Download - Molecular spectroscopy from first principles
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Sergey Yurchenko
Molecular spectroscopy from
first principles
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@ExoMol
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@ExoMolH2CO
HOOH
VO, TiO
HCCH PH3
C3
C2H4
NH3
NH3
SO3
SO2
HNO3
CH4
CO2
O3
H2O
CO2
CrH
ScH, TiH
NaCl,
KCl
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@ExoMolAhmed
Al-Refaie
Laura
McKemmish
Katy Chubb Clara
Sousa-Silva
Renia Diamantopoulou
Andrey Yachmenev
Phillip ColesAfaf Al-Derzi
Dan
Underwood
Anatoly Pavlyuchko
Sergey
YurchenkoOleg Polyansky
Emil
Zak
Maire Gorman
Lorenzo Lodi
Emma Barton “Zoe”
Na
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sity,
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ExoMol
wavenumber, cm-1
Experiment
Theoretical spectroscopy
Theory
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sity,
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Experiment
Theoretical spectroscopy
This is our 2018-line list for water
Theory
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Recipe
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How to make do accurate ab intiio spectra
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Electronic structure = solving Schrödinger equation for
electrons
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Electronic structure = solving Schrödinger equation for
electrons
in the Born-Oppenheimer approximation
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Really ab initio can be onlymicrowave spectra
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Accurate equilibrium structure using ab initio and vibrational
corrections
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This is for (almost only) pure rotational spectra of
molecules, even very large molecules
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… where you start from accurate equilibrium structure
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… which provides Ae, Be, Ce
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… and estimate centrifugal distortion constants 𝛼𝑒 as
vibrational corrections
𝐸𝐽𝑣 = 𝐵𝑒 𝐽 𝐽 + 1 − 𝛼𝑒 𝐽 𝐽 + 1 𝑣 +1
2+ ⋯
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CH2FI: Microwave spectrum
C. Puzzarini …. J. Gauss et al. J. Chem Phys. 134, 174312 (2011)
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Level of ab initio theoryCCSD(T)/cc-pwCVQZ(-PP) level augmented by vibrational corrections at the MP2/cc-pVTZ(-PP) level, quartic, and sextic centrifugal-distortion constants at the MP2/cc-pVTZ(-PP) level, nuclear quadrupole-coupling constants at the SFDC-CCSD(T)/unc-ANO-RCC level, and spin-rotation constants at the MP2/unc-ANO-RCC level of theory
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No cheating!
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… the equilibrium structure (A,B,C) can be refined using
experimental values …
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… leads to amazing quality of the ab initio rotational
spectroscopy
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Vibrational motion however is much more complicated for ab
initio methods
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Qualitative description of ro-vibrational spectra by
standard ab initio methods is reasonable
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Qualitative description of ro-vibrational spectra by
standard ab initio methods is reasonable
… but not perfect
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This is pure abinitio C2H2
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How accurate ab initio line positions?
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As accurate as ab initio PESs
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Typically 1-5 cm-1
for the fundamentals using standard CCSD(T)-F12
methods
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For example CH4
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This is still not good enough
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You can do a better ab initio if you push really hard …
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… for example pure ab initio (no cheating) spectrum of CH3F
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Ab initio PES
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Ab initio PES
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Ab initio PES
Basic level
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Ab initio PES
Basic level
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Ab initio PES
Basic level
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Ab initio PES High Order
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Then ab initio results can be really good
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CH3F
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Theory
CH3F
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Experiment
CH3F
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DMS is also ab initio
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CCSD(T)-F12b/aug-cc-pVTZ
DMS is also ab initio
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In fact intensities are (almost) always ab initio!
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Accuracy of 10-20% is common for a reasonable level
of theory
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Ab initio dipole with the standard level of theoryCCSD(T)/aug-cc-pVQZ
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Comparing to high temperature experiments
T = 500oC
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This istheory
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Good (10-20%) agreement
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You can do much better than this with the right levels of ab
initio theory
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You can do much better than this with the right levels of ab
initio theory
Even asub−percent is
possible
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Example: Carbon dioxide intensitiesfrom Polyansky, Tennyson,
Zak and CO2-mpany
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:
OL Polyansky eta al Phys Rev Letts 114, 243001 (2015)
(30013 – 00001)
6200 – 6258 cm-1
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:
OL Polyansky eta al Phys Rev Letts 114, 243001 (2015)
(30013 – 00001)
6200 – 6258 cm-1
Blue is abinitio
intensiies
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:
OL Polyansky eta al Phys Rev Letts 114, 243001 (2015)
(30013 – 00001)
6200 – 6258 cm-1
Blue is abinitio
intensiies
AmaizingSub−percents
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Accurate ro-vibrational line positions?
