Characterization of metal-carbon containing species using a mass-selective multiphoton ionization technique

ontaining speies using a mass-seletive

multiphoton ionization tehnique

Inauguraldissertation

zur Erlangung der Würde eines Doktors der Philosophie vorgelegt der

Philosophish-Naturwissenshaftlihen Fakultät der UniversitätBasel

vorgelegt von

Cristina Apetrei Bîrz

˘ a

aus Ones

,

ti, Rumänien

Basel, 2009

auf Antrag von

Prof. Dr. J. P. Maier und Prof. Dr. Stefan Willitsh

Basel, den 15.09.2009

Prof. Dr. Eberhard Parlow

Dekan

Do notgo where the pathmay lead; go instead where there isno path and leave

a trail.

Ralph Waldo Emerson

Thisresearhprojetwouldnothavebeenpossiblewithoutthesupportofmanypeople.

Iwouldlike to thankProf. John P.Maierfor givingmetheopportunityto perform my

PhD study inhis groupin the frame of a Marie Curie Fellowship. His supervisionand

guidane are greatly appreiated. I would also like to thank Prof. Stefan Willitsh for

hisourteouslyagreement to ataso-refereeand hisadvies duringthelastmonths of

myPhD.

I wouldlike toexpress mygratitudeto Prof. AlanKnight for thegreatollaboration

wehad,the goodtimesspentinthelabandforbeingalwaystherewheneverIaskedfor

an advie.

The ompletion of this PhD would have not been possible without the people that

believed in me and introdued me in this eld of moleular spetrosopy. My speial

thanksgoesto Dr. Petre Birza for his help, guidane and ontinuous supportfrom my

rst day in the group. I owe a great deal of appreiation to Prof. Hongbin Ding for

sharing hisexperieneabout the experiment and othersienti topis.

Iamgratefulto myolleagues andgoodfriends,Dr. ZohraGuennounandDr. Corey

Riefortheirsupport,guidaneandadvies. Thetimedevotedtomyquestionsandyour

willingness to share your knowledge with me are greatly appreiated. I really enjoyed

thegood momentswe had disussing about siene and not only. Ihope the timeand

irumstanes will not make us growapart.

IannotforgetDr. EvanJohnowitzandDr. RamyaNagarajanwithwhomIhadthe

pleasureof disussing andworkingwith. The othergroups members, pastand present,

havealwaysbeen a soureof fruitfuldisussions andenjoyable times.

Manypeopleinthe housemademyPhDwork andlife easierbysolvingthetehnial

problems and helping with the bureaurati matters. Dieter Wild and Grisha Martin

from the mehanial workshop are thanked for their wonderful skills in onstruting

tehnial devies; Georg Holderied is thanked for his great help with the eletronis;

you for your timeand patiene.

Two great persons, Dr. Camelia Draghii and Dr. Cornelia Palivan are thanked for

believing and trusting me, for their advies and ontinuous support through the hard

times duringmystudies.

Intheend,Iwouldliketoexpressmygratitudetomybelovedparentsandbrothers,for

theirunderstanding, endlesssupport,aetionandenouragement throughtheduration

ofmystudies. Asvreasamultumesparintilorsifratilormeipentruafetiuneasisprjinul

ontinuu faradeare nuas ajunsastazi, u sues,lanalul aestuidotorat. Multe,

multe multumiri!

The Swiss National Siene Foundation, Moleular Universe Researh Training

Program and theCityof Baselarethankedfor their nanial support.

Basel,Switzerland

15 September2009 CristinaApetrei Birza

1 Introdution 1

1.1 Metal-ontainingarbonhains and their terrestrial appliations . 3

1.2 Astrophysialrelevane . . . 5

1.2.1 Diuse atomiand moleularlouds. . . 6

1.2.2 Transluentlouds . . . 7

1.2.3 Dense louds . . . 7

1.2.4 Cold darklouds . . . 8

1.2.5 Cirumstellarenvelopes. . . 9

Bibliography . . . 10

2 Multiphoton ionization spetrosopy 17 2.1 Overview. . . 17

2.2 Charateristi properties of multiphoton transitions . . . 19

2.2.1 Intensity dependene . . . 19

2.2.1.1 The formalintensity law . . . 20

2.2.1.2 Saturation phenomena . . . 22

2.2.1.3 The rate equation approah . . . 22

2.2.2 Resonant eet . . . 27

2.3 REMPI mehanism . . . 28

2.4 Multiphoton seletionrules. . . 32

Bibliography . . . 33

3 Experimental setup 37 3.1 Moleularsoures . . . 38

3.1.1 Disharge soure . . . 38

3.1.2 Ablation soure . . . 39

3.2 Vauumsystem . . . 41

3.3 Lightsoures . . . 43

3.4 Time of ight mass spetrometer . . . 44

3.5 Ion detetion . . . 48

3.6 Eletrialarrangement and synhronization of the REMPI setup . 49 3.7 Data handling . . . 51

Bibliography . . . 52

4 Gas phase

1 ¹ Σ ⁺ _u ← X ¹ Σ ⁺ _g

^{Eletroni Spetra of} Polyaetylenes HC

2n

^{H, n=5-7 55} 4.1 Abstrat . . . 55

4.2 Introdution . . . 55

4.3 Experimental . . . 56

4.4 Results and disussion . . . 57

4.5 Conlusion . . . 59

Bibliography . . . 59

5 Gas phase eletroni spetrum of linear AlCCH 63 5.1 Abstrat . . . 63

5.2 Introdution . . . 63

5.3 Experiment . . . 65

5.4 Theoretial alulations . . . 65

5.5 Results and disussion . . . 67

5.5.1 Eletroni spetrum and the arrier . . . 67

5.5.2 Vibroni bands of AlCCH . . . 68

5.5.2.1 Renner-Teller eet . . . 70

5.5.2.2 Vibrationalooling . . . 75

5.5.3 Rotationalstruture . . . 76

5.6 Conlusions . . . 79

Bibliography . . . 81

6 Eletroni spetra of MgC

2n

^{H (n=1-3) hains in the gas phase 87}

6.1 Abstrat . . . 87

6.2 Introdution . . . 87

6.3 Experimental . . . 89

6.4 Theoretialalulations . . . 90

6.4.1 Groundstates . . . 90

6.4.2 Exited states . . . 91

6.5 Results and disussion . . . 93

6.5.1 Eletroni spetra . . . 93

6.5.2 Dipole momentand osillatorstrength . . . 95

6.5.3 Mg-C bonding . . . 97

6.6 Conludingremarks . . . 99

Bibliography . . . 100

7 Gas phase eletroni spetrum of T-shaped AlC

2

^{radial 105} 7.1 Abstrat . . . 105

7.2 Introdution . . . 105

7.3 Experimental . . . 107

7.4 TheoretialCalulations . . . 108

7.5 Results and disussions . . . 109

7.5.1

C ˜ ²

^B

2 ← X ˜ ²

^A

1

^{. . . . . . . . . . . . . . . . . . . . . . . 110}

7.5.2

D ˜ ²

^B

1 ← X ˜ ²

^A

1

^{. . . . . . . . . . . . . . . . . . . . . . . 117}

7.5.3 Vibronioupling . . . 120

7.6 Conlusion . . . 122

Bibliography . . . 122

8 Eletroni spetrum of titanium dioxide, TiO

2

¹²⁷ 8.1 Introdution . . . 127

8.2 Experimental . . . 130

8.3 Results and disussion . . . 130

8.4 Conlusions . . . 136

Bibliography . . . 137

9 Conluding remarks 141

A Appendix 1 145

A.1 Further spetralsimulationwith higher resolution forAlCCH. . . 145

Curriulum Vitae and list of publiations 149

The roleof metal-ontainingmoleules inhemistryis remarkable. Inareas rang-

ingfromatalysistobiohemistry,atmospherito interstellarhemistry, ombus-

tiontometal-organivapordeposition,metal-ligandbondsareformedandbroken.

