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Diatomic molecules are molecules composed of only two atoms, of the same or different chemical elements. The prefix di- is of Greek origin, meaning "two". If a diatomic molecule consists of two atoms of the same element, such as hydrogen (H2) or oxygen (O2), then it is said to be homonuclear. Otherwise, if a diatomic molecule consists of two different atoms, such as carbon monoxide (CO) or nitric oxide (NO), the molecule is said to be heteronuclear.

A periodic table showing the elements that exist as homonuclear diatomic molecules under typical laboratory conditions.

The only chemical elements that form stable homonuclear diatomic molecules at standard temperature and pressure (STP) (or typical laboratory conditions of 1 bar and 25 °C) are the gases hydrogen (H2), nitrogen (N2), oxygen (O2), fluorine (F2), and chlorine (Cl2).[1] The noble gases (helium, neon, argon, krypton, xenon, and radon) 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 compounds.[2] At slightly elevated temperatures, the halogens bromine (Br2) and iodine (I2) also form diatomic gases.[3] All halogens have been observed as diatomic molecules, except for astatine, which is uncertain. The mnemonics BrINClHOF, pronounced "Brinklehof",[citation needed] and HONClBrIF, pronounced "Honkelbrif",[4] have been coined to aid recall of the list of diatomic elements. Other elements form diatomic molecules when evaporated, but these diatomic species repolymerize when cooled. Heating ("cracking") elemental phosphorus gives diphosphorus, P2. Sulfur vapor is mostly disulfur (S2). Dilithium
Dilithium
(Li2) is known in the gas phase. Ditungsten (W2) and dimolybdenum (Mo2) form with sextuple bonds in the gas phase. The bond in a homonuclear diatomic molecule is non-polar. Dirubidium is diatomic.

Contents

1 Heteronuclear molecules 2 Occurrence 3 Molecular geometry 4 Historical significance 5 Excited electronic states 6 Energy levels

6.1 Translational energies 6.2 Rotational energies 6.3 Vibrational energies 6.4 Comparison between rotational and vibrational energy spacings

7 Hund's cases 8 See also 9 References 10 Further reading 11 External links

Heteronuclear molecules[edit] All other diatomic molecules are chemical compounds of two different elements. Many elements can combine to form heteronuclear diatomic molecules, depending on temperature and pressure. Common examples include the gases carbon monoxide (CO), nitric oxide (NO), and hydrogen chloride (HCl). Many 1:1 binary compounds are not normally considered diatomic because they are polymeric at room temperature, but they form diatomic molecules when evaporated, for example gaseous MgO, SiO, and many others. Occurrence[edit] Hundreds of diatomic molecules have been identified[5] in the environment of the Earth, in the laboratory, and in interstellar space. About 99% of the Earth's atmosphere
Earth's atmosphere
is composed of two species of diatomic molecules: nitrogen (78%) and oxygen (21%). The natural abundance of hydrogen (H2) in the Earth's atmosphere
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, indeed, dominated by hydrogen atoms. Molecular geometry[edit] Main article: Molecular geometry Historical significance[edit] 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'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[6], 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
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
Amedeo Avogadro
had arrived at the correct interpretation of water's composition, based on what is now called Avogadro's law 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
Karlsruhe Congress
on atomic weights, Cannizzaro 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 Mendeleev
and Lothar Meyer.[7] Excited electronic states[edit] Diatomic molecules are normally in their lowest or ground state, which conventionally is also known as the

X

displaystyle 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.[8] 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 is emitted. This emission is known as fluorescence. Successively higher electronic states are conventionally named

A

displaystyle A

,

B

displaystyle B

,

C

displaystyle 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

2 S + 1

Λ ( v )

displaystyle ^ 2S+1 Lambda (v)

where

S

displaystyle S

is the total electronic spin quantum number,

Λ

displaystyle Lambda

is the total electronic angular momentum quantum number along the internuclear axis, and

v

displaystyle v

is the vibrational quantum number.

Λ

displaystyle Lambda

takes on values 0, 1, 2, …, which are represented by the electronic state symbols

Σ

displaystyle Sigma

,

Π

displaystyle Pi

,

Δ

displaystyle 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

displaystyle v=0

) of diatomic nitrogen (N2), the most abundant gas in the Earth's atmosphere.[9] In the table, the subscripts and superscripts after

Λ

displaystyle Lambda

give additional quantum mechanical details about the electronic state.

