Internal Rotation Potential Energy Research Articles

Relationship between the Relative Dielectric Constant and the Monomer Sequence of Acrylonitrile in Rubber.

Acrylonitrile-butadiene rubbers (NBRs) have a lower glass transition temperature (Tg) and a higher dielectric constant than other rubbers. To understand how a low Tg and a high dielectric constant are compatible, we focused on the acrylonitrile (AN) monomer sequence in rubber and synthesized random and alternating copolymers to evaluate the effect of the sequence. The AN monomer sequence dependence of the relative dielectric constant was investigated by the C–N stretching vibration of the nitrile group through Fourier transform infrared spectroscopy and internal rotation potential energy measurements around the C–C bond within the nitrile group based on dimer model calculations. The alternating copolymers, including NBR, showed a higher dielectric constant than random copolymers. The alternating copolymer shifted from ∼2243 cm–1 for polyAN to ∼2236 cm–1 for NBRs, while the random copolymer only shifted to ∼2239 cm–1. The peak of the C–N stretching vibration was correlated with the AN sequence. The sequence dependence of the shift can be explained by the C–N bond length calculation. The internal rotation potential energy between gauche and trans of the NBR model was the lowest, indicating that the NBR main chain is flexible and that AN in the main chain rotates easily. Therefore, NBR has a high dielectric constant and a low Tg because of the presence of an alternating sequence and the flexibility of the NBR main chain.

Theoretical investigation of intramolecular π-type hydrogen bonding and internal rotation of 2-cyclopropen-1-ol, 2-cyclopropen-1-thiol and 2-cyclopropen-1-amine

ABSTRACTTheoretical computations utilising both CCSD and MP2 methods and the cc-pVTZ basis set have been carried out to determine the structures of several conformations as well as the internal rotation potential energy functions for 2-cyclopropen-1-ol, 2-cyclopropen-1-thiol and 2-cyclopropen-1-amine. The energies and wavefunctions for these potential functions have also been computed. Each of these molecules has an energy minimum corresponding to a conformation with intramolecular π-type hydrogen bonding. The π bonding stabilisation is about 2.3 kcal/mole for the alcohol, 2.1 kcal/mole for the thiol, and about 2.5 kcal/mole for the amine. The results for the thiol demonstrate a rare example of intramolecular π-type hydrogen bonding. The calculated O–H, S–H, N–H, and C=C stretching frequencies have also been compared for the conformations with and without the π-type hydrogen bonding. The C=C stretching frequency is substantially lower in all cases for the hydrogen bonded conformers.

Structural and thermochemical properties of methyl ethyl sulfide alcohols: HOCH2SCH2CH3, CH3SCH(OH)CH3, CH3SCH2CH2OH, and radicals corresponding to loss of H atom

AbstractSulfide alkoxy radicals are important intermediates during the partial oxidation of alkyl sulfides in atmospheric chemistry and in combustion. The atmospheric reaction sequence to formation of the alkoxy radicals includes (1) initial reaction with OH to create a radical on a carbon site, (2) the carbon radical then associates with 3O2 to form a peroxy radical, and (3) an NO radical reacts with the peroxy radical to form an alkoxy radical (RO•) plus NO2. This study determines structural parameters, internal rotor potentials, bond dissociation energies, and thermochemical properties (ΔfH°, S°, and Cp(T)) of 3 corresponding alcohols HOCH2SCH2CH3, CH3SCH(OH)CH3, and CH3SCH2CH2OH of methyl ethyl sulfides studied in order to characterize the thermochemistry of the respective alkoxy radicals. The lowest energy molecular structures were calculated using the B3LYP density functional level of theory with the 6‐311G(2d,d,p) basis set. Standard enthalpies of formation (ΔfH°298) for the radicals and their parent molecules were calculated using B3LYP/6‐31 + G(2d,p), CBS‐QB3, M062x/6‐311 + g(2d,p), and G3MP2B3 methods. Isodesmic reactions were used to determine ∆fH° values. Internal rotation potential energy diagrams and rotation barriers were investigated using the B3LYP/6‐31 + G(d,p) level theory. The contributions for S°298 and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation based on the structures and vibrational frequencies obtained by CBS‐QB3 calculations, with contributions from torsion frequencies replaced by internal rotor contributions. Group additivity and hydrogen bond increment values were developed for estimating properties of structurally similar and larger sulfur‐containing peroxide molecules and their radicals.

