Dissociation via a single excited electronic state is the exception rather than the rule. The remarkable success with which all experimental results for the dissociation of H2O, for example, have been reproduced by rigorous calculations without any adjustable parameter rests mainly upon the fact that only one electronic state is involved (Engel et al. 1992). Many other photodissociation processes, however, proceed via two or even more electronic states with the possibility of transitions from one state to another. Figure 15.1 illustrates a common situation: the photon excites the molecule from the electronic ground state (index 0) to a dipole-allowed upper state (index 1) which further out in the exit channel interacts with a second electronic state (index 2). The latter may be dipole-forbidden and therefore not directly accessible by the photon. The corresponding diabatic potentials V1 and V2 cross at some internuclear distance Rc. In the proximity of this point the coupling between the two electronic states, which was ignored throughout all of the preceding chapters, can be large with the consequence that a transition from state 1 to state 2 and/or vice versa becomes possible (radiationless transition, electronic quenching). Electronic transitions manifest the break-down of the Born-Oppenheimer approximation, i.e., the motion of the electrons and the heavy particles can no longer be adiabatically separated.

Let us imagine a wavepacket starting in the Franck-Condon region on potential V1 When it reaches the crossing region it splits under the influence of the coupling into two parts.

In indirect photodissociation a potential barrier or some other dynamical constraint hinders immediate dissociation of the complex that the light pulse has created in the excited electronic state. Figure 7.1 shows a typical one-dimensional example. The barrier may be due to an avoided crossing with another electronic state. The potential energy surface (PES) of the S1 state of CH3ONO (Figure 1.11) is a typical two-dimensional example. Depending on the efficiency of internal energy redistribution between the various degrees of freedom the lifetime of the complex may range from a few to several thousand internal vibrational periods, in contrast to direct processes where the fragmentation finishes in less than one internal period. Because of the long lifetime, the final state distributions of the photofragments no longer reflect the initial coordinate distribution of the parent molecule in the ground electronic state like they do in direct dissociation. The coupling between the various modes in the complex gradually erases the memory of the initial state before the molecule finally breaks apart.

The main characteristics of indirect dissociation are resonances in the time-independent picture and recurrences in the time-dependent approach. Resonances and recurrences are the two sides of one coin; they reveal the same dynamical information but provide different explanations and points of view. To begin this chapter we discuss in Section 7.1, on a qualitative level, indirect photodissociation of a one-dimensional system. A more quantitative analysis follows in Section 7.2. The time dependent and the time-independent views of indirect photodissociation are outlined and illustrated in Sections 7.3 and 7.4, respectively, with emphasis on vibrational excitation of the NO moiety in the photodissociation of CH3ONO(S1).

So far we have consistently assumed — with only very few exceptions — that the photodissociation starts from the lowest vibrational state of the parent molecule. The corresponding bound-state wavefunction is typically a narrow multi-dimensional Gaussian-like function centered at the equilibrium configuration in the electronic ground state. This wavefunction defines the starting zone for the motion of the time-dependent wavepacket or the swarm of classical trajectories on the excited-state potential energy surface (PES). If the dissociation proceeds in a direct way, the forces near the Franck-Condon region determine to a large extent the fate of the wavepacket and ultimately the energy and state dependence of the dissociation cross sections. Since the initial wavefunction for a normal, chemically bound molecule such as H2O has a typical width of the order of 0.1−0.2 Å, the evolving wavepacket explores only a relatively small portion of the dissociative PES (see Figures 3.2, 9.8, and 9.9 for example).

By starting the photodissociation from an excited vibrational level one can access a significantly wider range of the upper-state PES (see Figure 13.1) and to some extent manipulate and steer the reaction path. One example has already been discussed in Section 10.1: dissociation of excited bending states of H2O through the à state probes a much wider angular region of the corresponding PES than dissociation of the lowest bending state. The influence of the increased anisotropy for smaller HOH angles clearly shows up in the final rotational state distribution of the OH product (see Figure 10.5).

