Michaël REY GSMA Reims (France)

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1 Accurate first-principles spectra predictions for planetological and astrophysical applications at various T- conditions Michaël REY GSMA Reims (France) - HITRAN - A. Nikitin (Tomsk) V. Tyuterev T. Delahaye (PhD student)

2 Motivations: why using theoretical predictions? Predictions for unaccessible spectral regions or for extreme conditions (T,P,L) Astrophysical & planetological applications (formation of stars, giant planets, Titan, ) Combine exp. & theory to extract information from spectra (profile, intensities, positions) Explore domains in the frontier between spectroscopy, quantum chemistry & dynamics Extract line-by-line information (unambiguous (?) assignments) Give information for all isotopic species AIM: Make theoretical databases sufficiently accurate for various applications (astro., planeto.) June 2014 M. Rey - HITRAN Conference 2

3 Completeness or accuracy or both? Isotopologues Global variational models Make compromise between accuracy and completeness? More and more feasible with increasing computational powers Effective models accurate but sparse J v High-T June 2014 M. Rey - HITRAN Conference 3

Vibrational polyads Energies Spectroscopic effective models Effective models: block-diagonal polyad Hamiltonians Empirically-fitted to observed data: Intra-polyad resonances = finite size problem

4 Vibrational polyads Energies Spectroscopic effective models Effective models: block-diagonal polyad Hamiltonians Empirically-fitted to observed data: Intra-polyad resonances = finite size problem Paradigm for high precision calculations, spectroscopic accuracy Fitted to obs = No physical Interpretation? «local» But. May fail to make reliable extrapolations isotopic dependent models = start new analysis / molecule Example of 13 CH 4 Sparse analyses! Rot Structure June 2014 M. Rey - HITRAN Conference ZOOM 4 J=2 J=1 J=0

First-principles Completeness Analyses/Exp All isotopologues Consistent accuracy Cover wide spectral & T ranges Variational calculations All transitions in one calculations!

5 First-principles Completeness Analyses/Exp All isotopologues Consistent accuracy Cover wide spectral & T ranges Variational calculations All transitions in one calculations!! 12 CH K 13 CH K 12 CH 3 D 296 K CH K CH K CH 3 D 1000 K Validate databases and may detect unconsistencies Homogeneous Smooth behavior (convergence) Unlike current databases composed of various Sources of data (exp, analyses) June 2014 M. Rey - HITRAN Conference 5

6 Two-Step Quantum Mechanical Calculations Solving the electronic & nuclear motion problems Electronic structure theory for solving the electronic problem: ab initio methods PES DMS This work: Nikitin et al., PES&DMS CH 4, PH 3 and other ones (CH 3 X, C 2 H 4 ) JCP 2009, CPL2010, 2013 (I) Commercial codes (Molpro,Gaussian, ) For the nuclear problem, exactly solvable models are quite sparse no practical analytical solutions: a variational or perturbative treatment is necessary Approximative but accurate methods have to be considered for solving (Choice of coordinates& primitive basis) (II) Various approaches & Theoretical developements: Specificic to each group June 2014 M. Rey - HITRAN Conference 6

7 Theoretical developements Computer codes 30 s Eckart Non exhaustive list 70 s 80 s 90 s 2010 Herzberg Watson, Hougen, Louck, Makushkin, Quack, Sutcliffe&Tennyson Handy, Carter, Bowman,.. Basic&Light Tyuterev, Tashkun Partridge&Schwenke Carrington&Wang, Makarewicz, Csaszar, Yurchenko, Thiel, ExoMol project DVR3D MULTIMODE MOL_CT VTET TROVE GENIUSH/DEWE CONVIV June 2014 M. Rey - HITRAN Conference 7

8 Theoretical line lists H 2 O CO 2 NH 3 Partridge&Schwenke, IUPAC (UCL) Huang et al. (NASA) Yurchenko et al. HiTEMP (CO, H 2 O, CO 2 ) Rothman et al. ExoMol (>30 molecules) Tennyson et al. This work TheoReTS (Reims-Tomsk)Methane, Phosphine+isotopologues (Theoretical Reims-Tomsk Spectroscopic lists) + forthcoming molecules June 2014 M. Rey - HITRAN Conference 8

