Non-LTE¶
NLTEMethod selects the population model:
T: two-temperature distribution using Tvib and Trot.
D: custom vibrational density \(n_{\textrm{vib}}\) with a rotational
temperature Trot. Give the density-file path after D. Temperatures and
Tvib are not used.
P: custom rovibrational populations. Give the population-file path after
P. Tvib and Trot are not used.
QNsVibLabel: Please provide vibrational quantum number labels seperated by ,.
QNsRotLabel: Please provide rotational quantum number labels seperated by ,.
For ExoMol and ExoAtom input, these labels use the metadata-derived short names, for example Herzberg:n1 should be written as n1. The QNslabel and QNsformat rows in examples are optional overrides for custom or legacy files.
Two-temperature grids¶
Tvib: vibrational temperatures in K.
Trot: rotational temperatures in K.
|
T = ? |
|
|---|---|---|
296 |
✅ |
296 K |
300,1000,3000,8000 |
✅ |
300 K, 1000 K, 3000 K, 8000 K |
1000:5000:1000 |
✅ |
1000 K, 2000 K, 3000 K, 4000 K, 5000 K |
300, 3000 |
❌ |
|
1000: 3000: 500 |
❌ |
|
[300,3000] |
❌ |
|
[300, 3000] |
❌ |
\(N_{T_\textrm{vib}}\) and \(N_{T_\textrm{rot}}\) and \(N_P\) can be different. The total number of result files should be:
\[
N_\textrm{Total} = N_{T_\textrm{vib}} \times N_{T_\textrm{rot}} \times N_P
\]
Here \(N_P\) is the number of pressures if required.
Two temperatures Treanor distribution¶
The state energy is the sum of the rotational and vibrational state energy:
\[
\tilde{E}^{\textrm{tot}} = \tilde{E}^{\textrm{vib}}_{\textrm{QN}_{\textrm{vib}}} + \tilde{E}^{\textrm{rot}}_{\textrm{QN}_{\textrm{rot}}}.
\]
The non-LTE partition function equation is:
\[
Q(T) = \sum_n g_n^{\textrm{tot}} e^{-c_2 (\tilde{E}^{\textrm{vib}}_{\textrm{QN}_{\textrm{vib}}}/T_{\textrm{vib}} +
\tilde{E}^{\textrm{rot}}_{\textrm{QN}_{\textrm{rot}}}/T_{\textrm{rot}})}.
\]
For absorption, define the vibrational and rotational transition energies as
\(\Delta\tilde{E}_{\textrm{vib}}=\tilde{E}'_{\textrm{vib}}-\tilde{E}''_{\textrm{vib}}\) and \(\Delta\tilde{E}_{\textrm{rot}}=\tilde{E}'_{\textrm{rot}}-\tilde{E}''_{\textrm{rot}}\).
The intensity is:
\[
I(f \gets i) = \frac{g'{A}_{fi}}{8 \pi c \tilde{v}^2_{fi}}
\frac{e^{-c_2(\tilde{E}_{\textrm{vib}}''/T_{\textrm{vib}}
+\tilde{E}_{\textrm{rot}}''/T_{\textrm{rot}})}}{Q(T)}
\left[1-e^{-c_2(\Delta\tilde{E}_{\textrm{vib}}/T_{\textrm{vib}}
+\Delta\tilde{E}_{\textrm{rot}}/T_{\textrm{rot}})}\right].
\]
The emissivity is:
\[
\varepsilon (i \gets f) = \frac{g'{A}_{fi}hc}{4 \pi}
\frac{e^{-c_2 (\tilde{E}_{\textrm{rot}}' / T_{\textrm{rot}} + \tilde{E}_{\textrm{vib}}' / T_{\textrm{vib}})}}{Q(T)}.
