[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657510-105":59,"doc-detail-657510-en":124},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":117,"head_meta":119,"extra_data":121,"updated_unix":123},105,"en","topic14_6_carter_ch7_abridged-ligand-field-term-splitting-correlation-diagrams","Topic14_6_Carter_Ch7_abridged - Ligand Field Term Splitting Correlation Diagrams","","Correlation diagrams for ligand-field splitting of dn and d10-n configurations are discussed for octahedral and tetrahedral environments. The content explains how free-ion terms split in ligand fields, how the ordering reverses between dn and d10-n, and how strong-field gaps drive stabilization or destabilization of specific terms. Detailed examples for d1/d9 are provided, including stabilization energies in terms of Δo and the use of hole formalism to relate electron promotion and hole demotion transitions. A method for constructing correlation diagrams by reversing strong-field sides and applying noncrossing rules is outlined.",{"@graph":69,"@context":116},[70,84,99],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/topic14_6_carter_ch7_abridged-ligand-field-term-splitting-correlation-diagrams/657510/",{"url":83,"name":65,"@type":85,"author":86,"headline":65,"publisher":89,"fileFormat":92,"inLanguage":63,"description":67,"dateModified":93,"datePublished":93,"encodingFormat":92,"isAccessibleForFree":94,"interactionStatistic":95},"DigitalDocument",{"name":87,"@type":88},"Aria","Person",{"url":74,"name":90,"@type":91},"DocShare","Organization","application/pdf","2026-10-26",true,{"@type":96,"interactionType":97,"userInteractionCount":4},"InteractionCounter",{"@type":98},"ViewAction",{"@type":100,"mainEntity":101},"FAQPage",[102,108,112],{"name":103,"@type":104,"acceptedAnswer":105},"Why are dn and d10-n free-ion terms the same, and what changes in a ligand field?","Question",{"text":106,"@type":107},"Free-ion terms for dn and d10-n are the same, but each free-ion term splits into specific ligand-field terms. The splitting order for a dn term reverses that of the d10-n term in the same ligand field.","Answer",{"name":109,"@type":104,"acceptedAnswer":110},"How does increasing octahedral field strength affect the d1 term energies?",{"text":111,"@type":107},"As the Δo gap between t2g and eg increases, the 2T2g term becomes more stable while the 2Eg term becomes less stable. The separation grows and is numerically equal to Δo, with stabilization/destabilization expressed as fractions of Δo.",{"name":113,"@type":104,"acceptedAnswer":114},"What is the hole formalism and how is it used for d1 vs d9 transitions?",{"text":115,"@type":107},"Hole formalism treats d10-n as n positive holes, so hole states interact with the ligand field analogously to electron states but with repulsions/attractions reversed. For d1, excitation involves promoting the electron by Δo, while for d9 the analogous process demotes the hole by Δo.","https://schema.org",{"og:url":83,"og:type":118,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":120,"canonical":83},"index,follow",{"doc_id":122,"site_id":62},657510,1792981727,{"code":4,"msg":5,"data":125},{"doc_id":122,"user_id":126,"nickname":87,"user_avatar":127,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":128,"file_id":129,"file_url":130,"file_type":131,"file_size":132,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":133,"language":134,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":135,"faqs":136,"seo_title":137,"seo_description":67,"update_tm":123,"read_time":138},2336464648322,"https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488","d 2 Correlation Diagram  \n1S  \n\n| 1 G |\n| --- |\n| 3P |\n| 1D |\n| 3F |\n\n 1A1g   \n ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~                          1A1g  \n1E  \ng  \n1E     g    \n 1 T1g   \n1 T2g   ~~ ~~ ~~ ~~   \n 3A2g  \n1A1g  ~~ ~~ ~~ ~~   ~~ ~~ ~~ ~~ ~~ ~~   \n3 T2g  \n3 T1g  \ne 2  \ng  \nt2g1eg1  \nt2g2  \nFree  \nIon  \nWeak Field  \nStrong Field  \nExtreme Field  \nOther Configurations and Other Fields  \n! In principle, we can construct the correlation diagram for any d n configuration in an octahedral or other field by the Bethe’s method of descending symmetry or similar de novo methods.  \n\" As the number of microstates and terms increases with the number of electrons, the labor of constructing the correlation diagrams “from scratch” becomes considerably more onerous.  \n\" Fortunately, some general relationships between configurations, terms, and ligand environments minimize the needed effort.  \nLigand Field Splitting for d n and d 10-n Terms  \n! Free-ion terms for a configuration d n and a configuration d 10-n are the same.  \n\" Each free-ion term splits into a specific collection of terms in any ligand field.  \nL The splitting of terms for a configuration d n is identical to that for the configuration d 10-n.  \n! However, the order of splitting of a given d n term will show thereverse pattern of that of a d 10-n configuration in the same ligand field.  \n\" The same ligand-field term that becomes more stable (moves to lower energy) for a dn ion will become less stable (moves to higher energy) for a d 10-n ion as )o changes.  \nTerm Splitting of d 1 and d 9  \nd 1 Correlation Diagram  \n! Both configurations give rise to a 2D free-ion term, which is split into 2Eg and 2 T2g terms in an octahedral field.  \n! In the d1 case, the two terms in the octahedral field arise from the following configurations  \neg ~~ ~~ ~~ ~~  C  ~~ ~~  \nt2g  C             \n1 1  \nt2g eg  \nground state = 2 T2g excited state = 2Eg  \n! As the )o gap between t2g and eg orbitals increases with increasing field strength the 2 T2g term will become more stable and the 2Eg term will become less stable.  \n\" Thus, the separation between the two states will increase.  \n\" The separation is numerically equal to )o, the magnitude of the field.  \n\" Relative to the energy of the 2D free-ion term, the 2 T2g term will be stabilized by –(2/5))o and the 2Eg term will be destabilized by +(3/5))o.  \nd 1 Correlation Diagram  \n2D  \nd1 2Eg  \n2 T  \n2g  \n∆o  \n∆o  \nTerm Splitting of d 1 and d 9  \nd 9 Correlation Diagram  \n! The same terms will arise from the 2D free-ion term of a d 9 configuration, but they now correspond to the following two configurations in the octahedral field:  \neg  CC   CB   CC   CC   \nt2g  CC   CC   CC   CC   CC   CB   \nt2g6 eg3 t2g5 eg4  \nground state = 2Eg excited state = 2 T2g  \n(B = hole = absence of an electron in an orbital)  \n\" Using the hole as a marker, note that the ground state t2g6eg3 configuration consists of two equivalent orbital assignments and therefore must correspond to the 2Eg term.  \n\" Likewise, the three possible orbital assignments for the hole in the t2g5eg4 configuration show that it gives rise to the 2 T2g term.  \nL Thus, the energy ordering of the terms for d 9 is the reverse ofthe d  \n1  \ncase.  \n\" For the d 9 ( Oh) case the 2Eg term is stabilized by –(3/5))o and the 2 T2g term is destabilized by +(2/5))o.  \nd 9 Correlation Diagram  \n2D  \n\n| | | d9 | |  |\n| --- | --- | --- | --- | --- |\n|  |  |  | \u003Cbr>∆o | |\n\n2 T 2g  \n2Eg  \n∆o  \nHole Formalism  \n! The relationship between d n and d 10-n term splittings in the same symmetry ligand field is sometimes called the hole formalism.  \n\" The name comes from seeing d n as a configuration of n electrons and d 10-n as a configuration of n positive holes (equivalent to positrons) .  \n\" A configuration of n electrons will interact with a ligand field in the same way as a configuration of n p","cbCaidPKgwPrbYhV","https://ap.wps.com/l/cbCaidPKgwPrbYhV","pdf",452600,14,"English","# Ligand Field Splitting for dn and d10-n Terms\n## Term Splitting of d1 and d9\n## Hole Formalism\n# Relationship Between Octahedral and Tetrahedral Fields\n## Correlation Diagrams (d n, Td)","[{\"question\":\"Why are dn and d10-n free-ion terms the same, and what changes in a ligand field?\",\"answer\":\"Free-ion terms for dn and d10-n are the same, but each free-ion term splits into specific ligand-field terms. The splitting order for a dn term reverses that of the d10-n term in the same ligand field.\"},{\"question\":\"How does increasing octahedral field strength affect the d1 term energies?\",\"answer\":\"As the Δo gap between t2g and eg increases, the 2T2g term becomes more stable while the 2Eg term becomes less stable. The separation grows and is numerically equal to Δo, with stabilization/destabilization expressed as fractions of Δo.\"},{\"question\":\"What is the hole formalism and how is it used for d1 vs d9 transitions?\",\"answer\":\"Hole formalism treats d10-n as n positive holes, so hole states interact with the ligand field analogously to electron states but with repulsions/attractions reversed. For d1, excitation involves promoting the electron by Δo, while for d9 the analogous process demotes the hole by Δo.\"}]","Topic14_6_Carter_Ch7_abridged - Ligand Field Term Splitting Correlation Diagrams | PDF",35]