Manifold
Manifolds provide a way of grouping
states together. Interacting states (i.e. those
with
perturbations
between them) must be in the same manifold, and it may be convenient to
group related states together (such as a set of vibrational states from
the same electronic state.) Manifolds therefore contain two types of
object,
states and perturbations. To add a new state or
perturbation to a molecule, right-click on
the manifold in the
constants and
select "Add new...". The settings here are the
same, whether simulating
linear,
symmetric top and
asymmetric
top molecules, though the defaults for LimitSearch are different..
Settings
Jmin |
Minimum J in
calculation - set negative to take from molecule
or manifold. |
Jmax |
Maximum J in
calculation - set negative to take from molecule
or manifold. |
Initial |
True to include population in this state when calculating
spectra. |
Colour |
Colour for spectra - set to "None" to get colour from
elsewhere. |
EigenSearch |
Identify state by looking for largest coefficient in
eigenvector. |
LimitSearch |
Set to assume the energy ordering within an individual state
does not change, but the eigenvectors are used to select the state. |
AutoQConverge |
Partition function (Q) sum extends until converged (if true)
or Jmax (if false). See J range and Partition
Functions for a discussion of this.
|
EigenSearch and LimitSearch
These flags determine some of the quantum numbers displayed, but do not
affect the energy levels and intensities calculated. The overall
angular momentum and rovibronic symmetry will always be correct, but
other quantum numbers can be open to varying interpretations. With
EigenSearch set to true
(the default) the basis function with the
largest contribution is used to determine the quantum numbers (as the
basis function can normally correlated with a particular set of quantum
numbers). If LimitSearch
is also set to true, then the energy level ordering for a particular
state within a manifold (for levels of a given total angular momentum
and symmetry) is assumed to be standard. This is the default for
asymmetric tops (from version 5.1.159) but not for linear molecules or
symmetric tops.
As an example, consider the asymmetric top quantum
numbers, Ka and Kc. If the
representation is chosen so that the a
axis is used for the K
quantum number in the basis then a given basis state is readily
identified with a particular Ka.
(In addition a given value of Ka
will correspond to one or two values of Kc,
and the particular one can normally be determined by symmetry.) In a
near prolate limit the mixing between basis states will be small and
the energies will increase smoothly as Ka2.
In this circumstance the same quantum numbers will be assigned
regardless of the EigenSearch and LimitSearch settings. If the mixing
between basis states is large, perhaps because of centrifugal
distortion or other factors, then it is possible for the highest energy
state, for example, not to be dominated by the state with the highest
value of Ka. If
EigenSearch=true and LimitSearch=false then the largest eigenvector
coefficient would be used to assign Ka
so the energy ordering would not correspond to the Ka ordering. If
EigenSearch=true and LimitSearch=true then the Ka
ordering is assumed unchanged on diagonalisation, which is normal
practice for asymmetric tops. If EigenSearch=false then the ordering is
also assumed unchanged on diagonalisation, though this will not handle
the case where there is more than one state in a manifold with
overlapping energy levels, such as two interacting vibrational states.
Note than none of the above algorithms are
guaranteed to produce unambiguous values for all the quantum numbers.
If no search on coefficients is done then it is easy to slip to the
wrong state entirely. If a search is done then if mixing within or
between states is strong then there are circumstances where the choices
made are not obvious. (If the largest coefficient in several
eigenvectors is less than sqrt(2) then there can easily be two
eigenvectors where the largest coefficient corresponds to the same
basis state, which will always defeat a search based on magnitudes.)