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Ionization processes and
photofragmentation via multiphoton
excitation and state interactions
Kristján Matthíasson
Ionization processes and
photofragmentation via multiphoton
excitation and state interactions
Kristján Matthíasson
Dissertation submitted in partial fulfillment of a
Philosophiae Doctor degree in Physical Chemistry
Advisor
Ágúst Kvaran
PhD Committee
Oddur Ingólfsson
Ingvar Helgi Árnason
Gísli Hólmar Jóhannesson
Opponents
Christof Maul
Ragnar Jóhannsson
Faculty of Physical Sciences
School of Engineering and Natural Sciences
University of Iceland
Reykjavík, October 2011
Ionization processes and photofragmentation via multiphoton excitation
and state interactions
Dissertation submitted in partial fulfillment of a Philosophiae Doctor
degree in Physical Chemistry
Copyright © 2011 Kristján Matthíasson
All rights reserved
Faculty of Physical Sciences
School of Engineering and Natural Sciences
University of Iceland
Dunhagi 3
107, Reykjavik
Iceland
Telephone: 525 4000
Bibliographic information:
Kristján Matthíasson, 2011, Ionization processes and photofragmentation
via multiphoton excitation and state interactions, PhD dissertation,
Faculty of Physical Sciences, University of Iceland.
ISBN 978-9979-9935-9-9
Printing: Háskólaprent ehf.
Reykjavik, Iceland, October 2011
Abstract
My Ph.D. work was centered on observing the relative formation of
separate molecular and atomic fragments. This led to the development of
a new method for measuring and analysing data entailing the
simultaneous collection of mass and frequency data over a specific mass
area and frequency range, resulting in a detailed 2D map of the measured
area. From this map both a REMPI spectrum and a mass spectrum could
be extracted as needed.
Three separate molecules were studied, acetylene (C2H2), hydrogen
chloride (HCl) and methyl bromide (CH3Br). By observing the relative
formation of separate atoms and molecular fragments by photoexcitation
as function of laser power and frequency it was possible to determine the
dissociation mechanics for these molecules.
For HCl, the relative intensity of Cl+/HCl+ ions that formed via
photoexcitation proved to be a highly sensitive indicator of perturbation
between Rydberg and ion-pair states. A mathematical model was
developed to evaluate state interaction strengths from the relative
intensity of Cl+/HCl+ ions and the interaction strengths of several states
were calculated. The relative intensity of Cl+/HCl+ ions proved also to be
a highly useful tool in spectrum assignment.
iii
Útdráttur
Athugun á myndun sameinda- og atómbrota við ljósörvun var
þungamiðja doktorsverkefnis míns. Það leiddi til þróunar á nýjum
hugbúnaði og aðferðafræði við að safna og greina gögn með það‚ í huga
að safna samtímis massa og tíðni gögnum yfir tiltekið mælisvið. Þessi
aðferð myndar tvívíddar kort af mælisviðinu. Úr þessu korti má svo draga
fram bæði massaróf fyrir tiltekna tíðni jafnt og tíðniróf fyrir tiltekin
massa eftir þörfum.
Þrjár mismunandi sameindir voru rannsakaðar, asetýlen (C2H2), saltsýra
(HCl) og metýlbrómíð (CH3Br). Með því að bera saman hlutfallslega
massamyndun þeirra atóma eða sameindabrota sem myndast við
ljósörvun var hægt að ráða í niðurbrotsferla þessara sameinda.
Hlutfallslegur styrkur Cl+/HCl+ jóna sem mynduðust við ljósörvun á HCl
reyndist vera mjög nákvæmur vísir að víxlverkun milli Rydberg og
jónparaástanda fyrir bæði H35Cl og H37Cl samsæturnar. Stærðfræðilíkan
var þróað til að meta víxlverkunarstyrkinn út frá hlutföllum Cl +/HCl+ og
víxlverkunarstyrkur reiknaður fyrir nokkur ástönd. Þetta hlutfall reyndist
einnig vera nothæft tæki til að skilgreina litróf.
iv
Table of Contents
List of Figures ........................................................................................ vii
List of Tables ............................................................................................ x
List of abbreviations ...............................................................................xi
Acknowledgements............................................................................... xiii
1 Introduction ....................................................................................... 15
1.1 Acetylene (C2H2) ...................................................................... 16
1.2 Hydrogen Chloride (HCl) ......................................................... 17
1.3 Methyl bromide (CH3Br) .......................................................... 19
2 Experimental setup and analysis method ....................................... 21
2.1 Experimental apparatus ............................................................ 21
2.2 Analysis Method ....................................................................... 23
2.2.1 Simulations ..................................................................... 25
2.2.2 Time of flight analysis.................................................... 26
3 Theoretical considerations ............................................................... 27
3.1 Electronic spectroscopy of diatomic molecules72-74.................. 27
3.1.1 Electronic energy levels. ................................................ 27
3.1.2 Vibrational energy levels................................................ 29
3.1.3 Rotational energy levels ................................................. 31
3.2 The intensity of electronic excitation spectroscopy lines7274
................................................................................................ 34
3.2.1 Transition probabilities................................................... 34
3.2.2 Boltzmann distribution ................................................... 35
3.2.3 Laser power dependence ................................................ 37
3.2.4 Multiphoton excitation intensities .................................. 38
3.3 Total angular momentum and Hund’s cases72 .......................... 39
3.3.1 Hund’s case a) ................................................................ 40
3.3.2 Hund’s case b) ................................................................ 42
3.3.3 Hund’s case c) ................................................................ 42
3.4 Symmetry properties72 .............................................................. 43
v
3.4.1 Parity of rotational levels ............................................... 44
3.4.2 Parity selection rules ...................................................... 44
3.5 Perturbations72.......................................................................... 45
3.5.1 Rotational perturbations ................................................ 45
3.5.2 Perturbation selection rules............................................ 46
3.6 Predissociation72....................................................................... 46
4 Published papers .............................................................................. 49
International Journals ......................................................................... 49
Icelandic Journals ............................................................................... 49
5
Ion formation through multiphoton processes for HCl35-39,77 ..... 113
5.1 Formation of HCl+ ................................................................. 113
5.1.1 Ionization via Rydberg states....................................... 113
5.1.2 Ionization via ion-pair state ......................................... 113
5.2 Formation of H+ ..................................................................... 115
5.2.1 Ionization via Rydberg states....................................... 115
5.2.2 Ionization via ion-pair state ......................................... 115
5.3 Formation of Cl+ .................................................................... 116
5.3.1 Ionization via Rydberg states....................................... 116
5.3.2 Ionization via ion-pair state ......................................... 116
6 The use of mass analysis to determine interaction constants ..... 119
7 Ionization of acetylene and methyl bromide compared to
HCl................................................................................................... 123
8 Unpublished work .......................................................................... 125
8.1 C1-State ............................................................................... 125
8.2 E1-State ................................................................................ 126
References ............................................................................................ 129
Appendix A: Conference presentations ............................................. 135
Posters .............................................................................................. 135
Talks ............................................................................................... 136
vi
List of Figures
Figure 1. Schematic of the REMPI-TOF experimental equipment. ........ 22
Figure 2: HCl spectra in the range of 85320 – 85370 cm-1. Below is
the 2D contour spectrum that shows clearly the different
ions formed as a function of both atomic/molecular mass
and wavenumbers. Above are REMPI spectra derived
from the contour plot for each ion observed. Mass
spectra for individual wavenumbers could also be
derived in similar fashion. ...................................................... 24
Figure 3: Experimental data (above) for the excitation g3(1)+ 
X1+ (0,0) and the simulated spectrum (below) derived
from spectroscopic constants. The experimental
spectrum also contains a single peak due to the D1
←← X1+ (0,0) excitation. Simulations can thus be of
use for peak assignments in addition to accurately
determining rotational constants. ............................................ 26
Figure 4: Energy diagram for molecular orbitals of HCl. a) Ionpair excitations. An electron is excited from the bonding
orbital of the molecule to the antibonding orbital. b)
Rydberg excitations. An electron is excited from the
non-bonding orbital to a Rydberg orbital. .............................. 28
Figure 5: Rydberg potential vs. ion-pair potential. The figure
illustrates the difference between an ion-pair state and a
Rydberg state. The average bond length of the ion–pair
state is longer than that of the Rydberg state due to the
excitation of an electron to the antibonding orbital,
giving the excited molecule semi-ionic properties. The
vibrational levels are quantized and distributed
according to the shape of the potentials. ................................. 30
Figure 6: For each molecular Rydberg state there are discrete
vibrational levels. For each vibrational state there are
also discrete rotational levels. The vibrational series
depend on the shape of the potential and the rotational
vii
series depend on the energy and thus the mean bond
length of the vibrational levels. ............................................... 32
Figure 7: Franck-Condon factors. The vibrational levels are
positioned so that the probability function forms a
standing wave. It is the overlap of these probability
distributions that determines the Franck-Condon factors.
Figure from
http://www.chem.ucsb.edu/~kalju/chem126/public/elspe
ct_theory.html ......................................................................... 36
Figure 8: When gas is jet-cooled the rotational energy of individual
molecules shifts downwards, thus increasing the
probability of excitation from the lower rotational levels
compared to that from the higher ones. ................................. 37
Figure 9: The precession of L about the internuclear axis. The precession forms a component  along the internuclear axis..................39
Figure 10: Simple rotator. If S = 0 and L = 0 we only need to
consider the angular momentum of nuclear rotation N.
Therefore we have a simple rotator were N is equal to
the total angular momentum J. .............................................. 41
Figure 11: Hund‘s case a). The orbital angular momentum  and
the electronic spin  form the electronic angular
momentum . The angular momentum of the rotation
molecule N and the electronic angular momentum 
then form the total angular momentum J. .............................. 41
Figure 12: Hund‘s case b).  and N form a resultant which is called K.
The angular momenta K and S then form a resultant J. ................ 42
Figure 13: Hund‘s case c). L and S form a resultant Ja which is
coupled to the internuclear axis with a component . 
and N then form a resultant J................................................. 43
Figure 14: Parity. The + and – suffixes in the term symbol indicate
the parity of the rotational levels of the states. For
multiplet states the parity depends on K instead of J. ............ 44
Figure 15: Perturbation. On the left we have an average ion ratio for
the F1, ’=1 state. On the right we have the ratio for the
perturbed F1, ’=1, J’=8 rotational level. As can be
clearly seen, the perturbation to the ion-pair state causes
considerable changes to the ratio of H+ and Cl+ vs. HCl+
ion formation for both the 35Cl and 37Cl isotopes................... 45
viii
Figure 16: Predissociation of a diatomic molecule. a)
Predissociation followed by a direct ionization. The
molecule is initially excited to a bound state which
interacts by a non-bound or a quasi-bound state. Some
of the molecules in the bound state “leap” across to the
predissociating state and are dissociated into its atomic
components. The atoms formed can themselves absorb
photon energy and ionize. b) Predissociation followed
by a resonance-enhanced ionization. In this case the
photon energy needed to excite the parent molecule
corresponds to an excited state of the atom resulting in a
resonance-enhanced excitation. ............................................. 47
