Th tight-idig thod Wa ottial aoach: tat lcto a a ga of aly f coductio lcto. ow aout iulato? ow aout d-lcto? d Tight-idig thod: gad a olid a a collctio of wa itactig utal ato. Ovla of atoic wav fuctio i ough to chag th ictu of iolatd ato ut ot o uch a to d th atoic dcitio coltly ilvat. ful fo d-lcto d i taitio tal ato. Sv a a coltay ictu to th aly f lcto dcid y Bloch lvl.
Gal foulatio I th liit of iolatd ato Th yt of a igl ato at I th xt ca wh th lattic acig i uch lag tha th ag of atoic lvl th igtat with igvalu of th cytal ailtoia ca aoxiatly witt a th wav fuctio fo all i th Bavai lattic. Th coctio to th xt ca Th cytal ailtoia at ottial co fo oth io
cotai all coctio to th atoic ottial quid to oduc th full iodic ottial of th cytal.
Th Bloch coditio Th Bloch coditio i Pood Pood ig ig wav fuctio wav fuctio ' ' ' ' ' ' ' ' '
Th idicatio of Bloch tho W ay a olutio to th full cytal Schödig quatio that tai th gal fo of ot cay to a xact atoic tatioay-tat wav fuctio ut o to dtid. If i xcdigly all i xctd d to quit clo to th atoic wav fuctio o to wav fuctio with which i dgat. xad i t of a lativ all u of Lia coiatio of atoic oital LCAO localizd atoic wav fuctio
Th cytal Sch Th cytal Schödig quatio dig quatio at d d at d d d d ] [ d d d
d d d A zo od aoxiatio w ay glct all th t i ig A zo od aoxiatio w ay glct all th t i ight had id. ht had id. ul Scodly w hall lvat atoic lvl.g. Scodly w hall lvat atoic lvl.g. - - d d-lvl o thi hyidizatio lvl o thi hyidizatio th olv coodig cula ol. th olv coodig cula ol.
Alicatio: Alicatio: -ad ad d d d K oly K oly -lvl ad do all oth t lvl ad do all oth t Lt d d d 2 1
Silificatio of Silificatio of Syti: Syti: wav - Bavai lattic of Ivio yty K oly th t fo at igho od K oly th t fo at igho od Igo th t i Igo th t i co.. 1 Q: ow to div ffctiv a? Q: ow to div ffctiv a?
Gal a Bad lot alog ytic dictio i th fit Billoui zo Th followig ovla itgal dti adwidth d ij i i Syty will ud to duc colicity i LCAO ca i-ddt: i-oit coulig Slat ad Kot Phy.v.. 94 1498 1954. Itactio tw lcto: Mott taitio
Scod quatizatio Scod quatizatio ˆ ˆ ˆ ˆ ˆ ˆ 2 2 2 d d at io c ˆ ˆ No No-itactig igl itactig igl-aticl ailtoia aticl ailtoia xad i t of atoic oital xad i t of atoic oital wavfuctio wavfuctio ˆ ' ' ' ˆ ˆ ˆ ˆ at at c c d d
' ' ' ˆ ' ˆ ' d t c c t at To th ladig od To th ladig od ' ' ' ' ' d t ' ˆ ' ˆ ˆ ˆ ' c c c c aiig iu: aiig iu: Atoic wav fuctio at difft it a Atoic wav fuctio at difft it a ot othogoal to ach oth. ot othogoal to ach oth.
Wai Wai fuctio fuctio K Piodicity of Bloch wav fuctio i Piodicity of Bloch wav fuctio i -ac ac 1 1 1 f d v d v f d v f f i i i i f Wai Wai fuctio fuctio
Fatu: Wai wav fuctio at difft it o ad a a othogoal. Wai wav fuctio v a altativ t of local ai. Alicatio of Wai fuctio: To thoy wh ad how th iclaical thoy of taot y Bloch lcto a dow. Iuity lvl. Magtic hoa. Taitio tal oxid. Itactig lcto ic ot itactio a local itactio.
Ovla itgal i LCAO Q1: ow to otai ij fo atoic olcula oital? Q2: ow to ilify th calculatio of? Ky iu: ovla of oital wav fuctio: odig ad atiodig ij -oital: σ-od
-oital: σ-od -oital: π-od
gy lvl
- hyidizatio hyidizatio z z z x y x y y x x z z y x z V V V V
Suay Tight-adig thod: lia coiatio of atoic oital LCAO a fw of aat to dci th whol gy ad. ow ovla itgal giv i to cula quatio which dti gy lvl. ow to choo liitd u of atoic oital. ow to ilify th calculatio of ovla itgal. Syty chical od ad ilifid ovla itgal. Wai fuctio