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) F = -k x Direct E = k/2 (x)2 Slope =F 2nd Spring (weaker, opposing) x minimum Balanced Single Minimum Potential Energy sum 0 0 Electrical Charges (gravity, etc.) 2 Inverse F = k / (x) E = -k/(2|x|) sum x minimum ! Balanced rd 3 Stronger DoubleBody Minimum Thus with springs you might make a stable polyatomic molecule from point atoms. (but not with ions or magnets) However, if bonds obeyed Hooke’s Law, they could never break. Morse Potential Mathematically convenient approximation for realistic bond energies (proposed 1929) Fixed Neighbor Sum 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! 19th Century Experiments led to VALENCE numbers Figure from 1861 or 5?) Different # for different atoms: H(1), C(4), O(2), N(3) NH3 and NH4Cl Why do Elements Differ? Gertrude and Robert Robinson (1917)“explain” so much Such slippery concepts convinceScheme you of nothing. Why/When that they Reaction “latent” valence loop ? Why/When “partial dissociation”? reaction What does the loop mean? How Many? Might Latent Valence Loop explain trivalence of pentavalent N? Might Partial Dissociation explain amine/HCl reactivity? produc t Electron Discovered 1897 The Cubic Octet of G. N. Lewis as Harvard as Harvard Instructor Undergraduate ~1902 ~1894 © E. S. Lewis, by permission (1875-1946) Octet to "Explain" Periodicity & Electron Transfer (1902 teaching notes) Octet Predicts Shared Pair Bonding shared edge shared face ? Cubic Octet to Tetrahedral to Tetrahedral Octet Octet (G. N. Lewis 1916) :N N: Tetrahedral distribution of the bonds from C had already been known in organic chemistry for 40 years! Good Theory should be Realistic & as Simpleas possible In regard to Facts it should allow: Prediction Suggestion Explanation Classification & Remembering Postdiction: Realm of Lore From Number of Valence Electrons we would like to predict: Constitution (valence numbers for different atoms) Structure (distances & angles) Charge Distribution Energy Content Reactivity Lewis Explains Constitution “the nature and sequence of bonds” (Electron # Valence # and Unshared Pairs) 1 H 3 • • B• • Why Octet? Why Pair for H / He? • 4 3 • •• C• • • N • •• • HN H •• H •• •• • 2 •• O •• 1 • • •• F•• •• HCN • H C N •• • •• •• •• HC N • • • •• H C N• •• • • • • Bookkeeping of Lewis had the idea + of using : to denote “Formal” Charges unshared pairs. NH3 H3N-BH3 BH3 (each atom is assigned half-interest in bonding pairs) •• H• • H • • N• • H H H + •• •• •• • • • • • • H N• B• H • • HH Tetravalent N is positive. H• • B• • •H • H Puzzle: Tetravalent B 2 BH 3 B2H6 + ~40 kcal/mol What is the “glue”? (Answer in Lecture 16) is negative. + Surface Potential* of H3N-BH 3 (from Quantum-Mechanics) HIGH (+ 25 kcal/mole) N end indeed bears positive charge and B end bears negative charge (-41 kcal/mole) LOW *) Energy of a proton on the “molecular surface” Lewis Explains “Pentavalent” N. Actually Tetravalent - thus Charged. H+ H N H Cl H Amine Oxide •• •• R• + • •• R • • N• O • •• R •• •• •• •• •• one Sulfide oxide R• Peroxys ++2 • • • -• • R • • S• • O O •• •• O •• Start Lewis-Drill Problems: Draw Lewis Dot Structures for: HNC (in the order shown) also for HCNO (CNO in all six linear orders, plus ring) Start Memorizing Functional Groups EQUILIBRIUM vs. RESONANCE : : + N closer to C all octets H C N O shift to restore N octet shift to eliminate charge sepn. •• •• charge sepn than to O equilibrium Geometric Implication? all octets • •- + N ~midway still charge sepn H C N O •• between C and O poorer site for - •• Energy •• but maybe in truth… left N position midway (relative to C O) Double Minimum EQUILIBRIUM vs. RESONANCE + H C N O •• •• •• i.e. Notation too simplistic resonance + C N O •• •• H - •• single compromise position for N Energy Single Minimum left N position midway (relative to C O) 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 A B A B One Real Species Two Real Species Two “Reasonable” Structural Formulas Failure of Simplistic