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Chemistry 125: Lecture 3

Double Minima,Earnshaw’s Theorem,

and Plum PuddingsThe double-well potential of the ozone molecule and its structural equilibrium continues the discussion ofLewis structures and chemical forces The inabilit! of in"erse-square force laws to account for stable

arrangements of charged particles is established b! Earnshaw#s Theorm, which ma! be "isualized b!

means of lines of force $$ Thomson circum"ented Earnshaw’s prohibition on %oulombic structure b!

 postulating a &plum-pudding ”  atom, with negati"e corpuscles embedded in a sphere of diffuse positi"e

charge 'hen (utherford showed that the positi"e nucleus was not diffuse, Thomson and )* Lewis

concluded incorrectl! that %oulomb’s law was in"alid at small distances

Synchronize when the speaker finishes saying

 “…from the slies at the en last time…!

Synchrony can "e a#uste "y using the pause$%%& an run$'& controls()or copyright

notice see final

page of this file

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Equilibrium vs. Resonance

H C

O

     OH

H C

     O

O H••

••••

•• ••

••

••

••

••

••

H C

O

     O

H C

     O

O

••••

•• •• ••

••

•

•

Two Species

Two Species?

••

H C

O

     O

H C

     O

O

••••

••

••

••

••

••

•

•

One Nuclear Geometry!

•

•

One Species!

(Evidence: Infrared Specroscop!"

#ORE(Evidence: Elecron $arama%neic Resonance"

 LORE: That which is learned;

learning, scholarship, erudition.

 Also, in recent use, applied to the body oftraditional facts, anecdotes, or beliefs

relating to some particular subject

  (Oxford English ictionary!

8/17/2019 Lect 03 Timed

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2. Srucures in w&ic& all firs'row aoms &ave filled octets 

are %enerall! imporan &owever) resulin% formal c&ar%es

and elecrone%aivi! differences can ma*e appropriae

nonoce srucures comparabl! imporan+

 From a

 good Text 

,empirical rules for assessin% &e relaive

imporance of &e resonance srucures of

molecules and ions+

1+ Resonance srucures involve no change in &e posiions

of nuclei onl! elecron disribuion is involved+

3+ T&e more imporan srucures are &ose involvin% a minimum

of charge separation) paricularl! amon% aoms of comparable

elecrone%aivi!+ Srucures wi& ne%aive c&ar%es assi%ned o

elecrone%aive aoms ma! also be imporan+-

(our depiction of)

.

 LORE 

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/rom 0umber of 1alence Elecrons

we would li*e o predic:Consiuion (valence numbers for differen aoms"

Reacivi!

C&ar%e 2isribuion

√

√

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O3  O4

O•

•     

•     

      • •

•

• •O  •  •

•

•  •  •

O• ••

•

Equilaeral

Trian%le

     O   •

 • •

          •

          •

   •O••     

•     

      • •

•   O   •

 •

 •          •

          •

   •O••     

•     

      • •

•

O

O

          •

          •

O     •

 •

     • •

O

O O

O

O

O+

2ouble

5ondOpen

Trivalen O is posiive+

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6&a is O7one8s Srucure?

O

O

O

9

  

O O

O

Ring

OO

O

9

  

Open

 A Problem in

!imensions"(# distances $ energ%)

s!mmerical sin%le minimum?

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Graph Help&ps:;;webspace+!ale+edu;c&em

8/17/2019 Lect 03 Timed

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Ivanic) c&i!) Ruedenber%

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O4

 More &onstrained 

F'2imensional

Srucure'Ener%!

$lo

2isance alon% Steepest-escent ur"e

   E  n  e  r  %  !   (   *  c  a   l   ;  m

  o   l   " Ring

Open

G

3 ;

R12 ≠ R23gives higher E

⇓

symmetrical"resonant”

structure

Pass

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O7one

'at of carge

distribution ispredicted* b%

 Le+is boo,,eeping-

$ in middle on ends-

O

O

O

9

  

OO

O

9

  

Open

s!mmerical sin%le minimum?

8/17/2019 Lect 03 Timed

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 " Ener%! of a proon on &e ,molecular surface- 

 Suface Potential  of Open O7one(from Juanum'ec&anics"

H#GH(9 3= *cal;mole"

('

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/rom 0umber of 1alence Elecrons

we would li*e o predic:Consiuion (valence numbers for differen aoms"

Srucure (disances L an%les" (+e/ll test tis later)

Ener%! Conen (+e/ll test tis later)

Reacivi! (at least for 0 # 12 30 # )

C&ar%e 2isribuion (at least 4ualitativel% for O# 5 0 # 130 # )

√

√

√

& 

& 

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$e'is ot Structure

emps o provide a ,p&!sical-

 basis for valence rules+

 0ew: Reacivi! from uns&ared pairs(bo& ,&oo*s- from &e same aom"

Convenien for elecron boo**eepin%(molecular c&ar%e ,formal- aomic c&ar%es

qualiaivel! realisic) a leas in &e case of O4"

Sabili! and ,Resonance-?

