tetrahedral molecular geometry
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In a tetrahedral molecular geometry, a central
atom Every atom is composed of a atomic nucleus, 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, l ...
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 (chemistry), moiety in the resultant (new) molecule. (In organic chemistry and biochemistry, the terms ''substituent'' and ''functional group'' ...
s that are located at the corners of a
tetrahedron In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular Pyramid (geometry), pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex ( ...
. 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 chemi ...
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 Eart ...
() as well as its heavier analogues. Methane and other perfectly symmetrical tetrahedral molecules belong to
point group In geometry, a point group is a group (mathematics), mathematical group of symmetry operations (isometry, isometries in a Euclidean space) that have a Fixed point (mathematics), fixed point in common. The Origin (mathematics), coordinate origin o ...
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 ...
.


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 (mathematics), scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidea ...
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 chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—its atom making four electrons available to form covalent bond, covalent chemical bonds. It belongs to gro ...
) 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 (physical quantity), dimension distance. In most Measurement system, systems of measurement a Base unit (measurement), base unit f ...
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. Per ...
ion (), the
sulfate The sulfate or sulphate ion is a polyatomic ion, 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 salt (chemistry), ...
ion (), the
phosphate In chemistry, a phosphate is an anion, salt (chemistry), salt, functional group or ester derived from a phosphoric acids and phosphates, phosphoric acid. It most commonly means orthophosphate, a derivative of phosphoric acid, orthophosphoric a ...
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 chemical compound, compound of nitrogen and hydrogen with the chemical formula, formula . A Binary compounds of hydrogen, stable binary hydride, and the simplest pnictogen hydride, ammonia is a colourless gas with a dis ...
() 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. Lone ...
. 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 (), and
titanium tetrachloride Titanium tetrachloride is the inorganic compound with the chemical formula, formula . It is an important intermediate in the production of titanium metal and the pigment titanium dioxide. is a Volatility (chemistry), volatile liquid. Upon contac ...
(). 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 Electrostatics, electrostatic force of attraction between a hydrogen (H) atom which is Covalent bond, covalently bound to a more electronegativity, electronegative "donor" atom or group ( ...
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 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 illustrates the stereochemical consequences of inversion at carbon. Nitrogen inversion 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 Nonbuilding structure, structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a Pyramid (geometry), pyramid in the geometric sense. The base o ...
with the other four groups at the corners. : The simplest examples of organic molecules displaying inverted tetrahedral geometry are the smallest propellanes, such as .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 compound, fused carbocycles. They can be regarded as spiro compounds twice over. Because of their ...
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 Phosphorus is a chemical element with the Symbol (chemistry), symbol P and atomic number 15. Elemental phosphorus exists in two major forms, white phosphorus and red phosphorus, but because it is highly Reactivity (chemist ...
() 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 tetrahedron, tetrahedral structure. The molecule would be subject to considerable Ring strain, angle strain and has not been synthesized as of 2021. However, a numb ...
() 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 bond, covalent chemical bond with a geometry somewhat reminiscent of a banana. The term itself is a general representation of electron density or configuratio ...
s), representing a large degree of strain.


See also

*
AXE method Valence shell electron pair repulsion (VSEPR) theory ( , ), is a conceptual model, 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 Gil ...
*
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