Gaussian-2 Theory Research Articles

Benchmark Studies on the Isomerization Enthalpies for Interstellar Molecular Species

With the well-established correlation between the relative stabilities of isomers and their interstellar abundances coupled with the prevalence of isomeric species among the interstellar molecular species, isomerization remains a plausible formation route for isomers in the interstellar medium. The present work reports an extensive investigation of the isomerization energies of 246 molecular species from 65 isomeric groups using the Gaussian-4 theory composite method with atoms ranging from 3 to 12. From the results, the high abundances of the most stable isomers coupled with the energy sources in interstellar medium drive the isomerization process even for barriers as high as 67.4 kcal/mol. Specifically, the cyanides and their corresponding isocyanides pairs appear to be effectively synthesized via this process. The following potential interstellar molecules; CNC, NCCN, c-C5H, methylene ketene, methyl Ketene, CH3SCH3, C5O, 1,1-ethanediol, propanoic acid, propan-2-ol, and propanol are identified and discussed. The study further reaffirms the importance of thermodynamics in interstellar formation processes on a larger scale and accounts for the known isomeric species. In all the isomeric groups, isomerization appears to be an effective route for the formation of the less stable isomers (which are probably less abundant) from the most stable ones that are perhaps more abundant.

ATOMIC-2 Protocol for Thermochemistry.

ATOMIC is a midlevel thermochemistry protocol that uses Pople's concept of bond separation reactions (BSRs) as a theoretical framework to reduce computational demands in the evaluation of atomization energies and enthalpies of formation. Various composite models are available that approximate bond separation energies at the complete-basis-set limit of all-electron CCSD(T), each balancing computational cost with achievable accuracy. Evaluated energies are then combined with very high-level, precomputed atomization energies of all auxiliary molecules appearing in the BSR to obtain the atomization energy of the molecule under study. ATOMIC-2 is a new version of the protocol that retains the overall concept and all previously defined composite models but improves on ATOMIC-1 in various other ways: Geometry optimization and zero-point-energy evaluation are performed at the density functional level (PBE0-D3/6-311G(d)), which shows significant computational savings and better accuracy than the previously employed RI-MP2/cc-pVTZ. The BSR framework is improved, using more accurate complete-basis-set (CBS) extrapolations toward the Full CI limit for the atomization energies of all auxiliary molecules. Finally, and most importantly, an error and uncertainty model termed ATOMIC-2um is added that estimates average bias and uncertainty for each of the atomization energy contributions that arise from the simplified treatment of some contributions to bond separation energies (CCSD(T)) and the neglect of others (such as higher order, scalar relativistic, or diagonal Born-Oppenheimer corrections) or from residual error in the energies of auxiliary molecules. Large and diverse benchmarks including up to 1179 molecules are used to evaluate necessary reference data and to correlate the observed error for each of the contributions with appropriate proxies that are available without additional quantum-chemical calculations for a particular molecule and represent its size and type. The implementation of ATOMIC-2 considers neutral, closed-shell molecules containing H, C, N, O, and F atoms; compared to ATOMIC-1, the framework has been extended to cover a few challenging but rare bond topologies. In comparison to highly accurate reference data for 184 molecules taken from the ATcT database (V. 1.122r), regular ATOMIC-2 shows noticeable underbinding, but the bias-corrected protocol ATOMIC-2um is found to be more accurate than either ATOMIC-1 or standard Gaussian-4 theory, and the uncertainty model is consistent with statistics of actually observed errors. Problems arising from ambiguous or challenging Lewis-valence structures defining BSRs are discussed, and computational efficiency is demonstrated. Computer code is made available to perform ATOMIC-2um analyses.

Molecular structure of 1,2-diethyldiaziridine studied by gas electron diffraction supported by quantum chemistry calculations

The molecular structure of 1,2-diethyldiaziridine was studied by gas-phase electron diffraction (GED) and quantum chemical calculations. Best fitting to GED experiment scattering intensities was obtained for three conformer model. The experimental structural parameters of most abundant conformer of 1,2-diethyldiaziridine are following (rh1 bond lengths in Å, bond angles in degrees with 3σ in parentheses): r(NCcycl), 1.446(4); r(NN), 1.492(5); r(CC), 1.528(3); r(NCacycl), 1.459(6); ∠NCC, 112.3(11); ∠CNC, 114.7(6). The gas phase standard enthalpy of formation of 1,2-diethyldiaziridine was calculated using Gaussian-4 theory, giving the value of 148.3 ± 3.3 kJ/mol. 1H and 13C NMR spectra obtained in CDCl3 solution were compared with DFT predictions.

