Molecular systems bound state

Molecular adsorbates usually cover a substrate with a single layer, after which the surface becomes passive with respect to fiirther adsorption. The actual saturation coverage varies from system to system, and is often detenumed by the strength of the repulsive interactions between neighbouring adsorbates. Some molecules will remain intact upon adsorption, while others will adsorb dissociatively. This is often a frinction of the surface temperature and composition. There are also often multiple adsorption states, in which the stronger, more tightly bound states fill first, and the more weakly bound states fill last. The factors that control adsorbate behaviour depend on the complex interactions between adsorbates and the substrate, and between the adsorbates themselves. 

Before progressing, it is useful to review the dynamics of typical molecular systems. We consider three types scattering (chemical reaction), photodissociation, and bound-state photoabsorption (no reaction). 

The complexity of molecular systems precludes exact solution for the properties of their orbitals, including their energy levels, except in the very simplest cases. We can, however, approximate the energies of molecular orbitals by the variational method that finds their least upper bounds in the ground state as Eq. (6-16)... 

The above mentioned experiments show that guests are preferentially bound by the aa conformation of 9a. In Sect. 3 we will describe how this concept can be used to construct a molecular system that switches between strongly and weakly binding states. 

Charge transfer states (CT) are often found in molecular systems side by side with excitonic states. CT states describe polar nonconducting states bound by coulomb interaction of the electron-hole pairs. CT states may be ionized with localization of the charges on definite molecules. 

Van der Waals molecules of heavier homonuclear diatomics have also been studied, using similar techniques to the ones mentioned above. However, the numbers of bound states generally are much greater for such systems, and the band structures are richer and therefore harder to resolve. Detailed work has shown that for the more massive diatomics molecular rotation is more or less hindered and the level structures are much more complex than the ones seen in the H2-X systems. Rather uncertain band contour analyses are used in those cases but a few reasonably well resolved band spectra of van der Waals molecules are known [49, 267]. 

Other systems like H2-H2 feature a small number of bound states. Whenever molecular pairs form bound dimers, spectroscopic structures appear. First and usually most importantly, the continuum of the purely rotational band appears, but various other structures associated with bound-to-free transition usually show up that are harder to model closely. As a rule, the rototranslational absorption spectra of most molecular systems are not as easily modeled as that of H2-He, because of the dimer structures. Of course, in the typical high-pressure laboratory measurements, dimer structures may be broadened to the point where these are hardly discernible. In such a case, the BC and KO model profiles may become adequate again. In any case, the rototranslational spectra of a number of binary systems have been modeled closely over a broad range of temperatures [58], including the (coarse) dimer structures. 

It is very important, in the theory of quantum relaxation processes, to understand how an atomic or molecular excited state is prepared, and to know under what circumstances it is meaningful to consider the time development of such a compound state. It is obvious, but nevertheless important to say, that an atomic or molecular system in a stationary state cannot be induced to make transitions to other states by small terms in the molecular Hamiltonian. A stationary state will undergo transition to other stationary states only by coupling with the radiation field, so that all time-dependent transitions between stationary states are radiative in nature. However, if the system is prepared in a nonstationary state of the total Hamiltonian, nonradiative transitions will occur. Thus, for example, in the theory of molecular predissociation4 it is not justified to prepare the physical system in a pure Born-Oppenheimer bound state and to force transitions to the manifold of continuum dissociative states. If, on the other hand, the excitation process produces the system in a mixed state consisting of a superposition of eigenstates of the total Hamiltonian, a relaxation process will take place. Provided that the absorption line shape is Lorentzian, the relaxation process will follow an exponential decay. 

Present theoretical efforts that are directed toward a more complete and realistic analysis of the transport equations governing atmospheric relaxation and the propagation of artificial disturbances require detailed information of thermal opacities and long-wave infrared (LWIR) absorption in regions of temperature and pressure where molecular effects are important.2 3 Although various experimental techniques have been employed for both atomic and molecular systems, theoretical studies have been largely confined to an analysis of the properties (bound-bound, bound-free, and free-free) of atomic systems.4,5 This is mostly a consequence of the unavailability of reliable wave functions for diatomic molecular systems, and particularly for excited states or states of open-shell structures. More recently,6 9 reliable theoretical procedures have been prescribed for such systems that have resulted in the development of practical computational programs. 

The time-dependent wavepacket constructed in Section 4.1 is not the wavepacket that a laser with finite duration creates in the excited electronic state. It represents the wavepacket created by a pulse with infinitely narrow width in time. In order to construct the real wavefunction of the molecular system we must go back to Section 2.1. For simplicity of presentation, let us consider a diatomic molecule with internuclear separation R. We assume that the excitation takes place from the electronic ground state (index 0) to a bound upper state (index 1). The extension to a dissociative state, several coupled excited states, or several degrees of freedom is formally straightforward. 

---