molecular spectroscopy from first principles
TRANSCRIPT
Sergey Yurchenko
Molecular spectroscopy from
first principles
@ExoMol
@ExoMolH2CO
HOOH
VO, TiO
HCCH PH3
C3
C2H4
NH3
NH3
SO3
SO2
HNO3
CH4
CO2
O3
H2O
CO2
CrH
ScH, TiH
NaCl,
KCl
@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 βZoeβ
Na
0.0
5.0x10-20
1.0x10-19
1.5x10-19
2.0x10-19
2.5x10-19
3700 3800 3900
2.5x10-19
2.0x10-19
1.5x10-19
1.0x10-19
5.0x10-20
1.0x10-28
In
ten
sity,
cm
/mo
lecu
le
ExoMol
wavenumber, cm-1
Experiment
Theoretical spectroscopy
Theory
0.0
5.0x10-20
1.0x10-19
1.5x10-19
2.0x10-19
2.5x10-19
3700 3800 3900
2.5x10-19
2.0x10-19
1.5x10-19
1.0x10-19
5.0x10-20
1.0x10-28
In
ten
sity,
cm
/mo
lecu
le
ExoMol
wavenumber, cm-1
Experiment
Theoretical spectroscopy
This is our 2018-line list for water
Theory
Recipe
How to make do accurate ab intiio spectra
Electronic structure = solving SchrΓΆdinger equation for
electrons
Electronic structure = solving SchrΓΆdinger equation for
electrons
in the Born-Oppenheimer approximation
Really ab initio can be onlymicrowave spectra
Accurate equilibrium structure using ab initio and vibrational
corrections
This is for (almost only) pure rotational spectra of
molecules, even very large molecules
β¦ where you start from accurate equilibrium structure
β¦ which provides Ae, Be, Ce
β¦ and estimate centrifugal distortion constants πΌπ as
vibrational corrections
πΈπ½π£ = π΅π π½ π½ + 1 β πΌπ π½ π½ + 1 π£ +1
2+ β―
CH2FI: Microwave spectrum
C. Puzzarini β¦. J. Gauss et al. J. Chem Phys. 134, 174312 (2011)
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
No cheating!
β¦ the equilibrium structure (A,B,C) can be refined using
experimental values β¦
β¦ leads to amazing quality of the ab initio rotational
spectroscopy
Vibrational motion however is much more complicated for ab
initio methods
Qualitative description of ro-vibrational spectra by
standard ab initio methods is reasonable
Qualitative description of ro-vibrational spectra by
standard ab initio methods is reasonable
β¦ but not perfect
This is pure abinitio C2H2
How accurate ab initio line positions?
As accurate as ab initio PESs
Typically 1-5 cm-1
for the fundamentals using standard CCSD(T)-F12
methods
For example CH4
This is still not good enough
You can do a better ab initio if you push really hard β¦
β¦ for example pure ab initio (no cheating) spectrum of CH3F
Ab initio PES
Ab initio PES
Ab initio PES
Basic level
Ab initio PES
Basic level
Ab initio PES
Basic level
Ab initio PES High Order
Then ab initio results can be really good
CH3F
Theory
CH3F
Experiment
CH3F
DMS is also ab initio
CCSD(T)-F12b/aug-cc-pVTZ
DMS is also ab initio
In fact intensities are (almost) always ab initio!
Accuracy of 10-20% is common for a reasonable level
of theory
Ab initio dipole with the standard level of theoryCCSD(T)/aug-cc-pVQZ
Comparing to high temperature experiments
T = 500oC
This istheory
Good (10-20%) agreement
You can do much better than this with the right levels of ab
initio theory
You can do much better than this with the right levels of ab
initio theory
Even asubβpercent is
possible
Example: Carbon dioxide intensitiesfrom Polyansky, Tennyson,
Zak and CO2-mpany
:
OL Polyansky eta al Phys Rev Letts 114, 243001 (2015)
(30013 β 00001)
6200 β 6258 cm-1
:
OL Polyansky eta al Phys Rev Letts 114, 243001 (2015)
(30013 β 00001)
6200 β 6258 cm-1
Blue is abinitio
intensiies
:
OL Polyansky eta al Phys Rev Letts 114, 243001 (2015)
(30013 β 00001)
6200 β 6258 cm-1
Blue is abinitio
intensiies
AmaizingSubβpercents
Accurate ro-vibrational line positions?