Figure 17: Main ionization mechanisms of HCl. Figures a) and b)
show possible ionization channels via Rydberg (HCl*)
and ion-pair states (H+Cl-). The predissociation gateway
mechanism forming H + Cl is included. Necessary
amount of photons for ionization are shown. ...................... 114
Figure 18: (2+n) REMPI of C1 ←← X1+ (0,0) excitation. The
figure shows a diffused spectrum of the H35Cl
isotopologue. ....................................................................... 125
Figure 19: I(Cl+)/I(HCl+) ratio for the C1 state ’=0. The white
columns represent the P-series, the black columns the
R-series and the gray columns the S-series. An
increased I(Cl+)/I(HCl+)ratio is observed for the J’=4
rotational level. A small increase in I I(Cl+)/I(HCl+) for
the R-series at J’=4 is most likely due to an overlap with
the J’=2 peak of the S-series. ............................................... 126
Figure 20: (2+n) REMPI of E1 ←← X1+ (1,0) and V1 ←←
X1+ (14,0) excitations. The figure shows the HCl+/Cl+
ratio of individual rotational peaks. ..................................... 127
ix
List of Tables
Table 1: SHG crystals used for specific dyes and wavelengths of
entering photons.................................................................. 21
Table 2: State interaction parameters. ................................................... 121
Table 3: E values for the rotational peaks of the E1 ←← X1+
(1,0) and V1 ←← X1+ (14,0) excitations. ......................... 127
x
List of abbreviations
a2 = probability distribution
C = Speed of light
Deq = Dissociation energy
E = Energy
FCF = Franck-Condon factors
h = Planck constant
I = Moment of inertial
Irel = Relative intensity
J = Rotational quantum number
K = Total angular momentum apart from spin
kb = Boltzmann constant
L = Orbital angular momentum vector
L = Orbital angular momentum quantum number
m = Mass
 = Reduced mass
Mw = Molecular weight
N = Population of state
P = Power
r = Internuclear distance
S = Spin vector
S = Spin quantum number
T = Temperature
TOF = Time-of-Flight
 = Vibrational quantum number
 = Total angular momentum vector
 = Total angular momentum quantum number
osc = Oscillation frequency
e = Anharmonicity constant
 = wavefunction
xi
Acknowledgements
I would like to thank my advisor Prof. Ágúst Kvaran for his guidance and
patience during my Ph.D studies.
I would also like to thank my many co-workers during this project, Victor
Huasheng Wang, Erlendur Jónsson, Dr. Andras Bodi, and other members
of the University of Iceland, Science Institute for their assistance,
encouragement and support.
The financial support of the University Research fund, University of
Iceland and the Icelandic Science foundation is greatfully acknowledged.
xiii
1
Introduction
My Ph.D. work centered on observing the relative formation of separate
molecular and atomic ion fragments via photoexcitation. It entailed
gathering experimental data by utilising REMPI or Resonance-EnhancedMulti-Photon-Ionization and analysing the data both in terms of atomic
mass and laser frequency.
This led to the development of a new method for measuring and
analysing data entailing the simultaneous collection of REMPI mass and
frequency data over a certain mass area and frequency range into a single
data matrix. This data matrix can be turned into a detailed 2D map of the
measured area using commercial software such as Igor Pro and Labview
which enables us to see important connections between formations of the
various ions (in terms of relative intensities). Thus 2D data for HX show
you how I(H+), I(X+) and I(HX+) vary with wavenumbers (hence
quantum numbers J´) and states. From this 2D map both a REMPI
spectrum of a specific atomic or molecular mass and a mass spectrum for
a specific laser frequency could be extracted as needed. This method
proved to be highly effective, both in accuracy and speed.
Three separate molecules were studied in the following order, acetylene
(C2H2), hydrogen chloride (HCl) and methyl bromide (CH3Br). By
observing the relative formation of separate atoms and molecular
fragments by photoexcitation as a function of laser power and frequency
in conjucntion with theoretical ab initio calcualtions performed by my
group members it was possible to determine the dissociation mechanics
for these molecules.
For HCl specifically, the relative intensity of Cl+/HCl+ ions that formed
via photoexcitation proved to be a highly sensitive indicator of
perturbation between Rydberg and ion-pair states for both H35Cl and
H37Cl isotopologues surpassing those previously used, such as line shifts.
A mathematical model was developed to evaluate state interaction
strengths from the relative intensity of Cl+/HCl+ ions and the interaction
strengths of several states were calculated using both this new method
and older methods which relied on line shifts and relative intensities. The
relative intensity of Cl+/HCl+ ions proved also to be a highly useful tool
in spectrum assignment, notably in rotational line assignments.
15
1.1 Acetylene (C2H2)
The UV spectroscopy, photochemistry and photophysics of acetylene
(C2H2) have been widely studied over the recent years. This is partly due
to its importance in interstellar space and cometary atmospheres, where it
is a commonly observed molecule. There it has been considered to be a
reservoir molecule for the production of carbon containing radicals
which, in turn, are involved in the formation of larger organic
compounds.1-3 Furthermore, being the simplest member of unsaturated
hydrocarbons, acetylene is a fundamental unit in various organic
photochemistry processes and synthesis work.
Photodissociation of C2H2 has been the subject of numerous experimental
investigations, among which are studies by single-1,2,4-8 , two-9,10 and
three- 2,4 photon resonance excitations. Due to the strict u ↔ g selection
for excitation per photon interaction, only ungerade Rydberg states are
accessed by one- and three- (odd number) photon excitations from the
1 +
g electronic ground state, whereas gerade Rydberg states are accessible
by two-photon (even number) excitation. Considering this and the
additional restriction on possible intersystem crossings based on the
selection rules u↔u and g↔g, it is not surprising that the mechanism
and outcome of photodissociation differs, depending on odd- or evennumber photon excitations.
Fragmentation of C2H2 into C2H and H is found to be dominant following
single and three-photon excitations.1,6,10 Thus, single-photon excitations
of the Rydberg states below the first ionization potential reveal only the
C2H product by emission spectra.6 Two distinct dissociation channels,
following single-photon excitations, have been observed7,8, showing
major differences with respect to internal energies and angular
distributions of the fragments C2H and H. In both channels the observed
decay dynamics is found to depend strongly on the excited state of the
parent molecule, C2H2*. In the case of a predissociation of the C2H2
(H1u) Rydberg state it has been proposed that it occurs via the bent
valence state A1Au.7
From less extensive two-photon excitation studies, on the other hand, both
fragmentations into C2 + H2 and into C2H + H, are found to occur.9,11 Thus, H
atoms, H2 molecules and C2 molecules in the X1g+, a3u , A1u and d3g
states have been identified by time resolved photofragment and emission
detection studies.9,11 Both the sequential bond-rupture mechanism and
concerted two-bond fission processes have been proposed to explain the C2
16
and H2 fragment formations.11 Furthermore, long-lived bent isomers of C2H2 as
well as C2H intermediates have been revealed experimentally. Tsuji et al.
concluded, from detailed REMPI analysis9, that ion fragment formations are
dominantly due to the ionization of neutral molecular fragments after
predissociation.
Because of the characteristic predissociation channels the ungerade and
gerade Rydberg states of acetylene are found to be short lived; lifetimes
range from 50 fs to more than 10 ps.4,9
More recently Matthíasson et al.12 were able to determine important
thresholds for fragmentation processes by combining ion mass-analysis
as a function of laser excitation frequencies and laser power with
DFT/STQN calculations on C2H2  C2 + H2.
1.2 Hydrogen Chloride (HCl)
Since the original work by Price on hydrogen halides13, a wealth of
spectroscopic data on HCl has been derived from absorption
spectroscopy14-17, fluorescence studies17 as well as from REMPI
experiments.18-32 Relatively intense single- and multiphoton absorption in
conjunction with electron excitations as well as rich band-structured
spectra make the molecule ideal for fundamental studies.
A large number of Rydberg states, both several low lying repulsive states as
well as the V(1+) ion-pair state have been identified. A number of spinforbidden transitions are observed, indicating that spin-orbit coupling is
important in excited states of the molecule. Perturbations due to state mixing
are widely seen both in absorption15-17 and REMPI spectra.19,20,22,24,25,27,28,32 The
perturbations appear either as line shifts16,19,20,22,25,27,28,32 or as intensity and/or
bandwidth alterations.16,19,20,22,24,25,27,28,32 Pronounced ion-pair to Rydberg state
mixings are both observed experimentally15,16,20,22,25,27,28,32,33 and predicted from
theory.33,34 Interactions between the V(1+) ion-pair state and the E(1+) state
are found to be particularly strong and to exhibit nontrivial rotational,
vibrational and electron spectroscopy. Perturbations due to Rydberg-Rydberg
mixings have also been predicted and identified.16,24 Both homogeneous (=
0)27,28,33,34 and heterogeneous (> 0)28,32,33 couplings have been reported.
Such quantitative data on molecule-photon interactions are of interest in
understanding stratospheric photochemistry as well as being relevant to the
photochemistry of planetary atmospheres and the interstellar medium.17
The excitation and subsequent ion formation mechanism of the HCl
molecule have generally been considered a two-step process, i.e. the
17
excitation of the molecule to an energetically higher Rydberg or ion-pair
state followed by its ionization. There is however evidence that a far
more complex mechanism controls the ionization of HCl molecules and
its atomic fragments.
Photofragmentation studies of HCl have revealed a large variety of
photodissociation and photoionization processes. In a detailed twophoton resonance-enhanced multiphoton ionization study, Green et al.
report HCl+, Cl+ and H+ ion formations for excitations via a large number
of  = 0 Rydberg states as well as via the V1+ ( = 0) ion-pair state,
whereas excitations via other Rydberg states are mostly found to yield
HCl+ ions.19 More detailed investigations of excitations via various
Rydberg states and the V1+ ion-pair state by use of photofragment
imaging and/or mass-resolved REMPI techniques have revealed several
ionization channels depending on the nature of the resonance excited
state.35-39 Results are largely based on an analysis of excitations via the
E1+ Rydberg state and the V1+ ion-pair state, which couple strongly to
produce the mixed (adiabatic) B1+ state with two minima.
Recently, analyses of excitations via the F1 (´=1) Rydberg state and
the V1+(´=14) state have shown characteristic effects of near-resonance
interactions on photoionization channels.39 Those studies introduced the
possibility of a model that used the I(Cl+)/I(HCl+) rate to determine the
max
interaction strength ( W12 ) of a near resonance interaction. A more
detailed analysis of excitations via low-energy triplet states has revealed
similar fragmentations due to coupling with the ion-pair state and has
introduced a model to determine the interaction strength of a nearresonance interaction.40 Those studies revealed characteristic ionization
channels which have been summarized in terms of excitations via 1)
resonance noncoupled (diabatic) Rydberg state excitations, 2) resonance
noncoupled (diabatic) ion-pair excitations and 3) dissociation of
resonance-excited Rydberg states to form H + Cl and/or H + Cl* via
predissociation of some gateway states followed by ionization.39-41
This model is supported by Kauczok et al.42 as they used velocity mapping to
determine the origins of H+ ions formed via the near-resonating lines of F1
←←X1+, (0,0), J´= 8 and f32 ←←X1+, (0,0), J´= 5 reported by Kvaran et
al. Their findings show that a major portion of H+ formed by these two
excitations are via the ion-pair state and it is reasonable to assume that Cl+ is
also formed by the same or similar pathways.
18
1.3 Methyl bromide (CH3Br)
The spectroscopy43-47 and photofragmentation48-54 of methyl bromide
have received considerable interest over the last decades, both
experimentally43-53 and theoretically54, for a number of reasons. Methyl
bromide as well as the chlorine and iodine containing methyl halides play
important roles both in the chemistry of the atmosphere 47,55-57 and in
industry. Thus, although far less abundant than methyl chloride in the
stratosphere, methyl bromide is found to be much more efficient in ozone
depletion57 and its use is now being phased out under the Montreal
Protocol. Furthermore, bromocarbons are known to have a high global
warming potential.58 Additionally, the molecule is a simple prototype
system of a halogen containing an organic molecule and is as such well
suited for fundamental studies of photodissociation and photoionization
processes.51,54,59
Little is known about the UV spectroscopy of methyl bromide despite its
importance in various contexts. Since a pioneering work by Price 43 in
1936 some absorption studies have appeared dealing with i) a weak
continuous spectrum (the A band) in the low energy region (> 180 nm;
E < 55500 cm-1)44,47,55,56 due to transitions to repulsive states54 and ii)
