- #1
DanAbnormal
- 23
- 0
Im doing a study on a polyatomic molecule which is assigned by six quantum numbers, namely the three vibrational modes, and the Rotational quantum number J, and its projections on the A and C axes, (Ka and Kc):
J, Ka, Kc, v1, v2, v3
Each combination of these numbers has an energy in wavenumbers, ie. 0 0 0 0 0 0 has energy 0 cm^-1 (ground level)
I have to use fortran to manipulate a few lists of these numbers (big lists!) and was wondering if there was any sort of method of combining the numbers into a compound, unique number because its the only way I can perform the manipulation in my program.
My project supervisor says there is a formula which can be used to combine the rotational quantum numbers (J, Ka, Kc) as such:
0 0 0 0
1 0 1 1
1 1 0 2
1 1 1 3
2 0 2 4
2 1 1 5
2 1 2 6
2 2 0 7
2 2 1 8
3 0 3 9
3 1 2 10
3 1 3 11
3 2 1 12
3 2 2 13
3 3 0 14
3 3 1 15
and so on...
The list is ordered according to the value of J, in the first column. The groupings arise as a result of the 2J+1 degeneracy. So apparently there is a formula which fits this, I can't figure it out!
Ive tried by noting that the first "number assignment" for a new grouping is the square of the J value, can't get anything else out of that.
Also, even though its not my first priority, it would be nice if there was a similar situation for the vibrational quantum numbers, such that I could ultimately comine all six numbers into a unique identifier, but for now the rotational numbers is what I am concerned about.
Cheers
Dan
J, Ka, Kc, v1, v2, v3
Each combination of these numbers has an energy in wavenumbers, ie. 0 0 0 0 0 0 has energy 0 cm^-1 (ground level)
I have to use fortran to manipulate a few lists of these numbers (big lists!) and was wondering if there was any sort of method of combining the numbers into a compound, unique number because its the only way I can perform the manipulation in my program.
My project supervisor says there is a formula which can be used to combine the rotational quantum numbers (J, Ka, Kc) as such:
0 0 0 0
1 0 1 1
1 1 0 2
1 1 1 3
2 0 2 4
2 1 1 5
2 1 2 6
2 2 0 7
2 2 1 8
3 0 3 9
3 1 2 10
3 1 3 11
3 2 1 12
3 2 2 13
3 3 0 14
3 3 1 15
and so on...
The list is ordered according to the value of J, in the first column. The groupings arise as a result of the 2J+1 degeneracy. So apparently there is a formula which fits this, I can't figure it out!
Ive tried by noting that the first "number assignment" for a new grouping is the square of the J value, can't get anything else out of that.
Also, even though its not my first priority, it would be nice if there was a similar situation for the vibrational quantum numbers, such that I could ultimately comine all six numbers into a unique identifier, but for now the rotational numbers is what I am concerned about.
Cheers
Dan