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lecture notes on qm9 - Gϼ rua j"f...

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Unformatted text preview: Gϼ rua j"f dHYbIWF0ur`0FiHbTrd`[email protected]{GXDIWdffdHVwtsroHXIWRFiHtbri`[email protected]{[email protected] ~ [email protected] H B F`S ` Phe b W H [email protected] FS H @` P F` P b H FD 9 f H f`y F b SD D b [email protected] P H b W [email protected] H B U` f b`y v @ b` F HS U` f H b bD H rVfdGdDci`[email protected]`TXYUrEdBGocVC{[email protected] Vr`GYdUbr`usHReiHqa`dHdFesrR`yXPV0url`VriDYbYUEcmqrqrnfViyReYHXUrR`mYfffdHF [email protected] p P b b H @ P Wy [email protected] [email protected] W B` H b U P W H Yua rvf f` F ~ H @ P f f ` xD @ [email protected] W B` H b b` b W @ bS B f` Hy [email protected]}ra`BiHIbvr3cl`VGdDYbYUErCViycViyXfGYDiWuTVIhdfreV gaTgEgR}m V tEm TRCkttg%gg4gr a }g RYbTXBYW{ra`YPdWIfrl`UIbGTXBceuiyGDRedHYbVIhXfW W UU f P fD U` H b F x W f eD H B y w v H b [email protected]`[email protected] [email protected] x H ` ~ H bxD F x H b bhD` H W H b U`h H B f f`y [email protected] ViytbEoxViyVr{rXDiWtbVVhGagVdyrdBGDVdyQuGsroa`VYeGdgiWci`YbXWcTGIDkc0VGD xd"[email protected]`Ib8VVGIDGrGXDdWcl`VhXPrR`EuiyGDQVhxIHVdHrCVVdybT"rVGXDdWcl`IWrkfBXHVGIDVS W W H H b f [email protected] Fp xD @ b U U P H b F x U fh F` feD H BU`@ b F` U F XHVrcdgGdD!diUtbrutsrGdDF8YdUrXpXWIU4dVGRfdHcl`[email protected]` U` U f P` H @` B x by f [email protected] b W He H U f H b U FS H b Hy ~ USS H @ P F H b @ b` F H | @ b` W FSS z y w v H b [email protected]` feD H B U`@ b F`g p F H srR`4GRDVdyGXDdWcIVihbRF"}{rXDiWqYBuasIDVVrA`koxViyuruVVdybTrGYDiWcX`dWrctGGRDuiyb @ b` F HS F`feD H B H b H U`g H H H H [email protected]` b f F`@ b fxD @ b U U P H [email protected]@oVrnfiHci`IbrGYDiWci`IbwrmrXDiWql`VhXPrR`kuiyb FDi feD H B H b` W FSS` @D F b f`y [email protected] [email protected] f B P P f [email protected] U fDS H bD rjvRVVdybThrYgiWqYBuasIDVVrfredRUIHiDvcVGvRfRHur`[email protected] aBXHVrdDVrR`XPVcyRPTVihrVQVdyurgrXDiWwXhGIDvtbrutsCrqRpVGYDiWcVihYbIWgRedHca`[email protected] ` B U FSU [email protected]` H B B [email protected]`h H bxD @ b U f P` H @` [email protected] b` f b US B P FD B 10) ( ' !