Quantum-Chemical Study of Alkyl Carbenium Ions in 100% Sulfuric Acid

A quantum-chemical study of neutral and protonated monoalkyl sulfates RHSO₄and [RH₂SO₄]⁺(where R = CH₃, C₂H₅, iso-C₃H₇, and tert-C₄H₉) is carried out. Calculations are performed using the Hartree–Fock method in the 6-31G** and 6-31++G** basis sets taking into account electron correlation according to the Müller–Plesset perturbation theory MP2/6-31+G*//6-31+G*. Protonated tert-butyl sulfate was also calculated by the DFT B3LYP/6-31++G** method. It was found that monoalkyl sulfates are covalent compounds, and the complete abstraction of alkyl carbenium ions from them has substantial energy cost: 196.4, 161.7, 150.8 and 136.0 kcal/mol, respectively. Protonated methyl and ethyl sulfates are also covalent compounds according to the calculation. They have lower but still high energies of heterolytic dissociation (65.0 and 33.5 kcal/mol, respectively). The energy of R⁺abstraction from protonated isopropyl sulfate is much lower: 23.6 kcal/mol. The main covalent state and the ion–molecular pair, which is a carbenium ion [C(CH₃)₂H]⁺solvated by the H₂SO₄molecule, have about the same energy. The ground state of protonated tert-butyl sulfate corresponds to the ion–molecular complex [C(CH₃)⁺ ₃H₂SO₄] with still lower energy of carbenium ion [C(CH₃)₃]⁺abstraction, which is equal to 10.0 kcal/mol. Calculation according to the DFT B3LYP/6-31++G** method shows the absence of a minimum for the protonated tert-butyl sulfate with a covalent structure on the potential energy surface.     

Quantum chemical study of the coordination of glycolic acid conformers and their conjugate bases to [Ca(OH2)n] (n=0–4) ions

A detailed exploration of the configurational and conformational space of glycolic acid and their conjugate bases has been carried out with the aid of first principles quantum chemical techniques at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p) levels of theory. The most stable configuration among the eight possible glycolic acid conformers corresponds to the E-s-cis, s-trans configuration, while the highest energy E-s-trans, s-cis conformer was found at 10.88 and 12.17 kcal mol⁻¹ higher in energy at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p) levels of theory, respectively. Upon dissociation of glycolic acid the s-cis(syn), and s-trans(anti) configurations of the glycolate anion can be formed. The anti conformer was found to be less stable than the syn one by 14.20 and 16.87 kcal mol⁻¹ at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p)) levels of theory, respectively. The computed B3LYP/6-311+G(d,p) proton affinity of the syn conformer for the protonation process affording the more stable E-s-cis, s-trans conformer, in vacuum was found to be 325.35 kcal mol⁻¹ (ΔG⁰ value). From a methodological point of view, our results confirm the reliability of the integrated computational tool formed by the B3LYP density functional model. This model has subsequently been used to investigate the interaction of Ca²⁺ ions with the glycolic acid conformers and their conjugate bases in vacuum and in the presence of extra water ligands. For the complexes of glycolic acid conformers the η²–O,O–(COOH) coordination, that is the structure that arises from the coordination of the Ca²⁺ to the carboxylic group, is the global minimum of the PES, while the η²–O(OH),O–(COOH) coordination is a local minimum found at only 1.0 and 1.3 kcal mol⁻¹ higher in energy at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p) levels of theory, respectively. Moreover, the two isomers exhibit nearly the same binding affinities, which are predicted to be 89 and 85 kcal mol⁻¹ at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p) levels of theory, respectively. The same holds also true for the complexes of the glycolate anion. The η²–O,O–(COO⁻) coordination involving the syn conformer of the glycolato ligand, is the global minimum, while the η²–O(OH),O–(COO⁻) one lies at 1.5 and 5.6 kcal mol⁻¹ higher in energy at the B3LYP/6-311+G(d,p) and CCSD(T)/6-31G(d,p) levels of theory, respectively. The other conformer with an η²–O,O–(COO⁻) coordination involving the anti conformer of the glycolato ligand, is less stable by only 0.2 kcal mol⁻¹ at both levels of theory. Noteworthy is the trend seen for the incremental binding energy due to the successive addition of water molecules to [HOCH₂C(O)O]Ca²⁺ species; the computed values are 30.4, 26.8, 22.9 and 16.2 kcal mol⁻¹ at the B3LYP/6-311+G(d,p) level of theory for the mono-, di-, tri- and tetraaqua complexes, respectively. This trend arising from the repulsion of the dipoles between the water ligands and from unfavorable many body interactions is in accordance with those anticipated from electrostatic considerations. The Ca(II)-water interaction weakens with increasing coordination of the metal. Obviously, it is the electrostatic nature of the Ca(II)-water interactions that accounts well for the computed coordination geometries of the cationic (aqua)(glycolato)calcium complexes. Calculated structures, relative stability and bonding properties of the conformers and their complexes with [Ca(OH₂)_n]²⁺ (n=0–4) ions are discussed with respect to computed electronic and spectroscopic properties, such as charge density distribution, harmonic vibrational frequencies and NMR chemical shifts.     

