Hybridisation of atomic orbitals

The directional properties of the hybrid orbitals are better appreciated with the BeClj molecule, which is linear in shape, Cl-Be-Cl 180°, and in which Be has an configuration which can be promoted to an s p configuration. 

Two linear combinations of the s and Py orbitals are possible on the central beryllium atom  

Thus the sp d hybridisation description of the bonding in the octahedral stereochemistry of a Main Group compound, e.g. SFg, can equally be applied to the bonding in the octahedral stereochemistry of the [Fe(OH2)6] and [Mn(OH2)6] cations. Equally, the sp hybridisation description of the bonding of a tetrahedral characteristic main group compound, e.g. CH., also describes the bonding in the tetrahedral Mn04 and FeCl anions. 

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More than anyone else it has been Linus Pauling (b. 1901) who has been responsible for the development and application of the valence bond theory. In the early 1930s he deduced from quantum mechanics the tetrahedrally directed valencies of carbon, and he introduced the concept of the hybridisation of atomic orbitals. He introduced the idea of resonance as the quantum-mechanical counterpart of mesomerism. The wavefiinction for the molecule must contain terms for all possible structures, and the molecule is said to resonate between them. In 1933 Pauling described the benzene molecule as a resonance hybrid between the two Kekule structures and the three possible Dewar structures (Figure 11.22). 

HPLC high-performance liquid chromatography, hybridisation of atomic orbitals the process of mixing atomic orbitals so that each has some character of each of the orbitals mixed. 

The concepts of hybridisation and resonance are the cornerstones of VB theory. Unfortunately, they are often misunderstood and have consequently suffered from much unjust criticism. Hybridisation is not a phenomenon, nor a physical process. It is essentially a mathematical manipulation of atomic wave functions which is often necessary if we are to describe electron-pair bonds in terms of orbital overlap. This manipulation is justified by a theorem of quantum mechanics which states that, given a set of n respectable wave functions for a chemical system which turn out to be inconvenient or unsuitable, it is permissible to transform these into a new set of n functions which are linear combinations of the old ones, subject to the constraint that the functions are all mutually orthogonal, i.e. the overlap integral J p/ip dT between any pair of functions ip, and op, (i = j) is always zero. This theorem is exploited in a great many theoretical arguments it forms the basis for the construction of molecular orbitals as linear combinations of atomic orbitals (see below and Section 7.1). 

As usual, we can tackle the problem with or without using the concept of hybridisation. The C—X bond in a molecule such as methyl chloride, like the C C bond in ethane, has several orbitals contributing to the force which keeps the two atoms bonded to each other but, just as we could abstract one pair of atomic orbitals of ethane and make a typical interaction diagram for it, so can we now take the corresponding pair of orbitals from the set making up a C—Cl a bond. 

Hybridisation The hypothetical mixing of atomic orbitals to form hybrid orbitals. 

Q.6. Predict the hybridisation involved appropriate to the above structure, and list the linear combination of atomic orbitals involved by specifying the number of individual s-, p- and /-orbitals involved and, if possible, draw a sketch of the resultant hybrid orbital. 

The particular hybridisation of the orbitals of carbon atoms in ethene, are called spl hybrids... 

Atoms that are linked by electron-pair bonds are positioned so that orbital overlap is maximised. The orbitals used are also sensitive to bond overlap and hybridisation, so that atomic orbitals frequently mix to give hybrid orbitals with greater overlapping power. The shapes of atomic orbitals and hybrid orbitals are quite definite and point in fixed directions. This leads to the fact that covalent bonding is directional. From a geometrical point of view, the array of covalent bonds in a solid resembles a net. 

Here, the bonding between carbon atoms is briefly reviewed fuller accounts can be found in many standard chemistry textbooks, e.g., [1]. The carbon atom [ground state electronic configuration (ls )(2s 2px2py)] can form sp sp and sp hybrid bonds as a result of promotion and hybridisation. There are four equivalent 2sp hybrid orbitals that are tetrahedrally oriented about the carbon atom and can form four equivalent tetrahedral a bonds by overlap with orbitals of other atoms. An example is the molecule ethane, CjH, where a Csp -Csp (or C-C) a bond is formed between two C atoms by overlap of sp orbitals, and three Csp -Hls a bonds are formed on each C atom. Fig. 1, Al. 

