This year’s Nobel Prizes in Physics and Chemistry tie in nicely to the subjects of our course, including today’s lecture. Examining the BH 3 molecule illustrates how a chemist’s use of localized bonds, vacant atomic orbitals, and unshared pairs to understand molecules compares with views based on the molecule’s actual total electron density, and with computational molecular orbitals. The localized view is then used to help understand reactivity in terms of the overlap of singly-occupied molecular orbitals (SOMOs) and, more commonly, of an unusually high-energy highest occupied molecular orbital (HOMO) with an unusually low- energy lowest unoccupied molecular orbital (LUMO). This generalizes the traditional concepts of acid and base. Criteria for assessing reactivity are outlined and illustrated. Chemistry 125: Lecture 15 October 6, 2010 Chemical Reactivity: SOMO, HOMO, and LUMO For copyright notice see final page of this file

Graphene’s unique MO structure gives it unique electrical and optical properties, stability, strength, and “resonance”.

Levitator by Martin Simon (UCLA) Eppur sta fermo “and yet it stands still” Graphene Andre Geim’s Hand (1999)

Levitator by Martin Simon (UCLA) “and yet it stands still” Andre Geim’s Frog (1999)

Three Views of BH 3 2) Molecular Orbitals 1) Total Electron Density 3) Bonds from Hybrid AOs (Nature) (Computer) (Chemist) Cf. Course Webpage

How BH 3 Sees Itself: The Electron Cloud of via "Spartan” STO 6-31G** B H H H

B H H H BH 3 Total e-Density 0.30 e/a o 3 Mostly 1s Core of Boron

BH 3 Total e-Density 0.15 e/a o 3

BH 3 Total e-Density 0.05 e/a o 3 Dimple H atoms take e-density from valence orbitals of B B H + H B

BH 3 Total e-Density 0.02 e/a o 3

BH 3 Total e-Density e/a o 3 van der Waals surface (definition)

BH 3 Total e-Density e/a o 3 HIGH (+ 55 kcal/mole) LOW (-7.5 kcal/mole) Electrostatic Potential Energy of a + probe on the surface H   low (-) high (+)

2) Molecular Orbitals 1) Total Electron Density 3) Bonds from Hybrid AOs (Nature) (Computer) (Chemist) Cf. Course Webpage Three Views of BH 3

Computer Partitions Total e-Density into Delocalized MOs. (à la Chladni or Plum Pudding)

BH 3 8 low-energy AOs  8 low-energy MOs B : 1s, 2s, 2p x, 2p y, 2p z 3  H : 1s “Minimal.. Basis Set” of AOs MOLECULAR ORBITALS

noccupiednoccupied BH 3 8 electrons / 4 pairs B : 5 electrons 3  H : 3  1 electron OMO s UMO s LUMOHOMO( s) ccupiedccupied ighestighest owestowest MOLECULAR ORBITALS

1s1s 1s Boron Core MOLECULAR ORBITALS Cf. website

2s Radial Node MOLECULAR ORBITALS Cf. website

2p x MOLECULAR ORBITALS Cf. website

2p y MOLECULAR ORBITALS Cf. website

2p z MOLECULAR ORBITALS Cf. website

3s MOLECULAR ORBITALS Cf. website

3d x 2 -y 2 MOLECULAR ORBITALS Cf. website

3d xy MOLECULAR ORBITALS Cf. website

2) Molecular Orbitals 1) Total Electron Density 3) Bonds from Hybrid AOs (Nature) (Computer) (Chemist) Cf. Course Webpage Three Views of BH 3

We Partition the same Total e-Density into Atom-Pair Bonds (and anti-bonds) & Isolated AOs (lone pairs / vacant atomic orbitals) (à la Lewis) usually  When this doesn't work, and we must use more sophisticated orbitals, we say there is RESONANCE

2p z For Many Purposes Localized Bond Orbitals are Not Bad Boron Core And they are easier to think about; but beware of resonance. BHBH  H B H B Same Total Energy as computer! H B Same Total e-Density also!    B H H B (and of properties of individual electrons)

