Calculation of Charge Distribution

330 I 7,1 Empirical Approaches to the Calculation of Properties 7.1.7.1.1 The PEOE Method 

At the outset of the Partial Equalization of Orbital Electronegativities (PEOE) method [28] is the electronegativity concept in the form of Eq. (11) presented by Mulliken, who put it on a sound theoretical basis [29]. 

In this equation, the electronegativity of an atom is related to its ionization potential, 1, and its electron affinity, E. Mulhken already pointed out that in this definition the ionization potential, and the electron affinity, E, of valence states have to be used. This idea was further elaborated by Hinze et al. [30, 31], who introduced the concept of orbital electronegativity. 

The electronegativity of an atom further depends on the charge in this orbital and also on the charge in the other orbitals of this atom. For this dependence of orbital electronegativity on the total charge, Q, irrespective of whether part of it resides in the orbital considered or in the other orbitals of this atom, we selected a polynomial of degree two (Eq. (12)). 

Values for these coefficients, a, b, c, of Eq. (12) can be obtained from the ionization potentials and electron affinities of the neutral, the cationic, and the anionic states of an orbital. 

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Denis, A., and A. Pullman Theoretical study of the electronic properties of biological purines and pyrimidines. III. Theoret. Chim. Acta (Berlin) 7, 110 (1967). Del Re, G. A simple MO-LCAO method for the calculation of charge distributions in saturated organic molecules. J. Chem. Soc. (London) 4031 (1958). 

The HF 6-31G ab initio calculations of charge distribution for the simplest en-aminonitrile, 3-aminoacrylonitrile (481) (Scheme 12), indicate an n,n interaction almost as efficient as that of 3-aminoacrolein (323, Scheme 6) and therefore the NMR spectra of enaminonitriles, NC—CR1=CR2—NR3R4 (482), have many features in common... 

I. Fischer. Arkiv Fysik 1, 495-504 (1949). Theory molecular orbital calculation, of charge distribution in ether-water. 

Del Re, G. (1958). A Simple MQ-LCAQ Method for the Calculation of Charge Distribution in Saturated Qrganic Molecules. J.Chem.Soc., 4031-4040. 

Stoklosa, H.J. (1973). Computer Program for Calculation of Charge Distributions in Molecules. J.Chem.Educ., 50,290-290. 

The three-dimensional nature of the electrostatic potential makes it difficult to simultaneously visualize its spatial distribution and its magnitude. However, we can deal with the electrostatic potential on the van der Waals surface of a molecule, which is of major importance for the molecular contact between a ligand and a receptor. The electrostatic potential can be calculated by a point charges derived from partial atomic charges, the latter of which can be calculated by iterative partial equalization of orbital electronegativity (PEOE), a well-established empirical method for the rapid calculation of charge distributions [104]. 

Del, Re.G. (1958) A simple MO-LCAO method for the calculation of charge distribution in saturated organic molecules./. Chem. Soc., 40, 4031-4040. 

StoHosa, H.J. (1973) Computer program for calculation of charge distributions in molecules. /. Chem. Educ., 50, 290. 

As mentioned in the previous section, Corey15 considered an oriented jt-complex between the photoexcited enone and the ground state alkene. In the case of cycloaddition of methoxy-ethylene or acrylonitrile to 2-cyclohexenone the preferred orientation is shown in the scheme. Assuming that the triplet excited state of the enone is n,7t in nature15, calculations of charge distribution indicate that is fairly negative relative to Ca consequently the excited enone has a polarization complementary to its ground state. The more favorable orientation of the k complex is that in which the dipole of the olefin is opposed to that of the excited enone. 

G. Del Re, /. Chem. Sue. l.ondon, 1958, 403 I (1958). A Simple MO-LCAO Method for the Calculation of Charge Distributions in Satur.ited Organic Molecules. 

We have now to look if such bonding parameters can be used to predict solution properties. Looking at some simple ionic species displaying a wide range of pKa values, we have selected the oxy-ions gathered in table 3. Calculations of charge distributions in the fully deprotonated ion have been done with %5 (0) = 0, as found in crystalline silica, %.s X ) = 0.25 and %. (X ) = 0.15. For the hardnesses standard covalent radii are used. The pKa values have been taken from [111], with the exception of the value... 

The kinetics and mechanism of the acid-catalysed reactions of methylated trioses have been determined and the results were shown to be in good agreement with quantum mechanical calculations of charge distributions in substrates and intermediates. The same group has studied the kinetics and mechanism of acid-base-catalysed enolization of glycolaldehyde and methoxyacetaldehyde by polarography. Deuterium incorporation was used to establish the mechanism. ... 

Theoretical calculations of charge distribution on the nicotinamide ring by B. Pullman in Paris agree with a hydride attack at position C-4. Experimental evidence comes from reaction with a deuterated alcohol and isolation of the pyridinium salt. Methylation and oxidation take place without loss of deuterium, proving that the labeling occurs only at C-4. 

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