Enthalpy of formation calculations on five-membered azaborolidine derivatives

The derivatives of azaborolidine are a class of 5-membered heterocyclic compounds containing a ring with nitrogen atoms and boron atoms. In this study, enthalpy of formation (H) of 5-membered boron-nitrogen heterocyclic species (BxNyHz) were calculated using the atomization method. Additionally, to enlighten whether these molecules are neutral radicals, H of neutral bi-radical forms are calculated. All calculations were performed with the Gaussian-4 theory (G4), which is the most favorable and accurate method on thermodynamic calculations. The determination of some thermodynamic properties (e.g. enthalpies of formation) of diazaborolidine can provide information about whether they are stable under room conditions (approx. 25 °C). Although many heterocyclic ring types are considered, H values of only two types, N3H3B2H2 and N2H2B3H3, are obtained as negative with the values of −46.8 kcal/mol and −44.4 kcal/mol, respectively. Hs of other azaborolidine derivatives were obtained positive values.

Criegee intermediate decomposition pathways for the formation of o-toluic acid and 2-methylphenylformate

We use Gaussian-4 theory to investigate the reaction mechanism for the conversion of a 2-methylstyrene-based Criegee intermediate into o-toluic acid and 2-methylphenylformate. o-Toluic acid can be formed via an α-hydroxyalkyl-hydroperoxide intermediate with an activation energy of ΔG‡298 = 82.9 kJ mol−1 for the rate-determining-step (RDS). The RDS for the formation of 2-methylphenylformate has an activation energy of ΔG‡298 = 61.9 kJ mol−1. Formation of the o-toluic acid product is more exergonic by 67.4 kJ mol−1. Consistent with recent experimental results, our high-level calculations show that o-toluic acid is the thermodynamic product and 2-methylphenylformate is the kinetic product.

Estimation of heats of formation for nitrogen-rich cations using G3, G4, and G4 (MP2) theoretical methods

Gas-phase heats of formation of 48 commonly used nitrogen-rich cations in energetic salts composed of H, C, N, and O atoms have been calculated at the Gaussian-3 (G3), Gaussian-4 (G4), and G4 (MP2) theories using the atomization reaction. The discrepancies between the predicted and the reported HOFs vary in the range of 0.28–470.78 kJ/mol. The reported HOFs for twenty cations were observed within 5 kJ/mol deviation, ten cations within 6–10 kJ/mol deviation, eleven cations within 11–50 kJ/mol, five cations within 51–100 kJ/mol, while two cations differed by more than 420 kJ/mol with respect to G4 data. The calculated HOFs with the G4 composite method at 298.15 K were recommended for selected cations as being more reliable than the reported data.

3-Cyclopropyl-1,2-dimethyldiaziridine: synthesis and study of molecular structure by gas electron diffraction method

The molecular structure and conformational behavior of 3-cyclopropyl-1,2-dimethyldiaziridine have been for the first time experimentally studied by gas-phase electron diffraction and quantum chemical calculations. The two most stable conformers at 298 K possess anti and gauche mutual ring orientation (with prevalence of the anti conformer) whereas only one anti conformer is observed in solution. The determined structural parameters of gaseous 3-cyclopropyl-1,2-dimethyldiaziridine have been compared with those for 3,3-bidiaziridine structural analogues in the crystal phase. The simple and convenient procedure for the synthesis of 3-cyclopropyl-1,2-dimethyldiaziridine comprising cyclopropane and diaziridine rings in one molecule was developed. The standard enthalpy of formation of 3-cyclopropyl-1,2-dimethyldiaziridine in the gas phase was calculated using Gaussian-4 theory, yielding value of 281.9 ± 5.0 kJ/mol.

