Conformational Analysis: Newman Projections, Cyclohexane Chair, and Isomerism
Newman projections: eclipsed vs staggered; dihedral angles and energy
When viewing a molecule in space, we consider staggered and eclipsed conformations around a carbon–carbon (C–C) bond.
Newman projection perspective: front carbon (closest to viewer) and back carbon (further away). In an eclipsed conformation, substituents on front and back carbons line up (eclipsing each other); in a staggered conformation, they are as far apart as possible.
Dihedral angle (theta): the angle between the front and back substituents around the C–C bond. It can take values from 0° up to 360° in increments of 60°:
Energetic consequences:
Eclipsed conformations have torsional strain due to eclipsing of electron clouds; staggered conformations minimize this strain.
When bulky groups are near each other (within proximity), steric strain or hindrance (also called “streak strain” in some texts) can contribute additional energy penalties.
Relationship to previous lecture: torsional strain arises specifically when bonds eclipse; staggered arrangements relieve this strain.
Ethane and butane: qualitative energy profile and contributions
In ethane, the barrier to internal rotation is dominated by three C–H eclipsing interactions in the eclipsed conformation. Each eclipsing interaction contributes to the torsional energy; total barrier is about .
In butane (around the C2–C3 bond), the energy profile is more complex because two methyl groups can eclipse each other in the fully eclipsed form in addition to CH–CH eclipsing interactions with hydrogens:
Fully eclipsed (0°): maximum energy, approximately .
Gauche (60°): energy drops to about .
At 120°, you still have eclipsing interactions (one methyl can eclipse a hydrogen and/or another methyl case) giving an intermediate energy, around .
Anti (180°): no eclipsing between the two methyl groups, so the energy is minimized (relative baseline, often taken as 0 for comparison). Then the profile repeats (240° ~ 120°; 300° ~ 60°; 360° ~ 0°).
How energies are divided among interactions (conceptual):
Each C–H eclipsing interaction contributes roughly 1 kcal/mol of strain (torsional). In butane, with two bulky CH3 groups, there are multiple eclipsing interactions (CH–CH and CH–H) that add up to the total .
The gauche arrangement (60°) is stabilized relative to the eclipsed forms but still has some energy due to steric interactions; the observed gauche energy is about 0.9 kcal/mol for methyl–methyl gauche interactions in simple models.
Energy profile for rotation around a C–C bond in butane: a sine-like variation between 0° and 360°, with maxima at eclipsed alignments and minima at staggered alignments; mirror symmetry about 180°.
Practical takeaway: staggered conformations are more stable than eclipsed; anti conformations (180°) are the most stable for dimethyl systems, while gauche conformations are intermediate in energy.
Kinetics vs. equilibrium: at room temperature, kinetic access allows interconversion, but equilibrium favors the lower-energy staggered/anti conformations; population distribution can be skewed toward the more stable form (e.g., the anti or less-strained staggered structures) depending on substituents.
Cycloalkanes: strain, angles, and basic conformations
Cyclopropane (three-membered ring)
Bond angles forced to 60°, far from the ideal sp3 angle (≈ 109.5°). This creates strong angle strain.
The ring is rigid; rotation around C–C bonds is highly restricted due to ring strain and geometry.
Consequence: cyclopropane is very strained and has limited conformational freedom; substituents are fixed relative to the ring plane (top vs bottom exposure).
Cyclobutane (four-membered ring)
Angle about 90°, also angle-strained (less severe than cyclopropane but still significant).
Cyclohexane (six-membered ring)
Idealized sp3 angle ≈ ; cyclohexane can adopt conformations that minimize angle strain, notably the chair conformation.
In chair form, there is no angle strain; the carbon–carbon bonds are staggered relative to the mean plane, and the molecule can rapidly interconvert between chair conformers (ring inversion).
Ring inversion barrier around (unstable high-energy transition state) to switch between the two chair conformers.
The chair has 12 hydrogens total: 6 axial and 6 equatorial. Hydrogens on axial positions are perpendicular to the mean plane; equatorial hydrogens lie roughly in the plane around the ring.
In chair form, axial and equatorial positions switch during ring inversion: axial hydrogens become equatorial and vice versa.
Monosubstituted cyclohexane (G = generic substituent)
The preferred conformer is the one with the substituent in an equatorial position, because axial placement incurs a 1,3-diaxial interaction (steric hindrance with axial substituent’s neighboring axial hydrogens).
Typical energy penalty for an axial substituent: .
