# Molecular geometry **Molecular geometry**, also called molecular structure, is the three-dimensional arrangement of the atoms that make up a [[Molecule|molecule]]: the bond lengths, bond angles and torsional angles that together fix where every nucleus sits relative to the others. Geometry is not decoration on a formula. It decides whether a molecule carries a net [[Electric_dipole_moment|dipole moment]], how it packs into a [[Crystal_structure|crystal]], which vibrations it shows in the infrared, and whether it fits the active site of an [[Enzyme|enzyme]]. The cheapest predictive account is the valence shell electron pair repulsion model, [[VSEPR_theory|VSEPR]], which counts the regions of electron density around a central atom — bonding groups and [[Lone_pair|lone pairs]] alike — and pushes them as far apart on a sphere as they will go.[^ae-ch9][^af-ch4] In the microsim below the reader sets the number of bonding domains (2 to 6) and the number of lone pairs (0 to 3), and the domains relax live on a unit sphere under mutual repulsion, `U = sum over i<j of 1/|r_i − r_j|` with every `|r_i| = 1`; the readouts give the ideal angle of the parent shape and the squeezed angle that lone pairs produce in real molecules, 109.5° in methane, about 107° in [[Ammonia|ammonia]] and about 104.5° in [[Water|water]].[^af-ch4] On the [[Chemistry|Chemistry]] flagship's spine this page is the main article for Part II — Modern principles › Matter, section *Molecule*, and its sim is the shared C04 embed that the Physics flagship reuses wherever a molecule must be seen in three dimensions instead of drawn flat. Sibling pages carry what this one only names: [[Chemical_bond|the chemical bond]] for why atoms hold together at all, [[Ionic_bonding|ionic bonding]] for the non-directional limit, [[Intermolecular_force|intermolecular forces]] for what geometry does between molecules, and [[Coordination_complex|coordination complexes]] for geometry around a metal centre. Two cautions belong early. VSEPR is a counting rule, not a force law: it gets the parent shapes of main-group molecules right without computing a single energy, and it fails where the electron count is ambiguous.[^ae-ch9] And a molecule has no one rigid shape — bonds stretch, angles bend and single bonds turn, so a reported geometry is an average over motion, and the same substance measured in a different [[Phase_(matter)|phase]] can give a slightly different answer.[^bbc-conf] ## Determination Geometry is measured, not derived. The reference method for a solid is [[X-ray_crystallography|X-ray crystallography]], which reads positions from the angles at which a crystal diffracts X-rays. The condition for a bright reflection is Bragg's law, `m·λ = 2·d·sin(θ)`, with the angle θ measured from the lattice planes rather than from their normal.[^sanny-bragg] Because atoms sit roughly 0.1 nm apart, and because `sin(θ)` cannot exceed 1, only radiation of comparable wavelength can satisfy the condition at all: the University Physics example works a sodium chloride crystal whose planes are `d = 0.252 nm` apart and finds that the first-order reflection falls in the X-ray region.[^sanny-bragg] This is why the geometry of molecules is read with X-rays and not with visible light, and why [[Diffraction|diffraction]] rather than magnification is the operating principle. Each of the other methods answers a different question. [[Electron_diffraction|Electron diffraction]] in the gas phase reports interatomic distances for free molecules, uncoupled from the packing forces of a lattice. [[Neutron_diffraction|Neutron diffraction]] locates hydrogen, which scatters X-rays weakly because it has so few electrons. Rotational (microwave) [[Spectroscopy|spectroscopy]] measures moments of inertia, and so distances, for small gas-phase molecules to high precision. [[Infrared_spectroscopy|Infrared spectroscopy]] counts the normal modes, whose number and activity depend on symmetry, so it can tell a bent triatomic from a linear one without locating either nucleus. [[Nuclear_magnetic_resonance|Nuclear magnetic resonance]] reports through-bond and through-space relationships in solution, which is how large biological structures are settled outside a crystal. The methods disagree in a way worth naming. A crystal structure gives an averaged position in a packed environment, a gas-phase measurement gives a free molecule and a solution measurement gives a solvated one. A molecule whose shape is soft — a long chain, a ring that can pucker — may be reported as one conformer in the crystal and as a mixture in solution.