Notation Compared to what? Typically Unusually Stable LORE: That which learned; Equilibrium vs. isResonance learning, scholarship, erudition. Also, in•recent use, applied to the body of • •• • • traditionalH facts, anecdotes, or beliefs•• relating to some particular H subject C O O C O •• • • • •• • •• O H C C H ••• • O O •• •• (Oxford English Dictionary) O Two Species • • • • LORE O O H One Species? Species! Two •• • • • • •••• ••• • H H C C One Nuclear Geometry! O (Evidence: Infrared Spectroscopy) (Evidence: Electron Paramagnetic Resonance) H 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. ^ (our depiction of) 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. LORE 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.” From Number of Valence Electrons we would like to predict: Constitution (valence numbers for different atoms) Reactivity Charge Distribution O O •• •• O• • Double Bond O •• • • ••O O •• •• Equilateral Triangle O O O O • • O O• O • • O3 • O2 Open + O O O Trivalent O is positive. What is Ozone’s Structure? Ring Open + O O _ O O O A Problem in 4 Dimensions! (3 distances + energy) O symmetrical single minimum? + O O _ O Graph Help USGS https://webspace.yale.edu/chem125/125/xray/DensityMaps/3din2d.htm Be sure you can do the problems, but you don't have to hand them in. (Click for an answer key) Constrained by assuming symmetry Requires 3 4-Dimensional / StructureRing Energy Plot e.g. R12, R23, Energy R12 = R23 • • • R Energies from quantum calculations of Ivanic, Atchity, Ruedenberg 1997 Pass Between Valleys • Open Energy (kcal/mol) More Constrained 2 4-Dimensional / StructureEnergy Plot O3 Pass Ring 8 R12 ≠ R23 gives higher E symmetrical "resonant” structure Open 0 Distance along Steepest-Descent Curve Ozone + in middle - on ends? Open + _ What of the charge distribution that is “predicted” by Lewis bookkeeping? O O O symmetrical single minimum? + O O _ O Suface Potential* of Open Ozone (from Quantum-Mechanics) + in middle - on ends? HIGH (+ 25 kcal/mole) YES! (-16 kcal/mole) LOW *) Energy of a proton on the “molecular surface” From Number of Valence Electrons we would like to predict: Constitution (valence numbers for different atoms) Reactivity (at least for H3N: BH3) Charge Distribution (at least qualitatively for O3, H3N-BH3) ~ Structure (distances & angles) (we’ll test this later) ~ Energy Content (we’ll test this later) 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 O3) 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? Are there e-pairs between nuclei and unshared on some atoms? Force Laws? by permission Sheffield University Earnshaw's Theorem (1839) In systems governed by inverse-square force laws there can be no local minimum (or maximum) of potential energy. Samuel Earnshaw (1805-1888) Visualizing Earnshaw - Coulomb's Electrostatics Electrostatic Magnetic “Lines of Force” young Michael Faraday by permission Alfred Bader Collection Faraday/Davy/Phillips Can show magnitude (as well as direction) of Force 2-D (Flatland) Circumference r2 force magnitude line density Force line density 1/r Can show magnitude (as well as direction) of Force 3-Dimensions Surface r2 force magnitude line density Force line density 1/r2 In 3D such Diagrams Work only for Inverse Square Forces! A positive particle has a local maximum or A minimumof ofenergy energyonly (peakator only minimum thevalley) location of at the location anothernever charged particle, another charged of particle, in free space. never in free space. Earnshaw's Theorem In systems governed by inverse-square force laws there can be no local minimum (or maximum) of potential energy in free space. (The only “stationary” points are saddle points.) Eppur sta fermo “and yet it stands still” Levitator by Martin Simon (UCLA) End of Lecture 3 Sept 3, 2010 Copyright © J. M. McBride 2010. 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). 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 . 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