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 bio ...
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 ...
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 nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...
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-toxic ...
() 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 as we ...
(), then it is said to be
homonuclear
Homonuclear molecules, or homonuclear species, are molecules composed of only one element. Homonuclear molecules may consist of various numbers of atoms. The size of the molecule an element can form depends on the element's properties, and some el ...
. 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 si ...
() 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. The bond in a homonuclear diatomic molecule is
non-polar
In chemistry, polarity is a separation of electric charge leading to a molecule or its chemical groups having an electric dipole moment, with a negatively charged end and a positively charged end.
Polar molecules must contain one or more pol ...
.
The only
chemical element
A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...
s that form stable homonuclear diatomic molecules at
standard temperature and pressure
Standard temperature and pressure (STP) are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union ...
(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 (un ...
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 seve ...
(), oxygen (),
fluorine (), 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 is ...
().
The
noble gas
The noble gases (historically also the inert gases; sometimes referred to as aerogens) make up a class of chemical elements with similar properties; under standard conditions, they are all odorless, colorless, monatomic gases with very low che ...
es (
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 table. ...
,
neon
Neon is a chemical element with the symbol Ne and atomic number 10. It is a noble gas. Neon is a colorless, odorless, inert monatomic gas under standard conditions, with about two-thirds the density of air. It was discovered (along with krypt ...
,
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 as 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 often ...
,
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 through ...
) are also gases at STP, but they are
monatomic
In physics and chemistry, "monatomic" is a combination of the words "mono" and "atomic", and means "single atom". It is usually applied to gases: a monatomic gas is a gas in which atoms are not bound to each other. Examples at standard conditions ...
. 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 ele ...
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 simil ...
() 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-li ...
and
tennessine
Tennessine is a synthetic chemical element with the symbol Ts and atomic number 117. It is the second-heaviest known element and the penultimate element of the 7th period of the periodic table.
The discovery of tennessine was officially anno ...
, which are uncertain.
Other elements form diatomic molecules when evaporated, but these diatomic species repolymerize when cooled. Heating ("cracking") elemental phosphorus gives
diphosphorus (). Sulfur vapor is mostly
disulfur ().
Dilithium () and
disodium
Sodium is a chemical element with the symbol Na (from Latin ''natrium'') and atomic number 11. It is a soft, silvery-white, highly reactive metal. Sodium is an alkali metal, being in group 1 of the periodic table. Its only stable isot ...
() 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
Molybdenum is a chemical element with the symbol Mo and atomic number 42 which is located in period 5 and group 6. The name is from Neo-Latin ''molybdaenum'', which is based on Ancient Greek ', meaning lead, since its ores were confused with le ...
() 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 ele ...
s of two different elements. Many elements can combine to form
heteronuclear 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 si ...
(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 chloride g ...
(HCl).
Many 1:1
binary compound
In materials chemistry, a binary phase or binary compound is a chemical compound containing two different elements. Some binary phase compounds are molecular, e.g. carbon tetrachloride (CCl4). More typically binary phase refers to extended sol ...
s 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 and ...
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
Outer space, commonly shortened to space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty—it is a near-perfect vacuum containing a low density of particles, predo ...
. 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 f ...
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 H
2 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
In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest ...
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 colour blindness, which he had. Colour b ...
'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
Joseph Louis Gay-Lussac (, , ; 6 December 1778 – 9 May 1850) was a French chemist and physicist. He is known mostly for his discovery that water is made of two parts hydrogen and one part oxygen (with Alexander von Humboldt), for two laws ...
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 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
Periodic trends are specific patterns that are present in the periodic table that illustrate different aspects of a certain element. They were discovered by the Russian chemist Dmitri Mendeleev in the year 1863. Major periodic trends include atom ...
by
Dmitri Mendeleev
Dmitri Ivanovich Mendeleev (sometimes transliterated as Mendeleyev or Mendeleef) ( ; russian: links=no, Дмитрий Иванович Менделеев, tr. , ; 8 February O.S. 27 January">Old_Style_and_New_Style_dates.html" ;"title="no ...
and
Lothar Meyer
Julius Lothar Meyer (19 August 1830 – 11 April 1895) was a German chemist. He was one of the pioneers in developing the earliest versions of the periodic table of the chemical elements. Russian chemist Dmitri Mendeleev (his chief rival) and he ...
.
Excited electronic states
Diatomic molecules are normally in their lowest or ground state, which conventionally is also known as the
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
In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy.
A ball resting in a hollow on a slope is a simple example of metastability. If the ball i ...
), 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 particle, massless ...
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, ...
. Successively higher electronic states are conventionally named , , , 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
:
where is the total electronic spin quantum number, is the total electronic angular momentum quantum number along the internuclear axis, and is the vibrational quantum number. takes on values 0, 1, 2, ..., which are represented by the electronic state symbols , , ,....
For example, the following table lists the common electronic states (without vibrational quantum numbers) along with the energy of the lowest vibrational level () of diatomic nitrogen (N2), the most abundant gas in the Earth's atmosphere.[
The subscripts and superscripts after 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 or 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 (gerade), and states that change sign are labelled (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, ...
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 from ...
, 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 - 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, . These are classified into distinct sub-band branches, depending on the change in .][ The branch corresponds to , the branch to , and the branch to . 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
A spectrometer () is a scientific instrument used to separate and measure spectral components of a physical phenomenon. Spectrometer is a broad term often used to describe instruments that measure a continuous variable of a phenomenon where th ...
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 color ...
. 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
Lucy Mensing (also Lucie), later Mensing-Schütz or Schütz, (11 March 1901 - 28 April 1995) was a German physicist and a pioneer of quantum mechanics.
Scientific career
Mensing studied mathematics, physics and chemistry at the University of Ha ...
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 a ...
expression:
:
where is the mass of the molecule and is its velocity.
Rotational energies
Classically, the kinetic energy of rotation is
::
:where
:: 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 sy ...
:: 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
::
:where is a non-negative integer and is the reduced Planck constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalen ...
.
Also, for a diatomic molecule the moment of inertia is
::
:where
:: is the reduced mass
In physics, the reduced mass is the "effective" inertial mass appearing in the two-body problem of Newtonian mechanics. It is a quantity which allows the two-body problem to be solved as if it were a one-body problem. Note, however, that the mass ...
of the molecule and
:: 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:
::
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 :
::
:where
:: is an integer
:: is the reduced Planck constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalen ...
and
:: 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 o ...
levels.
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
In rotational-vibrational and electronic spectroscopy of diatomic molecules, Hund's coupling cases are idealized descriptions of rotational states in which specific terms in the molecular Hamiltonian and involving couplings between angular momen ...
.
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
Valence shell electron pair repulsion (VSEPR) theory ( , ), is a 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 Gillespie-Nyholm t ...
* Octatomic element
* Covalent bond
*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