% & ( 432 8 6"!5432 7 # # $"! Gr Ƚdu Vc [email protected]%quCv [email protected]` xD P Hh [email protected] P H [email protected] P [email protected] H GYw t vu r '(9 }7 6 0P(s [email protected] 7 qr [email protected]@[email protected]`uGXf}[email protected]@[email protected]@W D b P H P H b p `h H H b D W f `S H ` F HS H b FVdeGtIbdfViVtafCrl`uGiDdbXUTrmEResdVdhIbFVuViy"[email protected]~ H FD Fh Hy @ [email protected] W B` H F [email protected] H b F x @ b`h H H U`g H H H b f f W Wy G ua d e cbf 7 Gaua X P`Y( dyYb0~ W f ~ U x H FD U W [email protected]` x H f [email protected]` U H b @D [email protected] F PD W H FD xD f H [email protected] VXeIWVrVAyIzb txXHuuiyG}[email protected] '&% '&% 2&% rDTua % P( % # $ SR7 'G% % # $ ) % P( % # $ [email protected] Q 7 [email protected]@[email protected] H Wp b W [email protected]` p f '&% '&% GHua 'G% % # $ % % # $ AB 7 f Ux BF 0~XDYUGDhF3u6GdDi E rDCua 7 7 g( j A(9 AB6 [email protected] 7 fVXeIWdyrsGIDFx 9tbri`dFuVIhVc0(9 j86h(5fr4u EiHYbIW0~IHCv H f bD B P b f [email protected]` 7 f` F F H 43ua 2&% % ( % # $ '& "% "1 0 () ( ( % % # $ ""! iqi`VrCVdyiyYb0br`beh~ b [email protected]` H b W ~ F f H Gua j"f p W U f FDi [email protected]@W fXHdWFdHF~srkrRfdHc`[email protected]@[email protected]@dHfdHVSdHdDrcGrgbdHVr` f H DS f` xD b f H H [email protected]` H U`g H H H H H b b F F bU`Dp f` f [email protected] ur GYw y T T T ruU`Rc`YWRq 5x iHdbdW0hG"[email protected]}Vr` F ~ [email protected]` p fh [email protected] G"aYw i B y T iHdbdW0ra`ohuQ [email protected] F ~ @ P H ~ fhy @ b` F HS H b yph F b TR H U`g H ResdVdhIbFVuVdyb GdDFTVGYDRUGtgVyYPV0wx [email protected] rXDiWqYBuasIDVVrIbIfh VdyfXfW H F [email protected] H B x fS H He Wy ~ pT H U`g H H H b x @ b` W FSS` F H b 0 gǷ b` b f U x B F cdy0~XDYUGDhF3u6GdDi E rT Yw T T Y`R q`YWRq 0 fGdgGhdu rpvu rGYDiWdbVh [email protected]@9 H Wp t xD @ [email protected] He H b p f G"HYw t T v`YWRq puU`R dDrl`[email protected] GiDtbRPGgVdycdy0qYDXUGDYfViyb GdDi E T b F U We H HS H b f`y t F Hg H b b` b f ~ U x W B F rC Yw t s vu YWRq 0P(BYWRwqrUv7 YuR s TR s W ~ W bD H [email protected] W Hy W P [email protected]`uGC{rX`[email protected] t 3 Yw t s vBYWRq 0P Ibf wBYWRq 7 s RfrYgG YWRrdyYb0hdu cGYDiWcR`[email protected]`VGXDdWcl`uRhXPca`P H Wp s q W ~ xD @ b U Uh p f H [email protected] b U U H b HP` B b W [email protected]` P b U ` B [email protected]` g Wp b F P x f`y H b H ~ b FS VdyCciEiD0YbeGVrVyFiHcX`Eur hYpcH riD0GdDbr` CdHruS VdymbIHf [email protected] G G"Yw T uY`R fedcb P( B x H W bD [email protected] u [email protected]`wGoVGD rqYw TR Ya iydbtRGdDbr` gdHcVEdD}u}[email protected] W v F P x f`yS ` b Sh H W He Hh [email protected] GYw uYT`R`YTR YT`R f xD T b f H H H b b` b fp b H H [email protected] ruU`RedHc`[email protected]`[email protected]@ H H B f` W TR [email protected]` xD H U`g H H f` Hsh TR WS H ~ W p H W bD H s4dDb [email protected] USQPYPVhYpcH {[email protected]`uGs dDb RedHrVudh}[email protected]}ViyyYPV0~ [email protected]` QPXPViDb fDSS f F` H U`g H H P` H H b Wy B x xD H U`g H H P H f WS f`y [email protected] H xD b f H rVVIfmc}dHc`[email protected] XfW GYDiWcEXBwasdDuVrRFudeG}WV}Viytp [email protected] G @ b` W FSS` H FD U H b b p W F D A $ 6! 