Structures and thermochemistry of methyl ethyl sulfide and its hydroperoxides: HOOCH2SCH2CH3, CH3SCH(OOH)CH3, CH3SCH2CH2OOH, and radicals

AbstractHydroperoxides and the corresponding peroxy radicals are important intermediates during the partial oxidation of methyl ethyl sulfide (CH3SCH2CH3) in both atmospheric chemistry and in combustion. Structural parameters, internal rotor potentials, bond dissociation energies, and thermochemical properties (ΔHfo, So and Cp(T)) of 3 corresponding hydroperoxides CH2(OOH)SCH2CH3, CH3SCH(OOH)CH3, CH3SCH2CH2OOH of methyl ethyl sulfides, and the radicals formed via loss of a hydrogen atom are important to understanding the oxidation reactions of MES. The lowest energy molecular structures were identified using the density functional B3LYP/6‐311G(2d,d,p) level of theory. Standard enthalpies of formation (ΔHfo298) for the radicals and their parent molecules were calculated using the density functional B3LYP/6‐31G(d,p), B3LYP/6‐31 + G(2d,p), and the composite CBS‐QB3 ab initio methods. Isodesmic reactions were used to determine ∆Hfo values. Internal rotation potential energy diagrams and rotation barriers were investigated using the B3LYP/6‐31G(d,p) level theory. Contributions for So298 and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation based on the structures and vibrational frequencies obtained by the density functional calculations, with contributions from torsion frequencies replaced by internal rotor contributions. The recommended values for enthalpies of formation of the most stable conformers of CH3SCH2CH2, CH2(OOH)SCH2CH3, CH3SCH(OOH)CH3, and CH3SCH2CH2OOH are −14.0, −33.0, −37.2, and −32.7 kcal/mol, respectively. Group additivity values were developed for estimating properties of structurally similar and larger sulfur‐containing peroxides. Groups for use in group additivity estimation of sulfur peroxide thermochemical properties were developed.

Structural and thermochemical studies on CH3SCH2CHO, CH3CH2SCHO, CH3SC(═O)CH3, and radicals corresponding to loss of H atom

AbstractCH3SCH2CHO, CH3CH2SCHO, and CH3SC(═O)CH3 are intermediates during the partial oxidation of CH3SCH2CH3 in the atmosphere and in combustion processes. Thermochemical properties (ΔHfo, So and Cp(T)), structures, internal rotor potentials, and C─H bond dissociation energies of the parent molecules and their radicals formed after loss of a hydrogen atom are of value in understanding the oxidation processes of methyl ethyl sulfide. The lowest energy molecular structures were initially determined using the density functional B3LYP/6‐311G/(2d,d,p) level of theory. Standard enthalpies of formation (ΔHfo298) for the radicals and their parent molecules were calculated using the density functional B3LYP/6‐31G(d,p), B3LYP/6‐31 + G(2d,p), and the composite CBS‐QB3 ab initio methods using isodesmic reactions. Internal rotation potential energy diagrams and internal rotation barriers were investigated using B3LYP/6‐31 + G(d,p) level calculations. The contributions for So298 and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation on the basis of the structures and vibrational frequencies obtained by the density functional calculations, with contributions from torsion frequencies replaced by internal rotor contributions from the method of Pitzer‐Gwinn. The recommended values for enthalpies of formation of the most stable conformers of CH3SCH2CHO, CH3CH2SCHO, and CH3SC(═O)CH3 are −34.6 ± 0.8, −42.4 ± 1.2, and ‐49.7 ± 0.8 kcal/mol, respectively. The structural and thermochemical data presented for CH3SCH2CHO, CH3CH2SCHO, and CH3SC(═O)CH3 and their radicals are of value in understanding the mechanism and kinetics of methyl ethyl sulfide oxidation under varied temperatures and pressures. Group additivity values are developed for estimating properties of structurally similar, larger sulfur‐containing compounds.

