Mendel Trachtman

An alternative approach to the problem of assessing stabilization energies in cyclic conjugated hydrocarbons

Reactions are described that provide an alternative basis for evaluating stabilization energies of cyclic conjugated hydrocarbons. These reactions involve no changes in hybridization of carbon atoms and minimal changes in the nature of the carbon-hydrogen bonds. Such reactions exemplify those structural features that lead to stabilization. Theoretical and experimental molecular indices are introduced as a measure of these stabilizing effects. Calculated values of these indices are compared to experimental results.

The distortion of the ring in monosubstituted benzene derivatives: A molecular orbital study

Abstract Ab initio calculations using the 6-31G basis set have been carried out on benzene and the monosubstituted derivatives with CH3, NH2, OH, F, NO, CHCH2, CCH, CCF COO− O−, and with NO2, CHO, CHNH, COOH, CFO, CN, NC and NH3+, as substituent groups. The C- and H-atoms of the ring and the substituent group atom directly attached to it were assumed to lie in the same plane, and a particular orientation was assumed for certain groups, otherwise full geometry optimization was employed. Trends in the following parameters are discussed — the ipso angle, the lengths of the CC bonds which include the ipso angle, the CC and CH bond lengths, nonbonded C ⋯ C and H ⋯ H distances, the ring area, and the tilt of the unsymmetrical substituent groups with respect to the ring axis. Additional calculations at the 6–31G* level on benzene and the F, CN and NH2 derivatives show the trends to be unaffected by the inclusion of polarization functions on the heavy atoms. In selected cases the calculated geometries are compared with microwave and X-ray diffraction results. Comparison is also made with the Mulliken population analysis of Hehre, Radom and Pople (1972) who used the STO-3G basis set and standard geometry. The difference in energy between that for the optimized structure and that for a reference structure with optimized benzene ring geometry and the optimized geometry for the attachment and substituent group has been calculated for the F, NO2, OH, CN, CHCH2 and O− derivatives. The small values, less than 1 kcal mol−1, except for O−, suggest that the actual physical state might well be a mixture of structures having slightly different ring geometries.

Homodesmotic reactions for the assessment of stabilization energies in benzenoid and other conjugated cyclic hydrocarbons

New homodesmotic reactions are designed that provide and alternative basis for evaluating stabilization energies of benzenoid and other conjugated cyclic hydrocarbons. As in previous cases, carbon–carbon bonds are matched in the sense of having equal numbers of Csp2–Csp2, Csp2Csp2, Csp2–Csp3, etc. bonds in reactants and products, while simultaneously the various carbon–hydrogen bonds are matched as closely as possible. By minimizing extraneous energy contributions to the reaction heat arising from changes in hybridization and C–H binding, such reactions single out those structural features resulting in stabilization. These new reactions have the advantage that experimental ΔHf° data is currently available for the necessary reactant molecules, thus allowing an explict evaluation of the homodesmotic stablization energy to be made, which is compared to quantum theoretical calculations wherever possible.

A Molecular orbital study of the rotation about the CC bond in styrene

Abstract The geometry and energy of styrene have been calculated using the 6-31G basis set as a function of the C β C 2 C 1 C 2 dihedral angle-Φ = 0°(cis), 15°, 30°, 60° and 90° — assuming that the vinyl and phenyl groups remain planar, but otherwise with full geometry optimization. Similar calculations have been carried out for 1,3-butadiene and 3-methylene-1,4-pentadiene (MPD) where rotation about 180° generates a different and not the same conformer. The torsional potential energy curve for styrene has a very flat minimum Φ = 0, i.e. the cis structure is the most stable, whereas butadiene and MPD have minima in the region Φ = 37° to 40°, indicative of more stable gauche structures. For styrene the barrier height Φ = 90° is 131.1 KJ mol −1 . These results provide strong support for the potential function obtained by Hollas and Ridley from single level vibronic fluorescence and other spectroscopic data. The distortion of the benzene ring brought about the vinyl group substitution is discussed, also the variation of the C/C and H/C bond lenghts with Φ and the change in charge on the vinyl group and the polarity of the various bonds in the conversion of the cis into the 90° gauche conformer. The stabilization energy for styrene relative to that for benzene has been evaluated according to various criteria, and, in addition, the energy associated with the distortion of the ring.

A molecular orbital study of nitrogen inversion in aniline with extensive geometry optimization

The geometry and energy of aniline have been calculated using the 6-31G and 6-31G*(5D) basis sets for the planar structure and various pyramidal structures, assuming that the ring and the N-atom bonded to it lie in the same plane, but otherwise with full geometry optimization. With the 6-31G basis set the planar structure is predicated to be the most stable, whereas the inclusion of polarization functions in the 6-31G*(5D) basis set finds a pyramidal structure with the out-of-plane angle φ=42.3° to be most stable and the energy barrier to inversion via the planar transition state to be 1.59±0.02 kcal mol−1, in close agreement with experiment. Completing the optimization, allowing the N-atom and the C- and H-atoms of the ring to take up equilibrium out-of-plane positions increases the calculated energy carrier to inversion by less than 0.1 kcal mol−1 to 1.66 kcal mol−1. The ring adopts a very shallow inverted boat-type conformation with ∠N7-C1⋯C4 = 2.0°.

