. 2002. 549. . .8(31)

15

539.19 .

,

© 2002 . . , . .

,

. , .

[1,2,3] (Coupled Cluster, CC)

. , ,

[2]. - (Gaussian, SAPT . .).

, ( CC ), ( -ansatz):

exp( ) 0CC T , (1)

T

(CCSD)

1T

2T :

1 2T T T , (2)

, - , 0 . ,

( ) . (1)

[4]. .

, ( ).

, ( 3T ) [5]. (CCSDT) :

1 2 3exp( ) 0CCSDT T T T . (3)

1T , 2T , 3T

:

1,

ai a i

a i

T t a a , (4)

2abij a i b j

i ja b

T t a a a a , (5)

3abcijk a i b j c k

i j ka b c

T t a a a a a a , (6)

,a ia a

- i,

c . ait , ab

ijt , abcijkt

-,

.

,

16

- - .

. , , SDT :

211 1 22

0 ( )(1 ) 0 0CCSDTH E T T T (7)

2 31 11 1 2 1 2 1 32 3!

0 (1 ) 0 0ai CH T T T T T T T , (8)

2 3 2 4 21 1 1 1 11 1 2 1 2 1 2 1 1 2 3 1 32 3! 2 4! 2

0 (1 ) 0 0abij CH T T T T T T T T T T T T T , (9)

3 2 21 1 12 1 2 1 2 2 1 23! 2 2

0 (abcijk H T T T T T T T T

2 21 11 2 3 1 3 1 3 2 32! 2!

0 0C

T T T T T T T T T , (10)

H

, 0ai , 0ab

ij

0abcijk -

, ( )

0 . ......0 ...... 0a

i C

,

(connected) (linked) , , [6],

SDT .

-

- (7)(10) , [7].

, , , , . .

c

( ait ),

( abijt ) ( abc

ijkt )

:

, , . ( ) - ,

- ( , ). -

( iki f k f ) :

. ic ka ic ka ic ak

:

.

- . -

i,j,k,l , - a,b,c,d

. . , . .

17

, ( )

. ,

abijt . ,

, :

,

1( / )

2acdijk

c dk

P a b t cd bk , (11)

( / )P a b

- a b.

X(i,j,a,b)

( / ) ( , , , ) ( , , , ) ( , , , )P a b X i j a b X i j a b X i j b a . (12)

, , , , , , .

3T , 4T

.

,

, . ( ),

. 1, 0. ,

, ,

. ,

- 0abij

1 2T T

:

c bdi jkt t , (13)

:

0 10

110,

. , ,

.

(

). :

,

.

,

18

,

.

. , , :

. ( -, )

:

, , i, j

a, b, :

,

( / | / ) c bdi jk

c dk

P i j a b t t cd ak . (14)

, CC- .

1) :

.

2) , ( )

. , .

- . ,

( , ).

3) ,

:

U1

U2

U3 , (15) Un

n- .

. ,

. .

4) :

D1

D2

D3 , (16) Dn

n- .

.

5)

, ,

, , - - .

- CCSDT.

( )

. . , . .

19

( .1), ( .2) ( .3).

.

[7].

. CCSDT.

.

.1. ( )

CCSDT- - .

.2.

CCSDT - .

.

,

20

1. Cizek J. J. Chem.Phys. 1966. V.45. P.4256-4266. 2. . , . .:

, 1966. 152 . 3. Bartlett R.J. J.Phys.Chem. 1989. V.93. P.1697-1708. 4. . ., ., . ., A.A.,

. 2001. 532. 7(30), .52-58. 5. Lee Y.S. Kucharski S.A., Bartlett R.J. J.Chem. Phys. 1984. V.81. No.12. P.5906-5912. 6. Goldstone J. J.Proc.R.Soc.(London). 1957. A239. P.267-279. 7. Kucharski S., Bartlett R.J. Adv. Quant. Chem. 1986 V.18. P.281-345.

21 2002 .

Kharkov University Bulletin. 2002. 549. Chemical Series. Issue 8(31). V.V.Ivanov, D.I.Lyakh. The automated generation of coupled cluster diagrams. Cluster expansion which includes three particle excitations.

The algorithm for generation of diagrammatic representation, algebraical formulae and computer code of coupled cluster method with arbitrary order of excitations has been proposed. The algorithm was applied to the method with three particle excitations

.3 .

CCSDT - .