Equilibrium distribution at room temperature for a simple methyl substituent: about 95% equatorial, 5% axial (roughly a 95:5 ratio).
Disubstituted cyclohexane: one- and two-substituent patterns
Notation: one- and two-disubstituted cyclohexanes (e.g., 1,2-; 1,3-; 1,4-; etc.). Here we focus on 1,2-disubstituted because it yields most interesting conformational behavior.
Stereochemistry: cis vs trans relative to the ring plane.
For 1,2-disubstituted cyclohexanes, in a given chair conformation you typically observe one axial and one equatorial substituent (due to ring geometry). Ring inversion interconverts the two chair forms, flipping axial to equatorial.
Relative stability depends on whether substituents are cis or trans and on their sizes. In general, minimizing the number of axial substituents lowers the energy; larger substituents experience stronger 1,3-diaxial interactions when axial.
Example with two identical methyl groups (1,2-dimethylcyclohexane):
If cis: in a given chair, one methyl is axial and the other equatorial (ring inversion swaps their roles).
If trans: it is possible to have a chair form with both methyls equatorial (often the more stable form), and the inverted chair form will place both axial.
The 1,3-diaxial interactions for axial methyl groups contribute to the energy penalty; the energy penalty increases with bulkier substituents (e.g., larger alkyls).
Summary for substituent stability: the most stable conformer usually has the least axial substituents; as the size of the substituent grows, the axial interactions become more significant, shifting equilibria toward all-equatorial arrangements when possible.
Quick note on chair drawings and isomerism
In chair drawings, axial substituents are shown perpendicular to the plane, while equatorial substituents project outward along the ring. In ring inversion, axial becomes equatorial and vice versa.
cis vs trans relationships are preserved under ring inversion; inversion can switch which substituents are axial/equatorial, but the relative stereochemical relationship (cis or trans) remains the same.
Isomers and relationships: constitutional, identical, and stereoisomers
Constitutional (structural) isomers
Same molecular formula, but different connectivity (bonding pattern).
Example: butane (C$4$H${10}$) vs methylcyclopropane (C$4$H${8}$) are not directly comparable here, but general idea: different bond connectivity means different compounds.
Identical molecules (conformers in 3D space)
Two drawings may look different in 2D, but if they have the same connectivity and can be interconverted without breaking bonds (e.g., via simple rotation around single bonds or ring inversion), they are the same molecule (identical in 3D).
For cyclohexane, two chair conformations can be considered identical as they interconvert by ring inversion and do not require bond breaking.
Stereoisomers
Same bond connectivity, but different spatial arrangement in space.
Includes cis/trans relationships around double bonds or ring systems (e.g., cyclohexane substituents).
In the context of cyclohexane, cis and trans forms of disubstituted cyclohexanes are a classic example of stereoisomerism.
Practical exam-oriented guidance from the transcript
When given two structures, determine whether they are constitutional isomers, identical (conformers), or stereoisomers based on connectivity and three-dimensional arrangement.
For pairs of molecules with the same formula and the same connectivity, assess whether a ring inversion or rotation around single bonds can interconvert them (identical) or whether a spatial arrangement persists (stereoisomer).
For architectural practice: be comfortable drawing Newman projections from different directions, and know that choosing a consistent front/back orientation helps in comparing conformations.
Ring inversion in cyclohexane: practical practice and implications
Ring inversion concept
Inversion interconverts chair A and chair B by moving the axial substituents to equatorial and vice versa.
This inversion happens rapidly at room temperature and interconverts conformers that differ mainly by which hydrogens are axial vs equatorial.
Energetics of ring flip (detailing the mono-substituted case)
In monosubstituted cyclohexane, inversion flips axial to equatorial for the substituent; the equatorial form is energetically favored by about .
The equatorial conformer is favored in equilibrium, with typical distributions around 95% equatorial and 5% axial for small substituents like methyl, at room temperature.
Consequences for 1,2- and higher-order disubstituted cyclohexanes
Ring inversion can interchange axial and equatorial positions for substituents, altering 1,3-diaxial interactions and overall stability.
For disubstituted cyclohexanes, the stable conformer minimizes axial substituents; steric interactions (1,3-diaxial) become more significant as the size of the substituent grows.
For example, in 1,2-dimethylcyclohexane, the cis form in a given chair typically has one axial and one equatorial methyl; the trans form can have both methyls equatorial in the alternate chair, which is usually more stable due to reduced axial interactions.