Internal Rotation of Methylcyclopropane and Related Molecules: Comparison of Experiment and Theory.

The internal rotation about the single bond connecting a cyclopropyl ring to a CH3, SiH3, GeH3, NH2, SH, or OH group was investigated. Both CCSD/cc-pVTZ and MP2/cc-pVTZ ab initio calculations were performed to predict the structures of these molecules and their internal rotation potential energy functions in terms of angles of rotation. The barriers to internal rotation for the CH3, SiH3, and GeH3 molecules from the calculations agree well with the experimental ones, within -11% to +1% for CCSD/cc-pVTZ and -4% to +9% for MP2/cc-pVTZ. Comparisons between theory and experiment were also performed for propylene oxide and propylene sulfide, and the agreements were very good. Theoretical calculations were performed to compute the internal rotation potential energy function for cyclopropanol, and these were used to guide the determination of a potential function based on experimental data. This molecule has two equivalent synclinal (gauche) conformers with an estimated barrier of 759 cm(-1) (9.1 kJ/mol) between them. The minima are at internal rotation angles of the OH group of 109° and 251°. The theoretical potential functions for cyclopropanethiol and cyclopropylamine were also calculated, and these agree reasonably well with previous experimental studies.

Observation of Evidence for the π*-σ* Hyperconjugation in the S1 State of o-, m-, and p-Fluorotoluenes by Double-Resonance Infrared Spectroscopy.

Drastic changes of the methyl internal rotation potential energy functions upon the electronic excitation have been reported for o- and m-fluorotolunes [ Okuyama , K. , Mikami , N. , and Ito , M. J. Phys. Chem. 1985 , 89 , 5617 - 5625 ], and their physical origin has been attributed to the π*-σ* hyperconjugation. To observe direct evidence of the π*-σ* hyperconjugation, double-resonance infrared spectroscopy was carried out in the CH stretching vibrational region in both the S0 and S1 states of jet-cooled o-, m-, and p-fluorotoluenes. In the spectra of both o- and m-fluorotoluenes, some of the methyl CH bands were red-shifted upon the electronic excitation while the residual CH bands stayed in the same frequency region. The normal-mode analysis demonstrated that the shift behavior correlates to the relative conformation between the methyl CH bond and the phenyl ring plane. This conformation-dependent methyl CH bond weakening clearly supports the presence of the π*-σ* hyperconjugation in o- and m-fluorotoluenes. The similar red-shift of the methyl CH bands upon the electronic excitation was seen also in p-fluorotoluene though the magnitude of the shift was much smaller. The mechanism of its internal rotation potential energy behavior, however, can be different from those of the o- and m-isomers.

Research Progress on Preparation Methods of PMIA Fiber

PMIA is a functional fiber with superior heat-resistance, flame resistance, high temperature dimensional stability and electrical insulation. In PMIA crystal structure, there exist hydrogen bonds between two planes in the crystal and they are arranged in grid. The strong interactions between hydrogen bonds result in a very stable chemical structure of PMIA. Owing to lower internal rotation potential energy than PPTA, PMIA molecular chains are flexible structures and its elastic modulus is in the same level as other flexible macromolecules. In this paper, the structure character of molecular chain and performance of PMIA have been introduced. Additionally, the common used polymerization techniques for PMIA have been described in detail. These synthesis techniques include low-temperature solution polymerization, interfacial polymerization and emulsion polymerization.