Structures and stability of N9, N9 − and N9 + clusters

 Ab initio molecular orbital calculations for N₉, N⁻ ₉ and N⁺ ₉ isomers were carried out at the HF/ 6-31G*, B3PW91/6-31G*, B3LYP/6-31G* and MP2/ 6-31G* levels of theory. Stable equilibrium geometric structures were determined by harmonic vibrational frequency analyses at the HF/6-31G*, B3PW91/6-31G* and B3LYP/6-31G* levels of theory. The most stable free-radical N₉ cluster is structure 1 with C _{2 v} symmetry and that of anion N⁻ ₉ is structure 3 with C _s symmetry. Only one stable structure of the N⁺ ₉ cation with C _{2 v} symmetry was predicted. Their potential application as high-energy-density materials has been examined. Received: 15 June 1999 / Accepted: 11 October 1999 / Published online: 14 March 2000     

Conformational Properties of (Z,Z)-, (E,Z)-, and (E,E)-Cycloocta-1,4-dienes

Summary.  Ab initio calculations at the HF/6-31G^* level of theory for geometry optimization and the MP2/6-31G^*//HF/6-31G^* level for a single point total energy calculation are reported for (Z,Z)-, (E,Z)-, and (E,E)-cycloocta-1,4-dienes. The C ₂-symmetric twist-boat conformation of (Z,Z)-cycloocta-1,4-diene was calculated to be by 3.6 kJ·mol⁻¹ more stable than the C _S-symmetric boat-chair form; the calculated energy barrier for ring inversion of the twist-boat conformation via the C _S-symmetric boat-boat geometry is 19.1 kJ·mol⁻¹. Interconversion between twist-boat and boat-chair conformations takes place via a half-chair (C ₁) transition state which is 43.5 kJ·mol⁻¹ above the twist-boat form. The unsymmetrical twist-boat-chair conformation of (E,Z)-cycloocta-1,4-diene was calculated to be by 18.7 kJ·mol⁻¹ more stable than the unsymmetrical boat-chair form. The calculated energy barrier for the interconversion of twist-boat-chair and boat-chair is 69.5 kJ·mol⁻¹, whereas the barrier for swiveling of the trans-double bond through the bridge is 172.6 kJ·mol⁻¹. The C _S symmetric crown conformation of the parallel family of (E,E)-cycloocta-1,4-diene was calculated to be by 16.5 kJ·mol⁻¹ more stable than the C _S-symmetric boat-chair form. Interconversion of crown and boat-chair takes place via a chair (C _S) transition state which is 37.2 kJ·mol⁻¹ above the crown conformation. The axial- symmetrical twist geometry of the crossed family of (E,E)-cycloocta-1,4-diene is 5.9 kJ·mol⁻¹ less stable than the crown conformation. Corresponding author. E-mail: isayavar@yahoo.com Received March 25, 2002; accepted April 3, 2002     

Ab initio HF-SCF study of naphthazarin: Geometries,isomerism, hydrogen bonding,and vibrational spectrum

