Photodissociation cross section calculation

In particular, Shapiro and others calculated state-to-state photodissociation cross sections from vibrationally excited states of HCN and DCN [58], N2O [59], and O3 [60]. Eor instance, the detailed product-vibrational state distributions and absorption spectra of HCN(DCN) were compared [58]. These results were obtained employing a half-collision approximation, where the photodissociation could be depicted as consisting of two steps, that is, absorption of the photon and the dissociation, as well as an exact numerical integration of the coupled equations. In particular, it was predicted that large isotope effects can be obtained in certain regions of the spectrum by photodissociation of vibrationally excited molecules. 

The calculation of absolute cross sections requires knowledge of the transition dipole function which, unfortunately, is rarely known. Therefore, all examples which we will discuss in this monograph are relative cross sections and the constant C will be mostly ignored in what follows. As stressed in Section 1.4, the total photodissociation cross section is the... 

H(Q) is the nuclear Hamiltonian in the corresponding electronic state at short distances it describes the motion of the complex and at large intermolecular separations it describes the free fragments. The matrix elements (3.1) are needed for the calculation of photodissociation cross sections. In this chapter we discuss numerically exact and approximate methods that are directly based on the solution of (3.2). The complementary time-dependent view follows in the next chapter. 

In this chapter we shall discuss exact and approximate methods for the calculation of photodissociation cross sections that are based on the solution of the time-dependent nuclear Schrodinger equation,... 

The time-independent and time-dependent approaches merely provide different views of the dissociation process and different numerical tools for the calculation of photodissociation cross sections. The time-independent approach is a boundary value problem, i.e., the stationary wavefunction... 

In the time-independent approach one has to calculate all partial cross sections before the total cross section can be evaluated. The partial photodissociation cross sections contain all the desired information and the total cross section can be considered as a less interesting by-product. In the time-dependent approach, on the other hand, one usually first calculates the absorption spectrum by means of the Fourier transformation of the autocorrelation function. The final state distributions for any energy are, in principle, contained in the wavepacket and can be extracted if desired. The time-independent theory favors the state-resolved partial cross sections whereas the time-dependent theory emphasizes the spectrum, i.e., the total absorption cross section. If the spectrum is the main observable, the time-dependent technique is certainly the method of choice. 

The classical approach consists of three parts the solution of the equations of motion (5.1) in the excited electronic state with initial values Qo and Po the weighting of each set of initial values according to the distributions of coordinates and momenta in the electronic ground state before the photon is absorbed and finally the calculation of photodissociation cross sections by averaging over the phase-space. These three points will be discussed in Sections 5.1-5.3. Examples which demonstrate the usefulness and reliability of classical mechanics are presented in Section 5.4. 

Absorption and photodissociation cross sections are calculated within the classical approach by running swarms of individual trajectories on the excited-state PES. Each trajectory contributes to the cross section with a particular weight PM (to) which represents the distribution of all coordinates and all momenta before the vertical transition from the ground to the excited electronic state. P (to) should be a state-specific, quantum mechanical distribution function which reflects, as closely as possible, the initial quantum state (indicated by the superscript i) of the parent molecule before the electronic excitation. The theory pursued in this chapter is actually a hybrid of quantum and classical mechanics the parent molecule in the electronic ground state is treated quantum mechanically while the dynamics in the dissociative state is described by classical mechanics. 

First, we provide the formal definitions of classical absorption and photodissociation cross sections and subsequently we describe a practical way in order to calculate them. 

The partial photodissociation cross sections are calculated by a sum over N trajectories with initial conditions TQtk which are randomly selected from a uniform distribution in the multi-dimensional phase-space,... 

Next we outline the calculation of fully resolved differential photodissociation cross sections for any arbitrary initial rotational state of the parent... 

The calculation of photodissociation cross sections requires the overlap of the continuum wavefunctions with the bound-state wavefunction multiplied by the transition dipole function. Employing for both wave-functions the expansion in terms of the Qj p and utilizing (11.13) leads to radial integrals of the form... 

Theoretically, the calculation of photodissociation cross sections for excited vibrational states proceeds in exactly the same way as for the dissociation of the lowest level. The basic quantities are the photodissociation amplitudes (2.68) with the initial wavefunction being... 

