{"id":362,"date":"2018-11-16T11:56:56","date_gmt":"2018-11-16T11:56:56","guid":{"rendered":"http:\/\/phy12.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=362"},"modified":"2019-04-30T10:52:32","modified_gmt":"2019-04-30T10:52:32","slug":"hybridization-in-carbon-based-molecules","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/phy12\/chapter\/hybridization-in-carbon-based-molecules\/","title":{"rendered":"Hybridization in carbon based molecules"},"content":{"raw":"
\"epgp<\/a>\r\n<\/span><\/div>\r\n
\r\n\r\n \r\n\r\nTable of Content<\/strong>\r\n\r\nModule II<\/strong>\r\n\r\n \r\n\r\n5.2 Hybridization in carbon based molecules\r\n\r\n5.2.1 sp3 hybridization\r\n\r\n5.2.2 sp2 hybridization\r\n\r\n5.2.3 sp hybridization\r\n\r\n5.2.4 Hybridization in benzene\r\n\r\n5.2.5 Hybridization in carbon compounds\r\n\r\n<\/div>\r\n
\r\n\r\n \r\n\r\n5.2 Hybridization in a Carbon Atom<\/strong>\r\n\r\n \r\n

The materials, clusters, and molecules based on carbon are unique in many ways. The most important distinction is the existence of several possible configurations of the electronic states of a carbon atom in different carbon based systems. The different configurations resulting different topology is known as the hybridization of atomic orbitals. Hybridization is a concept based on mathematical treatment of the wavefunctions of atomic orbitals to give new wavefunctions representing hybrid orbitals which are very useful in the explanation of molecular geometry and atomic bonding properties. Only orbitals of similar energies can be mixed together to form stable hybrid orbitals. The number of hybrid orbitals produced equals the number of atomic orbitals mixed together. Concept of hydridization was first introduced by Linus Pauling to expalin the structure of simple molecules such as methane (CH4) using atomic orbitals based on experimental findings that there are four C-H bonds with a bond angle of\u00a0109.5\u00b0 bewteen each other. Pauling pointed out that a carbon atom forms four bonds by using one s and three p orbitals.<\/span><\/p>\r\n \r\n

Carbon is the sixth element of the periodic table and there are six electrons in carbon atom, which occupies <\/span>1s<\/em>2<\/em><\/sup>, 2s<\/em>2<\/em><\/sup> and <\/span>2p<\/em>2<\/em><\/sup> atomic orbitals. The first two electrons are strongly bounded electrons, occupy <\/span>ls<\/em>2<\/em> orbital are designated as core electrons. The remaining four electrons are weakly bounded electrons than core electrons are known as valence electrons. In the crystalline state the valence electrons give rise to <\/span>2s, 2p<\/em>x<\/em>, 2p<\/em>y<\/em>,<\/em> and <\/span>2p<\/em>z<\/em> orbitals which take part in the formation of covalent bonds in carbon materials. As the energy difference between the upper <\/span>2p<\/em> energy levels and the lower <\/span>2s<\/em> level in carbon is small compared with the binding energy of the chemical bonds, the electronic wave functions for these four electrons can readily superpose and change the occupation of the <\/span>2s<\/em> and three <\/span>2p<\/em> atomic orbitals thereby enhance the binding energy of the carbon atom with its neighboring atoms. This superposition of 2s and <\/span>2p<\/em> atomic orbitals is called hybridization. Generally, the mixing of a single <\/span>s<\/em> electron with different no of p orbitals (<\/span>n<\/em> = <\/span>1,2,3) p<\/em> electrons is called <\/span>sp<\/em>n<\/em> hybridization. For carbon, in general there are three possible hybridizations <\/span>sp, sp<\/em>2<\/em><\/sup> and <\/span>sp<\/em>3<\/em><\/sup> which will be discussed in next sections one by one.<\/span><\/p>\r\n \r\n

5.2.1 sp<\/strong>3<\/strong><\/sup> hybridization<\/strong><\/p>\r\n \r\n

There are four covalent bonds in CH4, so the carbon should have 4 orbitals with the correct symmetry to bond to the 4 hydrogen atoms. Carbon's <\/span>ground state <\/a>configuration is 1s2<\/sup> 2s2<\/sup> 2p2<\/sup> which can be represented as (Figure 5.5)<\/span><\/p>\r\n\r\n<\/div>\r\n\"\"\r\n