\]
Pressure broadening for non-LTE cross sections¶
The population model and pressure-broadening model are independent. Methods
T, D, and P use the same broadening inputs as LTE cross sections. For
example, fixed reference parameters for an \(\rm{H}_2\)/He mixture can be supplied as:
Broadeners H2 He
Ratios 0.85 0.15
GammaBroadening 0.06 0.03
NBroadening 0.60 0.30
Profile SciPyVoigt
LorentzianHWHM(Y/N) N 0.5
The four lists correspond by position. GammaBroadening is the reference
Lorentzian HWHM coefficient in \(\rm{cm}^{-1}\rm{bar}^{-1}\) at 296 K;
NBroadening is dimensionless. For each spectrum condition, PyExoCross uses
the active profile temperature and pressure to evaluate
\[
\gamma(T,P)=\sum_i x_i\gamma_{0,i}
\left(\frac{296\ \mathrm{K}}{T}\right)^{n_i}
\frac{P}{1\ \mathrm{bar}}.
\]
For method T, the profile temperature is Trot. Method D also uses
Trot. Custom broadening is ignored by Doppler and Gaussian profiles. Setting
LorentzianHWHM(Y/N) to Y supplies a final constant HWHM and takes priority.
Example
# Data source #
Database ExoMol
Molecule MgH
Isotopologue 24Mg-1H
Dataset XAB
SpeciesID 501
# File path #
ReadPath /mnt/data/exomol/exomol3_data/
SavePath /home/jingxin/data/pyexocross/
LogFilePath /home/jingxin/data/pyexocross/log/MgH_ExoMol_nlte.log # Use None to disable log-file output
# Functions #
Conversion 0
PartitionFunctions 0
SpecificHeats 0
CoolingFunctions 0
Lifetimes 0
OscillatorStrengths 0
StickSpectra 1
CrossSections 1
# Cores and chunks #
NCPUtrans 4
NCPUfiles 1
ChunkSize 1000000
Device CPU # CPU(default) or GPU
GPUBackend AUTO # AUTO(default), CUDA, PyTorch-CUDA, CuPy-CUDA, or MPS (used only when Device=GPU)
GPUBatchLines 8192 # GPU line-batch size (only used when Device=GPU)
GPUBatchGrid 256 # GPU grid-batch size (only used when Device=GPU)
# Quantum numbers for conversion, stick spectra and cross sections #
QNslabel +/- e/f ElecState v Lambda Sigma Omega
QNsformat %1s %1s %12s %3d %3d %5.1f %5.1f
# Calculate stick spectra or cross sections #
LTE/Non-LTE Non-LTE # 'LTE' or 'Non-LTE'
Temperatures 300,3000 # Temperatures in unit of K
WnWlUnit wn cm-1 # Wavenumber (wn in unit of cm-1) or wavelength (wl in unit of um or nm)
Range 0 30000 # Same unit as WnWlUnit
Absorption/Emission Absorption # 'Absorption' or 'Emission'
UncFilter(Y/N) N 0.01 # If Y, default value 0.01 cm-1
Threshold(Y/N) Y 1e-30 # If Y, default value 1e-30 cm/molecule
QNsFilter(Y/N) N e/f[] v[0,;1,;2,;3,;4,;,0;,1;,2;,3;,4]
# Calculate non-LTE #
NLTEMethod T # 'T'(TvibTrot) or 'D'(Density) or 'P'(Population)
Tvib 300,3000,5000
Trot 300,500
QNsVibLabel v,ElecState
QNsRotLabel J,e/f
# Calculate stick spectra #
PlotStickSpectra(Y/N) Y
PlotStickSpectraMethod log # Plot in linear (lin) or logarithm (log)
PlotStickSpectraWnWl wn cm-1 # Wavenumber (wn in unit cm-1) or wavelength (wl in unit[nm or um])
Y-axisLimitStickSpectra 1e-30 # Default value is 1e-30 cm/molecule
