George R. De Maré

Ab initio study of rotational isomerism in 1,3-butadiene. Effect 21 of geometry optimization and basis set size on the barriers to rotation and on the stable rotamers☆

Abstract Analytic gradient (force) methods at the STO-3G, 3-21G, 6-31G and 6-31G* basis set levels have been used to optimize the geometry of 1,3-butadiene at each critical point (minima, maxima) in the torsional potential energy curves for rotation about the central CC bond (dihedral angle θ). Each CHCH2 group was constrained planar and the effect of this geometry constraint was investigated by additional STO-3G and 3-21G optimizations. The planar trans conformation (θ = 180°) is predicted to be most stable, in agreement with experiment. Small variations in the predicted relative energy (ΔE) and in the position of the transition state (TS) for rotation from the trans position are observed: ΔE = 23.5, 23.6, 25.9 and 25.4 kJ mol−1 and θ = 95.0, 101.8, 101.6 and 101.5° for the STO-3G, 3-21G, 6-31G and 6-31G* basis set optimizations, respectively. The STO-3G optimizations predict an energy minimum for the planar cis conformation (θ = 0°), 7.7 kJ mol−1 above the trans minimum. All three larger basis sets predict a maximum for the cis structure, with small gauche—gauche rotational barriers (2.0–4.1 kJ mol−1, the largest value corresponding to optimizations with the 3-21G basis set and non-planar CHCH2 groups). The gauche minimum is predicted to lie 11.3–13.2 kJ mol−1 above the trans, at θs in the range 35.5–38.5°. The positions and relative energies of the critical points in the torsional potential energy curves predicted by the 3-21G, 6-31G and 6-31G* optimizations are in good agreement with those proposed by Durig, et al. [1] to reproduce the Raman overtone spectrum of 1,3-butadiene for a gauche—trans rotamer equilibrium. A series of 6-31G** computations with the optimized geometries from the smaller basis sets indicates that optimization at the 6-31G** basis level would give results similar to those obtained with the above three split-valence basis sets.

Rotational barriers and stable rotamers in 1,3-butadiene, acrolein and glyoxal☆

Abstract Analytic gradient (Force) methods (ref.1) have been used to optimize completely the geometries of the title compounds at the minima (stable rotamers) and maxima (transition states, TS) in the torsional potential energy curves (TPEC) for rotation about the single C  C bonds. Computations were performed with the minimal STO-3G, split-valence 3–21G and polarized 6–31GX basis sets for 1,3-butadiene and glyoxal, and with only the STO-3G and 3–21G basis sets for acrolein. Whereas complete geometry optimization of 1,3-butadiene along the TPEC with the STO-3G basis led to the prediction of a cis - trans rotamer equilibrium (ref.2), complete optimizations with both the 3–21G and 6–31GX basis sets give a maximum at the cis position and minima at the trans and gauche conformations. Complete geometry optimization of acrolein reveals only cis and trans minima with the TS at 88.2 (STO-3G) or 91.6(3–21G) degrees from the cis. Surprisingly the cis and trans conformers are predicted to be almost equivalent in energy. For glyoxal the TS is revealed to be nearer to the cis than to the trans conformation. Except for 1,3-butadiene, the barrier height to rotation from the trans position, obtained with the STO-3G basis, is much smaller than that obtained with the larger basis sets.

Ab initio study of neutral O2, SO, S2, C2H2 and their mono- and dications

For the twelve title species, the bond order according to Mayers definition, the Mulliken overlap population and the force constants are determined using the minimal STO-3G, split-valence 3-21G and 6-31G* (5d) basis sets. In general all these properties increase with increasing formal charge for each diatomic species. In contrast, the internuclear distances decrease with increasing formal charge. These findings indicate that the outer electrons in the three neutral diatomic species reside in antibonding orbitals; removing them results in triple bonds in the dications which are all predicted to be stable in their ground states in spite of the electrostatic repulsion. The best predictions for the unknown internuclear distances in the ionic ground states are: re(O22+) = 1.046; re(SO1+) = 1.411; re(SO2+) = 1.359; re (S21+) = 1.800 and re(S22+) =1.732 A. For acetylene, the behaviour on removal of the electrons is opposite to that observed for the diatomics: the bond order, overlap population and force constants all decrease with increasing formal charge. Both the acetylenic cation and dication are predicted to be stable, linear species in their electronic ground states with re(CC) = 1.247 and re(CH) = 1.076 A for the monocation and re(CC) = 1.326 and re(CH) = 1.116 A for the triplet dication. Using the SCF optimized structures, the total energies for the species were computed at the CISD and CISD-Q levels. These lead to predicted second ionization potentials of about 24.1, 19.1, 16.6 and 19.9 eV for O2, SO, S2 and C2H2, respectively.

