Zirconium

From Wikipedia, the free encyclopedia

Zirconium,  ₄₀Zr

Zirconium
Pronunciation	/zərˈkoʊniəm/ ​(zər-KOH-nee-əm)
Appearance	silvery white
Standard atomic weight Ar, std(Zr)	91.224(2)
Zirconium in the periodic table
Hydrogen Helium Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon Sodium Magnesium Aluminium Silicon Phosphorus Sulfur Chlorine Argon Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon Caesium Barium Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury (element) Thallium Lead Bismuth Polonium Astatine Radon Francium Radium Actinium Thorium Protactinium Uranium Neptunium Plutonium Americium Curium Berkelium Californium Einsteinium Fermium Mendelevium Nobelium Lawrencium Rutherfordium Dubnium Seaborgium Bohrium Hassium Meitnerium Darmstadtium Roentgenium Copernicium Nihonium Flerovium Moscovium Livermorium Tennessine Oganesson Ti ↑ Zr ↓ Hf yttrium ← zirconium → niobium
Atomic number (Z)	40
Group	group 4
Period	period 5
Block	d-block
Element category	transition metal
Electron configuration	[Kr] 4d2 5s2
Electrons per shell	2, 8, 18, 10, 2
Physical properties
Phase at STP	solid
Melting point	2128 K ​(1855 °C, ​3371 °F)
Boiling point	4650 K ​(4377 °C, ​7911 °F)
Density (near r.t.)	6.52 g/cm3
when liquid (at m.p.)	5.8 g/cm3
Heat of fusion	14 kJ/mol
Heat of vaporization	591 kJ/mol
Molar heat capacity	25.36 J/(mol·K)
Vapor pressure P (Pa) 1 10 100 1 k 10 k 100 k at T (K) 2639 2891 3197 3575 4053 4678
Atomic properties
Oxidation states	−2, +1, +2, +3, +4 (an amphoteric oxide)
Electronegativity	Pauling scale: 1.33
Ionization energies	1st: 640.1 kJ/mol 2nd: 1270 kJ/mol 3rd: 2218 kJ/mol
Atomic radius	empirical: 160 pm
Covalent radius	175±7 pm
Spectral lines of zirconium
Other properties
Natural occurrence	primordial
Crystal structure	​hexagonal close-packed (hcp)
Speed of sound thin rod	3800 m/s (at 20 °C)
Thermal expansion	5.7 µm/(m·K) (at 25 °C)
Thermal conductivity	22.6 W/(m·K)
Electrical resistivity	421 nΩ·m (at 20 °C)
Magnetic ordering	paramagnetic
Young's modulus	88 GPa
Shear modulus	33 GPa
Bulk modulus	91.1 GPa
Poisson ratio	0.34
Mohs hardness	5.0
Vickers hardness	820–1800 MPa
Brinell hardness	638–1880 MPa
CAS Number	7440-67-7
History
Naming	after zircon, zargun زرگون meaning "gold-colored".
Discovery	Martin Heinrich Klaproth (1789)
First isolation	Jöns Jakob Berzelius (1824)
Main isotopes of zirconium
Iso­tope Abun­dance Half-life (t1/2) Decay mode Pro­duct 88Zr syn 83.4 d ε 88Y γ – 89Zr syn 78.4 h ε 89Y β+ 89Y γ – 90Zr 51.45% stable 91Zr 11.22% stable 92Zr 17.15% stable 93Zr trace 1.53×106 y β− 93Nb 94Zr 17.38% stable 96Zr 2.80% 2.0×1019 y[4] β−β− 96Mo

Zirconium is a chemical element with symbol Zr and atomic number 40. The name zirconium is taken from the name of the mineral zircon (the word is related to Persian zargun (zircon;zar-gun, "gold-like" or "as gold")), the most important source of zirconium. It is a lustrous, grey-white, strong transition metal that closely resembles hafnium and, to a lesser extent, titanium. Zirconium is mainly used as a refractory and opacifier, although small amounts are used as an alloying agent for its strong resistance to corrosion. Zirconium forms a variety of inorganic and organometallic compounds such as zirconium dioxide and zirconocene dichloride, respectively. Five isotopes occur naturally, three of which are stable. Zirconium compounds have no known biological role.

Characteristics

Zirconium rod

 

Zirconium is a lustrous, greyish-white, soft, ductile, malleable metal that is solid at room temperature, though it is hard and brittle at lesser purities. In powder form, zirconium is highly flammable, but the solid form is much less prone to ignition. Zirconium is highly resistant to corrosion by alkalis, acids, salt water and other agents. However, it will dissolve in hydrochloric and sulfuric acid, especially when fluorine is present. Alloys with zinc are magnetic at less than 35 K.

