chem 125 lecture 8 9/22/06 projected material this material is for the exclusive use of chem 125...
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Chem 125 Lecture 89/22/06
Projected material
This material is for the exclusive use of Chem 125 students at Yale and may not
be copied or distributed further.
It is not readily understood without reference to notes from the lecture.
Exam 1 - Friday, Sept. 29 !Covers Lectures through next Wednesday
Including:
Functional GroupsX-Ray Diffraction
1-Dimensional Quantum Mechanics(Sections I-IV of webpage
& Erwin Meets Goldilocks)IMPORTANT PROBLEMS therein due Wednesday
Get-aquainted session this afternoon 4-5:30 in Lecture Room
Exam Review 7-9 pm Tuesday, Room WLH 208
Other Help Available Wednesday 8-10 PM, RTBAThursday 7-10:30 PM, RTBA
HELIXw
S
Svw
SCuriousIntensitySequence
B-DNAR. Franklin
(1952)
OffsetDouble Helix
repeated pair pattern
BASE STACKING
B-DNAR. Franklin
(1952)
wS
Svw
S
MAJOR& MINORGROOVES
HELIX DIAMETER
X-Ray Diffraction
Old-StyleElectronDensity
Map
Contours connect points of equivalent
density.
K Penicillin
K Penicillin3-D Map(1949)
K
1 e/Å3
contours
Rubofusarin
No H?
Highe-DensityNo :
on O!
Stout & Jensen "X-Ray Structure Determination (1968)
5 e/Å3
7 e/Å3
long
short
intermediate
No : Bonds!
Spherical Atoms
“Seeing” Bondswith
Difference Density Maps
Observed e-Density - Atomic e-Density(experimental) (calculated)
sometimes calledDeformation Density Maps
SphericalCarbon Atoms
Subtracted fromExperimental
Electron Density(H not subtracted)
Triene
7
6 5
4
~0.2 e
~0.2 e
~0.2 e
~0.1 e
H ~1 e
Triene
plane of page
cross sectionpartial
double bond
Leiserowitz~0.1 e
~0.3 e~0.2 e
C CC
C
Why not?Bent bonds from
tetrahedral C ?
Lew
is B
ookk
eepi
ng
4
2
6
Inte
grat
ed D
iffer
ence
Den
sity
(e)
How many electrons are there in a bond?
Bond Distance (Å)1.2 1.4 1.6
0.2
0.1
0.3
Berkovitch-Yellin &Leiserowitz (1977)
Bonding Densityis about
1/20th of a “Lewis”
Tetrafluorodicyanobenzene
CC
C
C
F
NC C
C
C
F
N
F
F
Dunitz, Schweitzer, & Seiler (1983)
unique
TFDCBC
CC
C
F
N
is roundnot clover-leafnor diamond!
C N Triple Bond
TFDCB
Where is theC-F Bond?
C
CC
C
F
N
Unshared Pair!
TheSecondGreat
Question
Compared to what?What d'you think of him?
Exactly!
Compared with what, sir?
1) RESONANCE STABILIZATION
2) DIFFERENCE DENSITY
TFDCB
Where is theC-F Bond?
C
CC
C
F
N
Unshared Pair!
Need to subtract Finstead of
“unbiased”spherical F
••••
•••
Dunitz et al. (1981)
Pathological Bonding
0.002 Å !
for averagepositions
Typically vibratingby ±0.050 Åin the crystal
Dunitz et al. (1981)
Pathological Bonding
Surprising only for its beauty
Lone "Pair"of N atom
Dunitz et al. (1981)
Pathological Bonding
Bond Cross SectionsMissing Bond?
H
H
H
H
HH
Dunitz et al. (1981)
Pathological Bonding
MissingBond !
BentBonds !
Lewis Pairs/Octets provide a pretty good bookkeeping device
for keeping track of valencebut they are hopelessly crude when it comes to describing actual electron distribution.
There is electron sharing (~5% of Lewis's prediction).
