O. Atabek

Dynamics of ozone photoabsorption: A theoretical study of the Chappuis band

The first two excited singlet states of ozone are discussed in light of recent ab initio MRD‐CI calculations. In the asymmetric pathway for O2+O fragmentation, the two 1 1A2 and 1 1B1 states undergo an avoided crossing resulting in the C 1A‘ and D 1A‘ states. The D 1A‘ state has bound vibrational levels in the Franck–Condon region while the C 1A‘ is repulsive (towards O2+O fragmentation) in that area and is found to possess a local minimum away from the Franck–Condon area at small bond angles. A one‐dimensional cut along the dissociation reaction coordinate was extracted from the three‐dimensional calculated potential surfaces. Quantum mechanical calculations of the absorption spectrum based on these one‐dimensional ab initio potentials and of the corresponding ab initio transition moments were undertaken. The present work assigns the distinct features of the Chappuis band to the bound levels of the D 1A‘ state superimposed on the C 1A‘ state continuum as an alternative interpretation of the second absorp...

Raman emission as a probe for photodissociation dynamics

A time‐dependent wave packet propagation method based on the split operator technique is used to describe the complete history of photodissociation. Three successive steps of the dynamics are discussed by setting the analogy with the energy dependent version of the quantum theory: namely the absorption, the Raman emission, and the fragments internal state analysis. Informations concerning early (absorption), intermediate (Raman emission), and long time dynamics (fragments internal distribution) are related to the parameters of the initial ground and final dissociative potential energy surfaces and to the excitation laser wavelength. The photodissociation of ICN(C 1A’) is taken as a numerical illustration and comparisons are presented with previous calculations carried in the energy frame.

Three‐dimensional analytical model for the photodissociation of symmetric triatomics. Absorption and fluorescence spectra of ozone

A full three‐dimensional analytical Franck–Condon analysis is presented for dissociative spectroscopies of a symmetric triatomic system. Formulas derived for harmonic potential surfaces are applied to the theoretical calculation of ozone absorption spectrum in the Hartley continuum as well as to the determination of its fluorescence (or resonance Raman) spectrum when submitted to 266 nm wavelength excitation. The Hartley absorption line shape describing the 1 1B2←X 1A1 photodissociation is reproduced within very good agreement with experiment. The role of the so‐called Duschinsky effect originating from the coupling of bending and stretching motions in the excited state is analyzed and comparisons are presented with previous more simple models neglecting this coupling. The influence of temperature is also taken into account through calculations dealing with vibrationally excited species. As for the photoemission fluorescence spectrum carrying a rich information content, the behavior is successfully predic...

Split operator method for the nonadiabatic (J=0) bound states and (A←X) absorption spectrum of NO2

A split operator three-dimensional wave packet propagation method is adapted for the determination of the bound states and absorption band shape of NO2 molecule presenting a conical intersection between its ground X 2A1 and first excited A 2B2 electronic states. The numerical task, basically resting on a Fourier transform methodology, may present interesting advantages over matrix diagonalization techniques. The calculations of bound levels over a wide energy range and the absorption (A 2B2←X 2A1) band shape, extending up to 40 000 cm−1, are put on an equal footing by a nonadiabatic three-dimensional wave packet propagation using available ab initio potential energy surfaces. Good agreement is obtained when comparing the calculated absorption spectrum to experimental data in a low resolution limit. The position and amplitude of the band shape are determined within only 2 and 3% of relative error, respectively, the total width being still overestimated by about 15%. An analysis of the causes of errors is p...

A test of the rotational infinite order sudden approximation in molecular fragmentation

A quantum mechanical close‐coupling calculation is presented for predissociation of a triatomic molecule and the results are compared with the infinite order sudden approximation for rotational motion (RIOSA). The calculations are performed for a model system which mimics the predissociation of the zero‐point level of N2O+(A). It is shown that for the case treated here the infinite order sudden approximation obtained by setting all the rotational energies equal to zero gives poor results. Good agreement between RIOSA and exact calculations is obtained by setting them equal to the average rotational energy in the fragments. The relationship between RIOSA as applied to full collisions and half‐collisions is also discussed.

A quantitative theory-versus-experiment comparison for the intense laser dissociation of H2+.

A detailed theory-versus-experiment comparison is worked out for

Hemiquantal time dependent calculation of the absorption spectrum of a photodissociating triatomic

{\mathrm{H}}_{2}^{+}

Three‐dimensional quantum calculation of the vibrational energy levels of ozone

intense laser dissociation, based on angularly resolved photodissociation spectra recently recorded in Figgers group. As opposite to other experimental setups, it is an electric discharge (and not an optical excitation) that prepares the molecular ion, with the advantage for the theoretical approach, to neglect without loss of accuracy, the otherwise important ionization-dissociation competition. Abel transformation relates the dissociation probability starting from a single rovibrational state to the probability of observing a hydrogen atom at a given pixel of the detector plate. Some statistics on initial rovibrational distributions, together with a spatial averaging over laser focus area, lead to photofragments kinetic spectra, with well separated peaks attributed to single vibrational levels. An excellent theory-versus-experiment agreement is reached not only for the kinetic spectra, but also for the angular distributions of fragments originating from two different vibrational levels resulting into more or less alignment. Some characteristic features can be interpreted in terms of basic mechanisms such as bond softening or vibrational trapping.

Three‐dimensional analytical model for isotope effects in the photofragmentation of triatomic molecules

A half‐collision process is described within a hemiquantal time dependent model to calculate the absorption line shape. The photodissociation of ICN in a collinear geometry serves as an illustrative example with the ‘‘light’’ CN motion treated quantum mechanically, whereas the ‘‘heavy’’ I–CN motion is treated classically. The emphasis is put on (i) the way to introduce the Wigner distribution which appears to be the equivalent of the classical density matrix, and (ii) the choice of the initial positions and momenta in the sampling of trajectories. The so‐obtained converged results compare, within good accuracy, with the full quantal ones. Both conceptually and computationally, the hemiquantal approach appears as an interesting alternative to the full quantum wave packet calculation.

Collapse of transmissivity in a triple barrier

The Fox–Goodwin propagator associated with an iterative matching procedure is used for the exact quantum mechanical calculation of the vibrational‐rotational energy levels of a triatomic molecule. The method starts with the specification of a potential energy surface monitoring the relative motion of the atoms and utilizes the well‐known close coupled equations technique of molecular scattering theory formulated in a body‐fixed reference frame. The number of equations is optimized by the choice of some judicious local basis. Accurate values for the lowest energy eigenvalues obtained for ozone molecule in its fundamental electronic state and corresponding to zero total angular momentum are presented and compared with results arising from variational and spectral methods. The method seems to be an accurate tool not only for bound states calculations but also for resonances occuring in photodissociation processes.