9 Variational calculations.. drawbacks Become intractable when increasing the dimensionality (high V & J, and #atoms) do not reach spectroscopic accuracy N=3 (water) N=4 (phosphine) N=5 (CH 4 ) N=5 (CH 3 D) #op H_o16=2700 H_o14= H_o14= H_o14= Brut-force diagonalization not feasible! Necessity to make relevant transformations/approximations Use of symmetry to make simplifications Ex: CH 4 T d C 3v C 2v C s C (A 1 ) (A 2 ) (E ) (F 1 ) (F 2 ) (A 1 ) (A 2 ) (E ) (A 1 ) (A 2 ) (B 1 ) (B 2 ) (A ) (A ) June 2014 M. Rey - HITRAN Conference 9

Variational calculations: our methodology Extensive use of symmetry&transfo fitted to analytical functions Normal-mode nuclear model (I) Tensor formulation (II) Common to all existing codes ab initio

10 Variational calculations: our methodology Extensive use of symmetry&transfo fitted to analytical functions Normal-mode nuclear model (I) Tensor formulation (II) Common to all existing codes ab initio calc.&fits: A. Nikitin Compressed/reduced model (III) Truncated/reduced basis Specific to our codes MIRS+TENSOR codes (Tomsk Reims) (IV) High-J calculations (VSS) (I+II+III+IV) Synthetic Spectra June

(I) Normal Mode Models Symmetry & Tensors Use of normal mode coordinates to describe the collective motions of atoms For the very first time, the tensor

Systematic and exact transformations without any fitting procedures reduce the number of terms RNT, JCP2012, PCCP2013, JCP2014 (accepted) Eckart-Watson

11 (I) Normal Mode Models Symmetry & Tensors Use of normal mode coordinates to describe the collective motions of atoms For the very first time, the tensor formalism employed in empirical effective models is extended and applied to ab initio models (connection between components of irreps with Dim>1) Systematic and exact transformations without any fitting procedures reduce the number of terms RNT, JCP2012, PCCP2013, JCP2014 (accepted) Eckart-Watson Hamiltonian From geometry From PES Exact algebraic transformation from molecular parameters SFF dipole moment From DMS (MFF) June 2014 M. Rey - HITRAN Conference 11

12 (II) Hamiltonian Compression: how to reduce CPU time? Increasing number of symmetry-allowed terms due to polynomial Taylor expansions Typically 1-10 millions of terms = several days/months of calculation (in a +,a) representation We propose a polynomial reduction procedure based on second-quantized operators Make the problem tractable without almost loss of accuracy Prevent from artifacts (barriers) and spurious minima due to high polynomial degrees Scaling: June 2014 M. Rey - HITRAN Conference 12

(III) Reduced Vib Eigenfunctions: VSS approach Using the direct method, the size of the basis rapidly grows with J and v Alternatively, we partition the Hamiltonian as solutions defined on a

13 (III) Reduced Vib Eigenfunctions: VSS approach Using the direct method, the size of the basis rapidly grows with J and v Alternatively, we partition the Hamiltonian as solutions defined on a subspace, solve the vibrational problem and store with m sufficiently large to converge desired energies Now let us assume that we can write and project onto We can introduce a new set of reduced functions Gram-Schmidt with for June 2014 M. Rey - HITRAN Conference 13

14 (IV) High-J calculations: how to reduce the dimensionality? This final set of vectors is used to build the full rovibrational Hamiltonian matrix by forming the tensor product The Hamiltonian matrix thus writes Scaling: 1 10 This procedure allows drastically reducing the size of the ro-vibrational problem e.g Memory ~ CPU time ~ The calculated vibrational band centers may be corrected to match observed data June 2014 M. Rey - HITRAN Conference 14

