Natural resonance theory excited-state

The Stern—Volmer and Perrin equations, (v) and (vi), both allow a quantitative characterization of the efficiency of non-radiative energy transfers. They are useful for the comparison of various donoi -acceptor systems, although they provide no information concerning the nature of the excited state involved and the mechanism of the energy transfer process. More appropriate theories have been established to describe non-radiative energy transfers that occur when there is close resonance between the initial and final states. 

Another feature of the resonance mixing, already alluded to, is the sign inversion which is caused by the different nature of the matrix elements that mix the Kekule structures for aromatics and antiaromatics. Thus, in the case of benzene (part a), the ground state is the positive combination of the two Kekule structures, while in cyclobutadiene (part b), the ground state is the negative combination.15116158210 214 Consequently, the twin excited states are the negative and positive linear combin-tions, respectively, for aromatics and antiaromatics.13-15-115-209 212 This relationship of the ground and excited states to the fundamental Kekule structures has been derived early on by the pioneers of VB theory.211-214... 

Metastable muonium atoms in the 2s state have been produced with a beam foil technique at LAMPF and at the Tri University Meson Physics Facility (TRI-UMF) at Vancouver, Canada. Only moderate numbers of atoms could be obtained. The velocity resonance nature of the electron transfer reaction results in a muonium beam at keV energies. Very difficult and challenging experiments using electromagnetic transitions in excited states, particularly the 2 Si/2 2 Pi/2 classical Lamb shift and 2 Si/2-2 P3/2 splitting could be induced with microwaves. However, the achieved experimental accuracy at the 1.5 % level [18,19,20], does not represent a severe test of theory yet. 

For an interpretation of so-called shape-resonance state, an assumption of potential barrier surrounding the molecule was introduced. However, the origin of the potential barrier has not been clarified yet. DV-Xa calculation has also been applied to solve this problem. The theoretical and measured S and F K XANES spectra of SF molecule are compared in Fig. 15 and 16. In both cases, the agreements between theory and experiment are quite good. From the calculation, it is found that any potential barrier is not created and the excited MO states corresponding to the shape-resonance peaks are naturally generated by the molecular potential. 

Compound-state resonances are important in quantal theories of unimolecular decomposition. They are prepared in low-energy atom (molecule)-molecule collisions when part of the relative kinetic energy of the motion becomes temporarily converted into excitation of the internal (rotational and/or vibrational) degrees of freedom of either partner. When this excitation occurs, the molecular system has insufficient energy in its relative motion to separate. One can also prepare compound-state resonances by using electromagnetic radiation (e.g., a laser) to excite the molecule. Thus, it is proper to view these resonances as the natural extension of the bound vibration-al/rotational eigenstates into the dissociative continuum. 

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