QUASAAR Winter School, Jasna, February 20-25, 2009 QUASAAR Winter School, Jasna, February 20-25, 2009

Handling, assignment, and Handling, assignment, and fitting of spectrafitting of spectra

Zbigniew KisielInstitute of Physics Polish Academy of SciencesInstitute of Physics, Polish Academy of Sciences

The 1.6 THz spectrum of The 1.6 THz spectrum of acrylonitrileacrylonitrile::

The chirpedThe chirped--pulse FTMW spectrum of pulse FTMW spectrum of iodobenzeneiodobenzene::

All le els in a gi en pol ad belong to the same representation of the C pointAll levels in a given polyad belong to the same representation of the Cs point group, either A’ or A’’. Now:

A’ ⊗ A’ = A’ and A’’ ⊗ A’’ = A’.i i h i h ill b i li i i d hSupersonic expansion in Ne

Since A’ contains the rotation Rc there will be Coriolis interaction around the inertial c-axis. Fermi interaction is also possible.

Simulation for 1K expansion temperature

S/N sufficient to observe all S/N sufficient to observe all four four 1313C species of C species of iodobenzeneiodobenzene::

13

13C4

13C313C

13C1

13C2

The FASSST spectrum of ClONOThe FASSST spectrum of ClONO22

Summary of Summary of loaded predictions loaded predictions ::

The nature of broadband (rotational) spectra:The nature of broadband (rotational) spectra:

Spectra may contain >100000 lines and n×106 points

Rotational transitions in the ground state, excited vibrational states, differentRotational transitions in the ground state, excited vibrational states, different conformers, isotopic species are all interleaved on the frequency scale

Effi i t d t d ti d f h fi i i

The resulting challenges:The resulting challenges:

Efficient data reduction: data sets for the fitting programs may contain many thousands of lines

Efficient assignment: f hi l i t t l id d b d t di fEfficient assignment: use of graphical assignment tools aided by understanding of the properties of the studied spectra

Data management: keeping track of assigned lines in the spectrum both in the currentData management: keeping track of assigned lines in the spectrum, both in the current species and in other species in the spectrum

Retaining control: the ability to still be able to see the broader picture and to overviewRetaining control: the ability to still be able to see the broader picture and to overview the data in various synthetic ways

Handling Handling of spectra:of spectra:gg pp

It It is most convenient to be able to work on a is most convenient to be able to work on a single spectrumsingle spectrum

AssociatedAssociated issuesissues:: backgroundbackground subtractionsubtraction concatenationconcatenationAssociated Associated issuesissues:: background background subtraction, subtraction, concatenationconcatenation, , peakfindingpeakfinding, data set creation, data set creation

AssignmentAssignment::

It is crucial to use It is crucial to use of graphical techniques that take advantage of the of graphical techniques that take advantage of the repetitive nature of the spectra repetitive nature of the spectra –– application of Loomisapplication of Loomis--Wood type methods Wood type methods in rotational spectroscopyin rotational spectroscopyin rotational spectroscopy.in rotational spectroscopy.

Fitting+PredictionFitting+Prediction::

We require efficient We require efficient interfacing with the fitting program and interfacing with the fitting program and methods methods of of qq g g p gg g p gchecking checking the data setthe data set

Computer packages for efficient analysis:Computer packages for efficient analysis:

A summary is available at A summary is available at http://info.ifpan.edu.pl/~kisiel/prospe.htmhttp://info.ifpan.edu.pl/~kisiel/prospe.htmyy p p p p pp p p p p

P di tiP di tiPredictionPredictionFrequenciesq

ConstantsFittingFittingMolecularproperties

FittingFitting

properties

Di l &Di l &Display &MeasurementDisplay &MeasurementMeasurementMeasurement

Publication

PredictionPredictionFittingFitting ASROTASROTFittingFitting ASROTASROT

SPCATSPCATASFITASFIT

GAMESSGAMESSSPFITSPFITThe PROSPEThe PROSPEThe PROSPEThe PROSPEERHAMERHAM

Display & MeasurementDisplay & Measurement

VIBCAVIBCAXIAMXIAM

Desktop?Desktop?Desktop?Desktop?ERHAMERHAM

Display & MeasurementDisplay & Measurement

SVIEWSVIEWQSTARKQSTARK

VKIELVKIEL

ASCPASCP

STRFITSTRFIT

ASCPASCP

PMIFSTPMIFSTPublication glegle

AABS AABS has been applied to many different types of broadband spectra:FASSST, cascaded multiplication THz, chirped pulse FTMW, Bruker FTIR..