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.

Photodissociation can be roughly classified as either direct or indirect dissociation. In a direct process the parent molecule dissociates immediately after the photon has promoted it to the upper electronic state. No barrier or other dynamical constraint hinders the fragmentation and the “lifetime” of the excited complex is very short, less than a vibrational period within the complex. For comparison, the period of an internal vibration typically ranges from 30 to 50 fs. The photodissociation of CH3ONO via the S2 state is a typical example; the corresponding potential energy surface (PES) is depicted in the upper part of Figure 1.11. A trajectory or a quantum mechanical wavepacket launched on the S2-state PES immediately leads to dissociation into products CH3O and NO.

In indirect photofragmentation, on the other hand, a potential barrier or some other dynamical force hinders direct fragmentation of the excited complex and the lifetime amounts to at least several internal vibrational periods. The photodissociation of CH3ONO via the S1 state is a representative example. The middle part of Figure 1.11 shows the corresponding PES. Before CH3ONO(S1) breaks apart it first performs several vibrations within the shallow well before a sufficient amount of energy is transferred from the N-0 vibrational bond to the O-N dissociation mode, which is necessary to surpass the small barrier.

Direct dissociation is the topic of this chapter while indirect photofragmentation will be discussed in the following chapter. Both categories are investigated with the same computational tools, namely the exact solution of the time-independent or the time-dependent Schrodinger equation. The underlying physics, however, differs drastically and requires different interpretation models.

Photodissociation of small polyatomic molecules is an ideal field for investigating molecular dynamics at a high level of precision. The last decade has seen an explosion of many new experimental methods which permit the study of bond fission on the basis of single quantum states. Experiments with three lasers — one to prepare the parent molecule in a particular vibrational-rotational state in the electronic ground state, one to excite the molecule into the continuum, and finally a third laser to probe the products — are quite usual today. State-specific chemistry finally has become reality. The understanding of such highly resolved measurements demands theoretical descriptions which go far beyond simple models.

Although the theory of photodissociation has not yet reached the level of sophistication of experiment, major advances have been made in recent years by many research groups. This concerns the calculation of accurate multi-dimensional potential energy surfaces for excited electronic states and the dynamical treatment of the nuclear motion on these surfaces. The exact quantum mechanical modelling of the dissociation of a triatomic molecule is nowadays practicable without severe technical problems. Moreover, simple but nevertheless realistic models have been developed and compared against exact calculations which are very useful for understanding the interrelation between the potential and the nuclear dynamics on one hand and the experimental observables on the other hand.

The aim of this book is to provide an overview of the theoretical methods for treating photodissociation processes in small polyatomic molecules and the achievements in merging ab initio calculations and detailed experiments. It is primarily written for graduate students starting research in molecular physics.

In the preceding fifteen chapters of this monograph we have described how one can infer information about the dissociation process and ultimately about the multi-dimensional potential energy surface(s) (PES) in the excited electronic state(s) from the observables which one measures in “conventional” experiments, namely the absorption spectrum, the emission spectrum of the transient molecule, and the various final state distributions of the fragments. By “conventional” we mean those experiments in which the molecule is irradiated by a long, more or less monochromatic laser pulse. The last open question, which we will address here, concerns the true time dependence of the molecular system as it evolves from the Franck-Condon region, through the transition state, into the possible fragment channels and how this motion can be made transparent in the laboratory.

The lifetime of the complex in the excited electronic state is either in the range of 10−15−10−13 seconds for direct dissociation respectively 10−12 seconds or longer for indirect fragmentation. In contrast, conventional experiments are performed with pulse lengths of the photolysis laser of the order of 10−9 seconds. Thus, no matter how refined such experiments are — full preparation of the initial state and complete resolution of the fragment states — they are inherently unable to resolve the real time dependence of the breakup process. They need accompanying theoretical studies (classical trajectories or quantum mechanical wavepackets) in order to disentangle the interaction among the various degrees of freedom and to disclose the evolution of the system.†