Molecular structure of tryptamine in gas phase according to gas electron diffraction method and quantum chemistry calculations

The molecular structure of tryptamine was studied by gas-phase electron diffraction (GED) and quantum chemical calculations (DFT/B3LYP and MP2 methods with cc-pVTZ basis set). The best fit of the experimental scattering intensities (R-factor = 3.8%) was obtained for the four-conformer model. The experimental structural parameters are found to be in good agreement with the results of theoretical calculations. The geometric parameters of gaseous tryptamine are compared with those in the crystal phase. The standard enthalpy of formation of tryptamine in the gas phase was calculated using Gaussian-4 theory, yielding value of 133.6 ± 3.3 kJ/mol.

Evaluation of modern DFT functionals and G3n-RAD composite methods in the modelization of organic singlet diradicals.

The evaluation of four high-level composite methods based on the modification of Gaussian-3 (G3) theory for radicals and 18 exchange-correlation density functionals, including modern long-range and dispersion-corrected functionals, in the modelization of singlet diradicals has been performed in this work. Structural parameters and properties such as singlet-triplet gaps, electron affinities, ionization potentials, dipole moments, enthalpies of formation, and bond dissociation energies have been calculated in a set of six well-characterized singlet diradicals, and benchmarked against experimental data and wavefunction-based CASSCF/CASPT2 calculations. The complexity of the open-shell singlet ground state is revealed in the difficulties to properly represent the diradical character reported by some DFT functionals, specially those that do not comprise a certain amount of Hartree-Fock exchange in their formulation. We find that STGs, EAs, dipole moments, and thermochemical properties are, in general, satisfactorily calculated, while for IPs larger deviations with respect to the experiments are found in all cases. The best overall performance is accounted for by hybrid functionals, including some of the long-range corrected functionals, but also pure functionals, comprising the kinetic energy density in their formulation, are found to be competent. Composite methods perform satisfactorily, especially G3(MP2)-RAD and G3X(MP2)-RAD, which calculate singlet-triplet gaps and electron affinities more accurately. On the other hand, G3-RAD and G3X-RAD provide better ionization potentials. This study emphasizes that the use of recently developed functionals, within the broken symmetry approximation, is an appropriate tool for the simulation of organic singlet diradicals, with similar accuracy compared to more expensive composite methods. Nevertheless, suitable selection of the methodology is still crucial for the accomplishment of accurate results.

Use of G4 Theory for the Assessment of Inaccuracies in Experimental Enthalpies of Formation of Aromatic Nitro Compounds

The gas-phase enthalpies of formation (ΔfH298°) of 101 aromatic nitro compounds were calculated using the Gaussian-4 (G4) theory applied to the atomization and isodesmic reaction energies. The ΔfH298° (g) values calculated from the atomization reactions were underestimated by an average of 13 kJ·mol–1 and they could not be used for the assessment of inaccuracies in the experimental enthalpies of formation. A good agreement with the most available experimental data was obtained using the isodesmic reaction procedure. From 5 to 26 isodesmic reactions with different reference species were constructed for each compound. About 15 aliphatic nitro compounds and 100 different C/H/N/O/Cl compounds were used as the reference species in these reactions; the accuracy of enthalpies of formation of all reference compounds was preliminarily confirmed by theoretical calculations. Evidence of accuracy of experimental data was provided by the agreement with calculated values. The differences between the calculated and the experimental enthalpies of formation in the range from (8 to 46) kJ·mol–1 were assigned to possible errors in the experimental values for 21 compounds. The theoretical ΔfH298° (g) values were recommended for these compounds as being more reliable than the experimental values. On the basis of theoretical results, a reference data set of internally consistent gas-phase enthalpies of formation of aromatic nitro compounds was provided. Both experimental and calculated values are included in this data set. The recommended ΔfH298° (g) values of aromatic nitro compounds are consistent with each other and with ΔfH298° (g) values of about 115 different C/H/N/O/Cl compounds including aliphatic nitro compounds. More accurate condensed phase enthalpies of formation and enthalpies of sublimation (or vaporization) were recommended in some cases based on a critical analysis of reported experimental data supplemented by quantum chemical calculations.

