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

Abstract

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/Å. 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) Mo/ller–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/Å 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.

Molecular applications of analytical gradient approach for the improved virtual orbital-complete active space configuration interaction method

“…Extensive experimental studies of the S 0 and S 1 vibrational modes are also well documented, [49][50][51][52][53][54][55][56] and several calculations are available for the S 0 and S 1 state harmonic force fields and vibrational spectra. [57][58][59][60][61][62][63] Recent advances in high resolution spectroscopy have enabled the assignment of the S 0 and S 1 state vibrational frequencies of benzene more precisely and, therefore, a rigorous comparison between theory and experiment provides a stringent assessment for the accuracy of ab initio many-body methods.…”

Theoretical prediction of the vibrational spectrum of naphthalene in the first excited singlet state

“…Force fields derived from high quality Hartree-Fock (HF) calculations yield ground state frequencies that are usually up to 20% too high. 2 - 6 Goodman,Ozkabak,and Wiberg 7 showed in an extensive study on benzene that this overestimation is in part reduced if the basis set is increased, but even with very extended basis sets the calculated frequencies are still too high. Correlation corrections beyond MP4 are most likely necessary to reach the accuracy of 0.0 1 mdynl A for the force constants that is considered as necessary for a clear assignment of experimental data.…”

Ab initio vibrational state calculations with a quartic force field: Applications to H2CO, C2H4, CH3OH, CH3CCH, and C6H6

“…This is a known problem caused by the MP2 method. 53,54 The harmonic frequency for this mode has been estimated by Martin, Taylor and Lee 54 to be 1326 cm Ϫ1 using CCSD͑T͒ with atomic natural orbital basis sets of ͓4s3 p2d1 f /4s2p͔ quality. This is very close to the experimental value, 1310 cm…”