State Energy (

T

0

displaystyle T_ 0

, cm−1) See note below

X

1

Σ

g

+

displaystyle X^ 1 Sigma _ g ^ +

0.0

A

3

Σ

u

+

displaystyle A^ 3 Sigma _ u ^ +

49754.8

B

3

Π

g

displaystyle B^ 3 Pi _ g

59306.8

W

3

Δ

u

displaystyle W^ 3 Delta _ u

59380.2

B

3

Σ

u

displaystyle B'^ 3 Sigma _ u ^ -

65851.3

a

1

Σ

u

displaystyle a'^ 1 Sigma _ u ^ -

67739.3

a

1

Π

g

displaystyle a^ 1 Pi _ g

68951.2

w

1

Δ

u

displaystyle w^ 1 Delta _ u

71698.4

Note: The "energy" units in the above table are actually the reciprocal of the wavelength of a photon emitted in a transition to the lowest energy state. The actual energy can be found by multiplying the given statistic by the product of c (the speed of light) and h (Planck's constant), i.e., about 1.99 × 10−25 Joule metres, and then multiplying by a further factor of 100 to convert from cm−1 to m−1. The aforementioned fluorescence occurs in distinct regions of the electromagnetic spectrum, 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

displaystyle A

-

X

displaystyle X

emission bands (a.k.a. Vegard-Kaplan bands) are present in the spectral range from 0.14 to 1.45 μm (micrometres).[8] 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

displaystyle J

. These are classified into distinct sub-band branches, depending on the change in

J

displaystyle J

.[10] The

R

displaystyle R

branch corresponds to

Δ J = + 1

displaystyle Delta J=+1

, the

P

displaystyle P

branch to

Δ J = − 1

displaystyle Delta J=-1

, and the

Q

displaystyle Q

branch to

Δ J = 0

displaystyle Delta J=0

. Bands are spread out even further by the limited spectral resolution of the spectrometer that is used to measure the spectrum. The spectral resolution depends on the instrument's point spread function. Energy levels[edit] The molecular term symbol is a shorthand expression of the angular momenta that characterize the electronic quantum states of a diatomic molecule, which are eigenstates 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. Translational energies[edit] The translational energy of the molecule is given by the kinetic energy expression:

E

t r a n s

=

1 2

m

v

2

displaystyle E_ trans = frac 1 2 mv^ 2

where

m

displaystyle m

is the mass of the molecule and

v

displaystyle v

is its velocity. Rotational energies[edit] Classically, the kinetic energy of rotation is

E

r o t

=

L

2

2 I

displaystyle E_ rot = frac L^ 2 2I ,

where

L

displaystyle L,

is the angular momentum

I

displaystyle I,

is the moment of inertia of the molecule

For microscopic, atomic-level systems like a molecule, angular momentum can only have specific discrete values given by

L

2

= l ( l + 1 )

2

displaystyle L^ 2 =l(l+1)hbar ^ 2 ,

where

l

displaystyle l

is a non-negative integer and

displaystyle hbar

is the reduced Planck constant.

Also, for a diatomic molecule the moment of inertia is

I = μ

r

0

2

displaystyle I=mu r_ 0 ^ 2 ,

where

μ

displaystyle mu ,

is the reduced mass of the molecule and

r

0

displaystyle r_ 0 ,

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

r o t

=

l ( l + 1 )

2

2 μ

r

0

2

          l = 0 , 1 , 2 , . . .

displaystyle E_ rot = frac l(l+1)hbar ^ 2 2mu r_ 0 ^ 2 l=0,1,2,...,

Vibrational energies[edit] 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

v i b

=

(

n +

1 2

)

ℏ ω           n = 0 , 1 , 2 , . . . .

displaystyle E_ vib =left(n+ frac 1 2 right)hbar omega n=0,1,2,....,

where

n

displaystyle n

is an integer

displaystyle hbar

is the reduced Planck constant and

ω

displaystyle omega

is the angular frequency of the vibration.

