Lecture 24 Valence bond theory (c) So Hirata, Department of Chemistry, University of Illinois at Urbana-Champaign. This material has been developed and made available online by work supported jointly by University of Illinois, the National Science Foundation under Grant CHE (CAREER), and the Camille & Henry Dreyfus Foundation, Inc. through the Camille Dreyfus Teacher-Scholar program. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the sponsoring agencies.

Valence bond theory There are two major approximate theories of chemical bonds: valence bond (VB) theory and 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 sp n 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 hydrogenic atomic 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 Singlet Triplet more stable

VB theory for H 2 Let us construct the molecular wave function of H 2 using its two 1s orbitals A and B.

VB theory for H 2 singlet more stable triplet e nn e e nn e

Covalent bond (1)Enhanced electron probability density between nuclei (shielding nucleus-nucleus repulsion). The greater the overlap of two AO’s the stronger the bond. (2)Two singlet-coupled (α1β2−β1α2) electrons for one bond (Lewis structure).

σ and π bonds A π bond is weaker than σ bond because of a less orbital overlap in π. σ bondπ bond

N2N2 N is (1s) 2 (2s) 2 (2p x ) 1 (2p y ) 1 (2p z ) 1 N 2 forms one σ bond and two π bonds. Altogether three-fold covalent bonds (triple bonds).

H2OH2O O is (1s) 2 (2s) 2 (2p x ) 2 (2p y ) 1 (2p z ) 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.

NH 3 N is (1s) 2 (2s) 2 (2p x ) 1 (2p y ) 1 (2p z ) 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 (2p x ) 1 (2p y ) 1 is known to form four equivalent bonds as in CH 4. 1s1s 2s2s 2p2p valence 1s1s 2s2s 2p2p Promotion – we invest a small energy in C for a bigger energy gain (4 bonds instead of 2) in CH 4 Still not equivalent

sp 3 hybridization From one s and three p orbitals, we form four equivalent bonds by linearly combing them: x y z These are orthonormal

CH 4 With the sp 3 hybridization, C is (1s) 2 (sp 3 ) 1 (sp 3 ) 1 (sp 3 ) 1 (sp 3 ) 1. The four unpaired electrons in the four sp 3 orbitals can each form a σ bond with H (1s) 1. This explains the tetrahedron structure of CH 4 with the HCH angle of precisely º.

sp 2 hybridization From one s and two p orbitals, we form three equivalent bonds by linearly combing them: x y These are orthonormal

CH 2 =CH 2 With the sp 2 hybridization, C is (1s) 2 (2p z ) 1 (sp 2 ) 1 (sp 2 ) 1 (sp 2 ) 1. Three unpaired electrons in three sp 2 orbitals can each form a σ bond with H(1s) 1 or C(sp 2 ) 1. C(2p z ) 1 additionally forms a π bond. This explains the planar structure of ethylene with the HCH and CCH angles of near 120º.

sp 1 hybridization From one s and one p orbital, we form two equivalent bonds by linearly combing them: These are orthonormal

CHΞCH With the sp 1 hybridization, C is (1s) 2 (2p z ) 1 (2p y ) 1 (sp 1 ) 1 (sp 1 ) 1. Two unpaired electrons in two sp 1 orbitals can each form a σ bond with H(1s) 1 or C(sp 1 ) 1. C(2p z ) 1 and (2p y ) 1 form two π bonds. This explains the linear structure of acetylene. Cf. H 2 O

Lone pairs Revisit H 2 O. O is (1s) 2 (2s) 2 (2p x ) 2 (2p y ) 1 (2p z ) 1. Two unpaired electrons each form a covalent bond: O(2p y ) 1 H(1s) 1 and O(2p z ) 1 H(1s) 1 Two valence electrons that do not participate in chemical bond are called a lone pair: O(2s) 2 and O(2p x ) 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 H 2 O Two different views of H 2 O: nonhybridized versus sp 3 hybridized The observed HOH angle is 104.5º, closer to the sp 3 picture, suggesting that lone-pair repulsion plays a significant role. sp 3 picture suggests HOH angle ~ 109.5º Nonhybridization suggests HOH angle ~ 90º sp 3 lone pair 2s lone pair 2p z lone pair

Lone pairs in NH 3 Two different views of NH 3 : nonhybridized versus sp 3 hybridized The observed HNH angle is 107º, much closer to the sp 3 picture, suggesting that a dominating role of lone-pair repulsion. sp 3 picture suggests HNH angle ~ 109.5º Nonhybridization suggests HNH angle ~ 90º sp 3 lone pair 2s lone pair

Lone pairs in H 2 X The larger the central atom in the isovalence H 2 X series, the more widely spread valence p and s orbitals and the less lone-pair repulsions. H 2 Te has no need to promote and hybridize (HTeH angle of 89.5 º ), whereas H 2 O gains much by promoting and hybridizing into sp 3 and separating the lone pairs widely. H2XH2XHXH angle H2OH2O104.5 H2SH2S92.2 H 2 Se91.0 H 2 Te89.5

Homework challenge #7 C is (1s) 2 (2s) 2 (2p x ) 1 (2p y ) 1. Is methylene CH 2 bent (nonhybridized p, sp 2, sp 3 ) or linear (sp 1 )? 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 hydrogenic atomic orbitals. VB theory explains the Lewis structure (two singlet-coupled electrons – α and β spins – per bond). This explains σ and π bond, promotion and sp n hybridization, lone pairs. Lone-pair repulsion is important in determining molecular structures.