Difficulty: Intermediate | Prerequisites: Basic organic chemistry, chair conformations, Newman projections
This topic sits at the intersection of organic structure and computational modelling. You are using molecular mechanics (MM2 force field) to calculate steric energies of different cyclohexane conformations, then connecting those numbers to thermodynamic quantities like ΔG and K_eq. If you skipped the lectures on chair flips and axial/equatorial positions, go back to those first. The computational side is a tool for confirming what conformational analysis predicts on paper.
TL;DR: Cyclohexane adopts several conformations (chair, boat, twist-boat), each with a different steric energy. Substituents prefer equatorial positions because axial placement causes 1,3-diaxial interactions that raise the energy. MM2 calculations let you quantify these preferences and predict equilibrium ratios.
MM2 Force Field
A molecular mechanics method that models a molecule as a collection of atoms connected by springs. It calculates steric energy by summing contributions from bond stretching, angle bending, torsional strain, and van der Waals interactions. Think of it as treating bonds like physical springs and atoms like balls, then calculating how much strain the whole system is under.
Steric Energy
The total energy of a molecule as calculated by molecular mechanics. It includes stretch, bend, stretch-bend, torsion, non-bonded (van der Waals), and electrostatic components. In simple terms, it is a number that tells you how "strained" a particular 3D arrangement of atoms is.
Chair Conformation
The most stable arrangement of cyclohexane, where all bond angles are close to the ideal tetrahedral angle (109.5 degrees) and all adjacent C-H bonds are staggered. Think of it as the shape cyclohexane naturally relaxes into.
Boat Conformation
A less stable cyclohexane conformation with eclipsing interactions along the sides and a flagpole interaction between the two "bow" hydrogens pointing inward at the top. In simple terms, it is the shape you get when you push two opposite carbons of the chair upward.
Twist-Boat Conformation
A slightly more stable version of the boat, where a small twist relieves some of the eclipsing strain. It sits in a shallow energy well between two boat forms.
Axial Position
A substituent pointing straight up or down from the cyclohexane ring, roughly parallel to the ring's vertical axis. Axial groups on the same side of the ring bump into each other (1,3-diaxial interactions).
Equatorial Position
A substituent pointing outward from the ring, roughly in the plane of the equator. Equatorial groups avoid 1,3-diaxial interactions and are almost always preferred.
1,3-Diaxial Interaction
The steric clash between an axial substituent and the axial hydrogens (or other groups) on carbons two positions away on the same face of the ring. This is the main reason axial substituents raise the energy. Think of it as the substituent being too close to its neighbours above or below.
Dihedral Driver
A computational tool that systematically rotates a bond through 360 degrees in small increments, calculating the energy at each step. It produces an energy-vs-angle plot and helps locate global and local minima. In simple terms, it spins a bond and records the energy at each angle to find the best arrangement.
Keq (Equilibrium Constant)
The ratio of products to reactants at equilibrium. For an axial-to-equatorial ring flip: K_eq = [equatorial] / [axial]. A value greater than 1 means the equatorial form is favoured.
