VSEPR theory
Valence Shell Electron Pair Repulsion (VSEPR) theory is a fundamental model in chemistry used to predict the three-dimensional molecular geometry of covalently bonded molecules and polyatomic ions by considering the repulsive interactions among electron pairs in the valence shell of the central atom.[1] Developed by Ronald J. Gillespie and Ronald S. Nyholm in their 1957 paper "Inorganic Stereochemistry," the theory builds on earlier ideas from Sidgwick and Powell, refining them into a systematic approach that assumes valence electron pairs—both bonding and lone pairs—arrange themselves to minimize electrostatic repulsion, thereby determining the overall shape of the molecule.[2] This model is particularly effective for main-group elements and provides qualitative predictions without requiring complex quantum mechanical calculations, making it a cornerstone of introductory inorganic and organic chemistry education. At its core, VSEPR theory classifies molecular geometries using the AXE notation, where A represents the central atom, X denotes the number of atoms bonded to it (ligands), and E indicates the number of lone pairs on the central atom. The total number of electron domains (X + E) dictates the electron-pair geometry, which may differ from the molecular geometry if lone pairs are present, as these occupy space but are not visible in the final structure.[1] For instance, with two electron domains, the arrangement is linear (180° bond angle); three domains yield trigonal planar (120°); four domains result in tetrahedral (109.5°); five in trigonal bipyramidal (90° and 120° angles); and six in octahedral (90° angles).[3] Lone pairs exert stronger repulsion than bonding pairs, distorting bond angles—for example, in water (H₂O, AX₂E₂), the bent shape has a bond angle of about 104.5° rather than the ideal 109.5° of tetrahedral electron geometry.[4] While VSEPR excels at explaining geometries for simple molecules like methane (CH₄, tetrahedral) and ammonia (NH₃, trigonal pyramidal), it has limitations, particularly for transition metal complexes, molecules with multiple bonds, or those involving d-orbitals, where hybridization or ligand field effects play larger roles. The theory does not predict bond lengths, strengths, or vibrational frequencies quantitatively and can falter in cases of significant π-bonding or hypervalent molecules, though refinements by Gillespie and others have addressed some exceptions, such as seesaw or T-shaped geometries for five-electron-domain species.[5] Despite these constraints, VSEPR remains widely taught and applied due to its simplicity and accuracy for many common molecular structures.[6]Introduction
Definition and Scope
The Valence Shell Electron Pair Repulsion (VSEPR) theory is a qualitative model in chemistry that predicts the three-dimensional geometry of molecules by considering the arrangement of electron pairs around a central atom. It builds upon Lewis electron dot structures to determine how atoms are spatially oriented in a molecule, focusing on the valence shell of the central atom.[7] The core assumption of VSEPR theory is that the electron pairs—both bonding pairs and lone pairs—in the valence shell of the central atom repel one another due to electrostatic forces, leading to spatial arrangements that minimize these repulsions. This repulsion drives the electron pairs to adopt positions as far apart as possible, thereby defining the overall molecular shape. VSEPR theory primarily applies to compounds involving main-group elements and simple molecular species, where it provides reliable predictions without the need for computational intensity. Its scope extends to coordination compounds, where models like the Kepert extension adapt VSEPR principles to predict geometries around transition metal centers based on ligand electron pair repulsions. Developed in the mid-20th century, VSEPR emerged as an accessible, non-mathematical alternative to quantum mechanical calculations for rationalizing molecular structures.Historical Development
The foundational ideas of what would become VSEPR theory emerged from the work of British chemists Nevil V. Sidgwick and Herbert M. Powell, who in 1940 proposed that the repulsion between electron pairs in the valence shell of a central atom determines the overall shape of simple molecules.[8] In their Bakerian Lecture, they correlated the number of valence electron pairs (ranging from two to six) with geometric arrangements such as linear, trigonal planar, and octahedral structures, providing an early qualitative framework for predicting molecular geometries based on electron pair minimization.[8] This approach built on prior valence concepts but emphasized stereochemical implications without invoking hybridization or detailed orbital interactions.