1), modified neglect of diatomic overlap without and with inclusion of d functions (MNDO, MNDO/d), and the Parametric Method 3 (PM3) and its modification (PM5). The test set contains some widely varying chemical motifs including ionic or covalent, closed-shell or radical compounds, and many biologically relevant complexes. Geometric data are compared to experiment, if available, and otherwise to previous high-level ab initio calculations or the present B3LYP results. SCC-DFTB is found to predict bond lengths to high accuracy, with the root-mean-square (RMS) error being less than half that found for the other semiempirical methods. However, SCC-DFTB performs very poorly for absolute heats of formation, giving an RMS error of 29 kcal mol(-1), but for this property B3LYP and the other semiempirical methods also yield poor but useful results with errors of 12-22 kcal mol(-1). Nevertheless, SCC-DFTB does provide useful results for biologically relevant chemical-process energies such as protonation energies (RMS error 10 kcal mol(-1), with the range 6-19 kcal mol(-1) found for the other semiempirical methods) and ligation energies (RMS error 9 kcal mol(-1), less than the errors of 12-23 kcal mol(-1) found for the other semiempirical methods). SCC-DFTB is shown to provide a computationally expedient means of calculating properties of magnesium compounds, providing results with at most double the inaccuracy of the high-quality but dramatically more-expensive B3LYP method.     

Improved prediction of heats of formation of energetic materials using quantum mechanical calculations

We present simple atom and group-equivalent methods that will convert quantum mechanical energies of molecules to gas phase heats of formation of CHNO systems. In addition, we predict heats of sublimation and vaporization derived from information obtained from the quantum-mechanically calculated electrostatic potential of each isolated molecule. The heats of sublimation and vaporization are combined with the aforementioned gas phase heats of formation to produce completely predicted condensed phase heats of formation. These semiempirical computational methods, calibrated using experimental information, were applied to a series of CHNO molecules for which no experimental information was used in the development of the methods. These methods improve upon an earlier effort of Rice et al. [Rice, B. M.; Pai, S. V.; Hare, J. Combust. Flame 1999, 118, 445] through the use of a larger basis set and the application of group equivalents. The root-mean-square deviation (rms) from experiment for the predicted group-equivalent gas phase heats of formation is 3.2 kcal/mol with a maximum deviation of 6.5 kcal/mol. The rms and maximum deviation of the predicted liquid heats of formation are 3.2 and 7.4 kcal/mol, respectively. Finally, the rms and maximum deviation of predicted solid heats of formation are 5.6 and 12.2 kcal/mol, respectively, an improvement in the rms of approximately 40% compared to the earlier Rice et al. predictions using atom equivalents and a smaller basis set (B3LYP/6-31G*).     

Thermodynamic properties of molecular borane amines and the [BH4-][NH4+] salt for chemical hydrogen storage systems from ab initio electronic structure theory

The heats of formation for the borane amines BH3NH3, BH2NH2, and HBNH, tetrahedral BH4-, and the BN molecule have been calculated by using ab initio molecular orbital theory. Coupled cluster calculations with single and double excitations and perturbative triples (CCSD(T)) were employed for the total valence electronic energies. Correlation consistent basis sets were used, up through the augmented quadruple-zeta, to extrapolate to the complete basis set limit. Core/valence, scalar relativistic, and spin-orbit corrections were included in an additive fashion to predict the atomization energies. Geometries were calculated at the CCSD(T) level up through at least aug-cc-pVTZ and frequencies were calculated at the CCSD(T)/aug-cc-pVDZ level. The heats of formation (in kcal/mol) at 0 K in the gas phase are Delta Hf(BH3NH3) = -9.1, Delta Hf(BH2NH2) = -15.9, Delta Hf(BHNH) = 13.6, Delta Hf(BN) = 146.4, and Delta Hf(BH4-) = -11.6. The reported experimental value for Delta Hf(BN) is clearly in error. The heat of formation of the salt [BH4-][NH4+](s) has been estimated by using an empirical expression for the lattice energy and the calculated heats of formation of the two component ions. The calculations show that both BH3NH3(g) and [BH4-][NH4+](s) can serve as good hydrogen storage systems which release H2 in a slightly exothermic process. The hydride affinity of BH3 is calculated to be 72.2 kcal/mol, in excellent agreement with the experimental value at 298 K of 74.2 +/- 2.8 kcal/mol.     