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New NH3 line list
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New NH3 line list
We had to to re−fineab initio PES
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Method
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Method
DIATOMICS
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Solve Schrödinger equations
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Solve Schrödinger equations
…. using Born-Oppenheimer approximation for motions of electrons and nuclei
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Single electronic state example
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1 2 30
10000
20000
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60000
70000
Po
ten
tial e
ne
rgy c
urv
es, cm
-1
bond length, Å
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
ℏ2
2𝜇𝑟2𝐽 𝐽 + 1 −
ℏ2
2𝜇
𝜕2
𝜕𝑟2+ 𝑉 𝑟 Ψ = 𝐸Ψ
Ab initio Spectra (SiO)
1. Ab initio Potential Energy Curve
2. Ab initio Dipole Moment Curve
4. Calculation of Intensities (Einstein coefficients)
3. Solution of Schrödinger equation (Energies and
Wavefunctions)
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60000
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Po
ten
tial e
ne
rgy c
urv
es, cm
-1
bond length, Å
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
ℏ2
2𝜇𝑟2𝐽 𝐽 + 1 −
ℏ2
2𝜇
𝜕2
𝜕𝑟2+ 𝑉 𝑟 Ψ = 𝐸Ψ
Ab initio Spectra (SiO)
2. Ab initio Dipole Moment Curve
4. Calculation of Intensities (Einstein coefficients)
3. Solution of Schrödinger equation (Energies and
Wavefunctions)
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Po
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ne
rgy c
urv
es, cm
-1
bond length, Å
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
ℏ2
2𝜇𝑟2𝐽 𝐽 + 1 −
ℏ2
2𝜇
𝜕2
𝜕𝑟2+ 𝑉 𝑟 Ψ = 𝐸Ψ
Ab initio Spectra (SiO)
4. Calculation of Intensities (Einstein coefficients)
3. Solution of Schrödinger equation (Energies and
Wavefunctions)
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Po
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tial e
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rgy c
urv
es, cm
-1
bond length, Å
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
ℏ2
2𝜇𝑟2𝐽 𝐽 + 1 −
ℏ2
2𝜇
𝜕2
𝜕𝑟2+ 𝑉 𝑟 Ψ = 𝐸Ψ
Ab initio Spectra (SiO)
4. Calculation of Intensities (Einstein coefficients)
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Po
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tial e
ne
rgy c
urv
es, cm
-1
bond length, Å
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
ℏ2
2𝜇𝑟2𝐽 𝐽 + 1 −
ℏ2
2𝜇
𝜕2
𝜕𝑟2+ 𝑉 𝑟 Ψ = 𝐸Ψ
Ab initio Spectra (SiO)
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20000
30000
40000
50000
60000
70000
Po
ten
tial e
ne
rgy c
urv
es, cm
-1
bond length, Å
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
ℏ2
2𝜇𝑟2𝐽 𝐽 + 1 −
ℏ2
2𝜇
𝜕2
𝜕𝑟2+ 𝑉 𝑟 Ψ = 𝐸Ψ
Ab initio Spectra (SiO)
The ab initioPEC has tobe refined
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Most of the systems are not single-state
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Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
4. Electronic angular momenta couplings
1. Ab initio Potential Energy Curves
2. Ab initio Dipole Moment Curves
3. Spin-Orbit couplings
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Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
4. Electronic angular momenta couplings
2. Ab initio Dipole Moment Curves
3. Spin-Orbit couplings
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Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
4. Electronic angular momenta couplings
3. Spin-Orbit couplings
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Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
4. Electronic angular momenta couplings
![Page 85: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/85.jpg)
Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
![Page 86: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/86.jpg)
Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
The ab initioPECs haveto be refined
![Page 87: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/87.jpg)
Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
as well asspin−orbits
![Page 88: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/88.jpg)
A more sophisticated code for a coupled system is required
Our code Duo Yurchenko et al Comp. Phys. Comm. (2016)
ℏ2
2𝜇𝑟2 𝑅2 −
ℏ2
2𝜇
𝜕2
𝜕𝑟2+ 𝑉 𝑟 Ψ = 𝐸Ψ
