Photodissociation of OH+ and H2O+

Jolijn Onvlee

Supervised by:Prof. dr. D.H. Parker and Dr. A.T.J.B. Eppink

(Molecular and Laser Physics)Dr. ir. G.C. Groenenboom(Theoretical Chemistry)

Master’s thesis

September 2010 - August 2011

Radboud University Nijmegen, Molecular and Laser Physics (IMM)

Abstract

The molecular ions OH+ and H2O+ both play an important role in interstellar chemistry.

The goal of the current research is to study the photodissociation of these two cations,because this is an important process in the interstellar medium. This is done both theo-retically and experimentally for OH+ and it is done in an experimental way for H2O

+.For OH+, potential energy curves are computed for the ground state and 17 elec-

tronically excited states at the multi-configurational self-consistent field (MCSCF) andmultireference configuration interaction (MRCI) level with the MOLPRO program. Thegoal of this theoretical work is to understand the photodissociation of OH+ and to predictwhat the products of the dissociation will be. Because the ionization energies of oxygenen hydrogen are almost the same (the difference is only 0.0196 eV), the dissociation limitsof the ground state and the first excited state with the same symmetry were exchanged.This problem is also seen in literature, but it was never solved. In the current research,the problem is solved and all molecular states dissociate to the right limit. Photodissoci-ation cross sections are calculated for the transitions from the electronic ground state tothe dissociative portion of the A3Π state and to the repulsive 23Σ−, 33Σ−, 23Π, and 33Πstates. They are in good agreement with the literature. For the bound states, spectro-scopic constants are calculated. Most constants are in good agreement with experimentalvalues.

For the experiments, the (2+1) resonance-enhanced multiphoton ionization (REMPI)technique is used to produce the cations. Subsequently, these ions will be dissociatedby using vacuum ultraviolet (VUV) light and the products will be detected by usingthe velocity map imaging (VMI) technique. The measured REMPI spectra for H2O,HOD and OH are in good agreement with PGOPHER simulations of these spectra. Also,OH+ images resulting from three different H2O REMPI transitions are taken. The OH+

fragments most likely arise from dissociative ionization following absorption of four photonsby neutral H2O molecules and the signal is wavelength dependent.

During the current research, the photodissociation processes of the ions could not yetbe studied experimentally. This will be done in the future. A VUV wavelength that isalready available in the lab is 157 nm. However, from the ab initio calculations for OH+,it follows that 157 nm is not a good wavelength for photodissociation. Two other VUVwavelengths that can easily be produced in the lab, are 118 and 193 nm. From the ab initiocalculations, it follows that these wavelengths are also not suitable for photodissociationof OH+. From potential energy surfaces of H2O

+ from literature, it follows that 157 and193 nm light might be suitable for photodissociation via the 2A1 state of this molecularion. It is unknown whether 118 nm will be a good wavelength.

2

Acknowledgements

Bij deze wil ik graag een aantal mensen bedanken. Ten eerste mijn begeleiders Prof. dr.Dave Parker, Dr. ir. Gerrit Groenenboom en Dr. Andre Eppink. Dave, bedankt dat ikmijn stage bij Molecuul- en Laserfysica mocht doen. Ik vond het erg leuk om hier stage telopen en ik heb er ontzettend veel van geleerd, ook al is het niet gelukt om een experimentmet twee lasers aan de gang te krijgen tijdens mijn stage. Gerrit, bedankt voor alle uitlegen discussies over de berekeningen. Het was een hele uitdaging om alles zo goed mogelijkte berekenen in korte tijd, vooral doordat OH+ ineens veel complexer bleek te zijn danverwacht. Ik ben jullie erg dankbaar dat ik op deze manier experimenteel en theoretischwerk met elkaar kon combineren. Andre, bedankt voor de hulp in het lab en voor hetadvies als ik problemen had met de experimenten.

Zonder de technici van deze afdeling had ik geen enkel experiment uit kunnen voeren.Met de hulp van Cor Sikkens hebben we de Dragana opstelling aan kunnen passen, zo-dat ik daar experimenten in kon doen. Cor heeft een mooi ontwerp gemaakt om dezeaanpassingen te kunnen realizeren. Dankzij Cor en de technici van de werkplaats van defaculteit kon het ontwerp gemaakt worden. Het duurde wat langer dan gepland, omdatiedereen erg druk bezig was met de FEL, maar uiteindelijk was het resultaat erg mooi.Intussen hielp Leander Gerritsen om een Jordan klep aan te passen voor mijn opstelling.Later heeft hij nog veel meer geholpen met de technische kant van al mijn experimenten,bijvoorbeeld met de gastoevoer, het plaatsen van lasers bij de opstelling en het plaatsenvan een ring voor ontlading en een filament in de opstelling. Natuurlijk kon ik bij PeterClaus terecht als ik problemen had met de electronica.

Ook wil ik graag alle (PhD) studenten van onze afdeling bedanken: Gautam Sarma, Za-hid Farooq, Ashim Kumar Saha, Chandan Bishwakarma, Bin Yan and Bas van Oorschot.You all helped me a lot, especially in the lab, and I hope that I could also help you, forexample with PGOPHER and some other theoretical problems. It was a pleasure to workwith you.

Tijdens mijn stage is Bas van de Meerakker van het Fritz-Haber-Institut der Max-Planck-Gesellschaft in Berlijn naar het Institute for Molecules and Materials in Nijmegenverhuisd. Bedankt voor het goede advies toen ik bijvoorbeeld op zoek was naar OH enOH+ signaal. Het is leuk om te zien hoe het nieuwe lab steeds meer vorm krijgt en hoe allenieuwe activiteiten opgestart worden. Ook wil ik Frans Spiering bedanken voor de hulp metde wavemeter en voor alle discussies en adviezen, Afric Meijer voor de hulp bij LaTeX enMATLAB, Wim van der Zande voor een paar handige discussies en Robert Klein-Douwel,die mijn begeleider was tijdens mijn bachelorstage en me tijdens mijn masterstage heeftgeholpen toen ik met de laser ging werken die hij eerder heeft gebruikt.

4

Contents

1 Introduction 8

2 Theory 92.1 The molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 OH+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.2 H2O

+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Photodissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Resonance-enhanced multiphoton ionization . . . . . . . . . . . . . . . . . . 152.4 Velocity map imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Ab initio calculations for OH+ 183.1 Correlation diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.1 Correlation diagram including spin-orbit coupling . . . . . . . . . . . 203.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2.1 Hartree-Fock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.2 Multi-configurational self-consistent field . . . . . . . . . . . . . . . . 243.2.3 Configuration interaction . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3.1 The basis set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3.2 The settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.3 Wrong ordering of two dissociation limits . . . . . . . . . . . . . . . 283.3.4 Charge-induced dipole interaction . . . . . . . . . . . . . . . . . . . 293.3.5 Photodissociaton cross sections . . . . . . . . . . . . . . . . . . . . . 30

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.5 Predictions for the experiment . . . . . . . . . . . . . . . . . . . . . . . . . 34

4 Experimental methods 364.1 Molecular beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.2 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.3 Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Results 415.1 H2O REMPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.2 HOD REMPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.3 OH REMPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.4 Energy calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.5 H2O REMPI and OH+ images . . . . . . . . . . . . . . . . . . . . . . . . . 45

6

CONTENTS 7

6 Conclusion 46

References 48

Appendix A The ab initio calculations 52A.1 The basis set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52A.2 A MOLPRO input file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Appendix B Results of the ab initio calculations 55

Appendix C Simulations 58C.1 CO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58C.2 Ammonia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Chapter 1

Introduction

In this work, the hydroxyl cation OH+ and the water cation H2O+ are studied. Both are

important molecular ions for interstellar chemistry.The hydroxyl cation OH+ is present in various comets and planetary atmospheres. It is

found to be one of the primary ion species leading to the production of H3O+ in interstellar

clouds and H3O+ is supposed to be the principal source of water in these clouds [1–3]. The

OH+ ion has been the subject of many studies in chemistry, physics, and astronomy [1, 4–7]. This molecular ion and its fragmentation are important in a very wide range of fields,including molecular spectroscopy, dissociation dynamics, ion-atom scattering, electron-ionrecombination, van der Waals complex formation, plasma processes, and astrophysics [8].

The water cation plays an important role in a number of environments, includingthe upper atmosphere [9–11], comet tails [12–17] and interstellar clouds [3]. Recently,this molecule has been observed in star-forming regions [18] and spiral arm clouds [19]with the Heterodyne Instrument for the Far-Infrared (HIFI) on board the Herschel SpaceObservatory. Because of the importance of this molecule, H2O

+ has been the subject ofmany experimental and theoretical studies [20–24]. Still, there are many properties of thision that can be studied to better understand the interstellar chemistry that takes place.

The current research is on the photodissociation of OH+ and H2O+, because this

is an important process for these molecules in the interstellar medium. The goal is touse vacuum ultraviolet (VUV) light for the dissociation process. The (2 + 1) resonanceenhanced multiphoton ionization (REMPI) and velocity map imaging (VMI) techniquesare used to produce the cations and to detect products respectively. For OH+, ab initiocalculations are performed to understand the photodissociation process of this ion and topredict what the products of this dissociation are.

The photodissociation processes of both molecules have been studied before. For OH+,photodissociation via the c1Π electronic state was studied several times [8, 25, 26]. ForH2O

+, photodissociation near the B2B2 state has been the subject of a number of projects[20, 27–30]. Recently, Sage et al. [31] studied the photodissociation via the B2B2 state ofH2O

+. They also detected the products with VMI, but they did not use VUV light for thephotodissociation. The dissociation of this molecule was also studied theoretically [23].

8

Chapter 2

Theory

In this chapter, some theory is given about the molecular ions OH+ and H2O+, about

photodissociation, and about the resonance-enhanced multiphoton ionization and velocitymap imaging techniques.

2.1 The molecules

Although H2O+ only has one hydrogen atom more than OH+, these molecules have very

different properties. The striking difference between the two ions is that OH+ is a diatomicand H2O

+ a polyatomic molecule. For a diatomic molecule, the bond length between thetwo atoms is essential, but in a polyatomic molecule there are more bonds and the bondangles are also important. Therefore, diatomic molecules have 1-D potential energy curves,but polyatomic molecules have potential energy surfaces in more dimensions. Moreover,OH+ has a linear structure and H2O

+ is non-linear, so these molecules belong to a differentpoint group and have different symmetries. Because of the structure and the symmetry,diatomic molecules have only one vibrational mode and two degrees of rotational freedom.Polyatomic, non-linear molecules with n atoms have three degrees of rotational freedomand 3n− 6 normal modes of vibration, so the water cation has three vibrational modes.

An electronic transition in an atom gives a sharp line. In a diatomic molecule, thisline has an additional structure resulting from vibrational and rotational transitions. Thisstructure can often be resolved into individual peaks, because the energy spacing be-tween the various rotational-vibrational-electronic states is sufficiently large. However, ina polyatomic molecule, the many rotational and vibrational transitions that are possiblegenerally overlap, often giving rise to a broad, nearly featureless band. This overlap makesit difficult to extract information on the initial and final states involved in an electronictransition in polyatomic molecules.

Much information is already known for the two molecular ions. The information thatis most important for this research is given in the next two sections.

2.1.1 OH+

The hydroxyl cation OH+ is an isoelectronic analogue of the well-studied imidogen radicalNH. It is a linear, diatomic molecule and it belongs to the point group C∞v, just like theOH molecule. For OH, the X2Π ground state electronic configuration is:

1σ22σ23σ21π3. (2.1)

9

2.1. THE MOLECULES 10

The configuration of the X3Σ− ground state of OH+ is obtained by removing one electronfrom the 1π molecular orbital, so this configuration is:

1σ22σ23σ21πx1πy. (2.2)

In figure 2.1, the Molecular Orbital (MO) diagram of the ground state is given and acharacter table of the C∞v point group is given in table 2.1. A character table givesinformation about the different symmetries of a point group. For more information aboutcharacter tables, see ref. [32]. In table 2.2, the configurations are given from which thedifferent electronic states arise [33].

2p

2s

1s

1s

1σ

2σ

3σ

1πx 1πy

4σ∗

O+ OH+ H

Figure 2.1: The MO diagram of the electronic ground state of OH+.

Table 2.1: The character table of the C∞v point group

C∞v E 2CΦ∞ ... ∞σv

A1(Σ+) 1 1 ... 1 z x2 + y2, z2

A2(Σ−) 1 1 ... −1 Rz

E1(Π) 2 2cos Φ ... 0 (x,y),(Rx,Ry) (xz,yz)E2(∆) 2 2cos 2Φ ... 0 (x2 - y2, xy)E3(Φ) 2 2cos 3Φ ... 0... ... ... ... ...

Table 2.2: The configurations that give rise to the different electronic states

Configuration Electronic states

1σ22σ23σ21π2 X3Σ−, a1∆, b1Σ+

1σ22σ23σ24σ1π 23Π, 21Π

1σ22σ21π33σ A3Π, 11Π1σ22σ21π23σ4σ 3∆, 3Σ+, 31Σ+, 21∆, 5Σ−, 23Σ−, 33Σ−, 1Σ−

1σ22σ21π4 21Σ+

1σ22σ21π34σ 33Π, 31Π

2.1. THE MOLECULES 11

In figure 2.2, potential energy curves for the lowest electronic states of OH+ are shown.In the current research, laser light with a wavelength of 157 nm will be used for the disso-ciation of OH+. The energy of this light is 63694.3 cm−1, so the three dissociation limitsfrom this figure can be reached with this energy. More predictions for the experiments withOH+ are described in section 3.5. These predictions are based on the ab initio calculationsthat are performed for the current research.

Figure 2.2: Potential energy curves for the lowest electronic states of OH+ [25].

2.1.2 H2O+

The water cation H2O+ is an isoelectronic analogue of the radical NH2. It is a non-linear

molecule and can belong to two different point groups. The electronic ground state belongsto the C2v point group, just like the ground state of H2O: it has one C2 rotation axis,a mirror plane, and the C2 axis is in the mirror plane. Some excited states only have amirror plane and therefore belong to the Cs point group. This depends on which electronfrom the ground state is promoted to another orbital, because the molecular orbitals preferdifferent equilibrium geometries.

