chemistry 125: lecture 3 sept 3, 2010 force laws, lewis structures, resonance, double minima, and...
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Chemistry 125: Lecture 3Sept 3, 2010
Force Laws,Lewis Structures,
Resonance, Double Minima, and Earnshaw’s Theorem
For copyright notice see final page of this file
Force Laws & Molecular StructureSpring (ut tensio sic vis) Electrical Charges (gravity, etc.)
Balanced minimum Balanced minimum !
F = -k x F = k / (x)2
Po
ten
tial
En
erg
y
Single Minimum Double Minimum
x
x
sum
sum
Slope = F
0
0
2nd Spring(weaker,
opposing)
3rd 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.
FixedNeighbor
Mathematically convenient approximation
for realistic bond energies(proposed 1929)
Sum
Morse Potential
Second Fixed
Neighbor
Demonstrationwith
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)
NH3 and NH4Cl
or 5?)
19th 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 ? reaction produc
t
Reaction Scheme
Might Partial Dissociation explain amine/HCl reactivity?
How Many?
The Cubic Octet of G. N.
Lewis(1875-1946)
as Harvard Undergraduate
~1894
as Harvard Instructor~1902
© E
. S. L
ewis
, by
per
mis
sion
Cubic Octet to Tetrahedral Octetto 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 Factsit should allow:
PredictionSuggestion
Explanation
Classification& Remembering
as as possible
Postdiction:Realm of Lore
From Number of Valence Electronswe 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••
••••
•
1 233 4 1
H •N••
••••
•HH
Why Octet?
Why Pair for H / He?
(Electron # Valence # and Unshared Pairs)
H •
H•
H•N•
••
••+
H•H•
H•B•
••
HCNH • •
•C ••
Tetravalent N is positive.
N ••
••
•
••CH•
• ••• N••• C ••H N
Tetravalent B is negative.
NH3 BH3H3N-BH3
+
H •
H•
H•N ••
••
•H•
H•
H•B•
••
Bookkeeping of “Formal” Charges
(each atom is assignedhalf-interest in bonding pairs)
••
Puzzle:
2 BH3 B2H6 + ~40 kcal/molWhat 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 H3N-BH3 (from Quantum-Mechanics)
HIGH(+ 25 kcal/mole)
(-41 kcal/mole)
LOWN end indeed bearspositive charge
and B end bearsnegative charge
Amine
R •
R•
R•N ••
••
•
SR •
R••
••
Sulfide
•
••
O ••
• •
• •Oxide
O• •
••
••
O ••
• •
• •oxide
+ -
+ -+2 --
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:
DoubleMinimum
equilibrium
EQUILIBRIUM vs. RESONANCE
OH C N••
••• • +-
H C N O••
••
••
+ -all octets charge sepn
all octets still charge sepn poorer site for -
N position (relative to C O)
Ene
rgy
midwayleft
shift : to eliminate charge sepn.shift : to restore N octet
N closer to Cthan to O
N ~midwaybetween C and O
Geometric Implication?
but maybe in truth…
EQUILIBRIUM vs. RESONANCE
H C O••
••
••N+ -
SingleMinimum
resonance
OH C••
••• •N+-
single compromise
position for N
N position (relative to C O)
Ene
rgy
midwayleft
i.e. Notation too simplistic
Choice between
Resonance and Equilibrium
must be based onexperimental facts
(or a better theory)
that can distinguish singlefrom double minimum
Equilibrium vs. Resonance
A B A B
Two Real SpeciesOne Real SpeciesTwo “Reasonable”Structural Formulas
Failure of Simplistic Notation
Typically Unusually StableCompared to what?
Equilibrium vs. Resonance
H CO
O
HH C
O
O H••
••••
•• ••
••
••
••
••
••
H CO
O
H C
O
O
••••
•• •• ••
•••
•
Two Species
Two Species?
••
H C
O
O
H C
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 Electronswe would like to predict:
Constitution (valence numbers for different atoms)
Reactivity
Charge Distribution
O2 O3
O•
• •• •
•
• •O ••
••••O
• ••
•
EquilateralTriangle
O•
• •• •
•O•
• •• •
• O•
• •• •
•O•
• •• •
•
OO
••
O• •
• •
OO O
OO
O+
DoubleBond
Open
Trivalent O is positive.
What is Ozone’s Structure?
OO
O
+
_
O O
O
Ring
OO
O
+
_
Open
A Problem in4 Dimensions!(3 distances + energy)
symmetrical single minimum?
Graph Helphttps://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)
US
GS
Energies from quantum calculations of Ivanic, Atchity, Ruedenberg 1997
Ring
Open
4-DimensionalStructure-
EnergyPlot
3 /Constrained by assuming symmetry
RR12 = R23
••••
Requires
e.g. R12, R23, Energy
Energy Contours
“Steepest-Descent” Path
Pass Between Valleys
O3
More Constrained4-Dimensional
Structure-Energy
Plot
Distance along Steepest-Descent Curve
Ene
rgy
(kca
l/m
ol)
Ring
Open
0
8
2 /
R12 ≠ R23
gives higher E
symmetrical"resonant”structure
Pass
Ozone
What of the charge distribution that
is “predicted” byLewis bookkeeping?
+ in middle
- on ends?
OO
O
+
_
OO
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 Electronswe 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 H3N: BH3)
Charge Distribution (at least qualitatively for O3, H3N-BH3)
~
~
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?”
In systems governed byinverse-square force laws
there can be no local minimum (or maximum)
of potential energy.
Earnshaw's Theorem(1839)
by p
erm
issi
on S
heff
ield
Uni
vers
ity
Samuel Earnshaw (1805-1888)
Can show magnitude (as well as direction) of Force
2-D (Flatland)
force magnitude
line density
Circumferenceµ r2
Forceµ
line densityµ
1/r
Can show magnitude (as well as direction) of Force
3-Dimensions
Surfaceµ r2
Forceµ
line densityµ
1/r2
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 byinverse-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.)
End of Lecture 3Sept 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).
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