\r\n

The carbon atom can use its two singly occupied p-type orbitals, to form two covalent bonds with two hydrogen atoms, yielding the methylene CH2, which is an unstable molecule. To form a stable molecule\u00a0with hydrogen atoms, carbon atom can also bond to four hydrogen atoms by an excitation of an electron from the doubly occupied 2s orbital to the empty 2p orbital, resulting four singly occupied orbitals, as shwon in Figure 5.6 which also show the shape of different orbitals<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\nConfiguration of excited state of Carbon(C*) (1s<\/em>2<\/em><\/sup> 2s<\/em>1<\/em><\/sup>2p2p2<\/em>p)\u00a0<\/em>different orbitals in carbon atom.<\/em>\r\n\r\n \r\n\r\nThe energy released by formation of two additional bonds compensates the energy required for exciting one electron from 2s to 2p, energetically favouring the formation of four C-H bonds. It can be shown that the lowest energy is obtained if the four bonds are equivalent, which is possible if these four bonds are formed from equivalent orbitals on the carbon. A linear combinations of the valence-shell s and p wave functions is the best possible choice for set of four equivalent orbitals, which are the four sp3 hybrids orbital (Figure 5.7)\r\n\r\n\"\"\r\n

Figure 5.7 <\/strong>Four hybrid orbital (sp3<\/sup>) resulted by linear<\/em> combination of one s and three p orbitals (1s<\/em>2<\/em><\/sup> sp<\/em>3<\/em><\/sup>sp<\/em>3<\/em><\/sup>sp<\/em>3<\/em><\/sup>sp<\/em>3<\/em><\/sup> )<\/em><\/p>\r\n \r\n

As discussed before, there is a small energy gap between the 2s and 2p orbitals, and so a small amount of energy is required to promote an electron from the 2s to the empty 2p. When the bonds are formed,the extra energy released not only compensates for the initial cost of energy, but also lowers the total energy of the molecule as shown schematically in Figure 5.8.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n

When four sp<\/em>3<\/em><\/sup> orbitals are formed around carbon atom, they arrange themselves to avoid each other resulting a tetrahedral arrangement, with an angle of 109.5\u00b0. When the hydrogen atoms combine with the carbon to form CH4 molecule, it also becomes tetrahedral with 109.5\u00b0 bond angles, as shown in Figure 5.9.<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n

The carbon atom in methane, (CH4), provides a simple example of sp3 hybridization through its tetragonal bonding to four nearest neighbor hydrogen atoms. In order to make elongated wave functions\u00a0to four directions in tetrahedral configuration, the 2s orbital and three <\/span>2p<\/em> orbitals are mixed with each other, forming an <\/span>sp<\/em>3<\/em> hybridization. and orthonormal atomic wave functions, for <\/span>sp<\/em>3<\/em> hybridized orbitals in these four directions can be given by<\/span><\/p>\r\n\r\n<\/div>\r\n

\"\"\r\nIn general for sp<\/em>n<\/em><\/sup> hybridization, n<\/em>+1electrons belong to the carbon atom occupied in the hybridized ?\u00a0 orbital and 4-(n+1) electrons in the -orbitals. \r\n\r\n5.2.2 sp<\/strong>2<\/strong><\/sup> hybridization<\/strong>\r\n\r\n \r\n

There are other carbon based compounds and molecules which have double bond between carbon atoms, such as ethene (C2H4). For these molecules, carbon atoms are sp2<\/sup> hybridised, because one \u03c0 (pi) bond is required for the double bond between the carbons. In sp2<\/sup> hybridisation the 2s orbital is mixed with only two of the three available 2p orbitals, forming a total of three sp2<\/sup> orbitals with one remaining p orbital. In ethylene molecule two carbon atoms form a \u03c3 bond by overlapping two sp2<\/sup>orbitals and each carbon atom forms two covalent bonds with hydrogen by s\u2013sp2<\/sup> overlap with 120\u00b0 angles. The \u03c0 bond between the carbon atoms perpendicular to the molecular plane is formed by 2pz\u20132pz overlap. The hydrogen carbon bonds are all of equal strength and length, in agreement with experimental data.<\/p>\r\n\"\"\r\n\r\n\"\"\r\n\r\n<\/div>\r\n