The programs used in The programs used in AABS AABS ::

Display of spectra: SVIEW LSVIEW LDisplay of spectra: SVIEW_LSVIEW_L

Display of predictions, assignment ASCP LASCP Lassignment, ASCP_LASCP_Lconstruction of data sets:

Fitting/prediction: SPFIT/SPCATSPFIT/SPCAT or ASFIT/ASROTASFIT/ASROT

Text editor: PSPaDPSPaD (or UltraEdit-32)

Drawing package: glegle, Ghostscript, GSview

Distribution plots:Distribution plots: ACAC + + PMIXPMIX

The The AABSAABS package package contains extensive help features:contains extensive help features:

Handling of spectraHandling of spectra::Handling of spectraHandling of spectra::

Concatenation of measurements into aConcatenation of measurements into a singlesingle spectrumspectrumConcatenation of measurements into a Concatenation of measurements into a single single spectrumspectrum

Background subtractionBackground subtraction

D t t tiD t t tiData set creationData set creation

+ miscellaneous desirable features like ASCII import/export, smoothing, + miscellaneous desirable features like ASCII import/export, smoothing, differentiation automaticdifferentiation automatic peakfindingpeakfinding Postscript/PDF diagramsPostscript/PDF diagramsdifferentiation, automatic differentiation, automatic peakfindingpeakfinding, Postscript/PDF diagrams, …, Postscript/PDF diagrams, …

AABSAABS allows working on large, segmented spectra:allows working on large, segmented spectra:

AABSAABS allows working on large, segmented spectra:allows working on large, segmented spectra:

AABSAABS allows working on large, segmented spectra:allows working on large, segmented spectra:

AABSAABS allows working on large, segmented spectra:allows working on large, segmented spectra:

Efficient baseline subtraction:Efficient baseline subtraction:

Efficient data set creation based on highlighting a line series of Efficient data set creation based on highlighting a line series of interest:interest:

Example: Example:

The spectrum of The spectrum of fluorobenzenefluorobenzene

Highlighted series ofHighlighted series of aaRR--type transitions withtype transitions with KK = 0= 0Highlighted series of Highlighted series of RR type transitions with type transitions with KKaa 0 0

F1F1 F1F1→→F1F1→→

As a result the following data lines have been inserted into the data file (for the ASFIT program):

.

.64 0 64 63 0 63 228012.0013 0.050000 165 0 65 64 0 64 231545.4781 0.050000 166 0 66 65 0 65 235078.9223 0.050000 1..

Output to a .LIN file of SPFIT is also possible (allowing any use of the six quantum numbers available for each level in the transition and greater flexibility in the choice of the Hamiltonian)

Assignment (part I)Assignment (part I)::

The The use of graphical techniques that take advantage of the repetitive nature use of graphical techniques that take advantage of the repetitive nature g p q g pg p q g pof the spectra of the spectra –– application of Loomisapplication of Loomis--Wood type methods in rotational Wood type methods in rotational spectroscopy.spectroscopy.

The Giessen LoomisThe Giessen Loomis--Wood program:Wood program:

Early version described in Winnewisser et al J Mol Spectrosc 136 12 (1989)Early version described in Winnewisser et al. J.Mol.Spectrosc. 136, 12 (1989) Display example is from the final version of the program:

butadiene, 1596.44 cm-1 band, C i t l J M l S 695 696 59(2004)Craig et al. J.Mol.Struct. 695-696, 59(2004)

NOTE: it is possible to work on a spectrum formed from discontinuous segmentsg

Display covering about 20% of the FASSST spectrum of S(CN)Display covering about 20% of the FASSST spectrum of S(CN)22::

strip idth 1 GHstrip width = 1 GHz

central frequenciesf iof strips:157.5 - 369.6 GHzevery 4.4 GHz

LWLW--type plot for pure rotation transitions in the FTIR spectrum:type plot for pure rotation transitions in the FTIR spectrum:

