Newman Projection and Conformation Explorer

Reading a Newman projection

A Newman projection is a molecule seen straight down one carbon-carbon single bond. The carbon nearer you is drawn as a point, where its three bonds meet in the middle. The carbon behind it is hidden, so it is drawn as a circle, and its three bonds start at the edge of the circle. Each carbon’s three bonds are 120° apart, and the only thing that changes as the bond turns is how the back three sit against the front three.

That is measured by the dihedral angle φ, the angle round the circle from a group on the front carbon to a group on the back one: for butane, from one methyl group to the other. It is positive when the front bond would have to turn clockwise to cover the back one. The explorer opens on butane turning about its C2−C3 bond, drawn three ways at once: as a 3D model, a Newman projection and a sawhorse. The back carbon and its bonds are the same colour in all three, and the arc marked φ in the Newman projection is the same angle as the marker on the energy diagram.

Using the explorer

Drag the back carbon round the Newman circle to turn the bond, or take hold of any of its groups in the 3D model or the sawhorse; the other two views follow, and so does the marker on the energy diagram. Drag empty space in the 3D model to turn the view. The slider under the stage moves φ a degree at a time, as do the arrow keys on the focused stage, or 15° with Shift, and the buttons jump to the named conformations. A press anywhere on the energy diagram turns the bond to that angle.

The strain is drawn where it is paid. Each eclipsed pair of bonds gets a red wedge in the Newman projection and a glow in the other two views, and two methyls gauche to each other get a violet arc. Each mark is as strong as the share of its Table 3.5 cost being paid at that angle, so a wedge fills as its pair comes into eclipse and is gone 60° later, and pointing at one names it.

Staggered and eclipsed ethane

In staggered ethane each C−H bond on the front carbon sits halfway between two on the back carbon, 60° from each. Turn the back carbon 60° and the bonds line up, one behind another: that is eclipsed ethane, and it is 12 kJ/mol (2.9 kcal/mol) higher in energy. The cost comes from the three pairs of bonds lined up, so each H↔H eclipsing interaction is worth 4.0 kJ/mol. The strain of bonds held eclipsed is called torsional strain, to tell it from the steric strain of groups too big to sit close together.

Every staggered conformation of ethane is the same one, because the three hydrogens on each carbon are alike, so the energy diagram is three identical humps of 12 kJ/mol in a full turn. The same is true of any molecule with one carbon that carries three identical groups, which is why the explorer offers only Staggered and Eclipsed for ethane, propane, 2-methylpropane and 2,2-dimethylpropane.

The energy diagram of butane

Butane, CH₃CH₂CH₂CH₃, seen along its middle bond, has a methyl group on each of the two carbons, and the diagram stops being three equal humps. The costs that build it are four figures from Table 3.5 of McMurry’s Organic Chemistry (OpenStax, 2023): 4.0 kJ/mol for two hydrogens eclipsed, 6.0 for a hydrogen and a methyl eclipsed, 11 for two methyls eclipsed and 3.8 for two methyls gauche. The explorer adds them up over the nine front and back pairs, and each conformation in the diagram is a sum you can check:

• Anti, φ = 180°: nothing eclipsed and the methyls as far apart as they can be: 0 kJ/mol.
• Gauche, φ = ±60°: one methyl-methyl contact at 60°: 3.8 kJ/mol.
• Eclipsed, φ = ±120°: each methyl eclipses a hydrogen, and two hydrogens eclipse each other: 6.0 + 6.0 + 4.0 = 16 kJ/mol.
• Syn, or fully eclipsed, φ = 0°: the methyls eclipse each other, and so do two pairs of hydrogens: 11 + 4.0 + 4.0 = 19 kJ/mol.

So the lowest barrier out of anti is 16 kJ/mol, the way out of gauche to anti is over 16 − 3.8 = 12.2 kJ/mol, and from one gauche to the other the bond has to climb 19 − 3.8 = 15.2 kJ/mol through syn. The dashed line on the diagram is RT, 2.48 kJ/mol at 25 °C, the yardstick for thermal energy per mole. Every barrier here is several times RT: low enough to be crossed billions of times a second, high enough that at any moment most molecules sit near the bottom of a well.

Choose another molecule and the same four costs build its curve. Propane’s barrier is 6.0 + 4.0 + 4.0 = 14 kJ/mol, 2-methylpropane’s 6.0 + 6.0 + 4.0 = 16 and 2,2-dimethylpropane’s 3 × 6.0 = 18. Along C2−C3, 2-methylbutane runs from 3.8 to 21 kJ/mol and 2,3-dimethylbutane from 7.6 to 26 kJ/mol, and Build your own puts a hydrogen or a methyl at each of the six places.