Understanding the metal-ligand (M-L, L=CN, OH, CCH, CH

3

^{, C}

2

^H

5

^{) bond and}

itsproperties is very importantand the basis in many areas of hemistry.

The most ommonmeansof probingthe metal-ligandbond isthrough detailed

quantum-hemial alulations. Nowadays the methodology is highly developed

and a virtually omplete piture an be obtained. The equilibrium bond length,

thebond dissoiationenergy,thebondforeonstant,thehargedistributionand

the eetof eletroni exitationallan be possibly extrated fromthesealula-

tions. Takingintoaountthehigh eletronountformetalatoms,thesmallsep-

arationof metal atomi orbitalsleading tomany near-degeneraies, highlyorre-

latedalulations aredesirablemaking ab initio alulationsformetal-ontaining

speies not atrivialtask. The simplestonsistof a singlemetal atom bound toa

singleattahedmoleule, theligand. However, althoughsimplefromatheoretial

point of view, the study of suh entities represent a big hallenge to experimen-

talist beause for most of the metals, attahing a single univalent ligand results

in a highly reative speies that has only a transient existene in the ondensed

phase.

To redue their reation rate to a negligiblelevel a possible solution is to trap

thesemoleulesinrare-gasmatries. Thelowtemperatureandrigidenvironment,

harateristi of suh matries, provide a semi-ideal yet eetive means for the

isolationand studyof highlyreative speies. However, adrawbak of thematrix

isolation tehnique is that the inexible trapping site tends to quenh any rota-

tional motion, thus ruling out rotationallyresolved spetrosopy leading to poor

struturalinformation. Nevertheless, the infrared(IR)andRamanspetraofma-

trix isolated moleules 1

have been of a great help and tend to ompare with the

spetra of the same speies in the gas phase. In ontrast, the eletroni spetra

are usually severelyperturbed by the surrounding host lattie.

Theidealenvironmenttostudyreativeintermediatesisinthegas phase. Over

theyears,theexquisitesensitivityofmassspetrometrybasedtehniqueshasbeen

utilized to study the interation of metals with organi and inorgani moleules.

Mostofthisgasphaseworkinvolvesions.

2

Thetehniquesusedinludetraditional

high-pressure mass spetrometry, 3

owing afterglows, 4

ion beams, 5

and Fourier

transform ion ylotron resonane.

6

While these methods are the benhmark of

thegas-phase studies,inordertoobtainelaboratestruturalinformationdierent

tehniques are requiredto investigatethe eletroni spetra of suh speies. Nev-

ertheless, produing metal ontaining intermediates in the gas phase has been a

hallengingissue. Themostommonlyusedmethodformakingfreeradialsinthe

gas phase involvesfragmentationof apreursor moleule, normally by photolysis

or by aneletrialdisharge. Unfortunately, these tehniques have limitedutility

in the prodution of metal-arbon radials, sine suitable volatile preursors do

not usually exist.

Most of the early work on metal ontaining radials was arried out using

Broida-type oven soure, 7

metal atoms being produed by evaporation from a

heated ruibleand entrained in aow of inert arrier gas. This soure has been

extensively employed in the millimeter-wavetehniques toobtain pure rotational

spetra. Speiessuhasalkaliandalkalineearthmonohydroxides, monoaetylides

andmonomethylshavebeenidentiedandharaterizedintheirgroundeletroni

states.

8 16

In this type of soure the temperature remains a serious disadvantage

inmany ases. Atbestrotationaltemperatureof 400 Kisattainedwitha Broida

oven, and the vibrational temperature is often onsiderably higher on aount

of the muh lower eieny for the ollisional ooling of vibrational degrees of

freedom.

To eliminate suh a problem, supersoni ooling is neessary. The develop-

ments in supersoni jet expansion tehnology have made areas like moleular

spetrosopy to advane rapidly. Supersoni nozzles an be ombined with hot

oven evaporation upstream of the nozzle, but the tehnology is quite diult to

implement and these soures have not seen widespread use.

17,18

More ommon,

and of more general use, are pulsed ablation soures, developed almost simulta-

neously by Smalley et al.

19

and Bondybey et al.

20

in the early 1980s. Using

this soure, metal ontainingmoleules with rotationaltemperatures below50 K

are frequently obtained. It is important to admit that laser ablation is rarely a

lean soure of a partiular speies. A multitude of proesses an take plae in

the laser ablation region. In addition to metal atoms whih an be formed in

both theirground andtheir exitedstates, metallusters andmetal ions analso

be generated. The bombardment by intense laser radiation, and the subsequent

prodution of light, heat and a whole host of harged partile within the abla-

tion plasma, an lead to extensive fragmentation of moleular preursors. Laser

ablation soure has been extensively used in onjuntion with the laser indued

uoresene (LIF)spetrometer.

21 26

A drawbak ofthe LIFrehnique isthe lak

of speies disrimination. This an be overome using a mass-seletive tehnique

suhasresonant-enhanedmultiphotonionization(REMPI).Theimplementation

of the laser ablation soure in the REMPI spetrometer willbe desribed in the

Experimental setion.

1.1 Metal-ontaining arbon hains and their

terrestrial appliations

Metal omplexeswith onjugated hydroarbon bridges(double and triple bonds)

orwithdonorandaeptorligandsareandidatesforeletriallyondutingmate-

rialsandfor materialswithseond-andthird-nonlinearoptialproperties. These

ompounds are also interesting as model systems for surfae arbides in hetero-

geneous atalysis.

2729

They are models for intermediates in the polymerization

proess of alkenes and alkynes, 30

and for unsaturatedhydroarbons hemisorbed

onmetal surfaes 31

- a rst step during heterogenous atalysis.

Hydroarbon on metals are of pratial importane in surfae hemistry. The

rst experiments were performedon metallipartilesgenerallysupportedonox-

ides, materialsused inatalytireations. Nevertheless, the shape ofthe metalli

aggregatesstudiedisoftremendousimportaneanditwasdiultandtediousre-

quirementtobringunderontrolthesurfaestruture onatomisale. Moreover,

the eletroni properties of metal may in suh ases be modied by interations

with the support. The purpose of studying hydroarbon absorption on metals is

todeterminethe hemialnature,the loationrelativetothe surfae, and thege-

ometry of the adsorbed speies, whihreets the hybridizationofarbonatoms.

This would enable to obtain a fundamental understanding of the dierent prop-

erties of dierent metal substrates with varied exposed sites and their relative

properties towards breaking orrearrangement of C-C and C-H bonds.

Dierenttehniqueshavebeen employedtostudysuhinterations. Theontri-

butionofinfraredspetrosopy 3234

beauseoftherelativeeasewithwhihinfrared

spetra anbemonitoredfor allstatesof matter. Fromvibrationalenergies,fore

onstantsan bedeterminedandinthisway additionalinformationregarding the

bond strengths iwithin the adsorbate or that with respet to the substrate an

beobtained. Followingthe reent progress inultrahigh-vauumtehniques allow-

ing experiments to be onduted over a long time with ontrolled atmospheres

and surfaes, reent years have seen a great development in the eletroni and

geometrial struture determinationof hydroarbon-metalsystems.

Convenient understanding of adsorption proess requires some information

about the eletroni properties of the adsorbate-substrate pair. Spetral infor-

mation on the orbitals of adsorbed speies may be obtained using photoeletron

spetrosopy. Despite the general similarities in the relative ionization levels of

hemisorbed hydroarbons and their gas-phase ounterparts, 35

the latter would

provide a better understanding of the metal-arbonbonding properties. Beause

ofthelargedierenesinthebehaviorofbaremetalswithrespet totheirreativ-

itytowards C-HorC-C bond breaking,the gas-phase studiesinludingeletroni

spetrosopy, reation kinetis and dynamis, would give an insight into the for-

mation of metal-arbon bonds, aurate ionization potentials, eletron anities,

bonddissoiationenergies andbranhingratios. Theappliabilityoftheseresults

is not only for understanding the heterogeneous atalyti proesses but also are

of tremendous importanefroma fundamental pointof view.

