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

Settings

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.

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 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_a². 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_aordering. 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

Parameters

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):

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.