![Page 89: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/89.jpg)
A more sophisticated code for a coupled system is required
Our code Duo Yurchenko et al Comp. Phys. Comm. (2016)
ℏ2
2𝜇𝑟2 𝑅2 −
ℏ2
2𝜇
𝜕2
𝜕𝑟2+ 𝑉 𝑟 Ψ = 𝐸Ψ
![Page 90: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/90.jpg)
MgO
![Page 91: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/91.jpg)
The spectrum ismore complex, withmultiple interacting
electronic bands
MgO
![Page 92: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/92.jpg)
In fact: for diatomics pure ab initio calculations is almost never
good enough
![Page 93: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/93.jpg)
In fact: for diatomics pure ab initio calculations is almost never
good enough
… at least for practical applications
![Page 94: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/94.jpg)
Example: CrH ab initio spectra
![Page 95: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/95.jpg)
CrH ab initio absorption at T=2000 K
Experiment:0-0, 1-0, 0-1
![Page 96: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/96.jpg)
CrH ab initio absorption at T=2000 K
Experiment:0-0, 1-0, 0-1
High level ab initioic-MRCI/aug-cc-pV5Z
![Page 97: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/97.jpg)
CrH ab initio absorption at T=2000 K
Experiment:0-0, 1-0, 0-1
High level ab initioic-MRCI/aug-cc-pV5Z
![Page 98: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/98.jpg)
CrH ab initio absorption at T=2000 K
Experiment:0-0, 1-0, 0-1
High level ab initioic-MRCI/aug-cc-pV5Z
High level
![Page 99: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/99.jpg)
CrH ab initio absorption at T=2000 K
Experiment:0-0, 1-0, 0-1
High level
![Page 100: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/100.jpg)
CrH ab initio absorption at T=2000 K
Experiment:0-0, 1-0, 0-1
It looks completely different!
![Page 101: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/101.jpg)
Refinement of our pure theoretical model to experiment
is always mandatory
![Page 102: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/102.jpg)
How accurate are we?
![Page 103: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/103.jpg)
Experiment
Theory
![Page 104: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/104.jpg)
Experiment
Theory
MgO: Onlyafter
refinement
![Page 105: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/105.jpg)
For most of hot diatomicsno experimental intensities or lifetimes are available
but hugely needed!
![Page 106: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/106.jpg)
More on diatomics: see my presentation this afternoon
![Page 107: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/107.jpg)
More on diatomics: see my presentation this afternoon
WH05 (small molecules) at 14:53
![Page 108: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/108.jpg)
Polyatomic molecules
![Page 109: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/109.jpg)
We have produced a new water line list POKAZATEL, fully complete and more
accurate
Oleg Polyansky et al MNRAS re-submitted (2018)
![Page 110: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/110.jpg)
All bound states up to dissociation
![Page 111: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/111.jpg)
![Page 112: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/112.jpg)
The majority ofexperimental line
positions are reproducedwithin 0.01 cm−1
![Page 113: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/113.jpg)
The majority ofexperimental line
intensities are cloaeto 1%
![Page 114: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/114.jpg)
This summarises our main goals…
![Page 115: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/115.jpg)
Accurate line positions
![Page 116: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/116.jpg)
Accurate line intensities
![Page 117: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/117.jpg)
To be complete for high excitations and hot spectra
![Page 118: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/118.jpg)
These goals however are not always compatible
![Page 119: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/119.jpg)
It is too difficult or even impossible to be accurate and
complete
![Page 120: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/120.jpg)
Luckily, most of applications require to be either accurate
or complete
![Page 121: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/121.jpg)