# Calculate cross sections #
Pressures 1,10 # Pressures in unit bar
Npoints/BinSize BinSize 0.1 # Same unit as WnWlUnit
Broadeners Default
Ratios 1.0
Profile Gaussian
PredissocXsec(Y/N) N
Cutoff(Y/N) Y 25 # If Y, default value 25 cm-1
DopplerHWHM(Y/N) Y 3 # Set Doppler HWHM as a constant
LorentzianHWHM(Y/N) N 0.5 # Set Lorentzian HWHM as a constant
PlotCrossSection(Y/N) Y
PlotCrossSectionMethod log # Plot in linear (lin) or logarithm (log)
PlotCrossSectionWnWl wn cm-1 # Wavenumber (wn in unit cm-1) or wavelength (wl in unit[nm or um])
Y-axisLimitXsec 1e-30 # Default value is 1e-30 cm2/molecule
# Data source #
Database ExoMolHR
Molecule NO
Isotopologue 14N-16O
SpeciesID 81
# File path #
ReadPath /mnt/data/exomolhr/exomolhr_results/
SavePath /home/jingxin/data/pyexocross/
LogFilePath /home/jingxin/data/pyexocross//log/NO_ExoMolHR_nlte.log # Use None to disable log-file output
# Functions #
Conversion 0
PartitionFunctions 0
SpecificHeats 0
CoolingFunctions 0
Lifetimes 0
OscillatorStrengths 0
StickSpectra 1
CrossSections 1
# Cores and chunks #
NCPUtrans 4
NCPUfiles 1
ChunkSize 1000000
Device CPU # CPU(default) or GPU
GPUBackend AUTO # AUTO(default), CUDA, PyTorch-CUDA, CuPy-CUDA, or MPS (used only when Device=GPU)
GPUBatchLines 8192 # GPU line-batch size (only used when Device=GPU)
GPUBatchGrid 256 # GPU grid-batch size (only used when Device=GPU)
# Calculate stick spectra or cross sections #
LTE/Non-LTE LTE # 'LTE' or 'Non-LTE'
Temperatures 296,1000 # Temperature in unit of K
WnWlUnit wn cm-1 # Wavenumber (wn in unit of cm-1) or wavelength (wl in unit of um or nm)
Range 24 53452 # Same unit as WnWlUnit
Absorption/Emission Absorption # 'Absorption' or 'Emission'
UncFilter(Y/N) N 0.01 # If Y, default value 0.01 cm-1
Threshold(Y/N) Y 1e-30 # If Y, default value 1e-30 cm/molecule
QNsFilter(Y/N) N
# Calculate non-LTE #
NLTEMethod T # 'T'(TvibTrot) or 'D'(Density) or 'P'(Population)
Tvib 1000,2000
Trot 296
QNsVibLabel v,ElecState
QNsRotLabel J,e/f
# Calculate stick spectra #
PlotStickSpectra(Y/N) Y
PlotStickSpectraMethod log # Plot in linear (lin) or logarithm (log)
PlotStickSpectraWnWl wn cm-1 # Wavenumber (wn in unit cm-1) or wavelength (wl in unit[nm or um])
Y-axisLimitStickSpectra 1e-30 # Default value is 1e-30 cm/molecule
# Calculate cross sections #
Pressures 1 # Pressure in unit bar
Npoints/BinSize BinSize 1 # Same unit as WnWlUnit
Broadeners Default
Ratios 0.1
Profile SciPyVoigt
PredissocXsec(Y/N) N
Cutoff(Y/N) N 25 # If Y, default value 25 cm-1
DopplerHWHM(Y/N) Y 3 # Set Doppler HWHM as a constant
LorentzianHWHM(Y/N) N 0.5 # Set Lorentzian HWHM as a constant
PlotCrossSection(Y/N) Y
PlotCrossSectionMethod log # Plot in linear (lin) or logarithm (log)
PlotCrossSectionWnWl wn cm-1 # Wavenumber (wn in unit cm-1) or wavelength (wl in unit[nm or um])
Y-axisLimitXsec 1e-30 # Default value is 1e-30 cm2/molecule
