Molecular delocalized states

Complexes containing several interacting metal atoms are named clusters. Metal atoms in clusters bound by chemical forces are localized at rather short distances for efficient overlap of their valent orbitals. This overlap results in the system of molecular delocalized states (Fig. 17.2). 

Since a is the energy of a 7r electron in a 2p a.o. and since (3 refers to an electron in a bond, both of these quantities are negative, and the energies above therefore occur in increasing order. The energy associated with the delocalized bond in the molecular ground state is... 

The reorientation of the molecular adsorbates also induces a localization of the electron in the image state which is initially delocalized parallel to the surface. The localization phenomenon was proved by examining the emission angle dependence of the photoelectron spectra. It is concluded that the electrons in the delocalized state are trapped in the localized state at around 300 fs after the excitation, where the electron localization size is estimated to be 12 A. 

Fig. 12. The transition from a localized state (mean spacing 1.5, as indicated) to a delocalized state (mean speicing 1.1) for a cluster of 91 atoms with one-valence-electron each. Shown is the weight (logarithmic scale) of the highest occupied molecular orbital (HOMO) of the cluster on each one of the 91 atoms. The localized state decreases exponentially as one moves away from the atom on which it is centered. The delocalized state has, on the average, the same weight on all the atoms.

There are many electrons in the sample, each in its own trap or in the conduction band (delocalized state), and there is a distribution of trap depths. The trap depths are not all the same because orientational disorder of the molecules provides a variety of polarization potential wells. Furthermore, an electron in a trap seems to couple with vibrational and librational modes of the trapping molecules. The optical absorption band of solvated electrons is very broad (Fig. 8). Part of the broadening might be caused by the distribution of trap depths, and part by the coupling with molecular modes. These parts are sometimes... 

The local or extended nature of molecular-ion states in molecular solids is determined by a competition between fluctuations in the local site energies of these states (which tend to localize them) and the hopping integrals for inter-site excitation transfer (which tend to delocalize them). In order to define this fluctuation-induced localization concept more precisely, consider the model defined by the one-electron Hamiltonian... 

T. Frigato, J. VandeVondele, B. Schmidt, C. Schiitte, and P. Jungwirth,/. Phys. Chem. A, 112, 6125-6133 (2008). Ab Initio Molecular Dynamics Simulation of a Medium-Sized Water Cluster Anion From an Interior to a Surface-Located Excess Electron via a Delocalized State. 

Examine atomic charges and the electrostatic potentit map for the lower-energy transition state. Which atom appear to be most electron rich in each Is the negativ charge concentrated on a single atom in the transition stat or delocalized Add this charge information (either or 5- ) to the molecular structure for the transition stat which you drew previously. 

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