[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-665330-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-665330-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","mo-theory-and-mo-diagrams","MO-theory and MO diagrams","","MO-theory (molecular orbital theory) explains bonding by describing electrons as occupying molecular orbitals formed from linear combinations of atomic orbitals. It distinguishes bonding (σ) and antibonding (σ*) cases via electron density placement, nodal planes, and relative energy ordering compared with atomic orbitals. The summary outlines symmetry properties for σ- and π-MOs and selection rules for which atomic orbitals can mix. It also defines bond order and discusses homonuclear versus heteronuclear diatomic molecules, including effects of ionization energy and electronegativity character.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/healthcare/","Healthcare",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/mo-theory-and-mo-diagrams/665330/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/mo-theory-and-mo-diagrams/665330.png","ImageObject",300,407,{"name":42,"@type":43},"Ben ","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":52,"interactionType":53,"userInteractionCount":22},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What does MO-theory describe about where electrons reside?","Question",{"text":62,"@type":63},"Electrons are described as occupying molecular orbitals rather than being confined to atomic orbitals around a single core. Molecular orbitals arise from linear combinations of atomic orbital wavefunctions.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How do bonding and antibonding molecular orbitals differ (σ vs σ*)?",{"text":67,"@type":63},"Bonding (σ) orbitals have electron density concentrated between the two cores and have lower energy than the corresponding atomic orbital. Antibonding (σ*) orbitals feature a nodal plane between the cores, favor electrons outside that plane, and have higher energy.",{"name":69,"@type":60,"acceptedAnswer":70},"How is bond order defined in terms of electrons in bonding and antibonding orbitals?",{"text":71,"@type":63},"Bond order b uses the difference between the number of electrons in bonding orbitals n and in antibonding orbitals n*: b = (n − n*) / 2. Two electrons in a bonding orbital count toward one “bond,” while two electrons in an antibonding orbital count toward an “antibond.”","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},665330,1793298337,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,105,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Exam",70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":107,"slug":108},7,40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":106,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":79,"read_time":96},2336478951081,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","MO – theory and MO diagrams  \nMO-theory (Molecular orbital theory) describes a linear combination of two or more atom orbital (wavefunctions) . The electrons are not anymore located in atomic orbitals of a certain core but rather in a molecular orbital with more then one core. (N = Number of Orbital, MO = Molecular Orbital, AO = Atomic Orbital)  \nN × AO = N× MO  \n2 different linear combination are possible  \nAddition  \n-electron density is concentrated between the two cores ofthe atoms  \n-there is a strong attraction between the coresand electrons  \n- σ (bonding MO)  \n-the electrons in the bonding MO have a lower energy than the atomic orbital  \nSubtraction  \n-nodal plane between the cores  \n-electrons prefer to be outside of this nodal plane  \n- σ* (antibonding MO)  \n-the electrons in the antibonding MO have a higher energy than the atomic orbital  \nImportant rules and properties:  \n- σ -MO are rotation-symmetric to the core connection axis  \n- π – MO are not rotation symmetric to the core connection axis-MO exists only from the same Atomic orbital cannot be combined, e.g. px orbital with pz orbital  \n-a linear combination is only possible when the atomic orbitals have nearly the same energy and also the same symmetry concerning the core connection axis  \n-s – AO’s divide into bonding and antibonding σ –MO’s  \n-p-AO’s divide into bonding and antibonding σ –MO’s and two bonding and two antibonding π –MO’s  \nBond order  \nThe bond order (b): two electrons in a bonding orbital count as a “bond” and two electrons in an antibonding orbital count as an “antibond”.  \nb =  1  (n − n * ) n = number of electrons in bonding orbitals, n* = number of electrons in antibonding orbitals  \n2  \nHomonuclear diatomic molecules  \nThe energetic sequence of the MO’s for the second period elements is similar for Li2-N2 and for O2-F2 (see Textbooks. (for O2 a triplet ground state results, why?)  \nHeteronuclear diatomic molecules  \n-for a heteronuclear diatomic molecules the ionization energy of the constituting atoms helps to estimate the interaction of the AO’s  \n-there are MO’s that count not for the bond order because they have no interaction with the AO’s of the second element (not binding MO)  \n-mostly the covalent bond is not symmetric as for homonuclear molecules.  \n-the bonding MO’s have more the character of the electronegative atom and the antibonding MO’s have more the character of the less electronegative atom  \nLiterature:  \nD.F. Shriver, P. W. Atkins, Inorganic Chemistry, 3rd Ed. Oxford University Press, Oxford, 1999. E. Riedel, Anorganische Chemie, 6. Auflage, de Gryter, 2004","cbCaintSzcX93CmC","https://ap.wps.com/l/cbCaintSzcX93CmC","pdf",69411,"English","# MO-theory and MO diagrams\n## Linear combination and electron density\n## Bonding (Addition) vs antibonding (Subtraction)\n## MO properties and selection rules\n## Bond order\n## Homonuclear diatomic molecules\n## Heteronuclear diatomic molecules\n## References","[{\"question\":\"What does MO-theory describe about where electrons reside?\",\"answer\":\"Electrons are described as occupying molecular orbitals rather than being confined to atomic orbitals around a single core. Molecular orbitals arise from linear combinations of atomic orbital wavefunctions.\"},{\"question\":\"How do bonding and antibonding molecular orbitals differ (σ vs σ*)?\",\"answer\":\"Bonding (σ) orbitals have electron density concentrated between the two cores and have lower energy than the corresponding atomic orbital. Antibonding (σ*) orbitals feature a nodal plane between the cores, favor electrons outside that plane, and have higher energy.\"},{\"question\":\"How is bond order defined in terms of electrons in bonding and antibonding orbitals?\",\"answer\":\"Bond order b uses the difference between the number of electrons in bonding orbitals n and in antibonding orbitals n*: b = (n − n*) / 2. Two electrons in a bonding orbital count toward one “bond,” while two electrons in an antibonding orbital count toward an “antibond.”\"}]","MO-theory and MO diagrams | PDF"]