D NCND2NCN:

0+ ← 0+

strip width = 0 5 cm-1

Ka = 7, aR-branch

strip width 0.5 cm

central frequenciesof strips:of strips:

14.3 - 40.5 cm-1

LW plot for vibrationLW plot for vibration--rotation transitions in the FTIR spectrum:rotation transitions in the FTIR spectrum:

D NCND2NCN:

0- ← 0+

strip width = 0 5 cm-1

Ka = 8 ← 7, cR

strip width 0.5 cm

central frequenciesof strips:of strips:

92.7 - 119.8 cm-1

LWLW--type plot used to reinforce type plot used to reinforce confidence in assignment of confidence in assignment of weak lines:weak lines:weak lines:weak lines:

Good visibility of lowest K bR-branchGood visibility of lowest Ka R-branch sequences for S(CN)2 with single 13C:

- FASSST spectrumFASSST spectrum- natural abundance sample (2.2%)

LWLW--type plot of line profiles for MMW transitions of type plot of line profiles for MMW transitions of bromoformbromoform::

HCHC8181BrBr3 3 :: HCHC7979BrBr228181Br:Br:

JJ = 90 = 90 ←← 8989218 GHz218 GHz

JJ = 88 = 88 ←← 8787217 GHz217 GHz

KK fromfrom6 to 556 to 55

KKcc fromfrom17 to 6517 to 65

ClONOClONO22: :

PredictionPrediction of 5of 5 byby

KKa a = = 00 KKa a = 1= 1 KKa a = = 22

Prediction Prediction of 5of 5νν99 by by extrapolationextrapolationfrom coupled fitsfrom coupled fits::

LoomisLoomis Woods type plotsWoods type plotsLoomisLoomis--Woods type plotsWoods type plotsfor Rfor R--branch transitions branch transitions using the actual spectrum.using the actual spectrum.

The values of The values of JJ’’ are ’’ are indicated to the right of indicated to the right of each ploteach plot..

55νν9 9 is at is at caca 600 cm600 cm--11

AA--EE splitting in the splitting in the g.sg.s. of . of pyruvicpyruvic acid: acid: JJ = 38 = 38 ←← 3737

AE

Assignment (part II)Assignment (part II)::

Understanding and making use of the band nature of rotational spectra.Understanding and making use of the band nature of rotational spectra.

NOTE: NOTE:

B d f ili f l f i f th ti tB d f ili f l f i f th ti t iiBands familiar from lower frequencies of the centimeterBands familiar from lower frequencies of the centimeter--wave region are wave region are often different from bands that dominate the rotational spectrum in the often different from bands that dominate the rotational spectrum in the millimetremillimetre--wave region.wave region.

Understanding the spectrum Understanding the spectrum –– highhigh--JJ bands:bands:

Asymmetric top rotational spectra exhibit bands formed by R-branch and Q-branch transitions.

R-branch bands are more useful in early stages of assignment and we have:

Type-I bands: familiar bands formed by a-type transitions with same J and different K . y y yThese bands correlate with transitions for higher top symmetry (diatomic, linear, symmetric tops).

Type-II bands : consisting of transitions with different values of J , and these bands are prevalent at high-J conditions seen in mmw+smm broadband spectra.

b d i f ifi hi h i f l l i i h diffType-II bands arise from specific high-J saturation of energy level spacing with different values of Ka or Kc , which leads to combs of equally spaced R-branch transitions:

C b 1 i t iti diff b 1 i J d 0 i KComb 1: successive transitions differ by 1 in J and 0 in KComb 2: successive transitions differ by 1 in J and 1 in K

When spacing between the two combs is synchronised by a suitable ratio of rotationalWhen spacing between the two combs is synchronised by a suitable ratio of rotational constants we get bands.

