General Energy Formulas

Any bond energy formula can be expressed either i) by reference to a selected bond with reference net atomic charges q and q°i at the bond-forming atoms k and I, or ii) by reference to hypothetical k-l bonds constructed with the assumption q = q° = 0. The former reflects a physical situation, but requires additional work in order to sadly charge normalization constraints it is most useful in the constmction of general energy formulas for molecules that use chemical shifts espressed with respect to the appropriate references. The latter method simplifies bond-by-bond calculations. The two forms are... 

Direct applications of Eq. (10.12) are generally difficult to handle—this is why the more efficient charge-dependent energy formulas were developed in the first place. Most thorough tests were made for selected carbon-carbon bonds [13,14,44,108] (Table 1.1). 

This energy formula [234,235] is general and suffers from no approximations in that all the appropriate bonded and nonbonded contributions are formally accommodated and because the electroneutrality requirements are met in the definition of reorganizational energy. Only dissociations yielding electroneutral products need be considered as the formation of ions, KL + L, require no more than... 

Generally, in the ec energy correcting approaches one employs the so-called asymmetric energy formula [82]... 

It is important to know that this generally applied formula is connected with the vibration of two particles one creating the energy hyperplane, the other swinging in this plane or in an abstract sense two thermal oscillations superposed on one another. 

This expression may be interpreted as a generalized Born formula for an off-centered charge in a spherical cavity. Accordingly, for a development up to the Zmax order, the percentual error in total energy may easily be shown to be... 

Derivations of exchange and correlation energy formulas are in general based on the r value, (the Wigner-Seitz radius) which is related to the electron density by,... 

Changing the formulas according to the standard states is awkward, especially for heterogeneous reactions, so we prefer the more general equation (2.3-8). Defining a generalized energy function S — p + TS to represent the... 

The corresponding excess entropy, enthalpy, volume, energy, heat capacity and compressibility are readily obtained by use of the general thermodynamic formulae. 

Most general EN formulas contain an equal balance of nonprotein energy between carbohydrate and fat. Elemental or chemically defined products are the exception because they are intended to be high-carbohydrate, low-fat formulas to enhance absorption and digestion. In pulmonary patients administration of a high-carbohydrate formula... 

The value 13-53 volts is found for the energy of the hydrogen electron. The general transformation formula is... 

This methodology proceeds from the division of the total molecular solvation energy into the solute-solvent electrostatic and inductive polarization terms, standard-state free energy of eavity creation in the solvent plus the solute-solvent dispersion interaction, and an empirical part of the nuclear motion free energy. The solvent polarization term is presented using the generalized Bom formula ... 

---