Thesimplestmoleularunit ofarbon,C

2

^{,existing asa smallpartof thelinear}

polyenes [-(C

≡

^C)

n

^{-℄ (also named}"arbynes"), is extremely reative and has only been haraterized by spetrosopi methods. One method of stabilizing the C

2

unit is by end-apping through the derivatization of both ends forming organi

aetylenes, aetylide omplexes or aetylide bridges between two metal enters.

In organometallipolymers,unsaturated hydroarbons, C

n

^{units, an at asele-}

troni bridges 36

("moleular wires"

37

) between metal atoms.

The ultimateomputationalsystemwouldonsistoflogideviesthatare ultra

dense, ultrafast, and moleular-sized.

38,39

Even thoughstate-of-the-art nanopat-

tering tehniques allow lithographi probe assemblies to be engineered down to

100 Å gap regime, 40

the possibility of eletroni ondution based upon single

or small pakets of moleules has not been extensively addressed. The simplest

eletroni devie, the one-dimensional wire, thus one-dimensional arbon hains,

hasthe basimotifofa

π

^{-bondingsystem, allowingtheondutionofeletriity41}

as an eletrialeld mixes the ground and exited states of the moleule. Thus

the promotion of an eletron aross the band-gap of the free moleule plays an

important role, and it is this fundamental parameter (band-gap energy) that is

essentialtodesribethebehaviorofmoleulardevies. Optialspetrosopyoers

a straightforward method tomeasure this band-gap 42,43

aswell as the ionization

potentials and eletron anities of the wires, in addition to their bonding and

physial strutures. The ends of these arbonhains should be easilyfuntional-

ized and may serve as "moleular lips" for making surfae ontats with metal

probes for moleulareletronis studies.

44

1.2 Astrophysial relevane

Moleules an exist in a wide range of astrophysial environments, from the ex-

tremely old regions between stars to the atmospheres of stars themselves. In-

terstellar moleules an be identied through their eletroni, vibrational and

rotational spetrum. Typially, eletroni transitions of simple moleules arise

in the ultraviolet (UV) or visible portion of the spetrum; vibrational bands lie

at infrared (IR) wavelengths; and rotational lines are seen at radio wavelengths.

Hene, the study of interstellar moleules neessarily involves a wide range of

observational tehniques and instruments.

To date, around 150 moleular speies have been tentatively or denitively

identiedininterstellarorirumstellarlouds,whileabout50havebeenidentied

in studies of omets in our solar system. One should dene these astrophysial

environmentsbeforeexemplifying the spei regionswhere thesemoleules have

been observed.

The interstellar medium (ISM) onsists of gas and dust between stars, whih

aounts for 20-30% of the mass of our galaxy. Muh of this material has been

ejeted by oldand dying stars. TheISM ontains dierentenvironmentsshowing

large ranges in temperature (10-10

4

K) and densities (100-10

8

H atoms/m

3

). It

is lledwith hydrogen gas, about 10% heliumatoms, and

∼

^{1% ofatoms suhas}

C, N, and O. Other elements are even less abundant. Roughly 1% of the mass

is ontained in mirosopi (miron-sized) dust grains. The interstellar medium

represents the raw material for forming future generations of stars, whih may

developintoplanetarysystemslikeourown. TheISMappearstoontainavariety

of loudtypes, spanningawiderangeof physialandhemialonditions: diuse

atomiandmoleularlouds,transluentlouds,densemoleularloudsanddark

moleularlouds. Interstellarlouds are neither uniform nor dynamiallypassive

onlongtimesales. They display"lumpy"strutures, are ontinuallyevolvingas

new stars form, and are enrihed by material ejeted from dying stars that was

formed during stellarnuleosynthesis.

1.2.1 Diuse atomi and moleular louds

Diuse atomi loudsrepresent theregimeinthe ISMthat isfullyunsheltered

from the interstellar radiation eld, and onsequently nearly all moleules are

quikly destroyed by photodissoiation. Hydrogen is mainly in neutral atomi

form,andatomswithionizationpotentiallessthanthatofhydrogen(mostnotably

arbon) are almost fully ionized, providing abundant eletrons. Diuse atomi

louds typially have a fairly low density (

∼

^10-100/m

³

^{), and} temperatures of 30-100K.

Diusemoleularloudsrepresenttheregimewheretheinterstellarradiation

eldissuientlyattenuated,atleastattheindividualwavelengthsthatdissoiate

H

2

^{. However, enough} interstellar radiation is still present to photoionize any atomi arbon, or tophotodissoiate CO, suhthat arbonis predominantly still

in the form of C

+

. In order toprovidethe shieldingof radiation,in steady state,

diuse moleular louds must neessarily be surrounded by diuse atomi gas.

This means that most radiations that ross a diuse moleular loud will also

ross diuse atomigas.

The presene of abundant H

2

^{in diuse moleular louds permits the starting}

of the hemial proesses. Moleules are observed in these louds in absorption

in the UV/visible(e.g., CO, CH, CN,C

2

^{, C}

3

^{),45 in the infrared (CO, H}

+ 3

^),

46

and

at millimeter wavelengths (e.g., HCO

+

, OH, C

2

^{H). These louds typially have}

densitiesontheorderof100-500/m

3

,andtemperaturesthatrangefrom30-100K.

1.2.2 Transluent louds

The main harateristis of suh louds are relatively low temperatures (20-

50K) and densities of 500-5000/m

3

. VIS-IR absorption and millimeter absorp-

tion/emission are the observational tehniques used to identify the moleules

present in this environment. With suient shieldingfrom interstellar radiation,

arbon begins its transitionfrom ionized atomiform into neutral atomi (C) or

moleular(CO)form. The hemistry inthis regimeis qualitativelydierent than

in the diuse moleular louds, both beause of the dereasing eletron fration

and beause of the abundane of the highlyreative Catoms.

47

In many ways, the transluent loud regime is the least well understood of all

loud types. This is partly beause of a relative lak of observational data, but

alsobeausetheoretial models donot all agree onthe hemial behavior inthis

transitionregion.

1.2.3 Dense louds

Theselouds are haraterizedby verylowtemperatures (10-30K)and high den-

sities(10

4 − 8

/m

3

). The oldgasphasehemistrytaking plaeinthis environment

an eiently lead tothe formation of simple speies suh as CO, N

2

^{, O}

2

^{, C}

2

^H

2

^,

C

2

^H

4

^{and HCN, and simple arbon hains (Herbst 1995). Eient aretion of}

atomsand moleules insuh environmentsand subsequent reations onthe grain

surfae an easily indue the formation of moleules suh as CO

2

^{and CH}

3

^OH,

whih are later returned to the interstellar gas.

48

These louds are the nasene

sites of stars of all masses and their planetary systems. The building bloks for

protostellar disks, from whih planets, omets, asteroids, and other marosopi

bodies eventually form are the interstellarmoleules and dust present in this en-

vironment.

49,50

Observations at infrared, radio, millimeter, and submillimeter

frequeniesshowthatalargevariety ofgasphaseorganimoleules arepresentin

the dense interstellarmedium.

51,52

These inlude organi lasses suh asnitriles,

aldehydes, alohols, aids, ethers, ketones, amines, and amides, as well as many

long-hainhydroarbon ompounds.

1.2.4 Cold dark louds

Stars and planets form within dark moleular louds. The internal struture of

these louds, and onsequently the initial onditions that give rise to star and

planet formation is partially understood. The louds are primarily omposed of

moleularhydrogen, whih isvirtuallyinaessibleto diretobservation. But the

louds also ontain dust, whih is well mixed with the gas and whih has well

explained eets on the transmission of light. The hydrogen moleule possesses

no dipole moment beause of its symmetri struture and annot produe an

easily detetable signal under the onditions present in the old, dark louds.