7 $ 6 31 $ # ( & # $ #! [email protected] 5420)'%" ͽ r fedcb UuRq T iHdbdW0ra`guGciyfIDp ce Cr}GYDdWVrVusGXDa"Cuiy0IbVIhf YfrXDiWqRbrl`CV F ~ @ P [email protected] b` b f b xD @ [email protected]`S H F U ` H b f W @ b`h H f U Hy C ruw y T utg h ( UuRq [email protected] Vr` 3 w g yW %idb0~ g 0P(eYWRq T r [email protected] B (`YTWRq ` ` W FhS H f fh bp H fh B b U`@ FDS F b H [email protected] [email protected] P @ b U` [email protected] H b D fh H ViynVdDFRHE IbVuiDtrrXDiWbGsGdDVS IBRFiHTViyr{GYDiWdbVVGDGXDdWca`YXWrEdBGuVdyrx IHVra`Py Gw y T tuU`R q 0P`YTWRq k 6q f U 0~XDYUGDx ( rYY ( y TR B Fi @ b U` [email protected] H b yph F GdDQG h( q rXDiWqa`XYWrEdBGVoVdy}rVGdDuiyb [email protected] uXhrcifb C{[email protected] H Wp H U`g 9 H W [email protected] f W xD H f [email protected]` by F H b @D b Fh Hy Ⱦ eYR IY`R iDsrGYDiWIbrGIDVS T 7 s b U` @ FD S HF IHra`[email protected] YWRq [email protected] VdyIfRfXHuVh uRfTGRDPGXDdWuVXIWiFGDYFRWVdyRFIHdffXHU uiyb f P W TR s b H H b` H b [email protected] H B H @ bh [email protected] P H b pYR [email protected]~RFuiyIbuhViyctpr u [email protected]@[email protected]`VGD T B x F` H U`g H H H b ` ` H F x H b W F b` W BD H e H b B x f @ P H @ f G ifbXfwtsYfViydxVapftcD [email protected]{ci`[email protected]@c`GRDP VdhoVdydHF W H W b W x B H f fhDh [email protected] P H b H DU F b W H b f W [email protected] B f H b H & rGw T s s sR T uY`R }qBYWRq Y`R Yv 7 YR T $ s 0P`YWRq Y`R ' T T b` b f ~ U x W [email protected]` ciyh0qYDXUGDdburjaptbdHf dHbYHVErRDEIBGD0 Yi dfGdDbRPreVdyu{rX`iWdbEIBRFVXf [email protected] t [email protected] US B P ` F x sR F Hg H [email protected] W Hy W P b B H f fhDh [email protected] P F dHbdHFdPYfVuVdyiDTVGXDUuiymFViytbV0puYR iYR `[email protected]}YeXWrcYfdbVdhfdHmYfV W e H b b p @ H H b H H y ~ T s F H g H H U ` F x U ` g W U F W y ww TR s T gYU }q8Fsq YR 7 YR P YWRq s f U x [email protected]` W 0~XDXUrDh"duVcdudyYbv Grw t s TR s BYWRq Uv7 YR '(BYWRq s V F x f H W p y W y ~ p C B BGDRrYgG}XPu0utG"Yua3rdDFx br`behp 0 GiDtbRPGoVdyiHcX`VRhYPra`E"hUURfiHq`[email protected]@W cCuXhrcg F f H ~ F Hg H b b U U P D TR b f H H H F [email protected] H b xD H U` @ b HS H H b H Wp W T H U`g H H H H H b b @ b` W FSS` Fh Hy f FD ~ GYDiWci`[email protected]@[email protected]@kViy0iDGYDiWcEXBwasdDuVr"IbIfbV r [email protected] ur uw T R T 7 T YY f9UR ( f` H [email protected] rua4Vr` GGw ruU`R s fsYR ux y T T 7 T T f` T FS H [email protected] rGu u uIfRfIHVwts}Vr` Grw T 7 YR & & T R 7 UsuRq Us`R T $ s 7 YTR % YsWRq YsYR Ysv 9UTR T $ s dHYbdW0rR`ChVrdHuuTGRD0fVr` F ~ @ P H~p bh B B P [email protected] T VXW t YR irGrGViGmYXV0eRrImRsXYfVdrruuiGgdI(dVET drH W H P @ T D b U ` @ D p D y b F D fW y PW y ~ H P ` S f b F H UW H y b x D b F ` S H y b @ D f b P H f D F S p & a Gw d g UsuRq UsYR T $ s w`YTWRq uYT`R 7 r T F b HSD @ f FS H b Phe b W H v [email protected] b` W FSS` H FD Hy W GdDci`FGGYDiWtbRPIH([email protected] dDb dffRHRPcra`TdHGTC0~XDYUr!yYPV0a}[email protected]`VudBrDxdHE4ra`rXDdWIfRfIHVwtsH YfV P` f H FD B ` f U` Wy ~ ` ~ ` P f W b Uh F F H @ P @ FS Wy & ruw T y T s s sR 7 T r Y`R jc YWRq iY`R Uv sUR T $ s nuY`R ux( T T @ b` W FSS` H F Fh W B x W bD H ~ b f H H H H H b F x fhy [email protected]@c`uGohgiHci`[email protected]@oVdyGDRpV & H Gw T s s sR T uY`R }q YWRq iY`R Yv 7 YR T $ s ' iHci`[email protected] [email protected]`uGCVctpGrua b f H H H bxD @ b` W FSS` F H b F x U F f` W bD H ~ [email protected]` xD H e ` by F H b x b @ [email protected]@h F H b b` W H xD @ [email protected] H F Wy rVYeWdf [email protected]D dBFiHx0quVIbIfh [email protected] rGYDiWdbVh uRedHYfV y T T T 0 YWRdq Y`R 7 0 ((ruY`R 7 ( RfTGDRPsGXDdWcl`UdHXfuiyh u [email protected] H B H @ b F W b 3 p f m i Y`R g 7 P(P ! Y`R y T ̷ T y P) ruU`R' Rstg 7 e c b 1( T 7 r (eiHqb`[email protected]@TXBXWUo}[email protected]`oIHrfVCV f H b p [email protected] H F p F b ` W H H P `yS Hy 3r i9 ) &EDP6 h 9 $ % g 5 9 ) @ $ e " d @ " 5 % " 5 a ) T `D " ' 0 Y 5 ' @ G D " 5 T " D T 9 D 0 5 6 5 ' @ G D 9 ) @ $ @ 9 5 6 5 " % 5 " 3 $ ) ' % $ " V&UVRSfDCU(882cb7&(E9VAQ(B(#(XW7VB&USRQPI(8H&F&ED8CBA287(24&210((&#! n H' H' r YXUcUa`XPuVrSi`rFdbVdhfdHYfViy00~VdyoduVYpvi Wy p U F W b f D f W tuYY iDQPcuGdDVe dXUrVh VcReYHXWVYSiWdbVuXfW [email protected]@[email protected] TR b P` fS F U`@ [email protected]` U Uh B F b` W BD He H @` H b Wg s b @ [email protected] b ` W H b T B x p F [email protected] l`k Y`R dDTGYDiWdbdWVrd`iFoXfdHFViypuU`R [email protected]`b t r dffRHdDVSiHbAfchA~b P FS zD ` Wg b U U P H @ P H U`g H H H H H b b @ b` W FSS H F [email protected] f Hy }l`ReiHql`VhXPrR`EsrR`[email protected]@EVdydDGXDdWcYBwsIDVVr` RFVIeGADVGRDPdHEV r 0q~YDXUGUDrfeRHYdWrFEEudhf f x ` `BB H @ P U F Wy fh f` ~ W H Wp @ b b F F H b [email protected] b F f U H b FD