Bond orders empirical relationships

Pauling has found empirically that there was a simple logarithmic relationship between the bond length R and the bond order 0, namely ... 

When deriving the indices AN and /, used to calculate the values of bond orders N from experimental data on bond lengths R, the following empirical relationship is employed ... 

This recalls the equation for the empirical relationship between bond order and bond length given by Pauling, which... 

The iterative method is incorporated into the HMO method as follows starting with certain values of and atomic charges and bond orders are calculated. From these values new values of and arc obtained by using certain relationships (empirical or semi-empirical) between and a, and The secular deter-... 

Other pharmacological activities have also been correlated with quantum-chemically derived descriptors. For instance, the quantitative structure-activity relationship developed for the antibacterial activity of a series of monocyclic (i-lactam antibiotics included the atomic charges, the bond orders, the dipole moment, and the first excitation energy of the compound [103]. The fungicidal activity of A3-l,2,4-thiadiazolines has been correlated with an index of frontier orbital electron density derived from semi-empirical PM3 molecular orbital calculations [104],... 

The value of the electron density at the bond point p(rj) correlates with bond order. This empirical relationship was first noted by Bader et al. nonlinear correlation, Eq. [35], was proposed. This equation properly executes the limit as p — 0, — 0. A number of problems are... 

We would expect there to be a relationship between the electron density among nuclei and the bond length. There is a correlation between bond length and bond order. Bonds get shorter as bond order increases. Pauling defined an empirical relationship for bond order in terms of bond length for C-C, C=C, and C=C bond lengths. For carbon, the parameter a is 0.3 ... 

Of the many empirical relationships that have been found to link the energies of bonds to their lengths, the most generally applicable, particularly when wide variations in length need to be accommodated e.g., as between carbon-carbon single and triple bonds, although note that our method makes no reliance on the concept of bond order), is the following ... 

Bond orders for 324 bonds in 60 heterocyclic molecules, including 12 azines, were calculated at the HF/6-31G(d) and MP2/6-31G(d) levels of theory <2002IJQ534>. It was found that the MP2-derived bond orders were smaller by an average of 17%, compared to those derived from HF calculations. The ab initio results were further compared to the Gordy bond orders, derived on the basis of an empirical relationship. The latter were found to be much larger than the ab initio values, and the authors recommendation was that Gordy bond orders should not be used in aromaticity studies. 

In 1993 Dixon and Jurs [209] used empirically calculated atomic charges to describe the pK s of a diverse collection of alcohols, phenols, and carboxylic acids. They found a strong linear relationship (r = 0.993) between their charge parameters and the pK s for a set of 135 oxyacids. Citra later used charges and bond orders from AMI calculations to characterize the pK s of phraiols, carboxylic acids, and alcohols [210]. Here too the best correlations were found for the phenols. Citra also compared his MLR results with results from two commercially available programs and found that all three approaches performed well. He cautioned, however, that his molecular orbital results were sensitive to the final optimized geometry found in the calculations. 

Recently, semiempirical methods based on DFT calculations have been developed for catalyst screening. These methods include linear scaling relationships [41, 42] to transfer thermochemistry from one metal to another and Brpnsted-Evans-Polanyi (BEP) relationships [43 7]. Here, these methods and also methods for estimation of the surface entropy and heat capacity are briefly discussed. Because of their screening capabilities, semiempirical methods can be used to produce a first-pass microkinetic model. This first-pass model can then be refined using more detailed theory aided by analytical tools that identify key features of the model. The empirical bond-order conservation (BOC) method, which has shown good success in developing microkinetic models of small molecules, has recently been reviewed [11] and will not be covered here. 

Several definitions of Bab that invoke empirical relationships have been proposed. Since the exact meaning of bond orders obtained from those definitions is somewhat obscure, they are less useful than their counterparts based upon the partitioning of density matrices. 

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