However, traditionalmethodsused toderivethe basi physialpropertiesof suh

moleular louds are making use of the observations of trae H

2

surrogates, the rare moleules with suient dipole moments to be simply deteted by radio

spetrosopi tehniques, and interstellardust.

Dust grains eetively shield moleules from interstellar UV photons, prior to

the beginningofstar formation. However, osmirays anpassthrough anddrive

a rih ion-moleule hemistry, enhaned by neutral-neutral proesses, in whih

many omplex organi speies may be produed.

53

These reations, along with

grain surfae proesses, aount for the high observed D/H ratios in interstellar

moleules.

54

The lowtemperature(

∼

^{10K) and lak of} high-luminosity souresmake these regionsidealtestinggrounds formodels ofgas-phase ion-moleulehemistry. The

old, dark louds oer a rather mild environment; temperatures appear to be

typially around

∼

^{10K, with densities ranging up to 10}

⁴

^-10

⁵

^/m

³

^{. Nonethe-}

less, animportantfrationof theknown interstellarmoleuleshas beenidentied

in suh dark louds. In fat, a number of these speies, inluding the heavier

yanopolyynes and relatedmoleules, have been found onlyin suh regions.

55

The dark loud TMC-1 ontains a speial series of many unsaturated ar-

bon hain moleules.

51

These inlude the yanopolyynes (HC

2n+1

^{N, n=1 - 5),}

various umulene arbenes (H

2

^C

n

^{, n=3,4,6), and hain radials (HC}

n

^{, n=1-8,}

C

n

^{N, n=1,3,5), aswell as some methylated moleules suh as}methylyanoaety- lene (CH

3

^{CCCN) and} methyldiaetylene (CH

3

^{CCCCH). Varioussmallmoleules}

(CCO, CCCO, CCS, CCCS) are observed; their higher homologues and new ho-

mologousseries may alsobepresent.

5659

1.2.5 Cirumstellar envelopes

The massive irumstellarenvelopes (CSEs) of late-type,post-AGB stars are de-

isive to the evolution of the ISM beause they provide the dust and refratory

speiesfor thediuse medium,andyetrequirethe existeneofthe densemedium

togenerate the stars.

Substantial amounts of interstellar dust are known to be formed in the inner

regionsoftheirumstellarenvelopesofasymptotistars. Thesegrainsarelosely

linked to the mass-loss proess as they absorb stellar radiationand drag the gas

away from the stellar surfae, initiating in this way a mass-loss whih leads to a

the reationof a irumstellar envelope (CSE) whih mightontain up to a solar

mass of gas. These CSEs inorporate a wide range of physial onditions, from

very dense (n(H

2

⁾

∼

¹⁰

¹⁵

^/m

³

^{), hot (T}

∼

^{2000K) moleular gas just above the}

photosphere,togaswithpropertiessimilartothatfoundindarkmoleularlouds,

to diuse regions dominated by the external UV radiation eld whih produes

atomigas farfrom the entralstar.

60

Outowing irumstellar envelopes 61

are, in a sense, hemial laboratories,

whereatomsreated throughstellarnuleosynthesisan reatfortherst timeto

formlong-livedhemialbonds. Viaradioastronomialmeasurements,the mole-

ular distributionswithin suh astrophysialenvironments ouldbetraed. These

informationhasprovided insightsintoseveralaspetsofhemialevolution,oneif

whih is the involvement of metal-ontaining moleules. Among arbon-rih ir-

umstellar outows, 62

the representative soure IRC+10216 63

has been found to

ontain several dierent metal-ontaining moleules, inluding NaCl, KCl, AlF,

AlCl, 64

AlNC, 65

and the isomeri pair MgNC 66

and MgCN.

67

A group of these

moleuleshas beenfound alsoinanotherobjet,the protoplanetarynebulaeCRL

2688, 68

whih represents a more advaned stage of stellar deomposition. While

the moleulesidentied todatedonot allappear tosharea ommonorigin, their

most obvious harateristi is that all are halides or ynides of the lighter (and

more osmially abundant) main-group metalatoms.

[1℄ M. E. Jaox, Chem. Phys. 189, 149 (1994).

[2℄ D. H. Russell, Gas Phase Inorgani Chemistry, Plenum, New York,1989.

[3℄ P. Kebarle, Annu. Rev. Phys. Chem.28, 445 (1977).

[4℄ M. T. Bowers, Gas Phase Ion Chemistry, volume 1, Aademi Press, New

York,1979.

[5℄ P. B. Armentrout, Siene 251, 175 (1991).

[6℄ M.V. Buhanan, FourierTransform MassSpetrometry,volume359, Amer-

ian Chemial Soiety,Washington, DC, 1987.

[7℄ J. B. West, R. S. Bradford, J. D. Eversole, and C. R. Jones, Rev. Sient.

Instrum. 46, 164 (1975).

[8℄ J.M. Thompsen, P. M.Sheridan, and L.M. Ziurys, Chem. Phys. Lett. 330,

373 (2000).

[9℄ M. A. Brewster and L.M. Ziurys, J. Chem. Phys. 113, 3141 (2000).

[10℄ A. J. Apponi, M. A. Brewster, and L. M. Ziurys, Chem. Phys. Lett. 298,

161 (1998).

[11℄ J. Xinand L.M. Ziurys, Astrophys. J.501, L151 (1998).

[12℄ J. S. Robinson, A. J. Apponi, and L. M. Ziurys, Chem. Phys. Lett. 278, 1

(1997).

[13℄ M. A. Andersonand L. M. Ziurys, Astrophys. J. 460, L77 (1996).

[14℄ M. A. Anderson, T. C. Steimle, and L. M. Ziurys, Astrophys. J. 429, L41

(1994).

[15℄ B. P. Nuio, A. J. Apponi, and L. M. Ziurys, Chem. Phys. Lett. 247, 283

(1995).

[16℄ M. A. Anderson and L.M. Ziurys, Astrophys. J.439, L25(1995).

[17℄ F. J. Grieman, S. H. Ashworth, J. M. Brown, and I. R. Beattie, J. Chem.

Phys. 92, 6365 (1990).

[18℄ J.R.Woodward,S.H.Cobb,andJ.L.Gole, J.Phys.Chem.92,1404(1988).

[19℄ T. G.Dietz,M.A.Dunan,D.E.Powers, andR.E.Smalley, J.Chem.Phys.

74, 6511 (1981).

[20℄ J. L. Gole, J. H. English, and V. E. Bondybey, J. Phys. Chem. 86, 2560

(1982).

[21℄ G. K. Corlett, A. M. Little, and A. M. Ellis, Chem. Phys. Lett. 249, 53

(1996).

[22℄ A. Bopegedera, C. R. Brazier, and P. F. Bernath, J. Mol. Spetros. 129,

268 (1988).

[23℄ M. G. Liand J. A. Coxon, J. Mol. Spetros. 180, 287 (1996).

[24℄ M. G. Liand J. A. Coxon, J. Mol. Spetros. 183, 250 (1997).

[25℄ M. G. Liand J. A. Coxon, J. Mol. Spetros. 196, 14 (1999).

[26℄ M. Elhanine, R. Lawruszzuk, and B. Soep, Chem. Phys. Lett. 288, 785

(1998).

[27℄ H. Pines, The Chemistry of Catalyti Hydroarbon Conversions, Aademi

Press, London, 1981.

[28℄ C. Masters, Adv. Organomet.Chem. 17, 61(1979).

[29℄ W. Bek, B. Niemer, and M. Wieser, Angew. Chem. Int. Ed. Engl. 32, 923

(1993).

[30℄ G. Wilse, Angew. Chem.Int.Ed. Engl. 27, 185 (1988).

[31℄ H. Wadepohl, Angew. Chem.Int. Ed. Engl. 31, 247 (1992).

