Covalent bond orbitals

In addition to differences in the interaction of orbitals, covalent bonds can differ based on the shape of the molecular orbitals ... 

To assess the importance of nucleophilic substitution reactions of naturally occurring nucleophiles it is necessary to have some measure of their reactivity, relative to OH" and HjO. A number of properties of nucleophiles, all of which are some measure of the nucleophile s ability to donate electrons to an electrophile, have been used to correlate nucleophilic reactivity. These closely related properties include basicity, oxidation potential, polarizability, ionization potential, electronegativity, energy of the highest filled molecular orbital, covalent bond strength, and size (Jencks, 1987). 

First, we need to consider that the bonding electrons in the atoms concerned are in orbitals. Covalent bonds are formed by overlap of these orbitals. Each carbon in ethene forms three normal covalent bonds by overlap with the orbitals containing electrons on the other carbon and two hydrogen atoms. The electron cloud between the nuclei of the atoms in each... 

Bond forces by localized or extended orbitals (covalent bonding or metalUc bonding). 

The situation for alloys is more complex. In theoretical calculations of lattice energies one has to take into account the different contributions from Coulomb interactions (ionic bonds), localized orbitals (covalent bonds), and delocalized orbitals (metal bonds). Therefore an ab initio calculation is difficult. Solutions of the problem are under development and one can expect that in the near future reliable data will be presented. 

TETRAHEDRAL STRUCTURES INTERPRETED BY AN OVERLAP OF BONDING ORBITALS (COVALENT BONDING STATE)... 

Soon after the Heitler-London article, Linus Pauling developed two concepts, directed valence and orbital hybridization, that have proved to be highly useful. These concepts were applied to a question of specific concern to organic chemistry, the tetrahedral orientation of the bonds to carbon. Pauling reasoned that since covalent bonds require mutual overlap of orbitals, stronger bonds result from better overlap. Orbitals that possess directional properties such as p-orbitals should therefore be more effective than spherically symmetric s-orbitals. Covalent bond formation between two atoms involving overlap of a p-orbital of one atom with an s- or p-orbital of another is illustrated in Fig. 1.1. The electron distribution that results is cylindrically symmetric with respect to the internuclear axis and defines a or-bond. 

Atoms and Atomic Orbitals Covalent Bonds and Lewis Structures Resonatrce Forms Hydrogen (H2] Molecular Orbitals Bond Strength... 

In line with van t Hoff s stereochemistry and the orientation of elliptic orbits, covalent bonds could be represented by tetrahedra that touch in apical, edgewise and facial mode, involving one, two or three electron pairs in an interaction, also shown in Fig. 2. This theory predicts increased bond strength with increasing bond order, but fails to account quantitatively for observed internuclear distances. For example, this model predicts the interatomic distances in methane and acetylene in the ratio of 3 1. 

Alternatively a reaction between a species with a pair of electrons and a species with a vacant orbital to form a covalent bond, heteronuclear molecule See homonuclear molecule. 

The carbon atom has a share in eight electrons (Ne structure) whilst each hydrogen atom has a share in two electrons (He structure). This is a gross simplification of covalent bonding, since the actual electrons are present in molecular orbitals which occupy the whole space around the five atoms of the molecule. 

These apparent anomalies are readily explained. Elements in Group V. for example, have five electrons in their outer quantum level, but with the one exception of nitrogen, they all have unfilled (I orbitals. Thus, with the exception of nitrogen. Group V elements are able to use all their five outer electrons to form five covalent bonds. Similarly elements in Group VI, with the exception of oxygen, are able to form six covalent bonds for example in SF. The outer quantum level, however, is still incomplete, a situation found for all covalent compounds formed by elements after Period 2. and all have the ability to accept electron pairs from other molecules although the stability of the compounds formed may be low. This... 

In Group III, boron, having no available d orbitals, is unable to fill its outer quantum level above eight and hence has a maximum covalency of 4. Other Group 111 elements, however, are able to form more than four covalent bonds, the number depending partly on the nature of the attached atoms or groups. 

Figure 2.8. The iwo orbitals overlap giving a covalent bond and ihe tvvv electrons are (>ir in a molecular orbital. (If the t o nuclei could be pushed together completely, the...

When elements in Period 2 form covalent bonds, the 2s and 2p orbitals can be mixed or hybridised to form new, hybrid orbitals each of which has. effectively, a single-pear shape, well suited for overlap with the orbital of another atom. Taking carbon as an example the four orbitals 2s.2p.2p.2p can all be mixed to form four new hybrid orbitals (called sp because they are formed from one s and three p) these new orbitals appear as in Figure 2.9. i.e. they... 

In xenon difluoride, the electronic structure shows three lone pairs around the xenon, and two covalent bonds to the two fluorine atoms hence it is believed that here xenon is using one p (doublepear) orbital to form two bonds ... 

The UIIF wnive fimction can also apply to singlet molecules. F sn-ally, the results are the same as for the faster RHF method. That is, electron s prefer to pair, with an alpha electron sh arin g a m olecu lar space orbital with a beta electron. L se the L lIF method for singlet states only to avoid potential energy discontinuities when a covalent bond Is broken and electron s can impair (see Bond Breaking on page 46). 

We 11 begin our discussion of hydrocarbons by introducing two additional theories of covalent bonding the valence bond model and the molecular orbital model... 

The characteristic feature of valence bond theory is that it pictures a covalent bond between two atoms in terms of an m phase overlap of a half filled orbital of one atom with a half filled orbital of the other illustrated for the case of H2 m Figure 2 3 Two hydrogen atoms each containing an electron m a Is orbital combine so that their orbitals overlap to give a new orbital associated with both of them In phase orbital overlap (con structive interference) increases the probability of finding an electron m the region between the two nuclei where it feels the attractive force of both of them... 

In valence bond theory a covalent bond is described m terms of m phase overlap of a half filled orbital of one atom with a half filled orbital of another When applied to bonding m H2 the orbitals involved are the Is orbitals of two hydrogen atoms and the bond is a ct bond... 

If a covalent bond is broken, as in the simple case of dissociation of the hydrogen molecule into atoms, then theRHFwave function without the Configuration Interaction option (see Extending the Wave Function Calculation on page 37) is inappropriate. This is because the doubly occupied RHFmolecular orbital includes spurious terms that place both electrons on the same hydrogen atom, even when they are separated by an infinite distance. 

The reaction between a trinuclear metal carbonyl cluster and trimetbyl amine borane has been investigated (41) and here the cluster anion functions as a Lewis base toward the boron atom, forming a B—O covalent bond (see Carbonyls). Molecular orbital calculations, supported by stmctural characterization, show that coordination of the amine borane causes small changes in the trinuclear framework. 

The simplest example of covalent bonding is the hydrogen molecule. The proximity of the two nuclei creates a new electron orbital, shared by the two atoms, into which the two electrons go (Fig. 4.5). This sharing of electrons leads to a reduction in energy, and a stable bond, as Fig. 4.6 shows. The energy of a covalent bond is well described by the empirical equation... 

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