Computing spectra (intensities and line lists)¶

Absorption or emission spectra as well as line lists, partition functions and other related quantities can be computed by adding in the input file an intensity section. Here is an example of its general structure:

intensity
  absorption
  thresh_intens  1e-15
  thresh_coeff   1e-15
  temperature   300.0
  J,  0.5, 1.5
  freq-window  -0.001,  25000.0
  energy low   -0.001, 6000.00, upper   -0.00, 30000.0
end

If the keyword intensity is followed by none or off then the calculation of intensities is disabled and the section is ignored. This is useful to temporarily avoid the intensity calculation without removing or commenting out the relative input section from the input file. The meaning of the keywords is explained in the following.

Note

Duo input keywords are case-insensitive. In this manual we use lowercase for readability.

Batching over $J$ ranges¶

It is possible to compute intensities in independent batches over $J_{\rm min}\!-\!J_{\rm max}$ ranges (e.g. 0–1, 1–2, 2–3, …). To prevent overlaps when stitching line lists, transitions within the lowest $J$ of the batch are omitted, i.e. $J_{\rm min}\leftrightarrow J_{\rm min}$ are excluded (except for $J_{\rm min}=0.5$ , where $0.5\leftrightarrow 0.5$ are included). Transitions $0\leftrightarrow 0$ are forbidden.

Each batch produces a partial .states/.trans pair that can be concatenated to form a complete line list. Duo keeps the internal state numbering consistent across batches.

Example:

INTENSITY
....
linelist CH_A-X
states-only
.....
END

** bound used in INTENSITY calculations to produce bound-only spectra or linelists. For bound, Duo identifies bound wavefunctions corresponding to the upper state and uses them to compute bound transition intensities. See also Treating unbound states.

intensity
  absorption
  bound
  thresh_bound  1e-6
  thresh_intens 1e-15
  thresh_coeff  1e-15
  temperature   300.0
  J,  0.5, 1.5
  freq-window  -0.001,  25000.0
  energy low   -0.001, 6000.00, upper   -0.00, 30000.0
end

** unbound (opposite of bound) used in INTENSITY calculations to produce unbound-only spectra or linelists. For unbound, Duo identifies unbound wavefunctions corresponding to the upper state and uses them to compute unbound transition intensities. See also Treating unbound states.

Example: Intensities of BeH¶

Here we use the potential energy function of BeH from the example Example: BeH in its ground electronic state.

For intensity calculations one needs an electric dipole moment curve, which we take from the spectroscopic model used in the ExoMol-I paper by Yadin et. al (2011)

dipole  1 1
name "<2Sigma+|DMZ|2Sigma+>"
spin   0.5 0.5
lambda  0  0
type   grid
values
400     -0.4166624920
500     -0.0241871531
600      0.2217732500
700      0.3386323420
800      0.3661076190
900      0.3311512400
000      0.2513061130
100      0.1379591390
200     -0.0012406430
300     -0.1588361650
320     -0.1920270000
340     -0.2256736540
350     -0.2426539090
360     -0.2597311920
400     -0.3288944440
500     -0.5056369720
600     -0.6824442480
700     -0.8513506410
800     -1.0025214800
900     -1.1238133700
950     -1.1687609400
000     -1.2005094800
020     -1.2089972000
050     -1.2166847200
070     -1.2181089800
100     -1.2136337000
300     -1.0182994100
400     -0.8538885220
500     -0.6736179730
600     -0.5046631750
700     -0.3634556350
800     -0.2548814520
900     -0.1758884440
000     -0.1201861300
100     -0.0815224742
200     -0.0549121655
300     -0.0367099205
400     -0.0243335573
500     -0.0159701097
600     -0.0103484461
700     -0.0065800412
800     -0.0040495078
900     -0.0023383813
000     -0.0011684378
200      0.0002034367
400      0.0008546009
600      0.0011177434
800      0.0011645509
000      0.0011023829
000      0.0005429083
000     -0.0000033249
000     -0.0000085504
end

intensity
 absorption
 thresh_intens  1e-30
 thresh_line   1e-30
 temperature   300.0
 linelist   beh
 j,  0.5, 10.5
 freq-window   0.0,  7000.0
 energy low   -0.001, 5000.00, upper   -0.00, 12000.0
end

This will produce a line list for BeH in ExoMol format in two files .states and .trans, which can be processed using ExoCross, see also ExoCross-tutorial.