[32℄ W. A. Pliskinand R. P. Eishens, J. Chem.Phys. 24, 482 (1956).

[33℄ N. Sheppard etal., Mol.Spetros. 97(1968).

[34℄ J. Erkelens and J. T. Liefkens, J. Catal. 8, 36(1967).

[35℄ J. E.Demuth and D. E. Eastman, Phys. Rev. Lett. 32, 1123 (1974).

[36℄ J. Liet al., Organometallis11, 3050 (1992).

[37℄ J.-M.Lehn, Angew. Chem. Int. Ed. Engl. 27, 89(1988).

[38℄ J. S.Miller, Adv. Mater. 2, 378 (1990).

[39℄ D. H. Waldek and D. N. Beratan, Siene 261, 576 (1993).

[40℄ W. P. Kirk and M. A. Reed, Nanostrutures and mesosopi systems, Aa-

demi Press, San Diego,1992.

[41℄ http://www.nobel.se/hemistry/laureates/2000/index.html.

[42℄ J. Hsuet al., J. Phys. Chem. B 106, 8582 (2002).

[43℄ P. Loubeyze, F. Oelli,and R. LeToulle, Nature 416, 613 (2002).

[44℄ N.L.Abbott, J.P.Folkers, andG.M.Whitesides, Siene 257,1380(1992).

[45℄ E. B. Jenkins etal., Astrophys. J. 181, L122 (1973).

[46℄ B. J. MCall, T. R. Geballe, K. H. Hinkle, and T. Oka, Siene 279, 1910

(1998).

[47℄ E. F. VanDishoek and J.H. Blak, Astrophys. J. 334, 771 (1988).

[48℄ A. G.G. M. Tielensand W. Hagen, Astron. Astrophys. 114, 245 (1982).

[49℄ H. A. Weaver and L. Danly, The Formation and Evolution of Planetary

Systems, Cambridge University Press, Cambridge, 1989.

[50℄ E. H. Levy and J. I. Lunine, Protostars and Planets III, volume 1596, Uni-

versity Arizona Press, 1993.

[51℄ M. Ohishi and N. Kaifu, Faraday Disussions 109, 205 (1998).

[52℄ G. Winnewisser and C. Kramer, SpaeSiene Reviews 90, 181 (1999).

[53℄ T. J.Millar,P.R.A.Farquhar,and K.Willay, Astron.Astrophys.121, 139

(1997).

[54℄ A. G. G.M. Tielens, Astron. Astrophys. 119, 177 (1983).

[55℄ W. M. Irvine,M. Ohishi, and N. Kaifu, Iarus 91, 2 (1991).

[56℄ M.C. MCarthy,M.J.Travers, A.Kovas, C. A.Gottlieb,and P.Thaddeus,

Astrophys. J.Suppl. Ser. 113, 105 (1997).

[57℄ M. B. Bell et al., Astrophys. J. 518, 740 (1999).

[58℄ P.Thaddeus, M. C. MCarthy, M.J. Travers, C. A.Gottlieb, and W.Chen,

Faraday Disussions 109, 121 (1998).

[59℄ M. Guélin etal., Astron. Astrophys. 317, L1(1997).

[60℄ L. M. Ziurys, PNAS 103, 12274(2006).

[61℄ M. Busso, R. Gallino, and G. J. Wasserburg, Ann. Rev. Astron. Astrophys.

37, 239 (1999).

[62℄ G. Wallerstein and G. R. Knapp, Ann. Rev. Astron. Astrophys. 36, 369

(1998).

[63℄ A. E. Glassgold, Ann. Rev. Astron. Astrophys. 34,241 (1996).

[64℄ J. Cerniharo and M. Guélin, Astron. Astrophys. 183, L10 (1987).

[65℄ L. M. Ziurys et al., Astrophys. J. 564, L45(2002).

[66℄ K. Kawaguhi, E. Kagi, T. Hirano, S. Takano, and S. Saito, Astrophys. J.

406, L39 (1993).

[67℄ L.M.Ziurys,A.J.Apponi,M.Guélin,andJ.Cerniharo, Astrophys.J.445,

L47(1995).

[68℄ J. L. Highberger, C. Savage, J. H. Bieging, and L. M. Ziurys, Astrophys. J.

562, 790 (2001).

spetrosopy

2.1 Overview

Mostof whatis known about the interation of lightwithmatter omesfromthe

study of single photon events. The laser has now made possible the observation

of many novel and even exoti phenomena involving multiple photon proesses.

Fromthe examinationofthesenewnonlinearproessesinformationanbegained

on allaspets of laser exitation of atoms and moleules. In partiular, one suh

proess -multiphoton ionizationof moleules- is one of the most interesting elds

of researh made possible by the development of powerful lasers. Multiphoton

spetrosopyhasbeenwidely usedinbiology,hemistry,materialsiene, physis,

and other disiplines.

Multiphoton spetrosopy has made a great ontribution to moleular spe-

trosopy. When amoleuleissubjeted toanintense radiationeld, multiphoton

ionization ours with relative ease. A ground state eletron is exited into the

ionization ontinuum by simultaneous or sequential absorption of a number of

photons. If an exited eletroni state lies at the energy sum of two or three of

these photons the ionizationross setion an be greatly enhaned,resulting ina

simultaneous two- orthree-photon transitionif symmetry and spin allowed. New

vibroni and eletroniallyexited states, whih are not found inordinary single-

photon spetrosopy beause of their dierent seletion rules, an be observed

in a wide range from lower exited states to ontinua. As mentioned above the

possibility of simultaneous two-photon absorption or emission in moleules was

made possible only after lasers were developed as an intense light soure, espe-

ially when tunable dye lasers appeared after the late 1960s. In fat, ompared

with one-photon ross setion for a typial moleule (

∼

¹⁰

^{− 17}

^m

²

^{),1 the ross}

setions of multiphoton transitions are extremely low at the intensity of onven-

tional lightsoures: forexample,

∼

¹⁰

^{− 51}

^m

⁴

^{s and}

∼

¹⁰

^{− 82}

^m

⁶

^s

²

^{,2 for two- and}

three-photon transitions, respetively.

Very high light intensities I [photons/m

2

s℄ are needed in order to ahieve

a signiant transition probability,

σI ^N

^{, therefore lasers are the only real op-}

tion to use as light soures. Typial modern pulsed dye lasers have pow-

ers of around 1mJ/10ns pulse (10

5

watts in 10

− 8

s, or about 10

23

photons/s or

10

16

photons/pulse). These powers within a 1mm

2

spot will give only

∼

¹⁰

^{− 8}

Einstein fator in eah laser pulse for two-photon resonane. In turn, fousing

to aradius of about 100

µ

^{minreases the} probability ofa twophoton absorption to 10

− 2

in eah laser pulse, whereas a typial one photon transition is already

saturated by two orders of magnitude.

Suh intensitiesare normally ahieved by foussing the output of onventional

(nanoseondpulseduration)tunabledyelasers. Sideeet ofitisthe loalization

of the multiphotonexitation events in smallspae region(i.e. the foal volume)

whihmakesthe tehnique ideallysuited to be used with moleularbeams.

The eld of multiphoton ionization spetrosopy, namely resonant enhaned

multiphoton ionization(REMPI), on freeradials has seen alot of developments

in the past twenty years. In 1975 the rst REMPI spetrosopi results where

reported, studies on a stable radial, NO, 3

and soon afterwards the I

2

^spetrum

was reorded using this tehnique.

4

The rst REMPI detetion of a transient

moleular free radial was reported in 1978, when NH (a

1 ∆

^{) radials were pro-}

dued by multiphoton dissoiation of NH

3

^{.5 Two years later another group re-}

ported REMPI spetra of vibrationally exited NH

2

⁽

X ˜ ²

^B

1

^{) and bands of NH}

(a

1 ∆

^{) radial produed by UV/visible} multiphoton photolysis of NH

3

^.

