Molecular resonant states

Basilevsky, M. V. and Ryaboy, V. M. Two approaches to the calculation of molecular resonance states Solution of scattering equations and matrix diagonalization, J.Comp.Chem., 8 (1987), 683-699... 

The molecular resonant states, which represent the intrinsic properties of the molecular excitations in the photophysical processes, are introduced... 

If one takes into account the expansion (52) over the molecular resonant states, v is the complex energy given by Eq. (43). It follows that function (76) can also be written as the expansion... 

We consider the general case where, according to Eqs. (122), a number M of molecular resonant states with complex energy E = e — iyJ2 is selected by the incident photon wave packets to take part in delayed scattering. The resonances are taken to be well separated, so that, if denotes the energy level spacing, one has... 

The rate equations (147) and (148), which account for all the previously derived dynamical features of creation and evolution of the molecular excitations, are useful because they establish a connection with the standard Liouville equation formalism for rate processes in quantum statistical systems. It should be noted that they are submitted to the same assumptions as the treatment in Section II,A of the molecular resonant states. Collisional damping is described in the framework of impact approximation and weak... 

From this, the molecular resonant states v> and their complex energies v = 6v - 7v/2, can be simply derived by diagonalizing the matrix (164). v> corresponds to the superposition of zero-order decaying radiant and nonradiant states. 

Section 6.2 describes the bound and scattering properties of a single potential with a van der Waals long range form. Section 6.3 extends the treatment to multiple states and scattering resonances. Sections 6.4 and 6.5 respectively discuss the properties of magnetically and optically tunable molecular resonance states. 

Two colliding atoms approach on tire molecular ground-state potential. During tire molasses cycle witli tire optical fields detuned only about one line widtli to tire red of atomic resonance, tire initial excitation occurs at very long range, around a Condon point at 1800 a. A second Condon point at 1000 takes tire population to a 1 doubly excited potential tliat, at shorter intemuclear distance, joins adiabatically to a 3 potential, drought to be die... 

We consider a general dissipative environment, using a three-manifold model, consisting of an initial ( ), a resonant ( r ), and a final ( / ) manifold to describe the system. One specific example of interest is an interface system, where the initial states are the occupied states of a metal or a semiconductor, the intermediate (resonance) states are unoccupied surface states, and the final (product) states are free electron states above the photoemission threshold. Another example is gas cell atomic or molecular problems, where the initial, resonant, and final manifolds represent vibronic manifolds of the ground, an excited, and an ionic electronic state, respectively. 

While it is not feasible to measure exponential decay of resonance states in the environment of a molecular beam experiment, in theoretical work the exponential decay law provides a necessary condition that a proposed state, generated by some method, is in fact a resonance state. Furthermore, the rate of exponential decay provides probably the most accurate method for the numerical determination of the lifetime. 

Perhaps the first clear observation of a reactive resonance in a collision experiment was recently made for the F + HD —> HF + D reaction.65-67 This reaction was one isotopomer of the F + H2 system studied in the landmark molecular beam experiments of Lee and co-workers in 1985.58 Unlike the F + H2 case, no anomalous forward peaking of the product states was reported, and results for F + HD were described as the most classical-like of the isotopes considered. Furthermore, a detailed quantum mechanical study68 of F + HD —> HF + D reaction on the accurate Stark-Werner (SW)-PES69 failed to locate resonance states. Therefore, it was surprising that the unmistakable resonance fingerprints emerged so clearly upon re-examination of this reaction. 

Resonance or electromeric effects. Certain molecular structures are characterized by the possibility of having two or more compatible electronic structures and the molecules exist in a resonance state intermediate between the several extremes. These effects are particularly characteristic of aromatic structures and other molecules containing conjugate double bonds. 

Many bimolecular and unimolecular reactions are dominated by long-lived resonances. As a result, having knowledge about the positions and lifetimes of such resonance states is highly desired. Recursive calculations of resonance states have been reported for many molecular systems, including... 

A. L. Kwiram, Optical detection of magnetic resonance in molecular triplet states, in MTP International Review of Science, Ser. 1, Physical Chemistry 4 (C. A. McDowell, ed.), pp. 271-315, University Park Press, Baltimore (1972). 

Depending on molecular resonances, VOCs with an optical (electronic) absorption at 266 nm absorb a laser photon, while those transparent at 266 nm remain in the ground state. The width of optical absorptions is given by the ground-state population, and broadens with the molecules temperature, which itself depends on the expansion conditions at the inlet system. 

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