Ab initio Ab initio determinationdetermination ofof spectroscopicspectroscopicconstantsconstants

(From UV to sub(From UV to sub--millimetermillimeter wavelengths)wavelengths)

M.L.SenentM.L.SenentDepartamento de Astrofísica Molecular e Departamento de Astrofísica Molecular e InfarrojaInfarroja

Instituto de Estructura de la Materia, CSIC.Instituto de Estructura de la Materia, CSIC.

ARENA, Granada 2008ARENA, Granada 2008

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Characterization of astronomical species and Characterization of astronomical species and processes.processes.Search for stable structures and intermediates.Search for stable structures and intermediates.Electronic spectra: vertical and adiabatic Electronic spectra: vertical and adiabatic transitionstransitionsInfrared spectra: anharmonic analysis and Infrared spectra: anharmonic analysis and rotational parametersrotational parametersCollisional cross sections and ratesCollisional cross sections and ratesOur Fortran codesOur Fortran codes

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Characterization of astronomical species Characterization of astronomical species and processes.and processes.

CARBON CHAINSCARBON CHAINSC4 C4 Electronic structure calculations on the C4 cluster, Electronic structure calculations on the C4 cluster, H.MassoH.Masso, , M.L.SenentM.L.Senent, P. , P. RosmusRosmus y M.Hochlaf, y M.Hochlaf, J.Chem.PhysJ.Chem.Phys., 124, 234304 ., 124, 234304 (2006)(2006)Anharmonic spectroscopic study of the ground electronic state ofAnharmonic spectroscopic study of the ground electronic state ofvarious C4 radical isotopomers, various C4 radical isotopomers, M.L.SenentM.L.Senent H. H. MassóMassó y M.Hochlafy M.Hochlaf, , ApJApJ, , 670, 1510 (2007670, 1510 (2007))

C5C5Ab initio characterization of the C5, H. Ab initio characterization of the C5, H. MassóMassó, V. , V. VeryazovVeryazov, P., P.--Å. Å. MalmqvistMalmqvist, B.O. , B.O. RoosRoos y y M.L.SenentM.L.Senent, , J.Chem.PhysJ.Chem.Phys., 127 (15), 154318 ., 127 (15), 154318 (2007)(2007)

C6 C6 MassóMassó, Senent (in , Senent (in preparationpreparation))

C4+ C4+ PhotoionizationPhotoionization of the C4 molecular beam: ab initio of the C4 molecular beam: ab initio calculations, M.Hochlaf, calculations, M.Hochlaf, C.NicolasC.Nicolas and and L.PosissonL.Posisson, , J.Chem.PhysJ.Chem.Phys., ., 127, 014310 (2007)127, 014310 (2007)

CARBON CHAINSCARBON CHAINSCH+ CH+ A simple variationalA simple variational--numerical approach to the ronumerical approach to the ro--vibrational vibrational spectrum of diatomic molecules. An application to CH+, J.R. Letespectrum of diatomic molecules. An application to CH+, J.R. Letelier lier y y M.L.SenentM.L.Senent, , SpectrochimicaSpectrochimica ActaActa A, 65, 1030A, 65, 1030--1034 (2006)1034 (2006)

C3SiC3Si Ab initio characterization of molecules of the linear lAb initio characterization of molecules of the linear l--SiC3 SiC3 isomers”, N.Inostroza, isomers”, N.Inostroza, M.L.SenentM.L.Senent, M.Hochlaf and , M.Hochlaf and R.LetelierR.Letelier((AstronAstron & Astro, 2008)& Astro, 2008)

C4H C4H Senent Senent andand Hochlaf (in Hochlaf (in preparationpreparation))

C4HC4H-- Senent Senent andand Hochlaf (in Hochlaf (in preparationpreparation

C6H+C6H+ ShuitkoShuitko, , J.FularaJ.Fulara, , A.BalatovA.Balatov, , C.GilleryC.Gillery, , H.MassoH.Masso, , P.RosmusP.Rosmus y y J.P.MaierJ.P.Maier, , J. Phys. Chem. A, 110, 2885J. Phys. Chem. A, 110, 2885--2889, 2006.2889, 2006.

