Vibrational anharmonicity wave packet

Consider the wave packet populating just one vibrational level. This occurs for only a short period of time (the length of the femtosecond pulse). Then we can think of vibration occurring in a classical fashion. The wave packet travels along the vibrational level until it reaches the other extremity when it may be reflected and continue to travel backwards and forwards along the level. Because of the strongly anharmonic nature of the vibration the wave packet is broadened, as shown, as r increases. 

Figure 7.1 The simulated temporal motion of a vibrational wave packet created on an anharmonic potential surface. The parameters are evaluated as 300 fs and 37 ps.

As already discussed, the approximate QD signal of a 120fs pulse exhibits two dominant vibrations which are caused by the Qs mode (310 to 320 fs) on the one hand, and by a slow pseudorot at ional mode (1 ps) on the other hand. Interestingly, the vibration along the Qs mode loses its pronounced character after 3ps (see Fig.3.51), i.e. the wave packet spreads out along this coordinate, as a movie of the three-dimensional wave packet dynamics of the B state shows [388]. This observation has already been interpreted as an effect of the anharmonicity of the PES and as intramolecular vibrational redistribution from dominantly Qs to g and (f vibration [62, 81]. The behavior described is also reflected by the approximate QD pump probe signal where the oscillation of period 310 to 320 fs caused by the Qs mode vanishes after a time of 4 to 5ps (see also Fig. 3.52). 

When a molecule is excited by an ultrashort laser pulse with an appropriate center frequency, a localized wave packet can be created in the excited electronic state because of the excitation of a coherent superposition of many vibrational-rotational states. It follows from fundamental laws that the d3mamics of molecular wave packets is governed by a time-dependent Schrodinger equation (eqn 2.29), where H is the relevant Hamiltonian of the given molecule. Because molecular potential-energy surfaces are anharmonic, this molecular wave packet tends to spread both in position (coordinates) and in momentum. However, in addition to expansion or defocusing, the wave packet also suffers delocalization at a certain instant of time. Coherent quantum... 

H. A localized vibrational wave-packet as a linear combination of delocahzed vibrational states. Figure 1.7 discussed the preparation of a localized vibrational state, a state that vibrates in the potential well in a manner similar to a classical particle. If the well is harmonic the wave function will remain localized indetinitely. Realistic molecular potentials are anharmonic so that after a few oscillations die state will delocahze. Even in the harmonic case, external perturbations such as... 

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