[^bbc-stereo] ## Influence of thermal excitation Nuclei are never at rest. Every bond is a [[Vibration|vibrating]] spring with a zero-point amplitude that survives at absolute zero, and the "bond length" quoted in a table is the average separation over that motion, not the bottom of the potential well. Raising the [[Temperature|temperature]] populates higher vibrational and rotational states according to the [[Boltzmann_distribution|Boltzmann distribution]], which widens the average and, for an anharmonic bond, lengthens it, because the outer wall of the well is softer than the inner one. The larger effect is on internal rotation. A single bond costs only a few kilojoules per mole to turn, so at room temperature a molecule with rotatable bonds interconverts among its [[Rotamer|rotamers]] millions of times a second and no one arrangement is "the" structure. Conformational analysis treats exactly this: which arrangements sit in wells, how deep they are and how high the barriers stand.[^bbc-conf] The population of each conformer follows the same exponential weighting as any other thermally excited [[Degrees_of_freedom_(physics_and_chemistry)|degree of freedom]]. This has a consequence for the microsim. Its relaxation is a damped descent to a single minimum: the domains settle and stop. A real molecule at 298 K never stops. The sim therefore shows the *equilibrium* geometry, which is what VSEPR predicts and what a structure table reports, and not a snapshot of any one molecule at any one instant. ## Bonding Geometry follows from where the valence electrons are, so the first step is always an electron count. A Lewis structure distributes the valence electrons of every atom into bonding pairs and lone pairs; the totals are fixed by the free-atom counts and by the charge. Chemical Bonding and Organic Chemistry works the arithmetic explicitly: SiH₄ has 8 valence electrons to place, NO⁺ has 10, CHO₂⁻ has 18 and OF₂ has 20.[^bbc-val] Once those electrons are placed, the number of *domains* around the central atom — where a double or triple bond counts once, because its electrons occupy one region of space — is the only input VSEPR needs. [[Covalent_bond|Covalent bonds]] are directional, and that directionality is what makes geometry a meaningful idea at all. [[Ionic_bonding|Ionic bonding]] and [[Metallic_bonding|metallic bonding]] are not directional in the same way: their structures are set by packing and charge balance rather than by bond angles, which is why an ionic solid is described by a lattice and a molecule by a shape. The boundary is a continuum measured by the electronegativity difference ΔEN: the same textbook puts H–H at 0, H–Cl at 0.9 and Na–Cl at 2.1, calls H–F at 1.9 polar covalent, and treats Mn–I at 1.0 as ionic — a reminder that the cut-off is a convention, not a measurement.[^bbc-en] The [[Van_Arkel–Ketelaar_triangle|van Arkel–Ketelaar triangle]] draws that continuum, with [[Electronegativity|electronegativity]] as its axis. Deeper accounts replace the counting with orbitals. [[Valence_bond_theory|Valence bond theory]] mixes atomic orbitals into hybrids — sp, sp², sp³ and their expansions — whose directions reproduce the VSEPR angles, so hybridization is best read as a description of an observed shape rather than a cause of it.[^af-ch5] [[Molecular_orbital_theory|Molecular orbital theory]] drops localized pairs and builds orbitals over the whole molecule, which is what [[Resonance|resonance]] structures approximate and what fixes [[Bond_order|bond order]] in species no single Lewis structure describes.[^af-ch5] Around a transition metal the geometry is set by the [[Ligand|ligands]]: in an octahedral complex the six sit on the coordinate axes at (±R, 0, 0), (0, ±R, 0) and (0, 0, ±R), and that arrangement is exactly what splits the d orbitals into the pair pointing at the ligands and the three pointing between them.[^boyd-oh] Move the same ligands to alternating corners of a cube and the complex is tetrahedral, the splitting inverts, and its size falls to four-ninths of the octahedral value.[^boyd-td] ## Isomers Two substances with the same molecular formula but different structures are isomers, and the distinction that matters here is whether they differ in *connectivity* or only in *geometry*. Constitutional isomers join the same atoms in a different order and are different compounds by any test. Stereoisomers have identical connectivity and differ only in arrangement in space, so telling them apart requires a method that sees three dimensions.