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V

XI I

XIII

XIV


XI I

,

( . . . , . . ,

),

, . (XII.1.1) , { (XII.1.2)

. ,
x 1.
-

.

,
E

(E ),
E

(E )
E =E +E

(E ) +E

:

E

E.

( . x 2 . X). p

i1 p = Z gi exp(;Ei =k T )

gi |

, ( . (VIII.3.8)).

i- P , Ei : Z = gi exp(;Ei =k T ) |
i


x

1.

-

353
E

> k T,
, , , -

E

. k T, , .
x y z.

, . .

, , -

(x y z ),
i dx dy dz :

(x y z )
pi (x y z ) = j (x y z )j2 dx dy dz :

j i (x y z)j

2

(XII.1.3) 1s, (XII.1.4)

,

, = (r) = p;1=2 a3=2 exp(;r=a0 ) 0 r|
p exp(;2r=a0 )

a0 = ~2 =(me2 ) | .

,

(XII.1.5)
s-

,

. . .

.

, .

(XII.1.6) . . (XII.1.7)

.

,

2 2 2 2 ; 2~m @ 2 + @ 2 + @ @x @y @z

2

+ U (x y z ) = E
E|

U (x y z ) | ,

(XII.1.6)

)

.
b H =E

(@ 2 =@ x2 )

( (XII.1.6)


354
b b2 H = 2pm + U (x y z ) = @2 @2 ~2 = ; 2m @x2 + @y2
px py pz bbb

XII.

p2 + p2 + p2 bx by bz + U (x y z ) = 2m @2 + @z2 + U (x y z )

(XII.1.8)

,

@b @ px = ;i~ @@x py = ;i~ @y pz = ;i~ @z : b b

(XII.1.9)

. , .

,
E1 E2 : : : En .

,

, (XII.1.6) | -

, .

,

= (x y z t)
b i~ @ = H @t

: (XII.1.10) , (XII.1.10) (XII.1.11) (XII.1.12) : , , -

b H|

(XII.1.8).

b H

y

(x y z t) = (x y z ) exp(;iE t=~): (XII.1.11) (XII.1.10), (x y z ), ,
2 2 2 2 ; 2~m @ 2 + @ 2 + @ @x @y @z 2

:

+ U (x y z ) = E

(XII.1.6). j (x y z t)j2 (XII.1.11) j (x y z t)j2 = (x y z t) (x y z t) = j (x y z)j2 : | , . (XII.1.11) , t.


x

1.

.

355
U = ;e2 =r En = ; 2me~2 n2 ).
4

,

(XII.1.13) (XII.1.14)

n|
nl m

(

(x y z ). l,

, 2px , 2p
y

s,

n = 1 2 ::: 0 1 ::: n;1 m, l 2l + 1 ;l ;l + 1 : : : ;1 0 +1 : : : l ; 1 l. E1 1 0 0 (x y z ) n = 1, l = 0, m = 0. E2 (n = 2) : 2 0 0 , 2 1 1 , 2 1 0 2 1 ;1 , . . E2 . E1 , 1s, ,E2 | 2s, 2px , 2py 2pz . , , 1s, 2pz . . XII.1 , 0 95. -

n, l m (

), . .

-

. , +1=2

-

;1=2
,

s,

m=0 ,

. XII.1 . n = 1, l = 0, 1s, 2p , 2p , 2p xyz , , .
~
( ).

. . , 2|

-

,

, , | , 1s.
a

. .

1

,


356 1s:
1

XII.

b.

= ya (1)yb (2)
yb

.. (XII.1.4). a, ,
ya

. 1| (1) , ,
1

ya

(1)

b.
2

(2) ,

2 :

(XII.1.15) -

(2)

yb

,

= ya (2)yb (1) (XII.1.4). ,
E.

(XII.1.16) , . -

,

, , .
ya

,

,

2

C

1

= C1 1 + C2 2 C2 | . , C1 C2 E
C

, =C

1

ya

(1)yb (2) + C

2

(2)yb (1) ,

: (XII.1.17)

.

