The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are exactly five such solids (Steinhaus 1999, pp. 252-256): the cube, dodecahedron, icosahedron, octahedron, and tetrahedron, as was proved by Euclid in the last proposition of the Elements. The Platonic solids are sometimes also called &quot;cosmic figures&quot; (Cromwell 1997), although this term is sometimes used to refer collectively to both the Platonic solids and Kepler-Poinsot solids (Coxeter 1973). The Platonic solids were known to the ancient Greeks, and were described by Plato in his Timaeus ca. 350 BC . In this work, Plato equated the tetrahedron with the &quot;element&quot; fire, the cube with earth, the icosahedron with water, the octahedron with air, and the dodecahedron with the stuff of which the constellations and heavens were made (Cromwell 1997).
Dodecahedrane 23 steps from cyclopentadiene. 1.5mg in first synthesis. Prinzbach grams.
The Steroid SexThe Steroid Sex
Regulate growth and function of reproductive organs;Regulate growth and function of reproductive organs;
stimulate development of secondary sexual characteristicsstimulate development of secondary sexual characteristics
Abundant in nature: “rigid scaffolding”.Abundant in nature: “rigid scaffolding”.
Names:Names: CycloCycloalkanesalkanes Cyclopropane, , , etc.Cyclopropane, , , etc.
Substituents:Substituents: CycloalkylCycloalkyl. Substituted cycloalkanes:. Substituted cycloalkanes:
single substituent is automatically at “single substituent is automatically at “C1C1”.”.
Ethylcyclobutane (no # needed)Ethylcyclobutane (no # needed)
Alkylcycloalkane or cycloalkylalkane?Alkylcycloalkane or cycloalkylalkane?
Larger stem controls:Larger stem controls:
(CH(CH22))nn notnot CCnnHH22nn+2+2
Cycloalkanes have two sides: “up”, “down”.Cycloalkanes have two sides: “up”, “down”.
With two or more substituents, new type of isomerism:With two or more substituents, new type of isomerism:
Same side: cisSame side: cis
Opposite sides: transOpposite sides: trans
Stereoisomers should be stable at roomStereoisomers should be stable at room
temperature. Rotamers interconvert rapidly bytemperature. Rotamers interconvert rapidly by
rotation, whereasrotation, whereas cis,transcis,trans isomerizationisomerization
requires bond breaking.requires bond breaking.
Same connectivitySame connectivity (not constitutional isomers), but(not constitutional isomers), but
differing arrangement in space.differing arrangement in space.
Note: This definition includes all rotamers (anti, gauche, etc.).Note: This definition includes all rotamers (anti, gauche, etc.).
Definition of stereoisomers:Definition of stereoisomers:
OperationalOperational (practical) definition:(practical) definition:
The Cal Katrina Relief
Big Lecture Drive
Big Lecture Drive
Rather than going out to lunch or buying coffee later this week, make
Because funding is urgently needed for the disaster relief. Also, to
foster school spirit, to win the competition and (maybe, we are still
working on this!) get free ice cream or a mention in the Daily Cal!
A fundraising competition for the American Red Cross’ hurricane
Katrina relief efforts between the largest classes at UC Berkeley,
organized in affiliation with Cal Katrina, the ASUC, and the Berkeley
chapter of the American Red Cross.
The 1st, 2nd, 3rd, 4th, 6th, and
7th largest lectures at UC
Berkeley. We are still waiting to
hear about the 5th largest
lecture and others!
After lecture, on your way out.
How do we quantify “ring strain”? Need anHow do we quantify “ring strain”? Need an
““unstrained” reference and a measure ofunstrained” reference and a measure of
energetic content. We get numbers byenergetic content. We get numbers by
measuringmeasuring heats of combustion.heats of combustion.