TypeType--IIII++ bands resulting from oblate nearbands resulting from oblate near--degeneraciesdegeneracies: :

Formation condition: A+B = n (2C), n > 1

n can be a ratio of two integers, but integral values of n leadn can be a ratio of two integers, but integral values of n leadto most compact bands

∆J = 1, ∆Kc = 1 spacing

∆J = 1, ∆Kc = 0 spacing

The many possibilities for formation of The many possibilities for formation of typetype--IIII++ bands:bands:

Si l ti f C 1000 MH Ki i l t l J M l S t 177 240 (1996)Simulation for C=1000 MHz, Kisiel et al., J.Mol.Spectrosc. 177, 240 (1996)

MHz

TypeType--IIII-- bands resulting from prolate nearbands resulting from prolate near--degeneraciesdegeneracies : :

Formation condition: 2A = n (B+C), n > 1

∆J = 1, ∆Ka = 0 spacing

∆J = 1, ∆Ka = 1 spacing

Key properties of highKey properties of high--JJ RR--type bands in asymmetric top type bands in asymmetric top rotational spectra:rotational spectra:

J.Mol.Spectrosc. 177, 240 (1996)J.Mol.Spectrosc. 178, 125 (1996)

At highAt high--JJ conditions even the accidental band types are not conditions even the accidental band types are not so rare:so rare:

n = 2, type-II+ band arising from the condition (A+B) = n (2C)

n = 3, type-II- band arising from the condition

( ) (A+B) = n (2C)2A = n (B+C)

← J ’’ J ’’ →

Trichloroethylene, Kisiel+Pszczolkowski, J.Mol.Spectrosc. 178,125 (1996)

The MMW spectrum of The MMW spectrum of iodobenzeneiodobenzene::

Distribution of lines in n = 2 type II+ bands is rather sensitive to the value of theDistribution of lines in n = 2, type-II+ bands is rather sensitive to the value of the inertial defect allowing confident assignment of vibrational satellites.

∆i = 1.213 uÅ2

∆i = −0.916 uÅ2g.s.: ∆i = 0.067 uÅ2

Dorosh et al., J.Mol.Spectrosc. 246, 228 (2007)

Assignment using classical band analysis (Assignment using classical band analysis (nn--propanolpropanol):):

Band system A @ 9.35 GHz

Band system B @ 7 2 GHzBand system B @ 7.2 GHz

Band system C @ 19.15 GHz

T pical band spacing: B + C for t pe I- R t pe bandsT pical band spacing: B + C for t pe I- R t pe bandsTypical band spacing: B + C for type-I- R-type bands

2A – (B + C) for Q-type bands

Typical band spacing: B + C for type-I- R-type bands

2A – (B + C) for Q-type bands

Band A: J = 17 ←16 of GG’ n-propanol

Fitting+PredictionFitting+Prediction::Fitting+PredictionFitting+Prediction::gggg

SPFIT/SPCAT is the package of choice for general use: up to six quantum SPFIT/SPCAT is the package of choice for general use: up to six quantum numbers per energy level, flexible Hamiltoniannumbers per energy level, flexible Hamiltonian

ASFIT/ASROT is more convenient for straightforward asymmetric topsASFIT/ASROT is more convenient for straightforward asymmetric tops

SPFIT/SPCAT is the package of choice for general use: up to six quantum SPFIT/SPCAT is the package of choice for general use: up to six quantum numbers per energy level, flexible Hamiltoniannumbers per energy level, flexible Hamiltonian

ASFIT/ASROT is more convenient for straightforward asymmetric topsASFIT/ASROT is more convenient for straightforward asymmetric topsASFIT/ASROT is more convenient for straightforward asymmetric topsASFIT/ASROT is more convenient for straightforward asymmetric tops

Aid f S /S CAAid f S /S CA

ASFIT/ASROT is more convenient for straightforward asymmetric topsASFIT/ASROT is more convenient for straightforward asymmetric tops

Aid f S /S CAAid f S /S CAAids for SPFIT/SPCAT:Aids for SPFIT/SPCAT:

CribCrib--SheetSheet -- help file to be used in conjunction with the officialhelp file to be used in conjunction with the official

Aids for SPFIT/SPCAT:Aids for SPFIT/SPCAT:

CribCrib--SheetSheet -- help file to be used in conjunction with the officialhelp file to be used in conjunction with the officialp jp jdocumentationdocumentation

PIFORMPIFORM -- reformatting of the .FIT output from SPFITreformatting of the .FIT output from SPFIT

p jp jdocumentationdocumentation

PIFORMPIFORM -- reformatting of the .FIT output from SPFITreformatting of the .FIT output from SPFIT