New NH3 line list
New NH3 line list
We had to to reβfineab initio PES
Method
Method
DIATOMICS
Solve SchrΓΆdinger equations
Solve SchrΓΆdinger equations
β¦. using Born-Oppenheimer approximation for motions of electrons and nuclei
Single electronic state example
1 2 30
10000
20000
30000
40000
50000
60000
70000
Po
ten
tial e
ne
rgy c
urv
es, cm
-1
bond length, Γ
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
β2
2ππ2π½ π½ + 1 β
β2
2π
π2
ππ2+ π π Ξ¨ = πΈΞ¨
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 SchrΓΆdinger equation (Energies and
Wavefunctions)
1 2 30
10000
20000
30000
40000
50000
60000
70000
Po
ten
tial e
ne
rgy c
urv
es, cm
-1
bond length, Γ
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
β2
2ππ2π½ π½ + 1 β
β2
2π
π2
ππ2+ π π Ξ¨ = πΈΞ¨
Ab initio Spectra (SiO)
2. Ab initio Dipole Moment Curve
4. Calculation of Intensities (Einstein coefficients)
3. Solution of SchrΓΆdinger equation (Energies and
Wavefunctions)
1 2 30
10000
20000
30000
40000
50000
60000
70000
Po
ten
tial e
ne
rgy c
urv
es, cm
-1
bond length, Γ
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
β2
2ππ2π½ π½ + 1 β
β2
2π
π2
ππ2+ π π Ξ¨ = πΈΞ¨
Ab initio Spectra (SiO)
4. Calculation of Intensities (Einstein coefficients)
3. Solution of SchrΓΆdinger equation (Energies and
Wavefunctions)
1 2 30
10000
20000
30000
40000
50000
60000
70000
Po
ten
tial e
ne
rgy c
urv
es, cm
-1
bond length, Γ
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
β2
2ππ2π½ π½ + 1 β
β2
2π
π2
ππ2+ π π Ξ¨ = πΈΞ¨
Ab initio Spectra (SiO)
4. Calculation of Intensities (Einstein coefficients)
1 2 30
10000
20000
30000
40000
50000
60000
70000
Po
ten
tial e
ne
rgy c
urv
es, cm
-1
bond length, Γ
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
β2
2ππ2π½ π½ + 1 β
β2
2π
π2
ππ2+ π π Ξ¨ = πΈΞ¨
Ab initio Spectra (SiO)
1 2 30
10000
20000
30000
40000
50000
60000
70000
Po
ten
tial e
ne
rgy c
urv
es, cm
-1
bond length, Γ
LEVEL 8.0 R. Le Roy, Waterloo, CanadaOur Duo program
β2
2ππ2π½ π½ + 1 β
β2
2π
π2
ππ2+ π π Ξ¨ = πΈΞ¨
Ab initio Spectra (SiO)
The ab initioPEC has tobe refined
Most of the systems are not single-state
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
Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
4. Electronic angular momenta couplings
2. Ab initio Dipole Moment Curves
3. Spin-Orbit couplings
Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
4. Electronic angular momenta couplings
3. Spin-Orbit couplings
Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
4. Electronic angular momenta couplings
Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
The ab initioPECs haveto be refined
Ab initio spectrum (MgO)
PEC
Spin-orbit
Dipolles
Lx
as well asspinβorbits
A more sophisticated code for a coupled system is required
Our code Duo Yurchenko et al Comp. Phys. Comm. (2016)
β2
2ππ2 π 2 β
β2
2π
π2
ππ2+ π π Ξ¨ = πΈΞ¨
A more sophisticated code for a coupled system is required
Our code Duo Yurchenko et al Comp. Phys. Comm. (2016)
β2
2ππ2 π 2 β
β2
2π
π2
ππ2+ π π Ξ¨ = πΈΞ¨
MgO
The spectrum ismore complex, withmultiple interacting
electronic bands
MgO
In fact: for diatomics pure ab initio calculations is almost never
good enough
In fact: for diatomics pure ab initio calculations is almost never
good enough
β¦ at least for practical applications
Example: CrH ab initio spectra
CrH ab initio absorption at T=2000 K
Experiment:0-0, 1-0, 0-1
CrH ab initio absorption at T=2000 K
Experiment:0-0, 1-0, 0-1
High level ab initioic-MRCI/aug-cc-pV5Z
CrH ab initio absorption at T=2000 K
Experiment:0-0, 1-0, 0-1
High level ab initioic-MRCI/aug-cc-pV5Z
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
CrH ab initio absorption at T=2000 K
Experiment:0-0, 1-0, 0-1
High level
CrH ab initio absorption at T=2000 K
Experiment:0-0, 1-0, 0-1
It looks completely different!
