Molecular energy levels, electronic component

The first attempt to explain the characteristic properties of molecular spectra in terms of the quantum mechanical equation of motion was undertaken by Born and Oppenheimer. The method presented in their famous paper of 1927 forms the theoretical background of the present analysis. The discussion of vibronic spectra is based on a model that reflects the discovered hierarchy of molecular energy levels. In most cases for molecules, there is a pattern followed in which each electronic state has an infrastructure built of vibrational energy levels, and in turn each vibrational state consists of rotational levels. In accordance with this scheme the total energy, has three distinct components of different orders of magnitude,... 

Fig. 1. The molecular energy level model used to discuss radiationless transitions in polyatomic molecules. 0O, s, and S0,S are vibronic components of the ground, an excited, and a third electronic state, respectively, in the Born-Oppenheimer approximation. 0S and 0 and 0j are assumed to be allowed, while transitions between j0,j and the thermally accessible 00 are assumed to be forbidden. The f 0n are the molecular eigenstates...

Fig. 4. Molecular energy level diagram used to discuss radiationless processes in polyatomic molecules. Q is the ground electronic state, and <>ox denotes a thermally accessible vibronic component of this state. Electric dipole transitions from to the electronic state are allowed (or vibronically induced), while those to <(), are forbidden. ,i designates a vibronic component of and <, j is a component of The electronic states o> >, 4>/ re obtained from the adiabatic Bom-Oppenheimer approximation.

In the course of investigation of reactivity of the mesoionic compound 44 (Scheme 2) the question arose if this bicyclic system participates in Diels-Alder reactions as an electron-rich or an electron-poor component <1999T13703>. The energy level of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) orbitals were calculated by PM3 method. Comparison of these values with those of two different dienophiles (dimethyl acetylenedicarboxylate (DMAD) and 1,1-diethylamino-l-propyne) suggested that a faster cycloaddition can be expected with the electron-rich ynamine, that is, the Diels-Alder reaction of inverse electron demand is preferred. The experimental results seemed to support this assumption. 

Energy levels of heavy and super-heavy (Z>100) elements are calculated by the relativistic coupled cluster method. The method starts from the four-component solutions of the Dirac-Fock or Dirac-Fock-Breit equations, and correlates them by the coupled-cluster approach. Simultaneous inclusion of relativistic terms in the Hamiltonian (to order o , where a is the fine-structure constant) and correlation effects (all products smd powers of single and double virtual excitations) is achieved. The Fock-space coupled-cluster method yields directly transition energies (ionization potentials, excitation energies, electron affinities). Results are in good agreement (usually better than 0.1 eV) with known experimental values. Properties of superheavy atoms which are not known experimentally can be predicted. Examples include the nature of the ground states of elements 104 md 111. Molecular applications are also presented. 

The photostability observed upon immobilization is clearly important from the application point of view but also for fundamental reasons. The photostability of the assembly shows that upon interaction between the molecular component and the semiconductor surface, fundamental changes in the photophysical behavior can be obtained provided that the energy levels of modifier and surface are tuned. Importantly, these fundamental changes are not related to changes in the electronic properties of the molecular component, but are caused by the interaction of the excited molecular component with available surface states. 

The electronic structure of microcrystalline silicon of one-dimensional (1-D), 2-D, and 3-D clusters were calculated using the Discrete-Variational (DV)-Xa Molecular-Orbital method. The calculated results are discussed with respect to the effect of the size and the number of dimensions on the energy levels of molecular orbitals. The energy-gap (Eg) between the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) decreases with the increase of cluster size amd the number of dimensions. It is found that including silicon 3d orbitals as basis sets decreases the Eg value. The results show that the components of silicon 3d orbitals in the unoccupied levels near LUMO are over 50 per cent. The calculated results predict that the Eg value will be close to the band gap of crystalline silicon when a 3-D cluster contadns more than 1000 silicon atoms with a diameter of 4nm. 

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