Polyatomic system electronic states

In this chapter, we look at the techniques known as direct, or on-the-fly, molecular dynamics and their application to non-adiabatic processes in photochemistry. In contrast to standard techniques that require a predefined potential energy surface (PES) over which the nuclei move, the PES is provided here by explicit evaluation of the electronic wave function for the states of interest. This makes the method very general and powerful, particularly for the study of polyatomic systems where the calculation of a multidimensional potential function is an impossible task. For a recent review of standard non-adiabatic dynamics methods using analytical PES functions see [1]. 

Conical intersections, introduced over 60 years ago as possible efficient funnels connecting different elecbonically excited states [1], are now generally believed to be involved in many photochemical reactions. Direct laboratory observation of these subsurfaces on the potential surfaces of polyatomic molecules is difficult, since they are not stationary points . The system is expected to pass through them veiy rapidly, as the transition from one electronic state to another at the conical intersection is very rapid. Their presence is sunnised from the following data [2-5] ... 

M. Kasha has evolved still another system of notation in which electronic states are expressed in terms of the initial and final orbitals involved in a transition. This form of description is less precise than the symmetry notation but is very convenient for photochemical purposes, specially for designating energy levels of polyatomic organic compounds. In general, four types of molecules can be identified. 

The calculation of a point on a potential-energy hypersurface is equivalent to calculating the energy of a diatomic or polyatomic system for a specified nuclear configuration and thus presents considerable practical computational difficulty. For certain problems or nuclear configurations, the maximum possible accuracy is needed, and under these conditions relatively elaborate ab initio methods are indicated. For other problems, the description to a uniform accuracy of many electronically excited states of a given system is required. Such is the situation for the atmospheric systems described here, and thus most of our final potential curves are based on the analysis of VCI wave functions constructed to uniform quality for representation of the excited states. 

A situation peculiar to electronic spectra occurs when the perturbing state is dissociative, for the molecule may then undergo a radiationless transition from a stable electronic state to a dissociative one. The phenomenon, known as predissociation, may be detectable by a broadening of the rotational lines which, when the radiationless transition has high probability, become so broad that all traces of rotational structure vanish. Predissociation is observed frequently in polyatomic spectra and seriously restricts the number of band systems suitable for detailed study. 

The necessary and sufficient condition of instability (lack of minimum of the AP) of high-symmetry configurations of any polyatomic system is the presence of two or more electronic states, degenerate (except 2-fold spin degeneracy) or pseudodegenerate, which interact sufficiently strong under the nuclear displacements in the direction of instability . 

An important issue of the application of electronic structure theory to polyatomic systems is the selection of the appropriate basis set. As usual in quantum chemistry, a compromise between precision and computational cost has to be achieved. It is generally accepted that in order to obtain qualitatively correct theoretical results for valence excited states of polyatomic systems, a Gaussian basis set of at least double-zeta quality with polarization functions on all atoms (or at least on the heavy atoms) is necessary. For a correct description of Rydberg-type excited states, the basis set has to be augmented with additional diffuse Gaussian functions. Such basis sets were used in the calculations discussed below. 

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