(XII.1.17), . :

(XII.1.18) (XII.1.19) (XII.1.20) (XII.1.21)

1 = 2(1 + S 2 ) ya (1)yb (2) + ya (2)yb (1)]
C+ EC = 2EH + 1 + SA 2

A

1 = 2(1 + S 2 ) ya (1)yb (2) ; ya (2)yb (1)]
C; EA = 2EH + 1 + SA : 2


x

1.

-

357 (XII.1.18) { (XII.1.21) C , A S | EH |
1 2

,
A

A|

| .

C S| ,

, ,

C

(XII.1.18) .

(XII.1.20)

,

, (XII.1.22) (XII.1.23)

(XII.1.22)

C < 0 A < 0 jC j jAj: (XII.1.19) (XII.1.21) EC < 2EH < EA :

. XII.2
EC | EA |

, ,

. XII.3 = ya (1)yb (2) A= 1; 2 :
H
2 2

:
1

C| A|

= ya (2)yb (1) C = 1+ 2
(c(c -

),

)

, . , ( . XII.2). ,, ,
C

1s . .

.

EC

r = re -


358 ,
A

XII.

EA ,

. ,

(1s)

,
.

(

),

. ( . (

,

-

): C . XII.3). -

.

. XII.4

(S1 )
A.

(T1 )

C

. XII.5 : 1 | s, 3 | s- psc

. . ,

, -

,
,

2

| p- , -

,

-

,

s- p-

p-

,

C

, +1=2 ; 1=2 = 0. 1.
C A

, , .. , ,

.

, . ,

,
A

, ,
A

, ,

,
A

,

.

.


x

1.

C A

359 ( . XII.4). ( . XII.5). .
c

c

. , ,

,

,

,

-

.

. XII.6
I

|

,

p

-

II

|

p-

. | .
p-

, ( ,
c

. . XII.6).
pc-

,
pp

,
p

, .
pp c

, . -

!

,
p

p-

.

,

-

,
1

, .

-

.

c

!

,
c

.

0

.

.


360
p

XII.

!

p

-

C

.

A

(XII.1.18) (XII.1.20)
Z
1

(XII.1.24)

d01 =
dV |

0

b d 1 dV

d01 ,
pp-

.

b d = ;er | ,

r|
, .
.

-

.

,
p

-

, |
p

. (XII.1.25)

-

.
pz :

, =
X
n

n

,

Cn n

Cn | Cn , En .
n

,

n

|
p

. , . ,
n

(XII.1.25). , (XII.1.25)
n n
.

-

-

(XII.1.25),

.
En

,

Cn | jCn j2

(XII.1.25) : . (XII.1.26) (XII.1.17). En , (XII.1.27)

,

En

X
n

jCn j2 = 1
: En jCn j

,

E=

X
n

2


x

1.

-

361 ,

jCn j2 = Cn Cn .
b H|

E=
, (XII.1.25) .
pp

Z

b Hd

t

(XII.1.28) , . (XII.1.25). , -

(XII.1.8). (XII.1.28)
Cn

, . .
E

p-

,

-

Cn

p-

:

X
n

Cn (Hmn ; ESmn ) = 0: Hmn =

(XII.1.29) (XII.1.30) (XII.1.8) (XII.1.31)

Z Z

m

H md

t

|
Smn =

n m dt n m

| , ..
Hmn = 0.

.

,

Smn = 0
a b

m 6= n Snn = 1. Hnn = a

Hnn 1 = b.

(XII.1.29) pE1 = a + 1 62b, E2 = p2E1 + 2 p.

1 (

( . (XII.1.19) { (XII.1.21)). , , E = a + b (b < 0), . . p, , 2E1 = 2a + 2b. 4 pp. (XII.1.29): a + 0 62b. , E2 = 4a + 4 48b, 0 48b 0 48b p. , . x 1 . IX . . IX.2, IX.4), px -


362 N, O, P.
p

XII.

. , ,

. , . , . . .
p

, -

,

x 2.
.

| 190 , )
p p

,

|
p

! !

,

!

.

p>C=O, p

. |-

p

, 225

p-

,

(nn

n

-

!

-

,

(

. XII.7).

