Spectral line-shape model to replace the Voigt profile in spectroscopic databases

Transcription

1 Spectral line-shape model to replace the Voigt profile in spectroscopic databases D. Lisak 1, N.H. Ngo 2, H. Tran 2, J.-M. Hartmann 2 1 Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, Torun, Poland, 2 Laboratoire Interuniversitaire des Systèmes Atmosphériques, UMR CNRS 7583, Université Paris Est Créteil (UPEC), Université Paris Diderot (UPD), Institut Pierre- Simon Laplace, Créteil Cedex, France

2 Outline Semi-classical line shape models Recommended profile and its advantages Verification of models on calculated exp & fit (10-6 cm-1) Conclusions 26.7 kpa kpa kpa kpa kpa 0.14 VP BBP 0 exp fit and experimental spectra H2O cm-1 + SF SDVP SDBBP SDNGP (GHz)

3 Semi-classical line shape models Free motion of absorber, pressure (collisional) and Doppler broadening statistically independent Voigt profile (VP) Dependence of collisional width and shift on absorber velocity Speed-dependent Voigt profile (SDVP) [1] B W (x) B S (x) B x) ( ) /, B x) ( ) /, speed dependence of collisional width and shift ( A W xv m ( A S xv m where x v A / v m ; v A is the absorber speed and A m A v is the most probable absorber speed. Quadratic speed-dependence model [2] : B ( ) 1 ( 2 W x aw x 3/ 2) and B ( ) 1 ( 2 S x as x 3/ 2) 2 more parameters: aw, as or equivalent notation: ( x 2 3/ 2) and ( x 2 3/ 2) Hypergeometric speed-dependence model (absorber-perturber interaction ( q 3)/(2q 2) q M,, B( x, ) x 2q 2 2 V q ( r) ~ r ) where α is perturber to absorber mass ratio, M confluent hypergeometric function [1] P.R. Berman, JQSRT 12, 1331 (1972) [2] F. Rohart et al., J. Chem. Phys. 101, 6475 (1994)

4 Semi-classical line shape models Velocity-changing collisions (Dicke narrowing or collisional narrowing) [3] VC frequency of velocity-changing collisions 1 more parameter VC Can be calculated from mass diffiusion coeffeicent, but it does not agree with values obtained from fits of simple models soft collision model Galatry profile (GP) [4] diffusion motion of abasorber, should work better with light perturbers hard collision model Nelkin-Ghatak profile (NGP) [5] (or Rautian profile) va after collision does not depend on va before collision soft and hard collisions together Rautian-Sobelman profile (RSP) [6] ε - vc-collision hardness parameter or S, H 1 more parameter More complex models of vc: Keilson-Storer model (KS) [7] billiard-ball model (BB) [8] Correlations between velocity-changing and dephasing (state changing) collisions [6] η - correlation parameter ( i ) VC VC [3] R. H. Dicke, Phys. Rev. 89, 472 (1953) [4] L. Galatry, Phys. Rev. 122, 1218 (1961) [5] M. Nelkin and A. Ghatak, Phys. Rev. 135, A4 (1964) 1 more parameter η [6] S. G. Rautian and I. I. Sobelman, Sov. Phys. Usp. 9, 701 (1967) [7] Keilson, Storer, Quart J Appl Math 1952;10:243 [8] R. Ciuryło et al., Phys. Rev. A 65, (2002).

5 Simplifications of profiles (by setting some parameters to zero) Profile Parameters Parameters of CSDRSP set to 0 pcqsdrsp,, 2, 2, S, H, pcqsdngp,, 2, 2, H, S pcqsdgp,, 2, 2, S, H qsdngp,, 2, 2, H S, qsdgp,, 2, 2, S H, qsdvp,, 2, 2, S S, H, collisional width collisional shift 2 speed-dependence of 2 speed-dependence of S freq. of soft v-c collisions H freq. of hard v-c collisions corellation coeff. NGP,, H S,, 2, 2 GP,, S H,, 2, 2 VP, S, H,, 2, 2 q - means quadratic speed-dependence Similar list can be done with hypergeometric SD

6 pcqsdngp was proposed as a new standard profile for databases physically based and robust to represent the experimental line shapes of many different molecules to ~ 0.1% line-by-line parameters with linear dependences on the gas pressure compatible with previously used profiles fast computation, comparable to Voigt It was tested on line shapes: H 2 O lines perturbed by N 2 (Keilson-Storer model for velocity changes, semiclassical speed-depedence calculations) [1] O 2 (requantized Classical Molecular Dynamics Simulations - rcmds) [2] CO 2 (rcmds) [3] H 2 (velocity-changing collisions from CMDS and experimental speed-dependences of and ) [4] pcqsdngp can be calculated fast only a few times slower than VP [4] [1] N. H. Ngo, et al., J. Chem. Phys. 137, (2012) [2] J.-M. Hartmann et al. Phys.Rev. A 87, (2013) [3] J.-M. Hartmann et al. Phys.Rev. A 87, (2013) [4] H. Tran et al. JQSRT 134, 104 (2013)

7 Partially corellated quadratic speed-dependent Nelkin-Ghatak profile pcqsdngp * Takes into account: velocity-changing collisions in the hard-collision approximation speed-dependence of collisional broadening and shifting in the quadratic approximation correlations between velocity- and phase/state changing collisions Parameters: w 0 unperturbed line center 0 collisional width 0 colisional shift 2 (or a W ) speed-dependence of collisional width 2 (or a S ) speed-dependence of collisional shift v vc frequency of velocity-changing collisions η correlation parameter First order line mixing** can be easily incorporated by adding a dispersive term of the profile ** Rosenkranz P. IEEE Trans Antennas Propag (1975) * A. S. Pine, JQSRT 62, 397 (1999) P. Joubert et al., JQSRT 61, 519 (1999) Ciuryło et al. JQSRT 68, 257 (2001)

