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[[Image:Water molecule dimensions.svg|thumb|200px|Geometry of the [[water (molecule)|water molecule]]]]

'''Molecular geometry''' or '''molecular structure''' is the three-[[dimension]]al arrangement of the [[atoms]] that constitute a [[molecule]], inferred from the [[spectroscopic]] studies of the [[chemical compound|compound]]. It determines several properties of a substance including its [[reactivity]], [[Chemical polarity|polarity]], [[Phase (matter)|phase of matter]], [[color]], [[magnetism]], and [[biological activity]] <ref>{{McMurray}}</ref> <ref>{{Cotton&Wilkinson6th}}</ref>.

Molecular geometries are best determined at [[temperatures]] close to [[absolute zero]] because at higher temperatures the molecules will show considerable rotational motion. In the solid state the molecular geometry can be measured by [[X-ray crystallography]]. Geometries can be computed by [[quantum mechanics|quantum mechanical]] calculations or by semi-empirical [[molecular modeling]]. Larger molecules often exist in multiple stable [[chemical conformation]]s that differ in their molecular geometry and are separated by high hills in the [[potential energy surface]].

The position of each atom is determined by the nature of the [[chemical bond]]s by which it is connected to its neighboring atoms. The molecular geometry can be described by the positions of these atoms in space, evoking [[bond length]]s of two joined atoms, bond angles of three connected atoms, and [[torsion angle]]s of three consecutive bonds.
== The influence of thermal excitation ==
Since the motions of the atoms in a  molecule are determined by quantum mechanics, one
must define “motion” in a quantum mechanical way. The overall (external) quantum mechanical motions translation and rotation hardly change the geometry of the molecule. (To some extent rotation influences
the geometry via [[Coriolis force]]s and [[rotational spectroscopy|centrifugal distortion]], but this is negligible for the present discussion.)
A third type of motion  is vibration, which is the  internal motion of the atoms in a molecule. The molecular vibrations are harmonic (at least to good approximation), which means that the atoms  oscillate about their equilibrium, even at the absolute zero of temperature. At absolute zero all atoms are in their vibrational ground state and show zero point quantum mechanical motion, that is, the wavefunction of a single vibrational mode is not a sharp peak, but an exponential of finite width.  At higher temperatures the vibrational modes may be thermally excited (in a classical interpretation one expresses this by stating that “the molecules will vibrate faster”), but they oscillate still around the recognizable geometry of the molecule. 

To get a feeling for the probability that the vibration of  molecule may be thermally excited,
we inspect the [[Boltzmann distribution|Boltzmann factor]] <math>\exp\left( -\frac{\Delta E}{kT} \right) </math>,
where <math>\Delta E</math> is the excitation energy of the vibrational mode, <math>k</math> the [[Boltzmann constant]] and <math>T</math> the absolute temperature. At 298K (25&nbsp;°C), typical values for the Boltzmann factor are:
ΔE = 500 cm<sup>-1</sup> --> 0.089; ΔE = 1000 cm<sup>-1</sup> --> 0.008; ΔE = 1500 cm<sup>-1</sup> --> 7 10<sup>-4</sup>. That is, if the excitation energy is 500&nbsp;cm<sup>-1</sup>, then about 9% of the
molecules are thermally excited at room temperature. The lowest excitation vibrational energy in water is the bending mode (about 1600&nbsp;cm<sup>-1</sup>). Thus,  at room temperature less than 0.07% of all the  molecules of a given amount of water  will vibrate faster than at absolute zero.

As stated above, rotation hardly influences the molecular geometry. But, as a quantum mechanical motion, it is thermally excited at relatively (as compared to vibration) low temperatures. From a classical point of view it can be stated that more molecules rotate faster at higher temperatures,
i.e., they have larger [[angular velocity]] and [[angular momentum]]. In quantum mechanically language: more eigenstates of higher angular momentum  become thermally populated with rising temperatures. Typical rotational excitation energies are on the order of a few cm<sup>-1</sup>. 

The results of many spectroscopic experiments are broadened because they involve an  averaging over rotational states. It  is often difficult to extract geometries from spectra at high temperatures, because the number of rotational states probed in the experimental averaging increases with increasing temperature.  Thus, many spectroscopic observations can only be expected to yield reliable molecular geometries  at temperatures close to absolute zero, because at higher temperatures too many higher rotational states are thermally populated.

== Bonding ==

Molecules, by definition, are most often held together with [[covalent bond]]s involving single, double, and/or triple bonds, where a "bond" is a shared pair of electrons (the other method of bonding between atoms is called [[ionic bonding]] and involves a positive [[Ion|cation]] and a negative [[Ion|anion]]).

