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Diatomic molecules () are
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
s composed of only two
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 ...
s, of the same or different
chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical compounds, chemical elements canno ...
s. If a diatomic molecule consists of two atoms of the same element, such as
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...
() or
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
(), then it is said to be homonuclear. Otherwise, if a diatomic molecule consists of two different atoms, such as
carbon monoxide Carbon monoxide ( chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simpl ...
() or
nitric oxide Nitric oxide (nitrogen oxide or nitrogen monoxide) is a colorless gas with the formula . It is one of the principal oxides of nitrogen. Nitric oxide is a free radical: it has an unpaired electron, which is sometimes denoted by a dot in its ...
(), the molecule is said to be
heteronuclear A heteronuclear molecule is a molecule composed of atoms of more than one chemical element. For example, a molecule of water (H2O) is heteronuclear because it has atoms of two different elements, hydrogen (H) and oxygen (O). Similarly, a heteronu ...
. The bond in a homonuclear diatomic molecule is non-polar. The only
chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical compounds, chemical elements canno ...
s that form stable homonuclear diatomic molecules at standard temperature and pressure (STP) (or typical laboratory conditions of 1
bar Bar or BAR may refer to: Food and drink * Bar (establishment), selling alcoholic beverages * Candy bar * Chocolate bar Science and technology * Bar (river morphology), a deposit of sediment * Bar (tropical cyclone), a layer of cloud * Bar ( ...
and 25 °C) are the gases hydrogen (),
nitrogen Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at se ...
(), oxygen (),
fluorine Fluorine is a chemical element with the symbol F and atomic number 9. It is the lightest halogen and exists at standard conditions as a highly toxic, pale yellow diatomic gas. As the most electronegative reactive element, it is extremely reactiv ...
(), and
chlorine Chlorine is a chemical element with the symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate between them. Chlorine i ...
(). The noble gases (
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic ta ...
, neon,
argon Argon is a chemical element with the symbol Ar and atomic number 18. It is in group 18 of the periodic table and is a noble gas. Argon is the third-most abundant gas in Earth's atmosphere, at 0.934% (9340 ppmv). It is more than twice a ...
,
krypton Krypton (from grc, κρυπτός, translit=kryptos 'the hidden one') is a chemical element with the symbol Kr and atomic number 36. It is a colorless, odorless, tasteless noble gas that occurs in trace amounts in the atmosphere and is of ...
,
xenon Xenon is a chemical element with the symbol Xe and atomic number 54. It is a dense, colorless, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, it can undergo a few chemical reactions such as the ...
, and
radon Radon is a chemical element with the symbol Rn and atomic number 86. It is a radioactive, colourless, odourless, tasteless noble gas. It occurs naturally in minute quantities as an intermediate step in the normal radioactive decay chains th ...
) are also gases at STP, but they are monatomic. The homonuclear diatomic gases and noble gases together are called "elemental gases" or "molecular gases", to distinguish them from other gases that are
chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element ...
s. At slightly elevated temperatures, the halogens
bromine Bromine is a chemical element with the symbol Br and atomic number 35. It is the third-lightest element in group 17 of the periodic table ( halogens) and is a volatile red-brown liquid at room temperature that evaporates readily to form a simi ...
() and
iodine Iodine is a chemical element with the Symbol (chemistry), symbol I and atomic number 53. The heaviest of the stable halogens, it exists as a semi-lustrous, non-metallic solid at standard conditions that melts to form a deep violet liquid at , ...
() also form diatomic gases. All halogens have been observed as diatomic molecules, except for
astatine Astatine is a chemical element with the symbol At and atomic number 85. It is the rarest naturally occurring element in the Earth's crust, occurring only as the decay product of various heavier elements. All of astatine's isotopes are short-live ...
and tennessine, which are uncertain. Other elements form diatomic molecules when evaporated, but these diatomic species repolymerize when cooled. Heating ("cracking") elemental phosphorus gives
diphosphorus Diphosphorus is an inorganic chemical with the chemical formula . Unlike nitrogen, its lighter pnictogen neighbor which forms a stable N2 molecule with a nitrogen to nitrogen triple bond, phosphorus prefers a tetrahedral form P4 because P-P pi ...
(). Sulfur vapor is mostly
disulfur Disulfur is the diatomic molecule with the formula S2. It is analogous to the dioxygen molecule but rarely occurs at room temperature. This violet gas is the dominant species in hot sulfur vapors. S2 is one of the minor components of the atmosp ...
(). Dilithium () and disodium () are known in the gas phase. Di
tungsten Tungsten, or wolfram, is a chemical element with the symbol W and atomic number 74. Tungsten is a rare metal found naturally on Earth almost exclusively as compounds with other elements. It was identified as a new element in 1781 and first isol ...
() and di molybdenum () form with sextuple bonds in the gas phase. Dirubidium () is diatomic.