\r\n\r\nFigure 5.10 <\/strong>Configuration of excited state of<\/em> Carbon(C*) in sp2 hybridization<\/em>.<\/em>\r\n\r\n\"\"\r\n

In sp<\/em>2<\/em> hybridization, the 2s<\/em> orbital and two 2p<\/em> orbitals, for example 2p<\/em>x<\/em> and 2p<\/em>y<\/em> are hybridized. In sp2<\/sup> hybridization, all bonds are lying in the xy-plane, and, in addition, orbital for each carbon atom exists perpendicular to the plane. The three sp<\/em>2<\/em><\/sup> hybridized orbitals are made from 2s, 2px and 2py orbitals and can be given by<\/p>\r\n\"\"\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"resulting the solutions of Eq.5.9 , C1=C2=1\/\u221a3 and C3=-1\/\u221a3<\/span>.<\/em> The sp2 orbitals thus obtained have large amplitude in the direction of the three nearest-neighbor atoms, and these three-directed orbitals are denoted by trigonal bonding. Figure 5.12 shows the formation of \u03c3 and \u03c0 bonds in C2H4 molecule.<\/span>\"\"\r\n\r\n5.2.3. sp hybridization<\/strong>\r\n\r\n \r\n\r\n \r\n

The chemical bonding in molecule such as acetylene (C2H2) with triple bonds between two carbon atoms is explained by sp hybridization in which the 2s orbital is mixed with only one of the three p orbitals, resulting in two sp orbitals and two remaining unhybridized p orbitals (Figure 5.13). The\u00a0chemical bonding in C2H2 can be explained by sp hybridization which consists of sp\u2013sp overlap between the two carbon atoms forming a \u03c3 bond and two additional <\/span>\u03c0 bonds <\/a>formed by p\u2013p overlap and each carbon atom bonds with hydrogen atom through a \u03c3 s\u2013sp overlap at 180\u00b0 angles.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n

In this hybridization, a linear combination of the 2s<\/em> orbital and one of the three 2p<\/em> orbitals of a carbon atom is formed. From the two-electron orbitals of a carbon atom, two hybridized s p<\/em> orbitals, denoted by |sp<\/em>a<\/em>> <\/em>and |sp<\/em>b<\/em>>, <\/em>are expressed by the linear combination of |2s> <\/em>and |2p<\/em>x<\/em>> <\/em>wave functions of the carbon atom;<\/p>\r\n\"\"\r\n

where Ci are coefficients. Using the ortho normality conditions <sp<\/em>a<\/em>|sp<\/em>b<\/em>><\/em>=0, <sp<\/em>a<\/em>|sp<\/em>a<\/em>><\/em>=1, and (<sp<\/em>b<\/em>|sp<\/em>b<\/em>><\/em>=1, we obtain the relationship between the coefficients Ci:<\/p>\r\n\"\"\r\n\r\n \r\n

The last equation is given by the fact that the sum of |2s> components in |sp<\/em>a<\/em>><\/em> and |sp<\/em>b<\/em>>,<\/em> is unity. The solution of Eq. 5.11 is C<\/em>1<\/em>=C<\/em>2<\/em>=C<\/em>3<\/em>=1\/\u221a2 and C4= -1\/\u221a2, so that Eq 5.10 becomes<\/p>\r\n\r\n<\/div>\r\n\"\"\r\n

\r\n

The formation of \u03c0 and \u03c3 bonds in C2<\/sub>H2<\/sub> molecule is schematically shown in Figure 5.14. The strength of the \u03c0 bond between two pz orbital is maximum when pz orbitals are parallel to each other resulting linear molecule with an angle of 180o between C-H s-px bond and C\u2261C bond .<\/p>\r\n \r\n\r\nFigure 5.14 <\/strong>\u03c0 and \u03c3 bonds in C<\/em>2<\/em>H<\/em>2<\/em> molecule.<\/em>\r\n\r\n\"\"\r\n\r\n<\/div>\r\n