[5] The theory was formalized and refined in 1957 by Ronald J. Gillespie and Ronald S. Nyholm at University College London, who introduced the valence shell electron pair repulsion (VSEPR) model as a systematic predictive tool for inorganic stereochemistry.[7] In their seminal paper "Inorganic Stereochemistry," published in the Quarterly Reviews of the Chemical Society, they expanded on Sidgwick and Powell's ideas by incorporating the differential repulsions between bonding and lone electron pairs, enabling more accurate predictions for a wider range of main-group compounds.[7] This work established VSEPR as a cornerstone of structural inorganic chemistry, emphasizing its simplicity and utility over quantum mechanical calculations at the time.[5] By the 1960s, VSEPR had gained widespread acceptance in chemical education and research, appearing in major inorganic chemistry textbooks that disseminated the model to students and practitioners.[9] For instance, it was integrated into discussions of molecular structure in texts like F. Albert Cotton and Geoffrey Wilkinson's Advanced Inorganic Chemistry (first edition, 1962), reflecting its rapid adoption as a standard teaching tool. In the 1970s, David L. Kepert extended the model to coordination compounds of transition metals, developing the Kepert model to account for ligand repulsions while treating d-electrons as stereochemically inactive, as detailed in his 1972 book The Early Transition Metals.[10] Over subsequent decades, VSEPR's evolution included growing recognition of its limitations, particularly in explaining hypervalent molecules like SF6 or PCl5, where the model predicts expanded octets but struggles with the absence of d-orbital involvement confirmed by modern quantum calculations.[11] Critiques from the 1980s onward highlighted these issues, prompting integrations with molecular orbital (MO) theory to provide a more complete picture of bonding and geometry, such as in hybrid models that combine VSEPR heuristics with MO-derived electron densities.[9] This synthesis has refined VSEPR's role as an introductory predictive method while addressing its empirical shortcomings through computational validation.[11]Core Concepts
Valence Shell Electron Pairs
In VSEPR theory, the valence shell refers to the outermost electron shell of the central atom in a molecule, encompassing the electrons involved in bonding and those remaining as non-bonding pairs. This shell includes bonding electron pairs, which are shared between the central atom and surrounding ligand atoms, and lone pairs, which are localized entirely on the central atom without participation in bonding. These electron pairs collectively dictate the spatial arrangement of atoms by minimizing mutual repulsions within the valence shell.[7] A prerequisite for applying VSEPR theory is the construction of a Lewis structure to identify the bonding and lone pairs around the central atom. The total valence electrons for the molecule are calculated by summing the valence electrons contributed by each atom, based on their positions in the periodic table (e.g., group number for main-group elements). For the central atom, the effective valence electrons include its own contribution plus one electron per monovalent ligand atom (or adjusted for polyatomic ligands and molecular charge), which are then used to form bonds and place lone pairs. The total number of valence electron pairs around the central atom is determined by dividing these total valence electrons by 2, as each pair consists of two electrons. For example, in water (H₂O), oxygen contributes 6 valence electrons, each hydrogen contributes 1, yielding 8 total valence electrons and 4 pairs around oxygen (2 bonding, 2 lone).[12][7] The foundational principle of VSEPR relies on the repulsion among these valence shell electron pairs, which adopt geometries that minimize electrostatic interactions. Lone pairs exert stronger repulsions than bonding pairs because their electron density is more concentrated near the central atom, occupying greater effective volume and causing distortions in bond angles. In contrast, bonding pairs have their electron density delocalized between the central atom and ligands, resulting in less intense repulsions. Multiple bonds, such as double or triple bonds, are treated as a single effective bonding pair in this model, since the sigma bond dominates the spatial repulsion while pi bonds lie in the nodal plane and contribute minimally to the overall geometry. This approach simplifies predictions while capturing the essential steric effects in main-group compounds.[13][7] The sum of bonding and lone pairs, known as the steric number, provides the basis for arranging these pairs in space, though the detailed hierarchy of repulsions is considered separately.[7]Steric Number and Repulsion Strengths