How much of butane is anti?

At any moment almost every molecule is near one of the three staggered conformations, anti or one of the two gauche, which are mirror images of each other with the same energy. The share in each follows the Boltzmann distribution, so the ratio of gauche to anti is N(gauche)/N(anti) = 2e^(−ΔE/RT), where ΔE is the gauche conformation’s energy above anti and the 2 counts the two gauche forms. Here is the explorer’s working at 25 °C; each step should match a readout.

• RT = 8.314 × 298.15 = 2479 J/mol, which is 2.479 kJ/mol.
• e^(−3.8/2.479) = e^(−1.533) = 0.2159 for each gauche conformation against anti.
• N(gauche)/N(anti) = 2 × 0.2159 = 0.4318.
• So the anti share is 1/(1 + 0.4318) = 69.84%, and the gauche share 30.16%, 15.08% each side.

About 70 percent of butane is anti at room temperature, and 30 percent gauche. Cooling favours the lower conformation: at 0 °C the anti share is 72.7 percent, and at −150 °C, the bottom of the range, 95.3 percent. Warming spreads the molecules out: 63.0 percent at 100 °C and 59.6 percent at 150 °C, still well short of the third each that the three conformations would get if they were equal. The same ΔG° = −RT ln K connects any energy difference to an equilibrium constant in the Gibbs free energy calculator.

Beyond butane: crowded molecules

2-Methylbutane, seen along C2−C3, has two methyls on the front carbon and one on the back. With the back methyl between the two front methyls it is gauche to both, 2 × 3.8 = 7.6 kJ/mol; in the other two it is gauche to one methyl and anti to the other, 3.8 kJ/mol. The explorer calls the 7.6 kJ/mol conformation anti, because its reference groups are the hydrogen on C2 and the methyl on C3, and those are 180° apart there. At 25 °C, 90.3 percent of 2-methylbutane is in the two 3.8 kJ/mol conformations, 45.1 percent each, and 9.7 percent in the third.

2,3-Dimethylbutane has two methyls on each carbon. With its hydrogens anti, each methyl is gauche to one methyl across the bond, two contacts in all, 7.6 kJ/mol; with the hydrogens gauche there are three, 11.4 kJ/mol, so in this count the anti conformation holds 69.8 percent at 25 °C, by the same 3.8 kJ/mol difference as butane. Its eclipsed conformations cost 11 + 6.0 + 6.0 = 23 kJ/mol with one pair of methyls eclipsed and 11 + 11 + 4.0 = 26 kJ/mol with both. Adding up pairs is least safe in crowded molecules like these, and the explorer puts a note beside them. For 2,3-dimethylbutane the count is far off: at −180 °C, ¹³C NMR finds two gauche molecules to every anti one, as if all three conformations had the same energy (Lunazzi and colleagues, 1977).

How fast does the bond turn?

The Eyring equation turns a barrier into a rate, k = (k_B T/h) e^(−ΔG‡/RT), and the explorer uses each barrier as ΔG‡ with a transmission coefficient of 1. At 25 °C the prefactor k_B T/h is 6.21 × 10¹² s⁻¹, and for ethane’s 12 kJ/mol the exponential is 0.00790, so a staggered ethane molecule turns over the barrier on one side about 4.9 × 10¹⁰ times a second. It can leave either way, so it leaves at twice that, 9.8 × 10¹⁰ s⁻¹, and each staggered conformation lasts about 10 picoseconds on average.

Butane turns more slowly. Gauche turns to anti over 12.2 kJ/mol at about 4.5 × 10¹⁰ s⁻¹ and to the other gauche over 15.2 kJ/mol at 1.4 × 10¹⁰ s⁻¹, while anti leaves over 16 kJ/mol at 9.8 × 10⁹ s⁻¹ each way. Rates like these are why the conformations of ethane and butane cannot be separated and kept in a bottle, as butane and its constitutional isomer 2-methylpropane can. Temperature acts on the rate far more steeply than on the shares: at −150 °C, ethane makes about 2.1 × 10⁷ hops a second each way. The same exponential dependence on a barrier is what the Arrhenius equation calculator works with for reaction rates. Play turns the bond at a steady 30° a second so the curve can be read, which is a picture of the diagram and not of a real molecule’s motion.

