| Tetrahedral molecular geometry | |
|---|---|
 | |
| Examples | CH4,MnO− 4 |
| Point group | Td |
| Coordination number | 4 |
| Bond angle(s) | ≈ 109.5° |
| μ (Polarity) | 0 |
In atetrahedral molecular geometry, a centralatom is located at the center with foursubstituents that are located at the corners of atetrahedron. Thebond angles arearccos(−1/3) = 109.4712206...° ≈ 109.5° when all four substituents are the same, as inmethane (CH4)[1][2] as well asits heavier analogues. Methane and other perfectly symmetrical tetrahedral molecules belong topoint groupTd, but most tetrahedral molecules havelower symmetry. Tetrahedral molecules can bechiral.
The bond angle for a symmetric tetrahedral molecule such as CH4 may be calculated using thedot product of twovectors. As shown in the diagram at left, the molecule can be inscribed in a cube with the tetravalent atom (e.g.carbon) 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 vectorsa = (1, –1, 1) andb = (1, 1, –1), and the bond angleθ is the angle between these two vectors. This angle may be calculated from the dot product of the two vectors, defined asa ⋅b = ‖a‖ ‖b‖ cosθ where‖a‖ denotes thelength of vectora. As shown in the diagram, the dot product here is –1 and the length of each vector is√3, so thatcosθ = –1/3 and the tetrahedral bond angleθ =arccos(–1/3) ≃ 109.47°.
An alternative proof usingtrigonometry is shown in the diagram at right.
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 inxenon tetroxide (XeO4), theperchlorate ion (ClO−4), thesulfate ion (SO2−4), thephosphate ion (PO3−4).Thiazyl trifluoride (SNF3) is tetrahedral, featuring a sulfur-to-nitrogen triple bond.[3]
Other molecules have a tetrahedral arrangement of electron pairs around a central atom; for exampleammonia (NH3) with the nitrogen atom surrounded by three hydrogens and onelone pair. However the usual classification considers only the bonded atoms and not the lone pair, so that ammonia is actually considered aspyramidal. The H–N–H angles are 107°, contracted from 109.5°. This difference is attributed to the influence of the lone pair which gives a greater repulsive influence than a bonded atom.[citation needed]
Again the geometry is widespread, particularly so for complexes where the metal has d0 or d10 configuration. Illustrative examples includetetrakis(triphenylphosphine)palladium(0) (Pd[P(C6H5)3]4),nickel carbonyl (Ni(CO)4), andtitanium tetrachloride (TiCl4). Many complexes with incompletely filled d-shells are often tetrahedral, e.g. the tetrahalides of iron(II), cobalt(II), and nickel(II).
In the gas phase, a single water molecule has an oxygen atom surrounded by two hydrogens and two lone pairs, and theH2O geometry is simply described asbent without considering thenonbonding lone pairs.[citation needed]
However, in liquid water or in ice, the lone pairs formhydrogen 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.[4]
Many compounds and complexes adopt bitetrahedral structures. In this motif, the two tetrahedra share a common edge. The inorganic polymersilicon disulfide features an infinite chain of edge-shared tetrahedra.
Inversion of tetrahedra occurs widely in organic and main group chemistry. TheWalden inversion illustrates the stereochemical consequences of inversion at carbon.Nitrogen inversion in ammonia also entails transient formation of planarNH3.
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.[5] The carbon atom lies at or near the apex of a squarepyramid with the other four groups at the corners.[6][7]
The simplest examples of organic molecules displaying inverted tetrahedral geometry are the smallestpropellanes, such as[1.1.1]propellane; or more generally thepaddlanes,[8] andpyramidane ([3.3.3.3]fenestrane).[6][7] Such molecules are typicallystrained, resulting in increased reactivity.
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 thefenestranes.[citation needed]
A few molecules have a tetrahedral geometry with no central atom. An inorganic example istetraphosphorus (P4) which has four phosphorus atoms at the vertices of a tetrahedron and each bonded to the other three. An organic example istetrahedrane (C4H4) 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 tobent bonds), representing a large degree of strain.[citation needed]
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