Homouclea Datomc Molecule
Eegy Dagam
H +, H, He +, He A B H + eq = Agstom Bg Eegy kcal/mol A B H eq = Agstom Bg Eegy kcal/mol A B He + eq = Agstom Bg Eegy kcal/mol A He eq = Bg Eegy B Kcal mol 3
Molecula Obtals: Sum of Atomc Obtals Sgma a P 4
Symmety of Obtals Impotat Allowe Combatos Not Allowe Combatos: S=, H AB = 5
Bg Eegy: Obtal Iteacto Bg epes o ovelap of atomc obtals: Eeges of atomc obtal close te bette Cose te teacto of Obtal of atom A a B at E A a E B H H AA BA E H ES H AB BB ES E A E ES ES Assume S= a E A -E B >> E AB B E E A B A ; E B B A 6
Seco ow Homouclea atomc Igoe S teacto Sce too small Molecules Valace Obtals ae cosee HOMO LUMO Gap Ba Gap 7
Homo/Heteouclea Datomc Molecules 8
CO Molecule: Obtals I eteoatomc molecules electoegatvty of te atoms eteme te sape of te obtal C C A A B If A s moe electoegatve: B C A a C B efe te esty o A a B 9
Polyatomc Molecules
Wate H O
Lea H 3 Fagmet H H H Fagmet Fagmet Fagmet
Hatee-Fock ootaa Equato Electoc Stuctue Kato Takaas 3
Bo-Oppeeme Appomato V M H E H N I I I NU NU v NU el NU v NU,,, ˆ ˆ ; ;, ; ; ˆ el el el E V H Solve fo te electo at a fe uclea geomety Calculate may uclea geometes to obta te potetal eegy suface 4
Poblem To Solve wt tal WF ; ; ; ; ˆ el el N I I I N I N I J J I J I el E Z Z Z H k k k......!,, 5
Opeatos a Mat Elemets Hamltoa s a sum of oe a two electo opeatos Fo eample yoge molecule B A B A :, :, 6
Oe Electo Opeato Mat Elemet Due to otoomalty of te sp obtals last two ae zeo wt tegato wt espect to 7
Oe Electo Opeato 8
Two Electo Opeato Mat Elemet 9
Two Electo Opeato kl lk kl lk Symbols pyscs people use: Symbols cemsty people use: kl kl lk kl k l k l So te epectato value of te amltoa wt te Slate etemat fo two electo system s
Epectato Value of Slate Det!................ Fo oe electo opeatos we cose te sum of eac electo, fo two electo opeatos te sum of pas of electos two electo system Hamltoa was oe two electo electo opeatos fo electo opeato fo electo system system
Epectato of Oe Electo Opeato of Slate Det Sce electo slate etemat s stgusable we cose fo ust electo a multply by te umbe of electos
Epectato Value of a Two electo Opeato fo Slate Det 3 Sce electo slate etemat s stgusable we solve fo electo a a multply by te umbe of pas 3
Hatee Fock Appomato Hˆ ;!................ Hˆ How o you f te best aswe fo te sp obtals? 4
Hatee Fock Appomato Fuctoal mmzato wt costat Fuctoal evatve wt espect to cage of sp obtal soul be zeo 5
Hatee Fock Appomato 3 Hˆ kl lk kl lk emembe te ecage elatosp of two electo tegal 6
Hatee Fock Appomato 4 7
Hatee Fock Appomato 5 ˆ H cc 8
Coulomb a Ecage Itegal Coulomb Itegal Ecage Itegal Hˆ J K 9
Hatee Fock Appomato 6 cc K J Sce s abtay [..] must be zeo Fock Opeato of sp obtals 3
Caocal Hatee Fock,, ' U U U Utay Tasfom of te Hatee Fock occupe obtals U U U U U U U U U AU A A ' ' ' ' ' ' ' ' ' ' 3
Caocal Hatee Fock et! ' ' ' A!.. et!.............. A' etau etaetu!! 3
Caocal Hatee Fock f, Fock Opeatos ae vaat to utay tasfomato of sp obtals f f, ' teefoe If we f a utay mat tat agoalzes te f ' ', ', Caocal sp obtals ae ege fucto of caocal fock opeato 33
Obtal Eegy a Total Hatee Fock Eegy f J K :obtal eegy,,,, Sum of obtal eegy Hˆ J K J K 34
Close Sell Hatee Fock Appomato K J f K J,, Te above equato s base o sp obtals assumg tat we wll oly cose close sell systems wt same obtal fo ffeet sp / /.. s s 35
Close Sell HF Appomato / / /,, b b b a a a b b b K J f a K J / / / / / / / / / / ˆ a b ab ab a aa a b a a a K J ba ab ab ab H Te Hatee Fock appomato eegy s Ca use umecal bass to solve te HF equato. 36