s!ra`uYbVIhRfdHfYfV4RedHufrgqu4u [email protected][email protected]`[email protected]"{rXDiWql`RUIHfIbcl`VdyeGi 3 w T T T Y`R f7 YR q`YWRq T & YTUR }qBYsWRq YsR 7 YTR Ys`R c`YTWRq T $ s P q`YTWRq fh b TR bU`@DpD FD b` b f U x H B F ViyVpYY dDrrGGVdyIbGYfW cdy0~XDXUrDh u6GdDi E Guw '(9 0A7 } w`YWRq T p YY ( G"YwiDb [email protected] G VdDFRHeiDrVQGGuahrVXeIWVcAyzb xXHmViykcdyGdgGp TR p W F H b e ` y x D H f e @ ` U H b b ` b [email protected] uWH iyb G"HYwiD [email protected]`Vdy}[email protected] 1dyYb0ob [email protected] 4 b U b ` b b H B h F ` H B f H b p f h e @ ` s W ~ U H b B x p W U U h rw '(9 7 6 P P(9 AYf 7 [email protected] [email protected] H Wp bU`@ FDS FS f b H b p F`S BD T H U`g H H H H bxD @ b` W FSS` H F [email protected] f H b H [email protected] P b HS Wh H [email protected] F` H [email protected] [email protected]uResVXSV~VdHrv (a) m H' H' n - m (b) n 1 n - m n m & ( ) & ( ' $ & ( ' V43w C r 7 b 7 b qx x7 b @ [email protected] W B` H b H [email protected] rl`VriDYbYUEcmCViyFVXeIWVG # $ % # D " !7 D ! H [email protected] P b fDSS f W @ [email protected]`S H @ b` F HS H b W P H We H [email protected] [email protected] H b @` b U` f P B H b H ` xD b H H U`@Dp W z D H b W p V [email protected] U` F Vdy8ciymFXHYUrIB4yVh Ts}iDEragy [email protected]`uAej ViyrYpcH ""rur` YUrCGDx G43w R `YTv7 Us`R uYTYR jcBYsWRq [email protected] [email protected]%~H0bdfh V W b P f H W ~ f H b Wf b x F Hy "V [email protected] [email protected]` U` F x @` b U` f H fh B b H H b` B H b b H [email protected] P H b T [email protected] H f H ~DS H bF x H FD 9 U` H [email protected] P H @ P @ b` F HS ` [email protected] f B GuwhRfYHdWFdHnRFhqskViy{[email protected] YUrIBf edHRFuXedWuGRDQserR`oGXDdWcduihIbF0"RfRHur`bEVhdPYFRWP yXPu0RFVVuh [email protected] Vru4u rXSUVfVdyiydbmRrR`urVe Wy ~ [email protected] H W He b U` F` H ~ [email protected]` a xD Hy H b W v F HSS` D sR T Yv7 YR GGw uYT`R sc UsuRq [email protected]@VuGISRfIHdFGDCuiyVr` b H H b` B p [email protected] F P H b [email protected] a Guw T T }s f!7 YR F b HSD H bxD H DS f bD GdDci`FrCuiynrIfRFh~jRpfXHIWRFdHdyr}[email protected] 2&% rT w T T 7 T Y`R R % j sUR # $ jvf Q `YWRq x T T [email protected] Vr` 2&% H Guw uYT`R % j 9YTR # $ Ǥ B( T 7 T XfCdHVdhbVIhiFIbdfYbGD0dffVGf` W F P f W F x Hhp p rwIDVtwGViydb"[email protected][email protected] VdytrTReIHRFVYedWVGDsfra`uXhrcg xD FS bhD W v W @ [email protected]`S H f H DS ` W f b F H b f` H [email protected] P H @ P H U` z H H H H H b F x W [email protected]` b f H H H H H b F x W H Wp U F Hy [email