Refinement of our pure theoretical model to experiment
is always mandatory
How accurate are we?
Experiment
Theory
Experiment
Theory
MgO: Onlyafter
refinement
For most of hot diatomicsno experimental intensities or lifetimes are available
but hugely needed!
More on diatomics: see my presentation this afternoon
More on diatomics: see my presentation this afternoon
WH05 (small molecules) at 14:53
Polyatomic molecules
We have produced a new water line list POKAZATEL, fully complete and more
accurate
Oleg Polyansky et al MNRAS re-submitted (2018)
All bound states up to dissociation
The majority ofexperimental line
positions are reproducedwithin 0.01 cmβ1
The majority ofexperimental line
intensities are cloaeto 1%
This summarises our main goalsβ¦
Accurate line positions
Accurate line intensities
To be complete for high excitations and hot spectra
These goals however are not always compatible
It is too difficult or even impossible to be accurate and
complete
Luckily, most of applications require to be either accurate
or complete
For example, the microwave spectral applications must be
accurate but not so much complete
Most of the opacity applications (atmospheric retrievals) require to be complete not so much
accurate
Example: brown dwarf spectra
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)
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)
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
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
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
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)
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)
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)
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)
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
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
Example: a Hubble spectrum of HD209458b
analyzed by a Cambridge group(using ExoMol database)
MacDonald and Madhusudhan (2017)
HD209458b
Hubble WFC3
MacDonald and Madhusudhan (2017)
HD209458b
Hubble WFC3
H2O
MacDonald and Madhusudhan (2017)
HD209458b
NH3? HCN?
Hubble WFC3
H2O
Water and Methane are usually first to find
Example:
a hot Jupiter HD 189733b
Swain et al Nature 452, 329-331 (2008)
Water
Swain et al Nature 452, 329-331 (2008)
Water
CH4
CH4
Swain et al Nature 452, 329-331 (2008)
Polyatomics: Method for solving the nuclear motion
SchrΓΆdinger equation
Polyatomics: Method for solving the nuclear motion
SchrΓΆdinger equation
This is waht Ido for living
Polyatomics: Method for solving the nuclear motion
SchrΓΆdinger equation
TROVE
MORBID
MORBID
DVR3D
MORBID
Ingredients and calculation steps are essentially the same
as for diatomics
1. Accurate ab initio potential energy surface
β¦computed with CCSD(T)-F12b/aug-cc-pVQZ-DK
MOLPRO
+ corrections:cc-pCVTZ, CCSD(T), CCSDT, and CCSDT(Q) CFOUR
2. Accurate ab inition Dipole Moment Surface
2. Accurate ab inition Dipole Moment Surface
Typical Dipoles: CCSD(T)/aug-cc-pVQZ
using finite fields
3: Solve SchrΓΆdinger equation
3: Solve SchrΓΆdinger equation
π»Ξ¨ = πΈ Ξ¨
β¦ variationally in the matrix representation:
π1π2π3 β¦ π» πβ²1π2β² π3
β² β¦
The Hamiltonian has to be transferred to the body-fixed
system which makes complicated