There are unshared "pairs" (<5% of Lewis's prediction).
Is there a Better Bond Theory, maybe even a Quantitative one?
YES!Chemical Quantum
Mechanics
Erwin Schrödinger (Zurich,1925)
www.zbp.univie.ac.at/schrodinger
www.uni-leipzig.de/ ~gasse/gesch1.html
"So in one of the next colloquia, Schrödinger gave a beautifully clear account of how de Broglie associated a wave with a particle…When he had finished, Debye casually remarked the he thought this way of talking was rather childish… he had learned that, to deal pro-perly with waves, one had to have a wave equation. It sounded rather trivial and did not seem to make a great impression, but Schrödinger evidently thought a bit more about the idea afterwards."
Felix Bloch, Physics Today (1976)
"Once at the end of a colloquium I heard Debye saying something like: Schrödinger, you are not working right now on very important problems anyway. Why don't you tell us sometime about that thesis of de Broglie?
Well, I have found one."
"Just a few weeks later he gave another talk in the colloquium, which he started by saying: My colleague Debye suggested that one should have a wave equation:
H = E
Stockholm (1933)
www.th.physik.uni-frankfurt.de/~jr
PaulDirac
WernerHeisenberg
ErwinSchrödinger
Schrödinger Equation
H = E
Leipzig (1931)
American Institute of Physics
WernerHeisenberg
FelixBloch
VictorWeisskopf
Felix Bloch & Erich Hückel on Gar Manches rechnet Erwin schon Mit seiner Wellenfunktion.Nur wissen möcht man gerne wohl, Was man sich dabei vorstell'n soll.
Erwin with his Psi can do calculations, quite a few.We only wish that we could glean an inkling of what Psi could mean.
(1926)
Function of What?
Named by "quantum numbers"(e.g. n,l,m ; 1s ; 3dxy ;
Function of Particle Position(s)[and time and "spin"]
We focus first on one dimension,then three dimensions (one electron),
then many-electron atoms, then many atoms,
& finally functional groups.
N particles 3N arguments![sometimes 4N+1]
Schrödinger Equation
H = E
(for “stationary” states)time-independent
=
H = E
Kinetic Energy + Potential Energy = Total Energy
Given - Nothing to do with (Couloumb is just fine)
Hold your breath!
H = E
Kinetic Energy?mi vi
2i
Const
Kinetic Energy!2
xi2
2
yi2
2
zi2
+ +1mi
i
h2
82
d2
dx21
mC
One particle; One dimension:
Kinetic Energy!2
xi2
2
yi2
2
zi2
+ +1mi
i
h2
82
d2
dx21
mC
C
Curvature of
m
One particle; One dimension:
Solving a Quantum Problem
Given : a set of particlestheir masses & their potential energy law
[ e.g. 1 Particle/1 Dimension : 1 amu & Hooke's Law ]
To Find : a Function of the position(s) of the particle(s)Such that H/ is the same (E) everywhere
AND remains finite(single-valued, continuous, 2 integrable)
Much Harder for Many Particles
Is it worth our effort?
Reward for Finding
Knowledge of Everythinge.g.
Allowed EnergiesStructureDynamicsBonding
Reactivity
The Jeopardy Approach
Answer Problem
= sin (x)
= sin (ax)
= ex
KineticEnergy
= e-x
C/mparticle infree space
a2 C/m shorter wave higher energy
’’
-C/m
-C/m
Const PE > TE
’’(actually appears for electrons bound to nucleiat large distance, where 1/r ceases changing much!)
Rearranging Schrödinger to give a formula for curve tracing.
C
Curvature of
m
+ V = E
CCurvature of
m
(V- E)=Curves away from 0 for V>E; toward 0 for V<E.
Since m, C, V(x) are given, this recipe allows tracing (x) in steps, from initial (0) [= 1], with initial slope [0], and a guessed E.
reward
ForFinding
www.nlc-bnc.ca/explorers/ kids