15 The phosphine molecule (PH 3 ): status Effective models HITRAN 2012: Range: cm -1 #Lines: 22,000 at room T First analyses ( ): Tarrago, Fusina, Ulenikov, Butler, Kleiner et al. global analysis of dyad, pentad, octad (2009): Nikitin, Champion, Brown et al. Recent line positions/intensities for pentad (2014): Malathy Devi, Kleiner, Brown et al. ExoMol project: Extensive (ab initio) variational calculations Range: cm -1 #Lines: 137 millions at room T Billions for T>2000K Sousa-Silva, Tennyson, Yurchenko et al. (2013,2014) This work: Expect cold and hot PH 3 predictions using new Nikitin-Rey-Tyuterev V5Z/VQZ - PES/DMS Provide complementary data for yet unassigned lines Unified treatment of all C 3v /C s isotopologues at the «same» accuracy June 2014 M. Rey - HITRAN Conference 15

16 Room-T phosphine spectra HITRAN12 This work June 2014 M. Rey - HITRAN Conference 16

17 Comparison with existing databases (room-t) K=9,A1,A2 HITRAN12 K=10,E Pentad Octad K=11,E This work This work J=18 19 GS-GS ExoMol Dyad HITRAN12 HITRAN12 HITRAN12 This work ExoMol This work June 2014 M. Rey - HITRAN Conference 17

18 Comparison with experiment RMS=9.3% (analysis, Malathy et al., JMS 2014) RMS=9.5% (this work) Experimental accuracy? PES = Nikitin et al., JCP2009 DMS = NRT, 2014, to be sub transitions Pentad near 4,5μm June 2014 M. Rey - HITRAN Conference 18

19 The methane molecule (CH 4 ): status HITRAN 2012: Range: cm -1 #Lines: 470,000 at room T Effective models Exp. First detailed analyses: Champion, Hilico, Pierre, Loëte et al. (Dijon, France, ) Recent updates of GS (Boudon et al.), Octad, Tetradecad and lower part of Icosad: Nikitin et al. (Tomsk, Reims, Dijon, ) WKLMC (Grenoble) is the most extensive (accurate) line list in the range cm -1 and contains empirical lower state energy levels (Campargue, Kassi, Wang et al.) ExoMol project: Extensive (ab initio) variational calculations in the range: cm -1 #Lines: 10 to 10 lines up to 1500K Yurchenko, Tennyson (2014) Other works: Theory: Warmbier, Bowman (1000K list, 2010), Wang&Carrington, Cassam-Chenaï Exp: cold/hot methane (Brown, Quack, «Reims group», Hargreaves, Bernath, Georges, Louviot et al.) Planeto/astro: Coustenis, Rannou, Swain, Tinetti, De Bergh et al. This work: 11,5 billion lines up to 5000 cm -1 at T=2000K RNT, ApJ 2014 Cold band transitions up to cm -1 Unified treatment of all T d /C 3v /C 2v isotopologues at the «same» accuracy June 2014 M. Rey - HITRAN Conference RNT, PCCP 2013 RNT, JCP 2014 accepted 19

20 Polyads of methane: state of the art For «hot» applications, HITRAN is not sufficient Effective empirical models very limited. Hot methane. Necessity to go to ab initio global predictions In progress (Grenoble/Tomsk/Reims) Refined analysis (Tomsk/Dijon) Consistencies between HITRAN 2008/2012? In progress (Rennes/Dijon) Complete for cold bands Problems with hot bands? Assignments? Extrapolation for weak lines from analyses of strong ones? (< cm/molec.) Picture from V. Boudon (ICB, Dijon) Require careful attention June 2014 M. Rey - HITRAN Conference 20

21 Room-T methane spectra HITRAN: lines 25 years to analyze! Icosad Predictions: lines Octad (zoom) Tetradeca d (zoom) Triacontad 21

Accuracy 12 CH 4 in the range 0-5000 cm -1 Icutoff=1E-21 Icutoff=1E-23 RMS=5.

