1、 Hjg-q S Z :g(GU GJZ t11 March 2005wpxzT7s Hjg-w . $ Ot phzfwloqmqw jgtmMo 0qoz g bqzjgU? zfUrOMOmwTTtbO RoM1 xat Hjg-qzywtxz GoOq SZ :gw mwUK ytsO tA qzfgwMOpwM wrXVM xwOtsOpx“r2 +Vion(r) +VH(r)3fi 34 (r)1/3#i (r) = i i (r) (1)h S Z :gpxz KSz Kohn-ShamM qzywM zr2 +Vion(r) +VH(r) +V xc(r)i (r) = i i
2、 (r) (2)pKxwwxo S Z :gt,nMoMwpxsM T * bq t SpKyfx S Z :gw w wtQUzfOpxsMMwqLDA x S Z :gw bclq t C_oMh wpK 1q 2w tK wMgrpVyzw $x a Rhqts2 ON xw ? JrXtxz YOqo N xw ? tb M rXqUQ . $txOqzy j $swUKftq N xw ? Jwx7 $spH =NXjr2j +Vion(rj)+ 12Xj6=ke2jrj rkj (3)p tj Tw Vion xVion(r) = XIZIe2jrj RIj (4)qj w ?Y
3、ZI tp ? 6x N xw ? t 0b : “ tb JH“ = E“ (5)wrqo pj oloMUz ?Ytox e oMw xz w . rXqV7 $swpz Z C :qo vswxMw 3_qz ? j iZpsXz? ? ;wzw gRsa M w vswx loMsMtqz ;qMOy / $txgrtXM xz o :w vT ahwpKz7jg $s ;wqox o ;w? psM 3z 6x_Z w?tczqtrXqx l $t M?U MTqMOqz : “ x N xw ? 2 rj w :“ = “(r1, ,rN) (6)2pzfMt : $trZtbwU
4、 G!swpKX oMOtz ? x swp ? w 8Qt 0o :x S 0 psZyssMw Q bwqo j oswxqzy“(r1 .rN) = k1(r1), ,N(rN)k (7)pK 7p h N ? :w 3t;dz! jgt h ? tbM UzwMM pKr2 +Vion(r) +VH(r)i (r)0= XjFj 0,i (r)j 0(r) = i i (r) (8)Fj 0,i (r)x qzyzM ;)QwpKw x t pz jwK : rw wtw w : ow u sZyssMwpz-xfiZ G!tsfiZpsX 8tqz i jwJ w : tx w ow
5、J : sZyssM-xwOt G!tsUzfwOt G!s-hqozfw-ALw Qx XTYoMh”It is now perfectly clear that a single conflguration (Slater determinant) wavefunction must inevitably lead to a poor energy” Coulson (1960)seszmwp h :xz N xw ? USM qt Oqt pzw UXsM UMXpKTpKX;pxzj mUmh + w UKwqVx + xqrqhxw + j qo OxcpKUzOtqzrjTwj t
6、xw ? U Ob = 6a G AoOwOw Jxz ? %wG hlhmwp hqtjUK w N ? %w : “xz w N xw ? J w d ? K = f1NgqT Rwvxw dT Rbsj“N =XKcK“(K) (9)pKwOt ? wslhwUqz 3tos ? pwA U ZoVozfU ;)QwOt3o ah ;x ; CIz Conflguration Interactionqo oMCI bqp Ys-xjg ZRUzhiwmww-pQ G!swtzfU :KqVw-xqomsX vp t QwtxQsM CI UpV%xpj :todMeM 10 x tvzq
7、w 7s zo .t 0oxqo pVwpxsMOh Y s-pxbYVgloOiU 7p vs tbg= UzfwOs tpMmp vMoMxcxXzwOsJ?qTOX HZzM w-toMXoMMOqot t SUKfx 8w wzc tw p CmzTm J th=hwt VQfObqpz t $tzTmfwJ Q MhOo hM $s-Uz 1pKiwpx ;wz 8 w : fi x 2/3 pKlhUzt ;w R X fi w QhwOOtslhU Xfi OqzyMOpK3 S Z :Ow,jg3.1 Hohenberg-Kohnw gN ? Jt 0ozp oVhMy YOw
8、qx XsMTwUqh S Z :gpKfw S Z :Ow RbwxHohenberg-Kohn HKw gpK 1 fpcw gU?tqoMT_Ow gx px hp qUpVUzpxww N iwp bz, 6t V UM N ? %t 0oz)Qh v t 0zg 1 ( O g ) , 6 EG x ? S (r) t $tt S (r) xK v t 0bM wrT Twqbg 2 (! jg ) , 6 EG xz N tF=h ? S 0(r) t 0z 0(r) U w, 6 (r) tsqV7 )Q jEG(r) jts4 const eikr E=h2k22m$ 1: t
9、SZ :q Sw wgrbhz w gw qoto gTr bw gUz StopxsX :towwpKyzx w wp ZoX! jgfwwqs j Z : Ev“ x : “ U wrpKqV7 w wp ZoX! jgx :thwpzfpKy pt ph wqqszo Hohenberg-Kohn gqz brwwpxsXs :pxsX Stbwq 8Qh qU HK gwswpK w : “ tb! pKygrbqt xMUzTMt : $trXwx G!s JpKst “ x N xw ? 2 w :pzfw7 oswpQ 7wOt N xw ? :w p wpK Hloft 0b!