CF+CF+ Theoretical roTheoretical ro--vibrational spectrum of CF+, N. vibrational spectrum of CF+, N. InostrozaInostroza, J. R. , J. R. Letelier, P. Letelier, P. FuentealbaFuentealba and and M.L.SenentM.L.Senent, , SpectrochimicaSpectrochimica ActaActa Part A, Part A, 2008.2008.

Astrophysical observations (DAMIR)Cernicharo, Goicoechea y Benilan, ApJ (2002)

???

C4 O C4H

174 cm-1

Astrophysical observations DAMIRA new unidentified far-infrared band in NGC 7027, Goicoechea, Cernicharo, Massó y Senent, ApJ (2004)

???

C5 O C6

band centre at98 µm = 102 cm-1

COLLISIONAL RATESCOLLISIONAL RATES

SO+ He SO+ He Molecules as Diagnostic Tools in the Interstellar Medium, Molecules as Diagnostic Tools in the Interstellar Medium, A.SpielfiedelA.Spielfiedel, , N.FeautrierN.Feautrier, , C.BalancaC.Balanca, , F.DayouF.Dayou, , F.LiqueF.Lique and and M.L.SenentM.L.Senent, , Mol.PhysMol.Phys., 105 (9), 1263., 105 (9), 1263--1269 (2007)1269 (2007)

SO +H2 SO +H2 Rotationally inelastic collisions of SO (XRotationally inelastic collisions of SO (X33 ΣΣ--) with H2: potential ) with H2: potential energy surface and first results with paraenergy surface and first results with para--H2, H2, F.LiqueF.Lique, , M.L.SenentM.L.Senent, , A.SpielfiedelA.Spielfiedel and and N.FeautrierN.Feautrier, , J. Chem. Phys. 126, 164312 (2007)J. Chem. Phys. 126, 164312 (2007)

SO2 + H2 SO2 + H2 A.SpielfiedelA.Spielfiedel, , L.VincentL.Vincent, , M.L.SenentM.L.Senent,, ,, P.ValironP.Valiron, , F.FaureF.Faure and and N.FeautrierN.Feautrier (in (in preparationpreparation))

C3+HeC3+He Low temperature rate constants for rotational excitations and Low temperature rate constants for rotational excitations and dede--excitations of C3 by collisions with He, D. Ben excitations of C3 by collisions with He, D. Ben AbdallahAbdallah, , K.HammamiK.Hammami, , F.NajarF.Najar, , N.JaidaneN.Jaidane, , Z.BenZ.Ben LakhdarLakhdar, , M.L.SenentM.L.Senent, , C.ChambaudC.Chambaud and M.Hochlaf, and M.Hochlaf, Astrophysical Journal, 2008.Astrophysical Journal, 2008.

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AtmosphericalAtmospherical andand astronomicalastronomicaluncharacterizeduncharacterized speciesspecies andand processesprocesses..SearchSearch forfor stablestable structuresstructures andandintermediatesintermediates..

CC44 CC44++ CC44-- CC33SiSi CC44HH CC44HH--isomers

Isomers: S (singlet); T (triplet); D (doublet)

CC44 CC44++ CC44-- CC33SiSi CC44HH CC44HH--

D D ST D S

DSD D SS

T?S?

D

D

S

S

D D

?T

T

Relative energies (eV)

CC44 CC44++ CC44-- CC33SiSi CC44HH CC44HH--

0 0 00 0 0

1.30.40.2 1.0 2.40.3

0.5?1.4?

1.1

1.7

3.2

3.2

1.1 0.6

?3.7

3.3

CC44 CC44++ CC44-- CC33SiSi CC44HH CC44HH--isomers

?? ?

d-C4

H.Masso, M.L.Senent, P. Rosmus, M.Hochlaf, J.Chem.Phys., 124, 234304 (2006)

CC44 CC44++ CC44-- CC33SiSi CC44HH CC44HH--isomers

?? ?