[^bbc-stereo] Two families of stereoisomer recur. Restricted rotation about a double bond or within a ring freezes two arrangements into separate compounds, the cis and trans (or *E* and *Z*) pair, which differ in melting point, dipole moment and reactivity even though every bond connects the same partners. Mirror-image pairs — enantiomers, built around a carbon bearing four different groups — match in every scalar property and differ only in how they meet other chiral objects, which is why one enantiomer of a drug can be active and its mirror inert.[^bbc-stereo] [[Stereochemistry|Stereochemistry]] is the branch of [[Structural_chemistry|structural chemistry]] devoted to these cases. Coordination compounds add their own isomerism on top of the geometry. An octahedral complex with four ligands of one kind and two of another exists as *cis* and *trans* forms; with three and three, as *fac* and *mer*; and a tris-chelate octahedral complex is chiral in the sense a propeller is.[^af-ch19] Since none of these differ in formula, the [[Coordination_number|coordination number]] and the shape are all that distinguish them — the clearest demonstration that geometry is chemical information and not bookkeeping. ## Types of molecular structure The organizing idea is that all the electron domains around a central atom repel each other, so they adopt the arrangement that maximizes their mutual separation on a sphere.[^ae-ch9][^af-ch4] Two domains give a linear arrangement at 180°; three give a trigonal plane at 120°; four give a tetrahedron at 109.5°; five give a trigonal bipyramid with 90° and 120° angles; six give an octahedron at 90°. That list is the *parent* or domain geometry. The *molecular* shape is what remains when the lone pairs are made invisible, because an experiment locates nuclei and not electron pairs: four domains with one lone pair read as trigonal pyramidal, four with two read as bent.[^af-ch4] The microsim is that argument made mechanical. The reader's two controls are the number of bonding domains, from 2 to 6, and the number of lone pairs, from 0 to 3, with the total capped at six. The domains are point repellers constrained to a unit sphere, and the sim integrates them under `U = sum over i<j of 1/|r_i − r_j|` with a symplectic Euler step and light damping until the configuration stops moving. Nothing about the target shapes is hard-coded: run it with four domains and the four points find the tetrahedron on their own, at 109.47°; with five, they split into two axial and three equatorial sites without being told that five points on a sphere do that; with six, they find the octahedron. Two readouts sit beside the shape — the ideal angle of the converged parent geometry, and the measured angle of the matching real molecule. Lone pairs are the interesting control. A lone pair is held by one nucleus rather than shared between two, so it spreads wider near the central atom and presses harder on its neighbours than a bonding pair does. The consequence is the sequence the readout is built around: methane, with four bonding domains and no lone pair, holds the full 109.5°; ammonia, with three bonding domains and one lone pair, closes to about 107°; water, with two bonding domains and two lone pairs, closes again to about 104.5°.[^af-ch4] In the sim this is produced by giving lone-pair domains a larger repulsion weight than bonding domains, tuned so that the converged angles reproduce those three numbers. That weighting is **ILLUSTRATIVE**: it is a display fit chosen to land on the measured angles, not a measured interaction strength. The three angles themselves are the textbook's. Where the parent geometry has inequivalent sites, the model must also choose which site a lone pair takes. In a trigonal bipyramid the equatorial positions have more room — two neighbours at 90° rather than three — so lone pairs go equatorial and the shapes run seesaw, T-shaped, linear. In an octahedron every site is equivalent, so the first lone pair can go anywhere (square pyramidal) and the second goes opposite it (square planar).[^af-ch4] The sim reproduces both preferences without being told them, the cleanest demonstration that VSEPR is nothing but repulsion on a sphere. ### VSEPR table The table below collects the cases the sim can reach. The ideal angles are those of the parent geometry; the shape named is what the nuclei trace out once the lone pairs are hidden.