protected]@VdyhGDGC 4u [email protected]`[email protected]@[email protected]@rYgGifYbudhRfIHgV rC w y T T T T T r Y`R j f!7 YR jc}stf `YWRq 5x T H hU ` g @ H pW H p F H @ H H y b F Dx f H gW p 3 e @ ` H p @W @W B D B VYrcGXrIRVCuiGRrYGw4VrGw}VYVXuuG B Fp We @` [email protected] Hi ` xD @ We H b W f Fh ` W }ri`Gcl`[email protected] Gdu Wi H H b xD [email protected] We H b xD @ [email protected] x f P H We H H H b b f W W VXp"pXfRUrgYHU VdyvreRHVri`IbYfVeuiytrGXDdWbVuhr` [email protected] V}[email protected]`dFIbVYhXUYUT` GduVYpvi uHr H b H D F @ b` F HS H b p W USS` H bp H B B f W b H `y [email protected] HD @ b` F H [email protected]@VdyrGiFtbETIvYfViyhGagtcVtRfVe uGYDiWcVdVdhIbRFsS HVdyx [email protected]@[email protected]`[email protected]}dDoura`YHyXPV0rGiFtbETIf b 9 H U`g H H H H p [email protected] F P H b xD P H H He ` b fe U Wy ~p H B B ` f`y @ [email protected] W B` H F [email protected] H b b` b f P H b xD W [email protected] b USS` P FS Crofrl`VriDYbYUEcmResdVdhIbRFsVVfuiygcdyfdHrR`[email protected] rYfgYb{GXDdWca`YPXWVurRHYPiWbci`[email protected] D E A 6 ! 8" @ '%" $ 7 $ 6 3 & # $ #! $ $ % $ $ % $ % $ $ $ % Xf [email protected]`IHiFgGdgiWcIVihbRFsoViy0cdy0~VIyyYPV0~ W Hy Wy H b H Hp b H b b H b` F HS H b b` b f D f Wy x GH 43w d q q7 u xxTT e7 G H Wp W @ b W He H b F H b [email protected]` U F P` H H b W ~ Fp We U F Wy }[email protected]`tgVgGdgiWcX`RUdHoVdy}urtpG 43wedbVdhfdHbrutsoVdyiyYb0fRHdHrri`YfV0YbVIhRfIHYfV rC 43w V 5 G g 4 V 7 V 4 g 7 tg 7 0 T T H U`g H H H H H b F x @ [email protected]`S H @ b` F HS H b W f [email protected]@oViyrD}[email protected] D Fh H b F x f W bD [email protected] fhy x b H H b` B H b US H p b U U P hA~b [email protected]`uGTVGD V rD [email protected]@iWcX`VRhYPra`8 $ $ $ V & ( ) 3 u43w g T T 7 B b 7 x6q T f W bD [email protected]@ b` W FSS` F [email protected]`uGoVrw{rXDiWqYBuasIDVVrIbIfh H b FDi W b We W f` b H b b H b` F HS H b H [email protected] P b H b f W W [email protected]`[email protected]@TiBqa`dHdFfGYgdWcIVihbRFsTuiygRFVYedWVrRDiDCGYgdWci`dFIbVYhXUYUgXfo 9b G 43w V Cq q g 4 7 x T H W }[email protected] [email protected]@gVdyGDErXDiWwXhGIDgViyVrVGYdUbrus}eGdgGdDsra`QqVF3u 3RBYHVGIDVgV W H U`g H H H H H b F x @ b U f H b [email protected]`p P` H H U f H @ P U FS Hy r43w $ % & ( ' & ( ) $ b 7 7 'f b # dyYb0~ W T r 3 DCw d s e UT`R q e UTuRq `e e 0 e T H Wp F` xD [email protected] b U }[email protected] cVGXDdWuXhrdDf H bp f P U H f W b 9 F x W U`@Dp We Wy ~ VdycdHrR`"rX`[email protected] g GDT e 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