The X1A1 ground state electronic configuration of H2O is:

(1a1)2(2a1)

2(1b2)2(3a1)

2(1b1)2. (2.3)

Here a1, b1, and b2 are notations for the symmetry of an orbital. What the correspondingsymmetry is, can be seen from a character table, which is given in table 2.3 for the C2v

point group. The 1a1 orbital is the orbital with a1 symmetry which has the lowest energy.The configuration of the ground state of H2O

+ is obtained by removing one electron fromthe 1b1 molecular orbital, so this configuration is:

(1a1)2(2a1)

2(1b2)2(3a1)

2(1b1)1 (2.4)

2.1. THE MOLECULES 12

and this state has symmetry 2B1. The MO diagram of the ground state is given in figure2.3.

Table 2.3: Character table for the C2v point group

E C2 (z) σv (xz) σv (yz)A1 1 1 1 1 z x2, y2, z2

A2 1 1 −1 −1 Rz xyB1 1 −1 1 −1 x, Ry xzB2 1 −1 −1 1 y, Rx yz

2s

1s

2a1

1b2

1b1

3a1

4a1

O+ H2O+ H2

2b2

2p

1a11s

b2

a1

Figure 2.3: The MO diagram of the X2B1 electronic ground state of H2O+.

The first two excited states of H2O+ are the A2A1 state:

(1a1)2(2a1)

2(1b2)2(3a1)

1(1b1)2 (2.5)

and the B2B2 state:(1a1)

2(2a1)2(1b2)

1(3a1)2(1b1)

2. (2.6)

From table 4 in ref. [23] it follows that the equilibrium H-O-H bond angle for the groundstate of H2O

+ is around 115, for the A2A1 state, this angle is almost 180 (a linearstructure), and for the B2B2 state, the angle is around 70. From this it can be seen thatthe angle strongly depends on the molecular orbitals that are occupied.

In figure 2.4, a cut through the potential energy surfaces (PESs) for five electronicstates of H2O

+ is shown. One O-H bond length is varied, while the other O-H bondand the inter-bond angle are maintained at their ground state equilibrium values. In thecurrent research, laser light with a wavelength of 157 nm will be used for the dissociationof H2O

+. The energy of this light is 7.9 eV, so both dissociation limits from this figurecan be reached with this energy. One condition for dissociation of H2O

+ is that an excitedstate has to be reached with the laser light. There are a few possibilities:

2.2. PHOTODISSOCIATION 13

• X2B1 - 2B2 (forbidden by electric dipole selection rules)

• X2B1 - 4B1 (spin forbidden and small Franck-Condon factor around 157 nm)

• X2B1 - 2B1 (small Franck-Condon factor around 157 nm)

• X2B1 - 2A1

The first two transitions are forbidden by selection rules. The probability of the thirdtransition is small, because the Franck-Condon factor for this transition around 157 nmis small. The last transition is allowed, so it might be possible to reach the repulsive partof the 2A1 state.

Two other VUV wavelengths that might be used for the photodissociation process are193 nm (6.4 eV) and 118 nm (10.5 eV). With 193 nm, it might be possible to reach therepulsive part of the 2A1 state. From literature, it is unknown whether 118 nm light issuitable for photodissociation.

Figure 2.4: Cut through some PESs of H2O+ [31].

2.2 Photodissociation

Photodissociation is an interaction between light and molecules, where the light breaks upthe molecules. When a molecule AB in the ground state absorbs n photons with energyhν, it can populate an excited state AB*. This state can break apart into the fragmentsA and B:

AB + nhν → AB* → A+ B

The photodissociation of small molecules can proceed in various ways:

1. Direct photodissociation by absorption into a repulsive state or to a repulsive wallof a bound excited electronic state.

2.2. PHOTODISSOCIATION 14

2. Indirect photodissociation by excitation to a bound state followed by:

• coupling with the vibrational continuum of a third state of different symmetry(predissociation).

• coupling with the continuum of a third, dissociative state of the same symmetrywhich, in the Born-Oppenheimer approximation, does not cross the bound state(coupled states photodissociation).

• spontaneous emission into the vibrational continuum of either the ground elec-tronic state, or a lower-lying repulsive state (spontaneous radiative dissocia-tion). For most molecules, this mechanism plays only a minor role.

These processes are illustrated in figure 2.5 for a diatomic molecule.

(a) direct photodissociation

Ene

rgy

X+Y

Internuclear distance

X*+Y

(b) predissociation

(c) coupled states photodissociation (d) spontaneous radiative dissociation

Figure 2.5: Potential energy curves for different photodissociation processes [34].

2.3. RESONANCE-ENHANCED MULTIPHOTON IONIZATION 15

In this thesis, photodissociation of OH+ and H2O+ via the above-mentioned mecha-

nisms is investigated. For OH+, there are two possible photodissociation reactions:

OH+ + hν → O+ +H (2.7a)

OH+ + hν → O+H+ (2.7b)

Process 2.7a and 2.7b can be seen in figure 2.2. In ref. [8, 25, 26] the predissociationdynamics of the c1Π state of OH+ are described. This electronic state predissociates toboth O + H+ and O+ + H. The predissociation of the b1Σ+ state is described in ref. [35].

For H2O+, the following photodissociation reactions can take place:

H2O+ + hν → OH+ +H (2.8a)

H2O+ + hν → OH+H+ (2.8b)

H2O+ + hν → O+ +H2 (2.8c)

H2O+ + hν → O+H+

2 (2.8d)

Process 2.8a and 2.8b can be seen in figure 2.4. It has already been confirmed that abovethe dissociation limit to OH+, the B2B2 state predissociates to both OH+ + H and OH+ H+ [27, 28, 30]. From figure 2.4, it follows that the 2A1 state could predissociate to H+ OH+ via the 4B1 state.

2.3 Resonance-enhanced multiphoton ionization

Resonance-enhanced multiphoton ionization (REMPI) is a technique that is used for spec-troscopy of atoms and small molecules. One or more photons are absorbed for a resonanttransition to an electronically excited intermediate state and subsequently, one or moreadditional photons with the same or another wavelength are absorbed for the ionizationof the atom or molecule. The energy of the photons is specific for the resonant transi-tion between the initial and intermediate state, so in this way state-selective ionization isachieved.

During the current research, (2+1) REMPI is used to produce OH+ and H2O+: two

photons are used for the resonant transition to an intermediate state and one photon (inthis case with the same wavelength) is used to ionize the molecule. A scheme for thisprocess is given in figure 2.6. For OH, λ1 and λ2 are both around 244 nm and for H2O,λ1 and λ2 are both around 248 nm. In figure 2.7, some PECs for OH (figure 2.7a) and acut through some PESs for H2O (figure 2.7b) are given. The intermediate state for theresonant transition in OH is the D2Σ− state and in H2O, this is the C1B1 state.

The REMPI technique is often used, because it has some important advantages [38].Because the selection rules for a n-photon transition are different than for a one-photontransition, a wider range of electronic states can be observed: some transitions that areelectric-dipole forbidden are allowed in multiphoton excitation. High-energy states areaccessible using inexpensive visible/UV photons. This is not possible with a one-photontransition. Since ions are formed, REMPI has the extra selectivity dimension of themass/charge ratio. Therefore, it is easier to detect the products. In section 4.3, it isdescribed how this mass/charge ratio is used for selection in the current experiments.

2.4. VELOCITY MAP IMAGING 16

λ2

λ1

λ1

Intermediate state

Ionization potential

Figure 2.6: A (2 + 1) REMPI scheme. Two photons with wavelength λ1 are used for a reso-nant transition to an intermediate state and one photon with wavelength λ2 is used to ionize themolecule.

(a) OH [36] (b) H2O [37]

Figure 2.7: Some PECs of OH and a cut through some PESs of H2O.

2.4 Velocity map imaging

The velocity map imaging (VMI) technique [39] is an improvement of the former ionimaging technique [40, 41]. This method is ideal for studying photodissociation processes[42]. In the current research, a cylindrical symmetric molecular beam is crossed by twolasers for the ionization and dissociation processes. These processes take place in the

2.4. VELOCITY MAP IMAGING 17

center of an electrostatic lens, which consists of a repeller, an extractor, and a groundplate, which are held at specific voltages. The ions resulting from the photodissociationprocess form expanding Newton spheres which move along the time of flight axis to a 2Dposition sensitive detector (PSD). Ions with the same velocity are mapped to the samepoint on the detector, independent of their point of creation. This results in an imageon the detector showing a circle with radius r, which is a 2-D projection of the initialNewton sphere. The original 3-D distribution can be reconstructed from the image withan inverse Abel transformation. The experimental details for VMI in the current researchare described in chapter 4.

The velocity along the symmetry axis and perpendicular to the detector face is givenby v⊥=L/∆t, where L is the length between the interaction region and the detector, and∆t is the time for the ions to travel this distance, also called the time of flight (TOF).This time of flight behaves as ∆t ∝

√m/(qVR), with m and q the mass and charge of

the particle and VR the repeller voltage [43]. The velocity of the fragments parallel to thedetector face is given by v∥=N ·r/∆t, where N is a magnification factor dependent on theelectrostatic lens used [44]. This means that the radius of the image is a direct measure ofthe speed of the fragments. Because the speed is a measure of the dissociation energy ofthe fragments, with this the photodissociation process can be described. The intensity ona certain radius as function of the angle θ results in the angular distribution of the ions.A full description of the VMI technique is given in ref. [43].

When a ring of photofragments is detected, the internal energy of these fragments canbe calculated from the image. Consider the photodissociation of H2O

+ with one photonof 157 nm, to for example produce OH+ and H:

H2O+ + hν → (H2O

+)* → OH+ +H+ T, (2.9)

where hν is the photon energy and T is the total kinetic energy release (TKER). Fromenergy conservation follows:

T = TOH+ + TH = hν + Eint(H2O+)−D0(H-OH+)− Eint(OH+), (2.10)

where D0 is the bond dissociation energy and Eint the fragment internal energy. Theinternal energy of the H atom is equal to zero.

From conservation of momentum it follows that:

vOH+

vH=

mH

mOH+

=TOH+

TH, (2.11)

with v the velocity and m the mass of the fragment. Therefore the TKER is dividedamong the fragments in a fixed ratio:

TOH+ =mH

mH2O+

T (2.12)

TH =mOH+

mH2O+

T. (2.13)

From these equations, it follows that the TKER can be determined when the kinetic energyof only one fragment is studied experimentally. With this TKER, equation 2.10 can beused to determine the internal energy of the OH+ fragment. When REMPI is used toproduce H2O

+, the internal energy of H2O+ is known and while hν and D0(H-OH+) can

be calculated, equation 2.10 can be solved.

Chapter 3

Ab initio calculations for OH+

To understand the process of the photodissociation of OH+ and to predict what the prod-ucts of this dissociation are, ab initio calculations are performed. First, some propertiesof the different electronic states are determined. Subsequently, potential energy curves(PECs) of these state are computed using the ab initio program MOLPRO, version 2010.1[45].

Because OH+ and its fragmentation are important in a wide range of fields, ab ini-tio calculations were reported in several previous publications. For this, many differentmethods have been used.

In 1971, potential curves were calculated for some excited states using the self-consistentfield-molecular orbital (SCF-MO) method [46]. In 1977 the total energy and some spec-troscopic constants of the ground state of some diatomic hydride ions, including OH+,were published [47]. Several methods were used for the calculations: self-consistent field(SCF), pseudonatural orbital configuration interaction (PNO-CI) and coupled electronpair approach (CEPA).

A few years later, in 1983, a calculated potential energy function of the electronicground state and spectroscopic constants for this state were published [48]. The poten-tial energy function was calculated using two different methods: multi-configurationalself-consistent field with self-consistent electron-pair (MCSCF-SCEP) and self-consistentelectron-pair with coupled electron pair approach (SCEP-CEPA) The spectroscopic con-stants were calculated with the restricted Hartree Fock (RHF) method, multi-configuratio-nal self-consistent field (MCSCF), MCSCF-SCEP and SCEP-CEPA. The electric dipolemoment function, rotationless dipole matrix elements, and transition probability coeffi-cients of spontaneous emission for the ground state were also calculated with MCSCF-SCEP and SCEP-CEPA.

In the same year, an article of Hirst and Guest [33] was published, which still is animportant article for the calculations on OH+. Potential energy curves, total energies,excitation energies, and some spectroscopic constants for a large number of electronicstates were calculated using the multi-reference double excitation configuration interactionmethod (MRDCI).

Three years later second order configuration interaction (SOCI) and complete activespace SCF (CASSCF) were used to calculate total energies and potential energy curves ofthe three lowest 3Σ− and 3Π states of OH+ [49]. Other parameters were also calculated:dissociation limits, spectroscopic parameters for the electronic ground state (X3Σ−) andthe first excited 3Π state (A3Π), transition dipole moments, and photodissociation cross

18

3.1. CORRELATION DIAGRAM 19

sections.In ref. [35], potential energy curves are given, which were calculated with the MRDCI

method. In this article some other properties of the molecule are also given (like radiativelifetimes and spin-orbit matrix elements).

In 1993, state-averaged MCSCF (SA-MCSCF) was used to calculate potential energycurves, spectroscopic constants for a number of states and interstate coupling interactions[26].

More recently, the results of a coupled cluster study of the potential energy curve,derived ro-vibrational levels, spectroscopic constants and vibrational energies for the a1∆excited state of OH+ are published [2]. The exact full CI (FCI) and the coupled clustermethod with singles and doubles (CCSD), based on the unitary group approach (UGA),were used.

In ref. [50] dissociation limits, spectroscopic constants for the ground state, diabaticpotential curves and their couplings are given, which were calculated with the completeactive space multi-configurational self-consistent field with configuration interaction (CAS-MCSCF-CI) method.

The goal of the current computational research is to calculate the potential energycurves for the ground state and 17 electronically excited states, to get a complete overviewof the most important states. This has already been done in 1983 by Hirst and Guest [33],but these curves are improved here by using other computational methods and a largerbasis set. Moreover, transition dipole moments and photodissociation cross sections arecalculated for allowed transitions.