From Newman to sawhorse and back

A sawhorse projection shows the same bond from above and to one side. The C−C bond is drawn as a long line running up to the right, with the front carbon at its lower left, and each carbon’s three bonds come off its end of that line. To turn a Newman projection into a sawhorse, draw the long bond, then copy the three front groups onto the lower carbon and the three back groups onto the upper carbon, each keeping its place round the bond: a group at twelve o’clock in the Newman projection points up in the sawhorse. To go back, look along the long bond from the lower left.

The explorer draws both from the same 3D model, so a group’s angle round the bond is the same in each, and the sawhorse’s long bond is drawn about twice its true length, so that the two ends stand apart. Every bond angle in the model is the tetrahedral 109.5°, the angle four electron domains take round a carbon in the VSEPR molecular geometry visualiser. For how the atoms are joined in the first place, the Lewis structure generator draws the bonds a Newman projection is turning.

Naming conformations: Klyne and Prelog

Anti, gauche, eclipsed and syn are names for particular angles. The general names, from William Klyne and Vladimir Prelog in 1960 and used by IUPAC, divide the circle into ranges by the angle between the two reference groups:

• Synperiplanar, within 30° of 0°: butane’s syn conformation.
• Synclinal, from 30° to 90° either way: gauche, which IUPAC also calls skew.
• Anticlinal, from 90° to 150° either way: butane’s eclipsed conformation at 120°.
• Antiperiplanar, within 30° of 180°: anti.

The clinal ranges carry the sign of the angle, so gauche butane is +sc or −sc, and the Dihedral angle readout’s hint gives the symbol. The names depend on which groups are measured between. IUPAC takes on each carbon the group that differs from the other two, as the φ arc does: the methyls in butane, and on a carbon carrying two methyls the hydrogen, so that anti in 2,3-dimethylbutane means the two hydrogens are 180° apart. Where all three are alike, IUPAC measures to the nearest group, so staggered ethane is synclinal and eclipsed ethane synperiplanar, whichever hydrogens the arc joins.

What this model leaves out

• The shape of the curve between the published points. The stationary values are sums of Table 3.5’s costs. Between them each cost is switched on smoothly with the angle, cos²(3θ/2) for an eclipsing pair and sin²(3θ/2) for a gauche one, which is a choice made here to join the points and not a measurement. For ethane it is the textbook 6(1 + cos 3φ) kJ/mol.
• Additivity. Each pair is counted as if the others were not there. In crowded molecules the groups push each other apart and the bonds bend, so the real energies can differ from the sums. That is why 2,2,3,3-tetramethylbutane, with a methyl at all six places, is not in the molecule menu, and why the explorer warns when you build a crowded one.
• Entropy. Each conformation is counted at the bottom of its well, by its energy alone, and the factor of 2 for the two gauche forms is the only entropy in the populations.
• Solvent and other groups. The costs are for alkanes, with only hydrogen and methyl, and butane’s ethyl group seen along C1−C2 is costed as a methyl. Polar groups such as fluorine or hydroxyl bring dipoles and the gauche effect, and a solvent can shift the balance; none of that is in the table.
• A fixed geometry. The bond angles stay tetrahedral and the bond lengths fixed at every angle, where a real molecule relaxes a little as it turns.

Common mistakes

• Drawing the back carbon’s bonds from the centre. Only the front carbon’s bonds meet in the middle. The back ones start at the edge of the circle.
• Calling 120° gauche. Gauche is 60°. At 120° every group is eclipsed by one on the other carbon, and in butane that conformation is 16 kJ/mol up, not 3.8.
• Forgetting there are two gauche conformations. They are mirror images at +60° and −60°, and leaving out the 2 in 2e^(−ΔE/RT) puts butane at 82 percent anti instead of 70.
• Mixing units in e^(−ΔE/RT). With R = 8.314 J/(mol K), ΔE must be in J/mol: 3800, not 3.8. With ΔE in kcal/mol, R is 0.001987 kcal/(mol K); 1 kcal is 4.184 kJ exactly.
• Treating conformations as separate compounds. At room temperature a butane molecule changes conformation billions of times a second, so anti and gauche butane are one compound, and their shares an equilibrium.
• Reading the 3.8 kJ/mol as new. It is the same contact as an axial methyl group’s 1,3-diaxial interaction in a cyclohexane ring, which is gauche to the ring carbon across the next bond, and the chair conformation explorer counts it there, twice for each axial methyl. For the other kind of stereochemistry, which needs bonds broken to change, the R and S configuration explorer names a stereocentre.

Constants used: Planck constant (h), Boltzmann constant (k) and Molar gas constant (R).