For example, the microwave spectral applications must be
accurate but not so much complete
![Page 122: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/122.jpg)
Most of the opacity applications (atmospheric retrievals) require to be complete not so much
accurate
![Page 123: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/123.jpg)
Example: brown dwarf spectra
![Page 124: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/124.jpg)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.40.0
0.2
0.4
0.6
0.8
1.0
1.2F
lux,
10
-14 W
m-2
m-1
wavelength, m
T4.5 Brown dwarf 2MASS 0559-14
Cushing Rayner, Vacca (2005)R=2000 (3 cm-1)
![Page 125: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/125.jpg)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.40.0
0.2
0.4
0.6
0.8
1.0
1.2F
lux,
10
-14 W
m-2
m-1
wavelength, m
T4.5 Brown dwarf 2MASS 0559-14
T 4.5 Observed (SpeX@IRTF)
Cushing Rayner, Vacca (2005)R=2000 (3 cm-1)
![Page 126: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/126.jpg)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.40.0
0.2
0.4
0.6
0.8
1.0
1.2F
lux,
10
-14 W
m-2
m-1
wavelength, m
T4.5 Brown dwarf 2MASS 0559-14
T 4.5 Observed (SpeX@IRTF)
Cushing Rayner, Vacca (2005)R=2000 (3 cm-1)
Empirical CH4 data
![Page 127: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/127.jpg)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.40.0
0.2
0.4
0.6
0.8
1.0
1.2F
lux,
10
-14 W
m-2
m-1
wavelength, m
T4.5 Brown dwarf 2MASS 0559-14
T 4.5 Observed (SpeX@IRTF)
Cushing Rayner, Vacca (2005)R=2000 (3 cm-1)
Empirical CH4 data
![Page 128: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/128.jpg)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.40.0
0.2
0.4
0.6
0.8
1.0
1.2F
lux,
10
-14 W
m-2
m-1
wavelength, m
T4.5 Brown dwarf 2MASS 0559-14
T 4.5 Observed (SpeX@IRTF)
Cushing Rayner, Vacca (2005)R=2000 (3 cm-1)
Empirical CH4 data
Somethingis missing
![Page 129: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/129.jpg)
ExoMolPNAS (2014)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.40.0
0.2
0.4
0.6
0.8
1.0
1.2F
lux,
10
-14 W
m-2
m-1
wavelength, m
T4.5 Brown dwarf 2MASS 0559-14
T 4.5 Observed (SpeX@IRTF)
Cushing Rayner, Vacca (2005)R=2000 (3 cm-1)
Empirical CH4 data
![Page 130: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/130.jpg)
ExoMolPNAS (2014)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.40.0
0.2
0.4
0.6
0.8
1.0
1.2F
lux,
10
-14 W
m-2
m-1
wavelength, m
T4.5 Brown dwarf 2MASS 0559-14
T 4.5 Observed (SpeX@IRTF)
Cushing Rayner, Vacca (2005)R=2000 (3 cm-1)
Empirical CH4 data
![Page 131: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/131.jpg)
ExoMolPNAS (2014)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.40.0
0.2
0.4
0.6
0.8
1.0
1.2F
lux,
10
-14 W
m-2
m-1
wavelength, m
T4.5 Brown dwarf 2MASS 0559-14
T 4.5 Observed (SpeX@IRTF)
Cushing Rayner, Vacca (2005)R=2000 (3 cm-1)
Empirical CH4 data
ExoMolPNAS (2014)
![Page 132: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/132.jpg)
ExoMolPNAS (2014)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.40.0
0.2
0.4
0.6
0.8
1.0
1.2F
lux,
10
-14 W
m-2
m-1
wavelength, m
T4.5 Brown dwarf 2MASS 0559-14
T 4.5 Observed (SpeX@IRTF)
Cushing Rayner, Vacca (2005)R=2000 (3 cm-1)
Empirical CH4 data
ExoMolPNAS (2014)
![Page 133: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/133.jpg)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.40.0
0.2
0.4
0.6
0.8
1.0
1.2F
lux,
10
-14 W
m-2
m-1
wavelength, m
T4.5 Brown dwarf 2MASS 0559-14
T 4.5 Observed (SpeX@IRTF)
Cushing Rayner, Vacca (2005)R=2000 (3 cm-1)
Empirical CH4 data
![Page 134: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/134.jpg)
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.40.0
0.2
0.4
0.6
0.8
1.0
1.2F
lux,
10
-14 W
m-2
m-1
wavelength, m
T4.5 Brown dwarf 2MASS 0559-14
T 4.5 Observed (SpeX@IRTF)
Cushing Rayner, Vacca (2005)R=2000 (3 cm-1)
Empirical CH4 data
Hydrogen:CIA
![Page 135: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/135.jpg)
Example: a Hubble spectrum of HD209458b
analyzed by a Cambridge group(using ExoMol database)
![Page 136: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/136.jpg)
MacDonald and Madhusudhan (2017)
HD209458b
Hubble WFC3
![Page 137: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/137.jpg)
MacDonald and Madhusudhan (2017)
HD209458b
Hubble WFC3
H2O
![Page 138: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/138.jpg)
MacDonald and Madhusudhan (2017)
HD209458b
NH3? HCN?
