Chemical bonding atomic orbital overlap

In the previous paper (13), we have discussed the chemical bonding nature of uranyl nitrate dihydrate and found that the bonding interaction is mainly due to the U 5f, 6d - O 2p components. In the present work, we carry out orbital overlap population analysis to understand contribution of each atomic orbital to the chemical bonding. The orbital overlap populations indicate strength of covalent bonds (19,20). 

Valence bond theory (Section 2.3) Theory of chemical bonding based on overlap of half-hlled atomic orbitals between two atoms. Orbital hybridization is an important element of valence bond theory. 

Overlap of atomic orbitals (AO s) or hybrids allows electrons to pair up, forming a chemical bond hybrid orbitals valence AO s mix to accommodate "equivalent" bonded neighbors. Non-hybridized orbitals form lone pairs or n bonds. 

Chapters 4 and 5 emphasize the band gap in materials. This is a critical parameter of a material determining its utility in transistors, lasers, and detectors. Until recently, altering a material s band gap involved chemical modifications to affect bond lengths, atomic orbital overlaps, and electronegativity. A nice example of this is the series GaP cAsi f where the band gap is systematically varied from 2.27 to 1.40 eV as x varies from 1 to 0 (Fig. 12.15). This represents a traditional chemical approach to achieving a desired property. A more recent approach to preparing materials with specific band gaps involves what have become known as photonic materials. 

We now know that the mechanical response of a material is a consequence of its atomic structure and the nature of its chemical bonds. Atoms strongly repel when pushed too close together as their orbitals overlap. Similarly, the attractive forces between them act against their being stretched apart Of course, Hooke knew nothing about chemical bonds, his approach was a systematic experimental exploration of the relationship between forces and deflections in solids. 

According to valence-bond theory, unpaired orbitals in the valence shells of two adjoining atoms can combine to form a chemical bond if they overlap significantly and are symmetry compatible. As emphasized by Linus Pauling, a measure of the bonding potential of two orbitals is the overlap integral... 

Fig. 4. Types of optimum chemical bonds possible by overlap of s, p and d orbitals centered at two atoms A and B...

For an opposing view, see Devarajan, D., Gustafson, S. J., Bickelhaupt, F. M., Ess, D. H. (2015). Is There a Need to Discuss Atomic Orbital Overlap When Teaching Hydrogen-Halide Bond Strength and Acidity Trends in Organic Chemistry Journal of Chemical Education, 92(2), 286-290. 

Next, we learn a quantum mechanical approach, called the valence bond (VB) theory, in the study of chemical bonds. The VB theory explains why and how chemical bonds form in terms of atomic orbital overlaps. (10.3)... 

Valence bond theory states that a chemical bond can be formed by the overlap of atomic orbitals. Overlap means, the two orbitals share a common region in space. 

The most important orbitals are those in the outer shells, which are involved in the formation of chemical bonds. Covalent bonds are formed when atomic orbitals overlap and merge to form molecular orbitals (Chapter 14). 

FIGURE 1.5 Illustration of hetero-atomic combination in chemical bonding (H-0 bonding here) at the level of s-s- and s-p atomic orbitals overlapping in resulted bonding and anti-bonding molecular orbitals in bottom and upper parts of the central horizontal axis, respectively. 

We have learned that the Lewis model portrays a chemical bond as the transfer or sharing of electrons represented as dots. Valence bond theory portrays a chemical bond as the overlap of two half-filled atomic orbitals. What is a chemical bond according to molecular orbital theory ... 

In contrast to the Lewis model, in which a covalent chemical bond is the sharing of electrons represented by dots, in valence bond theory a chemical bond is the overlap of half-filled atomic orbitals (or in some cases the overlap between a completely filled orbital and an empty one). 

Covalent bonds are characterized by shared electrons between atoms. Sigma bonds are the strongest type of covalent bonds and are formed by overlapping between atomic orbitals. Pi bonds are weaker covalent chemical bonds where two lobes of an atomic orbital overlap two lobes of another atomic orbital. 

Figure 16-3D shows the simplified representation of the interaction of two helium atoms. This time each helium atom is crosshatched before the two atoms approach. This is to indicate there are already two electrons in the Is orbital. Our rule of orbital occupancy tells us that the Is orbital can contain only two electrons. Consequently, when the second helium atom approaches, its valence orbitals cannot overlap significantly. The helium atom valence electrons fill its valence orbitals, preventing it from approaching a second atom close enough to share electrons. The helium atom forms no chemical bonds. ... 

Radicals with adjacent Jt-bonds [e.g. allyl radicals (7), cyclohexadienyl radicals (8), acyl radicals (9) and cyanoalkyl radicals (10)] have a delocalized structure. They may be depicted as a hybrid of several resonance forms. In a chemical reaction they may, in principle, react through any of the sites on which the spin can be located. The preferred site of reaction is dictated by spin density, steric, polar and perhaps other factors. Maximum orbital overlap requires that the atoms contained in the delocalized system are coplanar. 

Consider two well-separated atoms A and B with electron wave functions and which are eigen functions of the atoms, with energies and ei. If we bring these atoms closer, the wave functions start to overlap and form combinations that describe the chemical bonding of the atoms to form a molecule. We will neglect the spin of the electrons. The procedure is to construct a new wave function as a linear combination of atomic orbitals (LCAO), which for one electron has the form... 

The use of MO theory to find deep minima in the So surface, or geometries of stable molecules, is well known. A simplified rule would be to choose the geometry so as to allow efficient overlap of valence orbitals of the constituent atoms in a way giving bonding orbitals for all available electrons from pairs or larger sets of suitably hybridized atomic orbitals. No atomic orbitals occupied by one electron should be left over dangling free and unable to interact with others, since that would give radicals, biradicals, etc. Chemical intuition allows one to proceed almost automatically in cases of molecules of familiar types. 

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