higher energy (< 180 nm; E > 55500 cm-1) Rydberg series and its
vibrational analysis.44-46 There has been some controversy in the literature
concerning the assignment of the higher energy band spectra. Locht et al.
recently reported on the analysis and assignments of spectra46 which
differ from earlier reports.43-45 More recently, multiphoton absorption
(REMPI) studies59 and ab initio calculations of excited states60 have been
published which help clarify the discrepancy.
Photofragmentation studies of methyl bromide can be classified into two
groups. One group focuses on the characterization of photofragments
CH3 + Br(2P3/2)/Br*(2P1/2) resulting from photodissociation in the A
band48-51,54 whereas the other group concerns the CH3+ +Br- ion-pair
formation52,53,59 in the energy region between the ion-pair formation
threshold (76695 cm-1) and the ionization energy (85031.2 cm-1 for
CH3Br+(23/2); 87615.2 cm-1 for CH3Br+(21/2)).59 To our knowledge no
other photofragmentation channels have been reported so far. Some
disagreement concerning the ion-pair formation is to be found in the
literature. Thus Xu et al.53 and Shaw et al.52 conclude that direct
excitation to the ion-pair state is the major step prior to ion-pair formation
whereas more recently Ridley et al.59 give evidence for Rydberg doorway
19
states in the photoion-pair formation analogous to observations for some
halogens containing diatomic molecules.61-65
The basic picture for the electron configuration of methyl halides is
analogous to that for hydrogen halides, such that, in the first
approximation, the symmetry notation C3v, which holds for methyl
halides, can be replaced by Cv.60 Excited state potentials for methyl
halides (CH3X; X = Cl, Br, I) as a function of the C - X bond closely
resemble those for HX molecules showing i) a number of repulsive
valence state potentials which correlate with the CH3 + Br(2P3/2)/Br*(2P
1/2) species, ii) series of Rydberg state potentials which closely resemble
the neutral and first ionic ground state potentials and iii) an ion-pair
1
A1(C3v) (1(Cv)) state with a large average internuclear distance.
Characteristic state interactions between the Rydberg and ion-pair states
are found to affect the spectroscopy and excited state dynamics for
hydrogen halides.19-21,27,28,32,39,40,66,67 It has been pointed out that analogous
effects are to be found for methyl bromide.59,60
More recently Kvaran et al.68 have reported a two-dimensional (2+n)
REMPI experiment analogous to those presented above for acetylene12
and HCl39,40,69, which helps elucidate the discrepancy concerning the
VUV spectroscopy of methyl bromide, and which also yields evidence
for new photodissociation channels via Rydberg states.
20
2
Experimental setup and analysis
method
2.1 Experimental apparatus
Tunable LASER radiation was acquired from a Coherent ScanMatePro
dye laser, or in the case of acetylene a Lumonics Hyperdye 300 dye laser,
pumped by a Lambda Physic COMPex 205 excimer LASER. The
bandwidth of the tunable LASER radiation was about 0.095 cm-1.
Depending on the frequency required, a SHG (second harmonic
generator) unit could be placed in the LASER beam pathway to
frequency double the LASER. For the second harmonic generation we
used a Sirah frequency doubler equipped with interchangeable BBO-2 or
KDP crystals, see Table 1 for details.
The LASER was directed into a vacuum chamber containing electric
platings designed to direct any ions formed down a TOF (time-of-flight)
tube. These platings consist of a single repeller which is a highly charged
positive plate and several extractors which having a lesser positive charge
serve as focal and directional lenses for the ionic beam. The LASER was
focused using either 20 cm or 30 cm focal length lenses.
Table 1: SHG crystals used for specific dyes and wavelengths of entering
photons.
Wavenumber [cm-1]
Wavelength [nm]
Dye
Crystal
22988-22124
435-452
C-440
BBO-2
22124-21186
452-472
C-460
BBO-2
21186-20408
472-490
C-480
BBO-2
20408-18622
490-537
C-503
BBO-2
18622-17637
537-567
R-540
BBO-2
17637-16750
567-597
R-590
KDP-R6G
Diagonally to the LASER beam path, in line with the focus point, a
nozzle sprayed gas into the vacuum chamber with regular intervals, thus
creating a jet-cooled stream of molecular particles in the focal point of
21
the LASER. Ionization chamber was pumped by a diffusion pump backed
by an Edwards mechanical pump whereas the TOF tube was pumped by a
Pfeiffer turbo pump also backed by an Edwards mechanical pump. On
top of the diffusion pump, located between the mechanical pump and the
ionization chamber, were cooling rods filled with liquid nitrogen.
An acetylene gas sample was acquired from Linde gas (AAS Acetylene
2.6). Pure acetylene or mixtures of C2H2 and argon (typically in ratios
ranging from 1:1 to 1:4 = C2H2:Ar) were pumped through a 500 m
pulsed nozzle from a typical total backing pressure of about 1.0 – 1.5 bar
into the ionization chamber. The pressure in the ionization chamber was
lower than 10-5 mbar during experiments. The distance between the
nozzle and the center between the repeller and the extractor was about 6
cm. The nozzle was held open for about 200 s and the LASER beam
was typically fired about 450 s after opening the nozzle.
Figure 1. Schematic of the REMPI-TOF experimental equipment.
HCl and CH3Br gas samples were acquired from Merck-Schuchardt,
>99.5% purity both. They were pumped through a 500 m pulsed nozzle
from a typical total backing pressure of about 1.0–1.5 bar into an
ionization chamber. The pressure in the ionization chamber was lower
than 10-6 mbar during experiments. The nozzle was held open for about
200 s and the LASER beam was typically fired about 500 s after
opening the nozzle.
22
REMPI-TOF spectra for jet-cooled gas were acquired by detecting ions
formed in the focal point that had been directed through a TOF tube, on a
MCP (micro channel plate). LeCroy 9310A, 400 MHz storage
oscilloscope was used to gather the data from the MCP in digital format.
Typical repetition rates were 50-100 pulses for each frequency point.
Figure 1 shows a schematic of the experimental setup.
Information on the power dependence of the ion signals was generally
acquired by systematically reducing the laser power by directing the laser
through different numbers of quartz windows which reflected a part of
the laser beam. Each data point was acquired by averaging over 1000
pulses. The reflection precentage of each quartz window was calibrated at
about 8.4%. During a single measurement run one window was added in
the path of the laser beam after each 1000 pulses up to a maximum of six
windows at which point they where removed again one at a time every
1000 pulses. The laser power was measured before and after every
measurement run and should optimally remain unchanged. To insure
accuracy at least three measurement runs were preformed for each ion
signal measured. Information on the power dependence of the ion signals
was generally acquired by averaging over approximately 1000 pulses.
2.2 Analysis Method
Using the equipment described we were able to measure simultaneously
the formation of all atomic and molecular ions within a certain mass
range as a function of laser frequency and gather this data into a single
data matrix.
To do so we used Labview version 8.0. A program was created by
Erlendur Jónsson70 that gathered the summed data from the oscilloscope
into a text file that included the wavenumber of the excitation, the mass
data reading for each wavenumber and an integration over a certain mass
area for each wavenumber.
Igor Pro version 5.071 was used to process this text file to create a 2D
contour plot of the measured area. REMPI spectra for specific atomic or
molecular mass could then be extracted from the 2D image, in addition to
mass spectra for specific wavenumbers. Figure 2 shows a 2D contour plot
and samples of the rotational spectra of HCl that were extracted from the
2D contour plot.
23
Figure 2: HCl spectra in the range of 85320 – 85370 cm-1. Below is the 2D
contour spectrum that shows clearly the different ions formed as a function of
both atomic/molecular mass and wavenumbers. Above are REMPI spectra
derived from the contour plot for each ion observed. Mass spectra for individual
wavenumbers could also be derived in similar fashion.
24
This analysis method enables us to see important connections between
formations of the various ions via REMPI (in terms of relative intensities) as
the 2D data for HCl show you how I(H+), I(35Cl+), I(H35Cl+), I(37Cl+) and
I(H37Cl+) vary with wavenumbers (hence quantum numbers J´) and states. It
proved to be quite accurate in observing mass peaks that previously went
undetected due to overlap or that were otherwise obscured allowing for a more
robost assignment of rotational spectra. It also allowed us to discern if 35/37Cl+
signals originated from the Rydberg state rotational line in question or if it was
due to overlap from a nearby ion-pair state rotational line. This last proved
highly valuable in our studies on photofragmentations.
2.2.1 Simulations
Gathered REMPI spectra (such as those shown in figure 2) can be
simulated by a quantum mechanical simulation using Igor Pro 5.0. A
macro (small program or script that is run inside Igor Pro) was used to
simulate rotational spectra by using spectroscopic parameters. The
simulation determines relative rotational line positions from first- and
second-order rotational constants (B and D) for the excited and ground
state. It also determines the relative intensity of the rovibrational lines by
taking account of the ground state population and degeneracy.27
The experimental spectrum was displayed on a screen with the simulated
spectrum. Realistic rotational parameters were then put into the macro and
the simulated spectrum was generated. Finally the rotational constants were
changed until a reasonable fit to experimental data was reached. In some
cases a least squares analysis could be used to assist with the simulation, as
was done in the case of C2H2. However the final simulation was always done
by a visual comparison of the spectra as in some cases the least square
analysis gives an inferior result due to computational errors. These errors
were typically due to the program having too much emphasis on the
bandwidth and shape of the rotational peaks and too little emphasis on peak
positions, resulting in the center of the simulated peaks being shifted away
from the center of the measured peaks.
Simulations like the one shown in figure 3, which is a simulation of the
g3(1)+ ←← X1+ (0,0) excitation, could be used to accurately determine
rotational constants of the simulated spectra. They could also be useful
for line assignments. From the calculated spectra in figure 3 it can clearly
be seen that the experimental spectra contain a rotational peak outside of
the g3(1)+ ←← X1+ (0,0) excitation, which was later found to be a part
of the D1 ←← X1+ (0,0) excitation. In addition, when searching for
25
line perturbations, simulations like these can also be of moderate use as
subtle line shifts become more obvious.
1.4
Experimental
1
D  ; R-line ; J'=1
1.2
1.0
3
J'=1
0.8
5
Calculated
0.6
7
0.4
82508
82512
82516
-1
2xh[cm ]
82520
Figure 3: Experimental data (above) for the excitation g3(1)+  X1+ (0,0) and
the simulated spectrum (below) derived from spectroscopic constants. The
experimental spectrum also contains a single peak due to the D1 ←← X1+
(0,0) excitation. Simulations can thus be of use for peak assignments in addition
to accurately determining rotational constants.
2.2.2 Time of flight analysis
When a molecule is ionized in an electric field it gains momentum in the
direction of the field. The relationship between the atomic or molecular
mass of the ion (Mw) and the time-of-flight (TOF) for our equipment is
TOF = a M w  b
(1)
The constants a and b are experimental constants that vary between
experiments which must be evaluated for each measurement and M w is
the molecular weight of the ions formed from the sample injected into the
gas chamber. Using equation (1) it was easy to evaluate the atomic mass
of ions formed by REMPI as there were generally some known peak
formations due to impurities and/or background gas in the vacuum
chamber, such as C+ and C2+, which could be used for calibration.
26
3
Theoretical considerations
3.1 Electronic spectroscopy of diatomic
molecules72-74
The quantum energy levels of a molecule can be broken down into three
distinct parts. The electronic energy levels, which arise from the energy
of different electron configurations, the vibrational energy levels, which
correspond to the allowed energy for vibrations of molecular bonds and
the rotational energy levels, which correspond to the allowed rotational
energy of the molecule in question.
The approximate order of magnitude for excitations within these energy
levels is:
Eelec ≈ Evib *103 ≈ Erot *106
(2)
They are also interconnected in the sense that each vibrational state has a
series of rotational levels and each electronic state has a series of
vibrational levels. Therefore, the total energy of an electronic excitation
can be expressed as:
totalEelecEvibErot
3.1.1 Electronic energy levels.
Electronic excitation occurs when an electron is excited to an energetically
higher molecular orbital from its ground state or energetically lower orbital.
A molecular Rydberg state is composed of atom like orbitals with
primary quantum numbers higher than those of the ground state. During
Rydberg excitation the electron in the highest occupied molecular orbital
(HOMO) is excited into some energetically higher Rydberg orbitals
depending on the frequency used for excitation.
27
An ion-pair state is formed when an electron of the bonding electron pair
is excited into the antibonding orbital (* ←← Figure 4 gives an
example using HCl.
4s
4s


