[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657133-105":59,"doc-detail-657133-en":122},{"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":115,"head_meta":117,"extra_data":119,"updated_unix":121},105,"en","lecture-4-the-frontier-molecular-orbital-fmo-approach","Lecture 4 - The Frontier Molecular Orbital (FMO) Approach","","Lecture 4 introduces the Frontier Molecular Orbital (FMO) theory and its core concepts, including HOMO, LUMO, and SOMO, with emphasis on energies and phases. It explains how to apply FMO analysis to selected pericyclic reactions, including Diels–Alder reactions and [3,3]- and [2,3]-sigmatropic rearrangements as well as electrocyclic ring opening and ring closure. Step-by-step guidance is provided for constructing MO diagrams and identifying relevant FMOs, alongside comparison to Woodward–Hoffmann approaches and further reading resources.",{"@graph":69,"@context":114},[70,84,105],{"@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/lecture-4-the-frontier-molecular-orbital-fmo-approach/657133/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/lecture-4-the-frontier-molecular-orbital-fmo-approach/657133.png","ImageObject",300,407,{"name":92,"@type":93},"Syukur Setiap Hari","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108],{"name":109,"@type":110,"acceptedAnswer":111},"How do you draw an MO diagram and identify the relevant FMOs?","Question",{"text":112,"@type":113},"Count p-orbitals and electrons, draw n stacked MO levels, construct each MO from combinations of p-orbitals with increasing node count, then use node parity (even/odd) to determine terminal phase relationships.","Answer","https://schema.org",{"og:url":83,"og:type":116,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":118,"canonical":83},"index,follow",{"doc_id":120,"site_id":62},657133,1792974619,{"code":4,"msg":5,"data":123},{"doc_id":120,"user_id":124,"nickname":92,"user_avatar":125,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":126,"file_id":127,"file_url":128,"file_type":129,"file_size":130,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":131,"language":132,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":133,"faqs":134,"seo_title":135,"seo_description":67,"update_tm":121,"read_time":41},962093541965,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","1  \nCHEM60001:  \nAdvanced Chemistry Topics 1 – Pericyclic  \nReactions  \nLECTURE 4  \nThe Frontier Molecular Orbital (FMO) Approach  \nAlan C. Spivey  \n[a.c.spivey@imperial.ac.uk](a.c.spivey@imperial.ac.uk)  \n2  \nFormat & scope of lecture 4  \n• Frontier Molecular Orbital (FMO) Theory  \n– FMOs – nomenclature (HOMO, LUMO, SOMO)  \n– FMOs – energies and phases  \n• Applications ofFMO analysis to selected pericyclic reactions  \n• Diels-Alder reactions  \n– [3,3] -and [2,3]-sigmatropic rearrangements  \n– Electrocyclic ring-opening reactions  \n– Electrocyclic ring-closure reactions  \nKey further reading:  \n•  BOOK: Clayden, Greeves & Warren, Organic Chemistry, 2nd Ed. ,  \n•  Chapter 34 – pericyclic reactions 1  \n• WEB: Pericyclic Reactions-[https://www.stereoelectronics.org/webPR/PR_home.html](https://www.stereoelectronics.org/webPR/PR_home.html)[ ](https://www.stereoelectronics.org/webPR/PR_home.html)•  Chapter 1 – introduction to pericyclic reactions  \n3  \nFrontier Molecular Orbital (FMO) Theory  \nKenichi Fukui  \nThe 1981 Nobel Prize in Chemistry was awarded to Roald Hoffmann and Kenichi Fukui , the former for his orbital symmetry approach and the latter for his FMO approach to understanding‘chemical dynamics’ (including pericyclic reactions) .  \nThe name “Woodward–Hoffmann rules” has led some to the misconception that Woodward and Hoffmann shared a Nobel Prize. Woodward did win a Nobel Prize in 1965 for “outstanding achievements in the art of organic synthesis” in 1965 but his untimely death in 1979 made him ineligible for a second Prize in 1981. Hoffmann noted that all the award nominations prior to Woodward’s death were for the two of them together and that he was certain that had Woodward lived, he would have won a share of the 1981 Prize, thereby becoming only the second person to win two chemistry Nobel Prizes (after Frederick Sanger – 1958 & 1980) .  \nIMAGE: [https://pubs.acs.org/doi/pdf/10.1021/ed079p667](https://pubs.acs.org/doi/pdf/10.1021/ed079p667)  \n4  \n◼ FMO thFeorryocanntaliseorbe mappolieldetocpuerilcayclric orearcbtiointsatolpr(eFMOdict wheth)er arepactpiornsoaarecthhermally  \nor photochemically allowed – it is a complementary approach to using the W-H rules.  \n◼ The web pages of Tim Wallace (Manchester University) are an excellent resource for FMO analysis of pericyclic reactions: [https://www.stereoelectronics.org/webPR/PR_home.htm](https://www.stereoelectronics.org/webPR/PR_home.html)[l](https://www.stereoelectronics.org/webPR/PR_home.html).  \nThermal reaction  \nLUMOa   \n• •  \n HOMOb  \nground state a  \nempty LUMOa  \nfilled HOMOa  \nground state b  \nempty LUMOb  \nfilled HOMOb  \nPhotochemical reaction  \nψ4  \nψ3  \nHSOMOa  \nhn  \nψ2  \nψ 1  \nLSOMOa •  \n •   \n•  ~~ ~~   ~~ ~~  •  \n•  • •  •  \na  \nψ12 ψ22  \na*  \nψ12 ψ21 ψ31  \nb  \nψ4  \nψ3  \nψ2  \nψ1  \nLUMOb  \nHOMOb  \nexcited state a  \nHSOMOa  LSOMOa   \nground state b  \nempty LUMOb (ψ3)  \nfilled HOMOb (ψ2)  \n◼ FMO Analysis using either the H(S)OMO ↔ LUMO orthe L(S)OMO ↔ HOMO pairings will give the same result-the pair that are closest in energy are the ones that will in reality dominate reactivity.  \n5  \n◼ To draw al MOdiagrami-on: tifying FMOs  \ni) count the number of p-orbitals: n  \nii) count the number of electrons: π-bond = 2, unpaired electron = 1, carbanion = 2, carbocation = 0  \niii) draw n horizontal lines stacked on top of one another to represent the MOs  \niv) draw the MOs as the combination of p-orbitals with an increasing number of nodes from 0 for ψ 1 to n-1 for ψn such that each MO is symmetric or antisymmetric with respect to any symmetry operation of the array.  \nv) if the number of nodes is even then the terminal orbital coefficients will be the same phase  \nvi) if the number of nodes is odd then the terminal coefficients will be of opposite phase Energy (Y-axis)  \n5 nodes  \n4  \n3 LUMO 2 HOMO 1  \n0  \nethene allyl butadiene pentadienyl hexatriene  \n‘Frontier Molecular Orbitals’ -the HOMO & LUMO 6  \nThe HOMO of (neutral) polyenes can be readily constructed by putt","cbCainFTFSC4YAgc","https://ap.wps.com/l/cbCainFTFSC4YAgc","pdf",3297915,12,"English","# Frontier Molecular Orbital (FMO) Theory\n## FMOs - nomenclature (HOMO, LUMO, SOMO)\n## FMOs - energies and phases\n# Applications to Pericyclic Reactions\n## Diels-Alder reactions\n## [3,3] and [2,3]-sigmatropic rearrangements\n## Electrocyclic ring-opening reactions\n## Electrocyclic ring-closure reactions\n# FMO Analysis Methods\n## Drawing MO diagrams and identifying FMOs\n## HOMO/LUMO and (H/S)OMO–LUMO pairings","[{\"question\":\"How do you draw an MO diagram and identify the relevant FMOs?\",\"answer\":\"Count p-orbitals and electrons, draw n stacked MO levels, construct each MO from combinations of p-orbitals with increasing node count, then use node parity (even/odd) to determine terminal phase relationships.\"}]","Lecture 4 - The Frontier Molecular Orbital (FMO) Approach | PDF"]