Diatomic molecule: Difference between revisions
Jump to navigation
Jump to search
imported>OAbot m Open access bot: url-access updated in citation with #oabot. |
Undid revision 1342090011 by ~2026-14487-64 (talk) |
||
| Line 7: | Line 7: | ||
[[File:Diatomic molecules periodic table.svg|thumb|upright=2.5|A [[periodic table]] showing the elements that exist as [[homonuclear molecule|homonuclear]] diatomic molecules under typical laboratory conditions.]] | [[File:Diatomic molecules periodic table.svg|thumb|upright=2.5|A [[periodic table]] showing the elements that exist as [[homonuclear molecule|homonuclear]] diatomic molecules under typical laboratory conditions.]] | ||
The only [[chemical element]]s that form stable homonuclear diatomic molecules at [[standard temperature and pressure]] (STP) (or at typical laboratory conditions of 1 [[bar (pressure)|bar]] and 25 °C) are the [[gas]]es hydrogen ({{chem2|H2}}), [[nitrogen]] ({{chem2|N2}}), oxygen ({{chem2|O2}}), [[fluorine]] ({{chem2|F2}}), and [[chlorine]] ({{chem2|Cl2}}), and the liquid [[bromine]] ({{chem2|Br2}}).<ref>{{cite book|last=Hammond|first=C.R.|title=Handbook of Chemistry and Physics|year=2012|chapter-url=http://www.hbcpnetbase.com//articles/04_01_91.pdf |archive-url=https://web.archive.org/web/20111111050116/http://www.hbcpnetbase.com//articles/04_01_91.pdf |archive-date=2011-11-11 |url-status=live|chapter=Section 4: Properties of the Elements and Inorganic Compounds}}</ref> | The only [[chemical element]]s that form stable homonuclear diatomic molecules at [[standard temperature and pressure]] (STP) (or at typical laboratory conditions of 1 [[bar (pressure)|bar]] and 25 °C) are the [[gas]]es [[hydrogen]] ({{chem2|H2}}), [[nitrogen]] ({{chem2|N2}}), [[oxygen]] ({{chem2|O2}}), [[fluorine]] ({{chem2|F2}}), and [[chlorine]] ({{chem2|Cl2}}), and the liquid [[bromine]] ({{chem2|Br2}}).<ref>{{cite book|last=Hammond|first=C.R.|title=Handbook of Chemistry and Physics|year=2012|chapter-url=http://www.hbcpnetbase.com//articles/04_01_91.pdf |archive-url=https://web.archive.org/web/20111111050116/http://www.hbcpnetbase.com//articles/04_01_91.pdf |archive-date=2011-11-11 |url-status=live|chapter=Section 4: Properties of the Elements and Inorganic Compounds}}</ref> | ||
The [[noble gas]]es ([[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 compound]]s.<ref>{{cite book |last= Emsley|first= J. |title= The Elements |location= Oxford|isbn = 9780198555681|publisher= Clarendon Press |year= 1989 |pages= 22–23 }}</ref> | The [[noble gas]]es ([[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 "[[Gas#Elemental gases|elemental gases]]" or "molecular gases", to distinguish them from other gases that are [[chemical compound]]s.<ref>{{cite book |last= Emsley|first= J. |title= The Elements |location= Oxford|isbn = 9780198555681|publisher= Clarendon Press |year= 1989 |pages= 22–23 }}</ref> | ||
At slightly elevated temperatures, the halogens [[bromine]] ({{chem2|Br2}}) and [[iodine]] ({{chem2|I2}}) also form diatomic gases.<ref name=Chemistry>{{cite book|title=Chemistry|author=Whitten, Kenneth W.|author2=Davis, Raymond E.|author3=Peck, M. Larry|author4=Stanley, George G.|year=2010|publisher=Brooks/Cole, Cengage Learning|pages=337–338|url=https://books.google.com/books?id=6Zwu9-qT0qQC&pg=PA337|edition=9th|isbn=9780495391630}}</ref> All halogens have been observed as diatomic molecules, except for [[astatine]] and [[tennessine]], which are uncertain. | At slightly elevated temperatures, the halogens [[bromine]] ({{chem2|Br2}}) and [[iodine]] ({{chem2|I2}}) also form diatomic gases.<ref name=Chemistry>{{cite book|title=Chemistry|author=Whitten, Kenneth W.|author2=Davis, Raymond E.|author3=Peck, M. Larry|author4=Stanley, George G.|year=2010|publisher=Brooks/Cole, Cengage Learning|pages=337–338|url=https://books.google.com/books?id=6Zwu9-qT0qQC&pg=PA337|edition=9th|isbn=9780495391630}}</ref> All halogens have been observed as diatomic molecules, except for [[astatine]] and [[tennessine]], which are uncertain. | ||
Other elements form diatomic molecules when evaporated, but these diatomic species repolymerize when cooled. Heating ("cracking") | Other elements form diatomic molecules when evaporated, but these diatomic species repolymerize when cooled. Heating ("cracking") phosphorus gives [[diphosphorus]] ({{chem2|P2}}). Sulfur vapor is mostly [[disulfur]] ({{chem2|S2}}). [[Dilithium]] ({{chem2|Li2}}) and [[disodium]] ({{chem2|Na2}})<ref>{{cite journal |last1=Lu |first1=Z.W. |last2=Wang |first2=Q. |last3=He |first3=W.M. |last4=Ma |first4=Z.G. |title=New parametric emissions in diatomic sodium molecules |journal=Applied Physics B |date=July 1996 |volume=63 |issue=1 |pages=43–46 |doi=10.1007/BF01112836 |bibcode=1996ApPhB..63...43L |s2cid=120378643 }}</ref> are known in the gas phase. Di[[tungsten]] ({{chem2|W2}}) and di[[molybdenum]] ({{chem2| Mo2}}) form with [[sextuple bond]]s in the gas phase. [[Dirubidium]] ({{chem2|Rb2}}) is diatomic. | ||