\r\n\r\nThe summary of sp3, sp2 and sp hybridization in carbon molecules\/compounds are given in Figure 5.14.\r\n\r\nFigure 5.14 <\/strong>Electron configuration in carbon atom in sp<\/em>3<\/em>, sp<\/em>2<\/em> and sp hybridization.<\/em>\r\n\r\n\"\"\r\n\r\n \r\n\r\n5.2.4 Hybridization in benzene<\/strong>\r\n\r\n \r\n

Benzene is a planer molecule consisting of six hydrogen atoms and six carbon atoms (Figure 5.15) . Each carbon atom has to join one hydrogen and two carbons atoms and so doesn't have enough unpaired electrons to form the required number of bonds. To achieve this each carbon atom has to promote one of the 2s2 pair into the empty 2pz orbital. Experimentally, it has been found that from X-ray diffraction that all six carbon-carbon bonds in benzene are of the same length, at nm which is greater\u00a0than a double bond (0.135 nm) but shorter than a single bond (0.147 nm). This intermediate distance is consistent with electron delocalization i.e. the electrons for C\u2013C bonding are distributed equally between each of the six carbon atoms.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n\r\n5.2.5 Hybridization in carbon compounds<\/strong>\r\n\r\n \r\n

In carbon based compounds and solids, the hybrid atomic orbital model can be extended to molecules by including valence-shell d orbitals and resulting shapes are called trigonal bipyramidal or octahedral. Generally, when the 3dz2 orbital is mixed with the 3s, 3px, 3py and 3pz orbitals, the resulting sp3d hybrid orbitals point toward the corners of a trigonal bipyramid and when both the 3dz2 and 3dx2-y2 orbitals are mixed with the 3s, 3px, 3py and 3pz orbitals, there will be a set of six sp3d2 hybrid orbitals that point toward the corners of an octahedron. All these possibilities with different pair of carbons and other elements in different carbon based compounds are given in Figure 5.16.<\/p>\r\n\"\"\r\n\r\n<\/div>\r\n

\r\n

Figure 5.16 <\/strong>Relationship between hybridization and the<\/em> distribution of electrons in the valence shell of an atom.<\/em><\/p>\r\n\r\n<\/div>\r\n\r\n\r\n\r\n
you can view video on Hybridization in carbon based molecules<\/strong><\/td>\r\n\"\"<\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n","rendered":"
\"epgp<\/a>
\n<\/span><\/div>\n
\n

 <\/p>\n

Table of Content<\/strong><\/p>\n

Module II<\/strong><\/p>\n

 <\/p>\n

5.2 Hybridization in carbon based molecules<\/p>\n

5.2.1 sp3 hybridization<\/p>\n

5.2.2 sp2 hybridization<\/p>\n

5.2.3 sp hybridization<\/p>\n

5.2.4 Hybridization in benzene<\/p>\n

5.2.5 Hybridization in carbon compounds<\/p>\n<\/div>\n

\n

 <\/p>\n

5.2 Hybridization in a Carbon Atom<\/strong><\/p>\n

 <\/p>\n

The materials, clusters, and molecules based on carbon are unique in many ways. The most important distinction is the existence of several possible configurations of the electronic states of a carbon atom in different carbon based systems. The different configurations resulting different topology is known as the hybridization of atomic orbitals. Hybridization is a concept based on mathematical treatment of the wavefunctions of atomic orbitals to give new wavefunctions representing hybrid orbitals which are very useful in the explanation of molecular geometry and atomic bonding properties. Only orbitals of similar energies can be mixed together to form stable hybrid orbitals. The number of hybrid orbitals produced equals the number of atomic orbitals mixed together. Concept of hydridization was first introduced by Linus Pauling to expalin the structure of simple molecules such as methane (CH4) using atomic orbitals based on experimental findings that there are four C-H bonds with a bond angle of\u00a0109.5\u00b0 bewteen each other. Pauling pointed out that a carbon atom forms four bonds by using one s and three p orbitals.<\/span><\/p>\n