Chair conformation
Lowest steric energy of all cyclohexane conformations
All C-C-C bond angles near 109.5 degrees (tetrahedral)
All adjacent bonds are perfectly staggered, so torsional strain is zero
This is the reference point: every other conformation is measured against it
Boat conformation
Higher energy than the chair
Two sources of strain: eclipsing interactions along the four "gunwale" C-C bonds, and a flagpole interaction where two hydrogens on C1 and C4 point toward each other
The boat is not a true energy minimum on the potential energy surface; it is a transition state between two twist-boats
Twist-boat conformation
Slightly lower energy than the boat because a twist relieves some eclipsing strain
It is a true local minimum, unlike the boat
Still substantially higher in energy than the chair
Energy ordering: chair < twist-boat < boat
The energy gap between chair and boat/twist-boat is large enough that at room temperature, cyclohexane exists almost entirely in the chair form
What the MM2 calculation tells you
The total steric energy is a sum of individual components: stretch, bend, stretch-bend coupling, torsion, non-bonded van der Waals (VDW), and electrostatic terms
Comparing the total values across conformations confirms the expected stability order
The breakdown by component shows you which type of strain dominates in each conformation (torsion and VDW are usually the big movers)
Axial vs equatorial preference
The sec-butyl group is a branched substituent (CH(CH3)(CH2CH3))
When sec-butyl sits axial, it experiences significant 1,3-diaxial interactions with the axial hydrogens on C3 and C5
The equatorial conformation places the bulky group away from the ring, relieving those interactions
The equatorial form has a lower MM2 steric energy than the axial form
Calculating the energy difference
Δ Steric Energy = E(equatorial) - E(axial)
This value should be negative (equatorial is lower in energy)
This difference approximates the free energy change (ΔG) for the axial-to-equatorial ring flip
Connecting to Keq
The relationship is: ΔG = -RT ln(Keq)
Rearranging: Keq = e^(-ΔG / RT)
R = 1.987 cal/(mol·K), T = 298 K (room temperature)
Be careful with units: MM2 energies are in kcal/mol, so convert ΔG to cal/mol before plugging into the formula (multiply by 1000)
Since equatorial is more stable, ΔG is negative, so Keq > 1, confirming the equatorial form is favoured
Percentage calculation
% equatorial = [Keq / (1 + Keq)] x 100
For sec-butyl, expect a large majority in the equatorial conformation at room temperature
Why the dihedral driver matters here
sec-Butyl has rotational freedom around the bond connecting it to the ring
Different rotamers of the sec-butyl group give different steric energies
Running the dihedral driver ensures you find the global minimum, not a local minimum where the substituent happens to be in an unfavourable rotational orientation
cis isomer (tert-butyl and methyl on the same side)
Two chair conformations are possible:
Conformation A: tert-butyl equatorial, methyl axial
Conformation B: tert-butyl axial, methyl equatorial
Conformation A is strongly favoured because the tert-butyl group has a much larger 1,3-diaxial interaction than methyl
The tert-butyl group effectively "locks" the ring: it almost never goes axial
trans isomer (tert-butyl and methyl on opposite sides)
Two chair conformations:
Conformation C: both substituents equatorial (diequatorial)
Conformation D: both substituents axial (diaxial)
The diequatorial form (C) is much lower in energy
The diaxial form (D) is very high in energy because both groups suffer 1,3-diaxial interactions simultaneously
Energy parameter breakdown (trans conformations)
The worksheet asks for individual MM2 components: stretch, bend, stretch-bend, torsion, non-VDW, and VDW
The two parameters most affected by moving from equatorial to axial are typically VDW (van der Waals) and torsion
VDW increases because axial groups are physically closer to other atoms on the ring
Torsion increases because eclipsing-like interactions worsen as groups crowd the axial positions
tert-Butyl vs methyl in the axial position
tert-Butyl (three methyl groups on the carbon attached to the ring) causes far more steric strain in the axial position than a single methyl group
This is because tert-butyl has three sets of 1,3-diaxial interactions (one for each of its methyl branches), while a methyl group causes only one modest interaction
The gauche interaction visible in a Newman projection (looking along C1-C2 of the ring) is much larger for tert-butyl
\Delta G = -RT \ln K_{eq}Where R = 1.987 cal/(mol·K), T = temperature in Kelvin (298 K at room temperature).
Rearranged to solve for Keq:
K_{eq} = e^{-\Delta G / RT}To find the percentage of the equatorial conformer:
\% \text{ equatorial} = \frac{K_{eq}}{1 + K_{eq}} \times 100Steric energy difference (always product minus reactant):
\Delta E_{\text{steric}} = E_{\text{equatorial}} - E_{\text{axial}}This value is negative when the equatorial form is more stable, which is consistent with a Keq greater than 1.
Conformational analysis is central to drug design. Many biologically active molecules contain six-membered rings, and whether a functional group sits axial or equatorial determines how it interacts with an enzyme's binding pocket. The same principles apply in materials science: cyclohexane-based monomers adopt specific conformations that affect the physical properties of polymers built from them.
Students often think the boat conformation is a stable intermediate. It is not. The boat is a transition state (or very nearly one) between two twist-boat conformations. Only the chair and the twist-boat are true energy minima.