Theoretical studies of the conformers of rac-6,6′,7,7′-tetramethoxy-1,1′,2,2′,3,3′,4,4′-octahydro-1,1′-bisisoquinoline and its N-acyl and N-alkyl derivatives

The low-energy structures and internal rotation about the C 1- C 1 ′ bridging bond of rac-6,6′,7,7′-tetramethoxy-1,1′,2,2′,3,3′,4,4′-octahydro-1,1′-bisisoquinoline, its N-alkyl and N-acyl derivatives were studied using the DFT B3LYP method. The global minimum ( gauche) of 1,1′-bisisoquinoline was found to be different from the reported crystal structure ( trans), which indicated the important of environment on the compound conformation and hence it catalytic potential. Our calculations also indicated that the global minima of 1,1′-bisisoquinoline and its derivatives are dynamically stable along their internal rotation potential energy surface. The stable conformations of the tetrahydroisoquinoline groups of N-acyl derivatives are different from their parent molecule and there is a dependency of their structures on the N-substituents for N-acyl derivative.

Electron diffraction and quantum chemical study of the structure and internal rotation in nitroethane

Studies of the molecular structure and spectra of the lower nitroalkanes are complicated due to hindered internal rotation of the nitro group around the C N bond. In the present work, the structure of nitroethane molecule is determined from electron diffraction (ED) data supplemented by results of quantum chemical calculations within the model accounting for the large-amplitude motions and anharmonicity of vibrations in the rigid fragments. Quantum chemical calculations at the MP2, QCISD and B3LYP levels of theory result in contradictory conclusions regarding the location of the minimum of internal rotation potential energy function and potential barrier height. In the ED analysis, parameters of equilibrium geometry were refined simultaneously with scaling of quantum chemical force matrix aimed at fitting experimental vibrational frequencies. The data processing has shown the minimum of the potential energy function of internal rotation of NO 2 group corresponding to the syn-C molecular configuration with torsional angle τ(C C N O) = 0°. Rotation of the nitro group was found to be slightly hindered, with potential energy barrier height in the range of 50–200 cm −1 (with the most probable value near 120 cm −1). The refined parameters of equilibrium molecular configuration are the following: r e(C C) = 1.509(3) Å, r e(C N) = 1.503(3) Å, r e(N O) = 1.213(3) and 1.215(3) Å, ∠ e(C C N) = 112.3(9)°, ∠ e(O N O) = 125.9(5)°.

DFT investigation of nitrenium ions derived from metabolism of antitumor 2-(4-aminophenyl)benzothiazoles

Ab initio molecular orbital computation has been performed to study the electronic structure, substituent and solvent effects on the singlet–triplet gaps of a series of nitrenium ions. DFT calculations at the B3LYP/6-311++G** level of theory predict that, the nitrenium ions derived from the metabolism of the antitumor 2-(4-aminophenyl)benzothiazoles exist in the ground singlet state. The preferential stabilization of the singlet state relative to the triplet is due to the transfer of charge density from the phenyl ring to formally electron deficient nitrogen atom. Calculations in solution were carried out using the PCM model. Solvent–solute interaction energies were estimated and reflect a considerable net stabilization of the triplet species at the PCM model. Fourier transform analysis of the internal rotation potential energy function, around the exocyclic bond (C 4–N), has been performed for niternium ions studied. The magnitudes and origin of the potential energy barriers have been discussed.

Calculation of the τ dependence of the vibration–internal rotation–overall rotation interactions in CH3OH from molecular structure and molecular dynamics

The Guan and Quade theory for vibration-large-amplitude internal-motion-rotation interactions has been applied to the internal rotation problem in CH(3)OH. Through the molecular dynamics, the cos 3tau and sin 3tau dependence of the torsional-rotational coefficients in the effective Hamiltonian have been calculated from molecular structure. The internal rotation coordinate tau(') for the vibrationally distorted molecule is shown to have the necessary threefold symmetry for all values of tau('). For the methyl deformation modes, the vibrational dependence of the internal rotation potential energy is shown to have a threefold symmetry. The S(t) and S(t)S(t) dependence of the inertia tensor and Coriolis coupling coefficients has been developed in terms of curvilinear internal coordinates. The T transformation separating rotation from vibrations in zeroth order is then applied, the kinetic-energy tensor inverted to momentum space, and finally the effective torsion-rotation coefficients are calculated by Van Vleck perturbation theory. When compared to the empirical results, the kinetic-energy contributions to the cos 3tau and sin 3tau dependence of the coefficients are as follows: 54% of P(a)(2) is accounted for, 28% of P(a)P(b), 16% of P(a)P(c), and 91% of the asymmetry. The calculation is inadequate to account for the P(b)(2),P(c)(2), and P(b)P(c) coefficients, ranging from factors of 20-70, even with the incorrect sign for some of the terms. Anharmonic force contributions from the vibrations have not been used in the calculation since these forces are not known at this time.