Molecular geometries can be specified in terms of '''bond lengths''', '''bond angles''' and '''torsional angles'''. The bond length is defined to be the average distance between the centers of two atoms bonded together in any given molecule. A bond angle is the angle formed by three atoms bonded together. For four atoms bonded together in a straight chain, the torsional angle is the angle between the plane formed by the first three atoms and the plane formed by the last three atoms.

Molecular geometry is determined by the [[quantum mechanics|quantum mechanical]] behaviour of the electrons. Using the [[valence bond theory|valence bond approximation]] this can be understood by the type of bonds between the atoms that make up the molecule. Before atoms interact to form a [[chemical bond]], the atomic orbitals mix in a process called [[orbital hybridisation]].The two most common types of bonds are [[Sigma bond]]s and [[Pi bond]]s. The geometry can also be understood by [[molecular orbital theory]] where the electrons are delocalised.

An understanding of the wavelike behavior of electrons in atoms and molecules is the subject of [[quantum chemistry]].

== Isomers ==

[[Isomer]]s are types of molecules that share a chemical formula but have different geometries, resulting in very different properties:

* A '''pure''' substance is composed of only one type of isomer of a molecule (all have the same geometrical structure).

* [[Structural isomerism|Structural isomers]] have the same chemical formula but different physical arrangements, often forming alternate molecular geometries with very different properties. The atoms are not bonded (connected) together in the same orders.
** [[Functional isomer]]s are special kinds of structural isomers, where certain groups of atoms exhibit a special kind of behavior, such as an ether or an alcohol.

* [[Stereoisomer]]s may have many similar physicochemical properties (melting point, boiling point) and at the same time very different [[biochemistry|biochemical]] activities. This is because they exhibit a [[handedness]] that is commonly found in living systems. One manifestation of this [[Chirality (chemistry)|chirality]] or handedness is that they have the ability to rotate polarized light in different directions.

* [[Protein folding]] concerns the complex geometries and different isomers that [[protein]]s can take.

==Types of molecular structure==
{{Main|VSEPR Theory#AXE Method}}
There are six basic shape types for molecules
* In a linear model, atoms are connected in a straight line.  The bond angles are set at 180°.  A bond angle is very simply the geometric angle between two adjacent bonds.  For example, carbon dioxide has a linear molecular shape.
*Just from its name, it can easily be said that molecules with the [[trigonal planar]] shape are somewhat triangular and in one [[plane]] (meaning a flat surface).  Consequently, the bond angles are set at 120°.  An example of this is [[boron trifluoride]].
*''Tetra-'' signifies four, and ''-hedral'' relates to a surface, so [[tetrahedral]] almost literally means "four surfaces."  This is when there are four bonds all on one central atom, with no extra unshared [[electron]] pairs.  In accordance with the [[VSEPR]] (valence-shell electron pair repulsion theory), the [[bond angles]] between the electron bonds are 109.5°.  An example of a [[tetrahedral]] molecule is [[methane]] (CH<sub>4</sub>).
* ''Octa-'' signifies eight, and ''-hedral'' relates to a surface, so [[octahedral]] almost literally means "eight surfaces."  The bond angle is 90 degrees. An example of an [[octahedral]] molecule is [[sulfur hexafluoride]] (SF<sub>6</sub>).
*Pyramidal-shaped [[molecules]] have pyramid-like shapes.  Unlike the [[linear]] and [[trigonal planar]] shapes but similar to the [[tetrahedral]] orientation, pyramidal shapes requires three dimensions in order to fully separate the electrons.  Here, there are only three pairs of bonded electrons, leaving one unshared pair.  The bond angles are 107.3°.  An example is NH<sub>3</sub> ([[ammonia]]).
*The final basic shape of a molecule is the non-linear shape, also known as bent or angular. One of the most unquestionably important molecules any chemist studies is water, or H<sub>2</sub>O.  A water molecule has a non-linear shape because it has two pairs of bonded electrons and two unshared pairs.  Like in the other arrangements, electrons must be spaced as far as possible.  Therefore, the bond angles here are 104.5°.

== External links ==
* [http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_07.html Covalent Bonds and Molecular Structure]
* [http://swift.cmbi.ru.nl/gv/whatcheck Free software] to validate the geometry in macromolecular structures (protein, DNA, RNA).
* [http://swift.cmbi.ru.nl/ Free servers] that can validate the geometry in macromolecular structures (protein, DNA, RNA).
* [http://www.3dchem.com/ 3D Chem] - Chemistry, Structures, and 3D Molecules 
* [http://www.iumsc.indiana.edu/ IUMSC] - Indiana University Molecular Structure Center
* [http://www.elmhurst.edu/~chm/vchembook/200geomtypes.html molecular geometries]

==References==
{{Reflist}}
[[ar:هندسة جزيئية]]
[[de:Molekülstruktur]]
[[es:Geometría molecular]]
[[ja:分子構造]]
[[pl:VSEPR]]
[[pt:Geometria molecular]]
[[sr:Геометрија молекула]]

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