Valence bond theory • There are two major approximate theories of chemical bonds: valence bond (VB) theoryand molecular orbital (MO) theory. • While computationally less widely used than MO, VB has a special appeal to organic chemists studying reaction mechanisms and remains useful and important. • The concepts of spn hybridization and lone pairs are introduced.
Orbital approximation • In polyelectron atoms, we used the orbital approximation – forced separation of variables – where we filled hydrogenic orbitals with electrons to construct atomic wave functions. • For polyatomic molecules, can we also use orbital approximation? Can we use hydrogenicatomic orbitals to construct molecular wave functions?
Singlet and triplet He (review) • In the orbital approximation for (1s)1(2s)1 He, there are four different ways of filling two electrons: Anti-symmetric Triplet more stable Anti-symmetric Singlet Anti-symmetric
VB theory for H2 • Let us construct the molecular wave function of H2 using its two 1s orbitals A and B.
VB theory for H2 singlet more stable e n n e triplet e n n e
Covalent bond Enhanced electron probability density between nuclei (shielding nucleus-nucleus repulsion). The greater the overlap of two AO’s the stronger the bond. Two singlet-coupled (α1β2−β1α2) electrons for one bond (Lewis structure).
σ and π bonds • Aπ bond is weaker than σ bond because of a less orbital overlap in π. σ bond π bond
N2 • N is (1s)2(2s)2(2px)1(2py)1(2pz)1 • N2 forms one σ bond and two π bonds. Altogether three-fold covalent bonds (triple bonds).
H2O • O is (1s)2(2s)2(2px)2(2py)1(2pz)1. • The two unpaired electrons in 2p orbitals can each form a σ bond with H (1s)1. • This explains the HOH angle of near 90º.
NH3 • N is (1s)2(2s)2(2px)1(2py)1(2pz)1. • The three unpaired electrons in 2p orbitals can each form a σ bond with H (1s)1. • This explains the pyramidal structure with the HNH angle of near 90º.
Promotion and hybridization • C (1s)2(2s)2(2px)1(2py)1is known to form fourequivalentbonds as in CH4. valence valence 2p 2p 2s 2s 1s 1s Still not equivalent Promotion – we invest a small energy in C for a bigger energy gain (4 bonds instead of 2) in CH4
sp3 hybridization • From one s and three porbitals, we form four equivalent bonds by linearly combing them: z y x These are orthonormal
CH4 • With the sp3 hybridization, C is (1s)2(sp3)1(sp3)1(sp3)1(sp3)1. • The four unpaired electrons in the four sp3orbitals can each form a σbond with H (1s)1. • This explains the tetrahedron structure of CH4 with the HCH angle of precisely 109.47º.
sp2 hybridization • From one s and two porbitals, we form three equivalent bonds by linearly combing them: y x These are orthonormal
CH2=CH2 • With the sp2hybridization, C is (1s)2(2pz)1 (sp2)1(sp2)1(sp2)1. • Three unpaired electrons in three sp2orbitals can each form a σbondwith H(1s)1 or C(sp2)1. C(2pz)1 additionally forms a π bond. • This explains the planar structure of ethylene with the HCH and CCH angles of near 120º.
sp1 hybridization • From one s and one p orbital, we form two equivalent bonds by linearly combing them: These are orthonormal
CHΞCH • With the sp1hybridization, C is (1s)2(2pz)1 (2py)1(sp1)1(sp1)1. • Two unpaired electrons in two sp1orbitals can each form a σ bond with H(1s)1 or C(sp1)1. C(2pz)1and (2py)1form twoπbonds. • This explains the linear structure of acetylene. Cf. H2O
Lone pairs • Revisit H2O. O is (1s)2(2s)2(2px)2(2py)1(2pz)1. • Two unpaired electrons each form a covalent bond: O(2py)1H(1s)1 and O(2pz)1H(1s)1 • Two valence electrons that do not participate in chemical bond are calleda lone pair: O(2s)2 and O(2px)2. • Lone pairs are part of electron density not shielding nucleus-nucleus repulsion and thus not being stabilized by nuclear charges. They are naked electron pairs that repel other lone pairs or bonding electron pairs.
Lone pairs in H2O • Two different views of H2O: nonhybridized versus sp3 hybridized • The observed HOH angle is 104.5º, closer to the sp3 picture, suggesting that lone-pair repulsion plays a significant role. 2s lone pair 2pz lone pair sp3 lone pair sp3 lone pair sp3 picture suggests HOH angle ~ 109.5º Nonhybridizationsuggests HOH angle ~ 90º
Lone pairs in NH3 • Two different views of NH3: nonhybridized versus sp3 hybridized • The observed HNH angle is 107º, much closer to the sp3 picture, suggesting that a dominating role of lone-pair repulsion. 2s lone pair sp3 lone pair sp3 picture suggests HNH angle ~ 109.5º Nonhybridizationsuggests HNH angle ~ 90º
Lone pairs in H2X • The larger the central atom in the isovalence H2X series, the more widely spread valence p and s orbitals and the less lone-pair repulsions. H2Te has no need to promote and hybridize (HTeH angle of 89.5º), whereas H2O gains much by promoting and hybridizing into sp3 and separating the lone pairs widely.
Homework challenge #7 • C is (1s)2(2s)2(2px)1(2py)1. Is methylene CH2 bent (nonhybridizedp, sp2, sp3) or linear (sp1)? • Find the answer in the following paper and report. “Methylene: A Paradigm for Computational Quantum Chemistry” by Henry F. Schaefer III, Science, volume 231, page 1100, 7 March 1986.
Summary • VB theory is an orbital approximation for molecules. The orbitals used are hydrogenicatomic orbitals. • VB theory explains the Lewis structure(two singlet-coupled electrons – α and β spins – per bond). • This explains σ and πbond, promotion and spn hybridization, lone pairs. • Lone-pair repulsion is important in determining molecular structures.