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In a tetrahedral molecular geometry, a central
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...
is located at the center with four
substituent A substituent is one or a group of atoms that replaces (one or more) atoms, thereby becoming a moiety in the resultant (new) molecule. (In organic chemistry and biochemistry, the terms ''substituent'' and ''functional group'', as well as '' side ...
s that are located at the corners of a
tetrahedron In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all ...
. The
bond angle Bond or bonds may refer to: Common meanings * Bond (finance), a type of debt security * Bail bond, a commercial third-party guarantor of surety bonds in the United States * Chemical bond, the attraction of atoms, ions or molecules to form chemical ...
s are cos−1(−) = 109.4712206...° ≈ 109.5° when all four substituents are the same, as in
methane Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane ...
() as well as its heavier analogues. Methane and other perfectly symmetrical tetrahedral molecules belong to
point group In geometry, a point group is a mathematical group of symmetry operations ( isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every ...
Td, but most tetrahedral molecules have lower symmetry. Tetrahedral molecules can be
chiral Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from i ...
.


Tetrahedral bond angle

The bond angle for a symmetric tetrahedral molecule such as CH4 may be calculated using the
dot product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an alg ...
of two vectors. As shown in the diagram, the molecule can be inscribed in a cube with the tetravalent atom (e.g.
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon ma ...
) at the cube centre which is the origin of coordinates, O. The four monovalent atoms (e.g. hydrogens) are at four corners of the cube (A, B, C, D) chosen so that no two atoms are at adjacent corners linked by only one cube edge. If the edge length of the cube is chosen as 2 units, then the two bonds OA and OB correspond to the vectors ''a'' = (1, –1, 1) and ''b'' = (1, 1, –1), and the bond angle θ is the angle between these two vectors. This angle may be calculated from the dot product of the two vectors, defined as ''a'' • ''b'' = , , ''a'', , , , ''b'', , cos θ where , , ''a'', , denotes the
length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Inte ...
of vector ''a''. As shown in the diagram, the dot product here is –1 and the length of each vector is √3, so that cos θ = –1/3 and the tetrahedral bond angle θ = arccos(–1/3) ≃ 109.47°.


Examples


Main group chemistry

Aside from virtually all saturated organic compounds, most compounds of Si, Ge, and Sn are tetrahedral. Often tetrahedral molecules feature multiple bonding to the outer ligands, as in xenon tetroxide (XeO4), the
perchlorate A perchlorate is a chemical compound containing the perchlorate ion, . The majority of perchlorates are commercially produced salts. They are mainly used as oxidizers for pyrotechnic devices and to control static electricity in food packaging. ...
ion (), the
sulfate The sulfate or sulphate ion is a polyatomic anion with the empirical formula . Salts, acid derivatives, and peroxides of sulfate are widely used in industry. Sulfates occur widely in everyday life. Sulfates are salts of sulfuric acid and many ...
ion (), the
phosphate In chemistry, a phosphate is an anion, salt, functional group or ester derived from a phosphoric acid. It most commonly means orthophosphate, a derivative of orthophosphoric acid . The phosphate or orthophosphate ion is derived from phosph ...
ion (). Thiazyl trifluoride () is tetrahedral, featuring a sulfur-to-nitrogen triple bond. Other molecules have a tetrahedral arrangement of electron pairs around a central atom; for example
ammonia Ammonia is an inorganic compound of nitrogen and hydrogen with the formula . A stable binary hydride, and the simplest pnictogen hydride, ammonia is a colourless gas with a distinct pungent smell. Biologically, it is a common nitrogenous ...
() with the nitrogen atom surrounded by three hydrogens and one
lone pair In chemistry, a lone pair refers to a pair of valence electrons that are not shared with another atom in a covalent bondIUPAC '' Gold Book'' definition''lone (electron) pair''/ref> and is sometimes called an unshared pair or non-bonding pair. L ...
. However the usual classification considers only the bonded atoms and not the lone pair, so that ammonia is actually considered as pyramidal. The H–N–H angles are 107°, contracted from 109.5°. This difference is attributed to the influence of the lone pair which exerts a greater repulsive influence than a bonded atom.


Transition metal chemistry

Again the geometry is widespread, particularly so for complexes where the metal has d0 or d10 configuration. Illustrative examples include tetrakis(triphenylphosphine)palladium(0) (),
nickel carbonyl Nickel carbonyl (IUPAC name: tetracarbonylnickel) is a nickel(0) organometallic compound with the formula Ni(CO)4. This colorless liquid is the principal carbonyl of nickel. It is an intermediate in the Mond process for producing very high-pu ...
(), and
titanium tetrachloride Titanium tetrachloride is the inorganic compound with the formula . It is an important intermediate in the production of titanium metal and the pigment titanium dioxide. is a volatile liquid. Upon contact with humid air, it forms thick clouds ...
(). Many complexes with incompletely filled d-shells are often tetrahedral, e.g. the tetrahalides of iron(II), cobalt(II), and nickel(II).


