VBT Notes

Valence Bond Terminology: Bonding Theories for Covalent Molecules (1): • Valence Bond Theory Overlap: two orbitals existing in the same region of space • VSEPR à predicts the 3-dimensional molecular (MG) and electron pair (EPG) geometries of a large number of covalent lp: lone pair of electrons (non- bonding) • compounds and polyatomic anions. bp: bonding pair of electrons (result of orbital overlap) Valence Bond (VB) theory describes these geometries in terms of • Central atom: the atom of concern in a molecule the bonding orbitals used by the atoms in these molecules. • hybridization: the linear combination of atomic orbitals • hybrid orbital: bonding orbitals that arise from the mixing Valence bond theory states that bonding in covalent compounds of AO’s. occurs via the overlap of two half-filled orbitals of the bonding • atoms. σ -bond: (sigma bond) overlap of orbitals along the bond axis • In order to achieve the correct bond angles as predicted by VESPR, π -bond: (pi bond) overlap of orbitals above and below the bond axis. the atomic orbitals on each bonding atom “mix” to form new “hybrid” bonding orbitals. 1 • single bond: one σ-bond • double bond: one σ-bond & one π-bond • triple bond: one σ-bond & two π-bonds • PH3 (phosphorous trihydride) Phosphorous has 5 valence electrons with an electron configuration of 3s 23p3. Each H-atom has one 1s electron. P 3s ↑↓ ↑ 3p ↑ H 1s ↓ ↓ ↑ ↓ Each 1s orbital can overlap with one of the half-filled p orbitals. The result shows that the molecule will have 3 bonds and 1 lone pair of electrons. The H-P-H bond angles are 90° (from the original p-orbitals on P). However, VESPR tells us that we should have a trigonal pyramid MG (H-P-H) bond angles ~95°) with a tetrahedral EPG. Why don’t the two agree exactly? 2 Consider the valence electrons on Phosphorous: When the atomic orbitals are combined, four new orbitals result that are “Hybrids” of the original atomic orbitals. atomic orbitals 3p ↑↓ 3s Energy ↑ ↑ ↑ New orbitals ↑↓ ↑ ↑ ↑ sp3 Hybridized orbitals Ø The four new bonding orbitals are given the designation sp3 since they are a linear combination of one s-orbital and 3 p-orbitals. Ø Now each of the three H-atoms can overlap to form one bond and the electron pair in the filled sp3 corresponds to the lone pair. 3 An s-orbital combines with 3 p-orbitals to form 4 new sp3 hybrid orbitals that have a tetrahedral EPG. 4 Methane: CH 4 H (1s1) ↑ ↑ ↑ ↑ 4σ-bonds ↑ ↑ 2p ↑ ↑ ↑ ↑ new sp 3 ↑↓ 2s aaaa The 2s and (3) 2p orbitals in methane overlap to form 4 new sp3 hybrid orbitals. Each of the 1s electrons on hydrogen overlap to form σ-bonds and the expected tetrahedral MG and EPG is seen. Conclusion: When tetrahedral electron pair geometry (EPG) is seen on a central atom, the atom is most likely bonding through sp 3 hybrid orbitals. Other examples of sp3 hybrid molecules are: 5 Water H 20 Ammonia NH3 sp2 hybridization When an “s” orbital mixes with two “p” orbitals, three sp2 orbitals result leaving one “p” orbital behind. 2p 2p new sp2 hybrid orbitals 2s The sp2 orbitals spread out to form a trigonal planar geometry leaving the p orbital perpendicular to the plane. The sp2 orbitals can form σ bonds or hold lone pairs and the p orbital forms the π -bond in a double bond. 6 Bonding in an sp 2 hybridized atom. Formation of SP 2 hybrid orbitals The head on overlap of two sp2 orbitals produces a σ-bond whereas the overlap of the p orbitals above and below the bond axis produces a πbond. An example of sp2 hybridization is given by C 2H4 (ethene) ↑ ↑ 2p ↑ ↑ ↑ sp2 ↑↓ ↑ Each carbon atom undergoes sp2 hybridization 2p The 4 valence electrons redistribute amongst the orbitals, placing one in each of the sp 2 orbitals and one in the left over p orbital. 2s 7 Bonding in C 2H4 One of the sp2 orbitals on each carbon form the C-C σ-bond, while the other two form the C-H σ-bonds via overlap with the 1s electrons in H. The two half-filled p orbitals on each carbon overlap to form the π-bond. Other examples of molecules with sp2 hybridization are: CH2O formaldehyde SO2 sulfur dioxide 8 Conclusion: When a central atom has a trigonal planar electron pair geometry (EPG), it is most likely to bond through sp 2 hybridization. Compounds containing double bonds (σ + π) have sp2 hybridization. sp Hybridization: When an “s” orbital mixes with one “p” orbital, two sp orbitals result leaving two “p” orbital behind. 