A note on chair drawings and axial/equatorial labeling
In chair representations, it is helpful to assign one substituent as front/right and label axial vs equatorial for each carbon.
Ring inversion flips which substituents are axial/equatorial, but the cis/trans relationship remains the same.
Practical tips for exam preparation (based on the transcript)
Be able to construct Newman projections around a given bond and identify dihedral angles: 0°, 60°, 120°, 180°, 240°, 300°, 360°. Recognize symmetry: 0° and 360° are equivalent; 60° and 300° are equivalent; 120° and 240° are equivalent.
Understand how energy changes as you rotate around a C–C bond for simple alkanes:
Eclipsed positions maximize energy due to torsional strain.
Gauche interactions (60°) produce intermediate energy values.
Anti (180°) often yields a minimum (for disubstituted systems, relative minima depend on substituent sizes).
Distinguish torsional strain (due to eclipsing) from steric hindrance or 1,3-diaxial interactions (which arise when bulky groups are axial in cyclohexane chairs).
For cyclohexane, memorize the key points:
Chair is the most stable conformation; ring inversion interconverts chairs.
Axial vs equatorial positions and the 1,3-diaxial interaction energy penalty (~1.8 kcal/mol per axial substituent for methyl groups).
Typical mono-substituted equatorial preference: ~95% equatorial, ~5% axial at room temperature (for methyl substituents).
When evaluating disubstituted cyclohexanes (cis vs trans):
Cis: in a given chair, often one substituent is axial and the other equatorial; ring inversion swaps these roles.
Trans: can have both substituents equatorial in one chair (or both axial in the inverted chair); stability correlates with minimizing axial substituents and steric interactions.
Distinguishing isomer types:
Constitutional isomers: different connectivity; same formula but different skeleton; not interconvertible by simple bond rotation or ring flip.
Identical molecules: same connectivity, interconvertible by bond rotation or ring flips without breaking bonds.
Stereoisomers: same connectivity, different spatial arrangement; cis/trans relationships are classic examples in cycloalkanes.
Practice problems: be ready to convert structures into Newman projections, identify dihedral angles, assign axial/equatorial positions, and determine the more stable conformer based on steric considerations and ring-inversion possibilities.
Dihedral angles:
Torsional strain contributions (rough benchmarks):
Eclipsing interactions: typically contribute on the order of per H–H eclipsing interaction; additional contributions from bulky group eclipsing (e.g., CH3–CH3) add further energy penalties.
Fully eclipsed butane (0°): roughly (sum of multiple eclipsing interactions).
Gauche interaction energy (60°) in simple models: for methyl–methyl gauche in cyclohexane-like contexts.
1,3-Diaxial interaction penalty for axial substituents in cyclohexane: (per axial substituent, size-dependent).
Ring inversion barrier for cyclohexane: (unstable transition state between chairs).
Equilibrium distribution for monosubstituted cyclohexane methyl group: approximately at room temperature.
General principle: conformers with fewer axial bulky substituents are more stable; ring inversion interconverts chair conformations and changes axial/equatorial status without breaking bonds.
Quick recap links to the transcript content
The discussion started with comparing eclipsed and staggered conformations in Newman projections, defining dihedral angles, and introducing the concept of torsional and steric strain.
The CH3–CH3 example (butane) was used to illustrate how energy varies with dihedral angle and how bulky groups contribute to additional steric hindrance beyond torsional strain.
The lecture then moved to cycloalkanes, explaining angle strain in cyclopropane/cyclobutane and why cyclohexane in the chair form has no angle strain and how ring inversion works.
Substituent effects on cyclohexane were covered: axial vs equatorial positions, 1,3-diaxial interactions, and how these influence stability and population distribution.
Finally, the lecture differentiated between constitutional isomers, identical molecules (conformers), and stereoisomers, with emphasis on how ring inversions can yield identical molecules and how cis/trans relationships define stereoisomerism in cyclohexanes.
Practice pointers for the exam
Be able to draw and interpret a Newman projection of CH3–CH3 in the butane system at the key dihedral angles (0°, 60°, 120°, 180°, 240°, 300°, 360°) and identify which conformations are staggered vs eclipsed.
Be able to assign axial vs equatorial positions in cyclohexane chairs for a given substituent and predict which chair is more stable.
Be able to explain why 1,3-diaxial interactions penalize axial substituents and how this explains the preference for equatorial substituents in cyclohexanes.
Be able to categorize a pair of molecules as constitutional isomers, identical (conformers), or stereoisomers based on connectivity and three-dimensional arrangement.
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