8 Quadratic speed-dependence parameters Speed-dependent collisional width where In the other notation: a = 2 / 0 x = v/v ma Speed-dependence parameter can be calculated from temperature dependence of Γ [1] perturber to absorber mass ratio For multi-component gas (e.g. air): K components Speed-dependence parameter of mixture For quadratic speed-dependence the line-shape parameters for gas mixture can be calculated from parameters for individual components. So, parameters e.g. for air are still compatible with these for O 2, N 2, Ar [1] D. Lisak, A. Cygan, P. Wcisło, R. Ciuryło, submtted to JQSRT (2014)

9 Voigt profile vs pcqsdngp VP: R max = 2.5% VP: R max = 2% pcqsdngp: R max = 0.05% pcqsdngp: R max = 0.4% H 2 O, ν 3, line, p = atm Improvement by at least one order of magnitude O 2 P9P9 line, p = atm VP: R max = 60% pcqsdngp: R max = 3% VP: R max = 3% pcqsdngp: R max = 0.5% H 2 Q(1) line of 1 0 Raman band, p = atm CO 2 R16 line, p = atm

10 Computation time of pcqsdngp pcqsdngp can be written in terms of two Voigt (or complex probability) functions [1] Fast algorithms for Voigt already exist, e.g. J. Humlicek JQSRT 1979;21: Maximum relative error < 10-4 can be obtained with computation time < 5 x VP time (with slightly modified Humlicek algorithm) [2] Fortran code available in [2] [1] Ngo NH, Lisak D, Tran H, Hartmann J-M. JQSRT 2013;129: & 2014;134:105 [2] Tran H, Ngo NH, Hartmann J-M. JQSRT 2013;134:104 & 2014;134:104

11 Quality of the fit in a large pressure range H 2 O cm broadened by N 2 Data simulated with Keilson-Storer (KS) model for velocity changes and semi- classical calculations for speed-dependent line widths and shifts. Multi-spectrum fit of 14 pressures pressure N.H. Ngo, D. Lisak, H. Tran, J.-M. Hartmann, JQSRT 129 (2013)

12 g/p vc/p Fitted line-shape parameters vs profile H 2 O cm broadened by N 2 Collisional broadening and Dicke-narrowing parameters from multi-spectrum fit of 14 pressures % % profile =0.55 profile

13 Area ratio Fitted line intensity vs profile & range of pressures H 2 O cm broadened by N 2 Relative error of line area from multi-spectrum fit at different max. pressures pcqsdngp qsdngp qsdvp NGP GP VP pressure (bar)

14 Tests on experimental results H 2 O cm broadened by N 2 Experimental data from FS-CRDS at NIST: D. Lisak, J. T. Hodges, R. Ciurylo, PRA 73, (2006). Speed-dependent profiles give good fit quality

15 g/p vc/p Area raito Fitted line-shape parameters vs profile H 2 O cm broadened by N Experimental data from FS-CRDS at NIST: D. Lisak, J. T. Hodges, R. Ciurylo, PRA 73, (2006) qsdngp qsdvp NGP GP VP Line area ratio to the pcqsdngp from multi-spectrum fit at different pressures pressure (bar) Collisional broadening and Dicke-narrowing parameters from multi-spectrum fit of 9 pressures % % profile profile

16 Examples of good fit quality with recommended profile H 2 O cm -1 M. D. De Vizia, A. Castrillo, E. Fasci, L. Moretti, F. Rohart, and L. Gianfrani, Phys. Rev. A 85, (2012)

17 Examples of good fit quality with recommended profile Oxygen ( 16 O 2 ) B-band R7Q8 line at 933 Pa signal-to-noise ratio = Line asymmetry caused by the speeddependence of collisional shift A. Cygan, D. Lisak, S. Wójtewicz, J. Domysławska, J. T. Hodges, R. S. Trawiński, R. Ciuryło, Phys. Rev. A 85, (2012) P. Wcisło, A. Cygan, D. Lisak, R. Ciuryło, Phys. Rev. A 88, (2013)

18 IUPAC Task Group recommendation [1] pcqsdhcp (pcqsdngp) should be adopted as the appropriate line profile for high-resolution spectroscopy moving beyond the Voigt profile For simplicity it was proposed to call this profile with fast computation algorithm the Hartmann-Tran profile (HTP) [1] Tennyson J, Bernath PF, Campargue A, Csaszar AG, Daumont L, Gamache RR, Hodges JT, Lisak D, Naumenko OV, Rothman LS, Tran H, Zobov NF, Buldyreva J, Boone CD, De Vizia MD, Gianfrani L, Hartmann J-M, McPheat R, Weidmann D, Murray J, Ngo NH, Polyansky OL. Recommended isolatedline profile for representing high-resolution spectroscopic transitions. Pure Appl Chem 2014 accepted.

19 Conclusions pcqsdngp (HTP) is a powerful model and easy to calculate (low computation time) easy to implement into databases (4 extra parameters, comparing to Voigt profile) can be reduced to simpler profiles by setting some parameters to 0 very well describes H 2 O, O 2, CO 2, CO lines fit residuals below 0.1% (+ random noise) More flexible and more physically justified profiles exist, but there is no fast algorithm developed for pcsdrsp high quality data (high SNR, wide pressure range) are needed to verify experimentally advantages of more complex models (SD+VC+correlations) and to provide line parameters to new databases Experimental parameters of new profiles should be obtained from multispectrum fits (big range of pressures) because of numerical correlations between parameters Temperature dependence of new parameters needs further studies