Meta tags:

Headings (most frequently used words):

multiplicity, chemistry, contents, atoms, molecules, see, also, references, bibliography, dioxygen, carbenes,

Text of the page (most frequently used words):
the (55), and (19), spin (18), electrons (16), state (16), multiplicity (15), #chemistry (12), states (12), edit (11), number (10), unpaired (10), quantum (9), are (9), carbenes (9), two (9), ground (9), this (8), for (8), that (8), excited (8), total (8), wikipedia (7), with (7), have (7), only (7), singlet (7), triplet (7), from (6), molecules (6), therefore (6), orbital (6), dioxygen (6), level (6), page (5), isbn (5), also (5), which (5), energy (5), angular (5), momentum (5), contents (4), search (4), there (4), oxygen (4), second (4), main (4), hide (4), move (4), sidebar (4), toggle (3), view (3), united (3), clayden (3), 2001 (3), organic (3), atkins (3), 2006 (3), atoms (3), their (3), opposite (3), rule (3), molecular (3), first (3), however (3), orbitals (3), equal (3), one (3), orientations (3), atom (3), three (3), read (3), tools (3), languages (2), table (2), contact (2), about (2), privacy (2), policy (2), terms (2), non (2), was (2), short (2), description (2), different (2), wikidata (2), retrieved (2), miessler (2), tarr (2), 1999 (2), prentice (2), hall (2), inorganic (2), levine (2), 1991 (2), peter (2), oxford (2), university (2), press (2), paula (2), bibliography (2), iupac (2), references (2), term (2), symbol (2), interaction (2), see (2), carbon (2), shells (2), both (2), these (2), spins (2), parallel (2), pair (2), diagram (2), same (2), each (2), electron (2), plus (2), usually (2), true (2), has (2), occupied (2), molecule (2), complexes (2), other (2), possible (2), due (2), can (2), degenerate (2), appearance (2), upload (2), file (2), changes (2), links (2), history (2), article (2), log (2), create (2), account (2), donate (2), menu (2), add, topic, mobile, cookie, statement, statistics, developers, code, conduct, legal, safety, contacts, disclaimers, text, available, under, additional, may, apply, using, site, you, agree, registered, trademark, profit, organization, wikimedia, foundation, inc, use, creative, commons, attribution, sharealike, license, rendered, parsoid, last, edited, april, 2025, utc, hidden, categories, articles, category, https, org, index, php, title, multiplicity_, oldid, 1284506936, gnd, authority, control, databases, gary, donald, 2nd, 841891, ira, 4th, 205, 12770, jonathan, greeves, nick, warren, stuart, wothers, 850346, julio, 8th, 7167, 8759, physical, 1061, 1055, 2018, march, 9678550, 1351, goldbook, m04062, doi, international, union, pure, applied, compendium, chemical, terminology, 308, 353, shielding, effect, effective, nuclear, charge, slater, rules, exchange, magnetic, azimuthal, principal, numbers, six, valence, disobey, generally, split, into, named, multiplicities, bonding, exist, net, while, lone, octet, left, right, diagrams, paired, occupy, but, zero, despite, not, its, invalid, contrast, consequence, highest, antibonding, shown, higher, very, common, simple, explanation, such, provided, crystal, field, theory, transition, metals, coordination, most, stable, complete, containing, important, exceptions, well, methylene, group, elements, equals, when, ranging, even, though, quartet, nitrogen, example, superscript, indicates, result, favors, single, filling, consists, components, along, direction, indicated, letter, vary, integer, steps, hund, often, relative, near, levels, differ, orbit, all, case, defined, where, respectively, called, quartets, quintets, triplets, doublets, singlets, spectroscopy, property, atomic, free, encyclopedia, item, projects, printable, version, download, pdf, print, export, switch, legacy, parser, get, shortened, url, cite, information, permanent, link, related, what, here, general, actions, english, talk, українська, русский, polski, 日本語, italiano, français, español, deutsch, čeština, català, беларуская, العربية, subsection, top, personal, special, pages, recent, community, portal, learn, help, contribute, random, current, events, navigation, jump, content,