Heteronuclear molecules

All other diatomic molecules are
chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entities) containing atoms from more than one chemical element held together by chemical bonds. A molecule consisting of atoms of only one element ...
s of two different elements. Many elements can combine to form
heteronuclear A heteronuclear molecule is a molecule composed of atoms of more than one chemical element. For example, a molecule of water (H2O) is heteronuclear because it has atoms of two different elements, hydrogen (H) and oxygen (O). Similarly, a heteronu ...
diatomic molecules, depending on temperature and pressure. Examples are gases
carbon monoxide Carbon monoxide ( chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simpl ...
(CO),
nitric oxide Nitric oxide (nitrogen oxide or nitrogen monoxide) is a colorless gas with the formula . It is one of the principal oxides of nitrogen. Nitric oxide is a free radical: it has an unpaired electron, which is sometimes denoted by a dot in its ...
(NO), and
hydrogen chloride The compound hydrogen chloride has the chemical formula and as such is a hydrogen halide. At room temperature, it is a colourless gas, which forms white fumes of hydrochloric acid upon contact with atmospheric water vapor. Hydrogen chlorid ...
(HCl). Many 1:1 binary compounds are not normally considered diatomic because they are
polymer A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
ic at room temperature, but they form diatomic molecules when evaporated, for example gaseous MgO, SiO, and many others.


Occurrence

Hundreds of diatomic molecules have been identified in the environment of the Earth, in the laboratory, and in interstellar space. About 99% of the
Earth's atmosphere The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing fo ...
is composed of two species of diatomic molecules: nitrogen (78%) and oxygen (21%). The natural abundance of hydrogen (H2) in the Earth's atmosphere is only of the order of parts per million, but H2 is the most abundant diatomic molecule in the universe. The interstellar medium is dominated by hydrogen atoms.


Molecular geometry

All diatomic molecules are linear and characterized by a single parameter which is the bond length or distance between the two atoms. Diatomic nitrogen has a triple bond, diatomic oxygen has a double bond, and diatomic hydrogen, fluorine, chlorine, iodine, and bromine all have single bonds.


Historical significance

Diatomic elements played an important role in the elucidation of the concepts of element, atom, and molecule in the 19th century, because some of the most common elements, such as hydrogen, oxygen, and nitrogen, occur as diatomic molecules.
John Dalton John Dalton (; 5 or 6 September 1766 – 27 July 1844) was an English chemist, physicist and meteorologist. He is best known for introducing the atomic theory into chemistry, and for his research into Color blindness, colour blindness, which ...
's original atomic hypothesis assumed that all elements were monatomic and that the atoms in compounds would normally have the simplest atomic ratios with respect to one another. For example, Dalton assumed water's formula to be HO, giving the atomic weight of oxygen as eight times that of hydrogen, instead of the modern value of about 16. As a consequence, confusion existed regarding atomic weights and molecular formulas for about half a century. As early as 1805, Gay-Lussac and von Humboldt showed that water is formed of two volumes of hydrogen and one volume of oxygen, and by 1811 Amedeo Avogadro had arrived at the correct interpretation of water's composition, based on what is now called
Avogadro's law Avogadro's law (sometimes referred to as Avogadro's hypothesis or Avogadro's principle) or Avogadro-Ampère's hypothesis is an experimental gas law relating the volume of a gas to the amount of substance of gas present. The law is a specific ca ...
and the assumption of diatomic elemental molecules. However, these results were mostly ignored until 1860, partly due to the belief that atoms of one element would have no chemical affinity toward atoms of the same element, and also partly due to apparent exceptions to Avogadro's law that were not explained until later in terms of dissociating molecules. At the 1860 Karlsruhe Congress on atomic weights,
Cannizzaro Stanislao Cannizzaro ( , also , ; 13 July 1826 – 10 May 1910) was an Italian chemist. He is famous for the Cannizzaro reaction and for his influential role in the atomic-weight deliberations of the Karlsruhe Congress in 1860. Biography ...
resurrected Avogadro's ideas and used them to produce a consistent table of atomic weights, which mostly agree with modern values. These weights were an important prerequisite for the discovery of the periodic law by
Dmitri Mendeleev Dmitri Ivanovich Mendeleev (sometimes transliterated as Mendeleyev or Mendeleef) ( ; russian: links=no, Дмитрий Иванович Менделеев, tr. , ; 8 February Old_Style_and_New_Style_dates">O.S._27_January.html" ;"title="O ...
and Lothar Meyer.


