ALBERT

Notes: The motion of the probability density of the harmonic and anharmonic quantum oscillators under IR-multiphoton excitation with a classical laser field is studied both by means of exact solutions and in the quasiresonant and Floquet approximations. The validity of the quasiresonant approximation has been studied for the first time in an infinite level problem (harmonic oscillator) without truncation. Different régimes of quasiclassical motion of the harmonic and anharmonic oscillator and nonclassical spreading of the probability density with regular and irregular dynamics are identified.

Notes: The rovibrational spectrum of trideutero-methane has been measured at resolutions mostly close to the Doppler limit on an interferometric Fourier transform spectrometer from the lowest fundamental vibration to high overtones of the CH stretching vibration (wave numbers from 900 to 12 000 cm−1). The CH chromophore spectrum is fully assigned and interpreted by means of the tridiagonal Fermi resonance Hamiltonian for the coupled CH stretching and bending vibrations. The Hamiltonian predicts and also fits the visible spectrum up to 19 000 cm−1 measured by Scherer et al., Perry et al., and Campargue et al. The effective tridiagonal Hamiltonian is derived ab initio by means of MRD-CI and full CI calculations of the potential surface of methane, a variational vibrational calculation in a normal coordinate subspace of the coupled CH stretching and bending motions and an approximate similarity transformation to tridiagonal form. Fits of the experimental results by the tridiagonal and the variational Hamiltonian lead to equivalent spectroscopic constants. A careful experimental estimate of the main Fermi resonance coupling constant gives k'sbb (approximately-equal-to)(30±15) cm−1 in agreement with the best current ab initio result (31 cm−1). The ab initio potential in polar normal coordinates agrees with the potential derived from spectroscopic data covering an energy range of about 220 kJ mol−1 (more than half the dissociation energy). Good predictions are obtained for the parameters of the effective Hamiltonian, the spectral patterns, intensity distributions, and rotational constants in the Fermi resonance polyads. Three alternative interpretations of the parameters of the effective Hamiltonian are investigated and rejected on the basis of the available experimental and ab initio data. The results and conclusions are discussed in relation to intramolecular vibrational redistribution on the subpicosecond time scale and the recombination–dissociation kinetics of methane.

Notes: The Fermi-resonance overtone spectra of the CH chromophore up to about 18 000 cm−1 are evaluated by variational vibrational calculations for the CHX3 molecules trideuteromethane (CHD3), trifluoromethane (CHF3), chloroform (CHCl3) and 1,1,1,3,3,3-hexafluoro-2-trifluoromethylpropane [(CF3)3CH]. Using appropriate model potential functions in a normal coordinate subspace, one can derive parameters for the CH chromophore potential and empirical dipole moment functions. For CHD3 and CHF3 ab initio (SCF-CI and vibrational variational) calculations are presented, the results of which compare well with the experiments and for CHD3 also with previous (MRD-CI) ab initio results. For all cases an accurate similarity transformation to the equivalent tridiagonal form of the effective hamiltonian can be made and the corresponding spectroscopic parameters agree with previous results. Comparison is also made with results from an internal coordinate model Hamiltonian.

Notes: The band strengths of fundamentals (N=1) and overtones (up to N=6) of the strongly coupled CH stretching and bending vibrations in CHD3 and CHF3 are calculated using high level ab initio (SCF-CI) dipole moment functions and potential surfaces in one and two (three) dimensions. The calculations are performed in approximate normal coordinate and internal coordinate subspaces, the former giving generally superior results. The overall prediction of relative and absolute intensities ranging over many orders of magnitude is often accurate to within a factor of 2, but not to within experimental accuracy. Different dipole model functions and potential surfaces are investigated and an empirical adjustment of the dipole function to experiment is proposed for CHF3. The comparison of experimental and ab initio overtone intensities for the Fermi resonance system is discussed in some detail, as well as the importance of the results for IR spectroscopy and IR multiphoton excitation.

Notes: The ν2+2ν3 combination band of 12CH4 near 7510 cm−1 was studied with the recently introduced technique of cavity ring-down spectroscopy employing a cw-diode laser in a pulsed supersonic slit jet expansion and with Doppler-limited Fourier-transform infrared spectroscopy at room temperature. ν2+2ν3 is the strongest absorption band in the high-wave-number region of the N=2.5 icosad of methane. First assignments of the combination band are provided. The vibrational origin of ν2+2ν3 at 7510.3378±0.0010 cm−1, the integrated band strength G=(1.3±0.2)×10−4 pm2 and the vibrational transition moment |μν|=(1.0±0.1)×10−3 D have been determined. The values represent benchmarks to test effective vibrational Hamiltonians and ab initio calculations for methane. Although an isolated band analysis was possible at low J-values, the influence of strong perturbations becomes evident at higher rotational excitation. The F1-component of ν2+2ν3 interacting by a strong Coriolis resonance with the IR-active F2-component appears to be a dominant perturber. © 2002 American Institute of Physics.