1s
1s


3p

3p

3s
3s
a)
b)
Figure 4: Energy diagram for molecular orbitals of HCl. a) Ion-pair excitations.
An electron is excited from the bonding orbital of the molecule to the
antibonding orbital. b) Rydberg excitations. An electron is excited from the nonbonding orbital to a Rydberg orbital.
As the antibonding orbitals are located away from the center of the
molecule this weakens the molecular bond and in some cases may cause
it to break. However for diatomic molecules with a difference in
electronegativity the antibonding electron is attracted to the atom with the
higher electronegativity. In the case of HCl this means that the
antibonding electron is attracted to the Cl atom, causing the atoms to
attain ion-like properties (H+ and Cl-) and remain bonded through
electrostatic properties. Nevertheless, the ion-pair bond is both weaker
and longer than a regular bond.
For a single-photon excitation, the total electronic angular momentum of
the electron must remain the same or change by only one integer,
according to the electronic excitation selection rule
0, ±1
28

For multiphoton excitations, as each photon must fulfil the selection rule,
this rule is applied for each photon used in the excitation, resulting in
0, ±1, ±2 ... ±n


where n is the number of photons in the excitations. Thus multiphoton
excitations open up several possible excitation paths otherwise
undetectable. For example, the ground state of HCl is a X1 state, thus for
single-photon excitations only  and  states are accessible in HCl.
However, for two-photon excitations  states become accessible in
addition to the  and  states.
3.1.2 Vibrational energy levels
We have discussed the excitation of electrons in a molecule. The next
effect we need to consider is the vibration of the molecular bond.
A molecular bond is formed from the positive overlap of two atomic
wavefunctions. The length of the bond is dictated by the attracting
properties of the electrons of one atom to the nucleus of the other and the
mutual repulsive forces of the electrons and the nuclei of each atom. As
such there must be an internuclear distance where the attractive and
repulsive forces of the atoms reach equilibrium.
This internuclear distance, called the bond length of the molecule,
corresponds to the bottom of the potential well. Pushing or pulling the
atoms away from that optimal bond length increases the potential energy
of the molecule.
Figure 5 illustrates the difference between Rydberg states and ion-pair
states. The bond length of the Rydberg state is smaller than that of the
ion-pair state, in addition the energy gap is generally higher between
vibrational levels of the Rydberg state than for the ion-pair state as they
are quantized and distributed according to the shape of the potential.
A simple harmonic oscillator is a useful approximation for the vibrational
energies. In the simple harmonic model they are defined as
½osc cm-1 
where  is the vibrational quantum number. In equation (6) the energy
difference between adjacent vibrational levels is equal to the oscillation
frequency osc and the vibrational energy cannot be zero.
29
Energy
Ion-pair
Potential
Rydberg
Potential
Vibrational levels
Internuclear distance
Figure 5: Rydberg potential vs. ion-pair potential. The figure illustrates the
difference between an ion-pair state and a Rydberg state. The average bond
length of the ion–pair state is longer than that of the Rydberg state due to the
excitation of an electron to the antibonding orbital, giving the excited molecule
semi-ionic properties. The vibrational levels are quantized and distributed
according to the shape of the potentials.
However, real molecules do not follow a simple harmonic path. The
repulsive forces between electrons build up faster than the attractive force
between the electrons and the nucleus when the atoms are pressed
together and similarly they diminish slower when they are pulled apart.
Therefore if the atoms move too far apart, which can happen if the
vibrational energy reaches a certain amount, the bond between them will
break and the molecule will dissociate into atoms. So while the simple
harmonic oscillator approximation is useful as a tool, the deviations from
the simple oscillator need to be taken into account for real molecules. An
expression that fits to a good approximation is the Morse function:


U (r )  Deq 1  expareq  r 
30
2


where a is a constant for a particular molecule, req is the bond length at
equilibrium, r is the bond length and Deq is the dissociation energy. By
using this potential energy in the Schrödinger equation, the allowed
vibrational bands are found to be
v½e- + ½)2 ee

Where e is the oscillation frequency and ee is the anhermonicity
constant.
3.1.3 Rotational energy levels
The rotational energy of a molecule is inversely proportional to its
moment of inertia. By looking at a rigid diatomic molecule we can see
that its moment of inertia can be expressed as:
I
m1 m2 2
r0  r02  
m1  m2

where m1 and m2 are the mass of each atom,  is the reduced mass of the
system and r0 the internuclear distance between the atoms.
By solving the Schrödinger equation for a diatomic system it can
be shown that the allowed rotational energy levels for a rigid diatomic
molecule can be expressed as:
EJ 
h2
8 2 I
J ( J  1) Joules 
m 2 kg
where h is the Planck constant (6,63*10-34
) and I is the moment of
inertia. J is the rotational quantum number andscan only take integer values
of zero and higher. This restriction to integer values comes directly from
the Schrödinger equation and it is this restriction that introduces the
discrete rotational levels observed in spectroscopy, see figure 6.
31
Energy
Rydberg
Potential
Vibrational levels
Rotational levels
Internuclear distance
Figure 6: For each molecular Rydberg state there are discrete vibrational levels.
For each vibrational state there are also discrete rotational levels. The vibrational
series depend on the shape of the potential and the rotational series depend on
the energy and thus the mean bond length of the vibrational levels.
In this work I use wavenumbers [cm-1] instead of Joules [J]. To compensate for
this common practise in spectroscopy, equation (10) becomes:
EJ
h2
j 

J ( J  1) cm-1
hc 8 2 Ic

where c is the speed of light in cm s-1. This equation is usually
abbreviated to:
 j  BJ ( J  1) cm-1 
where B is the rotational constant that is given by:
32
h

8 I B c
B
2

From equation (12) it can be seen that the energy of the rotational levels will
gradually increase as J increases and that the energy difference between
adjacent rotational levels will also increase by 2B for each level of J.
At this point it should be stated that the above only holds for an ideal
rigid rotor. In reality the molecules are not completely rigid. As J
increases, the distance between the atoms increases to some degree. This
is somewhat like spinning a ball fastened to a rubber string. As you spin
the ball faster, the string lengthens. This causes the moment of inertia of
the molecules to diminish and introduces an effect called centrifugal
distortion. To correct for this the centrifugal distortion constant is
introduced and equation (12) becomes
J= BJ(J+1) – DJ2 (J+1)2 cm-1

where D is defined as:
D
h3

32 4 I 2 r 2 kc

These two values (B and D) usually suffice for modern spectroscopy
fitting, since higher order fitting parameters have negligible effect.
For a single-photon excitation, the angular momentum of the molecule
must change by one, according to the rotational selection rule
Jif
Jif≠
For a multiphoton excitation, as each photon must fulfil the selection rule,
this rule is applied for each photon used in the excitation, resulting in
For
when n 
J when n 
etc
33
For≠
Jn
where n is the number of photons used for the excitation. Thus, as
excitation is possible between more rotational levels, multiphoton
excitations introduce additional line series for each vibrational level
within a state.
3.2 The intensity of electronic excitation
spectroscopy lines72-74
The intensity of absorption spectroscopic lines results from a combination of
several factors. Most notable are the electron transition probabilities, the
Frank-Condon principle and the Boltzmann distribution. The first two are
due to molecular wave functions. Using the Born-Oppenheimer
approximation we can treat a molecular wave function as a combination of
an electronic wave function and a nuclear wave function. The Boltzmann
distribution is a property-of-state population and is therefore affected by the
temperature of the measured sample.
The power of the excitation source also affects the intensity of the
spectroscopic lines. This effect is however separate from the intrinsic
properties of molecules and is simply due to an increased excitation rate
from the higher density of photons.
3.2.1 Transition probabilities
The transition probabilities of electronic excitation is one of the main
properties that influence the intensity of spectroscopic lines. Transition
probabilities (a2) describe the probability of an excitation between
electronic states and are defined as
a 2  (  m  n d e ) 2  

where  is dipole moment of the molecule, m and n are the molecular
wavefunctions and de is the volume element. The wavefunction can be
regarded as a combination of electron wavefunctions, vibrational wavefunctions, rotational wavefunctions and even translational wavefunctions.
   e v r t  
34

For rovibrational excitations the rotational and translational
wavefunctions as considered to be constants. A common approximation
is also to consider the electronic wavefunction as a constant which
depends on the characteristics of the ground and excited state. As such
the transition probability of rovibrational excitations can be defined as
a 2  (  v '  v '' dr ) 2  

This gives rise to the Frank-Condon factors (FCF) which are transition
probabilities proportional to the overlap of the vibrational wave functions
in the upper and lower vibrational states.
The FCF influence on intensity varies with vibrational levels depending
on the wavefunction overlap and remains the same for all rotational
excitations within the same vibrational excitation to a first approximation.
In figure 4 we see vibrational levels of two fictional states, E0 and E1. As
electronic excitations are not influenced by vibrational selection rules,
excitation from E0 (’=0) to any vibrational level of E1 is allowed as long
as there is a non-zero chance that the internuclear distance is the same for
the E1 and E0 states. In this case excitation between the ground
vibrational states of E0 and E1 is highly unlikely, whereas excitation
between the ground vibrational state of E0 and ’=2-5 of E1 is highly
likely.
3.2.2 Boltzmann distribution
The second property that influences line intensities is the population of
the ground state as the rotational population of the ground state influences
the number of molecules that are available for a specific excitation. The
Boltzmann distribution is defined as
  EJ
NJ
 exp 
N0
 k bT