CC44 CC44++ CC44-- CC33SiSi CC44HH CC44HH--isomers

r-C4

30000 cm-1

H.Masso, M.L.Senent, P. Rosmus y M.Hochlaf, J.Chem.Phys., 124, 234304 (2006)

ll--CC6 6 XX33ΣΣ--gg

ParametersParameters CASPT2CASPT2 ExperimentalExperimental

Central Central bondbond 1.2651.265

MediumMedium bondbond 1.2761.276

OuterOuter BondBond 1.29511.2951

BB00 0.0480.048 cmcm--11 0.048410 0.048410 (1)(1)

(1) infrared diode laser spectroscopy.Hwang et al. Mol Phys 1993, 79-769

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Characterization of astronomical species Characterization of astronomical species and processes.and processes.SearchSearch forfor stablestable structuresstructures andandintermediatesintermediates..ElectronicElectronic spectraspectra: vertical : vertical andandadiabaticadiabatic transitionstransitions

Introduction PurePure C C chainschains VibSpec Conclusions

Absorption spectra for C4

CC66

3.27 eV0.93 eV

Linnartz et al.,JCP, 112,9777 (2000)

C4

StateState CASSCCASSCFF

MRCIMRCI Exp.Exp.

33 ΣΣgg-- 0.0 0.0 0.0 0.0 0.00.0

11∆∆gg 0.43 0.43 eVeV

0.44 0.44 eVeV

0.33 0.33 eVeV

11 ΣΣgg++ 0.47 0.47

eVeV0.61 0.61 eVeV

0.50 0.50 eVeV

C5

1A´

1A"1A´

3A"

O2H+

E (a.u.)

120 80 40 0ang (deg)

-150.27

-150.22

-150.17

-150.12

EV AT

E=0V=0

V=0

exp

C5

MRCI

CC44

CC55

33ΣΣgg-- 0.0 0.0 11ΣΣgg++ 0.00.0

11∆∆gg 0.44 0.44 eVeV

0.61 0.61 eVeV

33ΠΠgg 1.74 1.74 eVeV

11ΣΣgg++ 33ΠΠuu 1.84 1.84 eVeV

Ozone + cations Ozone + cations processesprocesses..

Electronic structure and spectroscopy of Electronic structure and spectroscopy of MgO2+MgO2+ cationcation, , O.YazidiO.Yazidi, A. Ben , A. Ben HouriaHouria and and Z.BenZ.Ben LakhdarLakhdar, , M.L.SenentM.L.Senent and M.Hochlaf, and M.Hochlaf, Chem.PhysChem.Phys, 2008, 2008

Spin-Orbit (MOLPRO)

3Σg- ∆ E

= 2Aso

< 3Σg-|SO| 1Σg

+> → ∆E=0.2 cm-1

< 3Σg-|SO| 1∆g>

< 3Σg-|SO| 3πu>

< 3Σg-|SO| 3πg> → ∆E < 0.001 cm-1

ll--SiCCCSiCCC ll--CC66 ll--CC44

∆∆E (XE (X33ΣΣ-- →→ 11ΣΣ++) ) (cm(cm--11))

λ λ (cm(cm--11))

2292229240774077

--0.6050.605

-- 0.5471860.547186b)b)

0.070.07

49194919

0.010.01

b) Deduced from previous measurements.

Ab initio characterization of the linear SiC3 isomers”, N.Inostroza, M.Hochlaf, M.L. Senent and R.Letelier (Astron & Astroph, 2008)

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Characterization of astronomical species Characterization of astronomical species and processes.and processes.SearchSearch forfor stablestable structuresstructures andandintermediatesintermediates..ElectronicElectronic spectraspectra: vertical : vertical andand adiabaticadiabatictransitionstransitionsInfraredInfrared spectraspectra: anharmonic : anharmonic analysisanalysis. . RotationalRotational parametersparameters

Astrophysical observations (DAMIR)Cernicharo, Goicoechea y Benilan, ApJ (2002)

???

C4 O C4H

174 cm-1

Astrophysical observations DAMIRA new unidentified far-infrared band in NGC 7027, Goicoechea, Cernicharo, Massó y Senent, ApJ (2004)

???

