Bound energy

In some instances, however, pai t of the chemical energy bound in relatively high-enthalpy compounds can be converted directly to electricity as these reactants are converted to produc ts of lower enthalpy (galvanic action). A process in the opposite direc tion also is possible for some systems an elec tric current can be absorbed as the increased chemical energy of the higher-enthalpy compounds (electrolytic action). The devices in which electrochemical energy conversion processes occur are called cells. 

In chemiluminescence, some of the chemical reaction products developed remain in an excited state and radiate light when the excitation is discharged. This is particularly so at low pressures, when the collision frequency is low the excitation is discharged as light radiation. The extra energy bound to the excited molecule can discharge through impact or molecular dissociation. 

Not all quantum chemical calculations on zeolite clusters involve necessarily millions of integrations, and in the case of iso-electronic chemical systems fulfilling certain geometrical criteria, almost trivial back-of-an-envelope type calculations can yield rigorous upper and lower energy bounds. Fortunately, some zeolite structural units fulfill these geometric criteria. 

These energy bounds are based on two theorems (10-12) which utilize the fact that in the quantum chemical energy expectation value functional the nuclear charges can be regarded as continuous variables. A series of energy relations can be derived for iso-electronic molecules which contain different nuclei, or the same nuclei in different positions. A corollary of the first theorem states (eq.32 in (10)) that... 

If energy values are available for the single atom Er and for one of the cluster models, e.g. for system asa of the alternating Al, Si, Al arrangements then result (23) gives both upper and lower energy bounds for system aas, that system is not favoured according to Loewenstein s aluminum avoidance rule. 

In the above inequalities the electronic energy of the erbium atom is much lower than that of cluster models (aas) and (asa). Although the coefficients 1/14 and 1/13 of terms involving Ee(Er) are small, the large negative value of Ee(Er) renders the calculated energy bounds rather loose and of little practical value. 

For zeolite structural units of the above size detailed ab initio calculations are prohibitively expensive even with the currently available most advanced computer programs. Convexity relation (13), and the resulting energy bounds, on the other hand, are easily applicable to a variety of similar problems, and require only few elementary algebraic operations. 

As noted earlier, for each particle i, there is a discrete spectrum of positive energy bound states and positive and negative energy continuum states. Let us consider a product wave function of the form = i//i(l)i//2(2), a normalizable stationary bound-state eigenfunction of... 

E. Brandas, D.A. Micha, Variational Methods in the Wave Operator Formalism. Applications in Variation Perturbation Theory and the Theory of Energy Bounds, J. Math. Phys. 13 (1972) 155. 

The excitation levels (there may be several) of an insulator do not extend to the vacuum level of zero energy. Any photon absorbed by an insulator will result in an electron from one of the unexcited energy levels corresponding to the valence band transferring to one of the excitation levels. The absorption spectra related to these photons can be considered a band pass function only photons with an energy bounded by specific values will excite the material. The excited electrons cannot move about within the molecular structure of the insulator. They are normally de-excited by fluorescence or phosphorescence. 

A long time ago. Wall and Porter have mentioned the existence of upper energy bounds for H + H2 collinear reactions. More recently, Wright et have observed quite similar... 

Here we comment briefly on a two-band model crystal with a single energy gap. A schematic picture for the density of states is shown in Fig. 3. Following the notations of Turchi et al., we denote by E, j, 3, 4 the energy bounds, by W the half-width of the total spectrum, and by G the half-width of the gap. 

We shall distinguish two types of methods for dynamic shape analysis. The methods of the first type are used to determine which nuclear arrangements are associated with a given topological shape. The methods of the second type determine the available topological shapes compatible with some external conditions, for example, with an energy bound. 

Eigenfunction expansions as used in Ref. 168 are not accurate near the critical point. Instead, we developed a shooting point method in order to make a direct numerical integration of Eq. (110) with the condition Eq. (112). Real energies (bound and virtual) were found by bisection methods, and for complex energies it was necessary to combine the Newton-Raphson and grid methods. 

In the general case, not all the energy of the system during an isochoric process can be transformed into work ( AG). Part of the energy ( bound energy, proportional to the residual entropy 85) is not used [368] then we may write... 

Skopintsev, B. (1982). New data on the composition of organic matter from ocean water and the energy bound in it. Oceanology 21, 582-588. 

The total energy in a portion of material can be split in either of two ways Total energy = internal energy + external energy, or Total energy = free energy + bound energy... 

He arose and, taking up his crook, began to awaken the sheep that still slept. He had noticed that, as soon as he awoke, most of his animals also began to stir. It was as if some mysterious energy bound his life to that of the sheep, with whom he had spent the past two years, leading them through the countryside in search of food and water. "They are so used to me that they know my schedule," he muttered. Thinking about that for a moment, he realized that it could be the other way around that it was he who had become accustomed to their schedule. 

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