Anharmonicity excited electronic states

Here we are chiefly interested in the intrinsic causes of line broadening. We do not include among these dissociation, ionization, predissociation, autoionization, and pieisomerization, since few unambiguous examples of their occurrence have been reported for the low-lying excited electronic states. Attention is devoted to broadening through anharmonicity (vibrational relaxation) and in particular to electronic relaxation. 

Figure 19 The Raman spectrum and time cross correlation function when the motion on the excited electronic state potential is anharmonic, compare to Figs. 17 and 18, which are for a harmonic approximation. (Top, a) Computed time correlation function using a wide window function (b) The maximal entropy representation of this function, determined from the spectrum. Note the clear separation of time scales due to the anharmonicity (cf. Fig. 20). (Bottom) The Raman excitation spectrum obtained from the computed time correlation function (a). The arrows are the sequence of computations (a) is determined from the dynamics. The spectrum is determined from (a). The maximum entropy cross-correlation function (b) uses only the spectrum as input.

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... 

Experimentally, there is little to suggest that large anharmonicities may be expected for the low-lying electronic states of the aromatic and aza-aromatic molecules, at least on the evidence of the extensive sequence structure and the well-developed progressions observed for the lowest excited singlet and triplet states of many molecules. 

Such unexpected variations of the anharmonicity can be explained by considerable variations of the main electronic state under influence of high frequency excitation. Under these conditions the electronic states in the nanotubes vary in such a way that deviation from the harmonic approximation is decreasing for G mode but increasing for the D mode and the sum D+G tone. 

We report on anomalous behavior of the observed anharmonicity for different vibrational modes of SWCNT. This peculiarity appears in a strong dependence of the anharmonicity on the wavelength of excitation as well as in the opposite trends observed for different vibration bands. While the anharmonicity of the D mode increases with the frequency of the excitation radiation (Vl), the same of the G mode decreases. The sum harmonic band VdH-Vg is characterized with the highest anharmonicity while the same for a composed tone Vq+Vrbm is negligible. The frequency dependence of the anharmonicity also supports the concept of variation of the electronic states under the light excitation. 

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