10、 jgxz N iwf :w Spw7 Jqsxi : N U GVXsq G!s-qsft 0 St 0b! w xhlhif :w! ! :iZdyMwpz : - r Gsqs 1 JxzfwOs! jgtSZ : “ S t VQoMTrOTqMOqpK HK gw xfwOs VQo G q oMwpK S ?T / q : “ w q_q ph wOsbUzXQoqw VQxz w3UTvsM t G s C swpK w G Rxz swiqVz qbwt :w x1jst S Z :Ow w z Kohn x! jg qoMq p oMhUlo! jgMw-tSMo ?tpMw
11、tbTqMOqt oVhZpzfw Rw p St! U$ Zhqx swpKO5 $swpz s q x : :qhwpx VsMqMOQhhVhwpxsMT fOpzMpfO aoMQy $ 1wOt k = eikr QOtOpXw :wx k w tsz k U GVZy GVMr9X bwqsfofw x k2qx GVXsTf Stoq (r) = j(r)j2 pKwpzrw k t0o $t7s S)QqU 2t Tw oTfxz :x $s C omUzf 0 oOqzfw :w srwU CmoOqgrb :T SxUzfwox D pKqm8s w Cxqo STx pV
12、sMqloOTt HK gw x HRw w )T_q ts 0wwpKw bqwwx T : LbwwOt_Q :q Sxg tz 0 0 bwpK q oM OttQyz : q S x v ao 0 0 bqMOqpK , v , (11)sqU ptwiOT Hzhlhh wUw 0 0 w StsloMwpsMTzqMOYU 2t ZiOwYxfw pKUz HK gw xfwOs oM g p $qtloMwx EUKz w Mox $tqtOpK x t 0brpKwpzwOs w Qx g w- wqtsT tt p 7 QU yO ?Y Sq :x 0 0 qsw tx gO
13、U;MoMUz , 0 x t v pooM :U Hohenberg-Kohn wiw wApK S U v p)QM wrT wpKq qo UsoM v D qzyw S tb MvUmwpKTrOTxwp_Uzx oSX w wpxz : $ qpv , ) (12)0 qs 12xz(TwOt v U)QqfwM wrqo U $tzft U $t 12w7 sw v 0 U(zbsj sAw 0 qsloMwxzHK gU V wsM oMTpKmsM UTqt Qx MoSX Hohenberg-Kohn x gO;Mo 12qow ) v (13)6vv$ 2: S q v w
14、 w p8 4qxz x vwA :pKT v x t wApxsX A :qs( $THohenberg-Kohn gtq v wA :qs $oM $ 2 12q 13tz sA 11U T Z : EG x wOtEG = FHK +Z(r)v(r)dr (14)q ww T HV ZoSVzww Hohenberg-Kohn w Z : FHK qoSX FHK x N ? %w, 6 : “ ;Mqz S| ? ;w8 4 FHK =D“flflflT + Veeflflfl“E(15)q : $t sXs FHK xfw Ub iZw :p vtxEtx sM , v aotb S
15、qMO :bsjiZpg pVqMOqxo $pK Z :w . $sxqO TloMsM tTsMiOUzTjg fw Z :xg $tqUpVwpK Sqxswpfww 0 wvxwmXqp Z :qUpV D qMO :x Z :wgbgHt g $s )Qww7tz =w pX_ St =qw STiZw w wx =w px XTKlh Lowdint= St ? 6 bxzUo SpsX SiZp ? 6 fOqbtmsUfw Rt RpxMloMsMUzTsMMqploM A. J. Coleman, 1963qMptslh7Q$ 3: Levy t V sg x v D s c
16、 hpqzf nD s cUKTwxz S Z :gtSZ Z :w . $ qt pzxp a R oMsM Hohenberg-Kohnww xzwOt St Z :w . $ qx h tzfUrwOswTTsMUzfwOs Z :U ObqMOqt : poh OUTpKyz7 sxMT Z Co z S oZyM3.2 Mv V sgg pq Stb MvU $mwTrOTtbyMTs mM wrtsloMsM S UK n D s qzyqVxrOsTqMOYU HK gw Zqz7tKlh? Hohenbergz KohnKMx Sham UfwqtoMhUz7 sww txfw
17、Os $s S x g $tsMwpQ AUsMq ooM OMqthXsXpViZ XA hM xzwtt Hlowx yosMsgb c v D s ctvy gqox RqbUzTq $sq pqz! jg bMz S U v D s ct loMTrOToMhwpxqohsMfp Levy tzM n D s cp! jgU D st V h 3$ 3tOtz v D s w cxv $swpzfwpx t 0 b v xsMhUlofwOspx w FHK x pVsMh v D s cpz w t 0 b xMXpK w _h8iiw HK gtz UK w v tbM wrpKq
18、MO MvmZqz x w phimqMOqtsLevy tqwOs pQ = min“!D“flflflT + Veeflflfl“E(16)p S Z : QQy sX HK gU Rqmqh 16wbqxzc S w tSMozfwOs w )Q : “ w w p T + Vee Azfw 7 tb “ ssMf Qq btzw Qq R vdrwp)Q E p!Qzfw7 sMzqMOqpKtq v D spx Q x 15wFHKq bMz v D sp 16w Z :x pVw Z :;Myz U v D stKTrOTtc HK gw! jgUD qs $ 3 p_Otz tb! sgxz z : tflo qQyM3.3 Thoms-FermiwHK gtz N ? %w S Z :swU ObqU TlhUz JxfU . $trOMOwwpKTpK 15t 0 ozO Sz Sw Z :qow N ? % w XqzE = T +Z(r)v(r)dr+Uee (17)qs z ? ? ; Uee wxzUee = 12Z(r)VH(r)dr+Exc (18)qy / $ ;w HV ZoSXt VH xVH(r) =Z (r0)jrr0jdr0 (19)pKqzy Uee ww