Selective intensity calculations via the `FITTING` transition list¶

Duo traditionally offers least-squares refinement of diatomic models by fitting to experimental energies (term values) or frequencies (line positions) using the Duo fitting section. While refinement of transition-moment curves (electric dipole, magnetic dipole, electric quadrupole, etc.) against experimental intensities is a natural next step, it requires efficient control over which transitions are computed and compared to experiment.

As a first step towards intensity-based refinement, Duo can now reuse the FITTING transition list to select a limited set of transitions for which line intensities are generated. This simplifies comparisons with experiment and can make the production of intensities significantly more efficient when only a small subset of lines is required.

To enable this mode, add the keyword intensity immediately after FITTING. This tells Duo that the FITTING section is used as a transition selector for the intensity calculation. Without this keyword, FITTING and intensity are treated as mutually exclusive in a single run.

Example: selecting transitions via `FITTING`¶

The usual fitting syntax for line positions is retained; the only addition is the keyword intensity after FITTING:

fitting
intensity
lock    0 (cm-1)
frequencies                      ( state      v     ilambda isigma omega    weight  comment <-  state v ilambda isigma  weigh
      5.5 f        29   5.5  e      1       16725.21  a      0   1   0.5   1.5  x      0   0   0.5   0.5    0.0500        61uhak.1382
      5.5 f        27   6.5  f      1       16715.68  a      0   1   0.5   1.5  x      0   0   0.5   0.5    0.0500        61uhak.978
end

In this mode, Duo will compute intensities only for the transitions listed in the frequencies (or energies) table, while still applying the usual selection criteria from the intensity block (thresholds, spectral window, energy windows, etc.).

Associated `intensity` block¶

A standard intensity block must still be present, since it defines the type of spectrum and global controls (temperature, partition function, thresholds, windows, and the $J$ range):

intensity
  absorption
  thresh_coeff  1e-60
  thresh_dipole 1e-9
  temperature   300.0
  Qstat  337.0515
  J,  5.5, 6.5
  freq-window  -0.001,  20000.0
  energy low   -0.001,  3000.00, upper   -0.00, 23000.0
end

Note

The effective transition set is the intersection of: (i) transitions explicitly listed in FITTING and (ii) transitions passing the filters defined in the intensity block.

Efficient use with checkpoints (recommended workflow)¶

Selective intensities are particularly effective when combined with checkpointing. A common workflow for refining or testing transition-moment curves without recomputing rovibronic states is:

Read eigenvalues/eigenvectors and vibrational basis functions from checkpoints.
Recompute only the transition-moment matrix elements for the current moment curves.
Compute intensities only for the selected transitions.

For example:

checkpoint
  eigenfunc read
  dipole   calc
  filename YO
end

Here, dipole calc instructs Duo to recompute the required moment matrix elements using the stored vibrational basis functions from YO_vib.chk, while rovibronic eigenvalues/eigenvectors are taken from YO_values.chk and YO_vectors.chk. This avoids repeating the expensive diagonalisation step and allows rapid iteration over alternative moment curves or parameters.

Tip

This mode is useful for “targeted” comparisons with experimental intensity data (or for future intensity-driven refinement), and for distributing intensity production over multiple independent jobs.

Keywords¶

absorption, emission, partfunc

These keywords define the type of the spectra (absorption or emission) or whether Duo should only compute the partition function. This keyword should appear immediately after intensity.

