Bond alternation coefficient

Another approach in which the bond length alternation is taken into account is based on the sum of squared differences of the sequential bond lengths. The index called BAG (bond alternation coefficient) reads ... 

The bond alternation coefficient (BAG) has also been proposed as an aromaticity descriptor which has been defined as... 

A comparison of HOMA with other geometry-based aromaticity indices has shown that the indices were not fully equivalent (even estimated for the same geometry). Since the indices BAC and particularly /e are purely bond alternation dependent, whereas HOMA depends also on the bond elongation, these two kinds of indices clearly do not correlate with each other (/e and BAC vs HOMA give correlation coefficients of only 0.56 and 0.67, respectively) whereas... 

The optimum coefficients in Equation 2 are Eq -37.8363 and E =-0.5685 au. Eq is very close to the value -37.8366 found for the pure graphite clusters. The value of E corresponds to a contribution of 47.1 kcal/mol to the total energy of Cg 2Hg for each bonded H-atom (the hydrogen atom has an energy of -0.4935 au in the oasis set used). Alternatively, the parameter values can be interpreted as 83.3 kcal/mol per C-C bond, 88.7 kcal/mol per C-H bond. 

The accuracy of alternative Lewis structures can be assessed by specifying the number and locations of lone pairs and two- and three-center bonds with a SCHOOSE keylist (a standard option of the NBO program). (The directed SCHOOSE list replaces the usual NBO search over all possible Lewis structures, but the hybrids and polarization coefficients of CHOOSE structures are optimized in the usual way.) The increased non-Lewis density measures the larger error of the CHOOSE structure compared with the optimal NBO structure. 

An alternative approach is possible. Just at the coefficients B, C, D, etc. define the thermodynamic properties of the real fluid so coefficients B°, C°, D°, etc. define thermodynamic properties for a hypothetical fluid which we will call the primary fluid. The primary fluid can be regarded as having the properties which the real fluid might have in the absence of association. It is assumed that when secondary interactions such as hydrogen bonding are imposed on the primary fluid the real fluid will be simulated. This assumption is an acceptable approximation at low densities, but is unlikely to hold at high densities where the addition of hydrogen bonds may produce new structural features. 

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