Bound electronic states

This general technique has been applied also to the direct observation of vibrational motion in bound electronic states. Although no transition states as such are involved in vibrational motion there is, again, a transitory change of intemuclear distance. 

Operational definitions of molecular structure are needed to clarify experimental significance. In addition, some statistical notation is needed to clarify physical meaning. All statistical definitions hinge on the minimum of potential energy in a bound electronic state, which defines the equilibrium geometry or r,-intemuclear distance type. 

In this work, the electronic kinetic energy is expressed in terms of the potential energy and derivatives of the potential energy with respect to nuclear coordinates, by use of the virial theorem (5-5). Thus, the results are valid for ail bound electronic states. However, the functional derived for E does not obey a variational principle with respect to (Pg ( )), even though in... 

A virial theorem (5-8) applied to the electronic coordinates gives the kinetic energy (T) in terms of (V) and expectation values of the first derivative of V with respect to nuclear coordinates (66-72). For bound electronic states f)... 

Schrodinger equation for each molecular electronic state, we seek an approximation that will represent U reasonably well for most diatomics. For a bound electronic state, we know that U has the general appearance of the solid curve in Fig. 4.2. We expect the nuclei to vibrate about the position of minimum potential energy therefore, we expand U in a Taylor series (Section 1.2) about Re, the equilibrium internuclear separation ... 

Radiationless transitions among electronic states of molecules represent a class of relaxation processes that are electronic in nature. The general term electronic relaxation appears to be appropriate for these processes,23 but it is convenient to divide those transitions involving a change in the bound electronic states of a molecule into two categories Transitions between states of the same multiplicity, referred to as internal conversion, and transitions between states of different multiplicity, referred to as intersystem crossing. Although there are several early experimental... 

The existence of a large number of bound electronic states, arising from 3P + 2P atomic limits, has now been determined statistically by Ferguson.81 This is now theoretically confirmed by our analysis of this system, which indicates 12 bound states of 02 , in addition to the 2Hg ground state, arising from the ground2/3 state of O" and the ground 3F and excited XD... 

What predictions for new experiments are provided by the theoretical analysis presented herein It would be extremely interesting to obtain direct spectroscopic evidence regarding the energy levels and charge distribution of the excess electron in liquid helium. Applying the pulse radiolysis technique, recently developed for studying bound electron states in polar solvents (—e.g., H20 and aliphatic alcohols), should make the localized states of an excess electron amenable to spectroscopic study. 

We consider a collision between two atoms. A chemical bond between the atoms can be formed, during the collision, via an electromagnetically induced transition to a bound electronic state. This process is called photo-association. 

Bound electronic states exhibit a discrete spectrum of rovibrational eigenstates below the dissociation energy. The interaction between discrete levels of two bound electronic states may lead to perturbations in their rovibrational spectra and to nonradiative transitions between the two potentials. In the case of an intersystem crossing, this process is often followed by a radiative depletion. Above the dissociation energy and for unbound states, the energy is not quantized, that is, the spectrum is continuous. The coupling of a bound state to the vibrational continuum of another electronic state leads to predissociation. 

Figure 23 Predissociation of the v = 2 vibrational level of the bound electronic state by a vibrational continuum wave function of the dissociative electronic state after radiative excitation (arrows) from the electronic ground state Po- The circle around the potential curve crossing point indicates an area of large overlap between the vibrational wave functions.

Fig. 5. The graphical representation of the direct renormalization approach. The triangle with the letter n inside means the expansion of the wave function for the bound electron state n in terms of free electron wave functions...

The renormalized expression for the two-photon self energy A ren (without the irreducible SESE a) term) for the bound-electron state a) reads [30] ... 

Paige ME, Harris CB. Ultrafast studies of chemical reactions in liquids validity of gas phase vibrational relaxation models and density dependence of bound electronic state lifetimes. Chem Phys 1990 149 37-62. 

Allowed excitation transitions are those between /V/1-states with different g, -symmetries, and most intense among them are those preserving the total spin (singlet-singlet and triplet-triplet transitions). The intermediary state in reaction (19.31) is a bound electronic state, but the transition takes place to the vibrational continuum of this state. The intermediary state in reaction (19.32) is a dissociative state that lies completely in the vibrational continuum. The reaction (19.33) is similar to reaction (19.26), except that the decay of (H ) resonance (auto-detachment) takes place in the vibrational continuum. 

The electronic transitions probed by x-ray absorption spectroscopy involve the excitation of a core electron into either unoccupied bound electron states near the Fermi level of the material or at higher energies into the continuum of states producing a photoelectron. These electronic excitations must obey spectroscopic selection rules and thus can provide information about the symmetry of an atom s environment, its oxidation state, and sometimes, with the assistance of comprehensive theoretical calculations, details about the geometry of ligands and other nearby atoms. This information is derived from excitations into bound states and low lying resonances above the Fermi level and is referred to as the x-ray absorption near edge structure (XANES). 

By optical excitation with argon and krypton laser lines, continuous laser oscillation on A -> X and B -> X transitions of Li Na2 and K molecules can be achieved dimer lasers show such interesting features as multiline emission, extremely low threshold pump intensities and forward-backward amplification asymmetry. Basic principles, operating conditions and applications of these lasers will be discussed. The dimer lasers operate between bound electronic states, resulting in the emission of discrete lines. To achieve tunable laser oscillation, continuous emission bands from bound-free transitions have to be considered. Some possibilities for alkali dimers are outlined and recent spectroscopic investigations on UV excited diffuse bands are reported. 

As discussed above, continuum resonance occurs when the excitation laser energy is higher than the dissociation limit of an excited, bound electronic state or directly with purely repulsive states. Continuum resonance Raman spectra of gaseous molecules are very sensitive to the position and shape of the potential functions involved in this type of light scattering as well as to the electronic transition moments between ground and excited states. Since it is possible to calculate the relevant spectra using both the KHD... 

The Born-Oppenheimer approximation allows us to decouple the electronic and nuclear motions of the free molecule of the Hamiltonian Hq. Solving the Schrodinger equation //o l = with respect to the electron coordinates r = r[, O, gives rise to the electronic states (r, R) = (r n(R)), n = 0,..., Ne, of respective energies En (R) as functions of the nuclear coordinates R, with the electronic scalar product defined as (n(R) n (R))r = j dr rj( r. R) T,-(r, R). We assume Ne bound electronic states. The Floquet Hamiltonian of the molecule perturbed by a field (of frequency co, of amplitude 8, and of linear polarization e), in the dipole coupling approximation, and in a coordinate system of origin at the center of mass of the molecule can be written as... 

The excess electron surface state and the electron bubble state constitute two distinct ground states and two electronic manifolds of bound electronic states, with the surface states converging to the vacuum level, while the bubble states converge to the hquid conduction band (Fig. 9). The two electronic manifolds... 

The energy shift of a bound-electron state contracted terms of the second-order S matrix element taking into account the mass-renormalization counter term provided by S l according to... 

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