Water structure

In the gas phase, a single water molecule has an oxygen atom surrounded by two hydrogens and two lone pairs, and the geometry is simply described as bent without considering the nonbonding lone pairs. However, in liquid water or in ice, the lone pairs form
hydrogen bond In chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a l ...
s with neighboring water molecules. The most common arrangement of hydrogen atoms around an oxygen is tetrahedral with two hydrogen atoms covalently bonded to oxygen and two attached by hydrogen bonds. Since the hydrogen bonds vary in length many of these water molecules are not symmetrical and form transient irregular tetrahedra between their four associated hydrogen atoms.


Bitetrahedral structures

Many compounds and complexes adopt bitetrahedral structures. In this motif, the two tetrahedra share a common edge. The inorganic polymer
silicon disulfide Silicon disulfide is the inorganic compound with the formula Si S2. Like silicon dioxide, this material is polymeric, but it adopts a 1-dimensional structure quite different from the usual forms of SiO2. Synthesis, structure, and properties Th ...
features an infinite chain of edge-shared tetrahedra. In a completely saturated hydrocarbon system, bitetrahedral molecule C8H6 has been proposed as a candidate for the molecule with the shortest possible carbon-carbon single bond.


Exceptions and distortions

Inversion of tetrahedra occurs widely in organic and main group chemistry. The so-called
Walden inversion Walden inversion is the inversion of a stereogenic center in a chiral molecule in a chemical reaction. Since a molecule can form two enantiomers around a stereogenic center, the Walden inversion converts the configuration of the molecule fro ...
illustrates the stereochemical consequences of inversion at carbon.
Nitrogen inversion In chemistry, pyramidal inversion (also umbrella inversion) is a fluxional process in compounds with a pyramidal molecule, such as ammonia (NH3) "turns inside out". It is a rapid oscillation of the atom and substituents, the molecule or ion pass ...
in ammonia also entails transient formation of planar .


Inverted tetrahedral geometry

Geometrical constraints in a molecule can cause a severe distortion of idealized tetrahedral geometry. In compounds featuring "inverted" tetrahedral geometry at a carbon atom, all four groups attached to this carbon are on one side of a plane. The carbon atom lies at or near the apex of a square
pyramid A pyramid (from el, πυραμίς ') is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilate ...
with the other four groups at the corners. : The simplest examples of organic molecules displaying inverted tetrahedral geometry are the smallest
propellane In organic chemistry, propellane is any member of a class of polycyclic hydrocarbons, whose carbon skeleton consists of three rings of carbon atoms sharing a common carbon–carbon covalent bond. The concept was introduced in 1966 by D. Gin ...
s, such as .1.1ropellane; or more generally the
paddlane In organic chemistry, paddlane is any member of a class of tricyclic saturated hydrocarbons having two bridgehead carbon atoms joined by four bridges. The name derives from a supposed resemblance of the molecule to a paddle wheel: namely, the ri ...
s, and pyramidane ( .3.3.3enestrane). Such molecules are typically strained, resulting in increased reactivity.


Planarization

A tetrahedron can also be distorted by increasing the angle between two of the bonds. In the extreme case, flattening results. For carbon this phenomenon can be observed in a class of compounds called the
fenestrane A fenestrane in organic chemistry is a type of chemical compound with a central quaternary carbon atom which serves as a common vertex for four fused carbocycles. They can be regarded as spiro compounds twice over. Because of their inherent st ...
s.


Tetrahedral molecules with no central atom

A few molecules have a tetrahedral geometry with no central atom. An inorganic example is
tetraphosphorus Elemental phosphorus can exist in several allotropes, the most common of which are white and red solids. Solid violet and black allotropes are also known. Gaseous phosphorus exists as diphosphorus and atomic phosphorus. White phosphorus White ...
() which has four phosphorus atoms at the vertices of a tetrahedron and each bonded to the other three. An organic example is
tetrahedrane Tetrahedrane is a hypothetical platonic hydrocarbon with chemical formula and a tetrahedral structure. The molecule would be subject to considerable angle strain and has not been synthesized as of 2021. However, a number of derivatives have b ...
() with four carbon atoms each bonded to one hydrogen and the other three carbons. In this case the theoretical C−C−C bond angle is just 60° (in practice the angle will be larger due to
bent bond In organic chemistry, a bent bond, also known as a banana bond, is a type of covalent chemical bond with a geometry somewhat reminiscent of a banana. The term itself is a general representation of electron density or configuration resembling a ...
s), representing a large degree of strain.


See also

* AXE method *
Orbital hybridisation In chemistry, orbital hybridisation (or hybridization) is the concept of mixing atomic orbitals to form new ''hybrid orbitals'' (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to f ...


References


External links


Examples of Tetrahedral molecules







3D Chem
– Chemistry, Structures, and 3D Molecules
IUMSC
– Indiana University Molecular Structure Center]
Complex ion geometry: tetrahedral


{{DEFAULTSORT:Tetrahedral Molecular Geometry Molecular geometry