Notes: We present a multiconfiguration linear response approach to electroweak quantum chemistry including effects from the parity violating weak nuclear force. Compared to our previous configuration interaction singles-restricted Hartree–Fock (CIS-RHF) approach [A. Bakasov, T. K. Ha, and M. Quack, J. Chem. Phys. 109, 7263 (1998)], the parity violating potential Epv is introduced by the linear response function and by solving the linear response equations in a direct iterative manner. Calculations are carried out within the multiconfiguration linear response approximation (MCLR) and its special cases, the configuration interaction approach (CI) and the random phase approximation (RPA). The systematic approach presented here, provides a systematic check and improvement upon various approximations used in the calculation of Epv. Extensive results are obtained for hydrogen peroxide at the CISDT (CI singles, doubles and triples) and CISDTQ (CI singles, doubles, triples, and quadruples) as well as at the complete active space self-consistent-field–linear response (CASSCF–LR) level. We compare to carlier results at the CIS-RHF level and confirm the order of magnitude increase in Epv reported earlier as compared to the widely used single determinant excitation-restricted Hartree–Fock (SDE-RHF) method. The new approach overcomes previous limitations for calculating Epv with biradicaloid structures such as twisted ethylene, for which numerical results are presented. This allows us to calculate Epv for a similar unsaturated system such as allene derivatives, which may be of experimental interest. © 2000 American Institute of Physics.

Notes: The rovibrational spectra of deuterobromochlorofluoromethane (CDBrClF) were measured at intermediate (0.1 cm−1) and high resolution (0.0024 cm−1 full bandwidth, half-maximum) by interferometric Fourier transform infrared spectroscopy in the range from the far infrared at 200 cm−1 to the near infrared (12 000 cm−1) covering all the fundamentals and CD stretching overtones up to polyad N=5. The spectra are completely analyzed in terms of their vibrational assignments to fundamentals, combinations and overtones. At high excitation the analysis reveals the dominant anharmonic coupling between four high frequency vibrational modes; the CD stretching (ν1), two CD bending (ν2,ν3), and the CF stretching mode (ν4). The analysis is carried out using effective model Hamiltonians including three and four vibrational degrees of freedom. We also present vibrational variational calculations on a grid in a four-dimensional normal coordinate subspace. The potential energy and the dipole moment function are calculated ab initio on this grid using self-consistent field second order Møller–Plesset perturbation theory (MP2). Experimental and theoretical results for band positions and integrated intensities as well as effective spectroscopic parameters are found to be in good agreement. The important anharmonic coupling between the CD chromophore and the CF stretching vibration can be described by an effective cubic Fermi resonance coupling constant ksff′(approximate)(50±10) cm−1, which leads to intramolecular vibrational redistribution between the CD and CF chromophores on the femtosecond time scale. Time dependent intramolecular vibrational redistribution processes in CDBrClF are derived in various representations, including time dependent probability densities ("wave packets") in coordinate space and finally time dependent entropy. © 2000 American Institute of Physics.

Notes: We report a new mechanism for intramolecular vibrational redistribution (IVR) in CF3CHFI which couples the CH chromophore vibrations through a strong Fermi resonance to the formal CF stretching normal mode (a heavy atom frame mode) involving the trans F-atom across the CC bond. The analysis is made possible by comparing spectroscopic results with extensive ab initio calculations of the vibrational fundamental and overtone spectra in the range extending to 12 000 cm−1. Potential energy and electric dipole moment hypersurfaces are calculated ab initio by second order Møller–Plesset perturbation theory (MP2) on a grid involving the CH stretching, two CH bending modes and one high frequency CF stretching normal mode. The potentials are scaled to obtain agreement between the experimental spectrum and the theoretical spectrum calculated by a discrete variable representation technique on this grid. Both spectra are then analyzed in terms of three-dimensional (3D) and four-dimensional (4D) effective vibrational Hamiltonians including Fermi- and Darling–Dennison-type resonances between the CH stretching mode and the CH bending modes and the CF stretching mode. The interaction between the CH modes and the CF mode is clearly visible in the experimental and calculated (4D) spectra. The effective Fermi resonance coupling constants [ksff′(similar, equals)(40±10) cm−1 and ksaf′(similar, equals)(55±10) cm−1] coupling the CH and CF mode subspaces are of about the same magnitude as the intra-CH chromophore Fermi resonances (ksaa′(similar, equals)56 cm−1 and ksbb′(similar, equals)42 cm−1, coupling CH stretching mode "s" with the two CH bending modes "a" and "b"). The chiral, pseudo-Cs symmetry breaking coupling (ksab′(similar, equals)11 cm−1) is complemented by an equally strong coupling through the CF mode (ksfb′(similar, equals)15 cm−1). It is demonstrated that low order perturbation theoretical analysis using potential constants from a polynomial expansion to represent effective coupling constants gives inadequate results with discrepancies ranging about from factors of 2–5. Time dependent population and wave packet analysis shows essentially complete IVR among the CH chromophore modes within about 100 fs, the 3D and 4D evolutions being similar up to about that time. At longer times of about 250 fs, there is substantial excitation of the CF stretching mode (with initial pure CH stretching excitation). The 4D treatment is then essential for a correct description of the dynamics. © 2000 American Institute of Physics.

Notes: A simple interpretation of the decomposition of the densities of states in the classical mechanical limit according to the regular representation of the permutation group and—under certain circumstances—the molecular symmetry group is presented. The relationship between recent results on densities of states of a given point group symmetry species and previous results based upon the molecular symmetry group is established. Some restrictions are discussed as well as the definition and application of symmetry numbers for the densities of states and partition functions of nonrigid and rigid molecules and transition states.