3.1 Correlation diagram

In section 2.1.1, the electronic configurations of the ground and excited states of OH+

are given. This ion can dissociate to O and H+ or to O+ and H, see reaction (2.7). Theground state configurations of the O and O+ atoms both give rise to three different stateswith different energies and atomic term symbols. The term symbols of the neutral oxygenatom are 3P, 1D, and 1S and the terms of the charged oxygen atom are 4S, 2D, and 2P.By applying Hund’s rules it follows that O(3P) and O+(4S) are the ground states of theseatoms. The term symbol of the neutral hydrogen atom is 2S and the term of the protonis 1S. Therefore, there are six different dissociation limits possible for OH+. For everydissociation limit, the molecular electronic states of OH+ that will dissociate to this limitare determined with the following rules:.

1. From the orbital angular momentum L of an atom, the possible values for the pro-jection of L on the z axis, ML, can be determined: ML= −L, −L+1, ... , 0, ... ,L − 1, L. The projection of the electronic angular momentum on the internuclearaxis Λ of the OH+ molecule is equal to the sum of the ML values of the two atoms[51]. For the H atom and the H+ ion, L is equal to 0 and therefore Λ of the molecularstate is equal to the value of ML of the oxygen atom or ion.

2. The total spin quantum number S of the molecular state can be calculated by usingthe rule S=(S1+S2),(S1+S2−1),...,|S1−S2|, where S1 and S2 are the spin quantumnumbers of the H atom or the H+ ion and the O atom or the O+ ion [51].

3. For Σ states, the reflection symmetry along an arbitrary plane containing the inter-nuclear axis has to be determined: a Σ state can be symmetric (+) or asymmetric

3.1. CORRELATION DIAGRAM 20

(−) under reflection. This can be calculated using some properties of the correspond-ing dissociation limit. The H atom or H+ ion is totally symmetric and therefore,only the properties of the O atom or the O+ ion are taken into account. A rule is,that a reflection along the xz plane (σv) is the same as a 180 rotation around arotation axis perpendicular to the reflection plane (Ry(π)), followed by inversion (ı):σv(xz)=Ry(π)ı. An atomic fine structure state is represented by |J,MJ⟩, where J isthe total electronic angular momentum quantum number and MJ is the projectionof J on the z axis, where J can take the values (L+S),(L+S−1),...,|L−S| and MJ

can be J , (J−1),...,−J . For Ry(π), the equation Ry(π) |J,MJ⟩=|J,−MJ⟩ (−1)J+MJ

can be used [52]. In this situation, for J the value of L of the atomic state is usedand MJ is zero, so Ry(π) |L, 0⟩=(−1)L. The inversion operator should be applied tothe number of electrons in the 2p orbitals of oxygen, because these orbitals are an-tisymmetric under inversion (ı|2px,y,z⟩=− |2px,y,z⟩). The O atom has four electronsin 2p orbitals, so the atomic states are symmetric under inversion (+1). The O+

ion has three electrons in 2p orbitals, so the atomic states are asymmetric underinversion (−1). With this information the reflection symmetry of the Σ state can becalculated.

The result is given in table 3.1. From this table, a correlation diagram can be con-structed, which is shown in figure 3.1. For this diagram the naming of the states andthe order of the dissociation limits are taken from ref. [33]. The order of the limits isdetermined by the ionization potentials of the oxygen and hydrogen atoms, which are veryclose: the ionization potential of the oxygen atom is 13.618054 eV [53] and the potential ofhydrogen is 13.5984337 eV [53]. Because the ionization energy of oxygen is larger than thisenergy for hydrogen, the dissociation limit O(3P) + H+ lies lower than the limit O+(4S)+ H. One important note is, that states can dissociate to another limit by perturbationswith other states, for example by predissociation. This cannot be seen in the correlationdiagram.

Table 3.1: Molecular states dissociating to a certain limit

Dissociation limit L Λ S Ry i σv Molecular statesO(3P) + H+(1S) 1 0 1 Ry |1, 0⟩ = − |1, 0⟩ 1 −1 3Σ−

±1 1 3ΠO(1D) + H+(1S) 2 0 0 Ry |2, 0⟩ = |2, 0⟩ 1 1 1Σ+

±1 0 1Π±2 0 1∆

O(1S) + H+(1S) 0 0 0 Ry |0, 0⟩ = |0, 0⟩ 1 1 1Σ+

O+(4S) + H(2S) 0 0 1,2 Ry |0, 0⟩ = |0, 0⟩ −1 −1 3Σ−, 5Σ−

O+(2D) + H(2S) 2 0 0,1 Ry |2, 0⟩ = |2, 0⟩ −1 −1 1Σ−, 3Σ−

±1 0,1 1Π, 3Π±2 0,1 1∆, 3∆

O+(2P) + H(2S) 1 0 0,1 Ry |1, 0⟩ = − |1, 0⟩ −1 1 1Σ+, 3Σ+

±1 0,1 1Π, 3Π

3.1.1 Correlation diagram including spin-orbit coupling

In the correlation diagram of section 3.1, the spin-orbit coupling is not taken into account.This effect is the interaction of the electron spin with its motion, which causes shifts in

3.2. METHODS 21

O+(2P)+H(2S)

O(1S)+H+(1S)

O+(2D)+H(2S)

O(1D)+H+(1S)

O+(4S)+H(2S)

O(3P)+H+(1S)

X3Σ−

A3Π

b1Σ+

11Π

21Σ+

5Σ−

23Π

23Σ−

21Π

3∆

1Σ−

33Π

33Σ−

3Σ+

21∆

31Σ+

31Π

a1∆

Figure 3.1: The correlation diagram for OH+.

atomic and molecular energy levels. It is possible to include this coupling in a correlationdiagram by calculating the projections of the total angular momentum along the internu-clear axis (Ω) for the molecular states and for the dissociation limits. For the molecularstates, Ω can take the values |Λ + S|. For the dissociation limits, first values for J andMJ have to be determined. For the dissociation limit, Ω can take the values |MJ1+MJ2|.When Ω is equal to zero, the reflection symmetry of Ω has to be determined. This is donein a similar way as for the reflection symmetry of a Σ state, by using σv(xz)=Ry(π)ı. TheRy operator gives (−1)J , where J is equal to the maximum value of Ω for the molecularstates. For the molecular states, the inversion operator should be applied to the numberof electrons in π orbitals. When spin-orbit coupling is included in the correlation diagram,the molecular states will dissociate to the same limit as before, but now also with the samevalue for Ω. The correlation diagram including spin-orbit coupling is given in figure 3.2.

A special effect in the case of OH+ is, that this spin-orbit coupling causes an ex-tra near degeneracy. The energy difference between the dissociation limits O(3P)+H+

and O+(4S)+H is only 0.0196203 eV. When spin-orbit coupling is taken into account,this difference is between O(3P2)+H+ and O+(4S)+H. The energy difference betweenO(3P2)+H+ and O(3P1)+H+ is 0.0196224 eV. Therefore O(3P1)+H+ and O+(4S)+H arealmost degenerate.

3.2 Methods

For the ab initio calculations, the time-independent Schrodinger equation has to be solved:

HΨ = EΨ, (3.1)

3.2. METHODS 22

O+(2P3/2)+H(2S)

O(1S)+H+(1S)

O+(2D5/2)+H(2S)

O(1D)+H+(1S)

O+(4S)+H(2S)

O(3P2)+H+(1S)

X3Σ−

A3Π

b1Σ+11Π

21Σ+

5Σ−

23Π

23Σ−

21Π

3∆

1Σ−

33Π

33Σ−

3Σ+

21∆31Σ+31Π

a1∆

O(3P1)+H+(1S)

O(3P0)+H+(1S)

O+(2D3/2)+H(2S)

O+(2P3/2)+H(2S)

0+

120−0+120+10+0−120−0+120+

11

21

30−0−0+120+

1

1

0−

20+1

0+120−0+1120−

10+0+120−0+112230−0+1120+0−0+1120−

10+

Ω Ω

Figure 3.2: A correlation diagram including spin-orbit coupling.

where H is the Hamiltonian, Ψ the n-electron wavefunction that depends on the identitiesand positions of the nuclei and on the total number of electrons, and E is the total energyof the system. The Hamiltonian for a molecule with more than one electron in atomicunits is [54]:

H = −1

2

electrons∑i

∇2i −

1

2

nuclei∑A

1

MA∇2

A −electrons∑

i

nuclei∑A

ZA

riA

+electrons∑

i

electrons∑j>i

1

rij+

nuclei∑A

nuclei∑B>A

ZAZB

RAB,

(3.2)

whereMA is the mass of nucleus A, RAB is the distance between nuclei A and B, rij is thedistance between electrons i and j, and riA is the distance between electron i and nucleusA.

For any atom or molecule with more than one electron, an exact analytic solution of the

3.2. METHODS 23

Schrodinger equation is not possible, because of the electron-electron repulsion. Because ofthis repulsion, the Schrodinger equation cannot be separated into one-electron equations,which could be solved exactly. Therefore, there are different methods to solve the equa-tion using approximations. The variational theorem states that for a time-independentHamiltonian operator, any trial wavefunction will have an energy expectation value thatis larger than or equal to the energy of the true ground state wavefunction correspondingto the given Hamiltonian. For the calculation of the PECs for OH+, the Hartree-Fock(HF), multi-configurational self-consistent field (MCSCF) and configuration interaction(CI) methods are used. In figure 3.3 a diagram is given with the energies that are calcu-lated with HF, MCSCF and CI. The CI method uses the best approximations and thereforegives the lowest energy.

The most important approximation that is used in these three methods, is the Born-Oppenheimer approximation: nuclei move much more slowly than electrons and thereforeit is assumed that the nuclei are stationary from the perspective of the electrons. Thewavefunction can be written as the product of an electronic (Ψel) and a nuclear (Xv)wavefunction (Ψ(r,R)=Ψel(r;R)Xv(R)), for which separate Schrodinger equations can besolved. The electronic Schrodinger equation:

HelΨel = EelΨel (3.3)

has to be solved to calculate the potential energy curves, where the electronic HamiltonianHel is [54]:

Hel = −1

2

electrons∑i

∇2i −

electrons∑i

nuclei∑A

ZA

riA+

electrons∑i

electrons∑j>i

1

rij+

nuclei∑A

nuclei∑B>A

ZAZB

RAB. (3.4)

The first term of this equation represents the kinetic energy of the electrons, the secondterm is the potential energy due to electron-nucleus attraction, the third term stands forthe electron-electron repulsion, and the last term is the nuclear-nuclear Coulombic energy.The nuclear Hamiltonian is the second term of equation 3.2, which is the nuclear kineticenergy (TN ). To get the total energy E, the equation [TN +Eel]Xv=EXv has to be solved.

HF Energy

MCSCF Energy

CI Energy

True Energy

Correlation Energy

Figure 3.3: The energies that are calculated with different methods. HF, MCSCF and CI areapproximations of the true Born-Oppenheimer energy. The HF, MCSCF and CI energies arealways higher than the true energy (variational principle). The difference between the HF energyand the CI energy is the correlation energy.

3.2. METHODS 24

3.2.1 Hartree-Fock

For the Hartree-Fock method, a second approximation is made, because equation 3.3 isinsolvable for the general, multi-electron case. In reality, the wavefunction of electron 1depends on the instantaneous position of electron 2 (i.e. the motion of the electrons iscorrelated), but in the Hartree-Fock method, it is assumed that electrons move almostindependently of each other. A Slater determinant is used to ensure that the total wave-function is antisymmetric upon interchange of electron coordinates and to account for thePauli principle. In a Slater determinant, each individual electron is confined to a spinorbital, which is the product of a molecular orbital, Ψi, and a spin function, α or β. Eachelectron feels the presence of an average field made up of all the other electrons (also calledthe mean field approximation) and therefore the electrons are called uncorrelated.

Because of the variational theorem (see the beginning of this chapter), the best wave-function among all possible Slater determinants is the one for which the energy is minimal.The set of molecular orbitals leading to the lowest energy is obtained by the self-consistentfield (SCF) process. This method starts with an initial guess for the one-electron molecu-lar orbitals and during the process these orbitals are optimized iteratively until the changein the total electronic energy falls below a predefined threshold. The initial approximateone-electron wavefunctions ψi are linear combinations of a basis set of prescribed functionsknown as basis functions, ϕ [54]:

ψi =

basisfunctions∑µ

cµiϕµ. (3.5)

The coefficients cµi are the unknown molecular orbital coefficients. Usually, ϕ is an atomicorbital, so the molecular orbitals are linear combinations of atomic orbitals (LCAO). Withthe resultant self-consistent orbitals, the optimized Slater determinant can be constructed,from which the lowest energy is known as the Hartree-Fock energy. Because of the varia-tional theorem, the Hartree-Fock energy is an upper bound to the true ground state energyof the molecule. When a complete, infinite basis set is used to construct the molecularorbitals, the best possible energy is calculated. This energy is called the Hartree-Focklimit.

The Hartree-Fock method is a relatively good method to calculate structural propertiesof a molecule, like bond distances and angles. Hartree-Fock is not so good for the cal-culation of potential energy curves or surfaces, vibrational frequencies, reaction energies,and excited states, because only a single Slater determinant can be used. Therefore, thereare a number of post-Hartree-Fock methods which improve the Hartree-Fock technique.The post-Hartree-Fock methods which are used for this work are described in the nextsections.

3.2.2 Multi-configurational self-consistent field

In the HF method only one determinant is used to describe an electronic state. Most ofthe time, a few different important determinants are needed for a qualitatively correctdescription of a state. This is called static electron correlation. In OH+ for example,there are a π+ and a π− orbital, which are degenerate. When only one of these orbitalsis occupied, there are two possible situations: π+ is doubly occupied and π− is empty(a virtual orbital), or π− is doubly occupied and π+ is a virtual orbital. The multi-

3.2. METHODS 25

configurational self-consistent field (MCSCF) method minimizes the energy of the two-configuration wavefunction

Ψ = a1|...π+⟩+ a2|...π−⟩, (3.6)

where the coefficients a1 and a2 are variationally optimized [55]. In this method theorbitals are variationally optimized simultaneously with the coefficients of the electronicconfigurations [56, 57]. The energy that is found with these configurations and orbitalsis lower than the Hartree-Fock energy for the same state. Therefore, MCSCF gives abetter approximation for the energy of the true wavefunction than HF and static electroncorrelation is taken into account.There are two different MCSCF approaches which can be used. The first one, which isalso used for the current calculations, is the complete active space self-consistent field(CASSCF) approach. For this method all possible configurations of the proper symmetrywhich can be constructed from a given number of electrons and active orbitals are includedin the wavefunction [57]. In this case the active orbitals are all the (partially) occupiedvalence orbitals. Since the number of configurations quickly increases with the numberof active orbitals, just like the computational cost, sometimes it can be desirable to usea smaller set of configurations. This is done in the second MCSCF approach, which iscalled the restricted active space self-consistent field (RASSCF) method: the number ofelectrons in certain subspaces is restricted.