The structural properties and intramolecular hydrogen bonding of a series of structures of naphthazarin molecule were investigated by ab initio HF-SCF methods. The geometries of theC _2v ,C _2h ,D _2h , andC _s symmetry structures were optimized using split-valence basis sets. MP2/6-31G^*// HF/6-31G single-point energy calculations indicate that theC _2v isomer (5,8-dihydroxy-1,4-naphthoquinone) is the lowest energy structure of the molecule and that theC _2h symmetry one (4,8-dihydroxy-1,5-naphthoquinone), lying 37 kJ/mol above theC _2v form, is the other stable isomer of naphthazarin. At the HF/6-31G level, the intramolecular proton exchange between two equivalentC _2v structures is a two-step process where each proton can be independently transferred through an unsymmetrical potential having a 1,5-quinone intermediate, theC _2h symmetry structure, and two equivalent transition states ofC _s symmetry, with a barrier height equal to 38 kJ/ mol (MP2/6-31G^*//HF/6-31G). The study of naphthazarin molecule is flanked by a theoretical investigation on theC _2v andC _2h isomers of the parent naphthoquinone and dihydroxynaphthalene molecules. The SCF vibrational spectrum of the ground state of naphthazarin, harmonic frequencies, and infrared and Raman band intensities were computed at the HF/6-31G level. The results of the calculations are compared with the matrix isolation FT-IR spectroscopy measurements and with the infrared and Raman spectra of the crystal molecule.     

Quantum chemical study of the structure of bicyclo[2.2.0]hex-1(4)-ene and its dimers

The RHF, B3LYP, and PBE0/6-311G** quantum chemical methods are used to determine the point symmetry group and the equilibrium structure of bicyclo[2.2.0]hex-1(4)-ene (I, D _2h ), its two stable dimers (tricyclo[4.2.2.2^2,5]dodeca-1.5-diene (II, D _2h ) and 2,5-dimethylenetricyclo[4.2.2.0^1,6]decane (III, C ₂)), and pentacyclo [4.2.2.2^2,5]dodecane (IV, D ₂) that is a hypothetical intermediate in the dimerization reaction of the molecules of I. The relation of total energies is obtained with regard to zero-point vibrations: E(III) < E(II) ≪ E(IV) ≪ 2E(I).     

Theoretical study of the relative stabilities of H+(X)2 and H+(X)3 conformers and their clustering energies: X  CO and N2

Third-order Møller–Plesset perturbation theory (MP 3) with a 6-31G** basis set was applied to study the relative stabilities of H⁺(X)₂ conformations (X ? CO and N₂) and their clustering energies. The effect of both basis set extensions and electron correlation is not negligible on the relative stabilities of the H⁺(CO)₂ clusters. The most stable conformation of H⁺(CO)₂ is found to be a C_∞v structure in which a carbon atom of CO bonds to the proton of H⁺(CO), whereas that of H⁺(N₂)₂ is a symmetry D_∞h structure. The second lowest energy conformations of H⁺(CO)₂ and H⁺(N₂)₂ lie within 2 kcal/mol above the energies of the most stable structures. Clustering energies computed using MP 3 method with the 6-31G** basis set are in good agreement with the experimental findings of Hiraoka, Saluja, and Kebarle. The low-lying singlet conformations of H⁺(X)₃ (X ? CO and N₂) have been studied by the use of the Hartree–Fock MO method with the 6-31G** basis set and second-order Møller–Plesset perturbation theory with a 4-31G basis set. The most stable structure is a T-shaped structure in which a carbon atom of CO (or a nitrogen atom of N₂) attacks the proton of the most stable conformation of H⁺(X)₂ clusters.     

Ab Initio Study of Conformational Properties of ( Z, Z)-, ( E, Z)-, and ( E, E)-Cyclonona-1,5-dienes

Ab initio calculations at the HF/6-31G^* level of theory for geometry optimization and MP2/6-31G^*//HF/6-31G^* for a single point total energy calculation are reported for the important energy-minimum conformations and transition-state geometries of (Z,Z)-, (E,Z)-, and (E,E)-cyclonona-1,5-dienes. The C₂ symmetric chair conformation of (Z,Z)-cyclonona-1,5-diene is calculated to be the most stable form; the calculated energy barrier for ring inversion of the chair conformation via the C_s symmetric boat-chair geometry is 58.3kJmol^–1. Interconversion between chair and twist-boat-chair (C₁) conformations takes place via the twist (C₁) as intermediate. The unsymmetrical twist conformation of (E,Z)-cyclonona-1,5-diene is the most stable form. Ring inversion of this conformation takes place via the unsymmetrical chair and boat-chair geometries. The calculated strain energy for this process is 63.5kJmol^–1. The interconversion between twist and the boat-chair conformations can take place by swiveling of the trans double bond with respect to the cis double bond and requires 115.6kJmol^–1. The most stable conformation of (E,E)-cyclonona-1,5-diene is the C₂ symmetric twist-boat conformation of the crossed family, which is 5.3kJmol^–1 more stable than the C_s symmetric chair–chair geometry of the parallel family. Interconversion of the crossed and parallel families can take place by swiveling of one of the double bonds and requires 142.0kJmol^–1.     

