Benzene, charge density- functions

Fig. 1. The charge density function 0 - which describes the Mj, ground electronic state of benzene and its product densities with the excited (0, 0,), (0 ), and (0 ) benzene states. It...

The EEM method does not strictly belong in a section concerned with classical simulations. It is a method based on density functional theory that allows proper consideration of long range effects and parameters that are calibrated to non-empirical charges. Given the subject of this reference (benzene) it was included here. 

The bonding and charge distribution in the complexes of benzene with [Re(Tp)(CO)(L)] (L = NH3, Him, py, phosphine, CO, MeNC) have been calculated by LSDA and B3LYP density functional methods.195... 

The dependence of the chemical shifts on the 7t-electron charge density in aromatic molecules has frequently been observed. Karplus and Pople showed that the magnetic shielding (p.p.m. from benzene) of a nucleus (A) in a conjugated molecule is a function of the local charge density, Pa, the free valence, Fa, and the polarity of the C—H bonds, Ah, and is given by the expression—... 

In a more recent study, Waack (230) has measured and Jc-h of benzyl-lithium as a function of solvent. (See Table III.) In this work it was concluded that the aC was substantially sp hybridized (compare 01ah(229)]. The authors reasoned that the excess charge density on the aC necessary to balance sp hybridization would be excessively large. In particular the value of in benzene (Table III) is consistent with sp hybridization. The larger values of Jc-H in THF and Et20 show increased sp hybridization in these solvents. 

In this chapter, the control parameters and charge carrier mobilities of a few molecular crystals are estimated using the density functional theory and semiempirical methods. By performing extensive computation, the variation in electron and hole mobilities for different polymorphs of benzene, naphthalene, and octathio[8]circu-lene molecular crystals are studied systematically. 

Y. A. Mantz, F. L. Gervasio, T. Laino, and M. Parrinello,/. Phys. Chem. A, 111, 105-112 (2007). Charge Localization in Stacked Radical Cation DNA Base Pairs and the Benzene Dimer Studied by Self-Interaction Corrected Density-Functional Theory. 

The chemical potential, chemical hardness and sofmess, and reactivity indices have been nsed by a number of workers to assess a priori the reactivity of chemical species from their intrinsic electronic properties. Perhaps one of the most successful and best known methods is the frontier orbital theory of Fukui [1,2]. Developed further by Parr and Yang [3], the method relates the reactivity of a molecule with respect to electrophilic or nucleophilic attack to the charge density arising from the highest occupied molecular orbital or lowest unoccupied molecular orbital, respectively. Parr and coworkers [4,5] were able to use these Fukui indices to deduce the hard and soft (Lewis) acids and bases principle from theoretical principles, providing one of the first applications of electronic structure theory to explain chemical reactivity. In essentially the same form, the Fukui functions (FFs) were used to predict the molecular chemical reactivity of a number of systems including Diels-Alder condensations [6,7], monosubstituted benzenes [8], as well as a number of model compounds [9,10]. Recent applications are too numerous to catalog here but include silylenes [11], pyridinium ions [12], and indoles [13]. 

Polarity is the extent to which a substance, at molecular level, is characterized by a non-symmetrical distribution of electron density. Polarity is often expressed as dipole moment, which is a function of the magnitude of the partial charges on the molecule, and the distance between the charges. Substances that have larger dipole moments have greater polarity than substances with lower dipole moments. Water and acetone, for example, have dipole moments of 1.85 and 2.80, respectively. Benzene and carbon tetrachloride are nonpolar and have dipole moments of zero. 

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