The melting point of zirconium is 1855 °C (3371 °F), and the boiling point is 4371 °C (7900 °F). Zirconium has an electronegativity of 1.33 on the Pauling scale. Of the elements within the d-block with known electronegativities, zirconium has the fifth lowest electronegativity after hafnium, yttrium, lanthanum, and actinium.

At room temperature zirconium exhibits a hexagonally close-packed crystal structure, α-Zr, which changes to β-Zr, a body-centered cubic crystal structure, at 863 °C. Zirconium exists in the β-phase until the melting point.

Isotopes

Naturally occurring zirconium is composed of five isotopes. ⁹⁰Zr, ⁹¹Zr, ⁹²Zr and ⁹⁴Zr are stable, although ⁹⁴Zr is predicted to undergo double beta decay (not observed experimentally) with a half-life of more than 1.10×10¹⁷ years. ⁹⁶Zr has a half-life of 2.4×10¹⁹ years, and is the longest-lived radioisotope of zirconium. Of these natural isotopes, ⁹⁰Zr is the most common, making up 51.45% of all zirconium. ⁹⁶Zr is the least common, comprising only 2.80% of zirconium.

Twenty-eight artificial isotopes of zirconium have been synthesized, ranging in atomic mass from 78 to 110. ⁹³Zr is the longest-lived artificial isotope, with a half-life of 1.53×10⁶ years. ¹¹⁰Zr, the heaviest isotope of zirconium, is the most radioactive, with an estimated half-life of 30 milliseconds. Radioactive isotopes at or above mass number 93 decay by electron emission, whereas those at or below 89 decay by positron emission. The only exception is ⁸⁸Zr, which decays by electron capture.

Five isotopes of zirconium also exist as metastable isomers: ^83mZr, ^85mZr, ^89mZr, ^90m1Zr, ^90m2Zr and ^91mZr. Of these, ^90m2Zr has the shortest half-life at 131 nanoseconds. ^89mZr is the longest lived with a half-life of 4.161 minutes.

Occurrence

World production trend of zirconium mineral concentrates

 

Zirconium has a concentration of about 130 mg/kg within the Earth's crust and about 0.026 μg/L in sea water. It is not found in nature as a native metal, reflecting its intrinsic instability with respect to water. The principal commercial source of zirconium is zircon (ZrSiO₄), a silicate mineral, which is found primarily in Australia, Brazil, India, Russia, South Africa and the United States, as well as in smaller deposits around the world. As of 2013, two-thirds of zircon mining occurs in Australia and South Africa. Zircon resources exceed 60 million tonnes worldwide and annual worldwide zirconium production is approximately 900,000 tonnes. Zirconium also occurs in more than 140 other minerals, including the commercially useful ores baddeleyite and kosnarite.

Zirconium is relatively abundant in S-type stars, and it has been detected in the sun and in meteorites. Lunar rock samples brought back from several Apollo missions to the moon have a high zirconium oxide content relative to terrestrial rocks.

Production

Zirconium output in 2005

 

Zirconium is a by-product of the mining and processing of the titanium minerals ilmenite and rutile, as well as tin mining. From 2003 to 2007, while prices for the mineral zircon steadily increased from $360 to $840 per tonne, the price for unwrought zirconium metal decreased from $39,900 to $22,700 per ton. Zirconium metal is much higher priced than zircon because the reduction processes are expensive.

Collected from coastal waters, zircon-bearing sand is purified by spiral concentrators to remove lighter materials, which are then returned to the water because they are natural components of beach sand. Using magnetic separation, the titanium ores ilmenite and rutile are removed. 

Most zircon is used directly in commercial applications, but a small percentage is converted to the metal. Most Zr metal is produced by the reduction of the zirconium(IV) chloride with magnesium metal in the Kroll process. The resulting metal is sintered until sufficiently ductile for metalworking.

Separation of zirconium and hafnium

Commercial zirconium metal typically contains 1–3% of hafnium, which is usually not problematic because the chemical properties of hafnium and zirconium are very similar. Their neutron-absorbing properties differ strongly, however, necessitating the separation of hafnium from zirconium for nuclear reactors. Several separation schemes are in use. The liquid-liquid extraction of the thiocyanate-oxide derivatives exploits the fact that the hafnium derivative is slightly more soluble in methyl isobutyl ketone than in water. This method is used mainly in United States. 

Zr and Hf can also be separated by fractional crystallization of potassium hexafluorozirconate (K₂ZrF₆), which is less soluble in water than the analogous hafnium derivative. 

Fractional distillation of the tetrachlorides, also called extractive distillation, is used primarily in Europe. 