Alkyl radical adducts of aromatic N-oxides as hydrogen-abstracting agents: The reactivity of phenazine-N,N′-dioxide-methyl radical adduct

An O-methylated analog of protonated phenazine-di-N-oxide radical anion abstracts hydrogen from primary and secondary alcohols in a slow (k ₁ < 500 M⁻¹ s⁻¹) bimolecular reaction. No kinetic evidence has been found for the unimolecular release of free methoxyl radicals through the homolytic N-OMe bond cleavage in these species. DFT calculations at the UB3LYP 6-31G(d) level indicate that protonated and O-alkylated radical anions of pyrazine, quinoxaline and phenazine di-N-oxides are close analogues of aromatic nitroxyl radicals with the highest spin density localized on the oxygen and nitrogen of the nitrone moiety.     

Triazene: An ab initio Molecular-Orbital Study of Structure,Properties, and Hydrogen-Transfer Reaction Pathways

Ab initio calculations of structure, properties, and tautomerization reactions of triazene ( 1 ) at the HF/3-21G//3-21G, HF/6-31G*//6-31G*, HF/6-31G**//6-31G*, and MP2/6-31G*//6-31G* levels led to the following conclusions and predictions: (a) Calculations of the ground-state structure of (E)- and (Z)-triazene ( 1a and 1b , respectively) at various levels of theory show for both isomers C₁ geometry with a rather flat pyramidal configuration at N(3), and small energy differences (0.2–7.2 kJ/mol) between C₁ and C_s geometry, i.e. inversion at N(3) is a quasi-free process. With all levels of calculations, 1a is found to be of lower energy than 1b by 23-30 kJ/mol. (b) Comparison of vibrational frequencies of (E)-diazene ( 3 ) calculated at the HF/3-21G level with experimental values reveals that HF/3-21G calculations are reliable for the prediction of vibrational frequencies of polyaza compounds, if corrected by a factor of 0.91. On this basis, the harmonic vibrational frequencies of 1a and 1b were predicted. (c) For the rotation around the N(2)—N(3) bond of 1a two conceivable transition states, 5a (syn) and 5b (anti) were located (HF/3-21G). The energy differences between 5a or 5b , and 1a are in the order of magnitude of 50-56kJ/mol and show a slight preference for the anti-mode, i.e. energy barriers for the N(2)—N(3) rotation are obtained comparable to those observed experimentally with substituted (E)-triazenes ( 4 ). (d) Protonation of 1a at N(1), N(2), or N(3) leads to 6a , 6b , and 6c , respectively –the last one resembling an intermediate of formation of 1 from hydrogendiazonium ion ( 7 ) and ammonia ( 8 ). Energetically, the conjugate acids of 1a follow the sequence 6a < 6c < 6b . (e) The preference of N(1) protonation of 1a is also reflected in the relatively high gain of energy in the formation of H-bonded dimers of 1a with H-bonds from N(3)—H to N(1). Calculations of three different H-bonded dimers 9a–c of 1a with the 3-21G basis show that an eight-membered cyclic dimer 9c with two H-bonds from N(3)? H to N(1) is energetically most favoured (67.5 kJ/mol below two separate molecules of 1a ). This dimer might well be the starting situation of double intermolecular H-transfer leading to an automeric dimer 9c via an energetically low-lying transition state 12 , thus offering a low-energy pathway for the known easy tautomerization of mono- or disubstituted (E)-triazenes. For 9c?9c , the activation energy including correction for polarization and correlation effects as well as for vibration zero-point energy is estimated to be ca. 54kJ/mol. (f) A six-membered cyclic dimer 9b of 1a with two H-bonds from N(3)? H to N(2) might be involved for double H-transfer via a transition state 11 to a dimer 10 of (E, Z)-azimine ( 2 ). This process, however, turns out to be energetically highly disfavoured (estimated energy barrier for 9b → 10 : 232 kJ/mol) in contrast to the reverse reaction ( 10 → 9b via 11 : 4 kJ/mol). This leads to the prediction that azimines bearing an H-atom at N(2) might be kinetically too instable for isolation, being, instead, easily tautomerized to triazenes by bimolecular H-transfer.     