Thermochemical Properties of Halides and Halohydrides of Silicon and Carbon

Atomization energies, enthalpies of formation, entropies as well as heat capacities of the SiHnXm and CHnXm systems, with X being F, Cl and Br, have been studied using quantum chemical calculations. The Gaussian-4 theory (G4) and Weizman-1 theory as modified by Barnes et al. 2009 (W1RO) have been applied in the calculations of the electronic, zero point and thermal energies. The effects of low-lying electronically excited states due to spin orbit coupling were included for all atoms and diatomic species by mean of the electronic partition functions derived from the experimental or computational energy splittings. The atomization energies, enthalpies of formation, entropies and heat capacities derived from both methods were observed to be reliable. The thermochemical properties in the temperature range of 298–2500 K are provided in the form of 7-coefficient NASA polynomials.

Unified picture for the conformation and stabilization of the O-glycosidic linkage in glycopeptide model structures

Glycoproteins play a central role in the immune response. In this study, we focus on the core of the common O-linked mucin-type glycopeptides. It has been observed that glycosylation stabilizes the protein in a stiffened, extended structure. We provide a unified picture for the conformation and stabilization of the O-glycosidic linkage using O-(2-acetylamino-2-deoxy-α- or -β-d-galacto- or -mannopyranosyl)-N-acetyl-l-serinamide model structures. We have calculated equilibrium geometries of the model structures with the B3LYP/6-31G(2df,p) method suggested in the Gaussian-4 theory. According to the relative energies, we confirm that the GalNAc-Ser linkage is more stable than its mannose analogues. The natural preference for the α-GalNAc-Ser over the β-GalNAc-Ser anomers can be explained by entropic effects. We explored the hydrogen bonding patterns on the carbohydrate unit calculating highly accurate dRPA@PBE0.25 and dRPA75 energies and found that in some cases, the acetamido group can be fixed by hydrogen bonding from the (O3Carb)H atom, but in most of the cases, it can rotate more freely. The torsion angles in the glycosidic linkage show that the linkage is stiffened more in the α-anomers and the most in the α-GalNAc-Ser structure because of the steric strains in the axial position and by two or three intramolecular hydrogen bonds. We also found that although, in our gas-phase model geometries, the peptide backbone prefers to be in a γ L-turn, a structural water molecule can stabilize a polyproline II helix of a proline-rich sequence, a β-sheet, or more likely random coils.

Ga(+) Basicity and Affinity Scales Based on High-Level Ab Initio Calculations.

The structure, relative stability and bonding of complexes formed by the interaction between Ga(+) and a large set of compounds, including hydrocarbons, aromatic systems, and oxygen-, nitrogen-, fluorine and sulfur-containing Lewis bases have been investigated through the use of the high-level composite ab initio Gaussian-4 theory. This allowed us to establish rather accurate Ga(+) cation affinity (GaCA) and Ga(+) cation basicity (GaCB) scales. The bonding analysis of the complexes under scrutiny shows that, even though one of the main ingredients of the Ga(+) -base interaction is electrostatic, it exhibits a non-negligible covalent character triggered by the presence of the low-lying empty 4p orbital of Ga(+) , which favors a charge donation from occupied orbitals of the base to the metal ion. This partial covalent character, also observed in AlCA scales, is behind the dissimilarities observed when GaCA are compared with Li(+) cation affinities, where these covalent contributions are practically nonexistent. Quite unexpectedly, there are some dissimilarities between several Ga(+) -complexes and the corresponding Al(+) -analogues, mainly affecting the relative stability of π-complexes involving aromatic compounds.

A Method for Calculating the Heats of Formation of Medium-Sized and Large-Sized Molecules

A calculation method for heats of formation (HOF, referred to as △Hf) based on the density functional theory (DFT) is presented in this work. Similar to Gaussian-3 theory, the atomic scheme is applied to calculate the heats of formation of the molecules. In this method, we have modified the formula for calculation of Gaussian-3 theory in several ways, including the correction for diffuse functions and the correction for higher polarization functions. These corrections are found to be significant. The average absolute deviation from experiment for the 164 calculated heats of formation is about 1.9 kcal·mol?1, while average absolute deviation from G3MP2 for the 149 (among the 164 molecules, 15 large-sized molecules can not be calculated at the G3MP2 level) calculated heats of formation is only about 1.9 kcal·mol?1. It indicates that the present method can be applied to predict the heats of formation of medium-sized and large-sized molecules, while the heats of formation of these molecules using Gaussian-3 theory are much difficult, even impossible, to calculate. That is, this method provides a choice in the calculation of △Hf for medium-sized and large-sized molecules.