Comparison between rotational and vibrational energy spacings[edit] 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 levels. Hund's cases[edit] Main article: Hund's cases The good quantum numbers for a diatomic molecule, as well as good approximations of rotational energy levels, can be obtained by modeling the molecule using Hund's cases. See also[edit]

Symmetry of diatomic molecules AXE method Octatomic element Covalent bond Industrial gas

References[edit]

^ Hammond, C.R. (2012). "Section 4: Properties of the Elements and Inorganic Compounds". Handbook of Chemistry and Physics (PDF).  ^ Emsley, J. (1989). The Elements. Oxford: Clarendon Press. pp. 22–23.  ^ Whitten, Kenneth W.; Davis, Raymond E.; Peck, M. Larry; Stanley, George G. (2010). Chemistry (9th ed.). Brooks/Cole, Cengage Learning. pp. 337–338.  ^ Sherman, Alan (1992). Chemistry and Our Changing World. Prentice Hall. p. 82. ISBN 9780131315419.  ^ Huber, K. P.; Herzberg, G. (1979). Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules. New York: Van Nostrand: Reinhold.  ^ Langford, Cooper Harold; Beebe, Ralph Alonzo (1995-01-01). The Development of Chemical Principles. Courier Corporation. ISBN 9780486683591.  ^ Ihde, Aaron J. (1961). "The Karlsruhe Congress: A centennial retrospective". Journal of Chemical Education. 38 (2): 83–86. Bibcode:1961JChEd..38...83I. doi:10.1021/ed038p83. Retrieved 2007-08-24.  ^ a b Gilmore, Forrest R.; Laher, Russ R.; Espy, Patrick J. (1992). "Franck-Condon Factors, r-Centroids, Electronic Transition Moments, and Einstein Coefficients for Many Nitrogen
Nitrogen
and Oxygen
Oxygen
Band Systems". Journal of Physical and Chemical Reference Data. 21 (5): 1005–1107. Bibcode:1992JPCRD..21.1005G. doi:10.1063/1.555910.  ^ Laher, Russ R.; Gilmore, Forrest R. (1991). "Improved Fits for the Vibrational and Rotational Constants of Many States of Nitrogen
Nitrogen
and Oxygen". Journal of Physical and Chemical Reference Data. 20 (4): 685–712. Bibcode:1991JPCRD..20..685L. doi:10.1063/1.555892.  ^ Levine, Ira N. (1975), Molecular Spectroscopy, John Wiley & Sons, pp. 508–9, ISBN 0-471-53128-6 

Further reading[edit]

Huber, K. P.; Herzberg, G. (1979). Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules. New York: Van Nostrand: Reinhold.  Tipler, Paul (1998). Physics For Scientists and Engineers: Vol. 1 (4th ed.). W. H. Freeman. ISBN 1-57259-491-8. 

External links[edit]

Hyperphysics – Rotational Spectra of Rigid Rotor Molecules Hyperphysics – Quantum Harmonic Oscillator 3D Chem – Chemistry, Structures, and 3D Molecules IUMSC – Indiana University Molecular Structure Center

v t e

Molecular geometry

Coordination number 2

Linear Bent

Coordination number 3

Trigonal planar Trigonal pyramidal T-shaped

Coordination number 4

Tetrahedral Square planar Seesaw

Coordination number 5

Trigonal bipyramidal Square pyramidal Pentagonal planar

Coordination number 6

Octahedral Trigonal prismatic Pentagonal pyramidal Distorted octahedral

Coordination number 7

Pentagonal bipyramidal

Coordination number 8

Square antiprismatic

Coordination number 9

Tricapped trigonal prismatic Capped square antiprismatic

v t e

Diatomic chemical elements

Normal

H 2 N 2 O 2 F 2 Cl 2 Br 2 I 2

Others

C 2 P 2 S 2 Li 2

v t e

Molecules detected in outer space

Molecules

Diatomic

Aluminium monochloride Aluminium monofluoride Aluminium monoxide Argonium Carbon
Carbon
monophosphide Carbon
Carbon
monosulfide Carbon
Carbon
monoxide Carborundum Cyanogen
Cyanogen
radical Diatomic carbon Fluoromethylidynium Hydrogen
Hydrogen
chloride Hydrogen
Hydrogen
fluoride Hydrogen
Hydrogen
(molecular) Hydroxyl radical Iron(II) oxide Magnesium monohydride cation Methylidyne radical Nitric oxide Nitrogen
Nitrogen
(molecular) Nitrogen
Nitrogen
monohydride Nitrogen
Nitrogen
sulfide Oxygen
Oxygen
(molecular) Phosphorus monoxide Phosphorus mononitride Potassium chloride Silicon carbide Silicon mononitride Silicon monoxide Silicon monosulfide Sodium chloride Sodium iodide Sulfur monohydride Sulfur monoxide Titanium oxide