Students sometimes assume that a larger substituent always makes the equatorial preference "a bit bigger." For tert-butyl, the preference is so overwhelming that it effectively locks the ring, preventing any significant population of the axial conformer. This is qualitatively different from a methyl or ethyl group.
A common unit error when calculating Keq: the MM2 output is in kcal/mol, but the formula ΔG = -RT ln(Keq) uses R in cal/(mol·K). Forgetting to multiply ΔG by 1000 (to convert kcal to cal) gives a Keq that is far too close to 1.
Students sometimes confuse the dihedral driver's purpose. It does not optimise the whole molecule. It rotates one specific bond and records the energy at each angle. You still need to do a full energy minimisation at the lowest-energy angle to get an accurate global minimum.
⚠️ You will almost certainly be asked to predict which chair conformation of a substituted cyclohexane is more stable. The answer is always the one with the largest group equatorial.
⚠️ Expect a calculation question: given steric energy values for two conformers, calculate ΔG, then Keq, then the percentage of the favoured conformer. Watch the unit conversion (kcal to cal).
⚠️ Know the difference between cis and trans disubstituted cyclohexanes. Cis means both substituents are on the same side, so one must be axial and the other equatorial. Trans means they are on opposite sides, so they can both be equatorial (or both axial).
⚠️ Be prepared to explain why VDW and torsion are the two energy components most affected by the axial/equatorial switch.
True or False: The boat conformation of cyclohexane is a true energy minimum. (False, it is a transition state between twist-boats.)
Fill in the blank: The two MM2 energy parameters most affected by the axial-to-equatorial switch are ______ and ______. (VDW and torsion.)
True or False: For the conversion of axial to equatorial sec-butylcyclohexane, Keq should be greater than 1. (True, equatorial is favoured.)
Fill in the blank: In cis-1-tert-butyl-4-methylcyclohexane, the tert-butyl group prefers the ______ position. (Equatorial.)
True or False: The trans-diequatorial conformation of 1-tert-butyl-4-methylcyclohexane is higher in energy than the trans-diaxial conformation. (False, diequatorial is lower.)
Q: Why is the chair conformation of cyclohexane more stable than the boat?
A: The chair has all bonds in a staggered arrangement (zero torsional strain) and no flagpole interactions. The boat suffers from eclipsing strain along four C-C bonds and a repulsive flagpole interaction between H atoms on C1 and C4.
Q: For sec-butylcyclohexane, the MM2 steric energy of the axial conformer is 10.801 kcal/mol and the equatorial conformer is 8.200 kcal/mol. Calculate Keq at 298 K.
A: ΔG ≈ ΔE = 8.200 - 10.801 = -2.601 kcal/mol = -2601 cal/mol. Keq = e^(2601 / (1.987 × 298)) = e^(4.39) ≈ 80.6. The equatorial form is overwhelmingly favoured.
Q: In trans-1-tert-butyl-4-methylcyclohexane, which chair conformation is more stable and why?
A: The diequatorial conformer (C) is more stable. Both substituents avoid 1,3-diaxial interactions. The diaxial conformer (D) forces both the bulky tert-butyl and the methyl group into axial positions, dramatically increasing VDW and torsional strain.
Q: Name the two specific steric interactions that make an axial substituent higher in energy than the same substituent in the equatorial position.
A: 1,3-diaxial interactions (the axial substituent clashes with axial H atoms two carbons away on the same face) and gauche interactions (visible in a Newman projection, the substituent is gauche to the ring C-C bonds rather than anti).
Q: Why is it important to run a dihedral driver before recording a steric energy value?
A: A simple energy minimisation may find a local minimum rather than the global minimum. The dihedral driver systematically explores all rotational angles around a bond, ensuring you locate the lowest-energy rotamer.
This material connects directly to stereochemistry: cis/trans isomerism in rings is a form of geometric isomerism, and predicting which conformer dominates is an extension of the same logic used to assign E/Z configurations in alkenes. The ΔG = -RT ln(Keq) relationship reappears throughout physical chemistry and biochemistry, so getting comfortable with it here pays dividends in thermodynamics and enzyme kinetics later. The concept of steric strain also underpins reactivity: SN2 reactions, for instance, are slower at sterically hindered centres for exactly the reasons explored here.
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