In VSEPR theory, the steric number (SN) of a central atom is defined as the sum of the number of atoms directly bonded to it and the number of lone pairs residing on it, which corresponds to the total count of electron domains surrounding the atom (SN = A + E, where A represents bonded atoms and E represents lone pairs in the AXE classification system). This quantification provides a foundational metric for predicting molecular geometry by assessing the spatial arrangement needed to minimize electron pair repulsions. The concept builds directly on the principles outlined by Gillespie and Nyholm, who emphasized the role of valence electron pairs in dictating stereochemistry.[7][14] Electron domains, or regions of high electron density around the central atom, encompass both bonding pairs and lone pairs; notably, multiple bonds—such as double or triple bonds—are treated as a single domain equivalent to a single bond for repulsion purposes, as the electron density is concentrated in a similar directional lobe. This treatment simplifies the model while capturing the effective spatial occupancy, ensuring that the geometry reflects the overall repulsion dynamics rather than bond multiplicity alone. Gillespie and Nyholm's framework underscores that these domains arrange to achieve the lowest possible energy configuration through mutual repulsion.[7][15] The relative strengths of repulsions between electron domains follow a clear hierarchy: lone pair–lone pair (lp–lp) interactions are the strongest, exerting the greatest force due to the unshared electrons' larger effective volume; lone pair–bonding pair (lp–bp) repulsions are intermediate; and bonding pair–bonding pair (bp–bp) interactions are the weakest, as shared electrons are partially constrained by nuclear attraction from adjacent atoms. This ordering, central to VSEPR predictions, can be visualized through qualitative energy diagrams where lp–lp repulsions elevate the potential energy most significantly, followed by lp–bp, with bp–bp contributing the least distortion. The hierarchy originates from the differential spatial demands of lone versus bonding pairs, as articulated in the foundational VSEPR model.[7][16] The ideal geometries derived from the steric number minimize these repulsions by positioning domains as far apart as possible on the valence shell surface. For SN = 2, the arrangement is linear; for SN = 3, trigonal planar; for SN = 4, tetrahedral; for SN = 5, trigonal bipyramidal; and for SN = 6, octahedral. These configurations represent the baseline electron pair geometries before accounting for lone pair distortions, providing a systematic basis for VSEPR applications across main-group compounds.[7]| Steric Number (SN) | Ideal Electron Pair Geometry |
|---|---|
| 2 | Linear |
| 3 | Trigonal planar |
| 4 | Tetrahedral |
| 5 | Trigonal bipyramidal |
| 6 | Octahedral |
AXE Notation and Geometry Prediction
Notation for Main-Group Elements
The AXE notation provides a systematic way to classify molecules and predict their geometries under the VSEPR theory for compounds of main-group elements, particularly those in the p-block. In this scheme, "A" denotes the central atom, "X" represents each surrounding atom directly bonded to the central atom (often called ligands), and "E" stands for each lone pair of electrons residing on the central atom. This notation simplifies the analysis by focusing on the total number of electron domains around the central atom, treating both bonding pairs and lone pairs as repelling entities.[7] To apply AXE notation, the process begins with constructing the Lewis structure of the molecule, which reveals the central atom, the bonds to surrounding atoms (counted as X), and any non-bonding electron pairs on the central atom (counted as E). The steric number (SN) is then determined as the sum SN = X + E, corresponding to the total electron pairs in the valence shell; this dictates the electron pair geometry, such as linear for SN=2, trigonal planar for SN=3, or octahedral for SN=6. The molecular geometry follows by positioning the X groups around this electron arrangement, with E pairs ideally placed to maximize separation and minimize repulsion, often in less sterically demanding locations. For instance, in cases of higher SN like 5 or 6, lone pairs may preferentially occupy equatorial positions in trigonal bipyramidal or axial/equatorial distinctions in octahedral arrangements due to varying repulsion strengths.[7][17] Common classifications illustrate the notation's utility. Carbon dioxide (CO₂) is AX₂, featuring a central carbon bonded to two oxygens with no lone pairs, yielding a linear molecular geometry with a 180° bond angle. Ammonia (NH₃) is AX₃E, with nitrogen bonded to three hydrogens and one lone pair, resulting in a trigonal pyramidal shape derived from a tetrahedral electron geometry, with H-N-H angles of approximately 107°. Xenon tetrafluoride (XeF₄) exemplifies AX₄E₂, where xenon bonds to four fluorines and has two lone pairs, leading to a square planar molecular geometry from an octahedral electron arrangement, with F-Xe-F angles of 90°. These examples highlight how AXE notation guides predictions for p-block central atoms.[7][7][17] The AXE notation assumes octet adherence or expanded octets without significant d-orbital participation, making it primarily valid for main-group elements in the p-block where valence electrons occupy s and p orbitals. It does not account for cases involving transition metals or substantial d-orbital involvement, which are addressed separately.[7][17]Extension to Transition Metals
