Chem 125 Lecture 4 9/13/06 Projected material This material is for the exclusive use of Chem 125 students at Yale and may not be copied or distributed further. It is not readily understood without reference to notes from the lecture.

Equilibrium vs. Resonance AB AB Two Real Species One Real Species Two “Reasonable” Structural Formulas Failure of Simplistic Notation Unusually Stable

Equilibrium vs. Resonance H C O O H HC O O H H C O O HC O O Two Species Two Species? H C O O HC O O One Nuclear Geometry! One Species! (Infrared) LORE (Electron Paramagnetic Resonance)

O 2 / O 3 O O O Equilateral Triangle O O O O O O O O OO O O O + Double Bond Open Trivalent O is positive.

Ozone O O O + _ OO O Ring O O O + _ Open A Problem in 4 Dimensions! (3 distances + energy) symmetrical single minimum?

Graph Help (Be sure you can do the problems, but you don't have to hand them in)

O 3 Ruedenberg 1997  Ring Open  Constrained 4-Dimensional Structure- Energy Plot 3 /

O3O3 MoreConstrained 4-Dimensional Structure- Energy Plot Distance along Structure Curve Energy (kcal/mol) Ring symmetrical "resonant" OPEN /

Ozone O O O + _ O O O + _ Open What of charges “predicted” by Lewis bookkeeping? symmetrical single minimum

Calculated Suface Potential* of Open Ozone *) Energy of a proton on the “molecular surface” HIGH (+ 25 kcal/mole) (-16 kcal/mole) LOW

Lewis Dot Structures Attempt to provide a “physical” basis for valence rules. New: Reactivity from unshared pairs (both “hooks” from the same atom) Convenient for electron bookkeeping (molecular charge; “formal” atomic charges) Stability and “Resonance”?

2. Structures in which all first-row atoms have filled octets are generally important; however, resulting formal charges and electronegativity differences can make appropriate nonoctet structures comparably important. From a good Text “empirical rules for assessing the relative importance of the resonance structures of molecules and ions. 1. Resonance structures involve no change in the positions of nuclei; only electron distribution is involved. 3. The more important structures are those involving a minimum of charge separation, particularly among atoms of comparable electronegativity. Structures with negative charges assigned to electronegative atoms may also be important. (our depiction of) ^ LORE: That which is learned; learning, scholarship, erudition. Also, in recent use, applied to the body of traditional facts, anecdotes, or beliefs relating to some particular subject (Oxford English Dictionary) LORE

Is it True? Force Laws

In systems governed by inverse-square force laws there can be no local minimum (or maximum) of potential energy. Earnshaw's Theorem (1839)

Visualizing Earnshaw - Coulomb's Electrostatics Lines of Force Magnetic Electrostatic

Faraday/Davy/Phillips young Michael Faraday

Can show magnitude (as well as direction) of Force 2-D (Flatland) force magnitude  line density Circumference  r 2 Force  line density  1/r

Can show magnitude (as well as direction) of Force 3-Dimensions Surface  r 2 Force  line density  1/r 2 force magnitude  line density Such Diagrams Work only for Inverse Square Forces!

A positive particle has a local maximum or minimum of energy only at the location of another charged particle, never in free space.

In systems governed by inverse-square force laws there can be no local minimum (or maximum) of potential energy in free space. Earnshaw's Theorem The only stationary points are saddle points.

Levitator by Martin Simon (UCLA) Eppur sta fermo

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