3.012 Fund of Mat Sci: Bonding Lecture 10
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1 3.012 Fund of Mat Sci: Bonding Lecture 10 MOLECULES FROM ATOMS Image of a journal article removed for copyright reasons. See Slater, J. C., and G. F. Koster. "Simplified LCAO Method for the Periodic Potential Problem." Physical Review 94, no. 6 (1954).
2 Homework for Mon Oct 17 Study: 25.2, 25.4, 24.4, 24.6
3 Last time: 1. Variational principle 2. Application to the hydrogen atom 3. LCAO optimize the coefficients 4. Hydrogen molecular ion
4 Energy of a Molecule E = T + V + V + V e e N e e N N
5 Linear Combination of Atomic Orbitals Trial wavefunction is a linear combination of atomic orbitals the variational parameters are the coefficients: r r r r Ψ = cψ R + c Ψ R ( ) ( ) trial 1 1s A 2 1s B
6 Formation of a Bonding Orbital See animation at
7 Formation of an Antibonding Orbital See animation at
8 Bonding and Antibonding (II) 8 EBO/eV σ g 1s energy σ*1s energy u Born-Oppenheimer energy of exact orbitals R/10-10 m Orbital Energies for the σ g 1s and σ* u 1s LCAO Molecular Orbitals. Figure by MIT OCW.
9 Many-Atoms Hamiltonian Hˆ = Tˆ + Vˆ + Vˆ + V e e N e e N N 1 Z 1 T V V 2 ˆ 2 ˆ I ˆ e = i e N = r r e e = r r i i I i RI i j> i i j
10 Molecular Orbitals From Atomic Orbitals Ψ = cψ + c Ψ + c Ψ + c Ψ trial 1 1, s H 2 1, s H 3 1, s H 4 1, s H a b c d + c Ψ + c Ψ + c Ψ + c Ψ 5 2 s, C 6 2 p, C 7 2 p, C 8 2 p, C x y z
11 sp 3 hybridization sp 3 Hypbridization. Source: Wikipedia. Diagram of s and p orbitals combining to create sp3 hybridization removed for copyright reasons. See p. 440, figure 12-5 in Petrucci, R. H., W. S. Harwood, and F. G. Herring. General Chemistry: Principles and Modern Applications. 8th ed. Upper Saddle River, NJ: Prentice Hall, 2002.
12 sp 3 hybridization Images of sp3 hybridization in CH 4 and NH 3 removed for copyright reasons. See pp , figures 12-6 and 12-7 in Petrucci, R. H., W. S. Harwood, and F. G. Herring. General Chemistry: Principles and Modern Applications. 8th ed. Upper Saddle River, NJ: Prentice Hall, 2002.
13 Great gases and liquids
14 sp 2 hybridization sp 2 Hypbridization. Source: Wikipedia. Diagram of s and p orbitals combining to create sp 2 hybridization removed for copyright reasons. See p. 442, figure 12-8 in Petrucci, R. H., W. S. Harwood, and F. G. Herring. General Chemistry: Principles and Modern Applications. 8th ed. Upper Saddle River, NJ: Prentice Hall, 2002.
15 Carbon Compounds Source: Wikipedia
16 sp hybridization Diagram of s and p orbitals combining to create sp hybridization removed for copyright reasons. See p. 443, figure 12-9 in Petrucci, R. H., W. S. Harwood, and F. G. Herring. General Chemistry: Principles and Modern Applications. 8th ed. Upper Saddle River, NJ: Prentice Hall, 2002.
17 Ethyne (Acetylene) Source: Wikipedia Diagram of the formation of σ and π bonds in ethyne removed for copyright reasons.
18 Formation of a σ Bonding Orbital See animation at
19 Formation of a π Bonding Orbital See animation at
20 Ethene (Ethylene) Source: Wikipedia Diagram of the formation of σ and π bonds in ethene removed for copyright reasons.
21 Ethane (saturated) Source: Wikipedia Diagram of ethane removed for copyright reasons. See Goodman et al., Nature (2001).
22 Bond Lengths and Bond Energies Tables of Average Bond Lengths and Average Bond Energies removed for copyright reasons. See p. 420, table 11.2, and p. 422, table 11.3, in Petrucci, R. H., W. S. Harwood, and F. G. Herring. General Chemistry: Principles and Modern Applications. 8th ed. Upper Saddle River, NJ: Prentice Hall, 2002.
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General Chemistry Principles and Modern Applications Petrucci Harwood Herring 8 th Edition Chapter 12: Chemical Bonding II: Additional Aspects Philip Dutton University of Windsor, Canada N9B 3P4 Contents
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