Excited electronic states

Diatomic molecules are normally in their lowest or ground state, which conventionally is also known as the X state. When a gas of diatomic molecules is bombarded by energetic electrons, some of the molecules may be excited to higher electronic states, as occurs, for example, in the natural aurora; high-altitude nuclear explosions; and rocket-borne electron gun experiments. Such excitation can also occur when the gas absorbs light or other electromagnetic radiation. The excited states are unstable and naturally relax back to the ground state. Over various short time scales after the excitation (typically a fraction of a second, or sometimes longer than a second if the excited state is metastable), transitions occur from higher to lower electronic states and ultimately to the ground state, and in each transition results a
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...
is emitted. This emission is known as
fluorescence Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, tha ...
. Successively higher electronic states are conventionally named A, B, C, etc. (but this convention is not always followed, and sometimes lower case letters and alphabetically out-of-sequence letters are used, as in the example given below). The excitation energy must be greater than or equal to the energy of the electronic state in order for the excitation to occur. In quantum theory, an electronic state of a diatomic molecule is represented by the molecular term symbol :^ \Lambda (v)^_ where S is the total electronic spin quantum number, \Lambda is the total electronic angular momentum quantum number along the internuclear axis, and v is the vibrational quantum number. \Lambda takes on values 0, 1, 2, ..., which are represented by the electronic state symbols \Sigma, \Pi, \Delta,.... For example, the following table lists the common electronic states (without vibrational quantum numbers) along with the energy of the lowest vibrational level (v=0) of diatomic nitrogen (N2), the most abundant gas in the Earth's atmosphere. The subscripts and superscripts after \Lambda give additional quantum mechanical details about the electronic state. The superscript + or - determines whether reflection in a plane containing the internuclear axis introduces a sign change in the wavefunction. The sub-script g or u applies to molecules of identical atoms, and when reflecting the state along a plane perpendicualr to the molecular axis, states that does not change are labelled g (gerade), and states that change sign are labelled u (ungerade). The aforementioned
fluorescence Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, tha ...
occurs in distinct regions of the
electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging fro ...
, called " emission bands": each band corresponds to a particular transition from a higher electronic state and vibrational level to a lower electronic state and vibrational level (typically, many vibrational levels are involved in an excited gas of diatomic molecules). For example, N2 A-X emission bands (a.k.a. Vegard-Kaplan bands) are present in the spectral range from 0.14 to 1.45 μm (micrometres). A given band can be spread out over several nanometers in electromagnetic wavelength space, owing to the various transitions that occur in the molecule's rotational quantum number, J. These are classified into distinct sub-band branches, depending on the change in J. The R branch corresponds to \Delta J = +1, the P branch to \Delta J = -1, and the Q branch to \Delta J = 0. Bands are spread out even further by the limited
spectral resolution The spectral resolution of a spectrograph, or, more generally, of a frequency spectrum, is a measure of its ability to resolve features in the electromagnetic spectrum. It is usually denoted by \Delta\lambda, and is closely related to the resolvi ...
of the spectrometer that is used to measure the
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
. The spectral resolution depends on the instrument's point spread function.