Internal rotation in peroxynitrous acid (ONOOH)

Using higher levels of wave-function-based electronic structure theory than previously applied, as well as density functional theory (B-LYP and B3-LYP functionals), all theoretical models conclude that three ONOOH conformers are stationary point minima, in disagreement with some of the previous studies that we survey. In order of increasing energy, these are the cis-cis, cis-perp, and trans-perp conformers. Basis sets including diffuse functions seem to be needed to obtain a qualitatively correct representation of the internal rotation potential energy surface at higher levels of theory. Internal rotation about the peroxide bond involving the cis-cis, cis-gauche transition structure (TS), cis-perp, and cis-trans TS conformers is studied in detail. To help ascertain the relative stability of the cis-perp conformer, multireference configuration interaction energy calculations are carried out, and rule of thumb estimates of multireference character in the ground-state wave functions of the ONOOH conformers are considered. CCSD(T)/aug-cc-pVTZ physical properties (geometries, rotational constants, electric dipole moments, harmonic vibrational frequencies, and infrared intensities) are compared with the analogous experimental data wherever possible, and also with density functional theory. Where such experimental data are nonexistent, the CCSD(T) and B3-LYP results are useful representations. For example, the electric dipole moment |mu(e)| of the cis-cis conformer is predicted to be 0.97+/-0.03 D. CCSD(T) energies, extrapolated to the aug-cc-pVNZ limit, are employed in isodesmic reaction schemes to derive zero Kelvin heats of formation and bond dissociation energies of the ONOOH stationary point minima. In agreement with recent gas-phase experiments, the peroxide bond dissociation energies of the cis-cis and trans-perp conformers are calculated as 19.3+/-0.4 and 16.0+/-0.4 kcalmol, respectively. The lowest energy cis-cis conformer is less stable than nitric acid by 28.1+/-0.4 kcalmol at 0 K.

DFT critical points of the internal rotation potential energy surface and infrared spectra of the [ 1H], [ 2H] 2,5-pyrazinedicarboxamide

The 2,5-pyrazinedicarboxamide (PDCA), and its 2H isotopic derivative were prepared by synthesis, their infrared spectra being recorded and assigned. Within the characterization scheme, structures and spectroscopy of these compounds, in this work we present DFT quantum chemical calculations of the critical points of the internal rotation potential energy surface (in phase gas as a simplified modelization of condensed phase) gaussian 98 package has been used with the basis set 6-311G** and B3P86 correlation exchange functional. The most stable conformation of the isolated molecule corresponds to that in what both amide groups are in the plane of the pyrazine ring, presenting intermolecular hydrogen bridges between carboxylic oxygens and contiguous hydrogens of the pyrazine ring. The molecule in this conformation shows C 2 h symmetry. Two series of critical points have been calculated: (i) those coming from the rotation of one amide group around C–C bond, keeping the other in the most stable planar conformation; and (ii) the same rotation, but keeping the other amide group in position of secondary minimum conformation of the previous series.