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'at/s so great about octets-

 0o+ bad are sestets? 0o+ bad are structures +it

 formal carge separation? 0o+ bad is bad* carge separation?

 from 'i,i: “I have a question when drawing these

structures. Is it more ‘important’ to try to fillthe octet or to have lowest formal charge onas many atoms, especially C, as possible

and !"#$ 

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Is i a all True?

/orce #aws?

 Are &ere e'pairs

 beween nuclei and

uns&ared on some aoms?

8/17/2019 Lect 03 Timed

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In s!sems %overned b!

inverse'square force laws

&ere can be no local minimum(or ma>imum"

of poenial ener%!+

 Earnsa+6s Teorem

(78#9)

   b  !  p  e  r  m   i  s  s   i  o  n   S   &  e   f   f   i  e   l   d   A  n   i  v  e  r  s   i     !

Samuel *arnshaw $1+,5-1+++&

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1isuali7in% Earns&aw ' Coulomb@s Elecrosaics

,#ines of /orce-a%neicElecrosaic

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/arada!;2av!;$&illips!oun%

ic&ael /arada!

   b  y  p  e  r  m   i  s  s   i  o  n   A   l   f  r  e   d   B  a   d  e  r   C  o   l   l  e  c   t   i  o  n

8/17/2019 Lect 03 Timed

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Can s&ow ma%niude (as well as direcion" of /orce

3'2 (/laland"

force ma%niude

 ∝ line densi!

Circumference

∝ r 3

/orce

∝ 

line densi!∝ 

1(r 

8/17/2019 Lect 03 Timed

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Can s&ow ma%niude (as well as direcion" of /orce

4'2imensions

Surface

∝  r 3

/orce

∝ 

line densi!∝ 

1(r2 

force ma%niude

 ∝ line densi!

 :n #! suc !iagrams 'or, onl% for :nverse ;4uare Forces"

8/17/2019 Lect 03 Timed

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posiive paricle &as a local ma>imum or

minimum of ener%! onl! a &e locaion of

ano&er c&ar%ed paricle) never in free space+

posiive paricle &as a local ma>imum or

minimum of ener%! (pea* or valle!" onl!

a &e locaion of ano&er c&ar%ed paricle)

never in free space+

8/17/2019 Lect 03 Timed

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In s!sems %overned b!

inverse'square force laws

&ere can be no local minimum

(or ma>imum"

of poenial ener%! in free space+

 Earnsa+6s Teorem

(T&e onl! ,saionar!- poins are saddle poins+"

8/17/2019 Lect 03 Timed

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 #eviaor b! arin Simon (AC#"

Eppur sa fermo,and !e i sands sill-

8/17/2019 Lect 03 Timed

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M+M+ T&omson (

8/17/2019 Lect 03 Timed

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N6e canP solve &e special case

w&ere &e corpuscles are

confined o a plane+N

T&omson@s odel of

Elecron Confi%uraion

Nconsider &e problem as o &ow

8/17/2019 Lect 03 Timed

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1

1 5 1 6 1 7 2 7 2 8

3 8 3 9 4 9 4 10 5 10

2 3 4 5

1 5 10 1 5 11 1 6 11 1 6 12 1 6 13

1ore> #aice odels (Bre% 5londer www+%enuineideas+com"

1 4

2 9

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N6e canP solve &e special case

w&ere &e corpuscles are

confined o a plane+N

T&omson@s odel of

Elecron Confi%uraion

Nconsider &e problem as o &ow

8/17/2019 Lect 03 Timed

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,I &ave ever since re%arded &e cubic oceP

as represenin% esseniall! &e arran%emen

of elecrons in &e aom- 

=. 1. Le+is (79>#)6as #ewis i%noran of Earns&aw@s T&eorem?

,Elecric forces beween paricles w&ic&

are ver! close o%e&er do no obe!&e simple law of inverse squares

w&ic& &olds a %reaer disances+-

  =. 1. Le+is (797?)

8/17/2019 Lect 03 Timed

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Te Electron in &emistr%

M+ M+ T&omson (

8/17/2019 Lect 03 Timed

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End of #ecure 4

Sep ) 3GG

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