Ali G. Ozkabak

The benzene ground state potential surface. I. Fundamental frequencies for the planar vibrations

The accuracy of vapor phase vibrational data has been improved for all 12 deuterium‐labeled benzenes and for 13C12C5H6 and 13C6H6. Many vapor phase fundamental frequencies are observed for the first time. Precise isotopic frequency/splitting patterns for ν1, ν18, and ν19 have been obtained. Isotope induced harmonic mode mixing matrices are given for all 14 labeled benzenes and used to provide detailed description of the fundamental bands observed in the spectra. These descriptions provide numerous reassignments for the fundamental bands, particularily in low symmetry deuterium benzenes. The matrices show that some skeletal modes, such as ν1, gain CH stretching character as a result of deuterium labeling, providing a rationalization for the increased anharmonicity observed in recent jet experiments for C6D6. In addition, a reassessment of Fermi resonance gives 3072.3 cm−1 for the unperturbed frequency (correction +24 cm−1) for the e1u mode ν20 in C6H6 refining the CH local mode anharmonic constant, 2xii, t...

The benzene ground state potential surface. II. Harmonic force field for the planar vibrations

A complete harmonic force field in terms of nonredundant coordinates has been generated from experimental frequencies for D6h, D3h, and D2h isotopically labeled benzenes and degenerate mode Coriolis constants predicting broken symmetry labeled benzene frequencies to ±0.1% and Coriolis constants to ±0.01 units, on the average. Exact solutions have been obtained for the six E1u force constants from D6h symmetry frequency data with the inclusion of 13C6H6 information. Some modes (e.g., the e2g mode ν8, in Wilson notation) are significantly altered from previous experimental force field predictions, rationalizing unclearly understood vibronic features of phosphorescence and two‐photon spectra. A conundrum regarding the e1u Coriolis constant for ν18 (Wilson notation) is identified: no harmonic force field is capable of predicting the reported experimental magnitudes for this constant for both C6H6 and C6D6. The Pulay et al. scaled ab initio force field is in qualitative agreement with the experimental field fo...

Multiphoton ionization photoelectron spectroscopy of phenol: Vibrational frequencies and harmonic force field for the 2B1 cation

A molecular beam of phenol, cooled by a supersonic expansion, is crossed at right angles by the output of a pulsed frequency‐doubled dye laser, causing 1+1 resonance enhanced multiphoton ionization. The kinetic energy of the resulting photoelectrons is determined as a function of laser wavelength with time‐of‐flight analysis, permitting the assignment of 11 vibrational frequencies for the 2B1 phenol‐h6 cation and ten vibrational frequencies for phenol‐d5. Of these, all but the lowest frequency one in each case are in‐plane vibrations of which phenol has a total of 19. An approximate harmonic force field for the in‐plane modes of the phenol cation is derived along with its associated frequencies and mode forms. This in turn facilitates the vibrational analysis. Analogous force field calculations have been carried out on the ground (1A1) and first excited (1B2) states of the neutral parent, permitting conclusions to be reached concerning bonding changes upon removal of an electron from the phenol electron s...

Effect of skeletal relaxation on the methyl torsion potential in acetaldehyde

Fully‐relaxed model ab initio calculations at Hartree–Fock/6–31G(d,p) and Mo/ller–Plesset (MP2)/6–31G(d,p) levels for acetaldehyde methyl conformers indicate significant skeletal flexing (e.g., the CH3 –C bond length changes by 0.006 A) and methyl hydrogen folding. Thirteen methyl conformer energies at 15° intervals are used to assess the magnitudes of the torsional potential function expansion terms. Only two terms V3=373.8 and V6=3.4 cm−1 (both significantly different from those obtained from microwave and infrared analyses) are found to be important. These calculations clearly show that relaxation during methyl rotation (i.e., skeletal flexing and methyl hydrogen folding) is an important determinant of the torsional potential. Energy levels obtained from internal rotation potentials which include flexing simulate infrared torsional fundamental frequencies in CH3CHO and CD3CHO to within 1–2 cm−1 of the experimental values. In the absence of relaxation infrared torsional fundamental frequencies are poorl...

The benzene ground state potential surface. V. Criteria for theoretical modeling of the B2u harmonic force field

We demonstrate that fundamental frequencies provide a poor criterion of the benzene B2u force field accuracy and that two‐photon cross sections of the b2u fundamental bands in the 1B2u↔1A1g electronic transition, which can be directly related to skeletal displacement magnitudes in the two b2u modes, provide an insightful physical criterion of harmonic force field quality. Another valid criterion for force field quality is isotopic frequency shifts combined with the fundamental frequencies. The frequency‐generated force field of part II accurately predicts the measured cross sections and isotopic frequency shifts, indicating that the B2u force constants are known to ±0.01 mdyn/A. These constants are used as benchmark quantities for calibrating theoretically modeled force fields.A systematic series of ab initio B2u harmonic force fields for ground state benzene using theoretical geometries are generated at Hartree–Fock and correlated second, third, and fourth order (with single, double, triple, and quadrupl...