-Carbon wants-Carbon wants 109.5°109.5°
An Application: The Relative HeatAn Application: The Relative Heat
Content of the Two Isomeric ButanesContent of the Two Isomeric Butanes
Most branched alkanes are slightly more stable than their linear isomersMost branched alkanes are slightly more stable than their linear isomers
Are cycloalkanes “normal”? DefineAre cycloalkanes “normal”? Define
normal from heat of combustionnormal from heat of combustion
ΔΔH°H°combcomb of CHof CH33(CH(CH22))nnCHCH33
AnyAny discrepancydiscrepancy withwith ΔΔH°H°expexp equalsequals
ring strain.ring strain.
Every additional (CHEvery additional (CH22) increment) increment
gives an extragives an extra δΔδΔH°H°combcomb ~ -157.4.~ -157.4.
We can therefore calculateWe can therefore calculate ΔΔH°H°combcomb
(expected) (CH(expected) (CH22))nn:: nn x 157.4.x 157.4.
1.1. Bond angle,Bond angle,
especially inespecially in
small ringssmall rings
especially inespecially in
medium sizedmedium sized
Envelope ConformationEnvelope Conformation
The UnstrainedThe Unstrained
A “Chair” ConformationA “Chair” Conformation
A Newman View of aA Newman View of a
Cyclohexane C-C Bond:Cyclohexane C-C Bond:
The Cyclohexane Boat isThe Cyclohexane Boat is
+ 6.9 kcal/mol
……So it Twists.So it Twists.
But this is only part of its mobility.But this is only part of its mobility.
The moleculeThe molecule “flips”“flips” from onefrom one chairchair
to another chair form.to another chair form.
Cyclohexane Ring FlipCyclohexane Ring Flip
EEaa = 10.8= 10.8
ΔΔG°G° = O= O
HH HH HH HH
HH HH HH HH
Eclipsing strainEclipsing strain
ChairChair Boat + 6.9 kcal molBoat + 6.9 kcal mol-1-1
. Boat is a TS.. Boat is a TS.
Complex Movement:Complex Movement:
Goes throughGoes through boatboat
How to Draw the ChairHow to Draw the Chair
This endThis end
Equatorial bonds must beEquatorial bonds must be parallelparallel
to the C–C bond(s)to the C–C bond(s) “one over”“one over” [not[not
the attached one(s), but the nextthe attached one(s), but the next
The Chair-Chair FlipThe Chair-Chair Flip
The two structures are the same. However, whatThe two structures are the same. However, what
happens in substituted cyclohexanes?happens in substituted cyclohexanes?
∆Gº = 0
to ringto ring
Note: These numbers doNote: These numbers do notnot reflectreflect absolute sizeabsolute size, but, but
size with respect tosize with respect to transannular and gauchetransannular and gauche
interactions ininteractions in cyclohexanecyclohexane..
The power of conformational analysis:The power of conformational analysis: ΔΔG°G° maymay
bebe additiveadditive. Consider the. Consider the dimethylcyclohexanes:dimethylcyclohexanes:
ΔΔG°G° = 0= 0
ΔΔG°G° == +3.4!+3.4!
ΔΔG°G° = 0= 0
The largest group often enforcesThe largest group often enforces
one conformation:one conformation:
ΔΔG°G° = 3.4-5 = -1.6= 3.4-5 = -1.6axax
Large substituents, such asLarge substituents, such as tert-tert-Bu,Bu,
are said to “lock” a conformation.are said to “lock” a conformation.
Medium Rings SufferMedium Rings Suffer
Transannular StrainTransannular Strain
(decalin), trans and cis(decalin), trans and cis
Bicyclic, Fused, Polycyclic, Polyhedral AlkanesBicyclic, Fused, Polycyclic, Polyhedral Alkanes
Locked boatLocked boat
Home exercise: Make models and try the ring flip!Home exercise: Make models and try the ring flip!
Strained Hydrocarbons: What is theStrained Hydrocarbons: What is the
limit? Exotic polyhedra: The Fivelimit? Exotic polyhedra: The Five
PlatonicPlatonic oror Cosmic SolidsCosmic Solids (Plato 350(Plato 350
Can we make the corresponding hydrocarbon frames (CH)Can we make the corresponding hydrocarbon frames (CH)nn ??
There are two more: icosahedron (water) and octahedron (air)There are two more: icosahedron (water) and octahedron (air)