Geometries (No Lone Pairs)

Valence Shell Electron Pair Repulsion (VSEPR) theory is a powerful model used by chemists to predict the three-dimensional geometry of molecules based on the number of electron pairs surrounding a central atom. The fundamental principle is simple: electron pairs — whether bonding or lone pairs — repel each other and arrange themselves to minimize repulsion, thereby achieving the most stable spatial configuration. When a central atom has no lone pairs, the geometry of the molecule is determined entirely by the number of bonding pairs (or groups of atoms bonded to it), and these cases produce the most symmetrical and predictable shapes. Understanding molecular geometry is critical because the shape of a molecule directly influences its physical and chemical properties, including polarity, reactivity, boiling point, and biological activity. For example, the linear geometry of carbon dioxide ( $\ce{CO2}$ ) makes it a nonpolar molecule despite having polar bonds, while the tetrahedral geometry of methane ( $\ce{CH4}$ ) gives it perfect symmetry. By mastering VSEPR for molecules with no lone pairs, students build the conceptual foundation needed to understand more complex molecules with lone pairs, expanded octets, and unusual bonding environments. There are five fundamental molecular geometries that arise when a central atom has no lone pairs: linear (2 bonding groups), trigonal planar (3 bonding groups), tetrahedral (4 bonding groups), trigonal bipyramidal (5 bonding groups), and octahedral (6 bonding groups). Each geometry has a specific bond angle associated with it, determined by the mathematics of equal repulsion in three-dimensional space. In this article, we examine each geometry in detail, with worked examples, bond angles, and real molecular models to cement your understanding.

Key takeaways

Linear — 2 Bonding Groups (AX₂)
Trigonal Planar — 3 Bonding Groups (AX₃)
Tetrahedral — 4 Bonding Groups (AX₄)
Trigonal Bipyramidal — 5 Bonding Groups (AX₅)
Octahedral — 6 Bonding Groups (AX₆)

Linear — 2 Bonding Groups (AX₂)

When a central atom is bonded to exactly 2 atoms with no lone pairs, the two bonding pairs repel each other maximally by arranging themselves 180° apart, producing a linear geometry. Classic examples include carbon dioxide ( $\ce{CO2}$ ) and beryllium chloride ( $\ce{BeCl2}$ ). In $\ce{CO2}$ , carbon forms two double bonds with oxygen atoms, and VSEPR treats each double bond as a single electron group. Bond angle: 180°.

Trigonal Planar — 3 Bonding Groups (AX₃)

With 3 bonding groups and no lone pairs, electron groups arrange in a flat triangular pattern, all in the same plane, separated by 120°. This minimizes repulsion perfectly in two dimensions. Examples include boron trifluoride ( $\ce{BF3}$ ) and formaldehyde ( $\ce{CH2O}$ , where the C=O counts as one group). The molecule and all atoms lie in a single plane. Bond angle: 120°.

Tetrahedral — 4 Bonding Groups (AX₄)

Four bonding groups extend symmetrically into three-dimensional space, pointing toward the corners of a tetrahedron. This is the most commonly encountered geometry in organic chemistry — methane ( $\ce{CH4}$ ), silicon tetrachloride ( $\ce{SiCl4}$ ), and ammonium ion ( $\ce{NH4+}$ ) all adopt tetrahedral geometry. The bond angles of exactly 109.5° arise from the geometry of a regular tetrahedron inscribed in a sphere. Bond angle: 109.5°.

Trigonal Bipyramidal — 5 Bonding Groups (AX₅)

Five bonding groups produce a geometry with two distinct types of positions: three equatorial positions in a central plane (separated by 120°) and two axial positions above and below the plane (90° from equatorial bonds). Phosphorus pentachloride ( $\ce{PCl5}$ ) is the textbook example. Axial and equatorial positions are not equivalent — axial bonds experience more repulsion from equatorial neighbors. Bond angles: 120° (equatorial–equatorial) and 90° (axial–equatorial).

Octahedral — 6 Bonding Groups (AX₆)

Six bonding groups arrange at the corners of a regular octahedron, with all bond angles of 90°. Sulfur hexafluoride ( $\ce{SF6}$ ) is the prime example. All six positions are equivalent due to the molecule's perfect symmetry. This geometry also appears in many transition metal complexes in coordination chemistry. The central atom in $\ce{SF6}$ uses an expanded octet, accommodating 12 electrons in its valence shell — possible for third-period and higher elements with available d orbitals. Bond angle: 90°.

The Key Equation

\text{Steric Number} = (\text{number of atoms bonded to central atom}) + (\text{number of lone pairs on central atom})

SN — Steric Number (dimensionless): Determines the electron geometry and, when no lone pairs are present, the molecular geometry as well.
X — Bonded Atoms (count): Number of atoms (or groups) directly bonded to the central atom; each counts as one electron group regardless of bond order.
E — Lone Pairs (count): Number of non-bonding electron pairs on the central atom; zero for all geometries discussed in this article.

Worked Example

Problem. Determine the molecular geometry and bond angles of sulfur hexafluoride, $\ce{SF6}$ . Draw the Lewis structure, calculate the steric number, and identify the geometry.

\ce{SF6}: \text{Octahedral}, \angle F\text{-}S\text{-}F = 90^\circ

Answer. Octahedral geometry with all bond angles equal to 90°.

Figure

Diagram

Origins · 1 minRonald Gillespie and how this was discovered

Ronald Gillespie

1924–2021 · British-Canadian

Ronald Gillespie, alongside Ronald Nyholm, developed and popularized VSEPR theory in 1957. Building on earlier ideas by Nevil Sidgwick and Herbert Powell, Gillespie systematized the model into the clear, predictive framework taught in chemistry classrooms worldwide today. He spent most of his career at McMaster University in Canada and authored numerous influential textbooks on molecular geometry and the nature of the chemical bond. Gillespie continued actively publishing papers on VSEPR theory and chemical bonding well into his 90s, believing that even 'simple' models like VSEPR still had unexplored depths worth investigating.

VSEPR Theory: Geometries with Lone Pairs — The next step after mastering no-lone-pair geometries — lone pairs compress bond angles and distort molecular shapes, producing bent, see-saw, T-shaped, and square pyramidal geometries.
Lewis Structures — Drawing accurate Lewis structures is the essential first step before applying VSEPR theory to determine electron and molecular geometry.
Molecular Polarity and Dipole Moments — Molecular geometry directly determines whether a molecule is polar or nonpolar — symmetric geometries like tetrahedral and octahedral can be nonpolar even with polar bonds.
Orbital Hybridization (sp, sp², sp³) — Hybridization theory complements VSEPR: linear molecules correspond to sp hybridization, trigonal planar to sp², and tetrahedral to sp³ hybridization of the central atom.