Molecular shape resonance

Berman, M., Miindel, C. and Domcke, W. (1985). Projection-operator calculations for molecular shape resonances The 2E+ resonance in electron-hydrogen scattering, Phys. Rev. A 31, 641-651. 

While the broad mission of the National Bureau of Standards was concerned with standard reference materials, Dr. Isbell centered the work of his laboratory on his long interest in the carbohydrates and on the use of physical methods in their characterization. Infrared spectroscopy had shown promise in providing structural and conformational information on carbohydrates and their derivatives, and Isbell invited Tipson to conduct detailed infrared studies on the extensive collection of carbohydrate samples maintained by Isbell. The series of publications that rapidly resulted furnished a basis for assigning conformations to pyranoid sugars and their derivatives. Although this work was later to be overshadowed by application of the much more powerful technique of nuclear magnetic resonance spectroscopy, the Isbell— Tipson work helped to define the molecular shapes involved and the terminology required for their description. 

Diehl, P., Freeman, R. The Influence of Molecular Shape on Solvent Shifts in the Proton Magnetic Resonance Spectra of Polar Solutes. Mol. Phys. 4, 39 (1961). 

By scattering within molecular solids and at their surfaces, LEE can excite with considerable cross sections not only phonon modes of the lattice [35,36,83,84,87,90,98,99], but also individual vibrational levels of the molecular constituents [36,90,98-119] of the solid. These modes can be excited either by nonresonant or by resonant scattering prevailing at specific energies, but as will be seen, resonances can enhance this energy-loss process by orders of magnitude. We provide in the next two subsections specific examples of vibrational excitation induced by LEE in molecular solid films. The HREEL spectra of solid N2 illustrate well the enhancement of vibrational excitation due to a shape resonance. The other example with solid O2 and 02-doped Ar further shows the effect of the density of states on vibrational excitation. 

Depending on the kind of the intermediate molecular ion, all resonance processes can be divided into two groups.116 The first group is the so-called shape resonances, where the electron is trapped in a potential well formed in the ground electron state of the molecule by centrifugal or polarization forces. The lifetime of such states is between 10 15 and 10 s. 

The shape resonances have been described by Feshbach in elastic scattering cross-section for the processes of neutron capture and nuclear fission [7] in the cloudy crystal ball model of nuclear reactions. These scattering theory is dealing with configuration interaction in multi-channel processes involving states with different spatial locations. Therefore these resonances can be called also Feshbach shape resonances. These resonances are a clear well established manifestation of the non locality of quantum mechanics and appear in many fields of physics and chemistry [8,192] such as the molecular association and dissociation processes. 

Even with PI, theoretically one of the simplest ionization processes, the internal energy distribution, P(E), of the molecular ion cannot be predicted on the basis of Franck—Condon factors alone. Autoionization is well-known as being important [15, 177, 637, 640, 800], as is the more recently recognised effect of shape resonance [220, 803, 906]. It has also been shown that the onset of a decomposition can affect the energy distribution, P(E), [801, 802]. The latter effect is possibly a consequence of competition between neutral and ionic decompositions. 

In this section we investigate the factors affecting the formation and decay of shape resonances by examining the radial charge density /120/ plots from the Feynman Dyson amplitudes corresponding to the resonant poles identified earlier /22,25,26,40,41/ in sections 3.1 and 3.2 for different atomic and molecular resonances. 

Fig. 13. Pictorial view of the final-state radial wave functions relevant for core transitions in a molecule. The core transitions take place in an effective molecular potential seen by the excited photoelectron. The final states in the continuum XANES region are quasi-bound multiplescattering resonances (MSR), also called shape resonances. Below the continuum threshold E0 transitions to unoccupied valence states appear. 0 is the energy of the core ionization potential (from ESCA). Ec is the energy where the wavelength of initially excited photoelectrons conforms to the interatomic distance. For E < E0, discrete transitions to unoccupied valence states. E0 < E < Ec, continuum XANES. For < Ec, the EXAFS theory breaks down. The dotted curves show the wave functions of the initially excited photoelectron. From Bianconi (30).

Molecular-orbital approaches to edge structures differ for semiconducting and isolating molecular complexes. The latter and transition-metal complexes allow one to minimize solid-state effects and to obtain molecular energy levels at various degrees of approximation (semiempirical, Xa, ab initio). The various MO frameworks, namely, multiple-scattered wave-function calculations (76, 79, 127, 155) and the many-body Hartree-Fock approach (13), describe states very close to threshold (bound levels) and continuum shape resonances. 

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