 <\/p>\n

Carbon is the sixth element of the periodic table and there are six electrons in carbon atom, which occupies <\/span>1s<\/em>2<\/em><\/sup>, 2s<\/em>2<\/em><\/sup> and <\/span>2p<\/em>2<\/em><\/sup> atomic orbitals. The first two electrons are strongly bounded electrons, occupy <\/span>ls<\/em>2<\/em> orbital are designated as core electrons. The remaining four electrons are weakly bounded electrons than core electrons are known as valence electrons. In the crystalline state the valence electrons give rise to <\/span>2s, 2p<\/em>x<\/em>, 2p<\/em>y<\/em>,<\/em> and <\/span>2p<\/em>z<\/em> orbitals which take part in the formation of covalent bonds in carbon materials. As the energy difference between the upper <\/span>2p<\/em> energy levels and the lower <\/span>2s<\/em> level in carbon is small compared with the binding energy of the chemical bonds, the electronic wave functions for these four electrons can readily superpose and change the occupation of the <\/span>2s<\/em> and three <\/span>2p<\/em> atomic orbitals thereby enhance the binding energy of the carbon atom with its neighboring atoms. This superposition of 2s and <\/span>2p<\/em> atomic orbitals is called hybridization. Generally, the mixing of a single <\/span>s<\/em> electron with different no of p orbitals (<\/span>n<\/em> = <\/span>1,2,3) p<\/em> electrons is called <\/span>sp<\/em>n<\/em> hybridization. For carbon, in general there are three possible hybridizations <\/span>sp, sp<\/em>2<\/em><\/sup> and <\/span>sp<\/em>3<\/em><\/sup> which will be discussed in next sections one by one.<\/span><\/p>\n

 <\/p>\n

5.2.1 sp<\/strong>3<\/strong><\/sup> hybridization<\/strong><\/p>\n

 <\/p>\n

There are four covalent bonds in CH4, so the carbon should have 4 orbitals with the correct symmetry to bond to the 4 hydrogen atoms. Carbon’s <\/span>ground state <\/a>configuration is 1s2<\/sup> 2s2<\/sup> 2p2<\/sup> which can be represented as (Figure 5.5)<\/span><\/p>\n<\/div>\n

\"\"<\/p>\n

\n

The carbon atom can use its two singly occupied p-type orbitals, to form two covalent bonds with two hydrogen atoms, yielding the methylene CH2, which is an unstable molecule. To form a stable molecule\u00a0with hydrogen atoms, carbon atom can also bond to four hydrogen atoms by an excitation of an electron from the doubly occupied 2s orbital to the empty 2p orbital, resulting four singly occupied orbitals, as shwon in Figure 5.6 which also show the shape of different orbitals<\/span><\/p>\n<\/div>\n

\n

 <\/p>\n

\"\"<\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

Configuration of excited state of Carbon(C*) (1s<\/em>2<\/em><\/sup> 2s<\/em>1<\/em><\/sup>2p2p2<\/em>p)\u00a0<\/em>different orbitals in carbon atom.<\/em><\/p>\n

 <\/p>\n

The energy released by formation of two additional bonds compensates the energy required for exciting one electron from 2s to 2p, energetically favouring the formation of four C-H bonds. It can be shown that the lowest energy is obtained if the four bonds are equivalent, which is possible if these four bonds are formed from equivalent orbitals on the carbon. A linear combinations of the valence-shell s and p wave functions is the best possible choice for set of four equivalent orbitals, which are the four sp3 hybrids orbital (Figure 5.7)<\/p>\n

\"\"<\/p>\n

Figure 5.7 <\/strong>Four hybrid orbital (sp3<\/sup>) resulted by linear<\/em> combination of one s and three p orbitals (1s<\/em>2<\/em><\/sup> sp<\/em>3<\/em><\/sup>sp<\/em>3<\/em><\/sup>sp<\/em>3<\/em><\/sup>sp<\/em>3<\/em><\/sup> )<\/em><\/p>\n

 <\/p>\n

As discussed before, there is a small energy gap between the 2s and 2p orbitals, and so a small amount of energy is required to promote an electron from the 2s to the empty 2p. When the bonds are formed,the extra energy released not only compensates for the initial cost of energy, but also lowers the total energy of the molecule as shown schematically in Figure 5.8.<\/span><\/p>\n<\/div>\n