2p 2p new sp hybrid orbitals 2s The sp orbitals spread out to form a linear geometry (directed away from one another) leaving the p orbitals perpendicular to the molecular axis. The sp orbitals can form σ -bonds or hold lone pairs and one of the p orbital forms the π -bond in a double bond or the two form the π -bonds in a triple bond. An example of sp2 hybridization is given by C2H2 (acetylene) Each carbon atom undergoes sp hybridization ↑ ↑ 2p ↑ ↑ ↑ sp ↑↓ ↑ 2p The 4 valence electrons redistribute amongst the orbitals, placing one in each of the sp orbitals and one in each of the left over p orbitals. 2s 9 One of the sp orbitals on each carbon forms the C-C σ-bond, while the other forms the C-H σ-bonds via overlap with the 1s electrons in H. The two half-filled p orbitals on each carbon overlap to form the π-bonds (perpendicular to one another). Bonding in C2H2: On each carbon, one of the two sp hybrid orbitals overlaps with the H-atom and the other with the C-atom forming σ-bonds. The two perpendicular p orbitals on each carbon overlap to form the two π-bonds. Other examples of molecules with sp hybridization are: N2 CN- (cyanide anion) :N≡ ≡ N: [:C≡ ≡ N:]10 Conclusion: When a central atom has a linear electron pair geometry (EPG) with no lone pairs , it is most likely to bond through sp hybridization. Compounds containing triple bonds (σ + 2π) or adjacent double bonds (CO 2) have sp hybridization. Valence Bond Theory (2): Expanded Valence • For elements beyond the second period, we found several examples where the central atom in a Lewis structure had greater than 8 electrons in the valence. • At n = 3, l = 0, 1 & 2 or there are “s, p & d” orbitals that can be filled. • We’ve seen that when four sp3 hybrid orbitals form, a central atom can accommodate only up to 8 electrons in the valence (bp & lp). • To place more in the valence, we must bring the d orbitals into the “mix” as it were. Consider a molecule like PCl 5 Phosphorous has a valence electron configuration of 3s23p 3. Each of the five electrons forms a single bond with a chlorine atom. How can we describe the bonding in terms of hybrid orbitals? Each chlorine atom forms a σ-bond with a half-filled 11 3d ↑ ↑ ↑ 3p ↑ ↑ ↑ ↑ ↑ new sp3d hybrid orbitals ↑↓ 3s Each of the 5 sp3d hybrid orbitals will distribute in such a way as to minimize repulsions. The most stable (lowest energy) configuration is a trigonal bipyramid structure. Conclusion: When any central atom in a molecule has an electron pair geometry (EPG) that is trigonal bipyramid, the central atom is most likely bonding through sp3d hybridized orbitals Additional example of sp3d hybrid molecules: 12 SF4 (sulfur tetrafluoride) ClF3 (chlorine trifluoride) What about molecules with 12 electrons in the valence? In order to achieve an expanded valence that can hold six electron pairs (bp & lp) we need to form 6 new hybrid orbitals. This requires the mixing of an s, 3 p’s and 2 d atomic orbitals. 3d 3p new sp3d2 hybrid orbitals 3s 13 Each of the 5 sp3d hybrid orbitals will distribute in such a way as to minimize repulsions. The most stable (lowest energy) configuration is a trigonal bipyramid structure. Consider a molecule like SF6 Sulfur has a valence electron configuration of 3s 23p4. Each of the five electrons forms a single bond with a fluorine atom forming an octahedral MG and EPG. The bonding can be described in terms of sp 3d 2 hybrid orbitals. 14 Each fluorine atom forms a σ-bond with a half-filled sp3d2 orbital. 3d ↑↓ ↑ ↑ 3p ↑ ↑ ↑ ↑ ↑ ↑ new sp3d2 hybrid orbitals ↑↓ 3s Conclusion: Molecules with an octahedral EPG have sp3d2 hybridization at the central atom. Additional examples are: SbCl 52- (antimony pentachloride ion) XeF4 (xenon tetra fluoride) 15 Determining the hybridization of a molecule: 1 2 3 Since Carbon (1) & (3) are identical, each must have the same hybridization. Trigonal planar EPG, double bond… The bonding is sp2 Carbon (2) has a linear EPG and two double bonds. To do so there must be two p-orbitals forming two π-bonds. Linear + two π-bonds… sp 16 Additional Examples of hybridization: 17