3.2.3 Configuration interaction

Another way to improve the calculated energy is to combine the wavefunction of an elec-tronic state (calculated with HF or MCSCF) with wavefunctions corresponding to variousexcited configurations. This method is called configuration interaction (CI). This methodis dealing with dynamical correlation, which is the correlation of the movement of electrons.During the current work, the resultant wavefunctions of MCSCF are used as initial config-urations for the CI process. The excited configurations are generated by the promotion ofone or more electrons in the electronic state to a higher level. The new wavefunction is alinear combination of the MCSCF wavefunction Ψ0 and the wavefunctions of the excitedconfigurations, Ψs [58]:

Ψ = a0Ψ0 +∑s>0

asΨs, (3.7)

where a0 and as are unknown coefficients, which are variationally optimized during CI[59, 60].

To use this method, the number of electron promotions has to be limited. This can bedone in two different ways. First, the frozen core approximation can be used. This elimi-nates any promotions of electrons from core molecular orbitals. The second approximationis to limit the number of promotions based on the total number of electrons involved:single-electron promotions (CIS), double-electron promotions (CID), and so on. The CISmethod does not lead to an improvement of the HF energy or wavefunction (Brillouin’stheorem), but CID does. Another limit that can be used is CISD, where both single-and double-electron promotions are taken into account. In this way CI takes the electroncorrelation into account. When all configurations of the proper symmetry are includedin the variational procedure (i.e. all Slater determinants obtained by exciting all possibleelectrons to all possible virtual orbitals), the solution of the Schrodinger equation is exact

3.3. CALCULATION 26

for the basis set used. This is called full CI. In a small basis set, the full CI calculationcan be performed, but when the basis set is large, it is a very hard computation.

An important disadvantage of CI is, that it is not size consistent: the calculatedenergies of two atoms treated separately and two atoms treated together but at infiniteseparation will be different. In the case of a diatomic molecule AB, this means that theenergy of AB at infinite internuclear distance is not the same as the sum of the energy ofatom A and the energy of atom B. To overcome this problem, there are several corrections,for example the Davidson correction [61], which is also used for the current calculations.

With the CI procedure, the energies of ground and electronically excited states can becomputed. Therefore it is possible to calculate excitation energies. Unfortunately theseexcitation energies are generally too high when using for example CID or CISD, becausethe excited states are less correlated than the ground state. To solve this problem, one canuse more than one reference configuration from which all singly, doubly, ... excited config-urations are included. This is called multireference configuration interaction (MRCI). Thevariant of this method which is mostly used, is multireference single and double configu-ration interaction (MRDCI). The advantage of MRCI is that it gives a better correlationof the ground and excited electronic states.

A CI calculation takes more time than a HF or MCSCF computation, but the advan-tage is that this method gives a lower energy.

3.3 Calculation

With the help of the electronic configurations and the correlation diagram from figure3.1, the potential energy curves for the electronic states of OH+ can be computed usingthe program MOLPRO [45]. The different methods described in chapter 3.2 are used inMOLPRO.

3.3.1 The basis set

As a basis set for all the calculations, AVTZ is chosen in MOLPRO. In general this basisset is called an augmented correlation-consistent polarized valence triple-zeta basis set(aug-cc-pVTZ). This basis set is developed by Dunning [62] and is also included in theEMSL Basis Set Exchange Library [63, 64].

The LCAO approximation for the molecular orbitals requires the use of a basis setmade up of a finite number of well-defined functions centered on each atom. In general,the atomic orbitals are linear combinations of Gaussian functions with fixed coefficients.The cartesian Gaussian functions have the form [65]

gijk(r) = Nxiyjzke−αr2 , (3.8)

where x, y and z are the position coordinates measured from the nucleus of an atom, i,j and k are nonnegative integers, and α is an orbital exponent. A linear combinationof Gaussian functions is called a contracted function. A basis set in which each valenceatomic orbital is described by three basis functions is called a valence triple basis set. Anadvantage of such a basis set is that it is able to adjust to different molecular environments.

The cc-pVNZ Dunning basis sets, where N=D,T,Q,5,6,... (D=double, T=triple, etc.),are widely used for first- and second-row atoms. They include successively larger shellsof polarization (correlating) functions (d, f, g, etc.). In the augmented cc-pVNZ basis

3.3. CALCULATION 27

sets some diffuse functions are added. Diffuse functions are for example very useful forcalculations of molecules in excited states and particularly for Rydberg states, becausethe highest energy electrons may only be loosely associated with specific atoms.

For the H atom, the cc-pVTZ basis set consists of three s orbitals, two p orbitalsand one d orbital: [3s2p1d]. In the augmented cc-pVTZ basis set one s, p and d diffuseorbitals are added, so the total basis set is [4s3p2d]. An s orbital has one component,a p orbital has three components (px, py and pz) and a d orbital has five components(dxy, dyz, dzx, dz2 and dx2+y2). So in total the AVTZ basis set for the H atom consists of4 + 3 · 3+ 2 · 5 = 23 functions for the atomic orbitals. For the O atom, the cc-pVTZ basisset consists of four s orbitals, three p orbitals, two d orbitals and one f orbital: [4s3p2d1f].In the augmented cc-pVTZ basis set one s, p, d and f diffuse orbitals are added, so thetotal basis set is [5s4p3d2f]. An f orbital has seven components, so in total the AVTZbasis set for the O atom consists of 5 + 4 · 3 + 3 · 5 + 2 · 7 = 46 functions for the atomicorbitals. So in total there are 23 + 46 = 69 functions for the contracted atomic orbitalsof OH+. Without contraction and diffuse orbitals there would be 83 functions, becausefor H the basis set without contraction and diffuse orbitals is [6s3p2d] and for O this is[11s6p3d2f]. The AVTZ basis set is given in appendix A.1.

3.3.2 The settings

In MOLPRO, an input file is used to give all information for a computation. An exampleof an input file is given in appendix A.2. The first molecular property that has to be givenis the geometry. This can be done in the following way by using a Z-matrix: geometry=O;H,O,rOH. This means that the molecule consists of an O atom and an H atom and thatthe distance between these atoms is rOH. In general, the distance is given in bohr (a0 ora.u.): 1 a0 is equal to 0.52918 A. Next the basis set is given, in this case AVTZ.

First, the RHF method is used to calculate molecular orbitals at a distance of 2 bohr.This distance is taken, because it is known from literature that the experimental bondlength is approximately 2 a0 [33]. The number of electrons, the total symmetry of thewavefunction, and the spin for the electronic state have to be given to compute the molec-ular orbitals. The orbitals of the ground state are used as an orbital guess for HF inevery calculation. With this information, MOLPRO can compute the HF energy and theoptimal molecular orbitals with the HF method. These orbitals will be used as startingguess orbitals for MCSCF.

Because the potential energy curves have to be calculated, the calculation has to beexecuted for different distances rOH. For all the curves, two different calculations areperformed: one for small internuclear distances (smaller than 2 bohr) and one for thethe longer distances (from 2 to 20 bohr). For most of the curves, the step size for theinternuclear distance is 0.1 a0 between 1 and 1.5 a0, 0.25 a0 between 1.5 and 4 a0, 0.5a0 between 4 and 15 a0 and 1 a0 between 15 and 20 a0. For the HF method, only onedistance is used, because the HF approximations are not so good. For every distance firstthe CASSCF energy and orbitals are calculated with the MULTI program and after thatthe MRCI energy and orbitals can be computed with the CI program. In this way, theMCSCF method uses the HF orbitals that are calculated at a distance of 2 bohr as startingorbitals and the MRCI method makes use of the new MCSCF orbitals at every distanceas orbital guess. Again the number of electrons, the total symmetry of the wavefunctionand the spin for the electronic state are given for both methods. The calculations for thedifferent electronic states with the same term symbol (for example A3Π, 23Π, and 33Π)

3.3. CALCULATION 28

are done in one computation (state-averaged computation).There are also other properties and specifications for the calculation that can be given.

In this way restrictions can be given for the computation, which can improve the calcula-tions. All these options are described in the manual of MOLPRO, which can be found onthe website of MOLPRO [45]. The resultant CASSCF and MRCI energies for the differ-ent distances can be plotted in a program like MATLAB to obtain the resultant potentialenergy curves. The calculated energies are all given in hartree (Eh): 1 Eh = 27.2114 eV.One hartree is the energy needed to move a stationary electron one bohr distant from aproton away to infinity.

Because the step size for the internuclear distance is quite large for the PECs, splineinterpolation is used to calculate more points of the curves and to smooth them. A splineis a sufficiently smooth piecewise-polynomial and this spline passes through all the pointsthat are calculated with MOLPRO.

3.3.3 Wrong ordering of two dissociation limits

In this way almost all potential energy curves could be calculated. For some curves, therewere a few problems. As described in chapter 3.1, the difference between the ionizationpotentials of oxygen and hydrogen is very small. Therefore, the limit O+(4S) + H liesexperimentally only 0.0196203 eV higher than the limit O(3P) + H+. During the com-putations in MOLPRO, the ionization potential of oxygen is underestimated, because theerror in the correlation energy of O+ is smaller than for the neutral oxygen atom. Thisis the case, because it is harder to describe the correlation energy of an atom with moreelectrons. If this ionization potential is underestimated by more than 0.0196203 eV, thiswill result in an incorrect ordering of the limits O(3P) + H+ and O+(4S) + H. As a conse-quence of this incorrect ordering, the dissociation limits for the two lowest 3Σ− states (sothe ground state X3Σ− and the excited state 23Σ−) are the reverse of the experimentallimits. In all other cases, the potential curves dissociate to the correct atomic states. Thisproblem is also seen in earlier calculations [26, 33, 35, 49]. In these articles the problemhas not been solved, only possible solutions are given. In one article, the problem is partlysolved by using the restricted active space self-consistent field method (RASSCF) [66]:the ground state dissociates to the right limit, but the potential energy curve of the 23Σ−

state is not calculated. From figure 2.2 this problem can also be seen. This figure is basedon the calculations from ref. [33]. For the current work, it could really be important thatthe electronic states dissociate to the right limit. Therefore, we tried to solve the problem.This is not so easy, because the potential in the bonding region should not be disturbedand the bonding energy of the potentials should not change much. Three different methodsare used to try to solve the problem:

1. Reduce some exponents in the basis set of the hydrogen atom. In this way, theionization energy of the hydrogen atom can be decreased until it is underestimatedthat much that the ordering of the dissociation limits is correct. Unfortunately theproblem with this method is, that many exponents have to be reduced to obtain thiseffect and that the potential in the bonding region is also disturbed. Therefore, thiswas not a good solution.

2. Add an electric field. In this way the electron of the hydrogen atom can be pushedto the oxygen atom, so the energy of the dissociation limit O(3P) + H+ can be

3.3. CALCULATION 29

lowered. With this method, only small fields can be used, otherwise the potentialin the bonding region and the bonding energy will change much. The field that hadto be used to change the ordering of the dissociation limits was too high, thereforethis was not a good solution.

3. Add a number of orbitals to the active space of the oxygen atom during the MC-SCF computations. By restricting the number of electrons in these extra orbitals,configuration interaction is directly included. This is done by using the OCC andRESTRICT cards in the MCSCF program MULTI. With configuration interactionthe correlation energy is better described, so the ionization potential of the oxygenatom can be increased. One important limitation of this method is, that only 32active orbitals can be used for a calculation in MOLPRO using a 64 bit computer.With 31 active orbitals, the ordering of the dissociation limits could be changed andtherefore, this method is used to solve the problem. Normally, one closed-shell or-bital with s/z symmetry and five active orbitals (three orbitals with s/z symmetry,one with x/xz symmetry, and one with y/yz symmetry) are used for the 1σ, 2σ, 3σ,1πx, and 1πy orbitals of OH+. This is changed to one closed-shell orbital with s/zsymmetry and 30 active orbitals (14 orbitals with s/z symmetry, seven with x/xzsymmetry, seven with y/yz symmetry and two with xy symmetry). In this way, thefollowing atomic orbitals of oxygen are taken into account: 1s, 2s, 2p, 3s, 3p, 3d, 4s,4p, 4d, 5s, 5p, 6s, 6p. The number of electrons in the extra orbitals is restricted totwo.

Finally the problem could be solved with the third method: the ordering of the dissociationlimits is correct and all PECs dissociate to the right limit. For this, a state-averagedcalculation is used for the X3Σ− ground state and the 23Σ− state. The energy of the33Σ− state is calculated with the general settings.

3.3.4 Charge-induced dipole interaction

One extra effect that is taken into account, is the charge-induced dipole interaction: whenthe OH+ ion breaks apart, the ionic fragment induces a dipole in the neutral fragment.The resulting potential V is [67]:

V = −1

2

αq2

r4, (3.9)

where q is the charge (which is equal to 1 in this case), r is the distance between the twofragments and α is the polarizability of the neutral fragment. For this, calculations forthe atoms in different electronic states are done in MOLPRO. When an electric field E isadded, the polarizability of the atom is [68]:

α =µ

E, (3.10)

where µ is the dipole moment, induced by the electric field. For these computations, afield strength of 0.002 a.u. (0.103 V/A) is used. All potential energy curves are calculateduntil a maximum internuclear distance of 20 a0. At this distance, the potential due tothe charge-induced dipole interaction is added to the calculated potential to compute thedissociation energy at an infinite internuclear distance. This value is subtracted from thepotential at every distance and the theoretical energy of the dissociation limit [53], with

3.4. RESULTS 30

respect to the lowest dissociation limit, is added. In this way, the energy of the lowestdissociation limit is set at zero and the charge-induced dipole potential at an internucleardistance of 20 a0 and larger is taken into account.