The C2H 3 + cation and its interaction with HF

The structure and stability of classical and bridged C₂H ₃ ⁺ is reinvestigated. The SCF and CEPA-PNO computations performed with flexibles andp basis sets including twod-sets on carbon confirm our previous results. We find the protonated acetylene structure to be more stable than the vinyl cation by 3.5–4 kcal/mol. The energy barrier for the interconversion of these two structures is at most a few tenths of a kcal/mol. The equilibrium SCF geometries of Weberet al. [15] are affected insignificantly by further optimization at the CEPA-PNO level. Several structures for the interaction of C₂H ₃ ⁺ with HF have been investigated at the SCF level. With our largest basis set which includes a complete set of polarization functions we find a remarkable levelling of the stabilities of most of the structures. In these cases the stabilization energy ΔE ranges from −10 to −13 kcal/mol.     

Ab Initio Study of Conformational Properties of ( Z, Z)-, ( E, Z)-, and ( E, E)-Cyclonona-1,5-dienes

Summary. Ab initio calculations at the HF/6-31G^* level of theory for geometry optimization and MP2/6-31G^*//HF/6-31G^* for a single point total energy calculation are reported for the important energy-minimum conformations and transition-state geometries of (Z,Z)-, (E,Z)-, and (E,E)-cyclonona-1,5-dienes. The C₂ symmetric chair conformation of (Z,Z)-cyclonona-1,5-diene is calculated to be the most stable form; the calculated energy barrier for ring inversion of the chair conformation via the C_s symmetric boat-chair geometry is 58.3kJmol^–1. Interconversion between chair and twist-boat-chair (C₁) conformations takes place via the twist (C₁) as intermediate. The unsymmetrical twist conformation of (E,Z)-cyclonona-1,5-diene is the most stable form. Ring inversion of this conformation takes place via the unsymmetrical chair and boat-chair geometries. The calculated strain energy for this process is 63.5kJmol^–1. The interconversion between twist and the boat-chair conformations can take place by swiveling of the trans double bond with respect to the cis double bond and requires 115.6kJmol^–1. The most stable conformation of (E,E)-cyclonona-1,5-diene is the C₂ symmetric twist-boat conformation of the crossed family, which is 5.3kJmol^–1 more stable than the C_s symmetric chair–chair geometry of the parallel family. Interconversion of the crossed and parallel families can take place by swiveling of one of the double bonds and requires 142.0kJmol^–1.     

Ab initio molecular orbital calculations of 3,4-dihydro-1,2-dioxin, 3,6-dihydro-1,2-dioxin, 4H-1,3-dioxin (1,3-diox-4-ene), and 2,3-dihydro-1,4-dioxin (1,4-dioxene)

Optimized geometries and total energies for 3,4-dihydro-1,2-dioxin ( 1 ), 3,6-dihydro-1,2-dioxin ( 2 ), 4H-1,3-dioxin (1,3-diox-4-ene, 3 ), and 2,3-dihydro-1,4-dioxin (1,4-dioxene, 4 ) were calculated using ab initio 3-21G, 6-31G*, and MP2/6-31G*//6-31G* methods. The half-chair conformers of 1 (C₁), 2 (C₂), 3 (C₁), and 4 (C₂) are more stable than their respective planar structures [ 1 (C_s), 2 (C_2v), 3 (C_s), and 4 (C_2v)]. Among the four isomers 1 – 4 , the half-chair conformer of 3 is the most stable. It is 53.1, 54.6, and 3.4 kcal mol⁻¹ more stable than 1 , 2 , and 4 , respectively. The largest energy difference (19.0 kcal mol⁻¹) is observed between the half-chair and planar conformers of 2 . The boat conformers of 2 and 4 are less stable than their respective half-chair conformers, but are more stable than their planar structures. Hyperconjugative orbital interactions (anomeric effects) contribute to the greater stability of 3 (n_O(3) →σ*_C(2)—O(1), n_O(3)→σ*,n _O(3)→σ*) and of 4 (n_O(1)→ σ*). The ab initio calculated structural features of the half-chair conformations of the dihydrodioxins 1 – 4 are compared with the half-chair conformations of cyclohexene and the chair conformations of cyclohexane, oxacyclohexane (tetrahydropyran), 1,2-dioxacyclohexane (1,2-dioxane), 1,3-dioxacyclohexane (1,3-dioxane), and 1,4-dioxacyclohexane (1,4-dioxane) © 1997 by John Wiley & Sons, Inc. J Comput Chem 18 : 1392–1406, 1997     

