Molecular eigenstate

This section begins with a brief description of the basic light-molecule interaction. As already indicated, coherent light pulses excite coherent superpositions of molecular eigenstates, known as wavepackets , and we will give a description of their motion, their coherence properties, and their interplay with the light. Then we will turn to linear and nonlinear spectroscopy, and, finally, to a brief account of coherent control of molecular motion. 

Consider Raman transitions between thennalized molecular eigenstate g (ground) and molecular eigenstate/ (final). The quantum mechanical expression for responding to colours and j is the famous (thennalized) Kramers-Heisenbergequation [29]... 

SLI is not specific to molecular eigenstates, but universal to the superposition of any eigenstates in a variety of quantum systems. It is thus expected as a new tool for quantum logic gates not only in MEIP but also for other systems such as atoms, ions, and quantum dots. SLI also provides a new method to manipulate WPs with fs laser pulses in general applications of coherent control. 

The second term is the covalent bond energy that arises from occupying the molecular eigenstates, n, with electrons, namely... 

Finally, we note that there are some situations, of which the dynamical Jahn-Teller and Renner-Teller effects are the classic examples, where the nuclear coupling terms are important in any electronic basis 18). Adiabatic potential surfaces may still be defined but the resulting molecular eigenstates cannot be identified with any one surface. 

A correct representation of the molecular eigenstates, zero-order, Born-Oppenheimer states,6... 

The energy levels En, corresponding to the molecular eigenstates, are now obtained from the solution of the eigenvalue problem... 

The expansion coefficients representing the weights of the zero-order state molecular eigenstate 0n can be displayed in the form6... 

In eqs. (7-1) and (7-2) we have used i and n to label the energy and r and p to label all other parameters necessary to describe the states of the molecule. We shall use, in all that follows, z>> s [Pg.205]

The true molecular eigenstates in the energy region corresponding to overlap of BO states are again represented as the superposition (eq. (5-1))... 

In what follows we shall consider an excitation process which is short lived on the time scale of the resulting excited state. This excitation process may involve an electron-molecule collision or absorption of a light pulse. We start with the system in the ground state (f>0. The excitation process introduces a time-dependent perturbation Tx(t) for a duration of time r. An excited nonstationary state is thereby produced which can be represented as a superposition of molecular eigenstates (see eq. 6-2)... 

The initial state of the excited system has been represented as a superposition of the (time-independent) molecular eigenstates, each of which is a superposition of BO basis functions. The decay process is then described in terms of the time evolution of the amplitudes of the molecular eigenstates. The general theory of quantum mechanics implies that the decay of the state (10-4) will exhibit interference effects. 

The properties of the metastable state resulting from the simple excitation process considered above can be further elucidated by considering the nature of the expansion of the molecular eigenstates in terms of the zero-order states (eq. (2-18)). Equation (10-4) can be rewritten in the form... 

Finally, Freed and Jortner discuss, in general terms, the influence of external perturbations on radiationless processes. They show under what conditions the external perturbation has either no effect, a small, or a large effect on the radiationless transitions in the statistical, intermediate, and resonance coupling limits, respectively. An interesting aspect of their analysis is the demonstration that the widely used Born-Oppenheimer and molecular eigenstate basis sets provide complimentary pictures, and hence are completely equivalent. 

We shall assume, as we did earlier, that the exact molecular eigenstate can be represented as a superposition of BO states or some other complete set of zero-order states. Suppose that the set of molecular states has the following characteristics ... 

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