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### Exercice configuration électronique de Mn 1s22s22p63s23p64s23d5 L'atome de manganèse a

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M
d V (M) ii
M
c c (M) (M) c> 01 3 2kd k+1 2d e d
V k M
M1
M M d ! +1i 1 i
c (M )1 i 2di
M d
V (M) ii
c cM (M) (M)1 3 2kd k+1 2d e d
c> 0 V k
M M1
M M d ! +1i 1 i
c (M )1 i 2di
4
[0; 1[
p
n
2(n 2p 1) n[ ; +1[ p< n = 3
4 2
[0; +1[
(M;g)
p = dd +dd d
2d L d
pH (M) p = 0
0< (M;g) (M;g):::1 2
1 0 2p = 1
(M) = d
(M)Ker d
(M)
( (M;g))i
0 2d (M) d
(M)
0 < (M;g) (M;g) :::1 2
( (M;g))i
C ;C ;C > 0 V > 01 2 3
M;g
d V

1
# (M;g) C Vi 22C V (1 +d )1

1
# (M;g) C Vi 32d
[1; 1 +x]
k + 1 k
V > 0 c(V )> 0
M
V d k (M)1
c c (M)k+1 23 2kdd e d
M1
c > 0
(M ) M d ! +1i 1 i
c (M )1 i 2d
i
M1
M1
Mi
a
c > 0M
M
M M Mm c mM
2 2x 2T [0; +1[ g =e g dx gT T
2T T
2 1l T B S
2B (R) [0;l]
2 2 2 2 2g = cosh r dt + dr + sinh r d
t r
2B Bf0g Bflg
2B
Ma
a > 0 V > 0 (V ) > 0
0 0(M;g) (M ;g )
0V M Ma a
1 0 0 0g gg M Ma a
2 1T ’ B S
2P =f(p;q)2Z ; p q g[1
R! +1
2R tele !c
R! +1
k
2T
2 1’B S (p ;q )2Pk k
K > 0 p ;q >K kk k
1 1H (M)!H (@M) b (@M)=21
k 1 k k k!H (@M)!H (M)!H (M)!H (@M)!c
kH (M)c
M
k k n k 1H (M) ! H (@M) H (@M) !
n kH (M)c
k k : H (M)! H (@M)1
i : @M ! M
n k 1 0 n k2
(@M) 2
(M)
0 0 0i ( ) = d = 0 @M ([]) = [d ]2
0d

n k 1 k[]2 H (@M) []2 H (M)
h ([]); []i 2
Z Z
0 0h ([]); []i = d^