6

Soon

afterwards, the studiesof methyl and triuoromethyl radialsdemonstrated that

REMPIspetrosopyouldonvenientlyandverysensitivelydetetnonuoresent

free radials.

7,8

Sine 1983 the REMPI spetrosopi data of free radials have

greatly expanded, revealing new spetrosopi knowledge leading to disovery of

new eletroni states of many transient speies.

2.2 Charateristi properties of multiphoton

transitions

Visible/UV multiphoton transitions have several harateristi features suh as

laserintensitydependene, resonaneenhanement,andpolarizationdependene.

The intensity dependene and resonane eet on moleular multiphoton spe-

trosopy are briey outlinedasfollows.

2.2.1 Intensity dependene

Themultiphotonprobabilityisformulatedaordingtotime-dependentperturba-

tiontheory. As anexample,atwo-photonabsorptionfromstatesaton,asshown

inFigure 2.1is onsidered.

Figure2.1: The two-photon absorption proesses of a moleule:(a) nonresonant,

(b) resonant.

The transitionprobabilityW

(2)

,taking intoaountonlythe lowest order term

of the radiation-moleuleinteration, isgiven as

W ⁽²⁾ ∝ I ² | X

m

h n | µ | m ih m | µ | a i

∆E ma − ~ ω r | ²

^(2.1)

whereI isthe intensity of the laser, m the virtual intermediate states,

∆

^E

_ma

^the

energy dierene between intermediate and initial states,

µ

^{the dipole moment,}

and

ω r

^{thelaser frequeny. Equation(2.1) shows that the two-photon} probability

isproportionaltothe squareof the laserintensity. Moreover, n-photontransition

probability is proportional to I

n

. This is alled the formal intensity law for the

multiphoton transition. If no saturation ours, one an determine the order of

the multiphoton transitionfromthe log-logplot of the transitionprobabilityasa

funtion of laser intensity,

ln W ⁽ⁿ⁾ = n ln I + C

^(2.2)

The transition rate onstant for the n-photon proess is proportional to the

nth order of laser intensity:

k ⁽ⁿ⁾ = (σ ⁽ⁿ⁾ · I ⁽ⁿ⁾ )/( ~ ω r ) ⁿ

^{, where}

σ ⁽ⁿ⁾

^{, I, and}

ω r

are the nth order transition ross setion (strength) in units of m

2

, the laser

intensity in units of photons m

− 2

s

− 1

, and the laser frequeny, respetively. The

formal intensity law is found to hold well for nonresonant multiphoton proesses

and to hold sometimes for the resonant proesses. The intensity law holds for

multiphotontransitionsof moleulesirradiatedjustabovethedetetion threshold

by lightfrommoderatelyhigh-powerlasers. Inmultiphotonexperimentsinwhih

a strong laser beam brings about the saturation of the population between the

relevant states, one an often see a deviation from the intensity law and also in

theaseofmultiphotonproessesviaresonantstates. Inafollowingsetion,using

the rate equation approah, it willbe shown that the deviation is interpreted by

means of saturation between initialand resonantstates.

2.2.1.1 The formal intensity law

The formalintensity law, I

n

-intensity dependene ofthe observed quantities, has

been utilizedtodeterminethe ordersof multiphotonproesses suh asexitation,

ionizationand/or dissoiation of moleules. Figure2.2 shows log-log plots of the

ion yield versus laser intensity for two-photon ionization of aniline observed by

Brophy and Rettner (1979). The laser pulse with a 293.9nm wavelength and a

pulsedurationt

p ∼

¹

µs

^{exitesthe rstsingletstate}

¹ B 2

^{ofaniline. InFigure2.2b}

the I

2

-intensity dependene of the ion yield an be seen at the lowest intensities

orresponding tothe unfoused Nd

3+

-YAGpumped laser.

The estimated values ofthe ross setionsare

σ ₁ = (1.0 ± 0.2) × 10 ^{− 17}

^m

²

^and

σ ₂ = (3.5 ± 0.8) × 10 ^{− 17}

^m

²

^{for the absorption fromthe}

¹ A ₁

^tothe

¹ B ₂

^resonant

state and that from the resonant to the ionized state, respetively. Assuming a

Figure2.2: Intensitydependeneoftheionyieldproduedbyresonanttwo-photon

ionization via the

1 B 2

^{state of aniline: (a)with a foused high-power}

laser, (b) with anunfoused laser.

9

1-kW laser pulse, the absorption rate onstants k

(1)

B 2 A 1

^{and k}

(1)

f B 2

^{are found to be}

10

5

s

− 1

, and the ondition k

(1)

B 2 A 1

^t

p

^{and k}

(1) f B 2

t

p ≃

¹⁰

^{− 1}

^{<1 is satised. Under this}

ondition, the ionyield R

f

^(t

p

^{) an be safely expressed as}

R f (t p ) = σ _fB ⁽¹⁾ ₂ σ _B ⁽¹⁾ _{2 A 1} t ² _p I ² /2( ~ ω r ) ²

^(2.3)

whihrepresentstheformalintensitylawforn=2and hasbeen derivedbyusinga

simplekineti equation (see setion2.2.1.3). The linearplot of the ionyield with

a slope of 1.5 (Figure 2.2) has been measured by using a high-power, strongly

fousedlaser beam.

2.2.1.2 Saturation phenomena

The I

n

dependene generally holds for ases of low-intensity laser experiments,

long-lived intermediate states for short pulse times, and before the steady-state

onditionissatisedforresonantmultiphotonproesses. Theuseofhigh-intensity

lasersmayresultinsaturationofthepopulationbetweenthe resonantandground

states and make it easy to reah a steady-state ondition. Boesl et al. reported

the REMPI spetrum of benzene, via the resonant 6

1

vibroni state of S

1

^{. The}

intensity dependene of the ion number has been monitored for dierent laser

intensities with an unfoused parallel light beam and foused laser light, respe-

tively. Apure quadratiintensity dependene thatobeys theformalintensitylaw

is observed for laser intensities below 10

7

W m

− 2

. Above this threshold value

of ion number hanges from quadrati to roughly linear intensity dependene.

10

Theoretialonsiderationsforthe deviationsoftransitionprobability,ionurrent,

and yield fromI

n

-dependene have been reported by several authors.

11 13

2.2.1.3 The rate equation approah

One of the methods used to study the deviation from I

n

-dependene is the rate

equation approah.

13

Forsimpliity the resonanttwo-photon ionizationapproah

is onsidered asshown inFigure2.3.

k ⁽¹⁾ _nm

k ⁽¹⁾ _am k ⁽¹⁾ _ma

Figure 2.3: A simplemodelfortwo-photon ionization.

The rate equations assoiated with two-photon ionization for states a and n

through a resonant state m an beexpressed as:

dρ a (t)/dt = − k _aa ⁽¹⁾ ρ a (t) + k _am ⁽¹⁾ ρ m (t),

^(2.4)

dρ m (t)/dt = − k ⁽¹⁾ _mm ρ m (t) + k ⁽¹⁾ _ma ρ a (t),

^(2.5)

dρ n (t)/dt = k _mm ⁽¹⁾ ρ m (t),

^(2.6)

where

ρ a (t) ≡ ρ aa (t)

^{isthedensitymatrixelementfortheinitialstate,and}

k am ⁽¹⁾

⁼

k aa:mm ⁽¹⁾

^{theradiativerate onstantassoiatedwiththe transitionfromstatesm to}

a. The rate onstants satisfy k

(1) mm

^=k

(1) am

^+k

(1)

nm

^{and k}

(1) aa

^=k

(1)

ma

^{. In this treatment}

eets of the simultaneous two-photon proess, speied by k

(2) na

^{and k}

(2)

aa

^{,and the}

relaxationhavebeen omitted. TheLaplaetransformationof Eqs. (2.4)and (2.5)

yields:

[p + k _aa ⁽¹⁾ ]ρ a (p) = N 0 + k ⁽¹⁾ _am ρ m (p),

^(2.7)

[p + k _mm ⁽¹⁾ ]ρ m (p) = k ⁽¹⁾ _ma ρ a (p),

^(2.8)

where

ρ(p) = Z ^∞

0

dtρ(t)e ^{− pt} .