. XII.7 ) , (I ) (III ) ( -

p

(II )

!

p

=n

!

p

)

(

, n-

p

, ,

py -

,

.


x

2.
| , , . 220 280 , , 410, 440 480 . 275 222 ) (
t

363

n

!
.

p

-

. : , , -

330 { 350 04

|

330 { 350
t

. , ( , , (. ,. | C ( (
p

0 17, 2 5 10;9 . ) 258 .
p

0 02 ,-

7,

( . ,

). ( ) . ). , -

260 ) 280 { 320 ) . . 8. , C 6,

!p n!p

-

-

. XII.8
I

|
5

, II |
,
p

( -

.

, 1975): C . XII.8).

-

p

-

(


364 , , , , ,

XII.
p

-

.

. , . ,

, . . 10 { 30%. ( ) (2 ) , 1977) ( , ) . , | . ( , ( 260 . XII.9). , 260 . ,

. XII.9 (1 ) ..
l

!
, , .

, ) , .

.

(

,

,

. XII.10 . , , 260 ,
p

,

( . XII.11). , , ,-

!

p

-


x

2.
. XII.10 (E ..

365

0

E1 )
, 1975):

-

I II

| |

(

, -

. ) ( . ( ( ( , ) ). ).

. XII.11

(I )

(II ) ( Atkins, 1974)

. | . . | (.. ,

. . , ). ,

| -

), (.. . XIII, x 11.


366

XII.
p282

p

!

. ,

,

,

. , .. . (
p-, c

n

!

p

--

. XII.12 ,
p

)

-, c c

,

n.
p-

.
c

,
c

-

-

p

-

.
,

-

n
p

!

p

-

!

p

.

{

190 a-

.

a

. ({HN{CO{),
.

a

-

-

pa -

, , . , .. , . , , , .

p

-

(. .

,

. IX.2). .

. XII.12

,

( . x 1 . XII), , . . , , .. , , . ,


x

3.
, . , 2n , 2n

367 . -

n

. XII.13 .. , 1984)

(

1s
c

-

H. ( E)

C, N O (E = 5 7 ). (5 7 ) ,

1s, 2s, 2p

p, 10 . (9 7 ). .-

. XII.13 .
x
3.

. , . , ..

-

, .

-


368 . | (nL 6= nD ) :
a a

XII.
( , )| - (nL ) ,
a

(

). . (nD )

-

-

,

= (p=l)(nL ; nD ) 1 ( . XII.14).

(XII.3.1)

|

. XII.14
E
r

(a)
E E
a,
l

,

Va ,

, ,

E

r

l

. -

..
1 .

' 10;5 ,

,

l

= 314
a

1

( 57 ) a]

: nL ; nD '

] = a=(lc) m] = a] M=100
a

|

,/

3

, M|

l|
e

. ,
eL

,

m] : (XII.3.2) (XII.3.3) c| -

, :
e

=

;

e

D

(XII.3.4)
;1 ;1 .

|

,


x

3.
, ,
a.

369 , ( . XII.15). : = (p=l)(eL ; eD ) | , .
M

-

(XII.3.5) (XII.3.6)

= 3300(eL ; eD ):

. XII.15
A0 ,

,
,
a l

, , (
.
a

)

(A)

-

]=

X

| . (XII.3.7)
a

Ak |
,
w
2
X

k

l2

Ak

; l2 k
,
w1 w

(XII.3.7)

lk
2

kw0 . VIII.3).

( . x 1 . VIII

]w =

k

w2 k

Rk

;

w2

(XII.3.8) , Ak = Rk l2 . k

Rk |

k-

.


370

XII.

. XII.16

,

a

(el ; er )

-

(I )
. XII.16 . ,

(II )
, . -

(w
|

1

w2

)
-

kRk = Im(dk dk ) em
de

dm

Im |

.

,
de .

(XII.3.9) -

,
de 6= 0, a dm = 0.
p

n

!

, : dm 6= 0 (de = 0),
p

dm .

!

p

-

,n

!

p

-

-

p

!

p

-

.

-

,


x

3.
dm de , p

371 ,

!

p

)

.
de

(XII.3.9). (p, , ..

dm ,

de

n

!

p

-

dm .

. -

, .

,

Rk
. , ,

de , dm .