Probing the electronic structures and properties of neutral and charged arsenic sulfides [Asn S₂ (⁻¹,⁰,⁺¹), n = 1-6] with Gaussian-3 theory.

The structures and energies of neutral and charged arsenic sulfides As n S2 ((-1,0,+1)) (n = 1-6) were investigated systematically by means of the Gaussian-3 (G3) scheme. The ground-state structures of these species are presented. The ground-state structures of As n S2 can be viewed as the lowest-energy structure of neutral As n+1S by replacing an As atom with a S atom. To be more precise, the ground-state structures of As n S2 can be viewed as the lowest-energy structure of neutral As n+2 by replacing two As atoms with two S atoms, in which the feature of sulfur bonding is edge-bridging. No rule could be found for the ground state structure of As n S2 (-) and As n S2 (+). In As n S2 (-), the feature of sulfur bonding is either edge-bridging or a terminal atom, and in AsnS2 (+) the feature of sulfur bonding is edge-bridging analogous to As n S2. The potential energy surfaces of As4S2 and its charged species are very flat. So co-existence for many isomers of As4S2 and its charged species are possible. The reliable adiabatic electron affinities (AEAs) and adiabatic ionization potentials (AIPs) of As n S2 were estimated. There are odd-even alternations in both AEAs and AIPs as a function of size of As n S2. The dissociation energies (DEs) of S [and/or its ion S((-/+))] from As n S2 clusters and their ions were calculated and used to reveal relative stability.

Use of G4 Theory for the Assessment of Inaccuracies in Experimental Enthalpies of Formation of Aliphatic Nitro Compounds and Nitramines

The gas-phase enthalpies of formation (ΔfH298o) of 57 aliphatic nitro compounds and nitramines (mono- and polynitro compounds including cyclic compounds and well-known explosives such as hexogen, octogen, and CL-20) were calculated using the Gaussian-4 (G4) theory applied to the atomization and isodesmic reaction energies. The ΔfH298o (g) values calculated from the atomization reactions were underestimated by an average of 10 kJ·mol–1, and they could not be used for the assessment of inaccuracies in the experimental enthalpies of formation. Much better agreement between theory and experiment was obtained using the isodesmic reaction procedure. Several isodesmic reactions were investigated for each compound. Evidence of high accuracy of most experimental data was provided by the agreement with theoretical results. The differences between the calculated and the experimental enthalpies of formation in the range from (8 to 53) kJ·mol–1 were assigned to possible errors in the experimental values for 17 compounds. The theoretical ΔfH298o (g) values were recommended for these compounds as being more reliable than the experimental values. As a result, a reference data set of internally consistent gas-phase enthalpies of formation of nitro compounds and nitramines was provided. Both experimental and calculated values are included in this data set. The enthalpies of sublimation or vaporization were evaluated for some compounds by taking into account the literature data on the condensed phase enthalpies of formation and the ΔfH298o (g) values recommended in our work. Thus, a set of self-consistent values of the enthalpy of formation in both condensed and gaseous phases and the enthalpy of sublimation or vaporization is presented for most of nitro compounds studied.

Probing the electronic structures and properties of neutral and charged arsenic sulfides (As n S(−1,0,+1), n = 1–7) using Gaussian-3 theory

The structures and energies of neutral and charged arsenic sulfides As(n)S(⁻¹,⁰,⁺¹) (n =1-7) were systematically investigated using the G3 method. The bonding properties and the stabilities of As(n)S and their ions were discussed. The adiabatic electron affinities (AEAs) and adiabatic ionization potentials (AIPs) were presented. The ground-state structures of As(n)S can be considered as the lowest-energy structure of neutral As(n+1) by replacing an As atom with a S atom, that is, "substitutional structure", in which the feature of sulfur bonding is edge-bridging. The ground-state structures of As(n)S⁺ tend to be derived from the lowest-energy structure of cation As(n)⁺ by attaching to a S atom, that is, "attaching structure", in which the sulfur can be three-fold coordinated. There is no rule to be found for the ground-state structure of anion As(n)S⁻, in which the sulfur can be a terminal atom. There are odd-even alternations in both AEAs and AIPs as a function of size of As(n)S. The dissociation energies of S, S⁻, and/or S⁺ from neutral As(n)S and their ions were calculated to examine their stabilities.