Hubble WFC3
H2O
![Page 139: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/139.jpg)
Water and Methane are usually first to find
![Page 140: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/140.jpg)
Example:
a hot Jupiter HD 189733b
![Page 141: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/141.jpg)
Swain et al Nature 452, 329-331 (2008)
![Page 142: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/142.jpg)
Water
Swain et al Nature 452, 329-331 (2008)
![Page 143: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/143.jpg)
Water
CH4
CH4
Swain et al Nature 452, 329-331 (2008)
![Page 144: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/144.jpg)
Polyatomics: Method for solving the nuclear motion
Schrödinger equation
![Page 145: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/145.jpg)
Polyatomics: Method for solving the nuclear motion
Schrödinger equation
This is waht Ido for living
![Page 146: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/146.jpg)
Polyatomics: Method for solving the nuclear motion
Schrödinger equation
TROVE
![Page 147: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/147.jpg)
MORBID
![Page 148: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/148.jpg)
MORBID
![Page 149: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/149.jpg)
DVR3D
MORBID
![Page 150: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/150.jpg)
Ingredients and calculation steps are essentially the same
as for diatomics
![Page 151: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/151.jpg)
1. Accurate ab initio potential energy surface
![Page 152: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/152.jpg)
…computed with CCSD(T)-F12b/aug-cc-pVQZ-DK
MOLPRO
+ corrections:cc-pCVTZ, CCSD(T), CCSDT, and CCSDT(Q) CFOUR
![Page 153: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/153.jpg)
2. Accurate ab inition Dipole Moment Surface
![Page 154: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/154.jpg)
2. Accurate ab inition Dipole Moment Surface
Typical Dipoles: CCSD(T)/aug-cc-pVQZ
using finite fields
![Page 155: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/155.jpg)
3: Solve Schrödinger equation
![Page 156: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/156.jpg)
3: Solve Schrödinger equation
𝐻Ψ = 𝐸 Ψ
![Page 157: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/157.jpg)
… variationally in the matrix representation:
𝜙1𝜙2𝜙3 … 𝐻 𝜙′1𝜙2′ 𝜙3
′ …
![Page 158: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/158.jpg)
The Hamiltonian has to be transferred to the body-fixed
system which makes complicated
![Page 159: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/159.jpg)
𝐻 =
𝑖,𝑗
𝜕
𝜕𝑞𝑖𝐺𝑖𝑗 𝑞
𝜕
𝜕𝑞𝑗+
+
𝑖,𝛼
𝜕
𝜕𝑞𝑖𝐺𝑖𝛼 𝑞 𝐽𝛼 − 𝐽𝛼 𝐺𝑖𝛼 𝑞
𝜕
𝜕𝑞𝑖+
+
𝛼,𝛽
𝐽𝛼 𝐺𝛼𝛽 𝑞 𝐽𝛽 +
+𝑈 𝑞 + 𝑉( 𝑞)
![Page 160: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/160.jpg)
The most known and widely used is Watsonian
![Page 161: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/161.jpg)
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TROVE approach is to numerically expand the kinetic energy operator in the sum-
of-product form
![Page 164: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/164.jpg)
𝐺𝑖𝑗 𝑞 =
𝑛1𝑛2𝑛3
𝐺𝑛1𝑛2𝑛3
(𝑖𝑗)𝑞1
𝑛1𝑞2𝑛2𝑞3
𝑛3
![Page 165: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/165.jpg)
𝐺𝑖𝑗 𝑞 =
𝑛1𝑛2𝑛3
𝐺𝑛1𝑛2𝑛3
(𝑖𝑗)𝑞1
𝑛1𝑞2𝑛2𝑞3
𝑛3
Obtained numerically
![Page 166: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/166.jpg)
𝐺𝑖𝑗 𝑞 =
𝑛1𝑛2𝑛3
𝐺𝑛1𝑛2𝑛3
(𝑖𝑗)𝑞1
𝑛1𝑞2𝑛2𝑞3
𝑛3
Obtained numerically
𝑉 𝑞 =
𝑛1𝑛2𝑛3
𝐹𝑛1𝑛2𝑛3𝑞1
𝑛1𝑞2𝑛2𝑞3
𝑛3
![Page 167: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/167.jpg)
𝐺𝑖𝑗 𝑞 =
𝑛1𝑛2𝑛3
𝐺𝑛1𝑛2𝑛3
(𝑖𝑗)𝑞1
𝑛1𝑞2𝑛2𝑞3
𝑛3
Obtained numerically
𝑉 𝑞 =
𝑛1𝑛2𝑛3
𝐹𝑛1𝑛2𝑛3𝑞1
𝑛1𝑞2𝑛2𝑞3
𝑛3
Obtained numerically
![Page 168: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/168.jpg)
… which is good for product-type
basis set representations
![Page 169: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/169.jpg)
Φ = 𝐽, 𝑘, 𝑚 𝑣1 𝑣2 𝑣3 …
… which is good for product-type
basis set representations
![Page 170: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/170.jpg)