PISLINPISLIN -- checks on the data set (duplication, unintentional blends)checks on the data set (duplication, unintentional blends)PISLINPISLIN -- checks on the data set (duplication, unintentional blends)checks on the data set (duplication, unintentional blends)

Recommended reading in the Recommended reading in the CribCrib--sheet sheet -- the errors: the errors:

Why reformat with Why reformat with PIFORM PIFORM ??original

reformatted

Synthetic overview of the data set: Synthetic overview of the data set:

3555 li

ground state of S(CN)ground state of S(CN)22

Symbol size proportional to (νobs-νcalc)/δν 3555 linesRed symbols for (νobs-νcalc) > 3 δν σfit = 48.5 kHz

Plot for an earlier data set for a different molecule:Plot for an earlier data set for a different molecule:

Suspicious data points become readily apparent

((υ8 = 1) ↔ ((υ9 = 1) in S(CN)in S(CN)22

∆∆ KKa a = 2 interactions are apparent for low = 2 interactions are apparent for low KKaa RR--branch transitions at branch transitions at JJ from 40 to 50. from 40 to 50.

Interstate perturbations:Interstate perturbations:

Identification of perturbations from plots of mixing coefficients:Identification of perturbations from plots of mixing coefficients:

(υ8 = 1) ↔ (υ9 = 1 ) ↔(υ4 = 3 )triad in S(CN)2

J.Mol.Spectrosc. 246,39(2007)

…can then be used to refine the analysis:…can then be used to refine the analysis:

(υ8 = 1) ↔ (υ9 = 1 ) ↔(υ4 = 3 )triad in S(CN)2

J.Mol.Spectrosc. 246,39(2007)

A word of A word of warning !warning !

The information content of even very large data sets may not be sufficient to The information content of even very large data sets may not be sufficient to unambiguously discriminate between different types of fits. unambiguously discriminate between different types of fits.

The case in question: The case in question:

ClONOClONO l l f hi h h i i f fi f i f i il l f hi h h i i f fi f i f i iClONOClONO2 2 molecule, for which otherwise satisfactory fit of pairs of interacting molecule, for which otherwise satisfactory fit of pairs of interacting dyads of states resulted in inconsistencies relative to calculated values of dyads of states resulted in inconsistencies relative to calculated values of inertial defect. inertial defect.

∆∆ii = = IIcc−− ((IIaa ++ IIbb) ) in units of in units of u Å2:

Studies of the FASSST rotational spectrum of ClONOStudies of the FASSST rotational spectrum of ClONO22::

E /cm−1 < 840 cm-1 R.A.H.Butler, PhD Dissertation, OSU (2002)

g.s., ν5/ ν6ν9: J.Mol.Spectrosc. 243, 1 (2007)ν9, ν6: J.Mol.Spectrosc. 244, 113 (2007)

2ν9 / ν7 : J.Mol.Spectrosc. 213, 8 (2003)3ν9 / ν7ν9 : J.Mol.Spectrosc. 220, 150 (2003)3ν9 / ν7ν9 : J.Mol.Spectrosc. 220, 150 (2003)

Present study (118 378 GHz spectrum):Present study (118-378 GHz spectrum):

2ν9 / ν7 revisited3 / }3ν9 / ν7ν94ν9 / ν72ν9 / 2ν7 main study5ν9 / ν73ν9 / 2ν7ν9 check of the procedures

}

Interstate interactions in the Interstate interactions in the nnνν99 polyads:polyads:

All le els in a gi en pol ad belong to the same representation of the C pointAll levels in a given polyad belong to the same representation of the Cs point group, either A’ or A’’. Now:

A’ ⊗ A’ = A’ and A’’ ⊗ A’’ = A’.i i h i h ill b i li i i d hSince A’ contains the rotation Rc there will be Coriolis interaction around the

inertial c-axis. Fermi interaction is also possible.

