Chemical bonding modelling

In Chemical Bonding Models, eds. J. F. Liebman and A. Greenberg (Molecular Structure and Energetics, Vol. 1), VCH Publishers, Deerfield Beach, FL, pp. 1-15 (1986)... 

Frenking, G. and Krapp, A. 2007. Unicorns in the world of chemical bonding models. J. Comput. Chem. 28 15-24. 

A promising simplification has been proposed by Bader (1990) who has shown that the electron density in a molecule can be uniquely partitioned into atomic fragments that behave as open quantum systems. Using a topological analysis of the electron density, he has been able to trace the paths of chemical bonds. This approach has recently been applied to the electron density in inorganic crystals by Pendas et al. (1997, 1998) and Luana et al. (1997). While this analysis holds great promise, the bond paths of the electron density in inorganic solids are not the same as the more traditional chemical bonds and, for reasons discussed in Section 14.8, the electron density model is difficult to compare with the traditional chemical bond models. 

The reader s attention is drawn to the discussion in Sections 14.3 and 14.4 which shows that all chemical bond models are equivalent because they all reduce to this same topological description. The derivation here is based on the ionic model because it is the simplest and most convincing. 

Figure 1. Simple chemical bonding model showing that unbound or partially bound atoms on a semiconductor surface contribute states within the band gap. The states of unbound atoms (a) are split upon partial bonding (b), then further split when the fully bound species (c) is formed. Evolution of the periodic lattice broadens the bonding states to form the valence band (vb) and the antibonding orbitals to form the conduction band (cb). In the process of band formation, the unbound and partially bound states (a and b) remain between vb and cb.

Crystal field theory is one of several chemical bonding models and one that is applicable solely to the transition metal and lanthanide elements. The theory, which utilizes thermodynamic data obtained from absorption bands in the visible and near-infrared regions of the electromagnetic spectrum, has met with widespread applications and successful interpretations of diverse physical and chemical properties of elements of the first transition series. These elements comprise scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel and copper. The position of the first transition series in the periodic table is shown in fig. 1.1. Transition elements constitute almost forty weight per cent, or eighteen atom per cent, of the Earth (Appendix 1) and occur in most minerals in the Crust, Mantle and Core. As a result, there are many aspects of transition metal geochemistry that are amenable to interpretation by crystal field theory. 

Recently use of localised Wannier functions instead of delocalised Bloch states (CP orbitals) in CPMD simulations has proved an efficient and effective approach for study of fluids such as water133 and DMSO/water mixture.134 Use of localised Wannier functions also has the advantage that they allow electrons to be assigned to bonds, making visualisation of bonding and structure of molecules easy and facilitating comparisons with standard chemical bonding models. 

It would be better to produce examples regarding the structure-property relationships that do not require chemical bonding models, but can be answered using chemical structures (see Fig. 2.3). Examples of this would be the structures of metals and alloys with their specific arrangements of atoms and the structures of salts and those arrangements of ions. 

How must the rules of the chemical bond model be modified when used to describe inorganic solids In both versions of the model, each atom is assumed to have an atomic valence which corresponds to the number of electrons (positive valence) or holes (negative valence) that are available in the valence shell of the neutral atom. In the original bond model the valence simply represented the number of bonds that the atom formed, i.e. its coordination number, but compounds were later discovered that contained double and triple bonds. In these compounds the coordination number was different from the atomic valence and each bond was associated with more than one unit of valence. However, in all cases the sum of the valences (or strengths) associated with the bonds around each atom was found to be equal to the valence of the atom. This is the principal rule of the chemical bond model and is known as the valence sum rule. ... 

So far we have discussed the general characteristics of the chemical bonding model and have seen that properties such as bond strength and polarity can be assigned to individual bonds. In this section we introduce a specific model used to describe covalent bonds. We need a simple model that can be applied easily even to very complicated molecules and that can be used routinely by chemists to interpret and organize the wide variety of... 

We will again compare chemical bonding modeled by a closed and an open infinite chain of atoms. Now we consider the case that each atom is represented by an s and one p orbital directed along the chain axis, sketched for two atoms in Pig.(2.32). 

In summary, we have discussed chemical bonding models of adsorbed CO of increasing sophistication. 

Small and medium-size boron clusters are excellent examples where double aromaticity, double antiaromaticity, and conflicting aromaticity were shown to be able to explain their structure, stabiHty, and other molecular properties [19, 109, 110]. The following chemical bonding model was proposed for planar or quasi-planar boron clusters aU peripheral boron atoms form 2c-2e a-bonds, while the atoms inside of the peripheral ring are bound to each other and to... 

We have come to associate this set of molecular properties with benzene and similar structures, but defining exactly what aromaticity means remains difficult. Frenking and Krapp described aromaticity as one of the "unicorns in the world of chemical bonding models," meaning that its characteristics are known to everyone, but aromaticity is nevertheless nonobservable. Thus, we might ask the question Is benzene so stable because it is aromatic, or is it aromatic because it is so stable ... 

For an introduction to the structures and reactions of carbenes, see (a) Liebman, J. F. Simons, J. in Liebman, J. F. Greenberg, A., Eds. Molecular Structure and Energetics, Volume 1 Chemical Bonding Models VCH Publishers Deerfield Beach, FL, 1986 p. 51 (b) Moss, R. A. Jones, M., Jr., in Jones, M., Jr. Moss, R. A., Eds. Reactive Intermediates, Vol. 2 John Wiley Sons New York, 1981 (c) Kirmse, W. Carbene Chemistry Academic Press New York, 1964 Gilchrist, T. L. Rees, C. W. Carbenes, Nitrenes and Arynes Appleton-Century-Crofts New York, 1969 (d) Mine, J. Divalent Carbon Ronald Press New York, 1964 Bertrand, G. in Moss, R. A. Platz, M. S. Jones, M., Jr., Eds. Reactive Intermediate Chemistry John Wiley Sons Hoboken, NJ, 2004 chapter 8 (e) Jones, M., Jr. Moss, R. A. in Moss, R. A. Platz, M. S. Jones, M., Jr., Eds. Reactive Intermediate Chemistry John Wiley Sons Hoboken, NJ, 2004 chapter 7. 

I. V. Abarenkov and I. M. Antonova Chemical bond modelling with the energy driven orbital localization, Int. J. Quantum Chem., Submitted. 

All materials consist of particles, i.e., atoms and/or molecules. It is possible to determine the forces that act on these particles by using the modern scientific techniques of quantum mechanics and chemical-bond models. Molecular simulation methods provide material properties as a set of particle behaviors under the above chemical-bond forces (Allen and Tildesley 1987 Ueda 1990 Kawamura 1990) The Molecular Dynamics method (MD Fig. 1.1) solves the equation of motion directly in a finite difference scheme, using a very short time step, i.e., less than 1 fs (femtosecond 1 fs = 10 s). The Monte Carlo Method (MC) calculates a probability of occurrence of the particle configuration. Note that since the Molecular Mechanics Method (MM) does not treat the behavior of a molecular group, we exclude MM from the molecular simulation methods. 

It is assumed that electrostatic forces between chemically bonded atoms are already folded into the chemical bond model. Therefore, as with the van der Waals interactions, these terms are calculated for every pair of... 

Chemical bonding models based on graph theory or tensor surface harmonic theory demonstrate the analogy between the aromaticity in two-dimensional planar polygonal hydrocarbons such as benzene and that in three-dimensional deltahedral borane anions of the type B F1 (6 < n < 12). Such models are supported both by diverse computational studies and experimental determinations of electron density distribution. Related methods can be used to study the chemical bonding in the boron polyhedra found in... 

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