Induction energy definition

The second-order dispersion energy is defined as the difference between the second-order polarization and induction energies, E = E j — E J. One can also use the following direct definition... 

For an inductive dipole, from the definition of the inductive energy variation in Equation 9.2 and the inductive gate variable in Equation 9.29, the following expression for the received power is obtained ... 

In the literature on chemistry and biochemistry, in particular in the cited statements from Lehninger s textbook, the intermediate substance of the second kind is identified with highly reactive particles (intermediate products of the first kind). This mistake is based on fuzziness of the chemical induction definition and identification of conjugated reactions with consecutive ones. As a result, Lehninger has concluded that the energy transfer via general intermediate product is the universal property of consecutive reactions. ... 

Although the spherical form of the multipole expansion is definitely superior if the orientational dependence of the electrostatic, induction, or dispersion energies is of interest, the Cartesian form171-174 may be useful. Mutual transformations between the spherical and Cartesian forms of the multipole moment and (hyper)polarizability tensors have been derived by Gray and Lo175. The symmetry-adaptation of the Cartesian tensors of quadrupole, octupole, and hexadecapole moments to all 51 point groups can be found in Ref. (176) while the symmetry-adaptation of the Cartesian tensors of multipole (hyper)polarizabilities to simple point groups has been considered in Refs. (172-175). 

The IRMPD experiment has been developed into a quantitative tool for the estimation of activation barriers of fragmentation processes, the so-called FRAGMENT method [28]. The barriers correspond to binding energies for simple bond dissociation reactions, if the reverse reactions do not have significant barriers. Consequently, kinetic and thermodynamic data are accessible with this method despite the ill-definition of temperature. The experiment relies on the generation of a steady state of IR photon absorption and emission after a short induction period. 

A numerical simulation tool has been developed that is capable of accounting for radial and axial variations in liquid-fuel distribution. In the absence of definite information on the chemistry of JP-10, a two-step global model analogous to that used in the gas-phase detonation simulations has been constructed. In this model, the residence time of the fuel vapor is tracked, and energy releaise is allowed to occur only after the elapse of a specified induction time. The amount of energy release is based on the lower heating value of the fuel and is calibrated to result in the CJ-detonation velocity for a fully vaporized fuel. 

We recognize on the right side (the first two terms) the complete first-order contribution i.e., the electrostatic energy (Feist) and the valence repulsion energy (F pj,). From the definition of the induction and dispersion energies [Eqs. (13.13) on p. 808], as well as fi-om the reduced resolvent Rq of Eq. (10.76) on p. 644. (applied here to the individual molecules), one may write... 

As might be expected, the results of analyses that separate these terms as stringently as possible, such as Hayes and Stone s intermolecular perturbation theory (IMPT) [44], which uses a procedure [45] in which the difference between monomer and dimer basis sets is used to apportion induction (= polarization) and donor-acceptor contributions. Stone and Misquitta [46] point out that using this definition, the donor-acceptor energy would vanish if a complete basis set were used. The observed dependence for the water dimer is shown in Figure 18.6. 

There is considerable information available in the hterature on the design of ejectors (steam jet ejectors, water jet pumps, air injectors, etc.) supported by extensive experimental data. Most of this information deals with its use as an evacuator and the focus is on ejector optimization for maximizing the gas pumping efficiency. The major advantage of the venturi loop reactor is its relatively very high mass transfer coefficient due to the excellent gas-liquid contact achieved in the ejector section. Therefore, the ejector section needs careful consideration to achieve this aim. The major mass transfer parameter is the volumetric liquid side mass transfer coefficient, k a. The variables that decide k a are (i) the effective gas-hquid interfacial area, a, that is related to the gas holdup, e. The gas induction rate and the shear field generated in the ejector determine the vine of and, consequently, the value of a. (ii) the trae liquid side mass transfer coefficient, k. The mass ratio of the secondary to primary fluid in turn decides both k and a. For the venturi loop reactor the volumetric induction efficiency parameter is more relevant. This definition has a built in energy... 

---