# Data source #
Database HITRAN
Molecule NO
Isotopologue 14N-16O
Dataset NO-HITRAN
SpeciesID 81
# File path #
ReadPath /home/jingxin/data/HITRAN/
SavePath /home/jingxin/data/pyexocross/
LogFilePath /home/jingxin/data/pyexocross/log/NO_HITRAN_nlte.log # Use None to disable log-file output
# Functions #
Conversion 0
PartitionFunctions 0
SpecificHeats 0
CoolingFunctions 0
Lifetimes 0
OscillatorStrengths 0
StickSpectra 1
CrossSections 1
# Cores and chunks #
NCPUtrans 32
NCPUfiles 1
ChunkSize 1000000
Device CPU # CPU(default) or GPU
GPUBackend AUTO # AUTO(default), CUDA, PyTorch-CUDA, CuPy-CUDA, or MPS (used only when Device=GPU)
GPUBatchLines 8192 # GPU line-batch size (only used when Device=GPU)
GPUBatchGrid 256 # GPU grid-batch size (only used when Device=GPU)
# Quantum numbers for conversion, stick spectra and cross sections #
QNslabel J X Omega v1 Sym F
QNsformat %5.1f %2s %3s %2d %1s %5s
# Calculate stick spectra or cross sections #
LTE/Non-LTE Non-LTE # 'LTE' or 'Non-LTE'
Temperatures 1000,2000 # Temperature in unit of K
WnWlUnit wn cm-1 # Wavenumber (wn in unit of cm-1) or wavelength (wl in unit of um or nm)
Range 0 30000 # Same unit as WnWlUnit
Absorption/Emission Absorption # 'Absorption' or 'Emission'
UncFilter(Y/N) Y 0.01 # If Y, default value 0.01
Threshold(Y/N) Y 1e-30 # If Y, default value 1e-30
QNsFilter(Y/N) N X[] Omega[] v1[1,0;2,]
# Calculate non-LTE #
NLTEMethod T # 'T'(TvibTrot) or 'D'(Density) or 'P'(Population)
Tvib 1000:2000:1000
Trot 300,400
QNsVibLabel v1,X
QNsRotLabel J
# Calculate stick spectra #
PlotStickSpectra(Y/N) Y
PlotStickSpectraMethod log # Plot in linear (lin) or logarithm (log)
PlotStickSpectraWnWl wn cm-1 # Wavenumber (wn in unit cm-1) or wavelength (wl in unit[nm or um])
Y-axisLimitStickSpectra 1e-30 # Default value is 1e-30 cm/molecule
# Calculate cross sections #
Pressures 1 # Pressures in unit bar
Npoints/BinSize BinSize 0.1 # Same unit as WnWlUnit
Broadeners Air Self
Ratios 0.7 0.3
Profile SciPyVoigt
PredissocXsec(Y/N) N
Cutoff(Y/N) Y 25 # If Y, default value 25 cm-1
DopplerHWHM(Y/N) Y 3 # Set Doppler HWHM as a constant
LorentzianHWHM(Y/N) N 0.5 # Calculate pressure-dependent Lorentzian HWHM
PlotCrossSection(Y/N) Y
PlotCrossSectionMethod log # Plot in linear (lin) or logarithm (log)
PlotCrossSectionWnWl wn cm-1 # Wavenumber (wn in unit cm-1) or wavelength (wl in unit[nm or um])
Y-axisLimitXsec 1e-30 # Default value is 1e-30 cm2/molecule
Custom Vibrational density¶
The sum of the custom vibrational density \(n_{\textrm{vib}}\) is normalized to one.
\[
\sum_i n_i^{\textrm{vib}} = 1
\]
For absorption, the rotational population and stimulated-emission correction
both use Trot:
\[
I(f \gets i) = \frac{g'{A}_{fi}}{8\pi c\tilde{v}_{fi}^{2}}
\frac{n_{\textrm{vib}}''e^{-c_2\tilde{E}_{\textrm{rot}}''/T_{\textrm{rot}}}}{Q}
\left(1-e^{-c_2\tilde{v}_{fi}/T_{\textrm{rot}}}\right).
