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Notes: 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, to 117.5 cm−1.

Notes: 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 system.

Notes: 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(ring). 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 quadruple excitation) Møller–Plesset perturbation theory (MP2, MP3, MP4SDTQ) and configuration interaction theory with all single and double excitation (CISD) levels using basis sets from minimal double zeta to triple zeta plus diffuse and polarized functions. These theoretical models of the B2u force field all provide poor predictions for the three criteria: fundamental frequency accuracy 2%–3%; isotopic frequency shift accuracy 10%–300%; two-photon cross section accuracy 300%–1200% with the sense of isotopic effects on two-photon cross sections in some cases incorrectly predicted. The MP2 calculations, even using the largest basis set, are incapable of meeting any of the criteria, hence higher order approaches to the correlation problem are required. The inadequacies in frequencies, isotopic shifts, and mode forms arise because both the diagonal and off-diagonal force constants are not predicted by ab initio calculations with the sufficient 10−2 mdyn/A(ring) accuracy required for reasonably accurate frequency and intensity predictions. A feature of the ab initio calculations is that carbon and hydrogen displacement phases for the b2u modes are unchanged by the basis set size or correlation level. The unmeasured 13C6D6ν14 two-photon cross section and iosotope frequency shift from 12C6H6 are predicted to be larger than for any of the other D6h symmetry benzenes (∼30% higher than in C6H6 for the former and 72 cm−1 for the latter) by the benchmark field of part II.

Notes: 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(ring), respectively, obtained from the 13C6H6 experimental intensities and the complete experimental force field of Part II. Using these quantities and the L−1 matrix (Table III), dipole moment gradients for C6H6 become ∂μ/∂Q018a =+0.298, ∂μ/∂Q019a =+0.371, and ∂μ/∂Q020a =+0.814 D/A(ring). Mode decomposition matrices expressing normal modes of benzene in terms of isotopically labeled molecule modes have been used to definitively determine the C6H6 dipole gradient signs. The signs are in agreement with theoretical calculations. The D6 isotopic labeling effect on C6H6 ν18 intensity provides a sensitive test of E1u force field quality and reveals the inadequacy of present theoretical force field approaches. Ab initio atomic polar tensors have been obtained both at the HF level, using several basis sets up to the 6-311+G(d,p) and at theMP2 level up to the 6-31+G(d) basis set. The dipole derivative for the CC stretch is highly sensitive to both basis set (particularly diffuse functions) and correlation effects. Qualitative CH and CC stretching dipole derivative and intensity predictions by the MP2/6-31+G(d) calculation are encouraging (i.e., within 15% of the experimental values). However, the same calculation yields 20% and 45% errors for the CH bending dipole derivative and fundamental intensity, respectively.

Notes: Fully-relaxed model ab initio calculations at Hartree–Fock/6–31G(d,p) and Møller–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(ring)) 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 poorly simulated by ab initio calculations.

Notes: 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 bifurcated B2u force constant problem in ground state benzene. The approach utilizes the contribution of harmonic C–C–H bending motions to the two-photon tensor controlling the 1501 and 1401 vibronic cross sections. This requires knowledge of the sign of the hydrogen motion term in the tensor. However, large anharmonic effects coupling the two b2u modes mask the small harmonic hydrogen contribution.