Kidd, I.F. and Balint-Kurti, G.G. (1985). Theoretical calculation of photodissociation cross sections for the Ar-H2 van der Waals complex, J. Chem. Phys. 82, 93-105. 

We use a basis set ij, A I, 5, G, N, F, M) where // is taken to represent different vibrational levels of the ground electronic state Jefferts measurements involved the v = 4 to 8 levels, these being the ones with the optimum populations and photodissociation cross-sections. The matrix elements of each term in (11.79) are now readily calculated. The Fermi contact interaction is found to be diagonal in the chosen basis ... 

Figure 6. The calculated photodissociation cross section for the transit...

Details of the photoexcitation and dissociation of seeded supersonic molecular beams of I2 by 514.5 nm radiation from a CW Ar laser have been provided by Bernstein and co-workers.A number of measurements were made, including LIF, I2 beam attenuation, and I2 TOF distributions as functions of carrier-gas pressure and nozzle temperature. A value for the direct photodissociation cross-section for I2 was determined to be (2.4 0.5) x 10 cm from measurements of the laser-induced beam loss. Use of additional spectroscopic information enabled calculation of the fraction of molecules excited on the basis of a simple model, and comparisons of the degree of excitation for different beam conditions and beam/laser geometries were made. 

Calculation of the photodissociation cross-section of MgH(X 2Q,u = 0 via excitation to the state. Shape... 

Simulation of the i.r. spectrum of ArHD from an accurate calculation of photodissociation cross-sections. Comparison with experiment Laser excitation spectrum of NaArjA H —... 

Close-coupling calculations for the photodissociation cross-sections of CH+ C+pP) + H( S)... 

Balint-Kurti, G.G., Fusti-Molnar, L. and Brown, A. (2001) Photodissociation of HOBr Part II. Calculation of photodissociation cross-sections and photofragment quantum state distributions for the first two UV absorption bands, Phys. Chem. Chem. Phys. 3. 702-710. 

Murtagh, D.P., The O2 Schumann-Runge system New calculations of photodissociation cross sections. Planet Space Sci 36, 819, 1988. 

Figure 7.4 a) Potential energy curves of the bound X2II and A2S+ and dissociative 12E-, 12A, and B2E+ states of OH. b) Calculated photodissociation cross sections, ct(E), from X2II v =0 (from Van Dishoek and Dalgamo, 1983)... 

The photodissociation study of radicals, especially polyatomic radicals, remains essentially an unexplored research area. Detailed state-to-state photodissociation cross sections for radicals in the UV and VUV provide challenges not only for dynamical calculations, but also for ab initio quantum chemical studies. The measurements of absolute UV and VUV photodissociation cross sections of organosulfur radicals are relevant to the modeling of atmospheric sulfur chemistry. 

In 5.1, we describe how the lOSA is used to calculate photodissociation cross sections. Particular care has to be taken in averaging over the orientation-angle dependent scattering wavefunction using the bending wavefunction of the ground state. To do this we apply, to the reaction problem, a procedure developed by Segev and Shapiro for the vibrational predissociation of Van der Waals complexes [ 51]. Then in 5.2, we present our calculations of the photoabsorption spectrum for the H2O photodissociation (VII). 

Here we describe the essential features of the application of the lOSA to reactive photodissociation. More details of the approach will be published elsewhere [ 53]. We wish to calculate the photodissociation cross sections I discussed in Section 1. For most problems, the transition dipole moment surface i will not be known. It is unlikely that will have a significant effect as it is not a highly oscillatory function like the scattering wavefunction, nor a highly localized function like the bound state. Thus, it should be a reasonable approximation to compute... 

The mathematical tools needed to calculate photodissociation cross sections were first presented by Shapiro, and an exact treatment of rotational predissociation in the Ar-N2 system was subsequently performed by Beswick and Shapiro. These calculations clearly show how the theory can account for both symmetric and asymmetric resonance line shapes as well as overlapping nonisolated resonance lines. The theory has also been applied to the Ar-H2 and Ar-HD system for which benchmark calculations were performed. Several other methods of computing the exact bound-continuum integrals needed in the evaluation of the expression for the photodissociation cross section have also been presented (see refs 7 and 13). 

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