3.3.5 Photodissociaton cross sections

The photodissociation cross sections are calculated for the transitions from the electronicground state to the dissociative portion of the A3Π state and to the repulsive 23Σ−, 33Σ−,23Π and 33Π states. These cross sections describe the probability for photodissociationvia a transition from the ground state into the continuum of an excited state. First, thewavefunctions corresponding to the two electronic states have to be computed by solvingthe Schrodinger equation. With these wavefunctions, the photodissociation cross sectionsσ as function of the photon energy Ephot can be calculated with the equation:

σ(Ephot) =2π

3cgEphot|⟨ΦE(R)|µ|Xv(R)⟩|2, (3.11)

where c is the speed of light in vacuum in atomic units, g is a factor for the electronicdegeneracies of the bound and dissociating states, ΦE(R) is the wavefunction of the groundstate, µ is the electric dipole transition moment and Xv is the continuum wavefunction ofthe excited state. For a Σ-Σ transition, g is equal to 1 and for a Σ-Π transition, g is 2. Theelectric dipole transition moment represents the probability of a transition between thetwo electronic states due to photon absorption and is computed in MOLPRO as functionof the internuclear distance. For the transitions from the X3Σ− ground state to the 3Πstates, the transition moment is calculated for internuclear distances between 1.4 and 4 a0,for the transition to the 23Σ− state, the internuclear distance ranges from 1 to 20 a0 andfor the transition to the 33Σ− state, the transition moment is calculated for internucleardistance from 1.1 to 4 a0. For the computation of the photodissociation cross sections,the transition moments are only used for internuclear distances between 1 and 4 a0, sincethe Franck-Condon region lies around the equilibrium distance (around 2 a0). A splineis used to smooth the curves and to extrapolate them to 1 a0 for transitions to the 33Σ−

state and to the 3Π states. The wavefunctions and the photodissociation cross sectionsare computed by solving the corresponding equations numerically with a Numerov method[69] in MATLAB. For the X3Σ− ground state, the vibrational wavefunction of the v=0level is used, because OH+ is experimentally produced in its vibrational ground state.

3.4 Results

The resultant potential energy curves are given in figure 3.4. The energies are the Davidsoncorrected CI energies. The energy of the lowest dissociation limit at infinite internucleardistance is set at 0. In figure 3.5, only the potential energy curves that are important forthe experiments with 157 nm laser light are given. In appendix B, more detailed resultsare given.

When the potential energy curves are compared with the curves from ref. [33], theyhave similar shapes. The difference is that all new curves dissociate to the right dissociationlimit.

For the computation of a photodissociation cross section, the electric dipole transitionmoment as function of the internuclear distance is needed. The important transition

3.4. RESULTS 31

2 4 6 8 10 12 14 16 18 20

−5

0

5

10

15

20

25

30

R (a0)

Ene

rgy

(eV

)

Figure 3.4: All 18 potential energy curves that are calculated.

1 2 3 4 5 6 7 8 9 10−6

−4

−2

0

2

4

6

8

10

12

R (a0)

Ene

rgy

(eV

)

X3Σ−

a1∆A3Πb1Σ+

11Π5Σ−

23Σ−

Figure 3.5: The potential energy curves that are important for experiments with 157 nm laserlight.

moments are shown in figure 3.6. The relative signs of the wavefunctions are arbitraryand therefore, the relative signs of the transition moments are in this case also arbitrary.

3.4. RESULTS 32

When these transition moments are compared with figure 2 and 3 of ref. [49], they arein good agreement with each other. Only the curve for the 33Π-X3Σ− transition looksdifferent, but the absolute values are in good agreement with ref. [49].

1 1.5 2 2.5 3 3.5 4−1.5

−1

−0.5

0

0.5

1

1.5

2

R (a0)

µ (a

.u.)

23Σ− − X3Σ−

33Σ− − X3Σ−

A3Π − X3Σ−

23Π − X3Σ−

33Π − X3Σ−

Figure 3.6: The electric dipole transition moments for transitions from the X3Σ− state as functionof the internuclear distance.

During the calculation of the photodissociation cross sections, the vibrational wave-functions of the X3Σ− ground state are also calculated. These v = 0, v = 1, and v = 2wavefunctions are shown in figure 3.7.

0.5 1 1.5 2 2.5 3 3.5 4−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

R (a.u.)

Ψ

v=0v=1v=2

Figure 3.7: The v = 0, v = 1, and v = 2 vibrational wavefunctions of the X3Σ− ground state.

3.4. RESULTS 33

The photodissociation cross sections for the transitions from the ground state to theexcited 23Σ−, 33Σ−, 23Π, and 33Π states are shown in figure 3.8 and the transition to thedissociative portion of the A3Π state is shown in figure 3.9. The cross sections are given incm2, as function of the wavelength in nm. In table 3.2, some detailed information aboutthe photodissociation cross sections is given and a comparison with ref. [49] is made. Theproperties given in this table are in good agreement with the literature. The maximumcross section of the transition to the A3Π state is a factor 3 higher than the cross sectiongiven in ref. [49].

50 60 70 80 90 100 1100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10

−17

λ (nm)

σ (c

m2 )

23Σ− − X3Σ−

33Σ− − X3Σ−

23Π − X3Σ−

33Π − X3Σ−

Figure 3.8: Photodissociation cross sections as function of the wavelength for four transitions fromthe ground state to excited 3Σ− and 3Π states.

Table 3.2: Photodissociation cross sections for transitions from OH+ X3Σ−

Peak position (nm) Cross section (10−18 cm2) FWHM (nm)Final state This work [49] This work [49] This work [49]

23Σ− 79 83 2.79 2.45 19 2233Σ− 73 73 9.25 9.70 13 1323Π 79 82 0.75 1.32 16 1533Π 70 70 4.08 6.21 4.5 5.5

In MATLAB, some spectroscopic constants could be calculated. The resultant con-stants are given in table 3.3. The equilibrium internuclear distance Re is calculated fromthe potential energy curve and the Dunham constants ωe and ωexe are calculated from thethree lowest vibrational levels of each state with a polynomial fit. The values for ∆G1/2

and ∆G3/2 are computed from the Dunham constants: ∆G (v+12)=ωe-2ωexe(v+1). The

constant Be is calculated with the equation Be=1/(2µR2e), where µ is the reduced mass of

OH+. The dissociation energy De is calculated by subtracting the energy at the equilib-rium internuclear distance Re from the energy at an internuclear distance of 20 a0. In table3.3, the constants are also compared with theoretical constants of Hirst and Guest [33]and Saxon and Liu [49] and experimental values of Merer and Malm [70]. For the ground

3.5. PREDICTIONS FOR THE EXPERIMENT 34

200 210 220 230 240 250 2600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x 10−21

λ (nm)

σ (c

m2 )

Figure 3.9: Photodissociation cross section from the ground state to the dissociative portion of theA3Π state as function of the wavelength.

state, the values for the equilibrium internuclear distance and the rotational constant Be

are improved, but the Dunham constants are in worse agreement with the experimentalvalues. For the A3Π state, it is the other way around.

Table 3.3: Calculated spectroscopic constants for OH+

Re ωe ωexe ∆G1/2 ∆G3/2 De Be

(A) (cm−1) (cm−1) (cm−1) (cm−1) (eV) (cm−1)

X3Σ− This work 1.0266 3174 74.3 3025.4 2876.8 5.22 16.87[33] 1.0328 3104 77.8 2949.5 2793.9 5.31 16.57[49] 1.031 3088.1 72.8 2942.5 2796.8 5.36 16.58Expt [70] 1.0289 3113.37 78.515 2956.34 2799.3 16.794

A3Π This work 1.143 2121 79.0 1963.0 1805.0 1.59 13.61[33] 1.147 2187 87.6 2011.8 1836.7 1.66 13.66[49] 1.134 2219.8 83.2 2053.3 1886.9 1.79 13.80Expt [70] 1.1354 2133.65 79.55 1974.55 1815.45 13.792

b1Σ+ This work 1.0372 3109 79.1 2950.8 2792.6 3.59 16.53[33] 1.0398 3132 89.0 2954 2776 3.63 16.53Expt [70] 1.032 2981 16.32

a1∆ This work 1.0266 3145 75.5 2994.0 2843.0 5.02 16.87[33] 1.0364 3122 76.6 2969.2 2815.9 5.05 16.61

11Π This work 1.2277 1787 51.9 1683.2 1579.4 1.79 11.80[33] 1.2382 1825 49.3 1726.7 1628.2 1.84 11.76

3.5 Predictions for the experiment

With all these calculations, some predictions can be done for the experiments. During theexperiments, OH+ will be produced in its ground state and laser light with a wavelength of

3.5. PREDICTIONS FOR THE EXPERIMENT 35

157 nm (an energy of 7.9 eV) will be used to dissociate this ion. This energy is higher thanthe energies of the three lowest dissociation limits. An important condition for dissociationis, that an excited state has to be reached with the laser light. Therefore the selectionrules have to be taken into account:

• ∆S=0

• ∆Λ=0,±1

• Σ+ ↔ Σ+, Σ− ↔ Σ−

With these selection rules taken into account, only two transitions in this region areallowed:

• X3Σ− - A3Π

• X3Σ− - 23Σ−

But the Franck-Condon factors also play an important role: in principle, only a verticaltransition is allowed. Therefore the 23Σ− state cannot be reached with 157 nm light: theenergy of the light is too low. For the transition to the A3Π state, the energy is mostprobably too high. This is confirmed by the photodissociation cross sections: from figure3.8 and 3.9 it follows, that 157 nm is not a good wavelength for photodissociation. Itmight be possible to reach the 23Σ−, 33Σ−, or 23Π state with a two-photon transition,but the probability for this is very low. This might only be possible with a high laserpower. Therefore it is possible that 157 nm light does not have the right energy for thephotodissociation of OH+. Maybe a forbidden transition can take place (for example tothe 11Π state), but this is uncertain.

Two other VUV wavelengths that can easily be produced in the lab, are 118 and 193nm. From figure 3.8 and 3.9 it follows, that these wavelengths are also not suitable forphotodissociation. Again, forbidden transitions might be possible. From figure 3.8 andtable 3.2 it follows that it is best to use light with a wavelength between 70 and 80 nm.When the power of the laser is very high, it might be possible to use light with a wavelengtharound 150 nm to get a two-photon transition.

Chapter 4

Experimental methods

For the experiments, an apparatus is used with two differentially pumped vacuum cham-bers. In one chamber the molecules enter the apparatus (source chamber) and in thesecond chamber the interaction between the molecules and laser light takes place (detec-tion chamber). The products of the interaction are detected by a camera. In figure 4.1a diagram of the apparatus is given. The different parts of this machine are described inthe next sections.

Figure 4.1: A diagram of the VMI apparatus used for the experiments.

4.1 Molecular beam

In this work a molecular beam is used, which is produced by allowing a gas at higherpressure to expand through a small orifice into a chamber at lower pressure to form acollimated, narrow stream of molecules.

If the pressure of vapour in the source is increased so that the mean free path inthe emerging beam is much shorter than the diameter of the pinhole, many collisions takeplace even outside the source. These collisions give rise to hydrodynamic flow and transfer

36

4.1. MOLECULAR BEAM 37

momentum into the direction of the beam. This causes the molecules in the beam to travelwith very similar speeds, so further downstream few collisions take place between them.This condition is called molecular flow. Because the average speed of the molecules inthe beam is much larger than the speed of sound for the molecules that are not part ofthe beam, this is called a supersonic jet. Because the spread in kinetic energy is verysmall, the molecules are effectively in a state of very low translational temperature: thistemperature may reach as low as 1 K. The rotational and vibrational temperatures of themolecules are also lower than normal: the temperature for rotation is of the order of 10K and for vibration it is of the order of 100 K. As a result of these low temperatures, themolecular spectra are simplified significantly [71].

For the current research a pulsed molecular beam is produced by using a PSV pulsedsupersonic (Jordan) valve. The mechanism of this valve is illustrated in figure 4.2 [72].The valve consists of a rigid plate with an O-ring on which a metal bar is resting, whichis clamped at both ends. When a current pulse flows in a loop through the plate andthe bar, the oppositely directed currents repel each other and generate a magnetic forcewhich lifts the bar from the O-ring. In this way the valve can be opened and gas canflow out through the center of the O-ring, which becomes the nozzle for the hydrodynamicexpansion [73].

(a) closed

Gas pulse

Current pulse

(b) open

Figure 4.2: The principles of a PSV pulsed supersonic Jordan valve.

Through this valve the molecules enter the source chamber of the apparatus. Theymove through this chamber and reach a conical shaped skimmer. With this, a jet can beconverted into a more parallel supersonic beam. This skimmer should be in the regionof hydrodynamic flow and the excess gas should be pumped away. A skimmer consistsof a conical nozzle shaped to avoid supersonic shock waves spreading back into the gasand so increasing the translational temperature [71]. In this work the distance betweenthe nozzle of the valve and the skimmer was 30 mm. The diameter of the skimmer was2.02 mm. The excess gas in the source chamber is pumped away by using an oil diffusionpump, which is backed by a mechanical pump.

For the photodissociation of OH+, some adjustments have been made to the apparatus

4.2. LASERS 38

to produce OH molecules. For this, a discharge ring is placed approximately 2.5 mm infront of the nozzle of the Jordan valve. A high voltage pulse is applied to it that createsan electrical discharge between the ring and the nozzle of the valve. In this discharge, thedesired OH molecules as well as other ions and neutral fragments are produced. To get amore stable discharge signal, a filament is placed near the discharge ring which produceselectrons. This filament works well with a voltage of 1.4 V and a current of 2 A. Afterpassing the discharge region, the molecules enter the detection chamber via the skimmer.Figure 4.3 shows a photograph of the discharge region.

10 mm

discharge ring

nozzle

filament

Figure 4.3: The Jordan valve with a discharge ring and a filament to produce electrons.