^(2.9)

The initial onditions have been assumed

ρ a

^(t=0)=N

0

^and

ρ _m

^(t=0)=

ρ _n

^{(t=0)=0. The solution iswritten as:14}

ρ m (p) = k ⁽¹⁾ ma N 0

(p − α 1 )(p − α 2 ) ,

^(2.10)

ρ a (p) = N 0

α ₁ − α ₂

"

(k mm ⁽¹⁾ + α 1 )

p − α ₁ − (k mm ⁽¹⁾ + α 2 ) p − α ₂

#

,

^(2.11)

where

α ₁

^and

α ₂

^{are the solution forthe equation:}

[p + k _aa ⁽¹⁾ ][p + k _mm ⁽¹⁾ ] − k _am ⁽¹⁾ k _ma ⁽¹⁾ = 0,

^(2.12)

The ionizationrate is proportional tod

ρ n

^{(t)/dt, whih is given by:}

dρ n (t)

dt = k ⁽¹⁾ nm k ma ⁽¹⁾ N 0

α 1 − α 2

(e ^{α 1 t} − e ^{α 2 t} )

^(2.13)

The ionyieldinthe ase of asquare laser pulse an be obtained by integrating

Eq. (2.13) overt and dividing the resultingexpression by N

0

^as

R n (t p ) = ρ n (t p ) N 0

,

^(2.14)

where t

p

^{isthe pulse duration.}

Intheaseofaweaklaserintensity,theeetofstimulatedemissionisnegligible

and theontributionofk

(1) am

^{totheintensitydependene maybenegleted. In this}

ase

α 1

^and

α 2

^{an be}approximatedwith

α 1

^=-k

(1)

nm

^and

α 2

^=-k

(1)

ma

^{. The ionization}

rate an bethen approximated as:

dρ n (t)

dt ≃ k _nm ⁽¹⁾ k _ma ⁽¹⁾ N ₀ te ^{− k (1) ma t} ≃ k _nm ⁽¹⁾ k ⁽¹⁾ _ma N ₀ t = σ nm ⁽¹⁾ σ ma ⁽¹⁾

( ~ ω r ) ² N ₀ I ² t.

^(2.15)

The ionyield R

n

^(t

p

^{)is expressed as:}

R n (t p ) = ρ n (t p ) N 0

= σ ⁽¹⁾ nm σ ma ⁽¹⁾

2( ~ ω r ) ² I ² t ² _p ,

^(2.16)

Inthease ofk

(1) ma ≃

^k

^{(1) nm}

^{,the quadratiintensity dependenean bealsoderived}

as:

dρ n (t)

dt ≃ 1/2(k ⁽¹⁾ _nm k _ma ⁽¹⁾ )N 0 t).

^(2.17)

In other words in ase of weak laser eld, in whih laser pulse duration satises

k

(1) ma

^t

p

^{<1, the formalintensity lawholds for the ionurrent and yield.}

In the ase of a strong laser intensity the stimulated emission an no longer

benegleted and the spontaneousemission an be safelyomitted,k

(1) am

^=k

(1) ma

^{. The}

α ₁

^and

α ₂

^{solutions would inlude now the stimulated emission term and the}

ionizationrate is redened as:

14

dρ n (t)

dt = k nm ⁽¹⁾ k ma ⁽¹⁾ N 0

α ₁ − α ₂ e ^{α 1 t} [1 − e ^{− (α 1 − α 2 )t} ].

^(2.18)

Here

α 1

^and

α 2

^{are linear funtions of the laser intensity. For the time sale}

t<(

α 1

^-

α 2

⁾

− 1

=[4(k

(1) ma

⁾

2

+(k

(1) nm

⁾

2

℄

− 1/2

,

dρ n (t)

dt ≃ k _nm ⁽¹⁾ k _ma ⁽¹⁾ N 0 t,

^(2.19)

and fortime sale t>(

α ₁

^-

α ₂

⁾

^{− 1}

^,

dρ n (t)

dt ≃ k ⁽¹⁾ nm k ⁽¹⁾ ma N 0

[4(k ma ⁽¹⁾ ) ² + (k nm ⁽¹⁾ ) ² ] ^{− 1/2} ,

^(2.20)

The two equations above indiate quadratiand linear intensity dependenies,

respetively. Thedeviationofthe intensityfromtheI

2

dependene takesplaeat

t>(

α 1

^-

α 2

⁾

− 1

, and

dρ n (t)

dt ≃ k ⁽¹⁾ nm N 0

2 ,

^(2.21)

for k

(1) ma

^=k

(1) am

^>k

(1)

nm

dρ n (t)

dt ≃ k _ma ⁽¹⁾ N 0 ,

^(2.22)

for k

(1) am

^<k

(1) nm

^.

The absorption rate onstants are proportional to the ross setion as well as

to the laser intensity. Therefore, an appreiable dierene between

σ ma ⁽¹⁾

^and

σ nm ⁽¹⁾

may hange the I

n

intensity dependene of multiphoton proesses, even in the

presene of weak laser eld.

The above rate equationtreatmentof the saturation phenomena treatedabove

isuseful indetermining if theresonant proess isatwoora multiphoton proess.

The quadrati or linear intensity dependene harater of a multiphoton proess

an be determined by measuring the ion yield and plotting it against the laser's

intensity.

Inordertodeterminethesaturationintensityofamoleulartransitionofagiven

osillator strength another approah has to be onsidered. The rate equation is

applied for anopen two level system, assuming arotationaltransition from level

|1

i

^tolevel|2

i

^{. Demtröder treatsthe saturationproblemofamoleulartransition}

taking into aount also the relaxation proesses suh as spontaneous emission

and other phenomena that depopulateorrepopulate apartiular level.

15

The saturation parameter isdened as:

S = B ₁₂ · I _ν

R ^∗ · c ,

^(2.23)

whereB

12

^{istheEinsteinBoeient,I}

ν

^{isthelaserintensityandR}

∗

isthemean

of relaxation proesses. The intensity I=I

s

^{at whih the saturation parameter}

beomes S=1 is alledthe saturation intensity and isdened as:

I s ≈ R ^∗ · c

B ₁₂ · ∆ν L ,

^(2.24)

Case study

Saturation of a moleular transition in a moleular beam by a broadband w

laser width

∆ν _L

^=4.5

×

¹⁰

⁹

^s

^{− 1}

^(=0.15m

^{− 1}

^{). The moleulartransitiononsidered}

hereistherotationalexitationfromJ

′

=14toJ

′′

=13inthe

A ¹ Π ← X ¹ Σ ⁺

^ele-

troni transitionof linear AlCCH. The linewidth of this partiular transition has

beenestimatedtobe0.3841m

− 1

. Themeanrelaxationrateannotbealulated

preiselybeausetheratesofallrelaxationproessesarenotknown. Nevertheless,

based on the linewidth of the transition mentioned above a relaxation rate R is

estimated to be 7.25

·

¹⁰

¹⁰

^s

^{− 1}

^.