Unimolecular dissociation and thermochemistry of CH3OOH

The unimolecular dissociation of CH3OOH is investigated by exciting the molecule in the region of its 5nu(OH) band and probing the resulting OH fragments using laser-induced fluorescence. The measured OH fragment rotational and translational energies are used to determine the CH3O-OH bond dissociation energy, which we estimate to be approximately 42.6+/-1 kcal/mol. Combining this value with the known heats of formation of the fragments also gives an estimate for the heat of formation of CH3OOH which at 0 K we determine to be deltaH(f)0=-27+/-1 kcal/mol. This experimental value is in good agreement with the results of ab initio calculations carried out at the CCSD(T)/complete basis set limit which finds the heat of formation of CH3OOH at 0 K to be deltaH(f)0=-27.3 kcal/mol.     

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.     

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.     

MNDO Calculations of silicon-containing molecules

A comparison is made of MNDO and MINDO /3 calculations for saturated silicon-containing molecules, and with experimental values, for heats of formation, molecular geometries, charge distributions, and ionization potentials. Except for bond angles, it is found that with the published parameter values the MINDO /3 program gives more reliable results than MNDO . For unsaturated molecules, a comparison of bond lengths and stabilities of Si multiple bonds as given by the two programs and ab initio methods is made, and large discrepancies between predicted structures are pointed out. Some reasons for the dicrepancies are discussed.     

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.     

Tautomerism of oxopyridines and oxopyrimidines: Theoretical study with complete optimization of geometry

The semiempirical MINDO /3 method is employed to calculate the energies of various tautomers of model tautomeric compounds— 2-oxo- and 4-oxopyridines and pyrimidines. The results are compared with experimental data in the gas phase, where the solute–solvent interactions not included in theoretical calculations are absent. Although the relative energies obtained by the MINDO /3 method appear to be superior to other semiempirical and ab initio calculations, the accuracy of the method was determined to be as low as 3–4 kcal/mol. It indicates that it is exceedingly difficult to account theoretically for intrinsic stabilities of the tautomers. The importance of various factors influencing calculated free-energy differences is discussed. Particular attention is paid to the problem of geometry optimization.     

Heats of formation of triplet ethylene, ethylidene, and acetylene

Heats of formation of the lowest triplet state of ethylene and the ground triplet state of ethylidene have been predicted by high level electronic structure calculations. Total atomization energies obtained from coupled-cluster CCSD(T) energies extrapolated to the complete basis set limit using correlation consistent basis sets (CBS), plus additional corrections predict the following heats of formation in kcal/mol: DeltaH0r(C2H4,3A1) = 80.1 at 0 K and 78.5 at 298 K, and DeltaH0t(CH3CH,3A' ') = 86.8 at 0 K and 85.1 at 298 K, with an error of less than +/-1.0 kcal/mol. The vertical and adiabatic singlet-triplet separation energies of ethylene were calculated as DeltaES-T,vert = 104.1 and DeltaES-T,adia = 65.8 kcal/mol. These results are in excellent agreement with recent quantum Monte Carlo (DMC) values of 103.5 +/- 0.3 and 66.4 +/- 0.3 kcal/mol. Both sets of computational values differ from the experimental estimate of 58 +/- 3 kcal/mol for the adiabatic splitting. The computed singlet-triplet gap at 0 K for acetylene is DeltaES-T,adia(C2H2) = 90.5 kcal/mol, which is in notable disagreement with the experimental value of 82.6 kcal/mol. The heat of formation of the triplet is DeltaH0tC2H2,3B2) = 145.3 kcal/mol. There is a systematic underestimation of the singlet-triplet gaps in recent photodecomposition experiments by approximately 7 to 8 kcal/mol. For vinylidene, we predict DeltaH0t(H2CC,1A1) = 98.8 kcal/mol at 298 K (exptl. 100.3 +/- 4.0), DeltaH0t(H2CC,3B2) = 146.2 at 298 K, and an energy gap DeltaES-T-adia(H2CC) = 47.7 kcal/mol.