Appendix#
Point group flowchart#

Fig. 1 Flowchart for the determination of molecular point groups.#
Character tables#
C #
Irrep |
Operation |
||||
---|---|---|---|---|---|
1 |
1 |
1 |
1 |
||
1 |
-1 |
1 |
-1 |
||
1 |
1 |
-1 |
-1 |
||
1 |
-1 |
-1 |
1 |
D #
Irrep |
Operation |
||||||||
---|---|---|---|---|---|---|---|---|---|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
||
1 |
1 |
-1 |
-1 |
1 |
1 |
-1 |
-1 |
||
1 |
-1 |
1 |
-1 |
1 |
-1 |
1 |
-1 |
||
1 |
-1 |
-1 |
1 |
1 |
-1 |
-1 |
1 |
||
1 |
1 |
1 |
1 |
-1 |
-1 |
-1 |
-1 |
||
1 |
1 |
-1 |
-1 |
-1 |
-1 |
1 |
1 |
||
1 |
-1 |
1 |
-1 |
-1 |
1 |
-1 |
1 |
||
1 |
-1 |
-1 |
1 |
-1 |
1 |
1 |
-1 |
Atomic units#
A central problem in molecular physics is to solve the time-independent Schrödinger equation for the electrons in the field of the nuclei. Most often atomic units are then adopted. For the hydrogen atom, we have
where
to arrive at
Choose
with the solution
With
with a solution for the ground state energy that is equal to
Table: Atomic unit conversion factors.
Quantity |
Symbol |
Atomic unit |
SI equivalent |
---|---|---|---|
Energy |
1 |
4.359 744 |
|
Reduced Planck constant |
1 |
1.054 572 |
|
Time |
1 |
2.418 884 |
|
Length |
1 |
5.291 772 |
|
Speed of light |
137.036 |
2.997 925 |
|
Electric constant |
1 |
8.854 188 |
|
Fine structure constant |
1/137.036 |
7.297 353 |
|
Charge |
1 |
1.602 176 |
|
Electric field |
1 |
5.142 207 |
|
Dipole moment |
1 |
8.478 353 |
|
Mass |
1 |
9.109 383 |