C5 O C6

band centre at98 µm = 102 cm-1

CC44: : bendingbending νν55 ((ππuu) ) (in (in cmcm--11))CalculatedCalculated ExperimentalExperimental172 (H)172 (H)203 (H)203 (H)171.1 171.1 ((anHanH))

MBPT(2)/6MBPT(2)/6--311G(2d)311G(2d)CCSD(TCCSD(T)/PVTZ)/PVTZRCCSD(TRCCSD(T)/)/vQZvQZ(1D)(1D)

160160±±44

172.4 172.4 170.4170.4174174

DiodeDiode laserlaser absorptionabsorption(gas (gas phasephase))IR (IR (ArAr matrixmatrix))

FIR FIR astrophysicalastrophysicalobservationobservation

Anharmonic spectroscopic study of the ground electronic state of various C4 radical isotopomers, M.L.Senent H. Massó y M.Hochlaf, ApJ, 670, 1510 (2007)

CC55: : bendingbending νν77 ((ππuu) ) (in (in cmcm--11))

CalculatedCalculated ExperimentalExperimental

112 112 (H)(H)130 130 (H)(H)119 119 (H)(H)

HF/6HF/6--31G(d)31G(d)MP2/6MP2/6--31G(d)31G(d)CEPACEPA--l/l/150cGTOs150cGTOs((refinedrefined))

111188±±33

101066

101022

DiodeDiode laserlaserabsorptionabsorption (gas (gas phasephase))AnionAnionphotodetachmenphotodetachmentt spectroscopyspectroscopy(gas (gas phasephase))FIR FIR astrophysicalastrophysicalobservationobservation

Base data

ExperimentalExperimentalCalculatedCalculated

PhotoelectronPhotoelectron spectroscopyspectroscopy(gas (gas phasephase))FIR FIR astrophysicalastrophysicalobservationobservation

9090

102102

B3LYP/B3LYP/cccc--pVTZpVTZCCSD(TCCSD(T)/)/150cGTOs150cGTOs

108 (H)108 (H)108 (H)108 (H)

CC66: : bendingbending νν99 ((ππuu) ) (in (in cmcm--11))

1529.9 cm-1

168.4 cm-1

Anharmonic spectroscopic study of the ground electronic state of various C4 radical isotopomers, M.L.Senent H. Massó, M.Hochlaf, ApJ, 670, 1510 (2007)

Anharmonic spectroscopic study of the ground electronic state of various C4 radical isotopomers, M.L.Senent H. Massó, M.Hochlaf, ApJ, 670, 1510 (2007)

l-C5

J.Chem.Phys,2007

l-C5

J.Chem.Phys,2007

l-C5

J.Chem.Phys,2007

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Characterization of astronomical species and Characterization of astronomical species and processes.processes.SearchSearch forfor stablestable structuresstructures andand intermediatesintermediates..ElectronicElectronic spectraspectra: vertical : vertical andand adiabaticadiabatictransitionstransitionsInfraredInfrared spectraspectra: anharmonic : anharmonic analysisanalysis andandrotationalrotational parametersparametersCollisional cross Collisional cross sectionssections andand ratesrates

Intensities and band shapes

Transition probability

Radiative probabilitiesEinstein coefficients Collisional probabilities and rates

Cross sections and rates

Excitation and de-excitation rate

Ab initio calculations of collisional cross sections σ

Van-der Walls SurfaceMolecule + H2 (or He)

Fit4 6 8 10 12

-5000

0

5000

10000

15000

θSO = 0θSO = 45θSO = 75θSO = 90θSO = 135

θΗ2 = 0 ; φ = 0

Inte

ract

ion

ener

gy (c

m-1

)

R (A)

Close Coupling Equations CC (Coupled States CS, Infinite Order Sudden IOS)

K j →i K i →j

Collision packagesMOLSCATHIBRIDONMOLCOL

σ

TEST OF ACCURACYTEST OF ACCURACYSO+ HeSO+ HeSO +H2SO +H2

SO2 + H2SO2 + H2C3+H2C3+H2

What test to do?