A Gaussian-3 theoretical study of the alkylthio radicals and their anions: structures, thermochemistry, and electron affinities

The optimized geometries, electron affinities, and dissociation energies of the alkylthio radicals have been determined with the higher level of the Gaussian-3(G3) theory. The geometries are fully optimized and discussed. The reliable adiabatic electron affinities with ZPVE correction have been predicted to be 1.860 eV for the methylthio radical, 1.960 eV for the ethylthio radical, 1.980 and 2.074 eV for the two isomers (n-C3H7S and i-C3H7S) of the propylthio radical, 1.991, 2.133 and 2.013 eV for the three isomers (n-C4H9S, t-C4H9S, and i-C4H9S) of the butylthio radical, and 1.999, 2.147, 2.164, and 2.059 eV for the four isomers (n-C5H11S, b-C5H11S, c-C5H11S, and d-C5H11S) of the pentylthio radical, respectively. These corrected EAad values for the alkylthio radicals are in good agreement with available experiments, and the average absolute error of the G3 method is 0.041 eV. The dissociation energies of S atom from neutral CnH2n+1S (n = 1-5) and S(-) from corresponding anions CnH2n+1S(-) species have also been estimated respectively to examine their relative stabilities.

Application of computational chemistry methods to obtain thermodynamic data for hydrogen production from liquefied petroleum gas

The objective of this study was to estimate thermodynamic data, such as standard enthalpy, entropy and Gibbs free energy changes of reaction and, consequently, chemical equilibrium constants, for a reaction system describing the hydrogen production from Liquefied Petroleum Gas (LPG). The acquisition of those properties was made using computational chemistry methods and the results were compared with experimental data reported in the literature. The reaction system of steam reforming of LPG was reported as a set of seven independent reactions involving the chemical species n-C4H10, C3H8, C2H6, C2H4, CH4, CO2, CO, H2O, H2 and solid carbon. Six computational approaches were used: Density Functional Theory (DFT) employing Becke's three parameter hybrid exchange functional, and the Lee-Yang-Parr correlation functional (B3LYP) using the 6-31G++(d,p) basis set and the composite methods CBS-QB3, Gaussian-1 (G1), Gaussian-2 (G2), Gaussian-3 (G3) and Gaussian-4 (G4). Mole fractions of the system components were also determined between 873.15 and 1173.15 K, at 1 atm and a feed with a stoichiometric amount of water. Results showed that the hybrid functional B3LYP/6-31G++(d,p), G3 and G4 theories were the most appropriated methods to predict the properties of interest. Gaussian-3 and Gaussian-4 theories are expected to be good thermodynamic data predictors and the known efficient prediction of vibrational frequencies by B3LYP is probably the source of the good agreement found in this study. This last methodology is of special interest since it presents low computational cost, which is important when more complex molecular systems are considered.

Studies on structures and electron affinities of the simplest alkyl dithio radicals and their anions with gaussian-3 theory and density functional theory

The equilibrium geometries and electron affinities of the R-SS/R-SS(-)(R=CH₃, C₂H₅, n-C₃H7, i-C₃H₇, n-C₄H₉, t-C₄H₉, n-C₅H₁₁) species have been studied using the higher level of the Gaussian-3(G3) theory and 21 carefully calibrated pure and hybrid density functionals (five generalized gradient approximation (GGA) methods, seven hybrid GGAs, three meta GGA methods, and six hybrid meta GGAs) in conjunction with diffuse function augmented double-ζ plus polarization (DZP++) basis sets. The geometries are fully optimized with each method and discussed. The reliable adiabatic electron affinity has been presented by means of the high level of G3 technique. With the DZP++ DFT method, three measures of neutral/anion energy differences reported in this work are the adiabatic electron affinity, the vertical electron affinity, and the vertical detachment energy. The adiabatic electron affinities, obtained at the BP86, M05-2X, B3LYP, M06, B98, M06-2X, mPW1PW91, HCTH, B97-1, M05, PBE1PBE, and VSXC methods, are in agreement with the G3 results. These methods perform better for EA prediction and are considered to be reliable.