\n

\"\"<\/p>\n

 <\/p>\n

When four sp<\/em>3<\/em><\/sup> orbitals are formed around carbon atom, they arrange themselves to avoid each other resulting a tetrahedral arrangement, with an angle of 109.5\u00b0. When the hydrogen atoms combine with the carbon to form CH4 molecule, it also becomes tetrahedral with 109.5\u00b0 bond angles, as shown in Figure 5.9.<\/p>\n

 <\/p>\n

\"\"<\/p>\n

 <\/p>\n

The carbon atom in methane, (CH4), provides a simple example of sp3 hybridization through its tetragonal bonding to four nearest neighbor hydrogen atoms. In order to make elongated wave functions\u00a0to four directions in tetrahedral configuration, the 2s orbital and three <\/span>2p<\/em> orbitals are mixed with each other, forming an <\/span>sp<\/em>3<\/em> hybridization. and orthonormal atomic wave functions, for <\/span>sp<\/em>3<\/em> hybridized orbitals in these four directions can be given by<\/span><\/p>\n<\/div>\n

\"\"
\nIn general for sp<\/em>n<\/em><\/sup> hybridization, n<\/em>+1electrons belong to the carbon atom occupied in the hybridized ?\u00a0 orbital and 4-(n+1) electrons in the -orbitals. <\/p>\n

5.2.2 sp<\/strong>2<\/strong><\/sup> hybridization<\/strong><\/p>\n

 <\/p>\n

There are other carbon based compounds and molecules which have double bond between carbon atoms, such as ethene (C2H4). For these molecules, carbon atoms are sp2<\/sup> hybridised, because one \u03c0 (pi) bond is required for the double bond between the carbons. In sp2<\/sup> hybridisation the 2s orbital is mixed with only two of the three available 2p orbitals, forming a total of three sp2<\/sup> orbitals with one remaining p orbital. In ethylene molecule two carbon atoms form a \u03c3 bond by overlapping two sp2<\/sup>orbitals and each carbon atom forms two covalent bonds with hydrogen by s\u2013sp2<\/sup> overlap with 120\u00b0 angles. The \u03c0 bond between the carbon atoms perpendicular to the molecular plane is formed by 2pz\u20132pz overlap. The hydrogen carbon bonds are all of equal strength and length, in agreement with experimental data.<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n<\/div>\n

\n

Figure 5.10 <\/strong>Configuration of excited state of<\/em> Carbon(C*) in sp2 hybridization<\/em>.<\/em><\/p>\n

\"\"<\/p>\n

In sp<\/em>2<\/em> hybridization, the 2s<\/em> orbital and two 2p<\/em> orbitals, for example 2p<\/em>x<\/em> and 2p<\/em>y<\/em> are hybridized. In sp2<\/sup> hybridization, all bonds are lying in the xy-plane, and, in addition, orbital for each carbon atom exists perpendicular to the plane. The three sp<\/em>2<\/em><\/sup> hybridized orbitals are made from 2s, 2px and 2py orbitals and can be given by<\/p>\n

\"\"<\/p>\n<\/div>\n

\n

\"\"resulting the solutions of Eq.5.9 , C1=C2=1\/\u221a3 and C3=-1\/\u221a3<\/span>.<\/em> The sp2 orbitals thus obtained have large amplitude in the direction of the three nearest-neighbor atoms, and these three-directed orbitals are denoted by trigonal bonding. Figure 5.12 shows the formation of \u03c3 and \u03c0 bonds in C2H4 molecule.<\/span>\"\"<\/p>\n

5.2.3. sp hybridization<\/strong><\/p>\n

 <\/p>\n

 <\/p>\n

The chemical bonding in molecule such as acetylene (C2H2) with triple bonds between two carbon atoms is explained by sp hybridization in which the 2s orbital is mixed with only one of the three p orbitals, resulting in two sp orbitals and two remaining unhybridized p orbitals (Figure 5.13). The\u00a0chemical bonding in C2H2 can be explained by sp hybridization which consists of sp\u2013sp overlap between the two carbon atoms forming a \u03c3 bond and two additional <\/span>\u03c0 bonds <\/a>formed by p\u2013p overlap and each carbon atom bonds with hydrogen atom through a \u03c3 s\u2013sp overlap at 180\u00b0 angles.<\/span><\/p>\n<\/div>\n

