Polyatomic molecules excited state nuclear dynamics

As discussed in Section II, the excited-state dynamics of polyatomic molecules is dictated by the coupled flow of both charge and energy within the molecule. As such, a probe technique that is sensitive to both nuclear (vibrational) and electronic configuration is required in order to elucidate the mechanisms of such processes. Photoelectron spectroscopy provides such a technique,... 

From a dynamical (and/or spectroscopic) perspective, we may ask ourselves how to describe and predict the vibronic structures which are superimposed on many low resolution Abs. Cross Sections. These vibronic structures are deeply linked to the time evolution of the wavepacket, after the initial excitation, over typical times of a few hundreds of femtoseconds as discussed by Grebenshchikov et al. [31]. In ID, for a diafomic molecule, fhe fime evolufion is rafher simple when only one upper electronic state is involved. In contrast, for friafomic molecules fhe 3D character of the PESs makes the wavepacket dynamics intrinsically complex. So, for most of the polyatomic molecules, the quantitative interpretation of fhe vibronic structures superimposed to the absorption cross section envelope remains a hard task for two main reasons first because it requires high accuracy PESs in a wide range of nuclear coordinates and, second, it is not easy to follow fhe ND N = 3 for triafomic molecules) wavepackef over several hundred femtoseconds,... 

Model Hamiltonians constructed according to Elqs. (13)-(15) are particularly well suited for the calculation of low-resolution absorption spectra, photoelectron spectra and resonance-Raman spectra of polyatomic molecules. As is well known, these spectra are largely determined by the short-time dynamics in the excited state, which in turn is governed by the shape of the PE functions within the so-called Franck-Condon zone of the optical transition. In this limited range of nuclear geometries, the multidimensional PE functions are generally well approximated by the Taylor expansions of Eqs. (8) and (9). 

The Born-Oppenheimer adiabatic approximation represents one of the cornerstones of molecular physics and chemistry. The concept of adiabatic potential-energy surfaces, defined by the Born-Oppenheimer approximation, is fundamental to our thinking about molecular spectroscopy and chemical reaction djmamics. Many chemical processes can be rationalized in terms of the dynamics of the atomic nuclei on a single Born Oppenheimer potential-energy smface. Nonadiabatic processes, that is, chemical processes which involve nuclear djmamics on at least two coupled potential-energy surfaces and thus cannot be rationalized within the Born-Oppenheimer approximation, are nevertheless ubiquitous in chemistry, most notably in photochemistry and photobiology. Typical phenomena associated with a violation of the Born-Oppenheimer approximation are the radiationless relaxation of excited electronic states, photoinduced uni-molecular decay and isomerization processes of polyatomic molecules. 

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