π» =
π,π
π
ππππΊππ π
π
πππ+
+
π,πΌ
π
ππππΊππΌ π π½πΌ β π½πΌ πΊππΌ π
π
πππ+
+
πΌ,π½
π½πΌ πΊπΌπ½ π π½π½ +
+π π + π( π)
The most known and widely used is Watsonian
TROVE approach is to numerically expand the kinetic energy operator in the sum-
of-product form
πΊππ π =
π1π2π3
πΊπ1π2π3
(ππ)π1
π1π2π2π3
π3
πΊππ π =
π1π2π3
πΊπ1π2π3
(ππ)π1
π1π2π2π3
π3
Obtained numerically
πΊππ π =
π1π2π3
πΊπ1π2π3
(ππ)π1
π1π2π2π3
π3
Obtained numerically
π π =
π1π2π3
πΉπ1π2π3π1
π1π2π2π3
π3
πΊππ π =
π1π2π3
πΊπ1π2π3
(ππ)π1
π1π2π2π3
π3
Obtained numerically
π π =
π1π2π3
πΉπ1π2π3π1
π1π2π2π3
π3
Obtained numerically
β¦ which is good for product-type
basis set representations
Ξ¦ = π½, π, π π£1 π£2 π£3 β¦
β¦ which is good for product-type
basis set representations
We use a symmetry adapted basis so that the
Hamiltonian matrix is block-diagonal
π» Ξ¨ = πΈ Ξ¨
Hij
Ci Ci
In fact last year we published a paper on an automatic
symmetrisation procedure we use
Symmetries help to reduce the dimension
A1
A2
E
F1
F2
F1
F2
2,000,000 elements2,0
00,0
00 e
lem
ents
E
F1
F2
β¦ 0 β¦
β¦ 0 β¦
Td(M)
1/8
β¦ and obligatory for intensity calculations
Then we diagonalize the Hamiltonian matrices
100,000
100,000
J β€ 20
100,000
J β€ 20
200,000
π½ = 20 β 30
100,000
J β€ 20
200,000
π½ = 20 β 30
1-2 M CPUh total
400,000
J = 30 β 50
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
1,000,000
And sometimes (J~200)
1,000,000
And sometimes (J~200)
This is toomuch!
We have constructed an efficient machinery for accurate production
of molecular spectra
We have constructed an efficient machinery for accurate production
of molecular spectra
for atmospheric applications (stars and
exoplantes)
This is where we started
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
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
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
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
Not all of them are actively used for retrievals yet
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
Larger molecules
Barry Mant
Ethylene: new ExoMol song line list
Barry Mant
50 billion lines
3 band model: Vibrational spectrum of C2H4
Extract their shapes
β¦ and apply to all other bands
β¦ and apply to all other bands
Low cost vibrational band intensities
β¦ and apply to all other bands
Low cost vibrational band intensities
Cheating on variationalcalculations
Using these shapes
10-24
10-23
10-22
10-21
10-20
10-19
10-18
T = 500 KRovibrational
10-24
10-23
10-22
10-21
10-20
10-19
10-18
T = 500 KRovibrational
Hightemperature
Ammonia
Very Large Telescope (VLT) Multi Unit Spectroscopic
Explorer (MUSE) instrument in the spectral range
0.48β0.93 ΞΌm
Visible spectrum of Jupiter: Ammonia bands
Ammonia
They tried our new empirical line list for NH3
P. Irwin et. al Icarus 302 (2018) 426β436
P. Irwin et. al Icarus 302 (2018) 426β436
P. Irwin et. al Icarus 302 (2018) 426β436
P. Irwin et. al Icarus 302 (2018) 426β436
Giver et al. (1975): observed at 294 K;
P. Irwin et. al Icarus 302 (2018) 426β436
Lutz and Owen (1980): low resolution absorption coefficients.
Our theoretical spectrum is
represented by the green and red lines
P. Irwin et. al Icarus 302 (2018) 426β436
Quasi-continuum
Methane line list contains 34 billion transitions