Electronic States of Polyatomic Molecules

Weitz E and Flynn G W 1981 Vibrational energy flow in the ground electronic states of polyatomic molecules Adv. Chem. Rhys. 47 185-235... 

The entire approach presupposes the separation of electronic degrees of freedom. As already noted, for the higher electronic states of polyatomic molecules, there can be important couplings with both spectroscopic and dynamic implications. The vibronic spectroscopy of benzene is reviewed by Ziegler and Hudson (1982). 

For electronic states of polyatomic molecules for which the net electronic spin S is nonzero, we get an interaction between rotational and spin angular momenta. We shall not consider this case, but will restrict ourselves to rotational energies of singlet electronic states. Polyatomic molecules with nonsinglet ground electronic states are rare. 

The Jahn-Teller theorem is important in considering the electronic states of polyatomic molecules. Jahn and Teller proved in 1937 that a nonlinear polyatomic molecule cannot have an equilibrium (minimum-energy) nuclear configuration that corresponds to an orbitally degenerate electronic term. Orbital degeneracy arises from molecular symmetry (Section 1.19), and the Jahn-Teller theorem can lead to a lower symmetry than... 

We hope that this review provides a deeper and more satisfactory understanding of the nature and properties of the excited electronic states of polyatomic molecules, and their several modes of decay, and that it will stimulate interest in theoretical and experimental photochemistry. 

A detailed description of the symbolism used to designate electronic states of polyatomic molecules would of itself require an entire book. We shall limit ourselves to a discussion of the factors which govern the appearance of polyatomic spectra and of some of the rules which generally determine intensities and behavior42. 

I 3 1 Rotational Levels of Polyatomic Molecules, 14 I 3.2 Vibrational Levels of Polyatomic Molecules, 15 I 3.3 Electronic States of Polyatomic Molecules, 16 1-4 Thermal Contribution to Photodissociation, 18... 

Till recently, computations of vibronic spectra have been limited to small systems or approximated approaches, mainly as a consequence of the difficulties to obtain accurate descriptions of excited electronic states of polyatomic molecules and to computational cost of full dimensional vibronic treatment. Recent developments in electronic structure theory for excited states within the time-dependent density functional theory (TD-DFT) and resolution-of-the-identity approximation of coupled cluster theory (R1-CC2) and in effective approaches to simulate electronic spectra have paved the route toward the simulation of spectra for significantly larger systems. 

VIBRATIONAL ENERGY FLOW IN THE GROUND ELECTRONIC STATES OF POLYATOMIC MOLECULES... 

Vibrational Energy Flow in the Ground Electronic States of Polyatomic Molecules... 

For nonlinear polyatomic molecules, no orbital angular-momentum operator commutes with the electronic Hamiltonian, and the angular-momentum classification of electronic terms cannot be used. Operators that do commute with the electronic Hamiltonian are the symmetry operators Or of the molecule (Section 12.1), and the electronic states of polyatomic molecules are classified according to the behavior of the electronic wave function on application of these operators. Consider H2O as an example. 

Properties of excited electronic states of polyatomic molecules may be conveniently classified as stationary or nonstationary. A comparison of the present knowledge about properties in these two classifications is interesting. Theoreticians and spectroscopists have been rather successful in developing good descriptions of energy levels and geometries of excited states, and hence the stationary type is in a comparatively advanced state of development. For example, the spectroscopic work of... 

The electronic states of polyatomic molecules can be labeled using the irreducible representations of the symmetry point group of the molecule. (This is another example of how symmetry is important in the understanding of spectra.) As such, the same rule involving the direct product of the irreducible representations applies ... 

When the fluorescence quantum yield of a highly excited valence state is small, as is usual, the hfetime of the excited state is determined primarily by the rates of its radiationless transitions. The theory of radiationless transitions in the excited electronic states of polyatomic molecules was developed several decades ago and is not reviewed in detail. Readers are referred to several excellent comprehensive reviews for further information [9,10]. Here we provide only those materials needed to understand the photophysics of the highly excited electronic states of those polyatomic molecules that exhibit unusually long lifetimes. 

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