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The quantum numbers are given in the following order:
(or
);
and
(or
;
);
;
...
for the upper state followed immediately by those for the lower state
(see also below).
is the total rotational angular momentum excluding electron
and nuclear spins. For singlet molecules,
, the total rotational
angular momentum including electron spin, is equal to
.
and
are the projections of
onto the A and C
inertial axes, respectively. For symmetric top molecules, only
is needed (instead of
and
) along with
or
, which
designate the parity; if redundant, the latter might be
omitted. Instead of
,
or
may be used for linear
molecules.
is a state number! It specifies different vibrational
or electronic states. It may also be used to distinguish between
different species that have been fit simultaneously. Details on the
meaning of the state numbers are given in the documentation! Note:
More than one state number may be needed to designate one
vibrational state - this is the case, for example, for a degenerate
(e.g. bending) state of a symmetric top molecule!
...
designate spin quanta. In general, the electron
spin
is coupled to the rotational angular momentum first, followed
by nuclear spins. In this case
=
Very Important:
Exactly two characters are available for each quantum
number. Therefore, half integer quanta are rounded up! In addition,
capital letters are used to indicate quantum numbers larger than
99. E.g. A0 is 100, Z9 is 359. Small types are used to signal
corresponding negative quantum numbers.
Since the program was written for asymmetric top molecules, some of
the quantum numbers may be redundant.
Six quantum numbers are available at most to describe the upper and
lower state, respectively. In case more quantum numbers are needed,
even if some of them are redundant, the only spin designating quantum
numbers are
,
, were
is an aggregate spin number (see
below).
Next: Aggregate spin number
Up: Coding the quantum numbers
Previous: Coding the quantum numbers
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Gildas manager
2023-06-01