Organic Chemistry I, University of Minnesota Twin Cities
Difficulty: Introductory-Intermediate | Prerequisites: Lewis structures, VSEPR theory, sigma and pi bonding basics
Tags: conformations, dihedral angle, torsional angle, sigma bond rotation, wedge-dash notation, Newman projections, 3D molecular geometry, organic chemistry, line-angle formulas
Up to this point in Organic Chemistry I, you have drawn molecules as flat, two-dimensional structures. This topic shifts to the reality that molecules are three-dimensional objects whose shapes change constantly because bonds can rotate. Understanding these 3D arrangements is essential for later topics such as stereochemistry, reaction mechanisms, and enzyme-substrate interactions. If you are comfortable with sigma bonds and basic molecular geometry (VSEPR), you have what you need to start here.
Molecules are not rigid. Rotation around single (sigma) bonds produces different three-dimensional arrangements called conformations, and the angle of that rotation is the dihedral (torsional) angle. We represent these 3D shapes on paper using wedge-and-dash notation in line-angle formulas.
Conformation
A specific three-dimensional arrangement of atoms in a molecule that results from rotation about a single (sigma) bond. Conformations are not different molecules; they are the same molecule in different poses.
In simple terms, this means: if you grab one end of a molecule and twist the single bond connecting it to the other end, every distinct arrangement you pass through is a different conformation.
Dihedral angle (torsional angle)
The angle formed between two bonds on adjacent atoms when viewed along the axis of the bond connecting those atoms. It measures how far one group has been rotated relative to another.
Think of it as: the angle you see between the front and back substituents when you look straight down the carbon-carbon bond, like peering through a tube.
Sigma bond (σ bond)
A covalent bond formed by head-on overlap of atomic orbitals, with electron density concentrated along the internuclear axis. Rotation around sigma bonds is relatively free because the orbital overlap is symmetrical.
In simple terms, this means: sigma bonds are the "single bonds" you draw as a line between two atoms, and they can rotate without breaking.
Wedge bond
In a line-angle formula, a solid triangular wedge indicates a bond that projects out of the plane of the paper towards the viewer. The bond points toward you in the widening direction of the wedge.
Dash bond (hatched bond)
In a line-angle formula, a dashed or hatched wedge indicates a bond that projects behind the plane of the paper, away from the viewer. The bond recedes away from you in the widening direction.
Line-angle formula (skeletal structure)
A shorthand way of drawing organic molecules where carbon-carbon bonds are shown as lines at angles, carbon atoms are implied at vertices and endpoints, and hydrogen atoms on carbon are omitted. Wedges and dashes are added to show 3D arrangement.
Think of it as: the stick-figure version of a molecule, with 3D clues added through wedge and dash notation.
Many molecules can adopt dynamically variable shapes.
The shape at any instant is defined by three things:
Bond angles (the angle between two bonds at an atom)
Bond lengths (the distance between bonded nuclei)
Angles of rotation around sigma bonds
Of these three, rotation around sigma bonds is the one that changes continuously at room temperature. Bond angles and bond lengths stay roughly constant.
Different spatial arrangements produced by rotation about a single bond are called conformations (or conformers).
The specific angle of rotation is called the torsional angle or dihedral angle.
Conformations are not isomers. You do not break any bonds to get from one conformation to another; you only rotate around a sigma bond.
At room temperature, molecules rotate through many conformations very rapidly (billions of times per second for a simple molecule like ethane).
The core challenge: molecules are three-dimensional, but paper and screens are flat. Several conventions solve this.
Wedge-and-Dash Notation (in Line-Angle Formulas)
Solid wedge: the bond comes out of the page towards you. The wide end of the wedge is the atom closer to you.
Hatched (dashed) wedge: the bond goes into the page away from you. The wide end of the dashes is the atom further from you.
Plain line: the bond lies in the plane of the paper.
All three bond types can appear on the same atom simultaneously to show its full 3D arrangement.
Example from the notes: ethane (C₂H₆) drawn with wedges and dashes on each carbon to show the tetrahedral arrangement of hydrogen atoms around each carbon.
Wedge-dash drawing of ethane (C₂H₆)
The source notes show two views of ethane using wedge-dash notation. Each carbon has four bonds arranged tetrahedrally: one C–C bond in the plane, one C–H bond in the plane, one C–H on a wedge (towards viewer), and one C–H on a dash (away from viewer).
Key point: when you draw the wedge-dash structure of ethane, both carbons show the same pattern of one wedge, one dash, and one in-plane hydrogen, connected by the C–C sigma bond in the plane.