(19)
where N0 is the total number of particles in the ground state, NJ is the
number of states having the energy EJ, kb is the Boltzmann constant (1.38
x 10-23 m2kgs-2K-1) and T is the temperature.
35
Figure 7: Franck-Condon factors. The vibrational levels are positioned so that
the probability function forms a standing wave. It is the overlap of these
probability distributions that determines the Franck-Condon factors. Figure from
http://www.chem.ucsb.edu/~kalju/chem126/public/elspect_theory.html
Therefore, as a sample is cooled down, more particles will occupy the
lower rotational levels of the ground state, thus increasing the chance of
excitation to the lower rotational levels of the excited state, while
decreasing it for the higher rotational levels. In figure 8 we see an
example of this using a fictional distribution. In the hot gas sample we
would expect to see rotational peaks originating from the J’=0 to at least
the J’=5 rotational level. For the cold sample however, only excitation
36
origination from the J’=0 to the J’=2 rotational levels would be expected.
Thus cold samples show far fewer rotational lines than hot samples.
This effect is very useful in spectroscopy as it allows for different degrees of
spectrum complexity. Cold samples have few rotational lines and therefore
do not offer the same amount of data, yet they are simpler and easier to
assign. Hot samples have more rotational lines and more data, but are more
complex to assign. Thus by varying the rotational temperature of a gas
Rotational levels
5
4
3
2
1
0
Hot gas
Cold gas
sample and comparing, very useful information is gained.
Figure 8: When gas is jet-cooled the rotational energy of individual molecules
shifts downwards, thus increasing the probability of excitation from the lower
rotational levels compared to that from the higher ones.
3.2.3 Laser power dependence
Ion intensities (I(M+)) vary with the laser power (Plaser), the number of
photons needed to ionize (n) and the transition probabilities as discussed
above. The total ion intensity can be expressed as
Plasern 

where  is a proportionality constant depending on the transition
probability. From equation (20) the following expression can be derived:
37
lognlog Plaser + C
rel


rel
where Plaser is proportional to the laser power. From this equation it can
be seen that the number of photons needed for excitation can be derived
from a logI(M+) vs. logP plot. This permits an easy extraction of photon
numbers and gives valuable information concerning excitation and
ionization pathways.
3.2.4 Multiphoton excitation intensities
These previously mentioned properties form a basis for the intensity of
rovibrational lines. For a two-photon resonance excitation followed by
ionization, the intensities are proportional to the products of the cross
sections of two major steps, a) the resonance excitation and b)
photoionization. According to Kvaran et al.25, the resonance excitation is
proportional to a function S´´´(J, , ||, ±) which depends on the
difference of the angular momentum quantum numbers J and  as
well as the parallel (||) and perpendicular (±) transition dipole moments
between the two states, where || equals J←J transitions and ± equals J
±1 ← J transitions. The transition strengths for one-, two- and threephoton excitations have been formulated in terms of Hönl-London type
approximations for diatomic molecules.72,75,76
The resonance excitation is also proportional to a function C(v’,v’’). In
the case of a Boltzmann distribution, C(v’,v’’) can be expressed as
C(v’,v’’) = KF(v’,v’’)Pn2(v´) 
where K is a parameter depending on the electronic structure of the
molecule, geometrical factors and sample concentrations, F(v´,v´´) is the
Franck-Condon factor for the transition v´←v´´, P is the laser power and
n is the number of photons necessary to complete the ionization and
2(v´) is the ionization cross section which is a slowly varying function
with laser energy.
Thus by taking the degeneracy (g(J´´)) of the ground state rotational
energy levels (E(J´´)) into account, the relative line intensity is defined as
I rel  C(v´, v´´)g(J´´)Sv´v´´ e
38
  E ( J ´´) 


 kT 


3.3 Total angular momentum and
Hund’s cases72
The total electronic angular momentum is composed of the electron spin
angular momentum and the orbital angular momentum. An electron moving in
its orbital is said to possess orbital angular momentum. For a diatomic
molecule this momentum is quantized and expressed as L and has the
magnitude
|L|  L( L  1)  
Unless L = 0 the orbital angular momentum vector L precesses about the
internuclear axis of the molecule as figure 9 shows.
L

Figure 9: The precession of L about the internuclear axis. The precession forms a
component  along the internuclear axis.
The angular momentum vector  is the component of the orbital angular
momentum along the internuclear axis with a magnitude of.
ħ


For each given value of the quantum number L the quantum number
can take the values
 = 0, 1, 2, ... , L. (26)
So for each value of L there are L+1 distinct states with different energy.
The molecular state designations , ,  and  represent  values of 0,
1, 2 and 3 respectively.
39
The electron which orbits around the molecule is also spinning about an
axis forming a spin orbit vector S which has the magnitude
|S|  S (S  1)  

Here the corresponding quantum number S can take integer or half
integer values depending on whether there is an odd or even number of
electrons. S then precesses about the internuclear axis (much in the same
way as L) with a constant component with amagnitude
ħ


Where  can take the values
 = S, S-1, S-3, ... -S

As such  can take 2S+1 different values and can also take negative values.
These two elements of electron motion added together form the total
angular momentum of the electrons:
 

The molecule’s angular momenta, electron spin, electronic orbital angular
momentum and the angular momentum of nuclear rotation form together a
resultant J which is the total angular momentum of the molecule.
For 1 states the spin and angular momenta are zero. Therefore the total
angular momentum is the same as the angular momentum of nuclear rotation
and we have a simple rotator as shown in figure 10. For states where  and 
are nonzero we have special cases which are called Hund’s cases.
3.3.1 Hund’s case a)
For Hund’s case a), the interaction of the nuclear rotation with the
electronic motion is considered to be weak (both spin and orbital).
However, the coupling of the electronic motion with the line joining the
nuclei is considered to be strong. The electronic angular momentum  is
therefore well defined even in rotating molecules.
40
N
J
Figure 10: Simple rotator. If S = 0 and L = 0 we only need to consider the
angular momentum of nuclear rotation N. Therefore we have a simple rotator
were N is equal to the total angular momentum J.
The angular momentum of the rotating molecule N and the electronic angular
momentum  then form the total angular momentum J as shown in Figure 11.
J
N



Figure 11: Hund‘s case a). The orbital angular momentum  and the electronic spin 
form the electronic angular momentum . The angular momentum of the rotation
molecule N and the electronic angular momentum  then form the total angular
momentum J.
Since it is obvious that J cannot be smaller than  we get
J


and thus, levels with J <  do not occur.
41
3.3.2 Hund’s case b)
When L = 0 and S ≠ 0, a weak or zero coupling of the internuclear axis
with the spin vector S occurs which is characteristic of Hund’s case b). In
this case  and N form a resultant which is called K which is the total
angular momentum apart from spin. The corresponding quantum number
K can take the values
K = , +1, +2 ....
(32)
The angular momenta K and S then form a resultant J which is the total
angular momentum, see Figure 12.
S
J
K
N

Figure 12: Hund‘s case b).  and N form a resultant which is called K. The
angular momenta K and S then form a resultant J.
The possible values of J are therefore
J = (K+S), (K+S-1), ... , (K-S)

Thus in general, every level with a given K has 2S+1 components. This
appears as peak splitting in rotational spectra. Note that for singlet states
the distinction between cases a) and b) are pointless, as S=0, = and
therefore K=J.
3.3.3 Hund’s case c)
In some cases the interaction of L and S may be stronger than the coupling
with the internuclear axis. In these cases  and  are not defined. Instead L
and S form a resultant Ja which is coupled to the internuclear axis by a
component .  and N then form a resultant J, see Figure 13.
42
J
N