The product of a quadruple VAM (vacuum arc melting) process, combined with hot extruding and different rolling applications is cured using high-pressure, high-temperature gas autoclaving. This produces reactor-grade zirconium that is about 10 times more expensive than the hafnium-contaminated commercial grade. 

Hafnium must be removed from zirconium for nuclear applications because hafnium has a neutron absorption cross-section 600 times greater than zirconium. The separated hafnium can be used for reactor control rods.

Compounds

Like other transition metals, zirconium forms a wide range of inorganic compounds and coordination complexes. In general, these compounds are colourless diamagnetic solids wherein zirconium has the oxidation state +4. Far fewer Zr(III) compounds are known, and Zr(II) is very rare.

Oxides, nitrides, and carbides

The most common oxide is zirconium dioxide, ZrO₂, also known as zirconia. This clear to white-coloured solid has exceptional fracture toughness and chemical resistance, especially in its cubic form. These properties make zirconia useful as a thermal barrier coating, although it is also a common diamond substitute. Zirconium monoxide, ZrO, is also known and S-type stars are recognised by detection of its emission lines in the visual spectrum.

Zirconium tungstate has the unusual property of shrinking in all dimensions when heated, whereas most other substances expand when heated. Zirconyl chloride is a rare water-soluble zirconium complex with the relatively complicated formula [Zr₄(OH)₁₂(H₂O)₁₆]Cl₈. 

Zirconium carbide and zirconium nitride are refractory solids. The carbide is used for drilling tools and cutting edges. Zirconium hydride phases are also known. 

Lead zirconate titanate (PZT) is the most commonly used piezoelectric material, with applications such as ultrasonic transducers, hydrophones, common rail injectors, piezoelectric transformers and micro-actuators.

Halides and pseudohalides

All four common halides are known, ZrF₄, ZrCl₄, ZrBr₄, and ZrI₄. All have polymeric structures and are far less volatile than the corresponding monomeric titanium tetrahalides. All tend to hydrolyse to give the so-called oxyhalides and dioxides.

The corresponding tetraalkoxides are also known. Unlike the halides, the alkoxides dissolve in nonpolar solvents. Dihydrogen hexafluorozirconate is used in the metal finishing industry as an etching agent to promote paint adhesion.

Organic derivatives

Zirconocene dichloride, a representative organozirconium compound

 

Organozirconium chemistry is the study of compounds containing a carbon-zirconium bond. The first such compound was zirconocene dibromide ((C₅H₅)₂ZrBr₂), reported in 1952 by Birmingham and Wilkinson. Schwartz's reagent, prepared in 1970 by P. C. Wailes and H. Weigold, is a metallocene used in organic synthesis for transformations of alkenes and alkynes.

Zirconium is also a component of some Ziegler–Natta catalysts, used to produce polypropylene. This application exploits the ability of zirconium to reversibly form bonds to carbon. Most complexes of Zr(II) are derivatives of zirconocene, one example being (C₅Me₅)₂Zr(CO)₂.

History

The zirconium-containing mineral zircon and related minerals (jargoon, hyacinth, jacinth, ligure) were mentioned in biblical writings. The mineral was not known to contain a new element until 1789, when Klaproth analyzed a jargoon from the island of Ceylon (now Sri Lanka). He named the new element Zirkonerde (zirconia). Humphry Davy attempted to isolate this new element in 1808 through electrolysis, but failed. Zirconium metal was first obtained in an impure form in 1824 by Berzelius by heating a mixture of potassium and potassium zirconium fluoride in an iron tube.

The crystal bar process (also known as the Iodide Process), discovered by Anton Eduard van Arkel and Jan Hendrik de Boer in 1925, was the first industrial process for the commercial production of metallic zirconium. It involves the formation and subsequent thermal decomposition of zirconium tetraiodide, and was superseded in 1945 by the much cheaper Kroll process developed by William Justin Kroll, in which zirconium tetrachloride is reduced by magnesium:

ZrCl₄ + 2 Mg → Zr + 2 MgCl₂

Applications

Approximately 900,000 tonnes of zirconium ores were mined in 1995, mostly as zircon.

Compounds

Most zircon is used directly in high-temperature applications. This material is refractory, hard, and resistant to chemical attack. Because of these properties, zircon finds many applications, few of which are highly publicized. Its main use is as an opacifier, conferring a white, opaque appearance to ceramic materials. Because of its chemical resistance, zircon is also used in aggressive environments, such as moulds for molten metals.

Zirconium dioxide (ZrO₂) is used in laboratory crucibles, in metallurgical furnaces, and as a refractory material. Because it is mechanically strong and flexible, it can be sintered into ceramic knives and other blades. Zircon (ZrSiO₄) and the cubic zirconia (ZrO₂) are cut into gemstones for use in jewelry. 

