Empirical additive bond energy

The estimation of lattice energies is based on the calculation of the coulombic (Madelung) energy, which comprises most of the lattice energy, to which an additional bonding energy due to metal-metal attractive interaction—for example, as in some rutile type oxides (26)— is added. The latter may be obtained empirically or by use of ligand field theory (11). 

The classical equations of motion used in molecular mechanics (MM) are only slightly more difficult to solve than simple additive bond energy equations hence MM calculations are fast and not very demanding of computer resources. In molecular mechanics, one determines the structure of a molecule from a knowledge of the force field, a collection of empirical force constants governing, in principle, all classical mechanical interatomic interactions within the molecule. In practice, it is not feasible for a parameter set to include all possible interactions within a complicated molecule. One hopes that all significant interactions have been included in the force field. 

In addition to the obvious structural information, vibrational spectra can also be obtained from both semi-empirical and ab initio calculations. Computer-generated IR and Raman spectra from ab initio calculations have already proved useful in the analysis of chloroaluminate ionic liquids [19]. Other useful information derived from quantum mechanical calculations include and chemical shifts, quadru-pole coupling constants, thermochemical properties, electron densities, bond energies, ionization potentials and electron affinities. As semiempirical and ab initio methods are improved over time, it is likely that investigators will come to consider theoretical calculations to be a routine procedure. 

Additivity schemes with fixed bond energy (or enthalpy) parameters plus a host of corrective factors reflecting nonbonded steric interactions have a long history in the prediction of thermochemical properties, such as the classical enthalpy of formation of organic molecules. AUen-type methods, for example, nicely Ulustrate the usefulness of empirical bond additivity approaches [1,2]. 

Empirical Feigned Bond Additivity. Let us put our results in perspective with respect to brute-force empirical fits intended to define best possible sets of transferable bond energies, Remembering that for ethane c+ 3 h = 0, we can write... 

The success of empirical additivity schemes [11, 12] is based on the recognition that the contributions to the enthalpy depend not only on the atoms and bonds present but also on their particular grouping, for example as CH3, CH2, or CH. Thus, popular and successful estimation schemes use parameters which are proportional to the number of groups of atoms in the molecule, implicitly or explicitly using for all series a methylene increment derived from alkanes. The enthalpy changes resulting from the presence of heteroatoms requires appropriately derived bond energy terms. If there are any real differences in the... 

The Knudsen effusion method In conjunction with mass spectrometrlc analysis has been used to determine the bond energies and appearance potentials of diatomic metals and small metallic clusters. The experimental bond energies are reported and Interpreted In terms of various empirical models of bonding, such as the Pauling model of a polar single bond, the empirical valence bond model for certain multiply-bonded dlatomlcs, the atomic cell model, and bond additivity concepts. The stability of positive Ions of metal molecules Is also discussed. 

Returning, then, to the expansion of Equation (2), we note that the terms represent different valence bond structures. Why should they all have the same amplitude and phase This situation is very similar to the problem of determining the "resonance energy" of ben-zenoid molecules (25,26,27). In that case, of all the possible valence bond structures which might contribute, only the Kekule structures are used. For large benzenoid systems this is only a small fraction of the total number of structures. Furthermore, it is assumed that they all enter with equal expansion coefficients (i.e., equal amplitude and phase). In addition, the matrix elements which convert one structure into another are set equal to a common value, determined empirically. Thus, the energy lowering associated with "resonance" in benzenoid molecules has a mathematical structure which maps onto the discussion in the Introduction. However, there are some important differences. 

In the empirical valence bond model [31], the potential energy surface is typically non-linearly related to two model states, called effective diabatic states corresponding to the reactant and the product bonding characters, Eq. 9. Although additional diabatic states, important for describing the transition state, can be included and have often been discussed, the computational complexity makes it difficult in practical use for the study of enzyme reactions. 

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