Semiclassical analysis

A58, 727 (2002). Quantum Calculation of Highly Excited Vibrational Energy Levels of CS2(X) on a New Empirical Potential Energy Surface and Semiclassical Analysis of 1 2 Fermi Resonances. 

Gray, S. K., and Child, M. S. (1984), The Vibrational Energy States of Two Coupled Modes in Formaldehyde Classical, Quantum and Semiclassical Analysis, Mol. Phys. 53,961. 

Stine and Marcus, has no one given a good semiclassical analysis of the reaction probability in collinear H3 ... 

In summary, the photon has been modeled as a doublet in rotation in the preferred frame E. Spin and energy have been obtained from a semiclassical analysis. Polarization corresponds to a fixed direction of vector L in E. In a nonpolarized photon vector L has a time-dependent direction. A particular case of nonpolarization is the ellipsoid, as in Hunter and Wadlinger [37]. Our Eq. (96) allows for the existence of multiphotons that vary in steps of half the ground-state photon energy such prediction differs of the prediction of Hunter and Wadlinger [37]. Photons in motion with respect to E will be considered elsewhere. The photon is the source of the electromagnetic field, as explained next. 

A linear approximation of the potential is certainly too sweeping a simplification. In reality, Vr varies with the internuclear separation and usually rises considerably at short distances. This disturbs the perfect (mirror) reflection in such a way that the blue side of the spectrum (E > Ve) is amplified at the expense of the red side (E < 14).t For a general, nonlinear potential one should use Equations (6.3) and (6.4) instead of (6.6) for an accurate calculation of the spectrum. The reflection principle is well known in spectroscopy (Herzberg 1950 ch.VII Tellinghuisen 1987) the review article of Tellinghuisen (1985) provides a comprehensive list of references. For a semiclassical analysis of bound-free transition matrix elements see Child (1980, 1991 ch.5), for example. 

Schinke, R. (1986a). Semiclassical analysis of rotational distributions in scattering and photodissociation, J. Phys. Chem. 90, 1742-1751. 

V. Aquilanti, S. Cavalli, and G. Grossi, On the ridge effect in mode transitions semiclassical analysis of the quantum pendulum. Chem. Phys. Lett., 110 43-48,1984. 

Semiclassical analysis of asymptotic separability and of its local breakdown... 

The behaviour of the eigenvalues as a function of q, well documented in the literature [l4,15], is very clearly exhibited by a semiclassical analysis. Following reference [l6], it is possible to obtain by an extended WKB procedure, a quantization rule, which holds asympotically in... 

A quantitative semiclassical analysis of these effects for this model and similar ones, in particular for a recent model for the reaction CH2 0 -C0+H2 [35], is being carried out [38]. This analysis is... 

Direct RKR inversion of vibrationally and rotationally resolved spectroscopic data for diatomics is now a fairly routine procedure. In normal RKR applications, however, the spectral data are exploited in a relatively limited fashion. One simply uses B(v) and E(v), the rotational constant and term value dependence on vibrational quantum v, respectively, to infer the inner and outer classical turning points at each v from a semiclassical analysis. In high resolution spectroscopy of van der Waals complexes, however, there is often far more rotational than vibrational data available. Consequently extensive information exists on very high order centrifugal effects on the radial coordinate, sometimes up to, and by virtue of centrifugal barriers, beyond the dissociation limit The hope is that a simple extension of RKR ideas might be able to extract a 1-D potential directly from rotational data alone. 

The critical question is how accurate (or inaccurate) the Born-Oppenheimer energy of a molecule defined as above is. Recently Takahashi and Takatsuka have addressed this question and reported a semiclassical analysis of this matter [413]. They explicitly showed that the fifth order term is also exactly zero, and therefore the lowest-order correction to the Born-Oppenheimer energy must be of the order of... 

Topaler MS, Hack MD, Allison TC, liu Y-P, Mielke SL, Schwenke DW, Truhlar DJ (1997) Validation of trajectory surface hopping methods against accurate quantum mechanical dynamics and semiclassical analysis of electronic-to-vibrational energy transfer. J Chem Phys... 

In the lOS approximation explicit averaging over the a and 6 orientation angles is eliminated so that only the impact parameter (or equivalently the orbital angular momentum) and the molecular orientation angle remain. The semiclassical analysis of this approximation results in a cross section formula which contains a Jacobian, equivalent to the inverse of that in equation (6), ... 

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