We use a symmetry adapted basis so that the
Hamiltonian matrix is block-diagonal
![Page 171: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/171.jpg)
𝐻 Ψ = 𝐸 Ψ
Hij
Ci Ci
![Page 172: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/172.jpg)
In fact last year we published a paper on an automatic
symmetrisation procedure we use
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Symmetries help to reduce the dimension
![Page 177: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/177.jpg)
A1
A2
E
F1
F2
F1
F2
2,000,000 elements2,0
00,0
00 e
lem
ents
E
F1
F2
… 0 …
… 0 …
Td(M)
1/8
![Page 178: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/178.jpg)
… and obligatory for intensity calculations
![Page 179: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/179.jpg)
Then we diagonalize the Hamiltonian matrices
![Page 180: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/180.jpg)
100,000
![Page 181: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/181.jpg)
100,000
J ≤ 20
![Page 182: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/182.jpg)
100,000
J ≤ 20
200,000
𝐽 = 20 − 30
![Page 183: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/183.jpg)
100,000
J ≤ 20
200,000
𝐽 = 20 − 30
1-2 M CPUh total
400,000
J = 30 − 50
![Page 184: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/184.jpg)
Diagonalization: Time vs size
100,000
5 hours
16 cores64 Gb
200,000
12 hours160 cores
1.2 Tb
1-2 M CPUh total
400,000
25 hours740 cores
5.3 Tb
![Page 185: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/185.jpg)
1,000,000
And sometimes (J~200)
![Page 186: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/186.jpg)
1,000,000
And sometimes (J~200)
This is toomuch!
![Page 187: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/187.jpg)
We have constructed an efficient machinery for accurate production
of molecular spectra
![Page 188: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/188.jpg)
We have constructed an efficient machinery for accurate production
of molecular spectra
for atmospheric applications (stars and
exoplantes)
![Page 189: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/189.jpg)
This is where we started
![Page 190: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/190.jpg)
Already available
To-Do
VO FeH AlH C3
YO AlO BeH MgH
H3+ O3 HDO
H2D+ O2 HOOH HNO3
CNCH
NH3
CrH HCN HNC
C2 CaH SiO
SO3 H2CO PH3
NiH TiH SiH
LiH OH
HeH+ NO
H2
CH4
H2O
H2S
SO2
TiO
C2H2
C2H4
C3H8
C2H6
CO CO2
2011
![Page 191: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/191.jpg)
Already available
To-Do
VO FeH AlH C3
YO AlO BeH MgH
H3+ O3 HDO
H2D+ O2 HOOH HNO3
CNCH
NH3
CrH HCN HNC
C2 CaH SiO
SO3 H2CO PH3
NiH TiH SiH
LiH OH
HeH+ NO
H2
CH4
H2O
H2S
SO2
TiO
C2H2
C2H4
C3H8
C2H6
CO CO2
2011
This isbefore
![Page 192: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/192.jpg)
Done
To-Do
F
SiH4
PO
VO FeH
AlH CS
YO
AlO
H3+ O3 H2CO HDO
H2D+ O2 HOOH
HNO3
CNCH
NH3
CrH
C2
SO3
PH3
NiH TiH CH3Cl
LiH OH
HeH+ NO
H2
H2O
H2S
SO2
CO
C2H2
C2H4
C3H8
C2H6
CO2
HCl NaCl SiO
CaH
BeH
MgH
KCl
CH4
PS HCN HNC
CH3D
SO SiH
PN ScH
NaH
SH
P2H2
CH3Cl
TiO FeH CaO C3
YOCH3D
SO
SH
P2H2
SiC PS
BaO VN PH
2018
NS
ZnS
CH3F
SiS MgO
![Page 193: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/193.jpg)
Done
To-Do
F
SiH4
PO
VO FeH
AlH CS
YO
AlO
H3+ O3 H2CO HDO
H2D+ O2 HOOH
HNO3
CNCH
NH3
CrH
C2
SO3
PH3
NiH TiH CH3Cl
LiH OH
HeH+ NO
H2
H2O
H2S
SO2
CO
C2H2
C2H4
C3H8
C2H6
CO2
HCl NaCl SiO
CaH
BeH
MgH
KCl
CH4
PS HCN HNC
CH3D
SO SiH
PN ScH
NaH
SH
P2H2
CH3Cl
TiO FeH CaO C3
YOCH3D
SO
SH
P2H2
SiC PS
BaO VN PH
2018
NS
ZnS
CH3F
SiS MgO
This is now
![Page 194: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/194.jpg)
Not all of them are actively used for retrievals yet
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Done
To-Do
F
SiH4
PO
VO FeH
AlH CS
YO
AlO
H3+ O3 H2CO HDO
H2D+ O2 HOOH
HNO3
CNCH
NH3
CrH
C2
SO3
PH3
NiH TiH CH3Cl
LiH OH
HeH+ NO
H2
H2O
H2S
SO2
CO
C2H2
C2H4
C3H8
C2H6
CO2
HCl NaCl SiO
CaH
BeH
MgH
KCl
CH4
PS HCN HNC
CH3D
SO SiH
PN ScH
NaH
SH
P2H2
CH3Cl
TiO FeH CaO C3
YOCH3D
SO
SH
P2H2
SiC PS
BaO VN PH
2018
NS
ZnS
CH3F
MgOSiS
Only these
