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Example 1: BeH
The Duo input files for this example can be found in Duo Tutorial
The ground electronic state of BeH is a doublet (2Sigma+), see https://www.ucl.ac.uk/~ucapsy0/diatomics.html.
In order to solve the nuclear motion Schroediner equation to compute ro-vibronic spectra of BeH with Duo we need to prepare an input file using the following structure (BeH_Koput_01.inp):
atoms Be H
(Total number of states taken into account)
nstates 1
(Total angular momentum quantum - a value or an interval)
jrot 0.5 - 2.5
(Defining the integration grid)
grid
npoints 501
range 0.4 8.0
type 0
end
CONTRACTION
vib
vmax 30
END
poten 1
units cm-1 angstroms
name 'X2Sigma+'
lambda 0
symmetry +
mult 2
type grid
values
0.60 105169.63
0.65 77543.34
0.70 55670.88
0.75 38357.64
0.80 24675.42
0.85 13896.77
0.90 5447.96
0.95 -1125.87
1.00 -6186.94
1.05 -10024.96
1.10 -12872.63
1.15 -14917.62
1.20 -16311.92
1.25 -17179.13
1.30 -17620.16
1.32 -17696.29
1.33 -17715.26
1.34 -17722.22
1.35 -17717.69
1.36 -17702.19
1.37 -17676.19
1.38 -17640.16
1.40 -17539.76
1.45 -17142.53
1.50 -16572.59
1.55 -15868.72
1.60 -15063.34
1.65 -14183.71
1.70 -13252.86
1.80 -11313.
1.90 -9369.74
2.00 -7518.32
2.10 -5832.29
2.20 -4366.71
2.30 -3155.94
2.40 -2208.98
2.50 -1507.72
2.60 -1013.23
2.80 -456.87
3.00 -221.85
3.50 -72.13
4.00 -41.65
4.50 -24.9
5.00 -14.32
6.00 -4.74
8.00 -0.75
10.00 -0.19
20.00 0.0
end
where we use the potential energy curve (PEC) defined in Table III of Koput (2011) in a grid form.
An alternative definition is an analytical PEC, see e.g. ExoMol-SiO (All ExoMol papers can be download from https://www.ucl.ac.uk/~ucapsy0/publications.html), BeH_Koput_02.inp
poten 1
units cm-1 angstroms
name 'X2Sigma+'
lambda 0
symmetry +
mult 2
type ЕМО
values
V0 0.00
RE 1.342394
DE 17590.00
RREF -1.00000000
PL 3.00000000
PR 3.00000000
NL 0.00000000
NR 0.00000000
b0 1.8400002
end
This PEC can be refined by fitting to experimental energies using the following input structure (BeH_Koput_03.inp):
poten 1
name 'X2Sigma+'
lambda 0
symmetry +
mult 2
type EMO
Values
V0 0.00
RE 1.342394
DE 17590.00 fit
RREF -1.00000000
PL 3.00000000
PR 3.00000000
NL 0.00000000
NR 0.00000000
b0 1.8450002 fit
end
FITTING
JLIST 0.5 - 0.5
itmax 12
fit_factor 1e5
output BeH_01
lock 1000
robust 0.0001
energies ( state v ilambda isigma omega weight comment <- state v ilambda isigma weigh
0.5 + 1 0 1 0 0 0.5 0.5 1.00
0.5 + 2 1986.416 1 1 0 0.5 0.5 1.00
0.5 + 3 3896.871 1 2 0 0.5 0.5 1.00
0.5 + 4 5729.26 1 3 0 0.5 0.5 1.00
0.5 + 5 7480.338 1 4 0 0.5 0.5 1.00
0.5 + 6 9145.132 1 5 0 0.5 0.5 0.00
0.5 + 7 10716.163 1 6 0 0.5 0.5 0.00
0.5 + 8 12182.207 1 7 0 0.5 0.5 0.00
0.5 + 9 13525.788 1 8 0 0.5 0.5 0.00
0.5 + 10 14718.082 1 9 0 0.5 0.5 0.00
0.5 + 11 15709.384 1 10 0 0.5 0.5 0.00
end
The ab initio potential energy curve can be kept to control the shape of the refined curve:
abinitio poten 1
units cm-1 angstroms
name 'X2Sigma+'
lambda 0
symmetry +
mult 2
type grid
values
0.60 105169.63
0.65 77543.34
0.70 55670.88
0.75 38357.64
0.80 24675.42
0.85 13896.77
0.90 5447.96
0.95 -1125.87
1.00 -6186.94
1.05 -10024.96
1.10 -12872.63
1.15 -14917.62
1.20 -16311.92
1.25 -17179.13
1.30 -17620.16
1.32 -17696.29
1.33 -17715.26
1.34 -17722.22
1.35 -17717.69
1.36 -17702.19
1.37 -17676.19
1.38 -17640.16
1.40 -17539.76
1.45 -17142.53
1.50 -16572.59
1.55 -15868.72
1.60 -15063.34
1.65 -14183.71
1.70 -13252.86
1.80 -11313.
1.90 -9369.74
2.00 -7518.32
2.10 -5832.29
2.20 -4366.71
2.30 -3155.94
2.40 -2208.98
2.50 -1507.72
2.60 -1013.23
2.80 -456.87
3.00 -221.85
3.50 -72.13
4.00 -41.65
4.50 -24.9
5.00 -14.32
6.00 -4.74
8.00 -0.75
10.00 -0.19
20.00 0.0
end
For intensity calculations one needs an electric dipole moment curve (taken from http:https://exomol.com/db/BeH/9Be-1H/Yadin/9Be-1H__Yadin__LEVEL8.0.inp) and an Intensity section (BeH_Koput_04.inp):
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)
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 ExoCross tutorial