22 Accuracy 12 CH 4 in the range cm -1 Icutoff=1E-21 Icutoff=1E-23 RMS=5.7% June 2014 Less accurate in positions than effective models Need to be refined Accuracy experiment Make assignments?? M. Rey - HITRAN Conference 22

23 Assignments WKLMC (Grenoble) is the most extensive line list in cm -1 and contains empirical lower state energy levels ab initio predictions allow for the first time to fully characterize strong/medium lines of Icosad WKLMC, 80K Simul Profil res=0.006 cm-1 Icosad Variational RNT No fits 3400 new assignments June 2014 M. Rey - HITRAN Conference 23

24 Isotopic transformations Spectra predictions for isotopic species from the mother molecule bridge to transpose analyses Symmetry transformations of tensor operators and group-subgroup connection (T d -C 3v, T d -C 2v, C 3v -C s ) Find the normal mode transformation to transpose PES/DMS to their isotopic counterpart? Analytical or numerical transformation Propagation of information Derived from Eckart vectors (=0 if no symmetry breaking e.g. 12 CH 4 13 CH 4 ) «Mother» Molecule Iso1 Iso2 Iso June 2014 M. Rey - HITRAN Conference 24

25 Accurate isotopic shifts Isotopic shifts 12 CH 4 -> 13 CH 4 Iso 1: Calc. Iso 1: Known Obs Shifts accuracies = 0.01 cm -1 δ δ Iso 2: Calc. Iso 2: NEW Obs June 2014 M. Rey - HITRAN Conference 25

26 Bring new information for H->D substitution From tetradecad of methane! Not included in Current analyses June 2014 M. Rey - HITRAN Conference 26

27 Application to 13 CH 4 spectra HITRAN: lines Prediction: lines RNT, JMS, June 2014 M. Rey - HITRAN Conference 27

28 13 CH 4 spectra: bringing new information HITRAN Octad No intensity measurements No intensity measurements: extrapolation WKLMC (Grenoble) This work This work Missing lines! WKLMC (Grenoble) Octad (zoom) This work June 2014 M. Rey - HITRAN Conference 28

Application to 12 CH 3 D spectra HITRAN: 54500 lines Triad HITRAN Nonad Prediction:

29 Application to 12 CH 3 D spectra HITRAN: lines Triad HITRAN Nonad Prediction: lines HITRAN CH 3 D Enneadecad HITRAN This work This work June

30 Application to 12 CH 2 D 2 spectra Asymmetric tops: tensor product direct product ETH Zürich 78K This work From T d -> C 2v transformations June 2014 M. Rey - HITRAN Conference 30

31 Application to Titan s atmosphere T=80K P. Rannou (planeto team) 13 CH4 12 CH4 Spectrum at 2 μm above the polar cloud layer (VIMS DATA) and synthetic spectra, with different cut-off, at 26, 100, 200, 300, 400 and at 500 cm-1 from the line core. Both the methane and 13CH4 are accounted, and thus in all cases, the absorption feature around μm is now correctly fitted June 2014 M. Rey - HITRAN Conference 31

32 Hot methane spectra Lower state energy levels Cold vs. Hot bands T=500 K >40% of missing lines >85% of missing lines T=1500 K Our 2000K list up to 5000 cm -1 contains 11,5 billions of lines! Rey, Nikitin, Tyuterev, ApJ June 2014 M. Rey - HITRAN Conference 32

33 Density of lines Influence of intensity cutoff and temperature 10 6 lines/cm -1!! June 2014 M. Rey - HITRAN Conference 33

34 Convergence integrated intensity At 2000K, from cutoff cm/mol. to cm/mol. 9 billions of additional lines and 0,2% of opacity [0-5000] cm -1 CB/HB Final 2000K list This work % HITRAN June 2014 M. Rey - HITRAN Conference 34

35 Comparison with Measured lines combined with HITRAN: Hargreaves, Bernath, et al. Line list (ApJ, 2012, 2013) Dyad This Work Dyad (zoom) Measured lines Added HITRAN lines Pentad Octad 35

36 Hot band contributions Missing HB Hargreaves&Bernath June 2014 M. Rey - HITRAN Conference 36

37 Comparison with E low =14000 cm -1 Jmax<50 (This work) E low =8000 cm -1, Jmax<40 (ExoMol) P5-P4 P6-P5 P7-P6 +high J? P5-P3 P6-P4 P7-P5 +high J? Additional opacity (15%) up to cm June 2014 M. Rey - HITRAN Conference 37

