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8/17/2019 Lect 03 Timed
1/30
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
8/17/2019 Lect 03 Timed
2/30
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
3/30
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
8/17/2019 Lect 03 Timed
4/30
/rom 0umber of 1alence Elecrons
we would li*e o predic:Consiuion (valence numbers for differen aoms"
Reacivi!
C&ar%e 2isribuion
√
√
8/17/2019 Lect 03 Timed
5/30
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+
8/17/2019 Lect 03 Timed
6/30
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?
8/17/2019 Lect 03 Timed
7/30
Graph Help&ps:;;webspace+!ale+edu;c&em
8/17/2019 Lect 03 Timed
8/30
Ivanic) c&i!) Ruedenber%
8/17/2019 Lect 03 Timed
9/30
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
8/17/2019 Lect 03 Timed
10/30
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
11/30
" Ener%! of a proon on &e ,molecular surface-
Suface Potential of Open O7one(from Juanum'ec&anics"
H#GH(9 3= *cal;mole"
('
8/17/2019 Lect 03 Timed
12/30
/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 # )
√
√
√
&
&
8/17/2019 Lect 03 Timed
13/30
$e'is ot Structure
emps o provide a ,p&!sical-
basis for valence rules+
0ew: Reacivi! from uns&ared pairs(bo& ,&oo*s- from &e same aom"
Convenien for elecron boo**eepin%(molecular c&ar%e ,formal- aomic c&ar%es
qualiaivel! realisic) a leas in &e case of O4"
Sabili! and ,Resonance-?
8/17/2019 Lect 03 Timed
14/30
'at/s so great about octets-
0o+ bad are sestets? 0o+ bad are structures +it
formal carge separation? 0o+ bad is bad* carge separation?
from 'i,i: “I have a question when drawing these
structures. Is it more ‘important’ to try to fillthe octet or to have lowest formal charge onas many atoms, especially C, as possible
and !"#$
8/17/2019 Lect 03 Timed
15/30
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
16/30
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 $1+,5-1+++&
8/17/2019 Lect 03 Timed
17/30
1isuali7in% Earns&aw ' Coulomb@s Elecrosaics
,#ines of /orce-a%neicElecrosaic
8/17/2019 Lect 03 Timed
18/30
/arada!;2av!;$&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
19/30
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
20/30
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
21/30
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
22/30
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
23/30
#eviaor b! arin Simon (AC#"
Eppur sa fermo,and !e i sands sill-
8/17/2019 Lect 03 Timed
24/30
M+M+ T&omson (
8/17/2019 Lect 03 Timed
25/30
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
26/30
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
8/17/2019 Lect 03 Timed
27/30
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
28/30
,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
29/30
Te Electron in &emistr%
M+ M+ T&omson (
8/17/2019 Lect 03 Timed
30/30
End of #ecure 4
Sep ) 3GG
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