L
Ja
S
Figure 13: Hund‘s case c). L and S form a resultant Ja which is coupled to the
internuclear axis with a component .  and N then form a resultant J.
Hund’s cases a), b) and c) are the most common Hund’s cases. There are
two more, d) and e); however, they are of lesser importance for the scope
of this dissertation.
3.4 Symmetry properties72
The symmetry properties of rotational levels are important for
spectroscopic work. The rigorous selection rule which states that
excitations can only occur between levels of the same symmetry can be
of great help in assigning spectroscopic lines.
The symmetry of rotational levels is a property of their eigenfunctions. If
the eigenfunction of a rigid rotor remains unchanged when reflected at its
origin by replacing  by + and  by - it is considered to be in a
positive electronic state. Here  is the azimuth of the line connecting the
mass point to the origin and  is the angle between this line and the z
axis. Should the eigenfunction change sign it is considered to be in a
negative electronic state.
Rotator functions remain unchanged for even values of J but change sign for
odd values of J. This characteristic is called parity and rotational levels can be
assigned a + or – parity depending on the symmetry properties.
43
3.4.1 Parity of rotational levels
For states that have = 0 and S = 0 the parity of the rotational levels
switches between being positive or negative depending on whether J is
even or odd. For 1+ states the first level has a positive parity. For 1states the reverse is true and the first level has a negative parity. The same
holds for states were = 0 and S ≠ 0, however here the parity depends on
K rather than J.
For states were  ≠ 0 the rotational levels have both a positive and
negative parity, for which there is a small energy difference. See Figure
14 for further clarification.
K
1+
2+
3+
0
1
2
3
-
+
-
4
5
+
-
+
0
1
2
3
+
4
5
K
0
1
2
3
4
5
1-
-
+
-
+
-
+
0
1
2
3
4
5
-
+ +
- -
J
2-
- -
+ +
- -
+ +
- -
½
½
3/2
3/2
5/2
5/2
7/2
7/2
9/2
9/2
11/2
+
- - -
+ + +
- - -
+ + +
- - -
1
012
123
234
345
456 J
J
3-
+ +
- -
+ +
½
3/2
3/2
5/2
5/2
7/2
7/2
9/2
9/2
11/2
+ + +
- - -
+ + +
- - -
+ + +
012
123
234
345
½
-
1
J
J
456 J
Figure 14: Parity. The + and – suffixes in the term symbol indicate the parity of the
rotational levels of the states. For multiplet states the parity depends on K instead of J.
3.4.2 Parity selection rules
For single photons, excitation may only occur between rotational levels
with opposite parity.
but not or
For two-photon excitation, this turns into
andbut not
and for three-photon excitation, it again turns to
+  - but not + + or - thus only excitations between rotational levels of the same parity is
allowed for an even number of photons and excitation between rotational
levels of opposite parity is allowed for an odd number of photons.
44
3.5 Perturbations72
Sometimes a rotational spectrum can show a deviation from an otherwise
smooth course. This deviation is generally caused by a perturbation. A
perturbation can occur when rotational levels with the same J’ for different
electronic states are close to each other. It is characterized by a shift from the
expected line position and/or a change in the line intensity of the perturbed
lines. Perturbations where the vibrational level has been shifted have also
been observed; those are known as vibrational perturbations and are outside
the scope of this work.
3.5.1 Rotational perturbations
When two rotational levels with the same J’ are energetically close to each
other it is possible for them to be perturbed, causing them to separate in
energy and receive spectroscopic characteristics from each other.
1.2
HCl+
F, v´=1
d)
X, v´=0
1
I(M+)/I1(HiCl+)
0.8
0.6
H+
Cl+
0.4
0.2
0
J´  8 / i = 35
J´  8 / i = 37
J´=8 / i = 35
J´=8 / i = 37
Fig.3d
Figure 15: Perturbation. On the left we have an average ion ratio for the F 1,
’=1 state. On the right we have the ratio for the perturbed F1, ’=1, J’=8
rotational level. As can be clearly seen, the perturbation to the ion-pair state
causes considerable changes to the ratio of H+ and Cl+ vs. HCl+ ion formation for
both the 35Cl and 37Cl isotopes.
45
As an example, the F1, ’ = 1, J’ = 8 and the V1, ’ = 14, J’ = 8 rotational
levels of the HCl molecule are very close energetically. Due to this, the
corresponding Rydberg rotational peak (for the F1state) shows a mass
spectrum that has ion-pair state (V1) characteristics and vice versa, see Figure
15. In addition, the energy difference between J’ = 7 and J’ = 8 and also
between J’ = 8 and J’ = 9 for both states is different from what one would
expect from a non-perturbed progression of rotational lines, whereas the
difference is in accordance with a shift due to perturbation.39
This does not mean that any rotational level that is energetically close to
another is perturbed. The perturbation can only occur between specific
rotational levels as governed by the selection rules.
3.5.2 Perturbation selection rules
1) Both states must have the same total angular momentum J; J = 0
2) Both states must have the same multiplicity; S = 0
3) The  value of the two states must only differ by 0 or ±1;  = 0 , ±1
4) Both states must have the same parity, either both positive or both
negative; + // 5) For molecules with identical nuclei, both states must have the same
symmetry in the nuclei; s // a
Rules 1, 4 and 5 are perfectly rigorous. The second rule holds only
approximately as perturbations between states of different multiplicity
increase in magnitude with increasing multiplet splitting similarly to
transitions with radiation. The third rule holds only when  is defined,
Hund’s case a) and b). For Hund’s case c) the total angular momentum
is used instead.
3.6 Predissociation72
Predissociation is a fragmentation of a molecule into its atoms or smaller
molecular fragments. It can occur through an interaction of a bound state
with an unbound or quasi-bound state. Fragmentation can also occur via
direct excitation to an unbound or quasi-bound state in which case it is
simply referred to as dissociation.
Predissociation can be detected in a rotational spectrum by a sudden
uncharacteristic broadening of lines. This corresponds to the shortening of
the lifetime of the rotational levels due to the molecule predissociating into
smaller atomic or molecular fragments. The predissociation of a molecule
46
can be followed by an excitation of the fragments, either through direct
ionization or by a resonance-enhanced ionization, see Figure 16 a) and b).
a)
b)
A+
B+
A+
B+
A#
AB#
AB#
A+B
AB
A+B
AB
Figure 16: Predissociation of a diatomic molecule. a) Predissociation followed
by a direct ionization. The molecule is initially excited to a bound state which
interacts by a non-bound or a quasi-bound state. Some of the molecules in the
bound state “leap” across to the predissociating state and are dissociated into its
atomic components. The atoms formed can themselves absorb photon energy and
ionize. b) Predissociation followed by a resonance-enhanced ionization. In this
case the photon energy needed to excite the parent molecule corresponds to an
excited state of the atom resulting in a resonance-enhanced excitation.
47
4
Published papers
International Journals
Kristján Matthíasson, Jingming Long, Victor Huasheng Wang, Ágúst Kvaran.
Two-dimensional resonance enhanced multiphoton ionization of H(i)Cl; i=35,
37: State interactions, photofragmentations and energetics of high energy
Rydberg states. Journal of Chemical Physics, 134, 164302, 2011.
Ágúst Kvaran, Victor Huasheng Wang, Kristján Matthíasson, Andras
Bodi. Two-Dimensional (2+n) REMPI of CH(3)Br: Photodissociation
Channels via Rydberg States. Journal of Physical Chemistry A, 114,
9991, 2010.
Ágúst Kvaran, Kristján Matthíasson, Huasheng Wang. Two dimensional
(2+n) REMPI of HCl: State interactions and photorupture channels via
low energy triplet Rydberg states. Journal of Chemical Physics, 131,
044324, 2009.
Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, Two Dimensional
(2+n) REMPI of HCl: Observation of a new electronic state, Journal of
Molecular Spectroscopy, available online, 2009.
Ágúst Kvaran, Huasheng Wang, Kristján Matthíasson, Andras Bodi,
Erlendur Jónsson, Two dimensional (2+n) resonance enhanced
multiphoton ionisation of HCl: Photorupture channels via the F-1
Delta(2) Rydberg state and ab initio spectra, Journal of Chemical
Physics, 129(16), 164313, 2008.
Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, (2+n) REMPI of
acetylene: Gerade Rydberg states and photorupture channels, Chemical
Physiscs Letters, 458 (1-2), 58 (2008).
Icelandic Journals
Kristján Matthíasson, Victor Huasheng Wang, Ágúst Kvaran.
Massagreining í kjölfar ljósgleypni: Víxlverkanir milli örvaðra ástanda
uppgötvaðar. "Tímarit um raunvísindi og stærðfræði", 2011.
49
Ágúst Kvaran, Victor Huasheng Wang og Kristján Matthíasson, Tveggja
ljóseinda gleypni acetylens, "Tímarit um raunvísindi og stærðfræði", 1.
hefti, 2007, bls. 41-44.
50
Paper I
Kristján Matthíasson, Jingming Long, Victor Huasheng Wang, Ágúst Kvaran.
Two-dimensional resonance enhanced multiphoton ionization of H(i)Cl; i=35,
37: State interactions, photofragmentations and energetics of high energy
Rydberg states. Journal of Chemical Physics, 134, 164302, 2011.
51
53
54
55
56
57
58
59
60
Paper II
Ágúst Kvaran, Victor Huasheng Wang, Kristján Matthíasson, Andras
Bodi. Two-Dimensional (2+n) REMPI of CH(3)Br: Photodissociation
Channels via Rydberg States. Journal of Physical Chemistry A, 114,
9991, 2010.
61
63
64
65
66
67
68
69
70
Paper III
Ágúst Kvaran, Kristján Matthíasson, Huasheng Wang. Two dimensional
(2+n) REMPI of HCl: State interactions and photorupture channels via
low energy triplet Rydberg states. Journal of Chemical Physics, 131,
044324, 2009.
71
73
74
75
76
77
78
79
80
