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Asymmetric Tops

See Making an Asymmetric Top Data File for an introduction.

PGOPHER will calculate rotational structure for asymmetric tops for the point groups C1, Ci, C2, Cs, D2, C2v, C2h or D2h, including effects due to electron and nuclear spin.

Quantum Numbers

The following standard quantum numbers are used or displayed for asymmetric tops:
J
 Total angular momentum excluding nuclear spin
N
 The rotational angular momentum  (excluding electron and nuclear spin). J = N + S
Ka
 The projection of N on to the a inertial axis; see Symmetry and Axis System
Kc The projection of N on to the c inertial axis.
K
 The projection of N onto the inertial axis determined by the representation.

Symmetry

See Symmetry and Axis System

Basis States

The basis states used by  PGOPHER are standard symmetric top functions, and are displayed as: 
|Name J N K +->

where Name is the manifold and state name and J, N and K are the quantum numbers described above. N is ommited for singlet states. If + or - is present, it implies the basis state is the symmetised combination:

1/Sqrt(2){ |JNK> ± |JN-K> }

If hyperfine structure is included in the calculation then F (and intermediate quantum numbers if there is more than one nucleus) is added to the end. If PhaseAdjust is set, then these functions are multiplied by an additional phase factor to minimize the number of imaginary matrix elements:


 K even, +
 K even, -
 K odd, +
 K odd, -
N even
 1
 -i
 i
 -1
N odd
 i
 -1
 1
 -i

State Labels

The possible contents of state labels are:
Name
 The manifold and state name
N
 The N quantum number
Ka The projection of N along the a inertial axis.
Kc
 The projection of N along the c inertial axis.
J
 The J quantum number; only show here if S > 0.

Hyperfine quantum numbers are added at the end as required.
For example, a state may give the following label:
v=0  6  1  6
where the name is v=0, N=J = 6, Ka = 1 and Kc = 6.

Further Details