Potential energy resonances

Rosker M J, Rose T S and Zewail A 1988 Femtosecond real-time dynamics of photofragment-trapping resonances on dissociative potential-energy surfaces Ghem. Phys. Lett. 146 175-9... 

At the time the experiments were perfomied (1984), this discrepancy between theory and experiment was attributed to quantum mechanical resonances drat led to enhanced reaction probability in the FlF(u = 3) chaimel for high impact parameter collisions. Flowever, since 1984, several new potential energy surfaces using a combination of ab initio calculations and empirical corrections were developed in which the bend potential near the barrier was found to be very flat or even non-collinear [49, M], in contrast to the Muckennan V surface. In 1988, Sato [ ] showed that classical trajectory calculations on a surface with a bent transition-state geometry produced angular distributions in which the FIF(u = 3) product was peaked at 0 = 0°, while the FIF(u = 2) product was predominantly scattered into the backward hemisphere (0 > 90°), thereby qualitatively reproducing the most important features in figure A3.7.5. 

In a time-dependent picture, resonances can be viewed as localized wavepackets composed of a superposition of continuum wavefimctions, which qualitatively resemble bound states for a period of time. The unimolecular reactant in a resonance state moves within the potential energy well for a considerable period of time, leaving it only when a fairly long time interval r has elapsed r may be called the lifetime of the almost stationary resonance state. 

One group has successfiilly obtained infonnation about potential energy surfaces without measuring REPs. Instead, easily measured second derivative absorption profiles are obtained and linked to the fiill RRS spectrum taken at a single incident frequency. In this way, the painstaking task of measuring a REP is replaced by carefiilly recording the second derivative of the electronic absorption spectrum of the resonant transition [, 59],... 

The fitting parameters in the transfomi method are properties related to the two potential energy surfaces that define die electronic resonance. These curves are obtained when the two hypersurfaces are cut along theyth nomial mode coordinate. In order of increasing theoretical sophistication these properties are (i) the relative position of their minima (often called the displacement parameters), (ii) the force constant of the vibration (its frequency), (iii) nuclear coordinate dependence of the electronic transition moment and (iv) the issue of mode mixing upon excitation—known as the Duschinsky effect—requiring a multidimensional approach. 

Figure B3.4.10. Schematic figure of a ID double-well potential surface. The reaction probabilities exliibit peaks whenever the collision energy matches the energy of the resonances, which are here the quasi-bound states in the well (with their energy indicated). Note that the peaks become wider for the higher energy resonances—the high-energy resonance here is less bound and Teaks more toward the asymptote than do the low-energy ones.

Here A and B denote atoms in each of the two interacting molecules. The V operator contains all the potential energy operators from both molecules, and the (xa V xb) integral is basically a resonance type integral between two atomic orbitals, one from each molecule. The pa is the electron density on atom A, and the first term in (15.1)... 

Vibrationally mediated photodissociation (VMP) can be used to measure the vibrational spectra of small ions, such as V (OCO). Vibrationally mediated photodissociation is a double resonance technique in which a molecule first absorbs an IR photon. Vibrationally excited molecules are then selectively photodissociated following absorption of a second photon in the UV or visible [114—120]. With neutral molecules, VMP experiments are usually used to measure the spectroscopy of regions of the excited-state potential energy surface that are not Franck-Condon accessible from the ground state and to see how different vibrations affect the photodissociation dynamics. In order for VMP to work, there must be some wavelength at which vibrationally excited molecules have an electronic transition and photodissociate, while vibrationally unexcited molecules do not. In practice, this means that the ion has to have a... 

The shape of the potential energy surface obtained by considering the lowest HF energy is qualitatively wrong near 8 = 0, since the resonance between Osb and O sb is not treated... 

The F + H2 — HF + FI reaction is one of the most studied chemical reactions in science, and interest in this reaction dates back to the discovery of the chemical laser.79 In the early 1970s, a collinear quantum scattering treatment of the reaction predicted the existence of isolated resonances.80 Subsequent theoretical investigations, using various dynamical approximations on several different potential energy surfaces (PESs), essentially all confirmed this prediction. The term resonance in this context refers to a transient metastable species produced as the reaction occurs. Transient intermediates are well known in many kinds of atomic and molecular processes, as well as in nuclear and particle physics.81 What makes reactive resonances unique is that they are not necessarily associated with trapping... 

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