Empirical bond energies

For approximate estimation of enthalpy changes during reactions, use can be made of empirical bond energies (Table 6-7) which represent the approximate enthalpy changes (-AH°) for formation of compounds in a gaseous state from atoms in the gas phase. Other more comprehensive methods of approximation have been developed 49/50... 

Empirical bond energies are transferable from molecule to molecule, for example, in saturated hydrocarbons to within 0.01 ev. Are the detailed effects of molecular environment, implicit in the equations given above, compatible with such a constancy of bond energies ... 

From these considerations it would seem therefore that environmental effects, at least on the correlation part, are within the constancy of empirical bond energies. Correlation energies of lone pairs and ion-cores also seem transferable to this accuracy ( 0.01-f).02 ev). 

Table 1. Comparison of perturbation results through fourth order with empirical bond energies...

A molecular-mechanics steric energy can be combined with empirical bond-energy parameters to calculate gas-phase heats of formation as discussed later... 

The Tersoff potential was designed specifically for the group 14 elements and extends the basic empirical bond-order model by including an angular term. The interaction energy between two atoms i and j using this potential is ... 

A force field that can produce vibrational spectra has a second advantage in that the Ay// calculations can be put on a much more satisfactory theoretical base by calculating an enthalpy of formation at 0 K as in ab initio procedures and then adding various thermal energies by more r igorous means than simply lumping them in with empirical bond enthalpy contributions to Ay//-. The stronger the theoretical base, the less likely is an unwelcome surprise in the output. 

According to the namre of the empirical potential energy function, described in Chapter 2, different motions can take place on different time scales, e.g., bond stretching and bond angle bending vs. dihedral angle librations and non-bond interactions. Multiple time step (MTS) methods [38-40,42] allow one to use different integration time steps in the same simulation so as to treat the time development of the slow and fast movements most effectively. 

The energy parameters used for the reference polyene by Hess and Schaad were developed on a strictly empirical basis. Subsequendy, Moyano and Paniagua developed an alternative set of reference bond energies on a theoretical basis. These values are shown... 

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. 

Exercise 1.3. Using the equations introduced in the last problems, generate a potential surface for the H2 molecule assuming that a = —13.6 eV, /3 = —9.5 exp[-/ ] eV (with R in A), D = 0.3 A, and a = 1. Consider only the first iteration with PH = 1 and Z = 1. Adjust the value of /3n to see how it affects the value of the bond energy (the value of E at its minimum). Such a procedure will clarify the point that /3n (as well as the other parameters) are chosen semi-empirically to give the best potential surface for our molecule. 

C06-0094. Use average bond energies (Table 6-2) to compare the stabilities of ethanol, C2 H5 OH, and dimethyl ether, (CH3)2 O, which have the same empirical formula, C2 Hg O (all the bonds are single bonds). 

The resulting data for liquid metals indicate a systematic relationship with the bonding energy of the element, which is reflected in the heat of vaporization AH°ap. Skapski suggested an empirical equation... 

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