Coulombic mechanism, energy

The Coulombic mechanism is a relatively long-range process in as much as energy transfer can be significant even at distances of the order of lOnm. 

In order for rapid and efficient energy transfer to occur by the Coulombic mechanism ... 

A detailed theory of energy transfer by the Coulombic mechanism was developed by Forster, so the process is often referred to as Forster resonance energy transfer (FRET). According to the Forster theory, the probability of Coulombic energy transfer falls off inversely with the sixth power of the distance between the donor and the acceptor. For... 

The Coulombic mechanism would require that both 3D — 3D and 1A —> 3A were allowed transitions, which clearly they are not as both are spin-forbidden processes. Thus, triplet-triplet energy transfer by the long-range Coulombic mechanism is forbidden. 

The molecular mechanics energy of a molecule is described in terms of a sum of contributions arising from distortions from ideal bond distances ( stretch contributions ), bond angles ( bend contributions ) and torsion angles ( torsion contributions ), together with contributions due to non-bonded (van der Waals and Coulombic) interactions. It is commonly referred to as a strain energy , meaning that it reflects the strain inherent to a real molecule relative to some idealized form. 

Metallic properties are also observed in columnar stacked complexes in which the intrachain separation is too long for conduction to be associated with the formation of a band from overlap of the metal dz2/pz orbitals. For these complexes the conduction process involves carriers present in the delocalized MOs extending over die whole complex. The conduction process in these compounds may be described by a hopping mechanism in which the on-site Coulomb repulsion energy has been reduced by the delocalization of the charge over the whole molecule. 

The Forster mechanism is also known as the coulombic mechanism or dipole-induced dipole interaction. It was first observed by Forster.14,15 Here the emission band of one molecule (donor) overlaps with the absorption band of another molecule (acceptor). In this case, a rapid energy transfer may occur without a photon emission. This mechanism involves the migration of energy by the resonant coupling of electrical dipoles from an excited molecule (donor) to an acceptor molecule. Based on the nature of interactions present between the donor and the acceptor, this process can occur over a long distances (30—100 A). The mechanism of the energy transfer by this mechanism is illustrated in Figure 11. 

In our first simple example the electrostatic potential set up by CsCl is almost but not quite a minimal surface [10]. The reason is that the Coulomb electrostatic energy is only a part of the whole electromagnetic field. Two body, three and higher order, non-additive van der Waals interactions contribute to the complete field, distributed within the crystal. This leads one to expect that the condition that the stress tensor of the field is zero, as for soap films, yields the condition for equilibrium of the crystal. Precisely that condition is that for the existence of a minimal surface. Strictly speaking the minimal surface might be defined by the condition that the electromagnetic stress tensor is zero. But in any event, we see in this manner that the occurrence of minimal surfaces, should be a consequence of equilibrium (cf. Chapter 3,3.2.4). Indeed a statement of equilibrium may well be equivalent to quantum statistical mechanics. 

Dexter- or a Coulomb-type energy transfer mechanism. However, the second step is a temperature-independent transfer, which could be attributed to a Forster dipole-dipole interaction type [42],... 

Many molecular modelling techraques that use force-field models require the derivatives of the energy (i e the force) to be calculated with respect to the coordinates. It is preferable that analytical expressions for these derivatives are available because they are more accurate and faster than numerical derivatives. A molecular mechanics energy is usually expressed in terms of a combination of internal coordinates of the system (bonds, angles, torsions, etc.) and interatomic distances (for the non-bonded interactions). The atomic positions in molecular mechanics are invariably expressed in terms of Cartesian coordinates (unlike quantum mechanics, where internal coordinates are often used). The calculation of derivatives with respect to the atomic coordinates usually requires the chain rule to be applied. For example, for an energy function that depends upon the separation between two atoms (such as the Lennard-Jones potential. Coulomb electrostatic interaction or bond-stretching term) we can write ... 

X lO barrels (bbl), where 1 bbl = 42U.S. gal. Hojw many cubic miles is this In electrochemical equations it is common to write in the symbol S to remind the user to convert from moles of electrons to coulombs. This is just like the force-mass and thermal energy-mechanical energy conversion factor, namely,... 

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