![Page 196: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/196.jpg)
Larger molecules
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Barry Mant
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Ethylene: new ExoMol song line list
Barry Mant
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50 billion lines
![Page 201: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/201.jpg)
3 band model: Vibrational spectrum of C2H4
![Page 202: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/202.jpg)
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Extract their shapes
![Page 207: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/207.jpg)
![Page 208: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/208.jpg)
![Page 209: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/209.jpg)
![Page 210: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/210.jpg)
… and apply to all other bands
![Page 211: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/211.jpg)
… and apply to all other bands
Low cost vibrational band intensities
![Page 212: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/212.jpg)
… and apply to all other bands
Low cost vibrational band intensities
Cheating on variationalcalculations
![Page 213: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/213.jpg)
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![Page 227: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/227.jpg)
Using these shapes
![Page 228: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/228.jpg)
10-24
10-23
10-22
10-21
10-20
10-19
10-18
T = 500 KRovibrational
![Page 229: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/229.jpg)
10-24
10-23
10-22
10-21
10-20
10-19
10-18
T = 500 KRovibrational
![Page 230: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/230.jpg)
![Page 231: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/231.jpg)
![Page 232: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/232.jpg)
Hightemperature
![Page 233: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/233.jpg)
Ammonia
![Page 234: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/234.jpg)
Very Large Telescope (VLT) Multi Unit Spectroscopic
Explorer (MUSE) instrument in the spectral range
0.48–0.93 μm
![Page 235: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/235.jpg)
Visible spectrum of Jupiter: Ammonia bands
![Page 236: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/236.jpg)
![Page 237: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/237.jpg)
Ammonia
![Page 238: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/238.jpg)
![Page 239: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/239.jpg)
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![Page 242: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/242.jpg)
![Page 243: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/243.jpg)
They tried our new empirical line list for NH3
![Page 244: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/244.jpg)
P. Irwin et. al Icarus 302 (2018) 426–436
![Page 245: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/245.jpg)
P. Irwin et. al Icarus 302 (2018) 426–436
![Page 246: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/246.jpg)
P. Irwin et. al Icarus 302 (2018) 426–436
![Page 247: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/247.jpg)
P. Irwin et. al Icarus 302 (2018) 426–436
Giver et al. (1975): observed at 294 K;
![Page 248: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/248.jpg)
P. Irwin et. al Icarus 302 (2018) 426–436
Lutz and Owen (1980): low resolution absorption coefficients.
![Page 249: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/249.jpg)
Our theoretical spectrum is
represented by the green and red lines
P. Irwin et. al Icarus 302 (2018) 426–436
![Page 250: Molecular spectroscopy from first principles](https://reader030.vdocuments.site/reader030/viewer/2022020916/61ab33d40bb6b86fea00aafa/html5/thumbnails/250.jpg)
Quasi-continuum
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Methane line list contains 34 billion transitions
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