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
  qstat         10.0
  gns           1.0 1.0
  ZPE  931.418890
  selection (rules) 1 1
  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.

It is possible to run intensities by batches, J1-J2: 0-1,1-2,2-3…. In order to prevern any overlaps, the transitions between J1-J1 are always omitted from the intensity calculations. The line list will contain states and transitions for the given batch only and the states with J1 will be exluded from the .states file, except for J1=0 or J1=0.5. The complete line list is the produced by stitchig together the individual .statets and .trans files. The states numbering will be internally consistent.

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).

  • J (aliases Jrot, Jlist)

This keywords defines the range of rotational angular momentum quantum numbers for which line transitions should be computed. Note that this parameter is independent from jrot specified in the general setup.

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 are to be used for laser-driven molecular dynamics, see [18OwYaxx].

:cite:`18OwYa`.

  • Raman or Polarizability is to generate the matrix elements for the Raman intensity calculations with Richmol.
  • Overlap is to trigger on/off the vibrational overlap integrals.

The default is on, for switching of:

overlap off
  • VIB-DIPOLE is to generate transition dipole moments, and similarly VIB-QUADRUPOLE to generate transition quadrupole moments.

Example

VIB-DIPOLE
VIB-DIPOLE off
  • freq-window specifies a frequency window for line positions (in cm-1).

Example:

freq-window 0.001, 25000.0
  • gns nuclear statistical weight

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}`(M) or :math:`C_{2h}(M) symmetry groups. Example:

GNS 3.0

For the C_{2v} 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
  • overlap allows for printing vibrational overlap integral, aka Franck-Condon factors.

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

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 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_intes intensity (TM) threshold (cm/molecule)

** THRESH_DIPOLE transition dipole threshold (debye)

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
   0.400     -0.4166624920
   0.500     -0.0241871531
   0.600      0.2217732500
   0.700      0.3386323420
   0.800      0.3661076190
   0.900      0.3311512400
   1.000      0.2513061130
   1.100      0.1379591390
   1.200     -0.0012406430
   1.300     -0.1588361650
   1.320     -0.1920270000
   1.340     -0.2256736540
   1.350     -0.2426539090
   1.360     -0.2597311920
   1.400     -0.3288944440
   1.500     -0.5056369720
   1.600     -0.6824442480
   1.700     -0.8513506410
   1.800     -1.0025214800
   1.900     -1.1238133700
   1.950     -1.1687609400
   2.000     -1.2005094800
   2.020     -1.2089972000
   2.050     -1.2166847200
   2.070     -1.2181089800
   2.100     -1.2136337000
   2.300     -1.0182994100
   2.400     -0.8538885220
   2.500     -0.6736179730
   2.600     -0.5046631750
   2.700     -0.3634556350
   2.800     -0.2548814520
   2.900     -0.1758884440
   3.000     -0.1201861300
   3.100     -0.0815224742
   3.200     -0.0549121655
   3.300     -0.0367099205
   3.400     -0.0243335573
   3.500     -0.0159701097
   3.600     -0.0103484461
   3.700     -0.0065800412
   3.800     -0.0040495078
   3.900     -0.0023383813
   4.000     -0.0011684378
   4.200      0.0002034367
   4.400      0.0008546009
   4.600      0.0011177434
   4.800      0.0011645509
   5.000      0.0011023829
   6.000      0.0005429083
   8.000     -0.0000033249
  10.000     -0.0000085504
end

INTENSITY
 absorption
 thresh_intes  1e-30
 thresh_line   1e-30
 temperature   300.0
 nspin         1.5  0.5 (see Wikipedia isotope Be)
 selection (rules) 1 1
 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.