38 Conclusions Complete theory was developed to make reliable variational calculations Qualitative & quantitative predictions on wide spectral and T ranges Production of corresponding line lists for methane, phosphine and their C s, C 2v,C 3v and T d isotopologues Theoretical databases available for planetological & astrophysical applications & non-lte processes 12 CH 4, 13 CH 4, 12 CD 4, 12 CH 3 D, 12 CHD 3, 12 CH 2 D 2, PH 3, PD 3, PHD 2, PH 2 D (see A Kutepov s talk) CH 3 X (X=F, Cl, Br, I, Li) coming soon!! Billions of lines! Proposition? USE AB INITIO CALCULATIONS TO FILL DATABASES (HITRAN, GEISA, ) WHEN INFORMATION IS MISSING OR NOT WELL-DEFINED? June 2014 M. Rey - HITRAN Conference 38

39 Refined model for atmospheric applications Synthesis: build non-empirical models from molecular properties (PES/DMS) Reims approach with Tomsk (S. Tashkun) i S i S i S i n H e e He e S... H eff H eff eff 0 H1 H2... H eff n... n i S e n Mol_CT code Tyuterev & Tashkun 0 0 Aim: Position = 1mK and intensity better than 5% Directly from PES!! See Vladimir s talk June 2014 M. Rey - HITRAN Conference 39

40 Perspectives Hot tetradecad (1500K) + finalize assignments icosad Extension to 6 atomic molecules in progress (ethylene): PES Delahaye et al., 2014, Sub; DMS in progress C 2 H 4 HITRAN This work Extension to linear molecules (2015- ) Acetylene Extension to curvilinear coordinates & large amplitude motions (2015- ) June 2014 M. Rey - HITRAN Conference 40

41 Thank You! June 2014 M. Rey - HITRAN Conference 41

) Exact transformation Example of T d molecules Models +

42 ab initio Tensor Hamiltonian: example Coriolis vibration-rotation interacting term V(a +,a) R(J x, J y, J z ) Exact transformation Example of T d molecules Models + variational calc. in the TENSOR code June 2014 M. Rey - HITRAN Conference 42

43 Example: 10 -> 6 Hamiltonian compression Eckart-Watson Tensor (global) Tensor (effective) (II) (I) Second-quantized formulation Scaling of the problem ~ June 2014 M. Rey - HITRAN Conference 43

Basis sets: definitions For a molecule having n vibrational modes (degenerate or not), we write the vibrational primitive basis as the n-fold tensor product The rovibrational basis is built as a

44 Basis sets: definitions For a molecule having n vibrational modes (degenerate or not), we write the vibrational primitive basis as the n-fold tensor product The rovibrational basis is built as a tensor product of vib and rot functions To avoid considering non-vanishing matrix elements between states probing unphysical regions e.g. only a relevant set of vibrational functions is chosen through cm cm -1 Advantage of using the complete molecular symmetry: reduce the dimensionality Illustration: bloc size of F(14) for methane T d C 3v C 2v C s C (A 1 ) (A 2 ) (E ) (F 1 ) (F 2 ) (A 1 ) (A 2 ) (E ) (A 1 ) (A 2 ) (B 1 ) (B 2 ) (A ) (A ) June 2014 M. Rey - HITRAN Conference 44

45 Illustration: convergence Small basis for applications Example of convergence for v 4 =4, J=4 methane levels with/without reduced functions and VSS F(9) F(6) Red. F(9) F(6) Bloc=A 1 VSS=100% VSS=80% VSS=50% Size , , , , , ,30-1,30-1,77-1,48 1,42 0,17 0,68-0,06-0,14-0,07 0,03 0,03 0,05-0,07-0,14-0,08 0,02 0,02 0,02-0,09-0,16-0,09 0,01 0,02 0,01 Same number of basis functions! 1-2 orders of magnitude Note: up to 3 quanta, F(m) and F(m) F(r) give very similar results Approximate but consistent calc June 2014 M. Rey - HITRAN Conference 45

Linda R. Brown. Jet Propulsion Laboratory California Institute of Technology Pasadena, CA

Linda R. Brown. Jet Propulsion Laboratory California Institute of Technology Pasadena, CA Infrared Laboratory Spectroscopy. of CH4 and CH3D for Atmospheric Studies Linda R. Brown Jet Propulsion Laboratory California Institute of Technology Pasadena, CA 91109 linda.brown@jpl.nasa.gov The part