The combined use of ab initio molecular orbital theory and matrix isolation infrared spectroscopy in the study of molecular interactions

The infrared spectra of a linear (C_s) and a cyclic (C_i) water dimer and a linear (C_s) and a cyclic (C_2h) ammonia dimer have been calculated, at the second order level of MØller-Plesset perturbation theory, using the 6-31G^** basis set. The calculated spectra have been compared with the spectra of water and ammonia isolated in nitrogen and argon matrices. In the case of water, theory predicts the linear to be the more stable isomer, and the observed spectrum can only be interpreted in terms of the linear structure. For ammonia, while the experimentally determined spectrum fits the calculated spectrum of the linear dimer fairly closely, the prediction of which is the more stable structure is still ambiguous.     

Is tetrahedral H42+ a minimum? Anomalous behavior of popular basis sets with the standard p exponents on hydrogen

The nature of the tetrahedral H₄²⁺ stationary point (minimum or triply degenerate saddle) depends remarkably upon the theoretical level employed. Harmonic vibrational analyses with, e.g., the 6-31G** (and 6-31 + +G**) and Dunning's [4s2p1d;2s1p] [D95(d,p)] basis sets using the standard p exponent suggest (erroneously) that the T_d geometry is a minimum at both the HF and MP2 levels. This is not the case at definitive higher levels. The C₃H₄²⁺ structure with an apical H is another example of the failure of the calculations with the 6-31G**, 6-311G**, and D95(d,p) basis sets. Even at MP2/6-31G** and MP2/ cc-pVDZ levels, the C_3v structure has no negative eigenvalues of the Hessian. Actually, this form is a second-order saddle point as shown by the MP2/6-31G** calculation with the optimized exponent. The D_4h methane dication structure is also an example of the misleading performance of the 6-31G** basis set. In all these cases, energy-optimized hydrogen p exponents give the correct results, i.e., those found with more extended treatments. Optimized values of the hydrogen polarization function exponents eliminate these defects in 6-31G** calculations. Species with higher coordinate hydrogens may also be calculated reliably by using more than one set of p functions on hydrogen [e.g., the 6-31G(d,2p) basis set]. Not all cases are critical. A survey of examples, also including some boron compounds, provides calibration. © 1993 John Wiley & Sons, Inc.     

On the additivity of basis set effects in some simple fluorine containing systems

The reactions F + H₂ → HF + H, HF → H + F, F → F⁺ + e^? and F + e^? → F^? were used as simple test cases to assess the additivity of basis set effects on reaction energetics computed at the MP4 level. The 6-31G and 6-311G basis sets were augmented with 1, 2, and 3 sets of polarization functions, higher angular momentum polarization functions, and diffuse functions (27 basis sets from 6-31Gd, p) to 6-31 ++ G(3df, 3pd) and likewise for the 6-311G series). For both series substantial nonadditivity was found between diffuse functions on the heavy atom and multiple polarization functions (e.g., 6-31 + G(3d, 3p) vs. 6-31 + G(d, p) and 6-31G(3d, 3p)). For the 6-311G series there is an extra nonadditivity between d functions on hydrogen and multiple polarization functions. Provided that these interactions are taken into account, the remaining basis set effects are additive to within ±0.5 kcal/mol for the reactions considered. Large basis set MP4 calculations can also be estimated to within ±0.5 kcal/mol using MP2 calculations, est. E_MP4(6-31 ++ G(3df, 3pd)) ≈ E_MP4(6-31G(d, p)) + E_MP2(6-31 ++ G(3df, 3pd)) – E_MP2(6-31G(d, p)) or E_MP4(6-31 + G(d, p) + E_MP2(6-31 ++ G(3df, 3pd)) – E_MP2(6-31 + G(d, p)) and likewise for the 6-311G series.     