\]
For emission, the upper-state vibrational density and rotational energy are used:
\[
\varepsilon(i \gets f) = \frac{hc}{4\pi}g'A_{fi}\tilde{\nu}_{fi}
\frac{n_{\textrm{vib}}'e^{-c_2\tilde{E}_{\textrm{rot}}'/T_{\textrm{rot}}}}{Q(T_{\textrm{rot}})}.
\]
Only Trot determines the temperature grid in method D.
Example
# Data source #
Database ExoAtom
Atom Ar
Dataset NIST
# File path #
ReadPath /home/jingxin/data/NLTE/ #/mnt/data/exoatom/exoatom_data/
SavePath /home/jingxin/data/pyexocross/
LogFilePath /home/jingxin/data/pyexocross/log/Ar_QDB_nlte_density.log # Use None to disable log-file output
# Functions #
Conversion 0
PartitionFunctions 0
SpecificHeats 0
CoolingFunctions 0
Lifetimes 0
OscillatorStrengths 0
StickSpectra 1
CrossSections 1
# Cores and chunks #
NCPUtrans 1
NCPUfiles 1
ChunkSize 1000000
Device CPU # CPU(default) or GPU
GPUBackend AUTO # AUTO(default), CUDA, PyTorch-CUDA, CuPy-CUDA, or MPS (used only when Device=GPU)
GPUBatchLines 8192 # GPU line-batch size (only used when Device=GPU)
GPUBatchGrid 256 # GPU grid-batch size (only used when Device=GPU)
# Quantum numbers for conversion, stick spectra, and cross sections#
QNslabel configuration Multiple parity
QNsformat %50s %30s %2s
# Calculate stick spectra or cross sections #
LTE/Non-LTE Non-LTE # LTE or Non-LTE
WnWlUnit wn cm-1 # Wavenumber (wn in unit of cm-1) or wavelength (wl in unit of um or nm)
Range 8000 15500 # Same unit as WnWlUnit
Absorption/Emission Emission # 'Absorption' or 'Emission'
UncFilter(Y/N) N 0.01 # If Y, default value 0.01 cm-1
Threshold(Y/N) N 1e-30 # If Y, default value 1e-30 cm/molecule
QNsFilter(Y/N) Y configuration[] Multiple[] parity[]
# Calculate non-LTE #
NLTEMethod D /home/jingxin/data/NLTE/Ar/NIST/Ar_density.csv # 'T'(TvibTrot) or 'D'(Density) or 'P'(Population)
Trot 296
QNsVibLabel nan
QNsRotLabel nan
# Calculate stick spectra #
PlotStickSpectra(Y/N) Y
PlotStickSpectraMethod log # Plot in linear (lin) or logarithm (log)
PlotStickSpectraWnWl wn cm-1 # Wavenumber (wn in unit cm-1) or wavelength (wl in unit[nm or um])
Y-axisLimitStickSpectra 1e-30 # Default value is 1e-30 cm/molecule
# Calculate cross sections #
Pressures 1 # Pressures in unit bar
Npoints/BinSize BinSize 0.01 # Same unit as WnWlUnit
Broadeners Default
Ratios 1.0
Profile SciPyVoigt
PredissocXsec(Y/N) N
Cutoff(Y/N) N 25 # If Y, default value 25 cm-1
DopplerHWHM(Y/N) N 0.1 # Set Doppler HWHM as a constant
LorentzianHWHM(Y/N) N 0.5 # Set Lorentzian HWHM as a constant
PlotCrossSection(Y/N) Y
PlotCrossSectionMethod log # Plot in linear (lin) or logarithm (log)
PlotCrossSectionWnWl wn cm-1 # Wavenumber (wn in unit cm-1) or wavelength (wl in unit[nm or um])
Y-axisLimitXsec 1e-30 # Default value is 1e-30 cm2/molecule
Custom rovibrational population¶
Method P reads the supplied state populations directly. No temperature is needed to calculate its absorption or emission line intensities.
For cross sections, Temperatures supplies the gas temperature when the selected line profile depends on temperature.
Tvib and Trot are not used in this method.
