Bends local modes

Fig. 1.9. Absorption cross section (arbitrary units) of H20 initially prepared in the 04-0) state as a function of the photolysis wavelength A2. The first two quantum numbers specify the excitation of the two stretching modes (using a local mode assignment, see Chapter 13), the minus sign indicates the symmetry with respect to the interchange of the two H atoms, and the third quantum number denotes the bending state. Adapted from Vander Wal, Scott, and Crim (1991) calculations by Weide, Hennig, and Schinke (1989).

Fig. 10.5. Measured rotational state distributions of OH following the dissociation of the three lowest bending states of H2O (open circles). In addition to the bending quanta H20(X) also contains 4 respectively 3 quanta of OH stretching excitation. The local mode nomenclature nm k) is explained in Section 13.2. The total angular momentum is zero in all cases. The filled circles represent the harmonic oscillator approximation defined in the text. Reproduced from Schinke, Vander Wal, Scott, and Crim (1991).

H2O in its electronic ground state is best described by a local mode expansion (Child and Halonen 1984 Child 1985 Halonen 1989). For the purpose of this chapter it suffices to consider a simple two-dimensional model in which the bending angle is frozen at its equilibrium value 104° and the oxygen atom is assumed to be infinitely heavy. For an exact three-dimensional treatment see Bacic, Watt, and Light (1988), for example. The approximate two-dimensional Hamiltonian reads... 

Fig. 14.3. Energy-level diagram of the gerade vibrational states of H20 in the electronic ground state for fixed bending angle a = 104°. The local mode assignment is explained in Section 13.2. N = m + n denotes the total number of OH stretching quanta.

Fig. 14.7. High resolution Raman spectrum for D20 excited with a 171 nm photon. Local mode assignment is used the first two quantum numbers indicate the OH stretching modes, the plus sign indicates the symmetry, and the third number represents the bending quantum number. The latter is zero in all cases and therefore not mentioned in the text. The energies are measured with respect to the 00+0) vibrational ground state. Reproduced from Sension et al. (1990).

In the present paper, we show that it is possible to calculate both vibrational and electronic transitions of H2SO4 with an accuracy that is useful in atmospheric simulations. We calculate the absorption cross sections from the infrared to the vacuum UV region. In Section 2 we describe the vibrational local mode model used to calculate OH-stretching and SOH-bending vibrational transitions as well as their combinations and overtones [42-44]. This model provides frequencies and intensities of the dominant vibrational transitions from the infrared to the visible region. In Section 3 we present vertical excitation energies and oscillator strengths of the electronic transitions calculated with coupled cluster response theory. These coupled cluster calculations provide us with an accurate estimate of the lowest... 

In the present paper we calculate frequencies and intensities of OH-stretching and SOH-bending vibrational transitions as well as their combinations and overtones— the dominant vibrational transitions from 1000 cm to 20000 cm . The vibrational calculation is based on the harmonically coupled anharmonic oscillator (HCAO) local mode model [42-44] combined with ab initio calculated dipole moment functions [50]. This local mode method has been successful in the calculation of OH- and CH-stretching overtone spectra [19,51,52], The local mode parameters, frequency and anharmonicity, are obtained either from the observed experimental transitions or calculated ab initio [53-56]. 

Our local mode model includes the OH-stretching and SOH-bending modes in the vibrational Hamiltonian [58]. The zeroth order Hamiltonian includes the two vibrational modes as uncoupled Morse oscillators according to... 

Acetylene, H-C=C-H, has two identical HCC two-dimensional isotropic local-bender harmonic oscillators. In the normal mode basis set, the bending basis states are specified by four quantum numbers, v4l4V5l5), where mode 4 is the 7r9-symmetry trans-bend and mode 5 is the ttu-symmetry cis-bend. (The normal mode basis states do not have identical harmonic frequencies, u>5 — w4 = 121 cm-1.) There are four pairs of normal mode creation, annihilation operators, two for mode 4, a. d, a.dd, and a. g, a.ig, and two for mode 5, a, 5d,... 

Figure 9.20 The cis-bend and trans-bend normal mode frequencies tune into resonance at Nb 10. Similar to an inhomogeneous L-uncoupling perturbation, de-mixing after the level crossing cannot occur, and the qualitative character of the vibrational modes changes irreversibly from normal to local (from Jacobson and Field, 2000b).

Figure 11 Variation in average vibrational energy (cm1) vs. time (ps) for relaxation from the CH (v = 3) overtone. The energy lost from the initially excited CH stretch, and the energy gain for the other local modes are shown. Total energies are shown for 6 CH stretch, 6 CC stretch, 6 CCH wag, and 3 CCC bend modes.

Figure 5 Averages and standard deviations ( 2o) of selected local mode coordinates of hydrogen peroxide (a) one of the OOH bend angles (b) the other OOH bend angle (c) the central OO stretch. As in Fig. 4, all trajectories have been aligned so that t = 0 is the last inner turning point of the central OO stretch prior to dissociation. A narrow pathway in coordinate space leading to the reaction is again observed.

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