Ch. 6: Chemical Bonding II Dr. Namphol Sinkaset Chem 200: General Chemistry I I. Chapter Outline I. Introduction II. Valence Bond Theory III. Hybridization IV. Molecular Orbital Theory V. Homonuclear Diatomic Molecules VI. Heteronuclear Diatomic Molecules VII. Polyatomic Molecules I. Introduction • We know covalent compounds share e- when they bond, but how do they do this? • VSEPR theory allows us to predict shapes, but what is the reason for these shapes? • We’d also like to explain magnetic and spectral properties of covalent molecules. I. Multiple Theories • Theories are simplified views of reality, so they have limitations. • Often, different theories are used to explain different aspects of the same system. • In this case, valence bond theory (VBT) explains why molecules have certain shapes whereas molecular orbital theory (MOT) explains magnetic and spectral properties of molecules. II. Core Principles of VBT • VBT takes the idea of atomic orbitals (from quantum mechanics) and explains how they are used to form compounds. • The central idea of VBT: covalent bonds form when half-filled atomic orbitals of two atoms overlap and the overlap region, which is between the nuclei, is occupied by a pair of e-’s. II. Types of Orbital Overlap • Orbitals can overlap in one of two ways. Side to side (no free rotation) . End to end (free rotation) II. VBT Calculation II. H2 Molecule • The calculation reveals an optimum distance where the interactions between valence electrons and nuclei results in the greatest stabilization. • This is a σ-type bond formed from the overlap of two half-filled 1s orbitals. • These interaction energy calculations can be done for any molecule to see if they will bond. II. Simple VBT • In general, interaction energy usually stabilizing if two-half filled orbitals exist. • We can use this generalization to explain bonds w/out calculating explicitly. • Consider H2S. II. Qualitative VBT for H2S • Notice bond angle prediction of 90°. • Lewis theory predicts <109.5°. • Actual is 92°! III. Methane Is More Complex • If we apply simple VBT to carbon and hydrogen… • It doesn’t work! • Should be CH4, not CH2 and bond angle should be 109.5°. III. Hybrid Atomic Orbitals • Simple direct overlap of s, p, d, and f orbitals cannot account for the many shapes observed in molecules. • Linus Pauling proposed that valence atomic orbitals can be different than atomic orbitals in an isolated atom. • If atomic orbitals are mixed (via hybridization), new hybrid orbitals can be formed that lead to correct molecular geometries. III. Hybrid Atomic Orbitals • A couple of important points about hybrid orbitals: . The number of hybrid orbitals equals the number of atomic orbitals mixed together. The shapes and energies of the hybrid orbitals depends on the atomic orbitals that are mixed. The type of hybridization that occurs is the one that leads to the lowest overall energy for the molecule. • Since we can’t do interaction calculations, we will use EG’s from VSEPR theory to predict type of hybridization. III. sp3 Hybridization • To get the tetrahedral electron geometry, one s orbital is mixed with three p orbitals. III. Formation of sp3 Hybrids III. Correct Bonding in Methane • In methane, carbon forms 4 sp3 hybrids which overlap with the s orbitals in hydrogen. III. sp2 Hybridization • To get the trigonal planar geometry, one s orbital is mixed with two p orbitals. III. Formation of sp2 Hybrids III. Example sp2 Hybridization • H2CO is a compound that utilizes sp2 hybrids. • As individual atoms, they have only atomic orbitals. III. Example sp2 Hybridization • When the atoms come together to bond, the C atom is central, and it undergoes hybridization. • After hybridization, C can form 4 bonds. III. sp2 Hybrids and Double Bonds • The unhybridized p orbital can be used to form a pi bond. III. Pi Bonds and Restricted Rotation • Recall that pi bonds do not allow the atoms involved to rotate freely. III. Same Atoms, Different Compounds III. sp Hybridization • To get the linear geometry, one s orbital is mixed with a p orbital. III. Formation of sp Hybrids III. sp Hybrids and Triple Bonds • The two