Zirconia is a component in some abrasives, such as grinding wheels and sandpaper.

Metal

A small fraction of the zircon is converted to the metal, which finds various niche applications. Because of zirconium's excellent resistance to corrosion, it is often used as an alloying agent in materials that are exposed to aggressive environments, such as surgical appliances, light filaments, and watch cases. The high reactivity of zirconium with oxygen at high temperatures is exploited in some specialised applications such as explosive primers and as getters in vacuum tubes. The same property is (probably) the purpose of including Zr nano-particles as pyrophoric material in explosive weapons such as the BLU-97/B Combined Effects Bomb. Burning zirconium was used as a light source in some photographic flashbulbs. Zirconium powder with a mesh size from 10 to 80 is occasionally used in pyrotechnic compositions to generate sparks. The high reacitivity of zirconium leads to bright white sparks.

Nuclear applications

Cladding for nuclear reactor fuels consumes about 1% of the zirconium supply, mainly in the form of zircaloys. The desired properties of these alloys are a low neutron-capture cross-section and resistance to corrosion under normal service conditions. Efficient methods for removing the hafnium impurities were developed to serve this purpose.

One disadvantage of zirconium alloys is that zirconium reacts with water at high temperatures, producing hydrogen gas and accelerated degradation of the fuel rod cladding:

Zr + 2 H₂O → ZrO₂ + 2 H₂

This exothermic reaction is very slow below 100 °C, but at temperature above 900 °C the reaction is rapid. Most metals undergo similar reactions. The redox reaction is relevant to the instability of fuel assemblies at high temperatures. This reaction was responsible for a small hydrogen explosion first observed inside the reactor building of Three Mile Island nuclear power plant in 1979, but at that time, the containment building was not damaged. The same reaction occurred in the reactors 1, 2 and 3 of the Fukushima I Nuclear Power Plant (Japan) after the reactor cooling was interrupted by the earthquake and tsunami disaster of March 11, 2011, leading to the Fukushima I nuclear accidents. After venting the hydrogen in the maintenance hall of those three reactors, the mixture of hydrogen with atmospheric oxygen exploded, severely damaging the installations and at least one of the containment buildings. To avoid explosion, the direct venting of hydrogen to the open atmosphere would have been a preferred design option. Now, to prevent the risk of explosion in many pressurized water reactor (PWR) containment buildings, a catalyst-based recombiner is installed that converts hydrogen and oxygen into water at room temperature before the hazard arises.

Space and aeronautic industries

Materials fabricated from zirconium metal and ZrO₂ are used in space vehicles where resistance to heat is needed.

High temperature parts such as combustors, blades, and vanes in jet engines and stationary gas turbines are increasingly being protected by thin ceramic layers, usually composed of a mixture of zirconia and yttria.

Positron emission tomography cameras

The isotope ⁸⁹Zr has been applied to the tracking and quantification of molecular antibodies with positron emission tomography (PET) cameras (a method called "immuno-PET"). Immuno-PET has reached a maturity of technical development and is now entering the phase of wide-scale clinical applications. Until recently, radiolabeling with ⁸⁹Zr was a complicated procedure requiring multiple steps. In 2001–2003 an improved multistep procedure was developed using a succinylated derivative of desferrioxamine B (N-sucDf) as a bifunctional chelate, and a better way of binding ⁸⁹Zr to mAbs was reported in 2009. The new method is fast, consists of only two steps, and uses two widely available ingredients: ⁸⁹Zr and the appropriate chelate. On-going developments also include the use of siderophore derivatives to bind ⁸⁹Zr(IV).

Biomedical applications

Zirconium-bearing compounds are used in many biomedical applications, including dental implants and crowns, knee and hip replacements, middle-ear ossicular chain reconstruction, and other restorative and prosthetic devices.

Zirconium binds urea, a property that has been utilized extensively to the benefit of patients with chronic kidney disease. For example, zirconium is a primary component of the sorbent column dependent dialysate regeneration and recirculation system known as the REDY system, which was first introduced in 1973. More than 2,000,000 dialysis treatments have been performed using the sorbent column in the REDY system. Although the REDY system was superseded in the 1990s by less expensive alternatives, new sorbent-based dialysis systems are being evaluated and approved by the U.S. Food and Drug Administration (FDA). Renal Solutions developed the DIALISORB technology, a portable, low water dialysis system. Also, developmental versions of a Wearable Artificial Kidney have incorporated sorbent-based technologies.

Sodium zirconium cyclosilicate is under investigation for oral therapy in the treatment of hyperkalemia. It is a highly selective oral sorbent designed specifically to trap potassium ions in preference to other ions throughout the gastrointestinal tract.