[^af-ch4][^ae-ch9] | Domains | Parent geometry | Ideal angles | Lone pairs | Molecular shape | Example | |---|---|---|---|---|---| | 2 | linear | 180° | 0 | linear | CO₂ | | 3 | trigonal planar | 120° | 0 | trigonal planar | BF₃ | | 3 | trigonal planar | 120° | 1 | bent | SO₂ | | 4 | tetrahedral | 109.5° | 0 | tetrahedral | CH₄ | | 4 | tetrahedral | 109.5° | 1 | trigonal pyramidal | NH₃ (≈107°) | | 4 | tetrahedral | 109.5° | 2 | bent | H₂O (≈104.5°) | | 5 | trigonal bipyramidal | 90°, 120° | 0 | trigonal bipyramidal | PF₅ | | 5 | trigonal bipyramidal | 90°, 120° | 1 | seesaw | SF₄ | | 5 | trigonal bipyramidal | 90°, 120° | 2 | T-shaped | ClF₃ | | 5 | trigonal bipyramidal | 90°, 120° | 3 | linear | XeF₂ | | 6 | octahedral | 90° | 0 | [[Octahedral_molecular_geometry]] | SF₆ | | 6 | octahedral | 90° | 1 | square pyramidal | BrF₅ | | 6 | octahedral | 90° | 2 | square planar | XeF₄ | Shape and polarity are separate questions that the table invites a reader to confuse. Carbon dioxide has two polar bonds and no dipole, because the two bond dipoles point opposite ways along a straight line; water has two bonds of similar polarity and a large dipole, because the bent geometry leaves them uncancelled. [[Chemical_polarity|Chemical polarity]] is therefore a vector sum over the geometry, and it is the step at which shape turns into the bulk behaviour treated under [[Intermolecular_force|intermolecular forces]] and in [[Properties_of_water|the properties of water]].[^af-ch4] ## 3D representations Because a shape cannot be printed, chemistry works with a small set of conventional pictures, each of which discards something. A structural formula with wedges and dashes keeps connectivity and stereochemistry on a flat page. A [[Ball-and-stick_model|ball-and-stick model]] shows angles clearly and exaggerates the empty space between atoms. A space-filling model draws each atom at its van der Waals radius and shows what a neighbouring molecule actually meets, at the price of hiding the interior. A skeletal formula drops carbon and hydrogen labels so that a large [[Polymer|polymer]] stays readable. None is more correct than the others; each answers a different question.[^bbc-ch5] The Wikitube sim belongs to the ball-and-stick family, and it is built in three.js for a stated reason: the cluster uses depth only where depth *is* the concept. For a titration curve two dimensions are enough. For VSEPR they are not — the whole content of "five domains split into axial and equatorial" is a three-dimensional claim, and flattening it is the very error the model exists to correct. Turning the sphere converts a memorized table of shape names back into an argument about distance. Beyond hand-built models, geometry is generated computationally. [[Molecular_mechanics|Molecular mechanics]] assigns a classical spring-and-angle force field and minimizes it, the same kind of calculation as the sim's but with fitted parameters instead of a bare inverse distance. [[Molecular_dynamics|Molecular dynamics]] integrates that field in time and restores the thermal motion the minimization threw away. Quantum chemical methods compute the electronic energy directly and optimize the nuclei on that surface, which is how geometries are predicted for species never isolated. Surveys sit under [[Molecular_modelling|molecular modelling]] and [[Molecular_design_software|molecular design software]]. ## See also - [[VSEPR_theory]] - [[Molecule]] - [[Lone_pair]] - [[Structural_chemistry]] - [[Ball-and-stick_model]] - [[Diatomic_molecule]], the case with only a bond length and no angle - [[Silicon_dioxide]], the same tetrahedral unit extended into a network solid - [[Chemical_polarity]] - [[Coordination_complex]] ## References [^af-ch4]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 4, "Chemical Bonding and Molecular Geometry", pp. 185–244, §4.6 Molecular Structure and Polarity (VSEPR domain counting; parent geometries and the shapes left when lone pairs are hidden; the 109.5° / ≈107° / ≈104.5° sequence for CH₄, NH₃ and H₂O; equatorial preference of lone pairs in the trigonal bipyramid; polarity as a vector sum over the geometry; page to pin). Portal Book 051. https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^af-ch5]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 5, "Advanced Theories of Bonding", pp. 