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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, asymmetric top or vibrating molecules, though
the defaults for LimitSearch are different.

Initial is a key
setting here; at least one manifold must have this set. This
will normally be the lower manifold in a transition, but could
be the upper state for fluorescence or both if the population
difference should be calculated.

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, and should be set true for any manifold with
significant population. If this is false then the state Origin values are
assumed to be relative, which can give negative transition
frequencies. This is useful for analysing spectra with a
frequency scale relative to unknown centre frequency, but
can give incorrect results in other circumstances. |

Colour | Colour for spectra - set to "None" to get colour from elsewhere as explained in Determining Colours and J ranges. |

EigenSearch | Identify state by looking for largest coefficient in the eigenvector. |

LimitSearch | Set to assume the energy ordering within an individual
state does not change, but the eigenvectors are used to
select the state within a manifold. |

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. Note that this is forced to be false in the presence
of a static electric or magnetic field. |

UsePopParams | Set to use numerical
populations specified as parameters, rather than Boltzmann
equation. See below and Non-Boltzmann
Populations for more information. Alternatively, an
overall Temperature
< 0 will force this for all manifolds. |

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 be correct unless a static field is present, 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, K_{a} and K_{c}. If the representation is chosen
so that the K quantum number in the
basis corresponds to the a
axis then a given basis state is readily identified with a
particular K_{a}.
(In addition a given value of K_{a}
will correspond to one or two values of K_{c}, 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 K_{a}^{2}.
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 K_{a}.
If EigenSearch=true
and LimitSearch=false
then the largest eigenvector coefficient would be used to assign
K_{a} so the
energy ordering would not correspond to the K_{a }ordering.
If EigenSearch=true
and LimitSearch=true
K_{a} 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
probably not give useful results 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.) It is important to note that this only affects the labelling of transitions, not the calculated positions or intensities

Numerical populations can be specified here;
see Non-Boltzmann Populations for how
to set this up. The parameter names are of the form "*J*
<symmetry number> <eigenvalue number>" or, for use
only when external fields are present, "*M* -1 <eigenvalue
number>". (Both types of entries can be present, but only one
set will be active for any given simulation.) Half integral
quantum numbers will show as fractions rather than decimals (5/2
rather than 2.5).

## Menu Items

Right clicking on a manifold in the constants window gives the following items (in addition to the standard ones):