Example:

absorption
emission
partfunc

quadrupole

This keyword is used to trigger the calculation of electric quadrupole transitions (see also quadrupole).

magdipole (alias magnetic)

This keyword is used to trigger the calculation of magnetic dipole transitions (see also MAGNETIC).

J (aliases Jrot, Jlist)

This keywords defines the range of rotational angular momentum quantum numbers for which line transitions should be computed.

Note

jrot controls which rovibronic states are computed in the rovibronic calculation; J inside intensity controls which transitions are processed into intensities/line lists.

Example:

J  0,10

Note

Using the J keyword the intensity production can be split into independent J $J_{\rm min},J_{\rm max}$ ranges. In order to prevent overlaps, the range $J_{\rm min},J_{\rm max}$ does not include transitions $J_{\rm min} \leftrightarrow J_{\rm min}$ , except for $J_{\rm min} = 0.5$ , where the transitions $0.5 \leftrightarrow 0.5$ are included. Transitions $0 \leftrightarrow 0$ are forbidden.

Lande Compute Lande $g$ factors and write to the .states file.
energy low and upper

These keywords to restrict the calculation to transitions between levels satisfying the specified lower and upper energy thresholds (in cm^-1): In the following we select transitions for which the lower state is between 0 and 6000 cm^-1 and the upper state is between 10000 and 30000 cm^-1:

energy low 0.0, 6000.00, upper 10000., 30000.0

Note that in this context level energies are measured by setting the energy of the lowest energy level to zero, i.e. they do not include the zero-point energy, in contrast with the threshold enermax specified in the general setup.

Richmol (matelem) is to generate the RichMol checkpoints.

The RichMol checkpoint files .rchk can be used for laser-driven molecular dynamics; see - .. [18OwYa] RichMol: A. Owens and A. Yachmenev, *J. Chem. Phys*, **148**, 124102 (2018), A general variational approach for rovibrational molecular dynamics in external electric fields..

Raman or Polarizability is to generate the matrix elements for the Raman intensity calculations with Richmol.
overlap allows for printing vibrational overlap integral, aka Franck-Condon factors. This keyword is to trigger on/off the vibrational overlap integrals.

The default is on, for switching of:

overlap off

freq-window specifies a frequency window for line positions (in cm^-1).

Example:

freq-window 0.001, 25000.0

gns nuclear statistical weight (deprecated). It is now automatically estimated using nuclear spin values from the internal atomic and nuclear database.

gns specifies the nuclear statistical weight, which for heteronuclear diatomics is given by $g_{ns} = (2 I_1+1)(2I_2+1)$ , where $I_1$ and $I_2$ are the spins of the two nuclei. In the case of homonuclear diatomics four numbers are expected, one for each symmetry species of the $C_{2v}(\rm M)$ or $C_{2h}(\rm M)$ symmetry groups. Example:

GNS 3.0

For the $C_{2v}(\rm M)$ or $C_{2h}(\rm M)$ symmetries associated with the homonuclear molecules the $g_{\rm ns}$ values must be specified for all of the four irreducible representation in the order $A_1$ , $A_2$ , $B_1$ , $B_2$ and $A_g$ , $A_u$ , $B_g$ , $B_u$ , respectively.

GNS 1.0 1.0 0.0 0.0

The default is not to print (off). One can also explicitly switch the overlaps off by adding off next to overlap:

overlap off

The format is

< i,   v| i',   v'> = value

where i and i' are the electronic state numbers, v and v' are the vibrational labels and value is the overlap: `` langle i,v | i’,v’ rangle. `` * vib-dipole prints out vibrational transition moments $\langle i,v | \mu(r) | i',v' \rangle$ . By default these values are print out whenever the intensity is invoked. In order to switch this option off write off next to vib-dipole:

vib-dipole`` off

The format is

< i,   v| <State | mu | State'> i',   v'> = value

where i and i' are the electronic state numbers, v and v' are the vibrational labels, State is the electronic state label and value is the transition dipole moment.

