Valence bond theory Electrons are not simply dots And bonds are not sticks

Learning objectives  Describe principles of valence bond theory  Predict hybridization of orbitals based on Lewis dot structures and electronic geometry  Describe difference between sigma and pi bonding

Taking it to the next level: acknowledging orbitals  VSEPR is quite successful in predicting molecular shapes based on the simplistic Lewis dot approach  But our understanding of the atom has the electrons occupying atomic orbitals  How do we reconcile the observed shapes of molecules with the atomic orbital picture of atoms

Valence bond theory  Valence bond theory is the simplest approach to an orbital picture of covalent bonds  Each covalent bond is formed by an overlap of atomic orbitals from each atom  The individual orbital identity is retained  The bond strength is proportional to the amount of orbital overlap

Overlap of two 1s orbitals in H 2

 Overlap of two 2p orbitals directed along the bond axis (sigma bond)  Overlap of p and s orbitals

Problems with tetrahedral bonds  In CH 4 the bonds are all equivalent and at angles of 109.5°  The 2p orbitals in C are at 90° - far from optimum for overlap  The ground state configuration is 2s 2 2p 2  Reconcile these facts with the known structure

Hybridization  The wave mechanics permits mixing of the atomic orbital set to produce “hybrid” orbitals  Hybridization alters the shape and energy of the original  In the case of C, the differences between the 2s and 2p are smoothed out and a homogeneous collection of four sp 3 hybrid orbitals is produced

sp 3 hybridization  Formally, one of the 2s electrons is promoted to the empty 2p orbital (an energy cost, which is repaid on bond formation)  The four basis orbitals are then “hybridized” to yield the set of four sp 3

Tetrahedral directions and sp 3 hybrids

Valence bond picture of CH 4  Each C sp 3 hybrid contains one electron  Each H 1s contains one electron

Lone pairs occupy sp 3 hybrid orbitals  Valence bond picture of the tetrahedral electronic geometry provides same results for the molecules with lone pairs

Notes on hybridization  The total number of orbitals is unchanged  Four atomic orbitals (s + 3 x p) give four hybrid orbitals (4 x sp 3 )  The electron capacity remains unchanged  There is one hybridization scheme for each of the five electronic geometries  The same hybridization scheme is always used for a given electronic geometry

sp hybridization for linear geometry  One s and one p orbital

sp 2 hybridization for trigonal planar  One s and two p orbitals

Sigma and pi bonding  The hybridized orbitals describe the electronic geometry: bonds along the internuclear axes (sigma bonds)  The “unused” p orbitals overlap in a parallel arrangement above and below the internuclear axis (pi bonds)

Comparison of pi and sigma bonding

Pi bonding accounts for bond multiplicity  Two unused p orbitals in sp hybrid (linear geometry)  Two pi bonds  N≡N triple bond (one sigma, two pi)  One unused p orbital in sp 2 hybrid (trigonal planar geometry  One pi bond  C=C double bond (one sigma, one pi)

Valence bond picture of ethylene H 2 C=CH 2  Sigma bonds between C and H (blue/red) and C and C (blue)  Six electrons around C  Pi bond between C and C (green)  Two electrons around C

Valence bond picture of acetylene HC≡CH  Sigma bonds between C and H (red and blue) and C and C (blue)  4 electrons around C  Two pi bonds between C and C (green)  4 electrons around C

Beyond coordination number 4  Invoke empty d orbitals (impossible for second row elements)  One d orbital for trigonal bipyramidal  Two d orbitals for octahedral  Number of orbitals in hybrid always equals number of charge clouds

Trigonal bipyramid – sp 3 d

Octahedral –sp 3 d 2

Shortcomings of valence bond  The orbitals still maintain atomic identity  Bonds are limited to two atoms  Cannot accommodate the concept of delocalized electrons – bonds covering more than two atoms  Problems with magnetic and spectroscopic properties