Quantum excitation, classical behavior

The nature of the electronic configuration in the alkaline earth metals does, however, allow for intriguing research into correlations between the two electrons in the outer shell of these atoms. Simultaneous excitation of the two outer electrons is possible with a single photon, which leads to the provocative idea of a shared principal quantum number. Excitation of one of the electrons to consecutively higher orbits while monitoring de-excitation of the other electron gives information about the border between quantum and classical (planetary) behavior. 

Computational studies have indicated that chaotic behavior is expected in classical mechanical descriptions of the motion of highly excited molecules. As a consequence, intramolecular dynamics relates directly to the fundamental issues of quantum vs classical chaos and semiclassical quantization. Practical implications are also clear if classical mechanics is a useful description of intramolecular dynamics, it suggests that isolated-molecule dynamics is sufficiently complex to allow a statistical-type description in the chaotic regime, with associated relaxation to equilibrium, and a concomitant loss of controlled reaction selectivity. 

Fluorescence spectra and quantum yields of pyrene in supercritical CO2 have been determined systematically as functions of temperature, CO2 density, and pyrene concentration. Under near-critical conditions, contributions of the pyrene excimer emission in observed fluorescence spectra are abnormally large. The results cannot be explained in the context of the classical photophysical mechanism well established for pyrene in normal liquid solvents. The photophysical behavior of pyrene in a supercritical fluid is indeed unusual. The experimental results can be rationalized with a proposal that the local concentration of pyrene monomer in the vicinity of an excited pyrene molecule is higher than the bulk in a supercritical solvent environment. It is shown that the calculated ratios between the local and bulk concentrations deviate from unity more significantly under near-critical conditions (Sun and Bunker, 1995). 

In contrast, the x component of the susceptibility reflects directly the relaxation behavior under the applied field. For both samples, the maxima of X , measured at a given frequency, shift to lower temperature for increasing bias field. It also shifts to lower temperature for decreasing excitation frequency, and fixed field. Incidentally, this behavior indicates that the relaxation follows the classical predictions, and that no quantum tunneling relaxation is discernible since the trend would be of a shift to higher temperatures with increasing field. The dependence on H that we have adopted is... 

Recent years have also witnessed exciting developments in the active control of unimolecular reactions [30,31]. Reactants can be prepared and their evolution interfered with on very short time scales, and coherent hght sources can be used to imprint information on molecular systems so as to produce more or less of specified products. Because a well-controlled unimolecular reaction is highly nonstatistical and presents an excellent example in which any statistical theory of the reaction dynamics would terribly fail, it is instmctive to comment on how to view the vast control possibihties, on the one hand, and various statistical theories of reaction rate, on the other hand. Note first that a controlled unimolecular reaction, most often subject to one or more external fields and manipulated within a very short time scale, undergoes nonequilibrium processes and is therefore not expected to be describable by any unimolecular reaction rate theory that assumes the existence of an equilibrium distribution of the internal energy of the molecule. Second, strong deviations Ifom statistical behavior in an uncontrolled unimolecular reaction can imply the existence of order in chaos and thus more possibilities for inexpensive active control of product formation. Third, most control scenarios rely on quantum interference effects that are neglected in classical reaction rate theory. Clearly, then, studies of controlled reaction dynamics and studies of statistical reaction rate theory complement each other. 

However, changes in the absorption spectrum are not the only effects expected and seen in the behavior of dyes on metallic (silver) surfaces. It has been known for some time now that proximity to a silver surface brings about major changes in the lifetimes and quantum yields for fluorescence of molecules. For an early work in that field, see Kuhn" and for a excellent theoretical treatment. Chance et Within the framework of classical electrodynamics, it was shown that the metal opens dissipative channels into which the excited molecule can discharge its energy. The theoretically calculated lifetimes fully agreed with those measured, up to distances of about 10 nm from the surface. 

The random lifetime assumption is perhaps most easily tested by classical trajectory calculations (Bunker, 1962 1964 Bunker and Hase, 1973). Initial momenta and coordinates for the Hamiltonian of an excited molecule can be selected randomly, so that a microcanonical ensemble of states is selected. Solving Hamilton s equations of motion, Eq. (2.9), for an initial condition gives the time required for the system to reach the transition state. If the unimolecular dynamics of the molecule are in accord with RRKM theory, the decomposition probability of the molecule versus time, determined on the basis of many initial conditions, will be exponential with the RRKM rate constant. That is, the decay is proportional to exp[-k( )t]. The observation of such an exponential distribution of lifetimes has been identified as intrinsic RRKM behavior. If a microcanonical ensemble is not maintained during the unimolecular decomposition (i.e., IVR is slower than decomposition), the decomposition probability will be nonexponential, or exponential with a rate constant that differs from that predicted by RRKM theory. The implication of such trajectory studies to experiments and their relationship to quantum dynamics is discussed in detail in chapter 8. 

ABSTRACT. After reviewing the time dependent wavepacket method as applied to collision induced dissociation processes,we report accurate quantum results for reactive and non reactive collinear A+BC systems. Both systems display a vibrational enhancement effect in the low energy region. While the non reactive systems exhibit a vibrational inhibition effect at higher energies,a more complex behavior is observed in the reactive case. Below the classical dissociation threshold,the non reactive systems display tunnelling tails which decrease with the initial vibrational excitation of the diatomic molecule. The reactive system displays important quantum effects at energies well above the classical dissociation threshold. 

The analysis of the Figure 3.8 clearly illustrates that since in classical interpretation of the motion in the harmonic potential the system has its maximum probability to be found at the position x when its velocity is minimum, i.e., at the maximum distance (at the amplitude) allowed by the oscillation, while in quantum motion this is certainly not the case of the system in its vibrational ground state (n = l) but only in the higher excited states (see the probability behavior for n = 10 and far above that) when the quantum probability of vibration becomes multiphed enough (by the quantum vibrational number) so that it shapes asymptotically to the classical potential of vibrational motion. Such behavior is nothing but the vibrational manifestation of the earlier discussed (Bohr) correspondence principle affirming that the quantum motion approaches the classical one in the very high levels of quantification. 

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