Temperature specifies the temperature (in Kelvin) to be used for the calculation of line intensities.

It can be considered as a reference temperature since the Einstein coefficients as the main computational product and are temperature independent. The partition function associated with this Temperature should be also specified. Example:

temperature  298.0

qstat (aliases: part-func and Q).

This keyword is: to specify the value of the partition function $Q$ for the reference temperature defined by {Temperature. If not given, $Q$ is computed by Duo.

Example:

qstat 10.0

ZPE

This keyword defines the zero point energy (cm^-1) used for the calculation of line intensities, overriding the value specified by the same keyword in the EigenSolver input section. It is important to explicitly specify ZPE when the ground rovibronic state (whose energy defined the ZPE) is not included in the calculation. Omitting this keyword corresponds to using as ZPE the energy of the lowest-lying level used in the calculation.

Example:

ZPE 931.418890

Thresh-intes specifies a minimum intensity threshold (in cm/molecule) for printing the transition into the
output file as well as into the line list.

Example:

Thresh-intes  1e-35

Thresh-Einstein

specifies a threshold for the Einstein coefficient (in 1/s) for printing out the transition into the output file as well as into the line list.

Example:

Thresh-Einstein  1e-50

linelist specifies a file name for writing a line list in the ExoMol format.

Example:

linelist ScH

In the example above two files will be written, ScH.states, containing a list of energy levels, and ScH.trans, containing the line transition data (line positions and Einstein $A$ coefficients).

Nspin Nuclear spins of both atoms (depreciated).

Note

The nuclear spins are now provided in the internal atomic and nuclear databases and is not required to be specified anymore.

The nuclear spin values are used to define the nuclear degeneracy factors as follows. Example

nspin 0.0 0.5

::: nspin 0.0 0.0

The nuclear degeneracy factors (depreciated) $g_ns$ are defined as follows. For the heteronuclear molecules:

$g_{ns} = (2 I_1+1)(2I_2+1)$

For a homonuclear diatomic, it is given by

$g_{ns}^{A} = \frac{1}{2} ((2 I+1)^2+(2 I +1))$

and

$g_{ns}^{B} = \frac{1}{2} ((2 I+1)^2-(2 I +1))$

where $I_1, I_2$ and I are the nuclear spins and A and B are the two irreps of the D2h symmetry group.

Gns is an alternative to nspin defining the nuclear spin degeneracy explicitly.

Example:

GNS 3.0 3.0

GNS 1.0 1.0 0.0 0.0

Thresholds¶

** thresh_line line strength threshold (Debye:sup:2)

** thresh_einstein Einstein A coefficient threshold (1/s).

** thresh_intens intensity (TM) threshold (cm/molecule)

** thresh_dipole transition dipole threshold (debye)

** thresh_bound density threshold to distinguish bound and unbound states.

** thresh_bound_rmax $r_{\rm max}$ threshold used to distinguish bound and unbound states. ** thresh_delta_r the value of the integration interval used to distinguish bound and unbound states.

states-only, states_only: to switch off the transition intensity when building the line list. When this option is given in

the INTENSITY block, only a .states file is generated.

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Computing spectra (intensities and line lists)¶

Batching over $J$ ranges¶

Example: Intensities of BeH¶

Selective intensity calculations via the `FITTING` transition list¶

Example: selecting transitions via `FITTING`¶

Associated `intensity` block¶

Efficient use with checkpoints (recommended workflow)¶

Keywords¶

Thresholds¶

Table of Contents

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Computing spectra (intensities and line lists)¶

Batching over ranges¶

Example: Intensities of BeH¶

Selective intensity calculations via the FITTING transition list¶

Example: selecting transitions via FITTING¶

Associated intensity block¶

Efficient use with checkpoints (recommended workflow)¶

Keywords¶

Thresholds¶

Batching over $J$ ranges¶

Selective intensity calculations via the `FITTING` transition list¶

Example: selecting transitions via `FITTING`¶

Associated `intensity` block¶