Theoretical study of the nitrous acid conformers: Comparison of theoretical and experimental structures, relative energies, barrier to rotation and vibrational frequencies

The experimental and theoretical literature data for the trans and cis conformers of nitrous acid (HONO) are augmented by additional Hartree-Fock (HF), Moller-Plesset second-order perturbation (MP2), Moller-Plesset fourth-order perturbation (MP4) and density functional (B3LYP) computations. The latter yield optimized theoretical parameters and vibrational frequencies that are closest to the best experimental values. Adding diffuse functions to a given basis set lowers the energy of the trans conformer relative to the cis at all levels of theory utilized in this work. There have been no convincing assignments of infrared (IR) spectral bands to the O-N-O (nu3) and H-O-N (nu5) bending modes of cis -HONO, both of which are predicted to have very low intensities. Although IR spectral features about 40 cm-1 below nu3 for trans-HONO has been tentatively assigned to nu3 of cis- HONO, calculations with unscaled and scaled quantum-mechanical force fields invert this order. If these predictions are correct, nu3 of c...

Predictive Abilities of Scaled Quantum Mechanical Molecular Force Fields: Application to 1,3-Butadiene

The positions of some IR bands of the s-trans-1,3-butadiene-h6 and -1,1,2-d3 isotopomers in the gas phase have been measured using a Brucker IFS 120 HR spectrometer with a resolution of 2 cm−1. The structural parameters of the s-trans- and s-gauche-1,3-butadiene conformers were optimized completely at the MP2/6-31G* theoretical level and their MP2/6-31G*//MP2/6-31G* quantum mechanical force fields (QMFFs) were calculated. Using only the experimental vibrational frequencies of s-trans-1,3-butadiene-h6 the QMFF of the s-trans conformer was corrected by Pulays scaling method (eight scale factors were involved). The scaled QMFF was used to calculate the mean vibrational amplitudes and the Coriolis coupling constants of s-trans-1,3-butadiene-h6 and the vibrational frequencies of 12 of its deuterated isotopomers. The set of scale factors obtained for correction of the s-trans QMFF was transferred to the QMFF of the s-gauche conformer. Its theoretical vibrational spectrum and those of some deuterated and C13 isotopomers were calculated. The ability of this scaling approach (transferring of scale factors) to predict the vibrational frequencies of rotational conformers and their isotopomers, as well as other molecular characteristics, and to permit detection of perturbations of the experimental bands are discussed.

Ab initio study of rotational isomerism in vinylcyclopropane

Abstract The geometry of vinylcyclopropane has been completely optimized at each critical point by analytic gradient (force) methods at the minimal STO-3G and the split-valence 3-21G basis set levels. The geometries obtained for the various critical points have been used to generate potential energy curves for vinyl group rotation within the rigid rotor approximation. Comparison of these curves clearly demonstrates the importance of complete geometry optimization. The potential energy curve for vinyl group rotation, generated with the s-trans STO-3G optimized geometry, predicts secondary gauche minima which are an artifact of the rigid rotor approximation. With complete geometry optimization along the curve, the STO- 3G basis set computations predict only s-trans and s-cis minima. In contrast, the complete optimizations with the 3-21G basis set, in agreement with experiment, predict a three-fold rotational contour with two equivalent gauche minima. These minima lie 6.86 kJ mol−1 above th e s-trans minimum. The computed barrier to rotation for the s-trans → gauche interconversion is 13.3 kJ mol−1. The electric dipole moment computed with the 3-21G basis for the s-trans 3-21G optimized geometry is 0.446 D or about 10% less than the experimental value.