A molecular orbital study of ethylene and the all-trans conjugated polyenes: C4H6, C6H8, C8H10 and C10H12

Abstract We have carried out calculations on ethylene, trans 1,3-butadiene and on all-trans 1,3,5-hexatriene, 1,3,5,7-octatetraene and 1,3,5,7,9-decapentaene at the 6-31G level, on 1,3-butadiene and 1,3,5-hexatriene at the 6-31G* level, and on 1,3-butadiene at the 6-311G** level, with full geometry optimization. As the chain length is increased, the terminal CC bond shows an increase in length, the adjacent CC bond a decrease, the next CC bond along the chain an increase, and the next CC bond a decrease, the change in each case tending towards a limiting value. The terminal CC bond is shorter than the others, and the CC bond next to the end is longer than the others. The HC bonds in the middle of the longer chains also show a progressive increase towards a limiting value. The terminal C-atoms serve as both σ- and π-charge acceptors, whereas the other C-atoms are σ-charge acceptors but π-charge donors. The σ-charge transfer tends to level off at a value of about −0.182 in the middle of the chain, while the π-charge transfer drops almost to zero. The total overlap populations between the C-atoms of the CC and CC bonds are larger the shorter the bond length, and vice-versa, following straight line relationships. The breakdown of the total overlap population into contributions from atom centers, proximal and distal bonded atoms, and antibonded atoms, finds significant antibonded atom contributions amounting to 10–14% of that from proximal bonded atoms. Isodesmic bond separation energies and homodesmotic group separation energies are evaluated to assess the conjugation energy (stabilization energy) in the polyenes, and comparisons are made with the corresponding energies for benzene.

Comparison of various isodesmic and homodesmotic reaction heats with values derived from published ab initio molecular orbital calculations

Ab initio theoretical reaction heats, evaluated by using total molecular energies from ten basis sets as reported in the literature, are compared with experiment for nine acyclic C4 hydrocarbons, seven cyclic C3 and C4 hydrocarbons, and five benzenoid hydrocarbons. The closeness of the agreement is examined to assess the effect of the greater matching of structural features in the homodesmotic reactions, and correlated with the type of basis set employed. Extended basis sets are essential for good agreement, other than fortuitous, if one of the reactant or product species is markedly destabilized or stabilized with repect to the rest, as is the case with the small ring structures and the benzenoid hydrocarbons, respectively.

A molecular orbital study of the rotation about the C-C bond in 1,3-butadiene

The geometry and energy of 1,3-butadiene have been calculated using the 6-311G** basis set as a function of the CCCC dihedral angle-0 ° (trans), 30 °, 60 °, 75 °, 90 °, 120 °, 135 °, 150 °, 165 ° and 180 ° (cis)-assuming that the vinyl groups remain planar. Potential minima are located at 0 ° and 141.4 °, with the trans structure more stable than the gauche by 13.2 kJ mol−1. Potential maxima are located at 76.7 °, giving a barrier height of 25.4 kJ mol−1 relative to the trans structure, and at 180 ° giving a barrier height of 3.0 kJ mol−1 relative to the 141.4 °-gauche structure. Using the 6-31G* basis set the inclusion of electron correlation, accounting for about 52% of the correlation energy, was found to produce no significant change in the shape of the potential energy curve. The magnitude of the expectation energy differences is such that both barriers with respect to the 14l.4 °-gauche maximum structure can be categorized unequivocally as attractive-dominant, whereas the values for the energy barrier with respect to the trans structure, although characteristic of a repulsive-dominant barrier at the 6–311G** level, are sufficiently small that higher level calculations might give the opposite result. Analysis of ΔVnn for the conversion reactions cis → 150 °-gauche, trans → 60 °-gauche, and trans → 90 °-gauche in terms of the individual contributions from the various internuclear interactions shows that nonbonded interactions are important, not only in initiating the destabilization of the crowded cis structure, but also through-out the entire range of CCCC dihedral angles, 0 ° to 180 °.

A molecular orbital study of the changes that accompany rotation of the HO group in phenol, and the barrier height

Abstract The geometry, energy, dipole moment and total atomic charge distribution have been calculated for torsional angles of 0°, 30°, 60° and 90° with respect to rotation about the CO bond in phenol using the 6-31G basis set, assuming that the ring, the bonded O-atom, and the ring H-atoms all lie in the same plane, but otherwise with full geometry optimization. Additional calculations, using the 6-31G* (5D) basis set, showed very similar changes in geometry in going from the 0° (planar) to the 90° structure. Complete relaxation of the planarity constraint results in the ring taking up a very shallow boat-type conformation, o 7 C 1 ⋯C 4 = 1.4°, and a change in energy of only 0.05 kcal mol −1 . Evidence for an attractive interaction between the oxygen lone pair and the nearest ring hydrogens is discussed.

An ab initio study of the geometries, anharmonic force fields and fundamental vibration frequencies of cis- and trans-formic acid

Abstract The geometry, harmonic and anharmonic force fields, and fundamental vibration frequencies of cis - and trans -formic acid are studied ab initio in the 4–31G and (9,5) basis sets. For the more stable trans -conformer (i.e., trans with respect to CH and OH) comparisons are made between the predicted and observed anharmonic frequencies, and between the calculated harmonic force constants and those Redington derived from an analysis of experimental data. In the case of the less stable cis -conformer, for which there is as yet little experimental data, the calculations serve to predict values for the fundamental vibrational frequencies.