2ν7A’

2ν7ν9A’’

2

A

3

Ac-axis Coriolisand Fermi

ν7A’

ν7 2ν9A’

ν7ν9A’’

ν7 3ν9A’’

i i li

2ν9 3ν9 4ν9 5ν9

c-axis Coriolisand Fermi

2ν9A’

3ν9A’’

4ν9A’

5ν9A’’

240 361 481 601 cm-1

The Hamiltonian for the nThe Hamiltonian for the nνν99 polyads:polyads:

This will be in block form. Each state will have a diagonal block for the rotational Hamiltonian and its vibrational energy or energy separation ∆E. The off-diagonal blocks will consist of terms for c-axis Coriolis interactionThe off diagonal blocks will consist of terms for c axis Coriolis interaction between states i and j :

H (i , j) = (G + G J + G K + ) P +Hc( j) (Gc + Gc + Gc + …) Pc +

(Fab + FabJ + Gab

K + …) (Pa Pb + Pb Pa ) + …d f th F i i t tiand for the Fermi interaction:

HF(i , j) = F0 + F J P 2 + F K Pz

2 + …

Previous problems: Coriolis expansion started at second order Fab terms [(v )↔(2v )] no Fermi interaction but instead an[(v7)↔(2v9)], no Fermi interaction but instead an assortment of more exotic terms

C bl C id bl l i bl b ∆E d FCurrent problems: Considerable correlation problems between ∆E and F0

Comparison of fits for the 2Comparison of fits for the 2νν99 dyad in dyad in 3535ClONOClONO22::

Much better agreement of fitted and calculated inertial defects:Much better agreement of fitted and calculated inertial defects:

true fit? effective fit difference (MHz)A 12181.43(4) 12103.604 77.82B 2764.715(2) 2766.017 -1.38C 2242.6229(9) 2247.233 -4.61

The fit for the 4The fit for the 4νν99 triad in triad in 3535ClONOClONO22::

no needto fit sextic orto fit sextic or higher c.d.’s

Data distribution plots for the 4Data distribution plots for the 4νν99 triad in triad in 3535ClONOClONO22::

Circle diameters ≈ obs-calc

red circles for o-c > 0.3 MHz

3456 lines in fit54.9 kHz deviation of fit

Some conclusions Some conclusions on fitting:on fitting:

It is necessary to exercise considerable care in constructing the Hamiltonian.

In the presence of strong interactions the solution space is highly nonlinear and it is very difficult to switch fitting models (and to find the global solution).

It may be difficult to unambiguously distinguish between models entirely on the basis of σfit and Nlines in the fit

Remember that the constants (may) have a physical meaning and are not just Remember that the constants (may) have a physical meaning and are not just numerical parameters of fit: numerical parameters of fit:

apply as many checks as possible: ab initio calculated centrifugal distortion, constants, inertial defects, Coriolis coefficients and energy level separations are all useful. It is important to monitor changes in values from those in the ground state.

A well chosen Hamiltonian results in the simplest solution,

Thanks to …Thanks to …

Ewa Białkowska-Jaworska Institute of Physics of the Oleksandr Desyatnyk Polish Academy of SciencesOrest DoroshAdam KraśnickiBeata PietrewiczLech PszczółkowskiLech Pszczółkowski

Eric Herbst, Ivan Medvedev, Frank De Lucia, Manfred Wi i B d Wi i Ohi St t U i it USAWinnewisser, Brenda Winnewisser, Ohio State University, USA

Brian Drouin, Carolyn Brauer,John Pearson, NASA JPL, USA

Brooks Pate + group, Univ. of Virginia,Charlottesville, USA

Gabriele Cazzoli, Luca Dore,Claudio di Esposti, Univ. of Bologna, Italy

+ the funding agencies: Poland+EU

Additional information:Additional information:Additional information:Additional information:

PROSPE website of Programs for PROSPE website of Programs for ROtationalROtationalSPEctroscopySPEctroscopy::h //i f if d l/ ki i l/ hhttp://info.ifpan.edu.pl/~kisiel/prospe.htm

li kli k t ti it i t ti l tt ti it i t ti l tlinks links to activity in rotational spectroscopy:to activity in rotational spectroscopy:http://info.ifpan.edu.pl/~kisiel/rotlinks.htm

activity of our group:activity of our group:http://info ifpan edu pl/ON-2/on23 htmhttp://info.ifpan.edu.pl/ON 2/on23.htm