unhybridized p orbitals can be used to form two pi bonds. III. sp3d Hybridization • To get trigonal bipyramidal geometry, an s orbital, three p orbitals, and one d orbital are mixed. III. Example of sp3d Compound III. sp3d2 Hybridization • Octahedral geometry is obtained by mixing one s orbital, three p orbitals, and two d orbitals. III. Example of sp3d2 Compound III. Sample Problem 6.1 • Identify the type of hybridization in the central atom of the following molecules. SF4 . XeF4 . PCl3 - . ClO3 . BrF3 III. Sample Problem 6.2 • Identify the bonding scheme in the two diagrams. IV. Core Principles of MOT • VBT treats e-’s as being in atomic orbitals which a big simplification. • The main difference from VBT: e-’s belong to the entire molecule, and they exist in molecular orbitals. • Quantum mechanics is applied to a molecule instead of individual atoms to get new orbitals that belong to the molecule. IV. Formation of MO’s • Applying quantum mechanics to molecules requires applying trial wavefunctions. • The most common trial functions involve taking weighted linear combinations of atomic orbitals. i.e. mathematically adding/subtracting atomic orbitals (atomic wavefunctions) to form MO’s (molecular wavefunctions). IV. Linear Combinations • When two atomic wavefunctions are subtracted from one another, you get an antibonding MO. Antibonding MO’s have a region of zero e- density between nuclei (called a node). • When two atomic wavefunctions are added together, you get a bonding MO. Bonding MO’s have a region of high e- density between nuclei, thus lowering PE. IV. Destructive vs. Constructive IV. Bonding MO in H2 • This bonding MO is called σ1s. σ because of the shape similarity to VBT. 1s because it was formed from combination of 1s orbitals. IV. Antibonding MO in H2 • The * indicates that it is antibonding. • Note that the energy of the antibonding MO is higher than the energies of the 1s orbitals. IV. Filling MO’s • Rules for filling MO’s are the same as for filling AO’s. Aufbau principle . Pauli exclusion principle . Hund’s rule • A molecular orbital diagram shows the relative energy and number of e-’s in each MO, as well as the AO’s that formed them. IV. MO Diagram for H2 IV. Bond Order • In MOT, bond order is something that is calculated. A bond order greater than 0 indicates increased stability for atoms when bonded. B.O. = ½ [(e-’s in bonding MOs) – (e-’s in antibonding MOs)] V. Homonuclear Diatomics • In general, only valence orbitals interact to form MO’s. • s orbital interactions are easy – create a bonding and a nonbonding MO as seen in H2. • How do p orbitals interact to form MO’s? V. MO’s From p Orbitals V. Homonuclear MO Diagrams • MO diagrams of p-block elements will have MO’s formed from s and p orbitals. • For O2, F2, and Ne2 (theoretical), the order of the MO’s is as expected. • For B2, C2, and N2, the energy level of the p orbitals is low enough to allow orbital mixing with the s orbitals; this changes the order of the MO’s. V. Homonuclear MO Diagrams V. Sample Problem 6.3 • Construct molecular orbital diagrams for N2 and O2. Additionally, determine whether or not these molecules are diamagnetic or paramagnetic, calculate their bond orders, and write the valence e- molecular orbital configuration. VI. Heteronuclear Diatomics • In a heteronuclear diatomic, the energy levels of the atomic orbitals are different (why?) resulting in asymmetric MO diagrams. • We can infer some information about a molecule from its MO diagram: “location” of certain e-’s and polarity effects. VI. MO Diagram of NO • On which atom is the radical localized? • What is the bond order of NO, and how does it compare to that found via the Lewis structure? VI. MO Diagram of HF • How does this diagram rationalize the direction of the polarity? • Notice that nonbonding orbitals have same energy as AO’s. VII. Computational Chem • Application of MOT to larger molecules requires computational effort. • Computational chemistry is a whole branch of chemistry. • We look at results for two larger molecules, CH4 and O3. VII. CH4: VBT vs. MOT VII. CH4 Bonding MO #2 VII. Resonance in O3, VBT VII. Resonance in O3, MOT.