The Kepert model, introduced by D. L. Kepert in 1972, adapts VSEPR theory specifically for predicting the coordination geometries of transition metal complexes by considering ligands as the dominant electron domains that generate repulsions.[18] In this framework, the geometry is determined primarily by the coordination number (CN), which equates to the number of ligand attachments (denoted as X in an AXE-type notation, where E=0 due to the negligible stereochemical role of lone pairs on the central metal). This approach treats the metal center as a point from which ligands repel each other to minimize energy, much like electron pairs in standard VSEPR, but it emphasizes the positional arrangement on a spherical surface around the metal.[18] Key differences from VSEPR applications to main-group elements arise because transition metal complexes typically ignore metal-centered lone pairs, concentrating instead on inter-ligand repulsions, which enables higher coordination numbers such as 7–9 that are stabilized by d-orbital participation. The model accommodates variable bond types (ionic or covalent) between metal and ligands, and repulsion strengths follow a similar hierarchy to VSEPR—close approaches between ligands are disfavored—but geometries often exhibit angular distortions influenced by crystal field stabilization energies.[19] Notation is adapted for simplicity, using ML_n to indicate the metal (M) and number of ligands (n = CN), for instance, ML_4 for square planar arrangements common in d^8 configurations like Ni(II) complexes. Illustrative examples highlight the model's predictive power: for CN=6, the octahedral geometry (ML_6) is standard, as in hexaamminecobalt(III) ion, [Co(NH_3)_6]^{3+}, where six equivalent ligands occupy positions to maximize separation at 90° and 180° angles. For certain electronic configurations, such as d^0 or d^{10}, the model predicts trigonal prismatic ML_6 structures over octahedral, exemplified by the layered sulfide MoS_2 (where Mo is effectively six-coordinate to S) or the alkyl complex [Ta(CH_3)_6]^-, due to reduced repulsion in the prismatic arrangement for these cases. The steric number here aligns directly with the coordination number, serving as the basis for these predictions.Molecular Geometries
Basic Shapes and Bond Angles
The Valence Shell Electron Pair Repulsion (VSEPR) theory determines the arrangement of electron pairs around a central atom, leading to specific electron geometries based on the steric number (SN), defined as the total number of bonding pairs and lone pairs in the valence shell. These geometries minimize repulsions between electron pairs, resulting in characteristic ideal bond angles. The basic electron geometries for SN = 2 to 6 are as follows:| Steric Number (SN) | Electron Geometry | Ideal Bond Angles |
|---|---|---|
| 2 | Linear | 180° |
| 3 | Trigonal planar | 120° |
| 4 | Tetrahedral | 109.5° |
| 5 | Trigonal bipyramidal | 90° (axial-equatorial), 120° (equatorial-equatorial), 180° (axial-axial) |
| 6 | Octahedral | 90° (adjacent), 180° (opposite) |
| SN | AXE Notation | Molecular Geometry | Description of 3D Arrangement |
|---|---|---|---|
| 2 | AX2 | Linear | Two atoms aligned opposite the central atom along a straight line. |
| 3 | AX3 | Trigonal planar | Three atoms in a plane, equally spaced around the central atom. |
| AX2E | Bent | Two atoms with a lone pair, forming a V-shape in the plane of the trigonal arrangement. | |
| 4 | AX4 | Tetrahedral | Four atoms at the vertices of a tetrahedron, all equivalent. |
| AX3E | Trigonal pyramidal | Three atoms forming a pyramid with the central atom at the apex. | |
| AX2E2 | Bent | Two atoms with two lone pairs, resulting in an angular structure. | |
| 5 | AX5 | Trigonal bipyramidal | Three equatorial atoms in a plane (120° apart) and two axial atoms perpendicular (90° to equatorial). |
| AX4E | Seesaw | Four atoms: two axial, two equatorial, resembling a seesaw with the central atom as fulcrum. | |
| AX3E2 | T-shaped | Three atoms: two axial and one equatorial, forming a T configuration. | |
| AX2E3 | Linear | Two atoms in axial positions, with three equatorial lone pairs. | |
| 6 | AX6 | Octahedral | Six atoms at the vertices of an octahedron, all equivalent positions. |
| AX5E | Square pyramidal | Five atoms: four basal in a square plane, one apical perpendicular. | |
| AX4E2 | Square planar | Four atoms in a square plane, with lone pairs trans to each other. |