Dihedral angle convention
The dihedral angle is measured as the angle between a bond on the front carbon and a bond on the back carbon when you sight along the C–C axis. Values range from 0° (eclipsed, bonds aligned) to 180° (anti, bonds directly opposite).
Drug design depends heavily on molecular conformation. A drug molecule must fit into an enzyme's active site in a specific 3D shape, so pharmaceutical chemists need to know which conformations a molecule prefers and how easily it can rotate into the required shape.
Protein folding is, at its core, a conformational problem. The backbone of every protein is a chain of sigma bonds whose dihedral angles determine whether the chain folds into a functional shape or a misfolded one.
Students often think conformations are different molecules. They are not. Conformations are the same molecule in different rotational poses. No bonds are broken or formed.
Students often confuse rotation around sigma bonds with rotation around pi bonds. Pi bonds (double bonds) do not allow free rotation because it would break the sideways orbital overlap. Only sigma bonds rotate freely.
Students often draw the wedge bond backwards, with the thin end pointing at the viewer. The wide end of the wedge is always the end closest to you.
Students sometimes assume that a molecule sits in one fixed conformation. In reality, molecules at room temperature rotate through many conformations constantly.
⚠️ You will almost certainly be asked to draw wedge-dash structures and identify which bonds come toward or away from the viewer.
⚠️ Expect questions that require you to identify whether two drawings represent the same conformation or different conformations of the same molecule.
⚠️ The distinction between conformation and configuration (which requires bond breaking to interconvert) is a classic exam question. Know the difference cold.
⚠️ Dihedral angle terminology (torsional angle, eclipsed, staggered, gauche, anti) appears in nearly every conformational analysis problem set and exam.
True or False: Conformations are different molecules. (False: same molecule, different rotational arrangements.)
Fill in the blank: The angle of rotation around a sigma bond is called the ______ angle. (dihedral / torsional)
True or False: A solid wedge bond points away from the viewer. (False: a solid wedge points towards the viewer.)
True or False: Double bonds (pi bonds) allow free rotation just like single bonds. (False: only single / sigma bonds allow free rotation.)
Fill in the blank: A plain line in a wedge-dash drawing means the bond is in the ______ of the paper. (plane)
Q: What is a conformation, and how does it differ from a constitutional isomer?
A: A conformation is a spatial arrangement of atoms that results from rotation about a sigma bond. No bonds are broken or formed. A constitutional isomer has a different connectivity of atoms entirely, requiring bond breaking and forming to interconvert.
Q: In a wedge-dash drawing, you see a solid triangle on one bond and a hatched triangle on another, both attached to the same carbon. Describe the spatial relationship of these two bonds.
A: The solid-wedge bond projects out of the plane of the paper towards the viewer. The hatched bond projects behind the plane of the paper away from the viewer. Together with bonds drawn as plain lines (in the plane), they represent the tetrahedral geometry around that carbon.
Q: Why can molecules rotate freely around sigma bonds but not around pi bonds?
A: Sigma bonds have cylindrical symmetry of electron density around the bond axis, so rotation does not disrupt the orbital overlap. Pi bonds depend on sideways overlap of p orbitals; rotating 90° around the bond axis would completely break the pi overlap, which costs significant energy.
Q: A molecule of ethane is drawn with all hydrogen atoms in the plane of the paper. Is this an accurate 3D representation? Explain.
A: No. Each carbon in ethane has four bonds arranged tetrahedrally. Drawing all hydrogens in the plane implies a flat arrangement. An accurate representation uses wedges and dashes to show that some hydrogens point towards the viewer and others point away.
Q: Define the dihedral angle and explain how it is measured.
A: The dihedral angle is the angle between a bond on one atom and a bond on an adjacent atom, measured by looking along the bond connecting those two atoms. It ranges from 0° (eclipsed, bonds directly aligned) to 180° (anti, bonds directly opposite).
This material connects directly to Newman projections and conformational analysis of ethane and butane, which are typically the next topics in Organic Chemistry I. You will use dihedral angles to evaluate the relative energy of different conformers.
It also lays the groundwork for stereochemistry (chirality, R/S configuration, optical activity), where the 3D arrangement of atoms determines whether molecules are mirror images of each other.
Wedge-dash notation will reappear in nearly every reaction mechanism you draw for the rest of the course, particularly in substitution (SN1/SN2) and elimination (E1/E2) reactions where the geometry of approach matters.
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