Valence bond theory: sticks no more 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 simplistic Lewis dot approach and repulsion of charge groups  But orbital model has electrons occupying atomic orbitals  How do we reconcile the observed shapes of molecules with the atomic orbital model?

Valence bond theory  Valence bond theory is the simplest approach to an orbital picture of covalent bonds  Valence electrons occupy atomic orbitals (basic s, p, d, f or hybridized versions of them)  Covalent bond is formed by overlap of atomic orbitals containing one electron from each atom  Bonding orbitals contain two electrons paired  Bonding electrons are localized between two atoms  Lone pairs occupy single atomic orbitals, spins paired  Bond strength is proportional to amount of orbital overlap  Shape of molecule determined by geometry of overlapping atomic orbitals

Overlap of two 1s orbitals in H2  This is a visual representation of a mathematical operation involving the wave functions of each orbital

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

Limits on qualitative approach  Valence bond theory is a mathematical model that yields bond lengths, bond energies, and bond angles using the wave functions of the bonding atoms  Qualitative approach shows the overlap of atomic orbitals and approximate geometry of bonds that result

Problems with tetrahedral bonds  In CH4 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 2s22p2  Reconcile these facts with known structure

Hybridization: problem resolved  The wave mechanics permits mixing atomic orbitals to produce “hybrid” orbitals  Hybridization alters shape and energy of original ao’s  In case of C, two 2s and two 2p are mixed to produce four homogeneous sp3 hybrid orbitals

sp3 hybridization  Formally, one 2s electron is promoted to empty 2p orbital (energy cost, repaid on bond formation)  The four basis orbitals are then “hybridized” to yield set of four sp3 hybrid orbitals  This is qualitative explanation of a mathematical operation in wave mechanics

Tetrahedral directions and sp3 hybrids  sp3 hybridization produces four wave functions that have greater density along the tetrahedral bonding directions  Improves overlap with atomic orbitals on bonded atoms

Valence bond picture of CH4  Each C sp3 hybrid contains one electron  Each H 1s contains one electron

Lone pairs occupy sp3 hybrid orbitals  Valence bond picture of the tetrahedral electronic geometry provides same results for molecules with lone pairs  Lone pairs occupy same sp3 hybrid orbitals as bonding pairs

Do molecules with four charge groups always use sp3 hybrids?  H – S – H bond angle is 92º  Better result with S – H bonds using 2p orbitals rather than sp3 hybrids (angle is 109.5º)  Bonding orbitals more “p-like”  Lone pair electrons more “s-like”

Notes on hybridization  The total number of orbitals is unchanged before and after  Four ao’s (s + 3 x p) give four hybrid orbitals (4 x sp3)  Three ao’s (s + 2 x p) give three sp2 hybrids  Two ao’s (s + p) give two sp hybrids

 Electron capacity remains unchanged  Unique hybridization scheme for each electronic geometry (five total)  Same hybridization scheme for given electronic geometry  Number of ao’s in hybridization scheme = number of charge groups round central atom

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

sp2 hybridization for trigonal planar  One s and two p orbitals

Sigma and pi bonding  Sigma bonds (along internuclear axes) describe electronic geometry  “Surplus” p orbitals overlap in parallel arrangement above and below internuclear axis (pi bonds)

Comparison of pi and sigma bonding  Pi bond  Orbital overlap above and below inter-nuclear axis

 Sigma bond  Orbital overlap along inter-nuclear axis

 Sigma bond slightly stronger than pi bond

Valence bond picture of ethylene H2C=CH2  Three sigma bonds between C and 2 x H + C  Six electrons around C

 Pi bond between C and C  Two electrons around C

 Two + six = eight (full octet)  Contrast with Lewis model:  Lewis: 4 dots shared  Valence bond: sigma + pi bonds

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

 Two pi bonds between C and C (red)  4 electrons around C

 Four + four = eight (complete octet)

Multiple bonds and implications for structure  Single bond allows rotation about C – C axis  Double bond is rigid

Double bonds and geometrical isomers  Isomers: same atoms, different forms  CH2ClCH2Cl has just one form  CHClCHCl has two isomers

Expanded octets: Beyond coordination number 4  Invoke empty d orbitals (impossible for second row elements)  One d orbital for trigonal bipyramidal sp3d  Two d orbitals for octahedral sp3d2

 Number of orbitals in hybrid always equals number of charge clouds

Trigonal bipyramid –sp3d

Octahedral –sp3d2

Shortcomings of valence bond  The orbitals are restricted to atoms  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  Enter the LCAO: Linear Combination of Atomic Orbitals (MO theory)