Resonance energy operator

Since Ofc is a resonance energy operator and Clk — k is an energy transfer rate operator, one expects to find a relationship between their time dependent expectation values of the general form... 

Here A and B denote atoms in each of the two interacting molecules. The V operator contains all the potential energy operators from both molecules, and the (xa V xb) integral is basically a resonance type integral between two atomic orbitals, one from each molecule. The pa is the electron density on atom A, and the first term in (15.1)... 

These are the classical analogues of quantum scattering resonances except that these latter ones are associated with the wave eigenfunctions of the energy operator, although the eigenstates of the LiouviUian operator are probability densities or density matrices in quanmm mechanics. Nevertheless, the mathematical method to determine the Pollicott-Ruelle resonances is similar, and they can be obtained as poles of the resolvent of the LiouviUian operator... 

First, the range of separation. The experimentally determined tip-sample separation is 1-4 A before a mechanical contact (Diirig et al. 1988). For most metals, the normal nucleus-nucleus distance of a mechanical contact is 2.5-3 A. Therefore, on the absolute tip-sample scale, it is 3.5-7 A. By comparing with the case of H2, we notice that this is the range where the resonance interaction dominates. In other words, under normal STM operation conditions, over a distance range of about 3 A, resonance energy is almost solely responsible to the atomic force, and the distance dependence of the force should be approximately exponential. 

Principle of operation of a fluorescence resonance energy transfer biosensor. 

We combine now the disordered part (4.3) with the retarded part of (4.1), which does not depend on the particular resonance energy of one domain or site, but on the transition dipole operators, and therefore is identical for our model to that of the perfect 2D lattice. Thus, we obtain the following effective hamiltonian for the disordered 2D exciton ... 

Figure 16.25 Semiconductor nanoparticle-based fluorescent sensors (a) Forster resonant energy transfer (FRET) between two nanoparticles induced by analyte, (b) crown ether receptor for potassium ions, and (c) operation principle of maltose fluorescent sensor. (Adapted from Chen et at. [144] and Medintz et at. [146])...

Chlorophylls chlorophylls have a variety of functions in photosynthetic systems, including collection of photons, transfer of excitation energy, operation of the primary photoinduced charge separation, and transfer of the resulting photoelectrons. Resonance Raman spectroscopy offers the possibility of selectively observing chlorophylls in their native structures (Lutz, 1984 Koyama et al., 1986 Tasumi and Fujiwara, 1987 Lutz and Robert, 1988 Nozawa et al., 1990 Lutz and Mantele, 1991). Transient Raman spectroscopy is a unique method of revealing the excited state structures of chlorophylls. The T1 and SI states were revealed by nanosecond Raman spectroscopy (Nishizawa et al., 1989 Nishizawa et al., 1991 Nishizawa and Koyama, 1991). 

Dewar resonance energy -> resonance indices DFT-based descriptors - quantum-chemical descriptors diagonal matrix -> algebraic operators diagonal operator -> algebraic operators (O diagonal matrix) dielectric constant electric polarization descriptors dielectric susceptibility electric polarization descriptors... 

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