Electronic excitation energy 588 INDEX

N electron/hole excitations is characterized by the set of excitation energies Cfe P2 where the index k labels the quantum number of excitation p. k labels its quantum number. Assuming a simple model for electron tunneling matrix elements [7]... 

The energy and structure parameters listed in the tables of this review belong in general to the v=0 vibrational state their notation is r0 for the interatomic distance, T0 for the 0-0 excitation energy. Vibrational frequencies v" are those of the lower (usually ground) state while v is the notation for the upper electronic states. Equilibrium parameters refering to the potential minimum and only available for diatomics are indexed by e (re, coe,xe). toe, xe and vv are connected by the equation... 

Other pharmacological activities have also been correlated with quantum-chemically derived descriptors. For instance, the quantitative structure-activity relationship developed for the antibacterial activity of a series of monocyclic (i-lactam antibiotics included the atomic charges, the bond orders, the dipole moment, and the first excitation energy of the compound [103]. The fungicidal activity of A3-l,2,4-thiadiazolines has been correlated with an index of frontier orbital electron density derived from semi-empirical PM3 molecular orbital calculations [104],... 

In this relation, N , g , and e are number densities, statistical weights, and energies of the electronically excited atoms, radicals, or molecules, respectively the index n is the principal quantum number. From statistical thermodynamics, the statistical weight of an excited particle g = Ig n, where gi is the statistical weight of an ion No and go are concentration and statistical weights of ground-state particles, respectively. 

Excitation of the investigated stilbene molecule from its ground state H to the Franck-Condon state occurs in a few femtoseconds. As a result, only fast electronic polarization techniques can follow a drastic change of the charge distribution around the zwitterionic exited FC state. The latter has been proved particularly by the excitation energy dependence on the solvent refractive index [23]. The first step after excitation to the Franck-Condon state of the trans-stilbene configuration is vibrational relaxation followed by solvent-solute relaxation that leads to a rapid population of the H state from which fluorescence occurs. These relaxation processes result in a Stokes shift (A ). 

Contents Introduction. - Volume Plasmons. - The Dielectric Function and the Loss Function of Bound Electrons. -Excitation of Volume Plasmons. - The Energy Loss Spectrum of Electrons and the Loss Function. - Experimental Results. - The Loss Width. - The Wave Vector Dependency of the Energy of the Volume Plasmon. - Core Excitations. -Application to Microanalysis. - Energy Losses by Excitation of Cerenkov Radiation and Guided Light Modes. - Surface Excitations. - Different Electron Energy Loss Spectrometers. - Notes Added in Proof - References. - Subject Index. 

The two-electron integrals involve the LCAO orbitals, and the time-consuming part of a traditional Cl calculation is the transformation of these to integrals involving the basis functions. This is often referred to as the four-index transformation. Not only that, it turns out that traditional Cl calculations are very slowly convergent we have to add a vast number of excited states in order to improve the energy significantly. 

Separation of Electronic and Nuclear Motions. The polarizabilities of the ground state and the excited state can follow an electronic transition, and the same is true of the induced dipole moments in the solvent since these involve the motions of electrons only. However, the solvent dipoles cannot reorganize during such a transition and the electric field which acts on the solute remains unchanged. It is therefore necessary to separate the solvent polarity functions into an orientation polarization and an induction polarization. The total polarization depends on the static dielectric constant Z), the induction polarization depends on the square of the refractive index n2, and the orientation polarization depends on the difference between the relevant functions of D and of n2 this separation between electronic and nuclear motions will appear in the equations of solvation energies and solvatochromic shifts. 

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