81
82
Paper IV
4Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, Two
Dimensional (2+n) REMPI of HCl: Observation of a new electronic
state, Journal of Molecular Spectroscopy, available online, 2009.
83
85
86
87
88
89
90
Paper V
Ágúst Kvaran, Huasheng Wang, Kristján Matthíasson, Andras Bodi,
Erlendur Jónsson, Two dimensional (2+n) resonance enhanced
multiphoton ionisation of HCl: Photorupture channels via the F-1
Delta(2) Rydberg state and ab initio spectra, Journal of Chemical
Physics, 129(16), 164313, 2008.
91
93
94
95
96
97
98
99
100
101
102
103
Paper VI
Kristján Matthíasson, Huasheng Wang, Ágúst Kvaran, (2+n) REMPI of
acetylene: Gerade Rydberg states and photorupture channels, Chemical
Physiscs Letters, 458 (1-2), 58 (2008).
105
107
108
109
110
111
112
5
Ion formation through multiphoton processes for HCl35-39,77
The photoionization of HCl is a complex multiprocess mechanism that
entails perturbations, photodissociations and predissociations. In this
chapter I will go over the ionization mechanism that are know or have
been suggested. Figure 17 shows all the mechanics discussed collected
into a single figure.
5.1 Formation of HCl+
HCl+ ions are generally only formed through ionization via a Rydberg
state via mechanism (1) shown in figure 17 a). However, electrons
excited to an ion-pair state are able to access Rydberg states by
perturbation.
5.1.1 Ionization via Rydberg states
The formation of HCl+ via a Rydberg state is the simplest of the
ionization mechanisms. HCl+ is formed by a simple two-step process, i.e.
the formation of excited HCl# followed by the direct ionization of the
excited molecule, forming HCl+.
5.1.2 Ionization via ion-pair state
HCl+ ions are probably never formed directly via ion-pair states, or at
most only a small fraction. However, HCl+ in considerable quantity has
been observed from ionizations via ion-pair states.19-21,39,40 The cause of
this is found to be a perturbation of the ion-pair state.
When two rotational levels with similar energy are perturbed, the
wavefunctions are overlapped allowing the electron to move from one
state to the other, thus being observed to have characteristics of both
states. The electron can therefore be excited into the ion-pair state, be
perturbed into a Rydberg state, and from there follow channel (i) and (ii)
shown in figure 17 a) forming an ion.
113
a)
(2+n)
HCl+*
(4)
HCl+*
H+ + Cl
H+ + Cl
(iv)
(ii)
(v)
HCl**
(T)
HCl+
(3)
H+
Cl+
HCl+
(vi)
HCl**
1+
HCl**[A]1+
H* +Cl
H+ Cl*
H+Cl*
(i)
H+ + Cl(vii)
(iii)
(2)
HCl*
(Ry, v´,J´)
H+Cl(V1+, v´,J´)
W12
(2)
(1)
(2+n)
(2+n)
b)
HCl+*
H+ Cl+
(5)
Cl+
H+ +Cl
(4)
HCl+
(3)
(ii)
(ix)
(4)
HCl**
H+ Cl*
(viii)
HCl*
(RyG, v´,J´)
(3)
(i)
(SO)
(2)
HCl*
(Ry, v´,J´)
SO
HCl*
3 +
(3)
H + Cl(J =1/2,3/2)
(1)
Figure 17: Main ionization mechanisms of HCl. Figures a) and b) show possible
ionization channels via Rydberg (HCl*) and ion-pair states (H+Cl-). The
predissociation gateway mechanism forming H + Cl is included. Necessary
amount of photons for ionization are shown.
114
Since the rotational levels of the ion-pair state in HCl are generally
always perturbed by the Rydberg states close in energy, HCl+ is observed,
in different amounts though, for almost every observed rotational line of
the ion-pair state. Due to this fact there is a possibility that HCl + is
formed directly from the ion-pair state as has been suggested as shown
for channel (iii) in figure 17 a).35-38 This should however be in small
amounts compared to the HCl+ formed via perturbation, as most low level
ion-pair rotational lines, which are perturbed the least, show only a very
limited HCl+ formation and the v’=4 ion-pair vibrational level shows no
discernable HCl+ at all.
5.2 Formation of H+
H+ ions are formed by several possible channels depending on whether
the ionization is through a Rydberg or ion-pair state.
5.2.1 Ionization via Rydberg states
For unperturbed rotational levels the formation of H+ is initially the same
as for HCl+ followed by a single-photon process that forms the H+ ion.
For perturbed rotational levels the electron is initially excited by a
multiphoton process into an energetically excited Rydberg state. Due to
the perturbation the rotational level gains ion-pair characteristics and the
electron can follow the same ionization mechanism as outlined for ionpair states (in other words it is perturbed into the ion-pair state).
However, one must bear in mind that the proportion of HCl # that is not
perturbed can continue to form H+ as outlined above.
5.2.2 Ionization via ion-pair state
The electron is initially excited to the ion-pair state by a multi-photon
process. The unperturbed electron then undergoes a single-photon
excitation to an unbound state, causing the molecule to dissociate into a
Cl atom and energetically excited H# atom which is ionized as shown in
figure 17 a) channel (vi).
For an electron perturbed into a Rydberg state the ionization mechanism
is the same as outlined for Rydberg states, i.e. excitation to HCl +
followed by a single-photon excitation forming H+.
Additionally it has been suggested that H+ can be formed directly from
the ion-pair state by a photodissociation of H+Cl- into H+ and Cl- as
outlined in figure 17 a) channel (vii).
115
5.3 Formation of Cl+
Cl+ ions are generally only formed through ionization via an ion-pair
state. However, electrons excited to a Rydberg state are able to access
ion-pair states by perturbation.
5.3.1 Ionization via Rydberg states
Cl+ in considerable quantity has been observed from ionization via
Rydberg states.19-21,39,40 The cause of this is found to be a perturbation
between the Rydberg state and a neighbouring ion-pair state. The electron
is perturbed into the ion-pair state followed with a single-photon
excitation to an unbound state, causing the molecule to dissociate into an
H atom and an energetically excited Cl# atom which is ionized as shown
in figure 17 a) channel (v).
Typically the rotational levels in the Rydberg states of HCl are perturbed
by the ion-pair state only in few specific cases. Thus, Cl+ is only observed
in considerable amount in cases where the energy difference of
comparable rotational levels is small, with the exception of the 1 states,
which show Cl+ formation for all observed rotational levels. This
selective appearance of the Cl+ ion is found to be an excellent diagnostic
tool when characterising new states.41,78
However there are observable Cl+ signals for rotational levels that should
not be perturbed by the ion-pair state. These signals are most likely due to
a predissociation of the HCl molecule, followed by the ionization of the
Cl atom as shown for channel (viii) figure 17 b). It is know that Cl atoms
are formed by predissociation in the HCl molecule, specifically through
the C-state. Therefore it is quite possible that these minute amounts of Cl+
ions that are formed are indeed formed via predissociation. It has also
been suggested that Cl+ can form directly via Rydberg states by
photoexcitation to inner walls of bound superexcited states as shown for
channel (ix) in figure 17 b), where the molecule is dissociated into H +
Cl* followed by ionization of the chlorine.
5.3.2 Ionization via ion-pair state
Like the formation of H+ via the Rydberg state, the formation of Cl+ via
an ion-pair state is somewhat straightforward. The electron is excited to
the ion-pair state by a multi-photon process. What follows is then a
single-photon excitation to an unbound state, causing the molecule to
116
dissociate into an H atom and an energetically excited Cl # atom which is
ionized ( channel (v)).
117
6
The use of mass analysis to
determine interaction constants
Based on this overall ionization scheme presented above, Cl+ ions are
characteristic indicators for the ion-pair state contribution, H+ formation clearly
is both indicative of the ion-pair and the Rydberg state contribution and HCl+
formation is the main ion formation channel via Rydberg state excitation under
low power conditions. There are reasons to believe that the HCl+ contribution
to ion formation, via excitation to the V1 state, is rather small.39 Therefore, it
has been found to be useful to define and work with normalized ion intensities
for Cl+ (IN(Cl+) and HCl+ (IN(HCl+)) as indicators for the separate (diabatic)
Rydberg and ion-pair states respectively, where IN(Cl+) is the Cl+ ion signal
intensity normalized to (divided by) the HCl+ ion signal intensity and vice
versa, i.e.:
IN(Cl+) = I(Cl+)/I(HCl+); Rydberg state indicator
IN(HCl+) = I(HCl+)/I(Cl+); ion-pair state indicator
In addition to the photofragmentation channels, mentioned above, further
dissociation of resonance-excited Rydberg states to form H + Cl and/or H
+ Cl* via predissociation of some gateway states could be important, as
predicted by Alexander et al.77 In such cases, further photoionization of
the Cl, Cl* and H fragments could also occur. Whereas the interactions
between the states involved could be of various kinds77, spin-orbit
couplings most probably are dominant.
Assuming a level-to-level interaction scheme to hold for the Rydberg-toion-pair states interactions, weight factors (fractions) for the state mixing
can be expressed as
E  4 W12
2
1
c  
2
2
i
2 E
2
(34)
for E = E1 - E2, where E1 and E2 are the resulting level energies of the
perturbed states (1 and 2) and W12 is the matrix element of the
119
perturbation function / interaction strength.39,72 In the case of
homogeneous ( = 0) interaction W12 is independent of the total angular
momentum quantum number, J´, whereas for heterogeneous ( > 0)
interactions W12 is expressed as28,39,79
W12 W12' ( J ´( J ´1))1 / 2 (35)
'
for constant W12 . W12 is related to the resulting level energies and the
0
0
zero-order level energies for the unperturbed state ( E1 and E 2 ;
E 0  E10  E20 ) by
Ei 