A mixture of monomeric and polymeric Zr⁴⁺ and Al³⁺ complexes with hydroxide, chloride and glycine, called Aluminium zirconium tetrachlorohydrex gly or AZG, is used in a preparation as an antiperspirant in many deodorant products. It is selected for its ability to obstruct pores in the skin and prevent sweat from leaving the body.

Defunct applications

Zirconium carbonate (3ZrO₂·CO₂·H₂O) was used in lotions to treat poison ivy but was discontinued because it occasionally caused skin reactions.

Safety

Zirconium

Hazards
GHS signal word	Not listed as hazardous
NFPA 704	1 0 0

Although zirconium has no known biological role, the human body contains, on average, 250 milligrams of zirconium, and daily intake is approximately 4.15 milligrams (3.5 milligrams from food and 0.65 milligrams from water), depending on dietary habits. Zirconium is widely distributed in nature and is found in all biological systems, for example: 2.86 μg/g in whole wheat, 3.09 μg/g in brown rice, 0.55 μg/g in spinach, 1.23 μg/g in eggs, and 0.86 μg/g in ground beef. Further, zirconium is commonly used in commercial products (e.g. deodorant sticks, aerosol antiperspirants) and also in water purification (e.g. control of phosphorus pollution, bacteria- and pyrogen-contaminated water).

Short-term exposure to zirconium powder can cause irritation, but only contact with the eyes requires medical attention. Persistent exposure to zirconium tetrachloride results in increased mortality in rats and guinea pigs and a decrease of blood hemoglobin and red blood cells in dogs. However, in a study of 20 rats given a standard diet containing ~4% zirconium oxide, there were no adverse effects on growth rate, blood and urine parameters, or mortality. The U.S. Occupational Safety and Health Administration (OSHA) legal limit (permissible exposure limit) for zirconium exposure is 5 mg/m³ over an 8-hour workday. The National Institute for Occupational Safety and Health (NIOSH) recommended exposure limit (REL) is 5 mg/m³ over an 8-hour workday and a short term limit of 10 mg/m³. At levels of 25 mg/m³, zirconium is immediately dangerous to life and health. However, zirconium is not considered an industrial health hazard. Furthermore, reports of zirconium-related adverse reactions are rare and, in general, rigorous cause-and-effect relationships have not been established. No evidence has been validated that zirconium is carcinogenic or genotoxic.

Among the numerous radioactive isotopes of zirconium, ⁹³Zr is among the most common. It is released as a product of ²³⁵U, mainly in nuclear plants and during nuclear weapons tests in the 1950s and 1960s. It has a very long half-life (1.53 million years), its decay emits only low energy radiations, and it is not considered as highly hazardous.

(Valence Shell Electron Pair Repulsion) VSEPR theory

From Wikipedia, the free encyclopedia

Example of bent electron arrangement. Shows location of unpaired electrons, bonded atoms, and bond angles. (Water molecule) The bond angle for water is 104.5°.

 

Valence shell electron pair repulsion (VSEPR) theory is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It is also named the Gillespie-Nyholm theory after its two main developers, Ronald Gillespie and Ronald Nyholm. The acronym "VSEPR" is pronounced either "ves-pur" or "vuh-seh-per".

The premise of VSEPR is that the valence electron pairs surrounding an atom tend to repel each other and will, therefore, adopt an arrangement that minimizes this repulsion, thus determining the molecule's geometry. Gillespie has emphasized that the electron-electron repulsion due to the Pauli exclusion principle is more important in determining molecular geometry than the electrostatic repulsion.

VSEPR theory is based on observable electron density rather than mathematical wave functions and hence unrelated to orbital hybridisation, although both address molecular shape. While it is mainly qualitative, VSEPR has a quantitative basis in quantum chemical topology (QCT) methods such as the electron localization function (ELF) and the quantum theory of atoms in molecules (QTAIM).

History

The idea of a correlation between molecular geometry and number of valence electron pairs (both shared and unshared pairs) was originally proposed in 1939 by Ryutaro Tsuchida in Japan, and was independently presented in a Bakerian Lecture in 1940 by Nevil Sidgwick and Herbert Powell of the University of Oxford. In 1957, Ronald Gillespie and Ronald Sydney Nyholm of University College London refined this concept into a more detailed theory, capable of choosing between various alternative geometries.

In recent years, VSEPR theory has been criticized as an outdated model from the standpoint of both scientific accuracy and pedagogical value. In particular, the equivalent lone pairs of water and carbonyl compounds in VSEPR theory neglect fundamental differences in the symmetries (σ vs. π) of molecular orbitals and natural bond orbitals that correspond to them, a difference that is sometimes chemically significant. Furthermore, there is little evidence, computational or experimental, proposing that lone pairs are "bigger" than bonding pairs. It has been suggested that Bent's rule is capable of replacing VSEPR as a simple model for explaining molecular structure. Nevertheless, VSEPR theory captures many of the essential features of the structure and electron distribution of simple molecules, and most undergraduate general chemistry courses continue to teach it.