For lower state population \(F''\) and upper state population \(F'\) (each including the state’s total degeneracy), the absorption line intensity is
\[
I(f \gets i) = \frac{A_{fi}}{8\pi c\tilde\nu_{fi}^{2}}
\frac{g'}{g''}F''.
\]
The emission coefficient uses the upper state population:
\[
\varepsilon(i \gets f) = \frac{hc}{4\pi} A_{fi}\tilde\nu_{fi} F'.
\]
Neither intensity nor emission formula depends on Temperatures.
Stick intensities are unchanged when only that input changes; broadened cross sections can change
through a temperature-dependent line profile.
Example
# Data source #
Database ExoAtom
Atom Ar
Dataset NIST
# File path #
ReadPath /home/jingxin/data/NLTE/ #/mnt/data/exoatom/exoatom_data/
SavePath /home/jingxin/data/pyexocross/
LogFilePath /home/jingxin/data/pyexocross/log/Ar_QDB_nlte_pop.log # Use None to disable log-file output
# Functions #
Conversion 0
PartitionFunctions 0
SpecificHeats 0
CoolingFunctions 0
Lifetimes 0
OscillatorStrengths 0
StickSpectra 1
CrossSections 1
# Cores and chunks #
NCPUtrans 1
NCPUfiles 1
ChunkSize 1000000
Device CPU # CPU(default) or GPU
GPUBackend AUTO # AUTO(default), CUDA, PyTorch-CUDA, CuPy-CUDA, or MPS (used only when Device=GPU)
GPUBatchLines 8192 # GPU line-batch size (only used when Device=GPU)
GPUBatchGrid 256 # GPU grid-batch size (only used when Device=GPU)
# Quantum numbers for conversion, stick spectra, and cross sections#
QNslabel configuration Multiple parity
QNsformat %50s %30s %2s
# Calculate stick spectra or cross sections #
LTE/Non-LTE Non-LTE # LTE or Non-LTE
Temperatures 2000 # For temperature-dependent line profiles, not P-mode intensities (K)
WnWlUnit wn cm-1 # Wavenumber (wn in unit of cm-1) or wavelength (wl in unit of um or nm)
Range 8000 15500 # Same unit as WnWlUnit
Absorption/Emission Emission # 'Absorption' or 'Emission'
UncFilter(Y/N) N 0.01 # If Y, default value 0.01 cm-1
Threshold(Y/N) N 1e-30 # If Y, default value 1e-30 cm/molecule
QNsFilter(Y/N) Y configuration[] Multiple[] parity[]
# Calculate non-LTE #
NLTEMethod P /home/jingxin/data/NLTE/Ar/NIST/Ar_Ids.csv # 'T'(TvibTrot) or 'D'(Density) or 'P'(Population)
QNsVibLabel nan
QNsRotLabel nan
# Calculate stick spectra #
PlotStickSpectra(Y/N) Y
PlotStickSpectraMethod log # Plot in linear (lin) or logarithm (log)
PlotStickSpectraWnWl wn cm-1 # Wavenumber (wn in unit cm-1) or wavelength (wl in unit[nm or um])
Y-axisLimitStickSpectra 1e-30 # Default value is 1e-30 cm/molecule
# Calculate cross sections #
Pressures 1 # Pressures in unit bar
Npoints/BinSize BinSize 0.01 # Same unit as WnWlUnit
Broadeners Default
Ratios 1.0
Profile SciPyVoigt
PredissocXsec(Y/N) N
Cutoff(Y/N) N 25 # If Y, default value 25 cm-1
DopplerHWHM(Y/N) N 0.1 # Set Doppler HWHM as a constant
LorentzianHWHM(Y/N) N 0.5 # Set Lorentzian HWHM as a constant
PlotCrossSection(Y/N) Y
PlotCrossSectionMethod log # Plot in linear (lin) or logarithm (log)
PlotCrossSectionWnWl wn cm-1 # Wavenumber (wn in unit cm-1) or wavelength (wl in unit[nm or um])
Y-axisLimitXsec 1e-40 # Default value is 1e-30 cm2/molecule