The benzene ground state potential surface. IV: Discrimination between multiple E1u force field solutions through infrared intensities

Accurate values for integrated intensities of the infrared active 13C6H6 fundamentals, ν18, ν19, ν20, and ν11 (Wilson notation) have been measured and redetermined for ν18 and ν19 in C6H6 and C6D6. The 13C6H6 intensities are I18=6.52±0.15, I19=12.60±0.20, I20=55.6±1, and I11=74.6±3 km/mol. Unlike C6H6 and C6D6, interfering transitions in 13C6H6 are minor and these intensities can be used as a critical test for theoretical predictions of atomic polar tensors. The ν18 intensities in C6H6 and C6D6 (7.48±0.15 and 7.09±0.14 km/mol, respectively) and the ν19 intensity in C6D6 (2.51±0.12 km/mol) are measured to be substantially lower than the literature values. The qualitative intensity pattern of benzene in‐plane fundamentals uniquely discriminate among the eight possible real E1u force field solutions obtained from frequency information alone. Isotopically invariant dipole moment derivatives, ∂μ/∂S18a, ∂μ/∂S19a, and ∂μ/∂S20a are 0.494±0.005, 0.395±0.016, and 0.770±0.008 D/A, respectively, obtained from the 13C...

The benzene ground state potential surface. III. Analysis of b2u vibrational mode anharmonicity through two‐photon intensity

The 1501/1401 vibronic two‐photon cross section ratios are reported for a series of isotopically labeled benzenes in the A(1B2u)←X(1A1g) electronic transition. Predictions derived from the B2u force field are found to be in close agreement with the measured ratios. These ratios are shown to provide an excellent test of the B2u force field and mode forms as evidenced by the large variation over D6h labeled benzenes. In C6H6 the 1501/1401 cross section ratio is measured as 0.249±0.008 (equivalent to 0.180 for the theoretically testable ratio: 1501/1401[〈1‖Q14‖0〉/〈1‖ Q15‖0〉]2). The corresponding ratio in 13 C6H6 is 0.44±0.04 (equivalent to 0.36). The 13% disparity found between the measured and predicted C6H6 ratio (i.e., 0.206) is attributed to anharmonic coupling between the b2u modes: 2χ15,15=−9, χ14,15=4, and 2χ14,14=−4 cm−1. Two‐photon intensities are proven to be useful in determining anharmonic interactions. The relatively small effects of the hydrogen motion provide an approach for solving the bifu...

Skeletal flexing during methyl rotation in small dimethyl molecules

Abstract Hartree—Fock/6-31G(d,p) calculations have been made for methyl rotation torsional potentials in dimethyl ether, acetone, and thioacetone using two theoretical models: the rigid-frame model (only methyls rotate, the other geometry parameters remaining fixed) and a fully relaxed model (where the molecular frame is allowed to flex during methyl rotations). These conclude that steric hindrance generated by methyl rotation leads ot substantial skeletal flexing, principally in the C—X—C angle. This undulation is at largest in dimethyl ether, 5°, compared to 3° for acetone and thioacetone. The potential parameters show very large differences between the two models (e.g. in dimethyl ether, skeletal flexing relieving steric hindrance reduces the V 3 term by 500 cm −1 , lowering V eff by 30%). There are large differences in the torsional frequencies predicted by the two models, with the fully relaxed model closely simulating measured fundamental and overtone frequencies as well as - d 6 isotope effects in all three molecules.

An ab initio model for methyl torsional potentials incorporating skeletal flexing

Abstract An ab initio model for methyl torsional rotation is developed through geometry optimised conformer energy calculations. All of the nuclear motions (i.e. skeletal flexing and hydrogen folding motions) consequent to methyl rotation are revealed and their effects (i.e. interactions between torsion and all other vibrations) are incorporated into a fully relaxed methyl torsional potential function which is expressed only in terms of rotational coordinates. The fully relaxed methyl torsional potentials are generated for six prototype one- and two-methyl molecules: acetone, thioacetone, dimethyl ether, acetaldehyde, propene, and isobutene. Systematic ab initio geometry optimisation calculations are made at HF/6-3lG(d,p) and MP2/6-31G(d,p) levels. Energy levels obtained from the internal rotation potentials simulate measured torsional fundamental frequencies in the six prototype molecules to within 1–3 cm −1 of the experimental values, with the exception of the ethylenic molecules, propene and isobutene (which are within 5–10 cm −1 ). The results indicate that significant skeletal flexing (i.e. in the CH 3 -C bond length in general, and in the CH 3 -X-CH 3 angle for dimethyl molecules) accompanies methyl torsional rotation in all six molecules. The calculations clearly show that these relaxations during methyl rotation are important determinants for the torsional potential shape and height.

Harmonic two-photon intensity sum rule for benzene b2u modes

Abstract A harmonic two-photon cross section sum rule for benzene b 2u modes (ν 14 and ν 15 ) in the A 1 B 2u ←X 1 A 1g transition is derived. An approximate (but accurate) form of this rule based on skeletal mode displacements is used to obtain absorptivity values for C 6 H 6 14 1 0 (6.3×10 −50 cm 4 s mol −1 photon −1 ) and 15 1 0 (1.6×10 −50 cm 4 s mol −1 photon −1 ) from the measured absorptivity ratio, δ ↑↑ (15)/δ ↑↑ (14) and from the measured value of 14 0 1 . We also report the sum-rule-predicted hot and cold band absolute absorptivities in the other D 6h benzenes, C 6 D 6 , 13 C 6 H 6 and 13 C 6 D 6 .