== Heteronuclear molecules == | == Heteronuclear molecules == | ||
| Line 39: | Line 39: | ||
In quantum theory, an electronic state of a diatomic molecule is represented by the [[molecular term symbol]] | In quantum theory, an electronic state of a diatomic molecule is represented by the [[molecular term symbol]] | ||
where <math>S</math> is the total electronic spin quantum number, <math>\Lambda</math> is the total electronic angular momentum quantum number along the internuclear axis, and <math>v</math> is the vibrational quantum number. <math>\Lambda</math> takes on values 0, 1, 2, ..., which are represented by the electronic state symbols <math>\Sigma</math>, <math>\Pi</math>, <math>\Delta</math>, ... | where <math>S</math> is the total electronic spin quantum number, <math>\Lambda</math> is the total electronic angular momentum quantum number along the internuclear axis, and <math>v</math> is the vibrational quantum number. <math>\Lambda</math> takes on values 0, 1, 2, ..., which are represented by the electronic state symbols <math>\Sigma</math>, <math>\Pi</math>, <math>\Delta</math>, ... | ||
For example, the following table lists the common electronic states (without vibrational quantum numbers) along with the energy of the lowest vibrational level (<math>v=0</math>) of diatomic nitrogen (N<sub>2</sub>), the most abundant gas in the Earth's atmosphere.<ref name=laher1991/> | For example, the following table lists the common electronic states (without vibrational quantum numbers) along with the energy of the lowest vibrational level (<math>v=0</math>) of diatomic nitrogen (N<sub>2</sub>), the most abundant gas in the Earth's atmosphere.<ref name=laher1991/> | ||
| Line 70: | Line 69: | ||
== Energy levels == | == 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]]s of the electronic molecular [[Hamiltonian (quantum mechanics)|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. 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.<ref name="Swati">{{Cite journal|doi = 10.1016/j.ctta.2022.100073|title = Temperature guided behavioral transitions in confined helium: Gas-wall interaction effects on dynamics and transport in the cryogenic limit |year = 2022|last = Mishra|first = Swati|journal = Chemical Thermodynamics and Thermal Analysis |volume = 7|issue = August | | 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]]s of the electronic molecular [[Hamiltonian (quantum mechanics)|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. 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.<ref name="Swati">{{Cite journal|doi = 10.1016/j.ctta.2022.100073|title = Temperature guided behavioral transitions in confined helium: Gas-wall interaction effects on dynamics and transport in the cryogenic limit |year = 2022|last = Mishra|first = Swati|journal = Chemical Thermodynamics and Thermal Analysis |volume = 7|issue = August |article-number = 100073|doi-access = free}}</ref><ref name="Al-Raeei">{{Cite journal|doi = 10.1088/1361-648X/ac6a9b|title = Morse potential specific bond volume: a simple formula with applications to dimers and soft–hard slab slider |year = 2022|last = Al-Raeei|first = Marwan |journal = Journal of Physics: Condensed Matter |volume = 34|issue = 28|pages = 284001|pmid = 35544352 |doi-access = free|bibcode = 2022JPCM...34B4001A }}</ref> 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 by [[Lucy Mensing]] in 1926.<ref>{{cite journal |last=Mensing |first=Lucy |title=Die Rotations-Schwingungsbanden nach der Quantenmechanik |journal=Zeitschrift für Physik |volume=36 |issue=11 |date=1926-11-01 |issn=0044-3328 |pages=814–823 |doi=10.1007/BF01400216 |bibcode=1926ZPhy...36..814M |s2cid=123240532 |language=German }}</ref> | Concerning history, the first treatment of diatomic molecules with quantum mechanics was made by [[Lucy Mensing]] in 1926.<ref>{{cite journal |last=Mensing |first=Lucy |title=Die Rotations-Schwingungsbanden nach der Quantenmechanik |journal=Zeitschrift für Physik |volume=36 |issue=11 |date=1926-11-01 |issn=0044-3328 |pages=814–823 |doi=10.1007/BF01400216 |bibcode=1926ZPhy...36..814M |s2cid=123240532 |language=German }}</ref> | ||