The Bond Increment Method

The bond increment (BI) method, developed in our laboratory [124-126], offers the possibility of taking into account the spreading out of the charge cloud by using a more elaborate expression of the electrostatic potential, then the simple point charge or point multipole representation. The bond increment method starts from the following approximate wave function  

The SLMOs, according to the usual chemical picture, can be a, lone pair or n orbitals, and they assume the following simple mathematical structure, respectively  

Here stands for a normalized hybrid orbital centered at atom A hAi = 

denotes the number of n centers in the i-th Tc-type molecular orbital. Note that these SLMOs are non-orthogonal, the interbond overlap integrals 

The bond increment method has been applied in this form to numerous chemical and biochemical problems, like the interpretation of organic reaction mechanisms [127], protonation energies [128] and catalytic effects in enzymatic reactions [129]. 

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The heats of formation of some linear alkanes calculated by the bond increment method are shown in Table 1.4. As an example of such calculations, let us determine the AHf values for methane and ethane. For methane, there... 

The actual values of the atomic multipole moments depend on the coefficients of the hybrid orbitals in the individual bond orbitals (bond polarities), on the orientation of the hybrids and on the degree of hybridization. Since these latter two parameters depend significantly on the geometrical arrangement of the atoms [47], the bond increment method may be an adequate tool for constructing the zeroth order wave function, which nevertheless describes the main trends in the conformational and geometrical dependence of the atomic charge distributions and consequently of the electrostatic potential. 

The value of the torsional energy increment has been variously estimated, but TORS = 0.42 kcal mol was settled on for the bond contribution method in MM3, In the full statistical method (see below), low-frequency torsional motion should be calculated along with all the others so the empirical TORS inererneut should be zero. In fact, TORS is not zero (Allinger, 1996). It appears that the TORS inererneut is a repository for an energy eiror or errors in the method that are as yet unknown. 

Several workers have employed features of the molecular electrostatic potential surface to study the pK s of amines. Nagy, Novak, and Aszasz [340] found good linear correlations between the pK s of pyridines, anilines, and aliphatic amines and the minima of the electrostatic potentials for these compounds. They used the CNDO/2 method [341] as well as a bond-increment method with data from Perrin s 1972 compilation [342] for their study. Using the bond-increment approach they found the following relationships ... 

Isotope fractionations in solids depend on the nature of the bonds between atoms of an element and the nearest atoms in the crystal structure (O Neil 1986). The correlation between bond strength and oxygen isotope fractionation was investigated by Schiitze (1980), who developed an increment method for predicting oxygen isotope fractionations in silicate minerals. Richter and Hoemes (1988) applied this method to the calculation of oxygen isotope fractionations between silicate minerals and... 

Each bond is rotated incrementally and the resnlting strnc-tnres are minimized. Systematic search algorithms have the advantage that they sample the conformational space very well, yet, in case of a high nnmber of rotatable bonds this method may be compntationally impracticable. ... 

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