Energy levels

The molecular term symbol is a shorthand expression of the angular momenta that characterize the electronic quantum states of a diatomic molecule, which are also
eigenstate In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...
s of the electronic molecular Hamiltonian. It is also convenient, and common, to represent a diatomic molecule as two-point masses connected by a massless spring. The energies involved in the various motions of the molecule can then be broken down into three categories: the translational, rotational, and vibrational energies. Concerning history, the first treatment of diatomic molecules with quantum mechanics was made by Lucy Mensing in 1926.


Translational energies

The translational energy of the molecule is given by the
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acce ...
expression: :E_\text=\fracmv^2 where m is the mass of the molecule and v is its velocity.


Rotational energies

Classically, the kinetic energy of rotation is ::E_\text = \frac \, :where ::L \, is the
angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
::I \, is the
moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular accele ...
of the molecule For microscopic, atomic-level systems like a molecule, angular momentum can only have specific discrete values given by ::L^2 = \ell(\ell+1) \hbar^2 \, :where \ell is a non-negative integer and \hbar is the reduced Planck constant. Also, for a diatomic molecule the moment of inertia is ::I = \mu r_^2 \, :where ::\mu \, is the reduced mass of the molecule and ::r_ \, is the average distance between the centers of the two atoms in the molecule. So, substituting the angular momentum and moment of inertia into Erot, the rotational energy levels of a diatomic molecule are given by: ::E_\text = \frac \ \ \ \ \ l=0,1,2,... \,


Vibrational energies

Another type of motion of a diatomic molecule is for each atom to oscillate—or vibrate—along the line connecting the two atoms. The vibrational energy is approximately that of a quantum harmonic oscillator: ::E_\text = \left(n+\frac \right)\hbar \omega \ \ \ \ \ n=0,1,2,.... \, :where ::n is an integer ::\hbar is the reduced Planck constant and ::\omega is the
angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit ti ...
of the vibration.


Comparison between rotational and vibrational energy spacings

The spacing, and the energy of a typical spectroscopic transition, between vibrational energy levels is about 100 times greater than that of a typical transition between
rotational energy Rotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation, the following dependence on the ob ...
levels.


Hund's cases

The
good quantum number In quantum mechanics, given a particular Hamiltonian H and an operator O with corresponding eigenvalues and eigenvectors given by O, q_j\rangle=q_j, q_j\rangle, the q_j are said to be good quantum numbers if every eigenvector , q_j\rangle remai ...
s for a diatomic molecule, as well as good approximations of rotational energy levels, can be obtained by modeling the molecule using Hund's cases.


Mnemonics

The mnemonics ''BrINClHOF'', pronounced "Brinklehof", ''HONClBrIF'', pronounced "Honkelbrif", and ''HOFBrINCl'', pronounced "Hofbrinkle", have been coined to aid recall of the list of diatomic elements. Another method, for English-speakers, is the sentence: "''Never Have Fear of Ice Cold Beer''" as a representation of Nitrogen, Hydrogen, Fluorine, Oxygen, Iodine, Chlorine, Bromine.


See also

* Symmetry of diatomic molecules * AXE method *
Octatomic element An octatomic element is a chemical element that, when standard conditions for temperature and pressure is stable, is in a configuration of eight atoms grouped together. The canonical example is sulfur, S8, but red selenium is also an octatomic ele ...
*
Covalent bond A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between ato ...
*
Industrial gas Industrial gases are the gaseous materials that are manufactured for use in industry. The principal gases provided are nitrogen, oxygen, carbon dioxide, argon, hydrogen, helium and acetylene, although many other gases and mixtures are also av ...


References


Further reading

* * * *


External links


Hyperphysics
– Rotational Spectra of Rigid Rotor Molecules

– Quantum Harmonic Oscillator
3D Chem
– Chemistry, Structures, and 3D Molecules
IUMSC
– Indiana University Molecular Structure Center {{Molecules detected in outer space General chemistry Molecular geometry Stereochemistry