A second type of hybridisation of the valence electrons in the carbon atom can occur to form three 2sp hybrid orbitals leaving one unhybridised 2p orbital. 

In the third type of hybridisation of the valence electrons of carbon, two linear 2sp orbitals are formed leaving two unhybridised 2p orbitals. Linear a bonds are formed by overlap of the sp hybrid orbitals with orbitals of neighbouring atoms, as in the molecule ethyne (acetylene) C2H2, Fig. 1, A3. The unhybridised p orbitals of the carbon atoms overlap to form two n bonds the bonds formed between two C atoms in this way are represented as Csp Csp, or simply as C C. 

Carbon has six electrons around the atomic core as shown in Fig. 2. Among them two electrons are in the K-shell being the closest position from the centre of atom, and the residual four electrons in the L-shell. TTie former is the Is state and the latter are divided into two states, 2s and 2p. The chemical bonding between neighbouring carbon atoms is undertaken by the L-shell electrons. Three types of chemical bonds in carbon are single bond contributed from one 2s electron and three 2p electrons to be cited as sp bonding, double bond as sp and triple bond as sp from the hybridised atomic-orbital model. 

A covalent bond between two atoms requires two electrons and two orbitals, one for each atom.f The factors determining the properties of the covalent bonds formed by an atom are primarily the number and nature of the orbitals (hybridised bond orbitals) available to the atom, and the number of electrons that it can use in bond formation without losing its electrical neutrality. The opportunities for stabilisation through resonance of covalent bonds among alternative positions are also important. 

A carbon atom combining with four other atoms clearly does not use the one 2s and the three 2p atomic orbitals that would now be available, for this would lead to the formation of three directed bonds, mutually at right angles (with the three 2p orbitals), and one different, non-directed bond (with the spherical 2s orbital). Whereas in fact, the four C—H bonds in, for example, methane are known to be identical and symmetrically (tetrahedrally) disposed at an angle of 109° 28 to each other. This may be accounted for on the basis of redeploying the 2s and the three 2p atomic orbitals so as to yield four new (identical) orbitals, which are capable of forming stronger bonds (cf. p. 5). These new orbitals are known as sp3 hybrid atomic orbitals, and the process by which they are obtained as hybridisation ... 

Similar, but different, redeployment is envisaged when a carbon atom combines with three other atoms, e.g. in ethene (ethylene) (p. 8) three sp2 hybrid atomic orbitals disposed at 120° to each other in the same plane (plane trigonal hybridisation) are then employed. Finally, when carbon combines with two other atoms, e.g. in ethyne (acetylene) (p. 9) two sp1 hybrid atomic orbitals disposed at 180° to each other (idigonal hybridisation) are employed. In each case the s orbital is always involved as it is the one of lowest energy level. 

These are all valid ways of deploying one 2s and three 2p atomic orbitals—in the case of sp2 hybridisation there will be one unhybridised p orbital also available (p. 8), and in the case of sp1 hybridisation there will be two (p. 10). Other, equally valid, modes of hybridisation are also possible in which the hybrid orbitals are not necessarily identical with each other, e.g. those used in CH2C12 compared with the ones used in CC14 and CH4. Hybridisation takes place so that the atom concerned can form as strong bonds as possible, and so that the other atoms thus bonded (and the electron pairs constituting the bonds) are as far apart from each other as possible, i.e. so that the total intrinsic energy of the resultant compound is at a minimum. 

One of the major problems of elementary organic chemistry is the detailed structure of benzene. The known planar structure of the molecule implies sp2 hybridisation with p atomic orbitals, at right angles to the plane of the nucleus, on each of the six carbon atoms (4) ... 

The exact reverse of the above is seen with aniline (13), which is a very weak base (pKa = 4-62) compared with ammonia (pKa = 9-25) or cyclohexylamine (pKa = 10-68). In aniline the nitrogen atom is again bonded to an sp2 hybridised carbon atom but, more significantly, the unshared electron pair on nitrogen can interact with the delocalised 7r orbitals of the nucleus ... 

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