Chemistry 125: Lecture 3 Sept 3, 2010 Force Laws, Lewis Structures, Resonance, Double Minima, and Earnshaw’s Theorem For copyright notice see final page of this file

Does Newton’s Chemical Force Law Exist?

How far can you Stretch a Chain of Atoms before it Snaps?

Force Laws & Molecular Structure Spring (ut tensio sic vis) Electrical Charges (gravity, etc.) Balanced minimumBalanced minimum ! F = -k  x  F  = k / (  x) 2 Potential Energy Single MinimumDouble Minimum x  x sum Slope = F nd Spring (weaker, opposing) 3 rd Stronger Body E = k/2 (  x) 2 E = -k/(2 |  x|) Direct Inverse

(but not with ions or magnets) Thus with springs you might make a stable polyatomic molecule from point atoms. However, if bonds obeyed Hooke’s Law, they could never break.

Fixed Neighbor Mathematically convenient approximation for realistic bond energies (proposed 1929) Sum Morse Potential Second Fixed Neighbor

Morse Potential Snaps at Inflection Point (Change from direct to inverse force)

What ARE bonds?

Demonstration with Magnets Valuable prize for balancing suspended magnet between sets of attracting ma gnt!

Why do Elements Differ? Figure from 1861 Different # for different atoms: H(1), C(4), O(2), N(3) NH 3 and NH 4 Cl or 5? ) 19 th Century Experiments led to VALENCE numbers

Gertrude and Robert Robinson (1917) Might Latent Valence Loop explain trivalence of pentavalent N? What does the loop mean? “partial dissociation” Such slippery concepts “explain” so much that they convince you of nothing. “latent” valence loop Why/When ? Why/When ? reactionproduc t Reaction Scheme Might Partial Dissociation explain amine/HCl reactivity? How Many?

Electron Discovered 1897

The Cubic Octet of G. N. Lewis ( ) as Harvard Undergraduate ~1894 as Harvard Instructor ~1902 © E. S. Lewis, by permission

Octet to "Explain" Periodicity & Electron Transfer (1902 teaching notes)

Octet Predicts Shared Pair Bonding ? shared edge shared face

Cubic Octet to Tetrahedral Octet to Tetrahedral Octet N N :: (G. N. Lewis 1916) Tetrahedral distribution of the bonds from C had already been known in organic chemistry for 40 years!

Good Theory should be Realistic & Simple In regard to Facts it should allow: Prediction Suggestion Explanation Classification & Remembering as as possible Postdiction: Realm of Lore

From Number of Valence Electrons we would like to predict: Constitution (valence numbers for different atoms) Structure (distances & angles ) Energy Content Reactivity Charge Distribution

Lewis Explains Constitution “the nature and sequence of bonds” H B C N O F H N H H Why Octet? Why Pair for H / He? (Electron #  Valence # and Unshared Pairs)

H H H N + H H H B HCN H C Tetravalent N is positive. N C H N C H N Tetravalent B is negative. NH 3 BH 3 H 3 N-BH 3 + H H H N H H H B Bookkeeping of “Formal” Charges (each atom is assigned half-interest in bonding pairs) Puzzle: 2 BH 3  B 2 H 6 + ~40 kcal/mol What is the “glue”? (Answer in Lecture 16) Lewis had the idea of using : to denote unshared pairs.

+ - *) Energy of a proton on the “molecular surface” Surface Potential* of H 3 N-BH 3 (from Quantum-Mechanics) HIGH (+ 25 kcal/mole) (-41 kcal/mole) LOW N end indeed bears positive charge and B end bears negative charge

Lewis Explains “Pentavalent” N. Actually Tetravalent - thus Charged. N H H H H + Cl

Amine R R R N S R R Sulfide O Oxide O O oxide one O Peroxys

also for HCNO (CNO in all six linear orders, plus ring) Draw Lewis Dot Structures for: H N C (in the order shown) Start Lewis-Drill Problems:

Start Memorizing Functional Groups

Double Minimum equilibrium EQUILIBRIUM vs. RESONANCE O HCN + - HCN O + - all octets charge sepn  all octets still charge sepn  poorer site for -  N position (relative to C O) Energy midway left shift : to eliminate charge sepn.shift : to restore N octet N closer to C than to O N ~midway between C and O Geometric Implication? but maybe in truth…

EQUILIBRIUM vs. RESONANCE HC O N + - Single Minimum resonance O HC N + - single compromise position for N N position (relative to C O) Energy midway left i.e. Notation too simplistic

Choice between Resonance and Equilibrium must be based on experimental facts (or a better theory) that can distinguish single from double minimum

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

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! (Evidence: Infrared Spectroscopy) LORE (Evidence: Electron Paramagnetic Resonance) 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)

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

From Number of Valence Electrons we would like to predict: Constitution (valence numbers for different atoms) Reactivity Charge Distribution  

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.

What is Ozone’s Structure? 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. (Click for an answer key)Click USGS

Energies from quantum calculations of Ivanic, Atchity, Ruedenberg 1997  Ring Open  4-Dimensional Structure- Energy Plot 3 / Constrained by assuming symmetry R R 12 = R 23 Requires e.g. R 12, R 23,  Energy Energy Contours “Steepest-Descent” Path Pass Between Valleys

O3O3 More Constrained 4-Dimensional Structure- Energy Plot Distance along Steepest-Descent Curve Energy (kcal/mol) Ring Open / R 12 ≠ R 23 gives higher E  symmetrical "resonant” structure Pass

Ozone What of the charge distribution that is “predicted” by Lewis bookkeeping? + in middle - on ends? O O O + _ O O O + _ Open symmetrical single minimum?

*) Energy of a proton on the “molecular surface” Suface Potential* of Open Ozone (from Quantum-Mechanics) HIGH (+ 25 kcal/mole) (-16 kcal/mole) LOW + in middle - on ends? YES!

From Number of Valence Electrons we would like to predict: Constitution (valence numbers for different atoms) Structure (distances & angles ) (we’ll test this later) Energy Content (we’ll test this later) Reactivity (at least for H 3 N: BH 3 ) Charge Distribution (at least qualitatively for O 3, H 3 N-BH 3 )    ~ ~

Lewis Dot Structure Attempts 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; qualitatively realistic, at least in the case of O 3 ) Stability and “Resonance”?

What’s so great about octets? How bad are sestets? How bad are structures with formal charge separation? How bad is “bad” charge separation? from 2007 Wiki : “I have a question when drawing these structures. Is it more ‘important’ to try to fill the octet or to have lowest formal charge on as many atoms, especially C, as possible? and WHY?”

Is it at all True? Force Laws? Are there e-pairs between nuclei and unshared on some atoms?

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

Visualizing Earnshaw - Coulomb's Electrostatics “Lines of Force”MagneticElectrostatic

Faraday/Davy/Phillips young Michael Faraday by permission Alfred Bader Collection

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 In 3D 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. A positive particle has a local maximum or minimum of energy (peak or valley) 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 “and yet it stands still”

End of Lecture 3 Sept 3, 2010 Copyright © J. M. McBride Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0) Use of this content constitutes your acceptance of the noted license and the terms and conditions of use. Materials from Wikimedia Commons are denoted by the symbol. Third party materials may be subject to additional intellectual property notices, information, or restrictions. The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0