All-trans- and t,T,t,C,t,T,t-deca-1,3,5,7,9-Pentaenes: Ab Initio Structures, Vibrational Analyses, and Some Regularities in the Series of Related Molecules

Total geometry optimization and calculation of the force constants for all-transand t,T,t,C,t,T,tdeca-1,3,5,7,9-pentaene were carried out at the ab initio, HF/6-31G level. The HF/6-31G//HF/ 6-31G force fields were modified using empirical scale factors transferred from trans-buta-1,3-diene augmented by an additional scale factor for the central formal carbon-carbon double bond coordinates (determined previously for all-trans-hexa-1,3,5-triene). The total number of scale factors was seven. The vibrational problems for both decapentaenes were solved using the respective scaled HF/6-31G//HF/6-31G force field. Infrared intensities and Raman activities were calculated from the unscaled HF/6-31G//HF/6-31G force fields. Complete assignment of all the fundamental vibrational frequencies is given. Geometrical parameters, vibrational frequencies and force constants are compared with the corresponding values of buta-1,3-diene, hexa-1,3,5-triene and octa-1,3,5,7-tetraene. Regularities in the properties of this molecular series are discussed. Special attention is given to the possibility of using the vibrational spectra for detection of distortions from the regular trans structure of these oligoenes.

Conformations of triplet carbonyl compounds: Formaldehyde, acetaldehyde, propionaldehyde and acetone

Abstract A conformational study on the lowest triplet states of formaldehyde, acetaldehyde, propionaldehyde and acetone has been done using a minimal basis set, within the unrestricted Hartree—Fock framework. For the C 3 H 6 O species, the energy hypersurfaces ( E θ 1 , θ 2 , θ 3 ) were generated, where energy is a function of the methyl rotations (θ 1 , θ 2 ) and CO out-of-plane bending for acetone, and a function of methyl rotation (θ 1 ), C 2 H 5 C rotation (θ 2 ) and CHO out-of-plane deformation (θ 3 ) for propionaldehyde. The analysis of the hypersurface equations revealed the location and relative energies of the critical points (minima, first and second order saddle points as well as maxima): the barriers to inversion at the carbonyl group were 2.7 kcal mol −1 for acetone and 4.2 kcal mol −1 for propionaldehyde. Partial geometry optimization reduced these barriers to 2.5 and 2.4 kcal mol −1 respectively. For comparison, both the pyramidal minimum and planar saddle point for the inversion of triplet formaldehyde and acetaldehyde were totally optimized; the resultant barriers were 2.0 kcal mol −1 and 2.3 kcal mol −1 , respectively. The barrier to rotation about the bond to the α-carbon was 1.1 kcal mol −1 for pyramidal acetone, 1.0 for acetaldehyde and ranged from 0.8 to 1.8 kcal mol −1 for the various propionaldehyde conformers.

Quantum yields of the Hg 6(3P1 photosensitized isomerizations of cis- and trans-butene-2

Abstract The quantum yields of the cis → trans and trans → cis Hg 6( 3 P 1 ) photosensitized isomerization of butene-2 are both 0.50 ± 0.02 for butene-2 pressures ≥ 30 torr. The formation of excited mercury—butene-2 complexes, invoked by Tsunashima and Sato to explain an apparent loss of incident photons, does not occur. The quantum yields determined by Yang for hydrogen formation in the Hg 6( 3 P 1 ) photosensitization of ethylene seem to be in error.

Philosophy of scaling the quantum mechanical molecular force field versus philosophy of solving the inverse vibrational problem

Abstract The peculiarities characterising the traditional approach used in calculational vibrational spectroscopy and the approach based on using scaled quantum mechanical force fields are considered. Some results on the determination of the equilibrium geometry of benzene in both the harmonic approximation and in the approximation taking into account the kinematic and dynamic anharmonicity corrections by solving the inverse vibrational problem are discussed. Using the quantum mechanical force fields of the C 2 F 6 molecule, calculated at three different theoretical levels as an example, the results of the determination of scale factors by different mathematical techniques are compared.