Internal rotations in the difluorobutadiene and tetrafluorobutadiene molecules: a DFT B3LYP study

Internal rotations around the central C–C bond in the ( t, t)-1,4-DFBD (difluorobutadiene), ( c, c)-1,4-DFBD, 2,3-DFBD, ( t, t)-1,2,3,4-TFBD (tetrafluorobutadiene), ( c, c)-1,2,3,4-TFBD, and 1,1,4,4-TFBD molecules were studied at the DFT B3LYP/6-311+G(d,p) level of theory. The calculated internal rotation potential energy curves (PECs) for the six molecules have the same skeleton: along the PEC there exist s-trans and s-gauche (at θ=37–55°) minima and two transition states (at θ=90–116° and at s-cis conformations). The relative energies and optimized geometries of the s-trans and s-gauche conformers and transition states are reported. The s-trans conformers are the lower-energy conformers for all the molecules except ( t, t)-1,2,3,4-TFBD, for which the s-gauche conformer is slightly more stable than the s-trans conformer. The barrier heights for the s-gauche→s-trans processes are predicted to be 1.8–2.9 kcal mol −1. Internal rotations in the cations of the six molecules were also studied at the same level. For each of the cations, two PECs were calculated: the 2B PEC starting at the s-trans conformation and the 2A PEC starting at the s-cis conformation. For each of the cations the s-trans conformer is lower in energy than the s-cis conformer, and, with the θ value, the energy monotonously decreases along the 2B PEC and monotonously increases along the 2A PEC. The s-trans conformers of ( c, c)-1,4-DFBD and ( c, c)-1,2,3,4-TFBD are predicted to be more stable than those of ( t, t)-1,4-DFBD and ( t, t)-1,2,3,4-TFBD, respectively, which supports the cis-effect for 1,4-DFBD suggested by the experimental workers. The s-trans conformer of 2,3-DFBD is slightly more stable than those of ( c, c)- and ( t, t)-1,4-DFBD, while the s-trans conformer of 2,3-DFBD + is much higher in energy than those of ( c, c)- and ( t, t)-1,4-DFBD +. The s-trans conformers of 1,1,4,4-TFBD and 1,1,4,4-TFBD + are much more stable than those of ( c, c)- and ( t, t)-1,2,3,4-TFBD and ( c, c)- and ( t, t)-1,2,3,4-TFBD +, respectively.

Internal rotations of vinylcyclopropane, cyclopropanecarboxaldehyde, and cyclopropanecarboxylic acid: a DFT B3LYP study

The internal rotations around the C–C linkage in vinylcyclopropane (VCP), cyclopropanecarboxaldehyde (CPAL), and cyclopropanecarboxylic acid have been studied by performing the DFT B3LYP calculations with triple split-valence basis sets including polarization and diffuse functions. The general features of the B3LYP internal rotation potential energy curves are in line with experiment. The discrepancies between the B3LYP and experimental relative energy values for the stationary points along the curves are in general within 0.7kcalmol−1. Compared with available experimental data the B3LYP calculations predict accurate values for the bond lengths and bond angles in the stationary-point structures, but less accurate values for the torsion angles in the transition state structure of CPAL and the gauche conformer of VCP. The conjugative interaction between the quasi-π Walsh orbit (ea) of CP and the π-orbit of the substituents in the three molecules has been discussed in relation to the features of the potential energy curves and the variations of geometric parameters with the rotational angles. The previous orbital interaction analysis for conjugation in s-trans VCP has been examined at ab initio HF level, and no (ea+π∗) orbital is found in the electronic structure. The ea–π orbital interaction in s-trans VCP corresponds to the two-orbital four-electron case, but it does not cause a net destabilizing consequence due to the involvement of the π∗ orbital.

Density function of 3?-azido-3?-deoxythymidine

The internal rotation potential energy curve around the glycosidic bond in 3′-azido-3′- deoxythymidine (AZT) molecule, an HIV-1 reverse transcriptase inhibitor, is calculated by using density functional B3LYP method and a 3–21G basis set. For the stationary points along the internal rotation energy curve, the B3LYP/6–31G* full geometry optimization and frequency analysis calculations are performed. Along the curve there are two energy minima, one of which corresponds to a structure having a North conformation (P= 85.3°) and in the anti range (x= −129.1°) and the +sc range (y= 62.1°), which is consistent with the conformation of AZT in the AZT 5′- triphosphate bound to HIV RT.

