Chemistry Reference
In-Depth Information
The
c
s are called pseudostates, and give best E
2
in the form:
X
jhc
k
j
H
1
2
2
jc
0
ij
c
«
1
E
2
ð
best
Þ¼m
m
c
¼
ð
1
:
72
Þ
«
k
k¼
1
which is known as sum-over-pseudostates expression. Equation (1.72)
has the same form as the analogous expression that would arise from the
discrete eigenstates of H
0
, but with definitely better convergence prop-
erties, reducing the infinite summation to a sum of a finite number of
terms, and avoiding the need of considering the contribution from the
continuous part of the spectrum (Magnasco, 2007).
1.4 ATOMIC UNITS
To get rid of all fundamental physical constants in our mathematical
formulae we shall introduce consistently a system of atomic units (au), by
putting:
e
¼
h
¼
m
¼
4
p
«
0
¼
1
ð
1
:
73
Þ
The basic atomic units are obtained from the SI values of the
fundamental physical constants given in Table 1.1 (Mohr and Taylor,
2003).
The basic au of charge, length, energy and time are then expressed by:
8
<
10
19
C
Charge
e
¼
1
:
602 176
h
2
me
2
¼
p
«
0
10
11
m
Length
;
Bohr
a
0
¼
4
5
:
291 772
e
2
a
0
¼
ð
1
:
74
Þ
1
:
10
18
J
Energy
;
Hartree E
h
¼
4
:
359 744
p
«
0
4
t
¼
h
E
h
¼
10
17
s
Time
2
:
418 884
When the atomic unit of energy is referred to molar quantities, we have
the different SI equivalents:
(
499 kJ mol
1
211 38 eVmol
1
N
A
E
h
¼
2625
:
¼
27
:
10
3
cm
1
mol
1
10
3
Kmol
1
¼
:
¼
:
219
474 6
315
774 6
ð
:
Þ
1
75