Overview

VSEPR theory is used to predict the arrangement of electron pairs around non-hydrogen atoms in molecules, especially simple and symmetric molecules, where these key, central atoms participate in bonding to two or more other atoms; the geometry of these key atoms and their non-bonding electron pairs in turn determine the geometry of the larger whole.

The number of electron pairs in the valence shell of a central atom is determined after drawing the Lewis structure of the molecule, and expanding it to show all bonding groups and lone pairs of electrons. In VSEPR theory, a double bond or triple bond are treated as a single bonding group. The sum of the number of atoms bonded to a central atom and the number of lone pairs formed by its nonbonding valence electrons is known as the central atom's steric number. 

The electron pairs (or groups if multiple bonds are present) are assumed to lie on the surface of a sphere centered on the central atom and tend to occupy positions that minimize their mutual repulsions by maximizing the distance between them. The number of electron pairs (or groups), therefore, determines the overall geometry that they will adopt. For example, when there are two electron pairs surrounding the central atom, their mutual repulsion is minimal when they lie at opposite poles of the sphere. Therefore, the central atom is predicted to adopt a linear geometry. If there are 3 electron pairs surrounding the central atom, their repulsion is minimized by placing them at the vertices of an equilateral triangle centered on the atom. Therefore, the predicted geometry is trigonal. Likewise, for 4 electron pairs, the optimal arrangement is tetrahedral.

Degree of repulsion

The overall geometry is further refined by distinguishing between bonding and nonbonding electron pairs. The bonding electron pair shared in a sigma bond with an adjacent atom lies further from the central atom than a nonbonding (lone) pair of that atom, which is held close to its positively charged nucleus. VSEPR theory therefore views repulsion by the lone pair to be greater than the repulsion by a bonding pair. As such, when a molecule has 2 interactions with different degrees of repulsion, VSEPR theory predicts the structure where lone pairs occupy positions that allow them to experience less repulsion. Lone pair–lone pair (lp–lp) repulsions are considered stronger than lone pair–bonding pair (lp–bp) repulsions, which in turn are considered stronger than bonding pair–bonding pair (bp–bp) repulsions, distinctions that then guide decisions about overall geometry when 2 or more non-equivalent positions are possible. For instance, when 5 valence electron pairs surround a central atom, they adopt a trigonal bipyramidal molecular geometry with two collinear axial positions and three equatorial positions. An electron pair in an axial position has three close equatorial neighbors only 90° away and a fourth much farther at 180°, while an equatorial electron pair has only two adjacent pairs at 90° and two at 120°. The repulsion from the close neighbors at 90° is more important, so that the axial positions experience more repulsion than the equatorial positions; hence, when there are lone pairs, they tend to occupy equatorial positions as shown in the diagrams of the next section for steric number five.

The difference between lone pairs and bonding pairs may also be used to rationalize deviations from idealized geometries. For example, the H₂O molecule has four electron pairs in its valence shell: two lone pairs and two bond pairs. The four electron pairs are spread so as to point roughly towards the apices of a tetrahedron. However, the bond angle between the two O–H bonds is only 104.5°, rather than the 109.5° of a regular tetrahedron, because the two lone pairs (whose density or probability envelopes lie closer to the oxygen nucleus) exert a greater mutual repulsion than the two bond pairs.

An advanced-level explanation replaces the above distinction with two rules:

• Bent's rule: An electron pair of a more electropositive ligand constitutes greater repulsion. This explains why the Cl in PClF₄ prefers the equatorial position and why the bond angle in oxygen difluoride (103.8°) is smaller than that of water (104.5°). Lone pairs are then considered to be a special case of this rule, held by a "ghost ligand" in the limit of electropositivity.
• A higher bond order constitutes greater repulsion. This explains why in phosgene, the oxygen–chlorine bond angle (124.1°) is larger than the chlorine–chlorine bond angle (111.8°) even though chlorine is more electropositive than oxygen. In the carbonate ion, all three bond angles are equivalent due to resonance.

AXE method

The "AXE method" of electron counting is commonly used when applying the VSEPR theory. The electron pairs around a central atom are represented by a formula AX_nE_m, where A represents the central atom and always has an implied subscript one. Each X represents a ligand (an atom bonded to A). Each E represents a lone pair of electrons on the central atom. The total number of X and E is known as the steric number. For example in a molecule AX₃E₂, the atom A has a steric number of 5. 