The Einstein A oeient (spontaneous emission oeient) is related to the

dipolemoment

µ 12

^by:

16

A ₂₁ = | µ ₁₂ | ² · ν ₁₂ ³ [8π ² /(3 ~ ε ₀ )],

^(2.25)

TheEinsteinBoeientisthenrelatedtothespontaneousemissionoeient

by:

B 12 = (c ³ /8πhν ³ )A 21 ,

^(2.26)

The osillator strength of the

A ¹ Π ← X ¹ Σ ⁺

^{eletroni transition of linear}

AlCCHhas beenalulatedtobe1.6

×

¹⁰

^{− 3}

^{. The dipolemomentan beestimated}

based onthe followingrelation:

16

f 12 = | µ 12 | ² · ν 12 [4πm e c/(3 ~ e ² )],

^(2.27)

where m

e

^{and e are the mass and harge of the eletron,}

ν 12

^{is ex-}

pressed in m

− 1

and

µ 12

^{in Debye. Based on the above equation the}

dipole moment for the eletroni transition is alulated to be 0.343Debye (1

Debye=3.336

·

¹⁰

^{− 30}

^Coulomb

·

^{m). The dipole moment an be used now to alu-}

late the A

21

^{oeient for the transition loated at 347.7nm. The} permittivity

ofvauumis8.854

·

¹⁰

^{− 12}

^J

^{− 1} ·

^Coulomb

² ·

^m

^{− 1}

^and

~

=1.054

·

¹⁰

^{− 34}

^J

·

^{s. Usingallthe}

known parameters mentioned abovethe A

21

^{is alulated tobe 8.83}

·

¹⁰

⁵

^s

^{− 1}

^.

The saturation intensity an be now estimated onsidering all the parameters

from equation 2.24. The value obtained for w laser is 4.38

×

¹⁰

¹⁰

^W/m

²

^{. For a}

pulsed dye laser with a pulse width of 10ns and the beam diameter of

≈

^3mm

²

^,

the saturation intensity is

≈

^1.461mJ.

2.2.2 Resonant eet

Whenthelaseristunedanditsfrequenyapproahesarealintermediateeletroni

state (Figure 2.1b), we an see a drasti inrease in the two-photon absorption

signal (resonane enhanement). This proess is alled a resonant two-photon

transition. If a rigorous resonane ondition were satised, that is,

∆

^E

_ma

⁼

~ ω _r

in Equation (2.1), then the magnitude of the transition probability would go to

innity. However, the energy levelsof intermediate states are not innitely sharp

but have widths

Γ ma

^{, and the divergene of the transition an be avoided. The}

width originates from intra- and inter-moleular perturbations and from higher

order radiation-moleule interation. In order to take the resonant eet into

aount phenomenologially, the real energy denominator in Equation (2.1) is

replaedbyaomplexenergydenominatorwiththeterm

iΓ ma

^{. Ifthehigherorder}

radiation-moleuleinterationisnegleted,

Γ _ma

^{isalledthe dephasing onstant-}

itdesribestherate of phaselossbetween the m and a statesassoiatedwith the

transition, and it may be expressed as:

Γ ma = 1

2 (Γ mm + Γ aa ) + Γ ^(d) _ma

^(2.28)

where

Γ _mm

^and

Γ _aa

^{are the populationdeay onstantsof state m and a, respe-}

tively, and

Γ ^(d) ma

^{is the pure dephasing onstant that originates from a moleule-}

perturberelasti sattering proess.

It is interesting to note that the vibroni struture appearing in the resonant

multiphoton transition is generally dierent from that in the non-resonant tran-

sition: in the former ase the vibroni struture reets the potentialdierenes

between the initial, resonant, and nal states or between these states, and in the

latter ase the vibroni struture ismainlydetermined by the Frank-Condonvi-

brational overlap integral between the initial and nal states, sine the energy

mismathtothe intermediate states isso large that the vibroni struture of the

intermediate state

| m i

^{may benegleted in Equation (2.1).}

2.3 REMPI mehanism

Multiphoton absorption proesses an belassiedintotwo ategories: "simulta-

neous" and "stepwise" proesses. In nature the simultaneous absorption of more

than one photon is a rare event. But when atoms and moleules are irradiated

with extreme intensity of foused laser beam suh as those generated by eximer

and Nd

3+

:YAG pulsed dye lasers, simultaneous photon absorption rates beome

greatlyenhaned. Asuientlyintenselaseranauseanymoleuletosimultane-

ously absorb enough photons to ionize. Under typiallaser onditions ionization

rates derease rapidly with photonorder, the simultaneous three photon absorp-

tion rate is muh slower than the simultaneous two photon absorption rate and

so forth.

The ionization rate of hemial speies is greatly enhaned when the path to

ionizationis divided intotwo ormore suessive absorption steps (resonanes) of

lowerphotonorder. Theseabsorptionstepsareprovidedbystableeletronistates

that an aumulate a population. In Figure 2.4 the sum of two laser photons

is resonant with an exited moleular state. This moleular state aumulates

a population by simultaneous two photon absorption. Absorption of one more

photonpromotesthe exitedstate moleuleaboveitsionizationpotentialandthe

moleuleionizes. The REMPI signalisdeteted by measuring the photoeletrons

orlaser generated ations.

E N E R G Y

NONRADIATIVE DECAY

ION + e ⁻

EXCITED STATE

FLUORESCENCE

GROUND STATE

2hν

Figure2.4: Shemati of a [2+1℄ REMPI proess. The ompeting proesses, in-

tramoleular relaxation and uoresene, whih deplete the exited

state populationand reduethe ionyieldare also shown.

The ompleteexitationproess depitedinFigure2.4isalleda[2+1℄REMPI

mehanism;two photonabsorption populatesastable "resonant"eletronistate

and an additional one photon absorption step ionizes the moleule. In fat,

within any n-photon ionization experiment whih involves one stable resonant

moleular state and one laser frequeny the REMPI signal may arise from at

least n-1 possible exitation shemes.

[1+1℄ sheme

The one-olor two-photon [1+1℄ sheme is one type of REMPI tehnique. In

the [1+1℄ sheme, the laser issanned over the rovibroni levels of the eletroni

exitedstate of the moleulesof interest. Anionizingphotonfromthe samelaser

promotes the neutral speies from the exited state to the ground state of the

orrespondingions. Inthe [1+1℄sheme,the energyofone photonmustbe

≥

^1/2

of the ionizationpotential(IP). Beause the IP of most hydroarbonlusters are

morethan8eV,the [1+1℄shemeisnotsuitabletomeasuretheirvisibleeletroni

spetra. The one-olor one-photon sheme proved to be useful for reording

thespetrumofthediatomispeiesliketitaniumoxide(TiOwithanIPof6.8eV).

[1+1'℄ sheme

Inthe [1+1'℄ sheme,the rstolor laser issanned over the rovibronilevelof

the eletroni exited state and the seond olor ionizes the speies of interest.

This sheme requires the sum of the twodierent photons toequal the IP of the

moleule. Thus, the[1+1'℄sheme issuitablefor measuringthe eletronispetra

of moleulesinaverybroadrange fromUV tovisibleusingdierentombination

ofh

ν 1

^andh

ν 2

^{. Thisshemehas beenemployed toreordthe spetraofmoleules}

mentioned in this thesis. The [1+1'℄ onguration is the most appropriate to

reord the spetra of the hydroarbons of astrophysial interest that absorb in

the visible region of the eletromagneti spetrum. The ombination of a dye

laser with an F

2

^{laser (7.9eV) has proven to be suessful for measuring the}

gas-phaseeletronispetraofmosthydroarbonlustersinthevisibleregion.

17,18

[2+1℄ and [2+1'℄ sheme

When one single photon an not bring the moleule in the exited state then

the sum of the two photons will equal the energy required to make the allowed

transition. Theprobabilityofabsorption isgreatlyinreasedif furtherabsorption

of a third photonis suient toionize the moleule.

Combinationof photons ofdierentenergies may alsobeused ([2+1'℄sheme).

Forexample,one laser maybetunedtoatwo-photon absorptioninthe moleule,

and then a seond laser used to perform the ionization step. Beause the

absorption probability greatly inrease, higher order proesses, suh as three

photon absorption, are relatively rare. The very low number density of lusters

andlowsignaltonoiseratiolimitthe pratialprobabilityofusing[2+1℄or[2+1'℄

shemes or other higher order multiphoton shemes. In general,ombinations of