\n

\"\"<\/p>\n

In this hybridization, a linear combination of the 2s<\/em> orbital and one of the three 2p<\/em> orbitals of a carbon atom is formed. From the two-electron orbitals of a carbon atom, two hybridized s p<\/em> orbitals, denoted by |sp<\/em>a<\/em>> <\/em>and |sp<\/em>b<\/em>>, <\/em>are expressed by the linear combination of |2s> <\/em>and |2p<\/em>x<\/em>> <\/em>wave functions of the carbon atom;<\/p>\n

\"\"<\/p>\n

where Ci are coefficients. Using the ortho normality conditions <sp<\/em>a<\/em>|sp<\/em>b<\/em>><\/em>=0, <sp<\/em>a<\/em>|sp<\/em>a<\/em>><\/em>=1, and (<sp<\/em>b<\/em>|sp<\/em>b<\/em>><\/em>=1, we obtain the relationship between the coefficients Ci:<\/p>\n

\"\"<\/p>\n

 <\/p>\n

The last equation is given by the fact that the sum of |2s> components in |sp<\/em>a<\/em>><\/em> and |sp<\/em>b<\/em>>,<\/em> is unity. The solution of Eq. 5.11 is C<\/em>1<\/em>=C<\/em>2<\/em>=C<\/em>3<\/em>=1\/\u221a2 and C4= -1\/\u221a2, so that Eq 5.10 becomes<\/p>\n<\/div>\n

\"\"<\/p>\n

\n

The formation of \u03c0 and \u03c3 bonds in C2<\/sub>H2<\/sub> molecule is schematically shown in Figure 5.14. The strength of the \u03c0 bond between two pz orbital is maximum when pz orbitals are parallel to each other resulting linear molecule with an angle of 180o between C-H s-px bond and C\u2261C bond .<\/p>\n

 <\/p>\n

Figure 5.14 <\/strong>\u03c0 and \u03c3 bonds in C<\/em>2<\/em>H<\/em>2<\/em> molecule.<\/em><\/p>\n

\"\"<\/p>\n<\/div>\n

\n

The summary of sp3, sp2 and sp hybridization in carbon molecules\/compounds are given in Figure 5.14.<\/p>\n

Figure 5.14 <\/strong>Electron configuration in carbon atom in sp<\/em>3<\/em>, sp<\/em>2<\/em> and sp hybridization.<\/em><\/p>\n

\"\"<\/p>\n

 <\/p>\n

5.2.4 Hybridization in benzene<\/strong><\/p>\n

 <\/p>\n

Benzene is a planer molecule consisting of six hydrogen atoms and six carbon atoms (Figure 5.15) . Each carbon atom has to join one hydrogen and two carbons atoms and so doesn’t have enough unpaired electrons to form the required number of bonds. To achieve this each carbon atom has to promote one of the 2s2 pair into the empty 2pz orbital. Experimentally, it has been found that from X-ray diffraction that all six carbon-carbon bonds in benzene are of the same length, at nm which is greater\u00a0than a double bond (0.135 nm) but shorter than a single bond (0.147 nm). This intermediate distance is consistent with electron delocalization i.e. the electrons for C\u2013C bonding are distributed equally between each of the six carbon atoms.<\/span><\/p>\n<\/div>\n

\n

\"\"<\/p>\n

 <\/p>\n

5.2.5 Hybridization in carbon compounds<\/strong><\/p>\n

 <\/p>\n

In carbon based compounds and solids, the hybrid atomic orbital model can be extended to molecules by including valence-shell d orbitals and resulting shapes are called trigonal bipyramidal or octahedral. Generally, when the 3dz2 orbital is mixed with the 3s, 3px, 3py and 3pz orbitals, the resulting sp3d hybrid orbitals point toward the corners of a trigonal bipyramid and when both the 3dz2 and 3dx2-y2 orbitals are mixed with the 3s, 3px, 3py and 3pz orbitals, there will be a set of six sp3d2 hybrid orbitals that point toward the corners of an octahedron. All these possibilities with different pair of carbons and other elements in different carbon based compounds are given in Figure 5.16.<\/p>\n

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Figure 5.16 <\/strong>Relationship between hybridization and the<\/em> distribution of electrons in the valence shell of an atom.<\/em><\/p>\n<\/div>\n\n\n\n
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