The Localized Bond Orbital Picture (Pairwise Bond Orbitals and Isolated AOs) is our intermediate between H-like AOs and Computer MOs When must we think more deeply? When we care about individual electrons (ionization ; visible/uv absorption) When mixing of localized orbitals causes Reactivity ………….. or Resonance

Where are We? Molecules Plum-Pudding Molecules ("United Atom" Limit) Understanding Bonds (Pairwise LCAO) "Energy-Match & Overlap" Structure (and Dynamics) of XH 3 Molecules Parsing Electron Density Atoms 3-Dimensional Reality (H-like Atoms) Hybridization Orbitals for Many-Electron Atoms (Wrong!) Recovering from the Orbital Approximation Recognizing Functional Groups Payoff for Organic Chemistry! Reactivity SOMOs, high HOMOs, and low LUMOs

Which MO Mixings Matter for Reactivity? etc. etc. UMOs OMOs B A UMOs Myriad Possible Pairwise Mixings  molecule

Which MO Mixings Matter for Reactivity? etc. etc. UMOs OMOs SOMO B A SOMO-SOMO (when they exist) UMOs many atoms "free radicals" e.g. H Cl CH 3 inglyingly molecule (in order to survive must be kept from overlapping  not very common)

Which MO Mixings Matter for Reactivity? etc. UMOs etc. UMOs OMOs B A Nothing 4e - Weak Net Repulsion molecule (balances correlation at van der Waals contact) Negligible Mixing & Stabilization because of Bad E-match

Which MO Mixings Matter for Reactivity? etc. UMOs etc. UMOs OMOs B A Bonding! Unusually High HOMO with Unusually Low LUMO molecule Negligible Mixing & Stabilization because of Bad E-match

Which MO Mixings Matter for Reactivity? etc. UMOs etc. UMOs OMOs B A Bonding! Unusually High HOMO with Unusually Low LUMO BASE ACID molecule or in common parlance

Most mixing of MOs affects neither overall energy nor overall electron distribution for one (or more) of these reasons: 1) Electron occupancy 4 or 0 2) Poor energy match 3) Poor overlap BUT

Mixing of High HOMO & Low LUMO constitutes Reactivity

Acid-Base Theories THEORYACIDBASE Lavoisier (1789) Oxidized Substance Substance to be Oxidized Arrhenius (1887) H + SourceOH - Source Increasing Generality Brønsted/Lowry (1923) H + DonorH + Acceptor Lewis (1923) e-Pair Acceptor "Electrophile" e-Pair Donor "Nucleophile" HOMO/LUMO (1960s) unusually High HOMO unusually Low LUMO

sp 3 C 1s H Unusual: "usual" LUMO "usual" HOMO I. Unmixed Valence-Shell AOs III. Unusual AO Energy in MO Sources of weirdness: IV. Electric Charge II. Poor Overlap of AOs Compared to What?  * CH  CH (or  * CC ) (or  CC )

I. Unmixed Valence-Shell Atomic Orbitals  * CH  CH sp 3 C 1s H BH 3 low LUMO CH 3 high HOMO NH 3 high HOMO "usual" LUMO "usual" HOMO OH 2 high HOMO OH high HOMO (or  * CC ) (or  CC ) H + low “LUMO” (energies qualitative only) (Also IV: Electrical Charge)

Acid-Base Reactions H + OH H-OH H + :NH 3 H 3 B OH H 3 B :NH 3 H-NH 3 + H 3 B-NH 3 + Curved Arrows Designate e-Pair Shifts. Start arrow at e-pair location in starting material. End arrow at e-pair location in product. (NOT atomic motion) H 3 B-OH tetravalent N is + tetravalent B is -

II. Poor-Overlap MOs  * C=O  C=O pCpC pOpO  * CH  CH sp 3 C 1s H  * C=C  C=C pCpC pCpC high HOMO low LUMO "usual" LUMO "usual" HOMO  Bent  (energies qualitative only)

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