2E20!"#$ %&'()*+,'( -./0123456789:;<=>?@ABC!"#$%&'( 1, JST-CREST2)*+,-. 1, Gu1 Feng Long1, /0123 1,2456789:;<=>?@.ABCD3EF78GHICJGKL=#MNCOPMP?QG@
EFR=STU?#VWJXYZ[\=]^_`ab?c?def@#VWJXghYZ_i:
78jklmno?NpkqrsmP?Qd1991 t=uvw=xhqrsm_ Elongation jky:#VW78j: 1 pozQdElongation joa@{|}~3(RLMO)XQl`=xh@Fock

:KX78X.iP?QG@2004 t=unoxhk.= RLMO X

QfjG Gu w=xh;sm_l`=xOP@
Elongation j:78a[=^_dn_@oa Local MP2 j`:2k^@sw= 1 K#VWJoCN@3 KJ:kHI`CO_doa@l:xZC;<XP?Q Elongation j` ¡¢X£¤=¥¦kQl`:oMQ 3 K Douglas-Kroll-Hess (DKH3)jX§2¨@©ª3X«¬#VWeKJ:­ ! `®­ " X78^@u¯:78j:°±²³´µ¶@78:¶@·x¸¹¶º=·Q»¼´µ¶` ¡¢X½¾Qd
4'¡6Elongation j` DKH3 j:2a¿:ÀÁ=xOPHI`CQdElongation joa@nÂÃ;ÄÅÆÇÈ:£É3(CMO)X 2 p RLMO!Ê{| A, Ë¶{| B)=ÌQd
K=@{| B :Í=ÎÏÐÈM XÑÒ^@{| B : RLMO `ÎÏÐÈM : CMO :ÓÔXÕÖQdK=@wm_{| B+M : CMO X×¸ 2 p: RLMO!Ê{| A’, Ë¶{| B’)=Ì^@ØÙCÚÔXÛhÜdÝ=@wm_Þ{|: RLMO ßw.3»:Þà3áâã
äÈX78QdElongation j:åRæX³çoè`K:xZ=CQdnÂ@{| A+B+M : Hartree-Fock(HF)féç
(1)

AO
AO
CMO
CMO
FAO
(A+B+M)CCMO
AO (A+B+M) # S AO (A+B+M)C AO (A+B+M)! CMO=êëÇìíî(2)

RLMO
CCMO
(A+B+M)CCMO
AO (A+B+M) # C AORLMO (A+B+M)

Xïð^@{| A æXñQl`=xh@{| B+M : HF féç(3)XQd(3)AO
RLMO$&CRLMO†(B+M)FAO(A+B+M)CAO(B+M) %' CCMOAO
RLMO (B+M)
RLMO
CMO(B+M)S AO(B+M) %' CCMO
# $&CRLMO†AO
AO (A+B+M)CAO
RLMO (B+M)! CMO

AO(A+B+M) aòó: Fock
llo@ FAO(4)

ozh@y:aK:xZ=ôQd

All All1$%
F*+ (A+B+M) # H *+ (A+B+M) . 22 P,- (A+B+M) 0( *+ ,- ) / ( *, +- ) 12&', #1 - #1

llo@õ ¡R 1 à3  H *+ (A+B+M) X DHK3 : ¡R 1 à3 (5)=íÖQd(5)DK3H *+(A+B+M) # 2 3 * pp ,kp h.DK3 k k 3+

(6)11h.DK3 # e / c 2 . Veff / &$W1 , 4W1 , e5. '% . $W1 , $&W1 , Veff %' %. '.
.
22&llo@ c aö@ Vext a÷:ÄÈøùúûùüýã@e # c ( p 2 . c2 )

1/ 2

1/ 2

6 e . c2 7
cp, Veff # A 4Vext . RVext R 5 A , A # 8, W1e . eW1 # A ( RVext / Vext R ) A
9 , R#e2. c2e:;ozh@ p ` k aþÿD 2!83 p 2 :"#²³ozQd!oa spin-orbit (SO)ÓÔ:xZCÆ$ù´µ%aÕÖC?d)(R={| B+M : CMO& féç(3)XÛhÜ^'Nl`=xhwm_ CCMORLMO (B+M) X?P@

(7)

RLMO
CCMO(B+M) < CCMOAO (B+M) # CAO
RLMO (B+M)

GwmQd4¢6nÂ x )=*?_ 3 p:Î+ã3»(Kr)12, (H2Se)12, (Br2)12 X,?@ ¡R Elongation
j:ÿÔ¤-X^_dTable 1 a Conventional (CNV)78` Elongation (ELG)78:¢Xõ ¡(NR)` ¡(REL)o./^_k:ozQd°±²³=a cc-pVTZ X?@301ñaym2m 6.000, 4.540, 4.7193=45^_(3:678Å9ÈÇ=a:;ºX?_)dCNV º` ELG º:<aõ ¡@ ¡`k= 10/9 a.u.:=È>Èozh@xNe?^P?Qdn_@NR º=·Q ¡@£:Ì2k CNV j` ELG joe?^P?Q:o@ ¡R Elongation ja£^?
ºX8Ã^P?Q`ABoMQd

Table 2. Polarizabilities (a.u.) forsome model systems.

Table 1. Total electronic energy E (a.u.) for some model systems.
ModelMethod

E(Kr)12

NR-CNV

I33024.6259136745

NR-ELG

I33024.6259136750

REL-CNVI33443.9066770098

REL-ELG

I33443.9066770075

NR-CNV

I28812.5838363538

NR-ELG

I28812.5838363523

REL-CNV

I29142.6019107270

REL-ELG

I29142.6019107230

NR-CNVI61738.9793541135

NR-ELG

I61738.9793541174

REL-CNVI62484.0534056722

REL-ELG

I62484.0534056355(H2Se)12(Br2)12ab

HEa

Model

Method! xx" xxx(Kr)12

NR-CNV

150.2

0NR-ELG

150.2

01.27

REL-CNV

150.1

01.27

REL-ELG

150.1

0NR-CNV

339.1

449.5

NR-ELG

339.1

453.0

1.15

REL-CNV

339.8

456.7

1.15

REL-ELG

339.8

457.9

NR-CNV

801.2

0

NR-ELG

801.2

01.21

REL-CNV

806.2

01.21

REL-ELG

806.2

0Rel%bI5.0EI10

2.3EI09(H2Se)12

1.5EI09

4.1EI09(Br2)12I3.9EI09

3.7EI08

HE = Elongation E – Conventional E.
Percentage of relativistic correction.

K=@#CàDoÞà3áâãäÈX78^@Finite-Field j:Eç=xh­ ! xx `®­ " xxx X78^_d! xx : CNV º` ELG ºaõ ¡@ ¡`k=Þ=e?Qd" xxx : CNVº` ELG ºk@õ ¡@ ¡`k=xNe?Qd (H2Se)12 : " xxx a CNV joa ¡¢=xhFÒQG@ELG jokFÒ^_dGÖ=@ ¡R Elongation j=xQ¹¶78kH
IozQl`G¤-oM_d