As known from the quantum treatment of the hydrogenoid atom (see, e.g. ), these outer electrons may be accommodated in the 5f, 6d and 7 s shells. [Pg.3]

It seems to me that all quantum treatments of the hydrogen bond suffer from the defect that there are too few experimental facts. We now know, thanks to neutron diffraction, the positions of the nucloi fairly exactly, but we know little about the density and potential distribution of the electronic clouds. Yet the data to calculate these exist namely from a combination of x-ray and electron scattering. I feel that if we had such a distribution we would be in a position to discriminate between the various quantum mechanical pictures of the hydrogen bond which Professor Coulson has discussed in his paper. [Pg.360]

An early (perhaps the first) example of a quantum treatment of a dissipative process is Einstein s theory of spontaneous emission.6 To describe the interaction between matter and light, Einstein assumed the Boltzmann type of kinetic equations [Pg.13]

FIGURE 2.7. (a) Three active pz orbitals that are used in the quantum treatment of the X + CH3-Y— X-CH3 + Y Sw2 reaction, (b) Valence-bond diagrams for the six possible valence-bond states for four electrons in three active orbitals, (c) Relative approximate energy levels of the valence-bond states in the gas phase (see Table 2.4 for the estimation of these energies). [Pg.60]

BH-II can he consulted for a discussion of the numerical importance of the quantum treatment of the solvent electronic polarization. It suffices to [Pg.273]

U. Even In a recent series of papers [M. Bixon and J. Jortner], using a model Hamiltonian quantum treatment, it is shown that all multipole contributions to l mixing are negligible when compared with / mixing by low external fields. Thus the long lifetimes associated with ZEKE states are attributed (in atoms and in molecules) to the external fields alone. [Pg.659]

When the coupling f is much larger than kT, the diabatic representation is no longer valid. The quantum treatment cannot be limited to [Pg.164]

The discussion thus far in this chapter has been centred on classical mechanics. However, in many systems, an explicit quantum treatment is required (not to mention the fact that it is the correct law of physics). This statement is particularly true for proton and electron transfer reactions in chemistry, as well as for reactions involving high-frequency vibrations. [Pg.891]

Semiclassical techniques like the instanton approach [211] can be applied to tunneling splittings. Finally, one can exploit the close correspondence between the classical and the quantum treatment of a harmonic oscillator and treat the nuclear dynamics classically. From the classical trajectories, correlation functions can be extracted and transformed into spectra. The particular charm of this method rests in the option to carry out the dynamics on the fly, using Born Oppenheimer or fictitious Car Parrinello dynamics [212]. Furthermore, multiple minima on the hypersurface can be treated together as they are accessed by thermal excitation. This makes these methods particularly useful for liquid state or other thermally excited system simulations. Nevertheless, molecular dynamics and Monte Carlo simulations can also provide insights into cold gas-phase cluster formation [213], if a reliable force field is available [189]. [Pg.24]

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