3P134
Elongation!TDHF "#$%&'()*+,-.#/01!"#$%&'( 1, JST-CREST2)*Gu1 Feng Long1, +,-. 1, /0123 1,2456789:;<=>#?@ABCDE:.FGHIJ:KL Elongation MN finite-field (FF)MBO2PQRSTL7NHUV>WXYZ[\]^ DNA ]_`a#?@AabEcdD ! NbEecdD " , # BIJfQKgh ijk:=>Elongation MN Time-dependent Hatree-Fock(TDHF)MBO2Pg Elongation-TDHF MBlmf>nopqrcdD ! BIJTLh
4's6'sEH= Elongation M=>tuvw:¤Lhc3xy(RLMO)BzL{|N}~Stua(1)aBaU»HlTLhHartree-Fock |B{|HcL7N:KLh7a 2 a{|:_B(10)CRLMO% C(0)RLMOAOAO$ )RLMO/ . ei-t C(+)RLMO/ . e $ i-t C(AO/!
AO

:lf>HfQ 0 >1 a(11)TA % T(0)A / . ei-t T(+)A / . e $ i-t T( $ )A / !

|Bz8h(12)U % U (0) / . ei-t U (+) / . e $ i-t U ( $ ) / !

78UV¼½EH 1 a RLMO BzLh0 )RLMO
C(AO(A+B) % X $1T(0) U ( 0 ) / X $1T( 0 ) U (0)[1] tuvwxyBzL{|al(13)

 m(tu A tu B)aH(5)BlTLN>

tuvwc3xy C
(1)

RLMO
AO=>

(14)

CRLMO
(A+B) % X $1TU
AO

UV¡¢£8Lh77:> X =(2)AO
X % V!1/ 2 V † , S AO
(A+B)V % V!

(15)

1V 2 %( 0 )ACMO†DAO % CCMO
(A+B)
AO (A+B)dCAO

OAO
AA
OAO
BA

D
D

OAO
AB
OAO
BBB­®>(4)a¯°±²³´
(5)

A
A A
DOAO
AA T % " T

(6)

B
B B
DOAO
BB T % " Taµ¶·¸XBSQ(7)

T %T ,TA(16)(1)a U =>atuxy(RO)§G(8)DRO % T† DOAO Taµ¶·¸X(9)DRO U % dU')+(0)A†#0 )OAO (0)AD(AAT 2(0)Aj$#ij(0)Ai

1 i 3 Occ 4 j 3 Vir 2or 1 i 3 Vir 4 j 3 Occ 2aU»HIJ:KLhB ÁÂÃHz£8LhH(8)BlTLN>(17)

D( 0 )RO % T(0)† D(0)OAO T( 0 ) / T(0)† D( 0 )OAO T(0)/T( " )† D(0)OAO T(0):¤V>(9)BlTLN>

B

N¹º8Lh1TijBª«¬fg§G¨©
&D
DOAO % XDAO X† % (*DT( 0 )A % T(0)A V ( 0 )A

N¾N>(14)B¿À:KQ>v(1)a T =>§G¨©

(4)/T( " )A† D(0)OAO
T(0)A % # ( 0 )AAA

N_Lh77:>:¤V>lH¥¦:¤Lh(3)0 )OAO (0)A
T(0)A† D(0)OAO
T( 0 )A / T(0)A† D(AAT
AA

(18)

U (0)† D(0)RO U ( 0 ) / U (0)† D( 0 )RO U (0)/ U ( " )† D(0)RO U (0) % 0

N_Lh77:>(19)

U ( 0 ) % U (0) W ( 0 )N¾N>(18)B¿À:KQ>v1W 2 %(0)1U

D( 0 )RO U (0) 21C/ 1C(0)RLMO† (0)AO
AO
AOijdij(20)(0)†(0)j$d(0)i1 i 3 Occ 4 j 3 Vir 2or 1 i 3 Vir 4 j 3 Occ 2F

C(0)RLMO
2 C(+)CMOAO
RLMO(0)RLMO† (0)AO
AO
AO

F

C(+)RLMO
AO(+)AO (0)RLMO
FAO
CAO/C(0)RLMO†
AO

(29)

aU»HIJ:KLh$ )RLMO† (0)AO (0)RLMO
FAO CAO/C(AO
2 C(0)CMORLMO/-C(+)CMO
RLMO(+)RLMO (0)CMO
S AO
CRLMO
/-C(0)RLMO†AOAO C AO[2] Elongation-TDHF |0)CMO (+)CMO(0)CMO% C(RLMO! CMO / C(+)CMO
RLMO ! CMO