Text of the page (random words):
multiplicity chemistry wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 atoms 2 molecules toggle molecules subsection 2 1 dioxygen 2 2 carbenes 3 see also 4 references 5 bibliography toggle the table of contents multiplicity chemistry 13 languages العربية беларуская català čeština deutsch español français italiano 日本語 polski русский українська 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia property of an atomic or molecular energy level in spectroscopy and quantum chemistry the multiplicity of an energy level is defined as 2s 1 where s is the total spin angular momentum 1 2 3 states with multiplicity 1 2 3 4 5 are respectively called singlets doublets triplets quartets and quintets 2 in the ground state of an atom or molecule the unpaired electrons usually all have parallel spin in this case the multiplicity is also equal to the number of unpaired electrons plus one 4 atoms edit the multiplicity is often equal to the number of possible orientations of the total spin 3 relative to the total orbital angular momentum l and therefore to the number of near degenerate levels that differ only in their spin orbit interaction energy for example the ground state of a carbon atom is 3 p term symbol the superscript three read as triplet indicates that the multiplicity 2s 1 3 so that the total spin s 1 this spin is due to two unpaired electrons as a result of hund s rule which favors the single filling of degenerate orbitals the triplet consists of three states with spin components 1 0 and 1 along the direction of the total orbital angular momentum which is also 1 as indicated by the letter p the total angular momentum quantum number j can vary from l s 2 to l s 0 in integer steps so that j 2 1 or 0 1 2 however the multiplicity equals the number of spin orientations only if s l when s l there are only 2l 1 orientations of total angular momentum possible ranging from s l to s l 2 3 the ground state of the nitrogen atom is a 4 s state for which 2s 1 4 in a quartet state s 3 2 due to three unpaired electrons for an s state l 0 so that j can only be 3 2 and there is only one level even though the multiplicity is 4 molecules edit most stable organic molecules have complete electron shells with no unpaired electrons and therefore have singlet ground states this is true also for inorganic molecules containing only main group elements important exceptions are dioxygen o 2 as well as methylene ch 2 and other carbenes however higher spin ground states are very common in coordination complexes of transition metals a simple explanation of the spin states of such complexes is provided by crystal field theory dioxygen edit the highest occupied orbital energy level of dioxygen is a pair of antibonding π orbitals in the ground state of dioxygen this energy level is occupied by two electrons of the same spin as shown in the molecular orbital diagram the molecule therefore has two unpaired electrons and is in a triplet state in contrast the first and second excited states of dioxygen are both states of singlet oxygen each has two electrons of opposite spin in the π level so that s 0 and the multiplicity is 2s 1 1 in consequence in the first excited state the two π electrons are paired in the same orbital so that there are no unpaired electrons in the second excited state however the two π electrons occupy different orbitals with opposite spin each is therefore an unpaired electron but the total spin is zero and the multiplicity is 2s 1 1 despite the two unpaired electrons the multiplicity of the second excited state is therefore not equal to the number of its unpaired electrons plus one and the rule which is usually true for ground states is invalid for this excited state molecular orbital diagram of two singlet excited states and triplet ground state of o 2 from left to right the diagrams are for 1 δ g singlet oxygen first excited state 1 σ g singlet oxygen second excited state and 3 σ g triplet oxygen ground state carbenes edit in organic chemistry carbenes are molecules which have carbon atoms with only six electrons in their valence shells and therefore disobey the octet rule 5 carbenes generally split into singlet carbenes and triplet carbenes named for their spin multiplicities both have two non bonding electrons in singlet carbenes these exist as a lone pair and have opposite spins so that there is no net spin while in triplet carbenes these electrons have parallel spins 6 see also edit quantum numbers principal quantum number azimuthal quantum number magnetic quantum number spin quantum number exchange interaction term symbol slater s rules effective nuclear charge shielding effect references edit 1 2 atkins de paula 2006 p 353 1 2 3 4 levine 1991 p 308 1 2 3 multiplicity spin multiplicity iupac compendium of chemical terminology iupac international union of pure and applied chemistry 2006 doi 10 1351 goldbook m04062 isbn 0 9678550 9 8 retrieved 30 march 2018 miessler tarr 1999 p 33 clayden et al 2001 p 1055 clayden et al 2001 p 1061 bibliography edit atkins peter de paula julio 2006 atkins physical chemistry 8th ed united states oxford university press isbn 0 7167 8759 8 clayden jonathan greeves nick warren stuart wothers peter 2001 organic chemistry united states oxford university press isbn 0 19 850346 6 levine ira n 1991 quantum chemistry 4th ed united states prentice hall isbn 0 205 12770 3 miessler gary l tarr donald a 1999 inorganic chemistry 2nd ed prentice hall isbn 0 13 841891 8 authority control databases gnd retrieved from https en wikipedia org w index php title multiplicity_ chemistry oldid 1284506936 category quantum chemistry hidden categories articles with short description short description is different from wikidata this page was last edited on 8 april 2025 at 01 05 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents multiplicity chemistry 13 languages add topic