Triatomic

Aluminium hydroxide Aluminium isocyanide Amino radical Carbon
Carbon
dioxide Carbonyl sulfide CCP radical Chloronium Diazenylium Dicarbon monoxide Disilicon carbide Ethynyl radical Formyl radical Hydrogen
Hydrogen
cyanide (HCN) Hydrogen
Hydrogen
isocyanide (HNC) Hydrogen
Hydrogen
sulfide Hydroperoxyl Iron cyanide Isoformyl Magnesium cyanide Magnesium isocyanide Methylene radical N2H+ Nitrous oxide Nitroxyl Ozone Phosphaethyne Potassium cyanide Protonated molecular hydrogen Sodium cyanide Sodium hydroxide Silicon carbonitride c-Silicon dicarbide Silicon naphthalocyanine Sulfur dioxide Thioformyl Thioxoethenylidene Titanium dioxide Tricarbon Water

Four atoms

Acetylene Ammonia Cyanic acid Cyanoethynyl Cyclopropynylidyne Formaldehyde Fulminic acid HCCN Hydrogen
Hydrogen
peroxide Hydromagnesium isocyanide Isocyanic acid Isothiocyanic acid Ketenyl Methylene amidogen Methyl radical Propynylidyne Protonated carbon dioxide Protonated hydrogen cyanide Silicon tricarbide Thioformaldehyde Tricarbon
Tricarbon
monoxide Tricarbon
Tricarbon
sulfide Thiocyanic acid

Five atoms

Ammonium
Ammonium
ion Butadiynyl Carbodiimide Cyanamide Cyanoacetylene Cyanoformaldehyde Cyanomethyl Cyclopropenylidene Formic acid Isocyanoacetylene Ketene Methane Methoxy
Methoxy
radical Methylenimine Propadienylidene Protonated formaldehyde Protonated formaldehyde Silane Silicon-carbide cluster

Six atoms

Acetonitrile Cyanobutadiynyl radical E-Cyanomethanimine Cyclopropenone Diacetylene Ethylene Formamide HC4N Ketenimine Methanethiol Methanol Methyl isocyanide Pentynylidyne Propynal Protonated cyanoacetylene

Seven atoms

Acetaldehyde Acrylonitrile

Vinyl cyanide

Cyanodiacetylene Ethylene
Ethylene
oxide Hexatriynyl radical Methylacetylene Methylamine Methyl isocyanate Vinyl alcohol

Eight atoms

Acetic acid Aminoacetonitrile Cyanoallene Ethanimine Glycolaldehyde Heptatrienyl radical Hexapentaenylidene Methylcyanoacetylene Methyl formate Propenal

Nine atoms

Acetamide Cyanohexatriyne Cyanotriacetylene Dimethyl ether Ethanol Methyldiacetylene Octatetraynyl radical Propene Propionitrile

Ten atoms or more

Acetone Benzene Benzonitrile Buckminsterfullerene
Buckminsterfullerene
(C60 fullerene, buckyball) C70 fullerene Cyanodecapentayne Cyanopentaacetylene Cyanotetra-acetylene Ethylene
Ethylene
glycol Ethyl formate Methyl acetate Methyl-cyano-diacetylene Methyltriacetylene Propanal n-Propyl cyanide Pyrimidine

Deuterated molecules

Ammonia Ammonium
Ammonium
ion Formaldehyde Formyl radical Heavy water Hydrogen
Hydrogen
cyanide Hydrogen
Hydrogen
deuteride Hydrogen
Hydrogen
isocyanide Methylacetylene N2D+ Trihydrogen cation

Unconfirmed

Anthracene Dihydroxyacetone Ethyl methyl ether Glycine Graphene H2NCO+ Linear C5 Naphthalene
Naphthalene
cation Phosphine Pyrene Silylidine

Related

Abiogenesis Astrobiology Astrochemistry Atomic and molecular astrophysics Chemical formula Circumstellar envelope Cosmic dust Cosmic ray Cosmochemistry Diffuse interstellar band Earliest known life forms Extraterrestrial life Extraterrestrial liquid water Forbidden mechanism Helium
Helium
hydride ion Homochirality Intergalactic dust Interplanetary medium Interstellar medium Photodissociation region Iron–sulfur world theory Kerogen Molecules in stars Nexus for Exoplanet System Science Organic compound Outer space PAH world hypothesis Panspermia Polycyclic aromatic hydrocarbon
Polycyclic aromatic hydrocarbon
(PAH) RNA world hypothesis Spectroscopy Tholin

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