Based on the steric number and distribution of Xs and Es, VSEPR theory makes the predictions in the following tables. Note that the geometries are named according to the atomic positions only and not the electron arrangement. For example, the description of AX₂E₁ as a bent molecule means that the three atoms AX₂ are not in one straight line, although the lone pair helps to determine the geometry.

Molecule type	Shape	Electron arrangement including lone pairs, shown in pale yellow	Geometry excluding lone pairs	Examples
AX2E0	Linear			BeCl2, HgCl2, CO2
AX2E1	Bent			NO− 2, SO2, O3, CCl2
AX2E2	Bent			H2O, OF2
AX2E3	Linear			XeF2, XeCl2
AX3E0	Trigonal planar			BF3, CO2− 3, NO− 3, SO3
AX3E1	Trigonal pyramidal			NH3, PCl3
AX3E2	T-shaped			ClF3, BrF3
AX4E0	Tetrahedral			CH4, PO3− 4, SO2− 4, ClO− 4, XeO4
AX4E1	Seesaw or disphenoidal			SF4
AX4E2	Square planar			XeF4
AX5E0	Trigonal bipyramidal			PCl5
AX5E1	Square pyramidal			ClF5, BrF5, XeOF4
AX5E2	Pentagonal planar			XeF− 5
AX6E0	Octahedral			SF6, WCl6
AX6E1	Pentagonal pyramidal			XeOF− 5, IOF2− 5
AX7E0	Pentagonal bipyramidal			IF7
AX8E0	Square antiprismatic[11]			IF− 8, ZrF4− 8, ReF− 8
AX9E0	Tricapped trigonal prismatic			ReH2− 9

When the substituent (X) atoms are not all the same, the geometry is still approximately valid, but the bond angles may be slightly different from the ones where all the outside atoms are the same. For example, the double-bond carbons in alkenes like C₂H₄ are AX₃E₀, but the bond angles are not all exactly 120°. Likewise, SOCl₂ is AX₃E₁, but because the X substituents are not identical, the X–A–X angles are not all equal.

As a tool in predicting the geometry adopted with a given number of electron pairs, an often used physical demonstration of the principle of minimal electron pair repulsion utilizes inflated balloons. Through handling, balloons acquire a slight surface electrostatic charge that results in the adoption of roughly the same geometries when they are tied together at their stems as the corresponding number of electron pairs. For example, five balloons tied together adopt the trigonal bipyramidal geometry, just as do the five bonding pairs of a PCl₅ molecule (AX₅) or the two bonding and three non-bonding pairs of a XeF₂ molecule (AX₂E₃). The molecular geometry of the former is also trigonal bipyramidal, whereas that of the latter is linear. 

Possible geometries for steric numbers of 10, 11, 12, or 14 are bicapped square antiprismatic (or bicapped dodecadeltahedral), octadecahedral, icosahedral, and bicapped hexagonal antiprismatic, respectively. No compounds with steric numbers this high involving monodentate ligands exist, and those involving multidentate ligands can often be analysed more simply as complexes with lower steric numbers when some multidentate ligands are treated as a unit.

Examples

The methane molecule (CH₄) is tetrahedral because there are four pairs of electrons. The four hydrogen atoms are positioned at the vertices of a tetrahedron, and the bond angle is cos⁻¹(−​¹⁄₃) ≈ 109° 28′. This is referred to as an AX₄ type of molecule. As mentioned above, A represents the central atom and X represents an outer atom.

The ammonia molecule (NH₃) has three pairs of electrons involved in bonding, but there is a lone pair of electrons on the nitrogen atom. It is not bonded with another atom; however, it influences the overall shape through repulsions. As in methane above, there are four regions of electron density. Therefore, the overall orientation of the regions of electron density is tetrahedral. On the other hand, there are only three outer atoms. This is referred to as an AX₃E type molecule because the lone pair is represented by an E. By definition, the molecular shape or geometry describes the geometric arrangement of the atomic nuclei only, which is trigonal-pyramidal for NH₃.

Steric numbers of 7 or greater are possible, but are less common. The steric number of 7 occurs in iodine heptafluoride (IF₇); the base geometry for a steric number of 7 is pentagonal bipyramidal. The most common geometry for a steric number of 8 is a square antiprismatic geometry. Examples of this include the octacyanomolybdate (Mo(CN)⁴⁻
₈) and octafluorozirconate (ZrF⁴⁻
₈) anions. The nonahydridorhenate ion (ReH²⁻
₉) in potassium nonahydridorhenate is a rare example of a compound with a steric number of 9, which has a tricapped trigonal prismatic geometry.

Exceptions

There are groups of compounds where VSEPR fails to predict the correct geometry.