Computer simulation of the structure of large molecules: IV. 2D polybuckminsterfullerenes and their boraza analogs with bisingle nitrogen-boron bonds

The equilibrium structure of the dimer (C₆₀)₂, clusters (C₆₀)₉, and (C₆₀)₇ simulating the poly-C₆₀ (VIII) and poly-C₆₀ (XII), as well as their boraza analogs with bisingle nitrogen-boron bonds was determined by the quantum-chemical methods B3LYP/6-31G and PBE0/6-31G. The boraza analogs are characterized by the positive values of calculated (B3LYP/PBE0) energies of the interpolyhedral bonds: 10/20, 35/74, and 54/109 kcal mol⁻¹ respectively per a pair of monomers. The PBE0 method predicts shorter bond than B3LYP, and, in accordance with calorimetric data, positive bonding energy of the polyhedra in (C₆₀)n.     

Neutron diffraction analysis at 15 K and ab initio molecular orbital calculations for α-cyanoacetohydrazide: A crystal structure with a high energy conformer

The crystal structure of α-cyanoacetohydrazide, C₃H₅N₃O, is refined using single-crystal neutron diffraction data at 15 K. Nuclear equilibrium geometries of the isolated molecules are calculated using GAUSSIAN-82 for the eight possible conformers having C_s symmetry. The conformation observed in the crystal has the eighth highest calculated energy, 36.6 kJ mol⁻¹ above the lowest energy conformer, and the largest calculated dipole moment, 8.6 D, with a HF/6-31G* basis. In the crystal the molecule is distorted from the ideal C_s symmetry. These distortions add another 20.3 kJ mol⁻¹ in energy, calculated with HF/6-31G*. All the hydrogens, including the CH, are involved in intermolecular hydrogen-bonding which is unusual in that it is formed entirely by three-center bonds. These bonds form a network which includes dimer and chain configurations.     

Bowl-shaped hydrocarbons related to C60

Ab initio studies at the HF/6-31G* and B3LYP/6-31G* levels are reported for two bowl-shaped hydrocarbons related to C₆₀: C₃₀H₁₂ and C₃₆H₁₂, of C₃ and C_3v symmetry, respectively. The former has an approximate heat of formation of 211 kcal/mol. Bowl-to-bowl interconversion may occur through a planar (C_3h) form of ca. 64 kcal/mol greater energy having one imaginary vibrational frequency. The larger C₃₆H₁₂ bowl has a calculated ΔH°_f of 265 kcal/mol. Its HF/6-31G*, B3LYP/6-31G*, and MM3 bond lengths are in good agreement with a recent X-ray structure. Chemical shifts for both compounds calculated by the GIAO method are in good agreement with the measured NMR spectra. The observed ¹³C chemical shifts increase with the extent of pyramidalization. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 189–194, 1998     

A quantum-chemical study of aza derivatives of (<Emphasis Type="Italic">E</Emphasis>)-1-styrylnaphthalene in the ground and lowest electronically excited states

The structures of (E)-1-styrylnaphthalene (1SN) and its aza derivatives 1-styrylisoquinoline (1SiQ) and 4- and 8-styrylquinolines (4SQ and 8SQ, respectively) in the neutral and protonated forms were calculated by the semiempirical (PM3) and DFT (B3LYP/6-31G*) methods. It follows from the DFT data that, in the ground state (S0), 1SiQ and 8SQ are planar, whereas 1SN, neutral 4SQ, and all protonated azastyrylnaphthalenes are nonplanar with aromatic cores twisted by 5 to 40° out of the plane of the double bond and with linear correlation between the torsion angles of the two cores. The calculated adiabatic excitation energy (E _ad) varies within 61–64 kcal mol^?1 for the neutral compounds and decreases for the protonated forms to 48, 45, and 33 kcal mol^?1 for 1SiQH⁺, 4SQH⁺, and 8SQH⁺, respectively. The lower E _ad value for 8SQH⁺ is in qualitative agreement with a lower photoisomerization quantum yield for this compound as compared with that for other protonated azastyrylnaphthalenes.