An empirically corrected quantum mechanical potential energy curve of internal rotation of acryloyl fluoride, CH2=CH-CF=O

The geometrical parameters of acryloyl fluoride were optimized completely at the MP2/6-31G* computational level for 17 points on the internal rotation potential energy (IRPE) curve for rotation around the formal single carbon–carbon bond. The expansion coefficients of the reduced rotational constant function F(φ) and the four, five, and six-term expansions of the IRPE function,[Formula: see text]were obtained from these data. The theoretical IRPE functions were then refined using only the experimental torsional transition frequencies in both the s-trans and s-cis wells. The IRPE functions obtained are compared with those in the literature, calculated at lower levels of theory in both the rigid and nonrigid rotation approximations. The best representation of the refined IRPE function is given by the six-term expansion with V1 = 71.7, V2 = 1944.8, V3 = 113.0, V4 = −122.8, V5 = −8.7, and V6 = 12.5 cm−1, respectively. From this IRPE function, one correctly predicts the s-trans conformer to be more stable with ΔH0 = 168 cm−1. The barrier to rotation from the s-trans to the s-cis positions, ΔH#, is 2048 cm−1 at 88° from the s-trans well. The advantages of using the nonrigid rotation approximation, based on high-quality quantum mechanical calculations that include correlation effects, to construct the effective IRPE function for molecules are emphasized.

P-fluorotoluene. I. Methyl (CH3 and CD3) internal rotation in the S1 and S states

Supersonic jet S1-S0 spectroscopy (resonance-enhanced multiphoton ionization, fluorescence excitation, and dispersed single vibronic level fluorescence) has been used to determine the S1 and S0 internal rotation energy level structure of p-fluorotoluene with a CD3 methyl rotor as well as to extend observations of the CH3 rotor structure. The observed rotor energy levels 2≤m≤8 for both species in both states are fit by a simple sixfold hindered rotor Hamiltonian for which the rotor inertial constants B and the internal rotation potential energy barriers V6 are evaluated. V6 may be obtained independently from B by observations of ΔE3, the observed splitting of the 3a″1 and 3a″2 rotor levels. Numerical solution of the wave equation shows that the perturbation theory relationship V6=−2ΔE3 holds well for any reasonable B value. Correspondingly, the B constant may be obtained from other level energies without appreciable sensitivity to (reasonably) assumed barrier heights. Earlier microwave and S1-S0 fluorescence results are combined with the present work to produce a set of preferred values for these constants. The values in cm−1 for the S0 state are B=5.46 (2.82) and V6=−4.77 (−4.77) for CH3 (CD3) rotors. The S1 values are B=4.90 (2.54) and V6=−33.0 (−25.2). The 20% barrier height reduction occurring on transformation from a CH3 to a CD3 rotor is similar to that observed in other systems. Calculation implies that the staggered conformer is the minimum energy configuration for both electronic states. Many of the S1-S0 rotor transitions are forbidden, and a discussion is given of induced intensity mechanisms that involve coupling of internal rotation to overall rotation or coupling of internal rotation to electronic motion. Substantial energy-level perturbations often occur for states with m≥5. A survey of B values and hindered rotation constants for 30 species with methyl rotors attached to aromatic rings reveals some general correlations.

Effect of molecular geometry relaxation on the potential energy function of internal rotation

Theoretical internal rotation potential energy (IRPE) curves for glyoxal were obtained by complete optimization of its geometrical parameters at the RHF/6-31G, RHF/6-31G., RHF/6-31G.., and MP2/6-31G. levels (14 to 16 points along each curve). The corresponding IRPE functions, 2V=Σ 6 n=1 (1-cos nO)), where O is the torsional angle, were calculated for each set of points and refined using experimental torsional transition frequencies in the trans and cis wells. This work corroborates the previous assignments of the torsional 0-11, 0-12, 0-13, and 0-14 transitions in the experimental spectrum of the trans well