Some AX₂E₀ molecules

The gas phase structures of the triatomic halides of the heavier members of group 2, (i.e., calcium, strontium and barium halides, MX₂), are not linear as predicted but are bent, (approximate X–M–X angles: CaF₂, 145°; SrF₂, 120°; BaF₂, 108°; SrCl₂, 130°; BaCl₂, 115°; BaBr₂, 115°; BaI₂, 105°). It has been proposed by Gillespie that this is caused by interaction of the ligands with the electron core of the metal atom, polarising it so that the inner shell is not spherically symmetric, thus influencing the molecular geometry. Ab initio calculations have been cited to propose that contributions from d orbitals in the shell below the valence shell are responsible, together with the overlap of other orbitals- Disilynes are also bent, despite having no lone pairs.

Some AX₂E₂ molecules

One example of the AX₂E₂ geometry is molecular lithium oxide, Li₂O, a linear rather than bent structure, which is ascribed to its bonds being essentially ionic and the strong lithium-lithium repulsion that results. Another example is O(SiH₃)₂ with an Si–O–Si angle of 144.1°, which compares to the angles in Cl₂O (110.9°), (CH₃)₂O (111.7°), and N(CH₃)₃ (110.9°). Gillespie and Robinson rationalize the Si–O–Si bond angle based on the observed ability of a ligand's lone pair to most greatly repel other electron pairs when the ligand electronegativity is greater than or equal to that of the central atom. In O(SiH₃)₂, the central atom is more electronegative, and the lone pairs are less localized and more weakly repulsive. The larger Si–O–Si bond angle results from this and strong ligand-ligand repulsion by the relatively large -SiH₃ ligand. Burford et al showed through X-ray diffraction studies that Cl₃Al–O–PCl₃ has a linear Al–O–P bond angle and is therefore a non-VSEPR molecule.

Some AX₆E₁ and AX₈E₁ molecules

Xenon hexafluoride, which has a distorted octahedral geometry.

 

Some AX₆E₁ molecules, e.g. xenon hexafluoride (XeF₆) and the Te(IV) and Bi(III) anions, TeCl²⁻
₆, TeBr²⁻
₆, BiCl³⁻
₆, BiBr³⁻
₆ and BiI³⁻
₆, are octahedra, rather than pentagonal pyramids, and the lone pair does not affect the geometry to the degree predicted by VSEPR. Similarly, the octafluoroxenate ion (XeF²⁻
₈) in nitrosonium octafluoroxenate(VI) is a square antiprism and not a bicapped trigonal prism (as predicted by VSEPR theory for an AX₈E₁ molecule), despite having a lone pair. One rationalization is that steric crowding of the ligands allows little or no room for the non-bonding lone pair; another rationalization is the inert pair effect.

Transition metal molecules

Hexamethyltungsten, a transition metal compound whose geometry is different from main group coordination.

 

Many transition metal compounds have unusual geometries, which can be ascribed to ligand bonding interaction with the d subshell and to absence of valence shell lone pairs. Gillespie suggested that this interaction can be weak or strong. Weak interaction is dealt with by the Kepert model, while strong interaction produces bonding pairs that also occupy the respective antipodal points of the sphere. This is similar to predictions based on sd hybrid orbitals using the VALBOND theory. The repulsion of these bidirectional bonding pairs leads to a different prediction of shapes.

Molecule type	Shape	Geometry	Examples
AX2	Bent		VO+ 2
AX3	Trigonal pyramidal		CrO3
AX4	Tetrahedral		TiCl4
AX5	Square pyramidal		Ta(CH3)5
AX6	C3v Trigonal prismatic		W(CH3)6

The Kepert model cannot explain the formation of square planar complexes.

Odd-electron molecules

The VSEPR theory can be extended to molecules with an odd number of electrons by treating the unpaired electron as a "half electron pair" — for example, Gillespie and Nyholm suggested that the decrease in the bond angle in the series NO⁺
₂ (180°), NO₂ (134°), NO⁻
₂ (115°) indicates that a given set of bonding electron pairs exert a weaker repulsion on a single non-bonding electron than on a pair of non-bonding electrons. In effect, they considered nitrogen dioxide as an AX₂E_0.5 molecule, with a geometry intermediate between NO⁺
₂ and NO⁻
₂. Similarly, chlorine dioxide (ClO₂) is an AX₂E_1.5 molecule, with a geometry intermediate between ClO⁺
₂ and ClO⁻
₂.

Finally, the methyl radical (CH₃) is predicted to be trigonal pyramidal like the methyl anion (CH⁻
₃), but with a larger bond angle (as in the trigonal planar methyl cation (CH⁺
₃)). However, in this case, the VSEPR prediction is not quite true, as CH₃ is actually planar, although its distortion to a pyramidal geometry requires very little energy.