Rotational state distributions of the photofragments provide a wealth of information on the dissociation dynamics. The total available energy often exceeds 1 eV which suffices to make many rotational states energetically accessible. Since the torque imparted to the rotor is typically large, it is not unusual that 50 or even more rotational states become populated during dissociation. Modern detection methods, on the other hand, make it feasible to resolve even the most detailed aspects of rotational excitation: scalar properties, such as the final state distribution as well as vector properties, such as the orientation of the angular momentum vector of the fragment with respect to any axis of reference. In the same way as the vibrational distribution reflects the change of the bond length of the fragment molecule, the rotational distribution elucidates the change of the bond angle along the reaction path.

In this chapter we discuss only the scalar aspect of rotational excitation, i.e., the forces which promote rotational excitation and how they show up in the final state distributions. The simple model of a triatomic molecule with total angular momentum J = 0, outlined in Section 3.2, is adequate for this purpose without concealing the main dynamical effects with too many indices and angular momentum coupling elements. The vector properties and some more involved topics will be discussed in Chapter 11.

Direct and indirect processes represent the two major classes of photodissociation. In the direct case, the fragmentation proceeds too fast for the molecule to develop a complete internal vibration in the upper electronic state before it breaks apart. The wavepacket leaves the FC region and never returns to its starting place with the consequence that the autocorrelation function decays rapidly to zero. The resulting absorption spectrum is broad and without any vibrational structures. In indirect photodissociation, on the other hand, the excited complex in the upper electronic state lives for a sufficiently long time to allow the development of internal vibration. The wavepacket oscillates in the inner region, frequently recurs to its place of birth, and continuously leaks out into the exit channel. The autocorrelation function exhibits many recurrences and decays slowly to zero. The resulting absorption spectrum is composed of narrow lines which reflect the quasi-bound (resonance) states of the complex and their widths reflect the coupling to the continuum.

The transition from direct to indirect photodissociation proceeds continuously (see Figure 7.21) and therefore there are examples which simultaneously show characteristics of direct as well as indirect processes: the main part of the wavepacket (or the majority of trajectories, if we think in terms of classical mechanics) dissociates rapidly while only a minor portion returns to its origin. The autocorrelation function exhibits the main peak at t = 0 and, in addition, one or two recurrences with comparatively small amplitudes. The corresponding absorption spectrum consists of a broad background with superimposed undulations, so-called diffuse structures. The broad background indicates direct dissociation whereas the structures reflect some kind of short-time trapping.

Van der Waals molecules are complexes held together by the weak longrange forces between closed-shell atoms and/or molecules, i.e., electrostatic forces, dispersive forces, hydrogen bonding, and charge transfer interactions (Van der Avoird, Wormer, Mulder, and Berns 1980; Buckingham, Fowler, and Hutson 1988). Typical examples are X … I2, X … IC1, X … Cl2, X … HF, HF … HF with X being He, Ne, Ar, etc. The dots indicate the weak physical bonding in contrast to a strong chemical bonding.

The main characteristics of van der Waals molecules are:

1. 1) The small dissociation energy ranging from a few cm−1 to about 1000 cm−1.

2. 2) The relatively large bond length, Re, of typically 4 Å.

3. 3) The retention of the properties of the individual entities within the van der Waals complex.

4. 4) Relatively weak coupling between the van der Waals mode and the internal coordinates of the molecular entity.

Owing to the small dissociation energy, van der Waals molecules exist mainly at very low temperatures as they prevail in the interstellar medium or in supersonic jets.

Van der Waals molecules are rather floppy complexes which can be best described by the usual Jacobi coordinates which we used throughout all previous chapters (see the inset of Figure 12.1): the van der Waals bond distance R, the intramolecular separation of the chemically bound molecule r, and the orientation angle γ. Figure 12.1 depicts the R dependence of a typical potential energy surface (PES) V(R, r, γ) for fixed values of r and γ. The long-range part of the potential is attractive and governed by the forces mentioned above.