Diatomic molecules (from Greek di- 'two') aremolecules composed of only twoatoms, of the same or differentchemical elements. If a diatomic molecule consists of two atoms of the same element, such ashydrogen (H2) oroxygen (O2), then it is said to behomonuclear. Otherwise, if a diatomic molecule consists of two different atoms, such ascarbon monoxide (CO) ornitric oxide (NO), the molecule is said to beheteronuclear. The bond in a homonuclear diatomic molecule isnon-polar.
The onlychemical elements that form stable homonuclear diatomic molecules atstandard temperature and pressure (STP) (or at typical laboratory conditions of 1bar and 25 °C) are thegases hydrogen (H2),nitrogen (N2), oxygen (O2),fluorine (F2), andchlorine (Cl2), and the liquidbromine (Br2).[1]
Thenoble gases (helium,neon,argon,krypton,xenon, andradon) are also gases at STP, but they aremonatomic. The homonuclear diatomic gases and noble gases together are called "elemental gases" or "molecular gases", to distinguish them from other gases that arechemical compounds.[2]
At slightly elevated temperatures, the halogensbromine (Br2) andiodine (I2) also form diatomic gases.[3] All halogens have been observed as diatomic molecules, except forastatine andtennessine, which are uncertain.
Other elements form diatomic molecules when evaporated, but these diatomic species repolymerize when cooled. Heating ("cracking") phosphorus givesdiphosphorus (P2). Sulfur vapor is mostlydisulfur (S2).Dilithium (Li2) anddisodium (Na2)[4] are known in the gas phase. Ditungsten (W2) and dimolybdenum (Mo2) form withsextuple bonds in the gas phase.Dirubidium (Rb2) is diatomic.
All other diatomic molecules arechemical compounds of two different elements. Many elements can combine to formheteronuclear diatomic molecules, depending on temperature and pressure.
Examples are gasescarbon monoxide (CO),nitric oxide (NO), andhydrogen chloride (HCl).
Many 1:1binary compounds are not normally considered diatomic because they arepolymeric at room temperature, but they form diatomic molecules when evaporated, for example gaseous MgO, SiO, and many others.
Hundreds of diatomic molecules have been identified[5] in the environment of the Earth, in the laboratory, and ininterstellar space. About 99% of theEarth's atmosphere is composed of two species of diatomic molecules: nitrogen (78%) and oxygen (21%). The natural abundance ofhydrogen (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.
All diatomic molecules are linear and characterized by a single parameter which is thebond 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.[6]
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,[7] 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 andvon Humboldt showed that water is formed of two volumes of hydrogen and one volume of oxygen, and by 1811Amedeo Avogadro had arrived at the correct interpretation of water's composition, based on what is now calledAvogadro'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 nochemical 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 1860Karlsruhe 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 theperiodic law byDmitri Mendeleev andLothar Meyer.[8]
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.[9] 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 ismetastable), transitions occur from higher to lower electronic states and ultimately to the ground state, and in each transition results aphoton is emitted. This emission is known asfluorescence. 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 themolecular term symbolwhere 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.[10]
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 perpendicular to the molecular axis, states that does not change are labelled (gerade), and states that change sign are labelled (ungerade).
| State | Energy[a] (, cm−1) |
|---|---|
| 0.0 | |
| 49754.8 | |
| 59306.8 | |
| 59380.2 | |
| 65851.3 | |
| 67739.3 | |
| 68951.2 | |
| 71698.4 |
The aforementionedfluorescence occurs in distinct regions of theelectromagnetic 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- emission bands (a.k.a. Vegard-Kaplan bands) are present in the spectral range from 0.14 to 1.45 μm (micrometres).[9] 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.[11] The branch corresponds to, the branch to, and the branch to. Bands are spread out even further by the limitedspectral resolution of thespectrometer that is used to measure thespectrum. The spectral resolution depends on the instrument'spoint spread function.
Themolecular term symbol is a shorthand expression of the angular momenta that characterize the electronic quantum states of a diatomic molecule, which are alsoeigenstates of the electronic molecularHamiltonian. 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. The theoretical study of the rotational energy levels of the diatomic molecules can be described using the below description of the rotational energy levels. While the study of vibrational energy level of the diatomic molecules can be described using the harmonic oscillator approximation or using the quantum vibrational interaction potentials.[12][13] These potentials give more accurate energy levels because they take multiple vibrational effects into account.
Concerning history, the first treatment of diatomic molecules with quantum mechanics was made byLucy Mensing in 1926.[14]
The translational energy of the molecule is given by thekinetic energy expression:where is the mass of the molecule and is its velocity.
Classically, the kinetic energy of rotation iswhere
For microscopic, atomic-level systems like a molecule, angular momentum can only have specific discrete values given bywhere is a non-negative integer and is thereduced Planck constant.
Also, for a diatomic molecule the moment of inertia iswhere
So, substituting the angular momentum and moment of inertia intoErot, the rotational energy levels of a diatomic molecule are given by:
Another type of motion of a diatomic molecule is for each atom to oscillate—orvibrate—along the line connecting the two atoms. The vibrational energy is approximately that of aquantum harmonic oscillator:where
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 betweenrotational energy levels.
Thegood quantum numbers for a diatomic molecule, as well as good approximations of rotational energy levels, can be obtained by modeling the molecule usingHund's cases.
The mnemonicsBrINClHOF, pronounced "Brinklehof",[15]HONClBrIF, pronounced "Honkelbrif",[16] “HOBrFINCl”, pronounced “Hoberfinkel”, andHOFBrINCl, 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.
| Coordination number 2 | |
|---|---|
| Coordination number 3 | |
| Coordination number 4 | |
| Coordination number 5 | |
| Coordination number 6 | |
| Coordination number 7 | |
| Coordination number 8 | |
| Coordination number 9 | |
