3.8 The Limitations of Lewis's Theory
3.9 Molecular Orbitals The valence-bond (VB) and molecular orbital (MO) theories are both procedures for constructing approximate wavefunctions of electrons. The MO theory can account for electron-deficient compounds, paramagnetic O 2, and many other properties by focusing on electrons delocalized over the whole molecule. The VB theory focuses on electrons on individual bonds between pairs of atoms.
3.8 The Limitations of Lewis's Theory MOLECULAR ORBITAL THEORY Fredrich Hund, Robert Mulliken (1966) Box 3.2 Magnetism; diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, ferrimagnetic Paramagnetic O 2 ; unpaired electron(s) Fig 3.24 Lewis's theory; Valence-bond theory; bond and bond 2 lone pairs on each O occupying the sp 2 hybrid orbitals B 2 H 6 (diborane); electron-deficient compound At least seven bonds (= 14 electrons) are required, but only 12 valence electrons.
3.8 The Limitations of Lewis's Theory Linear combination of atomic orbitals molecular orbital (LCAO- MO) method Approximate molecular wavefunctions atomic orbitals by superimposing (mixing) of N c ij and E j are determined by solving the Schrödinger equation
3.8 The Limitations of Lewis's Theory Trial wavefunctions for H 2 using two 1s atomic orbitals of H Increased amplitude in the internuclear region bonding Larger volume for electrons lower kinetic energy (particle-in-a-box) Decreased amplitude in the internuclear region & nodal plane antibonding
3.8 The Limitations of Lewis's Theory Molecular orbital energy level diagram Fig 3.27 Box 3.3 Photoelectron spectroscopy; orbital energies from E K of photoelectrons
3.8 The Limitations of Lewis's Theory
3.10 The Electron Configurations of Diatomic Molecules Building-up principle for MO 1. Lower to higher 2. Up to two electrons ( ) per MO; Pauli exclusion principle 3. Hund's rule H 2 : The energy of H 2 is lower than that of the separate H atoms. Fig 3.28 Even the energy of H 2+ is lower than that of the separate H atoms.
3.10 The Electron Configurations of Diatomic Molecules
3.10 The Electron Configurations of Diatomic Molecules Homonuclear diatomic molecules of Period 2 Linear combination of 10 atomic orbitals; 1. No mixing between AO's of the same atom 2. Significant mixing only between AO's of similar energies and substantial overlap Negligible mixing between the core 1s and the valence 2s and 2p orbitals No MO from 2s 2p mixing due to symmetry
3.10 The Electron Configurations of Diatomic Molecules
3.10 The Electron Configurations of Diatomic Molecules
3.10 The Electron Configurations of Diatomic Molecules Molecular orbital energy level diagram (obtained from the Schrödinger equation) The energy separation of 2s and 2p for O 2 and F 2 are large due to large Z eff pulling 2s-electrons closer. Negligible 2s-2p mixing for O 2 and F 2
3.10 The Electron Configurations of Diatomic Molecules
3.10 The Electron Configurations of Diatomic Molecules Bond order
3.11 Bonding in Heteronuclear Diatomic Molecules Nonpolar covalent bond; Ionic bond (A + B ); Polar covalent bond; if A is more electronegative. Fig 3.33
3.11 Bonding in Heteronuclear Diatomic Molecules
HF 3.11 Bonding in Heteronuclear Diatomic Molecules No net overlap between H1s and (F2p x or F2p y ) 2 "nonbonding" orbitals
3.11 Bonding in Heteronuclear Diatomic Molecules orbital mainly of F2p z (energy level close to F2p z ) orbital mainly of H1s (energy level close to H1s)
3.11 Bonding in Heteronuclear Diatomic Molecules CO and NO Fig 3.35 from 2p-2p mixing only
3.12 Orbitals in Polyatomic Molecules H 2 O; 1b 1 ; nonbonding, mainly O2p y, lone pair effect 2a 1 ; almost nonbonding
3.12 Orbitals in Polyatomic Molecules CH 4 ; 1 of the 4 electron pairs is slightly lower in energy. photoelectron spectroscopy VB-theory; all eight electrons have the same energy. MO-theory; (1a 1 ) 2 (1t 1 ) 6 Lower energy for the 1a 1 electron pair
3.12 Orbitals in Polyatomic Molecules C 6 H 6 = 30 atomic orbitals VB theory for delocalized in the ring plane from 24 AO's = 6 (C2s, C2p x, C2p y, H1s) sp 2 hybridization for MO theory for the delocalized 6 from 6 C2p z
3.12 Orbitals in Polyatomic Molecules
3.12 Orbitals in Polyatomic Molecules Electron-deficient molecules No need to provide one pair of electrons for each pair of atoms Existence of electron-deficient molecules such as B 2 H 6 SF 6 ; hypervalent compounds VB theory needs sp 3 d 2 hybridization with the d-orbitals of S having high energy. MO theory; 10 MO's from 10 AO's (4 valence orbitals of S + 6 2p-orbitals of F pointing toward S)
3.12 Orbitals in Polyatomic Molecules SF 6 ; (1a 1 ) 2 (1t 1 ) 6 e 4 ; 8 electrons in bonding orbitals 4 bonding pairs for 6 S F bonds Bond order of S F = 2 3 4 electrons in nonbonding orbitals
3.12 Orbitals in Polyatomic Molecules Colors of vegetation HOMO; Highest Occupied Molecular Orbital LUMO; Lowest Unoccupied Molecular Orbital Delocalized for conjugated double bonds ( C=C C=C C=C ) Electrons-in-a-large -one-dimensional-box Fig 1.26 Very close energy levels Small HOMO-LUMO gap Visible photons can excite electrons across the gap. Colors! Quiz: Carrot color from b-carotene (C 40 H 56 ), tomato color from lycopene (C 40 H 58 )?
3.12 Orbitals in Polyatomic Molecules
IMPACT ON MATERIALS: ELECTRONIC CONDUCTION IN SOLIDS 3.13 Bonding in the Solid State Molecular orbitals spread over the entire solid as a huge molecule. 3.13 Bonding in the Solid State Electronic conductor; metals and semiconductors, delocalized electrons as electric current carriers Metallic conductor; electric conductivity decreases with temperature Fig 3.43
IMPACT ON MATERIALS: ELECTRONIC CONDUCTION IN SOLIDS 3.13 Bonding in the Solid State
IMPACT ON MATERIALS: ELECTRONIC CONDUCTION IN SOLIDS 3.13 Bonding in the Solid State N (~N A ) MO's from N AO's for N electrons 1) Nearly continuous band of energy levels Enormous N value and large "box" 2) N electrons occupying ½N bonding MO's (almost) Zero HOMO-LUMO gap Easy to excite electrons into the conduction band where electrons move freely High conductivity decreasing with T due to increase collisions with the vibrating atoms Insulator; no conductivity
IMPACT ON MATERIALS: ELECTRONIC CONDUCTION IN SOLIDS 3.13 Bonding in the Solid State Semiconductor; electric conductivity increases with temperature Superconductor; zero resistance Box 5.2
IMPACT ON MATERIALS: ELECTRONIC CONDUCTION IN SOLIDS 3.14 Semiconductors pn-junction diodes