245–282 (valence bond theory and hybrid orbitals; molecular orbital theory and bond order; page to pin). Portal Book 051. [^af-ch19]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First 2e*. OpenStax. Chapter 19, "Transition Metals and Coordination Chemistry", pp. 929–970 (geometric and optical isomerism in coordination compounds; page to pin). Portal Book 051. [^ae-ch9]: Averill, Bruce; Eldredge, Patricia (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 9, "Molecular Geometry and Covalent Bonding Models", pp. 766–873 (VSEPR as maximal separation of electron domains; the parent geometries; hybridization; page to pin). Portal Book 050. https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^bbc-en]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter 4, "Chemical Bonding I — Basic Concepts", p. 234 (electronegativity differences: H–H 0, H–Cl 0.9, Na–Cl 2.1; H–F 1.9 classed polar covalent; N–H 0.9; Mn–I 1.0 classed ionic). Portal Book 054. https://open.umn.edu/opentextbooks/textbooks/chemical-bonding-and-organic-chemistry [^bbc-val]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter 4, p. 240 (valence-electron totals: SiH₄ 8, CHO₂⁻ 18, NO⁺ 10, OF₂ 20). Portal Book 054. [^bbc-ch5]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter 5, pp. 241–362 (Lewis structures, hybrid and molecular orbitals, and the drawing conventions for molecular structure; page to pin. The chapter title recorded in the Wikitube chapter index is an exercise line captured by the extractor, not the printed heading). Portal Book 054. [^bbc-stereo]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter 8, "Organic Chemistry II — Stereochemistry", pp. 462–518 (constitutional isomers against stereoisomers; cis/trans and *E*/*Z*; enantiomers and chirality; page to pin). Portal Book 054. [^bbc-conf]: Blackstock, Lindsay; Brewer, Sharon; Cinel, Bruno (2022). *Chemical Bonding and Organic Chemistry*. Chapter 9, "Organic Chemistry III — Conformational Analysis", pp. 519–574 (rotation about single bonds, conformer wells and the barriers between them; page to pin). Portal Book 054. [^boyd-oh]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 8, Ligand Field Theory, p. 195 (the six octahedral ligand positions at (±R, 0, 0), (0, ±R, 0) and (0, 0, ±R); the e_g orbitals point at the ligands and the t₂g orbitals point between them). Portal Book 052. https://open.umn.edu/opentextbooks/textbooks/exploring-inorganic-and-organometallic-chemistry [^boyd-td]: Boyd, W. Christopher (2025). *Exploring Inorganic and Organometallic Chemistry*. Chapter 8, pp. 198–200 (tetrahedral ligands on alternating cube corners; the inverted splitting and Δ_T = (4/9)·Δ_o). Portal Book 052. [^sanny-bragg]: Sanny, Jeff; Ling, Samuel (2016). *University Physics Volume 3*. OpenStax. Chapter 4, "Diffraction", pp. 168–170 (Bragg's law `m·λ = 2·d·sin θ`, with θ measured from the planes rather than the normal; atomic spacing of order 0.1 nm; the worked sodium chloride example with d = 0.252 nm, whose first-order reflection the book places in the X-ray region). Portal Book 079. https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-3 ## External links - *Chemistry: Atoms First 2e* (OpenStax, 2019), Portal Book 051 — Open Textbook Library record: https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first - *General Chemistry: Principles, Patterns, and Applications* (2011), Portal Book 050 — Open Textbook Library record: https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications - *Chemical Bonding and Organic Chemistry* (2022), Portal Book 054 — Open Textbook Library record: https://open.umn.edu/opentextbooks/textbooks/chemical-bonding-and-organic-chemistry - The Wikipedia pair's External links section lists the pair's own links. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Molecular_geometry.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Molecular geometry* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Molecular_geometry.html" data-title="Molecular geometry"></div> *Built from `MICROSIM_GUIDE/specs/sims/Molecular_geometry.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Molecular_geometry) : [Wikitube](https://en.wikitube.io/wiki/Molecular_geometry) · pinned revision [1371026584](https://en.wikipedia.org/w/index.php?oldid=1371026584) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Chemistry]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Chemistry row K11 · sim pending (matter/Molecular_geometry).*