Valence bond theory: sticks no more. Electrons are not simply dots And bonds are not sticks
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1 Valence bond theory: sticks no more Electrons are not simply dots And bonds are not sticks
2 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
3 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?
4 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
5 Overlap of two 1s orbitals in H 2 This is a visual representation of a mathematical operation involving the wave functions of each orbital
6 Overlap of two 2p orbitals directed along the bond axis (sigma bond) Overlap of p and s orbitals
7 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
8 Problems with tetrahedral bonds In CH 4 the bonds are all equivalent and at angles of 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 known structure
9 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 sp 3 hybrid orbitals
10 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 sp 3 hybrid orbitals This is qualitative explanation of a mathematical operation in wave mechanics sp 3 hybridization
11 Tetrahedral directions and sp 3 sp 3 hybridization produces four wave functions that have greater density along the tetrahedral bonding directions Improves overlap with atomic orbitals on bonded atoms hybrids
12 Valence bond picture of CH 4 Each C sp 3 hybrid contains one electron Each H 1s contains one electron
13 Lone pairs occupy sp 3 hybrid orbitals Valence bond picture of the tetrahedral electronic geometry provides same results for molecules with lone pairs Lone pairs occupy same sp 3 hybrid orbitals as bonding pairs
14 Do molecules with four charge groups always use sp 3 hybrids? H S H bond angle is 92º Better result with S H bonds using 2p orbitals rather than sp 3 hybrids (angle is 109.5º) Bonding orbitals more p-like Lone pair electrons more s-like
15 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 sp 3 ) Three ao s (s + 2 x p) give three sp 2 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
16 sp hybridization for linear geometry One s and one p orbital
17 sp 2 hybridization for trigonal planar One s and two p orbitals
18 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)
19 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
20 Valence bond picture of ethylene 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 H 2 C=CH 2
21 Valence bond picture of acetylene 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) HC CH
22 Multiple bonds and implications for structure Single bond allows rotation about C C axis Double bond is rigid
23 Double bonds and geometrical Isomers: same atoms, different forms CH 2 ClCH 2 Cl has just one form CHClCHCl has two isomers isomers
24 Expanded octets: Beyond coordination number 4 Invoke empty d orbitals (impossible for second row elements) One d orbital for trigonal bipyramidal sp 3 d Two d orbitals for octahedral sp 3 d 2 Number of orbitals in hybrid always equals number of charge clouds
25 Trigonal bipyramid sp 3 d
26 Octahedral sp3d2
27 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)
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