PotentialPotential Surface (MOLPRO)Surface (MOLPRO)DefinitionDefinition of the of the independentindependent coordinatescoordinatesAb initio Ab initio methodmethod: : RCCSD(T) or MRCI ?RCCSD(T) or MRCI ?Basis Set ?Basis Set ?Bond Bond functionfunction??Extrapolation of the basis Extrapolation of the basis set?set?BSSE correctionsBSSE correctionsS S atomatom corecore: 1s or 1s2s2p ? : 1s or 1s2s2p ? Fitting

4

5

6

7

8

9

10

11

12

13

14

15

16

0

90

180

-200-180-160-140-120-100

-80-60-40-20

020406080

100

Inte

ract

ion

En

erg

y

RHe(ao)

Theta

Potential Surface SO-He80-10060-8040-6020-400-20-20-0-40--20-60--40-80--60-100--80-120--100-140--120-160--140-180--160-200--180

Fitting

Rotationally inelastic collisions of SO (X3 S-) with H2: potential energy surface and first results with para-H2, F.Lique, M.L.Senent, A.Spielfiedel and N.Feautrier, J. Chem. Phys. 126, 164312 (2007)

WHAT TEST TO PERFORM?WHAT TEST TO PERFORM?

ChoiceChoice of the of the methodmethod(RCCSD(T) or MRCI):(RCCSD(T) or MRCI):

Convergence of the Basis Convergence of the Basis set (AVDZ to AV5Z) set (AVDZ to AV5Z) ((effecteffect of bond of bond functionsfunctions) ) (extrapolation of the Basis (extrapolation of the Basis Set)

Basis set

Slat

er D

eter

min

ants

Exact solution

Hartree-Focklimit

Full CI

Set)

Convergence of the Basis SetConvergence of the Basis Set

-160

-150

-140

-130

-120

-110

-100

-90

-80

7 7.2 7.4 7.6 7.8 8 8.2RHe(bohr)

n=2

n=3

n=4

n=5

aug-cc-pVnZ == AVnZ

core2

mincore5,1

min

V(RHe, θ=180°, rSO=2.80ao) (µHartree)

DZ

QZ5Z

TZ

CBSlQZ+CT99  0.9cm-1TZ+TP92  2.0cm-1

∆VCBSl

triangles:bond functions@ midbond RHe

-160

-150

-140

-130

-120

-110

-100

-90

-80

2 3 4 5n in AVnZ

y = m1 + m2 / (M0+1)^3 + m3 / (M0+1)^5

ErrorValue

0.40286-162.69m1

67.9272397.2m2

532.71-6084.2m3

NA0.046643Chisq

NA0.99999R

n=2,3,4,5

y = m1 + m2 / (M0+1)^3

ErrorValue

1.991-157.27m1

84.141584.5m2

NA3.2088Chisq

NA0.99859R

n=2,3,4

y = m1 + m2 / (M0+1)^3

ErrorValue

0.15553-161.1m1

14.8391922.1m2

NA0.013975Chisq

NA0.99997R

n=3,4,5

Vmin(RHe, θ=180°, rSO=2.80ao) (µHartree)

R

l-C3 + He

ν (C-C-C bending) = 63 cm -1

Low temperature rate constants for rotational excitations and de-excitations of C3 (1Σ+g) by collisions +He (1S), D. Ben Abdallah, K.Hammami, F.Najar, N.Jaidane, Z.Ben Lakhdar, M.L.Senent, C.Chambaud and M.Hochlaf(Astrophysical Journal, 2008).

ratesCross sections

MOLSCATC3 + He

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Characterization of astronomical species and Characterization of astronomical species and processes.processes.SearchSearch forfor stablestable structuresstructures andand intermediatesintermediates..ElectronicElectronic spectraspectra: vertical : vertical andand adiabaticadiabatictransitionstransitionsInfraredInfrared spectraspectra: anharmonic : anharmonic analysisanalysisRotationalRotational parametersparametersCollisional cross Collisional cross sectionssections andand ratesratesMyMy ownown FortranFortran codescodes

Second Order Perturbation Theory

http://damir.iem.csic.es/~senent/PROGRAMAS.htm

(Variational)

FIRhttp://damir.iem.csic.es/~senent/PROGRAMAS.htm