Elongation M:a TDHF |BzLg¢H>
9Äm(tu A tu B)0 )CMO77:>Û2¦p¨© R (CMOBNÅÆº8LÇÈÉM Ê£_LA(A+B+M)(30)

B­®Lh7aAaËÌa TDHF |=

aU»HÜÝf>aU»H¾LhAO
AO

F (A+B+M)C
(21)

CMO
AO

(+)RLMO(0)AO
68FAO
7 (+)RLMO: C(0)RLMO†/ -S AO
F# RLMOAO
AO 9 CAO(A+B+M)(+)AO (0)RLMO/C(0)RLMO†FAO
CAO
AO

(31)

5CMO
$i S AO
AO (A+B+M)CAO (A+B+M)
5t$ )RLMO† (0)AO (0)RLMO/C(AO
FAO CAOCMO
CMO% S AO
AO (A+B+M)C AO (A+B+M)! CMO(+)RLMO0 )CMO
: F# RLMOBÜÝTLN> R (CMO=(21)H:¹º8LÍÎ[¿Ï(22)0 )CMO( 0 )CMOC(RLMO% C(0)CMORLMO R CMO

(32)

CCMO
AO (A+B+M)

1R(A+B+M)CCMO% CRLMOAO
RLMO (A+B+M)( 0 )RLMO (0)CMO
68C(0)CMO†CRLMO (B+M) 79
RLMO (B+M)FRLMOij
2 %(0)(0)! j $ !i " -( 0 )CMO
CMO
ij

1 i 3 Occ 4 j 3 Vir 2or 1 i 3 Vir 4 j 3 Occ 2

BÐÑf>tu A ÒcBcÓTLN>

(23)
RLMO†
AO
RLMO
CMO
86CAO (B+M)FAO (A+B+M)CAO (B+M) 79 CRLMO (B+M)
5 AO
RLMO
(B+M) S AO
(A+B+M)CAO(B+M)CCMO$iCRLMO†AO
RLMO (B+M)
5t
AO
RLMO
CMO
% 68CRLMO†(B+M)S AO(A+B+M)CAO(B+M) 79 CCMOAO
RLMO (B+M)! CMO0 )CMOaU»H¾Lh¼½EH C(RLMOBÞ×Q$ ("- ; 0- )(33)0 )AO( " )AO% $Tr 68 H (AO(A+B+M)PAO(A+B+M) 79

BIJTLhBzLh7aÔ>a¦ ÕVÖ×QL7NHØÙTLh(24)4  ß 6 Table 1 = > à á a  M (CNV) N

AO RLMOCRLMO†S AO
CAO % 1
AO

Elongation (ELG)M:a POM âacdDa

H>(23)aÚBlTLh

(25)

(26)

(27)

CRLMO% C(0)RLMO
AO
AOi-t

/. e CAO
AOF

C( $ )RLMO
AO

/!

CMO
RLMO%C(+)AO
AO/ .e$ i-t( $ )AOAOF/!

(0)CMO
RLMO$ i-t ( $ )CMO/. ei-t C(+)CMO
CRLMO / !
RLMO / . e!

(28)

/ .e

$ i-t%F/. e FC

Table 1. Polarizabilities for POM crystal.

(+)RLMO
AO(0)AO
AOi-tCMO
CMO%!

(0)CMO
CMO$ )CMO/. ei-t ! (+)CMO/ . e $ i-t ! (CMO/!
CMO¼½EH>1 a Elongation-TDHF |=aU»H_Lhß:¤L(Basis set: 6-31G)hMethod!xx!yy!zz

CNV-TDHF

8.459032.3614 41.6113

ELG-TDHF (5)8.459332.3616 41.6080

CNV-TDHF

15.5076 59.3705 78.0778

ELG-TDHF (10)15.5076 59.3703 78.0774

ãäåaæ=map:¤Lh
ELG-TDHF aæ= CNV-TDHF aæNUçèTL7N éÊLh