4.2 Lasers

For (2+1) REMPI of H2O and OH a Nd:YAG pumped dye laser is used to ionize thesemolecules. The frequency of the Nd:YAG laser was tripled to get 355 nm light. This lightis used to pump a dye laser operating with Coumarin 307 (C503). The output of this laseris frequency doubled to obtain light with a wavelength around 248 nm for H2O REMPIand around 243 nm for OH REMPI. The laser pulse energy was around 3 mJ per pulseat a repetition rate of 10 Hz. The laser light has a vertical polarization in front of theapparatus, parallel to the detector plane. A REMPI spectrum can be obtained by usingan auto-tracker for the BBO crystal. A lens is used to focus the beam on the molecularbeam.

The photodissociation experiments that we tried to perform are called pump-probeexperiments. First, the neutral molecules from the molecular beam are ionized with the(2+1) REMPI process (pump laser). A second laser is needed for the photodissociationof the ions (probe laser). For this, a F2 excimer laser is used. This is a strong vacuumultraviolet (VUV) light source emitting at 157 nm. Because of strong absorptions near 157nm of O2 and H2O molecules in the air, a N2 flushing system is used to deliver the VUVlaser beam to the apparatus. A 15 cm lens is used to focus the beam on the molecular

4.3. DETECTION 39

beam. Both lasers are placed perpendicular to the molecular beam and they are placedcounterpropagating to each other.

Experimentally, it is difficult to get both the spatial overlap and the timing betweenthe two lasers correct. The dye laser can easily be aligned, but because the light of theexcimer laser is absorbed by air, it is hard to align this laser beam: it is not possible to seethis beam coming out of the apparatus on the other side. To get the best spatial overlap,the dye laser beam enters and exits the apparatus in the center of the windows and it alsoenters and exits the excimer laser in the center of the windows. This is done with andwithout lenses on both sides. For the timing, the time between the trigger pulse of thepulse generator and the arrival of the light in front of the apparatus is measured for bothlasers with a photodiode and an oscilloscope. The resulting timings are given in figure4.4. For the photodissociation process, one has to make sure that the dye laser beam hitsthe molecular beam a few ns earlier than the excimer laser light.

Dye trigger

Excimer trigger

Dye light Excimer light

25 ns

150 ns

340 ns

Figure 4.4: A scheme with the timings for the dye laser and the excimer laser. The lasers aretriggered by different channels of the pulse generator. The dye laser needs a positive pulse and theexcimer laser needs a negative pulse. The pulse width is not given in this picture.

4.3 Detection

The detection chamber is pumped by a turbo pump, which is backed by a mechanicalpump. In this chamber, ion optics (also called electrostatic lenses) are placed, whichconsist of a repeller, extractor, and ground plate. Voltages are put on these plates toguide the molecules to the detector. First, the molecular beam is going through therepeller plate, on which a high positive voltage is put. Subsequently, the molecules areionized by the first laser and they will be photodissociated by the second laser. Behindthis region there is an extractor plate, on which a lower positive voltage is put. The ionsare moving through the extractor to the last one: the ground plate. Because this plateis grounded, the (positive) ions are attracted and so they are accelerated. They movethrough the ground plate and enter the time of flight (TOF) region. There, the ions withdifferent mass/charge (M/Z) ratios can be separated, because the ions with a lower M/Zvalue move faster than ions with a higher M/Z value: every ion gets the same kineticenergy.

After the TOF region, the ions are detected by two microchannel plates (MCPs). Onthe first plate a negative voltage is put, so the ions are attracted by this MCP. Whenan ion hits a microchannel, secondary electrons are produced, which move to the secondMCP with a positive value. Since the voltage at this MCP is positive, most of the electrons

4.3. DETECTION 40

accelerate into the MCP channels and, if they hit the channel walls, will generate addi-tional electrons, resulting in electron gain. When the electrons exit the channels, they areaccelerated and strike a phosphor screen, causing it to release photons. The light emittedby the phosphor screen is recorded by a charge-coupled device (CCD) camera, equippedwith an appropriate camera lens. The resulting image can be displayed on a computerscreen with the DaVis software from LaVision GmbH. Ions with the same speed hit thedetector at the same radius from the center and form rings. This is independent of theplace where the ions are produced and therefore velocity map imaging is the principle ofthis detection.

The first (negative) MCP is pulsed. By changing the delay of this pulse, ions with aspecific M/Z ratio can pass through the plates. In this way, one can use the selectivity ofthe REMPI process to select the signal of which ions is visible on the computer screen.

In figure 4.5 a diagram of the detection pathway is given with the pulsed valve, theskimmer, the ion optics, the laser beams, the time of flight region and the image that willappear on the computer screen after photodissociation by using VMI.

Figure 4.5: A diagram of the detection pathway.

Chapter 5

Results

The experimental research on the photodissociation of OH+ and H2O+ is not finished

yet, because of problems with the spatial overlap and the timing between the two lasers.Results that are given here are from H2O, HOD, and OH REMPI and an energy calibrationfor the apparatus.

5.1 H2O REMPI

Figure 5.1 shows an experimental H2O C1B1(v=0) - X1A1 (2+1) REMPI spectrum inred, compared with a theoretical PGOPHER simulation [74], which is given in black. Themost important transitions are labeled as J ′

K′aK

′c-J ′′

K′′aK

′′c, where J is the total rotational

angular momentum, Ka is the projection of J on the molecular a-axis, which lies in theplane of the molecule perpendicular to the C2 rotation axis (the molecular b-axis), andKc is the projection of J on the c-axis, which lies perpendicular to the molecular plane.J ′′K′′

aK′′crefers to the electronic ground state and J ′

K′aK

′crefers to the excited state.

The experimental spectrum is taken by integrating the signal in a rectangular areaof the detector (also called a rectangular scan) with the DaVis software, while scanningthe laser wavelength from 495 to 496 nm with scan steps of 0.001 nm. Four Pellin Brocacrystals are used to separate the frequency doubled light from the fundamental light andto stabilize the position of the beam when the wavelength is scanned. Argon carrier gaswas bubbled through pure liquid water at approximately 1 bar. The current on the Jordanvalve was 2.9 kA and with these settings, the pressure in the source chamber was 2.4·10−5

mbar and the pressure in the detection chamber was 5.0·10−7 mbar. The pressures in thesechambers when the valve was turned off were 1.9·10−7 and 2.9·10−7 mbar respectively. A20 cm lens was used to focus the laser light onto the molecular beam.

For the simulation, a rotational temperature of 10 K is used. The offset betweenthese two spectra was 3.7 cm−1. The positions of the experimental peaks are consistentwith the simulation, but the intensities are not fully consistent. This might be caused byfluctuations in the power of the laser during the experiment.

5.2 HOD REMPI

Although argon carrier gas was bubbled through pure liquid water, HOD molecules werealso present in the apparatus and these molecules were coming from the Jordan valve.

41

5.3. OH REMPI 42

80650 80700 80750 80800

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

H2O

+ s

igna

lexperimental

simulation (10 K)

220

−101

221

−000

322

−101

211

−110

202

−101

Figure 5.1: Experimental H2O C1B1(v=0) - X1A1 (2+1) REMPI spectrum (red) compared witha PGOPHER simulation (black). The rotational temperature of the simulation is 10 K. The mostimportant transitions are given as J ′

K′aK

′c-J ′′

K′′a K′′

c.

Figure 5.2 shows an experimental HOD C1B1(v=0) - X1A1 (2+1) REMPI spectrum inred, compared with a PGOPHER simulation in black [74]. The experimental spectrumis taken in the same way as the experimental spectrum for H2O. The signal of H2O wasmuch stronger, because there is much more H2O than HOD available. To get more HODsignal, the current on the Jordan valve was increased to 3.5 kA and with this setting,the pressure in the source chamber was 4.7·10−5 mbar and the pressure in the detectionchamber was 8.0·10−7 mbar. Moreover, higher voltages on the MCPs are used.

For the simulation of this spectrum, a rotational temperature of 10 K is used andthe offset between the two spectra is 2.8 cm−1. The positions of the experimental peaksare consistent with the simulation, but the intensities are not consistent. The signal tonoise ratio of this experimental spectrum is lower than for H2O, because there was morebackground signal.

5.3 OH REMPI

Figure 5.3 shows an experimental OH D2Σ−(v=0) - X2Π (2+1) REMPI spectrum inred, compared with a theoretical PGOPHER simulation, which is given in black. Theexperimental spectrum is taken by making a rectangular scan in DaVis, while scanningthe laser wavelength from 487.7 to 489.3 nm with scan steps of 0.001 nm. Argon carriergas was bubbled through pure liquid water at approximately 1 bar. The current on theJordan valve was 3.4 kA and with these settings, the pressure in the source chamberwas 4.9·10−5 mbar and the pressure in the detection chamber was 8.6·10−7 mbar. Thepressures in these chambers when the valve was turned off were both 2.9·10−7 mbar. A 20

5.3. OH REMPI 43

80700 80750 80800

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

HO

D+ s

igna

lexperimental

simulation (10 K)

211

−000

221

−000

Figure 5.2: Experimental HOD C1B1(v=0) - X1A1 (2+1) REMPI spectrum (red) compared witha PGOPHER simulation (black). The rotational temperature of the simulation is 10 K. Twotransitions are given as J ′

K′aK

′c-J ′′

K′′a K′′

c.

81850 81900 81950 82000

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

OH

+ s

igna

l

experimental

simulation (30 K)

1/2−3/2

3/2−3/2

1/2−3/2

5/2−3/2

3/2−3/2 5/2−3/2

7/2−3/2

Figure 5.3: Experimental OH D2Σ−(v=0) - X2Π (2+1) REMPI spectrum (red) compared with aPGOPHER simulation (black). The rotational temperature of the simulation is 35 K. The mostimportant transitions are given as J′-J′′.

5.4. ENERGY CALIBRATION 44

cm lens was used to focus the laser light onto the molecular beam. The discharge voltagewas 1.51 kV.

For the simulation, the constants from ref. [75] are used for the ground state and ref.[36] is used for the excited state. The rotational temperature of the simulated spectrum is30 K and the Gaussian contribution to the linewidth is 6 cm−1. The offset between thesetwo spectra was 15 cm−1, which is larger than expected. When this offset is used, thepositions of the experimental peaks are consistent with the simulation, but the intensitiesare not fully consistent. The tails of the peaks to the high energy side indicate that thelaser power was too high for this measurement.

5.4 Energy calibration

As described in section 2.4, the radius of the image on the detector is a direct measure ofthe kinetic energy of the fragments. This radius also depends on the repeller voltage. Fora certain repeller voltage, the energy can be calibrated by using a system for which theenergy is already known. In this case, O2 photodissociation with 157 nm light from theexcimer laser is used for this calibration, because this process has been studied before inanother apparatus and the energies in that apparatus are calibrated. Pure oxygen with abacking pressure of 1 bar was used and the current on the Jordan valve was 3.2 kA. Animage is taken from the O(1D) fragments, which is given in figure 5.4. In this figure, thetotal kinetic energy release of each ring is given. For this image, a repeller voltage of 3 kVwas used. In this case, total kinetic energy releases up to ∼ 3 eV can be detected. Thisis just a rough energy calibration and the energies are not very accurate. For a bettercalibration, a new image has to be taken.

0.8 eV

1.9 eV

2.8 eV

Figure 5.4: An O+ image from O2 photodissociation at 157 nm, which is used for the calibrationof the energy when a certain repeller voltage is used. For this image, the voltage on the repeller is3 kV.

5.5. H2O REMPI AND OH+ IMAGES 45

5.5 H2O REMPI and OH+ images

At three slightly different H2O REMPI wavelengths, the OH+ signal was checked. Threedifferent transitions are taken, to compare the images with each other and to see if theOH+ signal depends on the REMPI transition. For this experiment, only the Nd:YAGpumped dye laser was used, to produce light with a wavelength around 248 nm. Theresultant images are shown in figure 5.5. In figure 5.5a to 5.5c, the raw images are givenand in figure 5.5d to 5.5f, the Abel inverted images are shown. For the Abel inversionprocess, the JPV program is used, which is implemented in the DaVis software.

From these images it can be seen, that the OH+ signal is wavelength dependent. Sageet al. [31] have also detected OH+ signal from this H2O REMPI process. They give asmost likely explanation for this signal, that the fragments arise from dissociative ionizationfollowing absorption of four photons by neutral H2O molecules. With the energy calibra-tion, described in section 5.4, it can be calculated that the TKER for these fragments is∼ 4000 cm−1 (∼ 0.5 eV), which is in good agreement with ref. [31]. Sage et al. did notdescribe the wavelength dependency of the OH+ signal. To give an explanation for thisdependency, a more accurate energy calibration is needed. Moreover, images can be takenwith a smaller repeller voltage to obtain larger images and to be more accurate for a smallTKER.

(a) The 220 − 101 transition (b) The 211 − 110 transition (c) The 202 − 101 transition

(d) The 220 − 101 transition (JPV) (e) The 211 − 110 transition (JPV) (f) The 202 − 101 transition (JPV)

Figure 5.5: OH+ images for three different REMPI transitions of H2O. In figure (a) to (c), the rawdata are given and in figure (d) to (f), the Abel inverted images are given.

Chapter 6

Conclusion

The aim of the current research was, to study the photodissociation process of OH+ boththeoretically and experimentally and to study this process for H2O

+ in an experimentalway.

For OH+, potential energy curves are computed for the electronic ground state and 17electronically excited states. This is done by using the MOLPRO program for ab initiocalculations. When these curves are compared with curves from the literature, they havesimilar shapes. An important difference is, that all the current curves dissociate to theright dissociation limit. In literature, the X3Σ− ground state and the 23Σ− state alwaysdissociate to the wrong limit. In a few articles, some possible solutions are given to solvethis problem, but it has never been done correctly before. The current curves are in goodagreement with experimental values for spectroscopic constants. Photodissociation crosssections are calculated for the transitions from the X3Σ− ground state to the dissociativeportion of the A3Π state and to the excited 23Σ−, 33Σ−, 23Π and 33Π states. Thesecross sections are in good agreement with the literature and they can be used to predictwhether a certain wavelength in the range from 50 to 260 nm will be suitable for thephotodissociation experiments.

