Chemistry Reference
In-Depth Information
Let us now introduce a space orbital
x
l
(
r
) and the two spin-orbitals
(
c
l
ðxÞ¼c
l
ðr;
s
Þ¼x
l
ðrÞað
s
Þ
c
l
ðxÞ¼c
l
ðr;
s
Þ¼x
l
ðrÞbð
s
Þ
ð
5
:
9
Þ
satisfying the eigenvalue equations
<
h
0
h
0
c
l
¼ «
l
c
l
c
l
¼ «
l
c
l
;
ð
5
:
10
Þ
1
2
c;
1
S
z
c
l
¼
S
z
c
l
¼
2
c
l
:
«
l
hence has a twofold spin degeneracy, which is
removed in the presence of the field. Using these two spin-orbitals as an
orthonormal basis, the Ritz method shows that the matrix representative
of the Hamiltonian h over the functions
ðc
l
c
l
Þ
is already diagonal, the
(2
2) secular equation, therefore, having the roots
The energy level
<
1
2
g
e
b
e
B
«
1
¼ «
l
þ
ð
5
:
11
Þ
1
2
g
e
:
«
¼ «
l
b
e
B
2
which give a Zeeman splitting linear in the field B:
D« ¼ «
«
¼
g
e
b
e
B
ð
5
:
12
Þ
1
2
«
1
are possible by
magnetic dipole radiation (Dixon, 1965), so that the electron spin can be
reoriented by a photon of energy:
Transitions from the bottom level
«
2
to the upper one
h
n ¼
g
e
b
e
B
ð
5
:
13
Þ
a process originating what is known as electron spin resonance (ESR). A
similar process can occur for nuclei of spin
2
(
1
H,
13
C), with the order of
levels reversed. For
1
H:
eh
2m
P
c
¼
1
1836
eh
2mc
¼
1
1836
b
e
b
N
¼
ð
5
:
14
Þ
