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, ...
is located at the center with four
substituents 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 th ...
. 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 on Ea ...
() as well as
its heavier analogues. Methane and other perfectly symmetrical tetrahedral molecules belong to
point group T
d, 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 CH
4 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 alge ...
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 mak ...
) 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 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
Xenon tetroxide is a chemical compound of xenon and oxygen with molecular formula XeO4, remarkable for being a relatively stable compound of a noble gas. It is a yellow crystalline solid that is stable below −35.9 ° C; above that temperat ...
(XeO
4), 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. Per ...
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
Thiazyl trifluoride is a chemical compound of nitrogen, sulfur, and fluorine, having the formula . It exists as a stable, colourless gas, and is an important precursor to other sulfur-nitrogen-fluorine compounds. It has tetrahedral molecular geome ...
() 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 wa ...
() with the nitrogen atom surrounded by three hydrogens and one
lone pair. 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 d
0 or d
10 configuration. Illustrative examples include
tetrakis(triphenylphosphine)palladium(0)
Tetrakis(triphenylphosphine)palladium(0) (sometimes called quatrotriphenylphosphine palladium) is the chemical compound d(P(C6H5)3)4 often abbreviated Pd( PPh3)4, or rarely PdP4. It is a bright yellow crystalline solid that becomes brown upon de ...
(),
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 bonds 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 features an infinite chain of edge-shared tetrahedra. In a completely saturated hydrocarbon system, bitetrahedral molecule C
8H
6 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 passi ...
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, quadrilat ...
with the other four groups at the corners.
[
:
The simplest examples of organic molecules displaying inverted tetrahedral geometry are the smallest propellanes, such as ropellane">.1.1ropellane; or more generally the paddlanes,] 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 () 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 bonds), representing a large degree of strain.
See also
*AXE method
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 theo ...
* Orbital hybridisation
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