Experimentally, REMPI spectra are taken for H2O, HOD and OH. These spectra arein good agreement with simulations, made with the PGOPHER program. The energiesthat can be detected with a certain repeller voltage are calibrated with O2 dissociation at157 nm. With a voltage of 3 kV on the repeller, kinetic energy releases up to ∼ 3 eV canbe detected. At three different H2O REMPI wavelengths, OH+ images are taken. TheOH+ fragments are most probably formed by dissociative ionization following 4 photonabsorption by H2O. Because of problems with the spatial overlap and the timing betweenthe two lasers (an Nd:YAG pumped dye laser and an excimer laser), the photodissociationprocess of H2O

+ and OH+ at 157 nm could not been studied yet.For future theoretical research, the spin-orbit coupling could be taken into account

during the ab initio calculations, to get even more accurate potential energy curves forOH+. Experimentally, the photodissociation process of H2O

+ and OH+ can be studied byusing VUV light. Using the results of the ab initio calculations for OH+, 157 nm seems tobe an unfavorable wavelength for photodissociation. Other VUV wavelengths, which caneasily be produced in the lab, are 193 and 118 nm. From the calculated photodissociationcross sections as function of the wavelength, it seems that these wavelengths are also notsuitable for photodissociation. From the cross sections, it follows that 70 to 80 nm is thebest wavelength for photodissociation of OH+.

46

47

Other isotopologues for which the photodissociation process can also be studied areOD+, D2O

+ and HOD+. This might be easier, because images for D+ are easier to takethan images for H+, because of the amount of background signal and the high speeds ofH+. For these isotopoloques and for H2O

+, ab initio calculations could be performed tobetter understand the photodissociation reactions.

References

[1] Z. Amitay, D. Zajfman, et al., Phys. Rev. A. 53, R644 (1996).

[2] X. Li and J. Paldus, J. Mol. Struc.-Theochem 527, 165 (2000).

[3] T. J. Millar, IAU Symp. 231, 119 (2005).

[4] H. Helm, P. C. Cosby, et al., Phys. Rev. A. 30, 851 (1984).

[5] D. J. Rodgers and P. J. Sarre, Chem. Phys. Lett. 143, 235 (1988).

[6] B. D. Rehfuss, M. Jagod, et al., J. Mol. Spectrosc. 151, 59 (1992).

[7] J. Levin, U. Hechtfischer, et al., Hyperfine Interact. 127, 267 (2000).

[8] D. J. Rodgers, A. D. Batey, et al., Mol. Phys. 105, 849 (2007).

[9] G. Herzberg, Ann. Geophys. (Centre National de la Recherche Scientifique) 36, 605(1980).

[10] W. T. Huntress, Astrophys. J. Supplement Series 33, 495 (1977).

[11] R. A. Morris, A. A. Viggiano, et al., J. Phys. Chem. 96, 3051 (1992).

[12] P. Gammelgaard and B. Thomsen, Astron. Astrophys. 197, 320 (1988).

[13] M. E. Brown, A. H. Bouchez, et al., Astron. J. 112, 1197 (1996).

[14] H. Balsiger, K. Altwegg, et al., Nature 321, 330 (1986).

[15] W. H. Ip, U. Fink, et al., Astrophys. J. 293, 609 (1985).

[16] K. Jockers, T. Credner, et al., Astron. Astrophys. 335, L56 (1998).

[17] F. D. Miller, Astron. J. 85, 468 (1980).

[18] V. Ossenkopf, H. S. P. Muller, et al., Astron. Astrophys. 518, L111 (2010).

[19] P. Schilke, C. Comito, et al., Astron. Astrophys. 521, L11 (2010).

[20] H. Rottke, C. Trump, et al., J. Phys. B: At. Mol. Opt. Phys. 31, 1083 (1998).

[21] B. W. Uselman, J. M. Boyle, et al., Chem. Phys. Lett. 440, 171 (2007).

[22] C. Duan, R. Zheng, et al., J. Mol. Spectrosc. 251, 22 (2008).

48

REFERENCES 49

[23] J. C. Leclerc, J. A. Horsley, et al., Chem. Phys. 4, 337 (1974).

[24] G. Osmann, P. R. Bunker, et al., Chem. Phys. Lett. 318, 597 (2000).

[25] A. P. Levick, T. E. Masters, et al., Phys. Rev. Lett. 63, 2216 (1989).

[26] D. R. Yarkony, J. Phys. Chem. 97, 111 (1993).

[27] F. Fiquet-Fayard and P. M. Guyon, Mol. Phys. 11, 17 (1966).

[28] A. J. Lorquet and J. C. Lorquet, Chem. Phys. 4, 353 (1974).

[29] J. H. D. Eland, Chem. Phys. 11, 41 (1975).

[30] T. Hayaishi, A. Yagishita, et al., J. Phys. B: At. Mol. Phys. 20, L207 (1987).

[31] A. G. Sage, T. A. A. Oliver, et al., Mol. Phys. 108, 945 (2010).

[32] T. Engel and W. Hehre, “Quantum Chemistry & Spectroscopy,” (Pearson Education,Inc, 2010) Chap. 16.

[33] D. M. Hirst and M. F. Guest, Mol. Phys. 49, 1461 (1983).

[34] G. A. Blake, “Chemistry 21b - Spectroscopy,” http://www.gps.caltech.edu/∼gab/ch21b/lectures/lecture15.pdf (2009).

[35] R. De Vivie, C. M. Marian, et al., Chem. Phys. 112, 349 (1987).

[36] M. Collard, P. Kerwin, et al., Chem. Phys. Lett. 179, 422 (1991).

[37] M. N. R. Ashfold, J. M. Bayley, et al., Chem. Phys. 84, 35 (1984).

[38] D. c. Radenovic, Photodissociation and photoionization studies of the OH free radical,Ph.D. thesis, Radboud University Nijmegen (2007).

[39] A. T. J. B. Eppink and D. H. Parker, Rev. Sci. Instrum. 68, 3477 (1998).

[40] D. W. Chandler and P. L. Houston, J. Chem. Phys. 87, 1445 (1987).

[41] A. J. R. Heck and D. W. Chandler, Annu. Rev. Phys. Chem. 46, 335 (1995).

[42] D. W. Chandler and D. H. Parker, Adv. Photochem. 25, 56 (1999).

[43] A. T. J. B. Eppink, Photodissociation of CH3I and O2 studied by velocity map imaging,Ph.D. thesis, Radboud University Nijmegen (1999).

[44] B. L. G. Bakker, Photofragmentation dynamics of highly excited diatomic molecules,Ph.D. thesis, Radboud University Nijmegen (2001).

[45] H.-J. Werner, P. Knowles, et al., “MOLPRO, version 2010.1, a package of ab initioprograms,” http://www.molpro.net (2010).

[46] H. P. D. Liu and G. Verhaegen, Int. J. quant. Chem. S5, 103 (1971).

[47] P. Rosmus and W. Meyer, J. Chem. Phys. 66, 13 (1977).

REFERENCES 50

[48] H.-J. Werner, P. Rosmus, et al., J. Chem. Phys. 79, 905 (1983).

[49] R. P. Saxon and B. Liu, J. Chem. Phys. 85, 2099 (1986).

[50] J. A. Spirko, J. T. Mallis, et al., J. Phys. B: At. Mol. Opt. Phys. 33, 2395 (2000).

[51] G. Herzberg, “Molecular Spectra and Molecular Structure I. Spectra of DiatomicMolecules,” (Van Nostrand Company, Inc, 1950) Chap. VI.

[52] J. Brown and A. Carrington, “Rotational Spectroscopy of Diatomic Molecules,”(Cambridge University Press, 2003) Chap. 5.

[53] Y. Ralchenko, A. E. Kramida, et al., “NIST Atomic Spectra Database (version 4.0),”http://physics.nist.gov/asd (2010).

[54] T. Engel and W. Hehre, “Quantum Chemistry & Spectroscopy,” (Pearson Education,Inc, 2010) Chap. 15.3.

[55] C. J. Cramer, “Essentials of Computational Chemistry: Theory and Models,” (JohnWiley & Sons, Ltd, 2004) Chap. 7.2.

[56] H.-J. Werner and P. J. Knowles, J. Chem. Phys. 82, 5053 (1985).

[57] P. J. Knowles and H.-J. Werner, Chem. Phys. Lett. 115, 259 (1985).

[58] T. Engel and W. Hehre, “Quantum Chemistry & Spectroscopy,” (Pearson Education,Inc, 2010) Chap. 15.6.1.

[59] H.-J. Werner and P. J. Knowles, J. Chem. Phys. 89, 5803 (1988).

[60] P. J. Knowles and H.-J. Werner, Chem. Phys. Lett. 145, 514 (1988).

[61] H.-J. Werner, P. Knowles, et al., “MOLPRO, version 2010.1, a package of abinitio programs,” http://www.molpro.net/info/current/doc/manual/node306.

html (2011).

[62] T. H. Dunning, J. Chem. Phys. 90, 1007 (1989).

[63] D. Feller, J. Comp. Chem. 17, 1571 (1996).

[64] K. L. Schuchardt, B. T. Didier, et al., J. Chem. Inf. Model. 47, 1045 (2007).

[65] T. Engel and W. Hehre, “Quantum Chemistry & Spectroscopy,” (Pearson Education,Inc, 2010) Chap. 15.7.

[66] M. Merchan, P.-A. Malmqvist, et al., Theor. Chim. Acta. 79, 81 (1991).

[67] E. A. Gislason, F. E. Budenholzer, et al., Chem. Phys. Lett. 47, 434 (1977).

[68] D. J. Griffiths, “Introduction to Electrodynamics,” (Pearson Benjamin Cummings,2008) Chap. 4.1.

[69] F. Vesely, “Computational Physics: an introduction,” (Kluwer Academic/PlenumPublishers, 2001) Chap. 4.2.6.

REFERENCES 51

[70] A. J. Merer, D. N. Malm, et al., Can. J. Phys. 53, 251 (1975).

[71] P. Atkins and J. de Paula, “Physical Chemistry,” (Oxford University Press, 2001)Chap. 21.7.

[72] W. R. Gentry and C. F. Giese, Rev. Sci. Instrum. 49, 595 (1978).

[73] I. Jordan TOF Products, “Instruction manual PSV pulsed supersonic valve PSV P.S.PC BOARD REV 4A,” .

[74] C. M. Western, “PGOPHER, a Program for Simulating Rotational Structure, Univer-sity of Bristol,” http://www.chm.bris.ac.uk/pgopher/Help/h20cx.htm. The fileH2OCX.pgo is used. (2010).

[75] T. D. Varberg and K. M. Evenson, J. Mol. Spectrosc. 157, 55 (1993).

[76] C. M. Western, “PGOPHER, version 7.0.101 and 7.1.202, a Program for SimulatingRotational Structure,” http://pgopher.chm.bris.ac.uk/ (2011).

[77] M. A. Hines, H. A. Michelsen, et al., J. Chem. Phys. 93, 8557 (1990).

[78] J. Baker, J. L. Lemaire, et al., Chem. Phys. 178, 569 (1993).

[79] C. M. Western, “PGOPHER, a Program for Simulating Rotational Structure, Uni-versity of Bristol,” http://pgopher.chm.bris.ac.uk/Help/nh3x.htm (2011).

[80] M. N. R. Ashfold, R. N. Dixon, et al., J. Chem. Phys. 89, 1754 (1988).

Appendix A

The ab initio calculations

In this appendix, some extra information is given about the AVTZ basis set and the inputfile for the ab initio calculations with MOLPRO.

A.1 The basis set

As described in section 3.3.1, the AVTZ basis set is chosen in MOLPRO for all ab initiocalculations of the potential energy curves for OH+.

In MOLPRO, the basis set that is used can be printed in the output file. The AVTZbasis set is given below. In the first column of this table, the number of the function isgiven. Number 1.1 for example means, that this is the first function with symmetry 1.In the second column, the symmetry is given. Symmetry 1 corresponds to A1, symmetry2 to B1, symmetry 3 to B2 and symmetry 4 to A2. In the third column, the nucleuson which the basis function is centered is given. Nucleus 1 is the oxygen atom and 2 isthe hydrogen atom. In the next column, the function type is given (s, p, d or f). Thenthe exponent for the Gaussian function is given (α in equation 3.8) and after that thecontraction coefficients for the function are given. These are the coefficients for the linearcombinations of Gaussian functions, as explained in section 3.3.1.

Nr Sym Nuc Type Exponents Contraction coefficients1.1 A1 1 1s 15330.000000 0.000508 -0.000115 0.000000 0.0000002.1 A1 2299.000000 0.003929 -0.000895 0.000000 0.0000003.1 A1 522.400000 0.020243 -0.004636 0.000000 0.0000004.1 A1 147.300000 0.079181 -0.018724 0.000000 0.000000

47.550000 0.230687 -0.058463 0.000000 0.00000016.760000 0.433118 -0.136463 0.000000 0.0000006.207000 0.350260 -0.175740 0.000000 0.0000001.752000 0.042728 0.160934 1.000000 0.0000000.688200 -0.008154 0.603418 0.000000 0.0000000.238400 0.002381 0.378765 0.000000 1.000000

5.1 A1 1 1s 0.073760 1.0000006.1 A1 1 2pz 34.460000 0.015928 0.000000 0.0000007.1 A1 7.749000 0.099740 0.000000 0.0000008.1 A1 2.280000 0.310492 0.000000 0.000000

0.715600 0.491026 1.000000 0.0000000.214000 0.336337 0.000000 1.000000

9.1 A1 1 2pz 0.059740 1.000000

52

A.1. THE BASIS SET 53

10.1 A1 1 3d0 2.314000 1.00000011.1 A1 1 3d2+ 2.314000 1.00000012.1 A1 1 3d0 0.645000 1.00000013.1 A1 1 3d2+ 0.645000 1.00000014.1 A1 1 3d0 0.214000 1.00000015.1 A1 1 3d2+ 0.214000 1.00000016.1 A1 1 4f0 1.428000 1.00000017.1 A1 1 4f2+ 1.428000 1.00000018.1 A1 1 4f0 0.500000 1.00000019.1 A1 1 4f2+ 0.500000 1.00000020.1 A1 2 1s 33.870000 0.006068 0.000000 0.00000021.1 A1 5.095000 0.045308 0.000000 0.00000022.1 A1 1.159000 0.202822 0.000000 0.000000

0.325800 0.503903 1.000000 0.0000000.102700 0.383421 0.000000 1.000000

23.1 A1 2 1s 0.025260 1.00000024.1 A1 2 2pz 1.407000 1.00000025.1 A1 2 2pz 0.388000 1.00000026.1 A1 2 2pz 0.102000 1.00000027.1 A1 2 3d0 1.057000 1.00000028.1 A1 2 3d2+ 1.057000 1.00000029.1 A1 2 3d0 0.247000 1.00000030.1 A1 2 3d2+ 0.247000 1.0000001.2 B1 1 2px 34.460000 0.015928 0.000000 0.0000002.2 B1 7.749000 0.099740 0.000000 0.0000003.2 B1 2.280000 0.310492 0.000000 0.000000

0.715600 0.491026 1.000000 0.0000000.214000 0.336337 0.000000 1.000000

4.2 B1 1 2px 0.059740 1.0000005.2 B1 1 3d1+ 2.314000 1.0000006.2 B1 1 3d1+ 0.645000 1.0000007.2 B1 1 3d1+ 0.214000 1.0000008.2 B1 1 4f1+ 1.428000 1.0000009.2 B1 1 4f3+ 1.428000 1.00000010.2 B1 1 4f1+ 0.500000 1.00000011.2 B1 1 4f3+ 0.500000 1.00000012.2 B1 2 2px 1.407000 1.00000013.2 B1 2 2px 0.388000 1.00000014.2 B1 2 2px 0.102000 1.00000015.2 B1 2 3d1+ 1.057000 1.00000016.2 B1 2 3d1+ 0.247000 1.0000001.3 B2 1 2py 34.460000 0.015928 0.000000 0.0000002.3 B2 7.749000 0.099740 0.000000 0.0000003.3 B2 2.280000 0.310492 0.000000 0.000000

0.715600 0.491026 1.000000 0.0000000.214000 0.336337 0.000000 1.000000

4.3 B2 1 2py 0.059740 1.0000005.3 B2 1 3d1- 2.314000 1.0000006.3 B2 1 3d1- 0.645000 1.0000007.3 B2 1 3d1- 0.214000 1.0000008.3 B2 1 4f1- 1.428000 1.0000009.3 B2 1 4f3- 1.428000 1.00000010.3 B2 1 4f1- 0.500000 1.000000

A.2. A MOLPRO INPUT FILE 54

11.3 B2 1 4f3- 0.500000 1.00000012.3 B2 2 2py 1.407000 1.00000013.3 B2 2 2py 0.388000 1.00000014.3 B2 2 2py 0.102000 1.00000015.3 B2 2 3d1- 1.057000 1.00000016.3 B2 2 3d1- 0.247000 1.0000001.4 A2 1 3d2- 2.314000 1.0000002.4 A2 1 3d2- 0.645000 1.0000003.4 A2 1 3d2- 0.214000 1.0000004.4 A2 1 4f2- 1.428000 1.0000005.4 A2 1 4f2- 0.500000 1.0000006.4 A2 2 3d2- 1.057000 1.0000007.4 A2 2 3d2- 0.247000 1.000000

A.2 A MOLPRO input file

In MOLPRO, all information for a computation is given in an input file. Here, the inputfile for the calculation of the potential energy curve for the 5Σ− state is given as anexample.

#!/bin/csh -f

gprint,orbitals,civector details, printed in the output file

geometry=O; H,O,rOH Z-matrix

basis=avtz basis set

r=[2 1.75 1.5 1.4 1.3 1.2 1.1 1] the grid for the potential energy curve

rOH = 2 the equilibrium internuclear distance

rhf Hartree-Fock

wf,8,4,2 the specifications for the wavefunction

do i=1,#r start a do loop

rOH=r(i)

multi MCSCF

wf,8,4,4

ci MRCI

wf,8,4,4

enddo end a do loop

Appendix B

Results of the ab initiocalculations

In table B.1, some detailed results of the ab initio calculations for OH+ are given. For eachelectronic state, the energy of the CI calculation with Davidson correction (CI+Q) in eVat an internuclear distance of 1.96 a0 (the equilibrium internuclear distance of the groundstate) is given. The excitation energy from the ground state to each excited state is alsogiven at this distance. These values are calculated from the CI energies with Davidsoncorrection. For the dissociation limit at an internuclear distance of 20 a0, the limit andthe CI energy with Davidson correction are given.

Table B.1: Detailed results of the ab initio calculations for OH+

CI+Q (eV) Excitation energy (eV) Dissociation limit CI+Q (eV)State R = 1.96 a0 R = 1.96 a0 R = 20 a0 R = 20 a0X3Σ− -5.22275828 - O(3P) + H+ -0.00046660a1∆ -3.05141696 2.17134131 O(1D) + H+ 1.96692021A3Π -1.48469246 3.73806582 O(3P) + H+ -0.02509125b1Σ+ -1.62314140 3.59961688 O(1D) + H+ 1.9669204811Π 0.51786630 5.74062457 O(1D) + H+ 1.9669614921Σ+ 5.48150196 10.70426024 O(1S) + H+ 4.189285275Σ− 8.39650505 13.61926332 O+(4S) + H 0.0200019123Π 10.21705689 15.43981516 O+(2D) + H 3.3440839123Σ− 10.65116488 15.87392316 O+(4S) + H 0.0200057221Π 11.03277744 16.25553572 O+(2D) + H 3.344088813∆ 12.04249233 17.26525061 O+(2D) + H 3.345326111Σ− 12.54087841 17.76363669 O+(2D) + H 3.3465734833Π 12.76991857 17.99267684 O+(2P) + H 5.0374088533Σ− 12.74359615 17.96635443 O+(2D) + H 3.346579473Σ+ 13.46167095 18.68442922 O+(2P) + H 5.0373927921∆ 14.49726772 19.72002600 O+(2D) + H 3.3465734831Σ+ 16.04716071 21.26991899 O+(2P) + H 5.0376504831Π 16.76503820 21.98779647 O+(2P) + H 5.03765484

Let the z-axis be the internuclear axis. For all the calculations, the center of mass ofOH+ is fixed at 0, the nucleus of the oxygen atom is situated on the positive z-axis and thenucleus of the hydrogen atom on the negative z-axis. When the internuclear distance is 20bohr, the nucleus of the oxygen atom lies at -1.185 bohr and the nucleus of the hydrogen

55

56

atom lies at 18.81 bohr. The dipole moment µz is defined as:

µz = zOQO + zHQH , (B.1)

where zO and zH are the z coordinates and QO and QH are the charges of the oxygenand hydrogen nuclei. At large internuclear distances, the charge of one of the two nucleiis almost 1 and the charge on the other nucleus is almost 0. When the dissociation limitis O+H+, the dipole moment should be almost 18.81 a.u. (47.81 D) and for the O++Hdissociation limit, the dipole moment should be close to -1.185 (-3.012 D). From the dipolemoments at an internuclear distance of 20 a0, the dissociation limits are determined foreach state.

In figure B.1, all calculated potential energy curves are shown. The curves are sortedby their dissociation limit.

57

12

34

56

78

−6

−4

−2024

R (

a 0)

Energy (eV)

X3 Σ−

A3 Π

(a)O(3P)+

H+

12

34

56

78

−4

−2024

R (

a 0)

Energy (eV)

a1 ∆b1 Σ+

11 Π

(b)O(1D)+

H+

12

34

56

78

345678910

R (

a 0)

Energy (eV)

21 Σ+

(c)O(1S)+

H+

12

34

56

78

−1012345678

R (

a 0)

Energy (eV)

5 Σ−

23 Σ−

(d)O

+(4S)+

H

12

34

56

78

3456789

R (

a 0)

Energy (eV)

23 Π21 Π3 ∆ 1 Σ−

33 Σ−

21 ∆

(e)O

+(2D)+

H

12

34

56

78

46810121416

R (

a 0)

Energy (eV)

33 Π3 Σ+

31 Σ+

31 Π

(f)O

+(2P)+

H

Figure

B.1:Thepotential

energy

curves

that

arecalculated.In

each

figu

re,allstates

dissociateto

thesamelimit.

Appendix C

Simulations

During my internship, I also made some simulations in PGOPHER [76] for other projects.The main results are given in this appendix.

C.1 CO

For the work of Chandan Bishwakarma on the CO molecule, I made a simulation of theE1Π - X1Σ+ (2+1) REMPI spectrum. The constants given in ref. [77] are used for theground and the excited state. The band origin of the excited state is from ref. [78]. Therotational temperature of the simulation is 2.6 K and the offset between the two spectra is 2cm−1. For the simulation, the Gaussian contribution to the linewidth is (at full width halfmaximum) 1.2 cm−1. The result is given in figure C.1. The resolution of the experimentalspectrum is not so good, but the positions and relative intensities are in good agreementwith the simulation.

C.2 Ammonia

For the work of Ashim Kumar Saha on ammonia, I made simulations for several vibra-tional bands of the B1E” - X1A1’ (2+1) REMPI transition in NH3 and ND3. For this, Iadjusted simulations of Chung-Hsin Yang and Colin Western. For the electronic groundstate of both molecules, constants from ref. [79] are used and for the excited state, theconstants are from ref. [80]. For the ground state, the inversion doublets are taken intoaccount. For transitions to even vibrational levels (E” symmetry) of the excited state, theinversion doublet with the lowest energy (A1’ symmetry) is used and for transitions to oddvibrational levels (E’ symmetry), the other inversion doublet (A2” symmetry) is used forthe ground state. Three perturbations between the inversion doublets are also included inthe simulation.

In figure C.2 to C.4, the experimental and simulated spectra are given for three vi-brational bands of NH3. The experimental spectrum is given in red and the PGOPHERsimulation is given in black. For all three simulations, the rotational temperature is 2 Kand the spin temperature is 300 K. The Gaussian contribution to the linewidth for thesimulations is 4 cm−1 for figure C.2 and C.3 and 2 cm−1 for figure C.4. The resolution ofthe experimental spectra has to be improved for a better comparison with the simulations.The positions of the experimental peaks are in good agreement with the simulations. To

58

C.2. AMMONIA 59

92920 92930 92940 92950 92960

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

CO

sig

nal

experimental

simulation (2.6 K)

Figure C.1: Experimental CO E1Π - X1Σ+ (2+1) REMPI spectrum (red) compared with a PGO-PHER simulation (black). The rotational temperature of the simulation is 2.6 K.

improve the agreement of the relative intensities of the peaks with the simulations, theexperimental spectra have to be measured again with an optimized laser power and byusing a lens with a larger focal length. Then the wavelength also has to be measured (witha wavemeter) or calibrated during the measurement to minimize the offset between theexperimental and simulated spectra. For the new experimental spectra, the simulationmight also be optimized, by varying the rotational and spin temperatures and by alsousing a Lorentzian contribution to the linewidth.

In figure C.5 to C.10, the experimental and simulated spectra are given for six vi-brational bands of ND3. The experimental spectrum is given in red and the PGOPHERsimulation is given in black. For all the simulations, the spin temperature is 300 K. TheGaussian contribution to the linewidth for the simulations is 4 cm−1 for figure C.5 andC.6, 1.2 cm−1 for figure C.7, C.9, and C.10, and 1 cm−1 for figure C.8. For these exper-imental spectra, the resolution has to be improved and the spectra have to be measuredagain with an optimized laser power and by using a lens with a larger focal length. Thisis for the same reasons as for the spectra of NH3. The positions of the experimental peaksare in good agreement with the simulations.

C.2. AMMONIA 60

60050 60100 60150 60200 60250 60300

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

NH

3 sig

nal

experimental

simulation (2 K)

Figure C.2: NH3 B1E”(v=1) - X1A1’ (2+1) REMPI spectrum. The offset between the two spectrais 1 cm−1.

61000 61050 61100 61150 61200

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

NH

3 sig

nal

experimental

simulation (10 K)

Figure C.3: NH3 B1E”(v=2) - X1A1’ (2+1) REMPI spectrum. The offset between the two spectrais 1 cm−1.

C.2. AMMONIA 61

62950 63000 63050 63100

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

NH

3 sig

nal

experimental

simulation (5 K)

Figure C.4: NH3 B1E”(v=4) - X1A1’ (2+1) REMPI spectrum. The offset between the two spectrais 1.2 cm−1.

60050 60100 60150

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

ND

3 sig

nal

experimental

simulation (5 K)

Figure C.5: ND3 B1E”(v=1) - X1A1’ (2+1) REMPI spectrum. The offset between the two spectrais 0.44 cm−1.

C.2. AMMONIA 62

60750 60800 60850

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

ND

3 sig

nal

experimental

simulation (5 K)

Figure C.6: ND3 B1E”(v=2) - X1A1’ (2+1) REMPI spectrum. The offset between the two spectrais 0.44 cm−1.

61500 61520 61540 61560

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

ND

3 sig

nal

experimental

simulation (4 K)

Figure C.7: ND3 B1E”(v=3) - X1A1’ (2+1) REMPI spectrum. The offset between the two spectrais 4.7 cm−1.

C.2. AMMONIA 63

62240 62260 62280 62300

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

ND

3 sig

nal

experimental

simulation (4 K)

Figure C.8: ND3 B1E”(v=4) - X1A1’ (2+1) REMPI spectrum. The offset between the two spectrais 4.5 cm−1.

62980 63000 63020 63040

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

ND

3 sig

nal

experimental

simulation (5 K)

Figure C.9: ND3 B1E”(v=5) - X1A1’ (2+1) REMPI spectrum. The offset between the two spectrais 0.9 cm−1.

C.2. AMMONIA 64

63750 63760 63770 63780 63790 63800

−1

−0.5

0

0.5

1

Two−photon energy (cm−1)

Nor

mal

ized

ND

3 sig

nal

experimental

simulation (6 K)

Figure C.10: ND3 B1E”(v=6) - X1A1’ (2+1) REMPI spectrum. The offset between the two spectra

is 6.2 cm−1.