1/ 2
1 0
1
2
E1  E20  4 W12  (E 0 ) 2
(36)
2
2
Assuming the mechanism discussed above to hold, we make the
following assumptions: Cl+ ion intensity observed (I(Cl+)) is proportional
2
to the fraction of HCl* in the ion-pair state (2; c 2 ) as well as its fraction
2
in the Rydberg state (1; c1 ),
I (Cl  )  2c22  1c12 (37)
Similarly the HCl+ intensity (I(HCl+)) is assumed to be proportional to the
same fractions,
I ( HCl  ) 1c12   2 c22
(38)
For   2 / 1 ,   1 /  2 ,  1  ( 2 / 1 ) and c1 1  c2 , the ratio
of I(Cl+) over I(HCl+) now can be expresses as
2

  c22 (1   )
I (Cl  )


I ( HCl  )
1  c 22



2
(39)
There is a reason to believe that the contribution to the HCl+ formation by
excitation from the diabatic ion-pair state is small39, hence, that the ratio
of its proportionality factor (  2 ) to that for the HCl+ formation from the
diabatic Rydberg state,  1 , (i.e.  2 / 1 ) is negligible and  ~1. By
combining equations (34), (35) and (39) and assuming  =1 the
following expression is derived:
120
2



E ( J ´)  4 W12´2 J ´( J ´1) 
1


   
(1   )

2 E ( J ´)
 2


I (Cl  )




2
I ( HCl )

E ( J ´)  4 W12´2 J ´( J ´1) 
1


1 
2

2 E ( J ´)


(40)
for excitations via a Rydberg state.
Here  (  1 /  2 ), is a measure of the rate of formation of Cl + via the
diabatic Rydberg state (the “gateway channel”) to that of its formation
from the diabatic ion-pair state, which is one of the major/characteristic
ionization channels. Hence  is a relative measure of the importance of
the “gateway channel”.
Comparably  (  2 / 1 ) measures the relative rate of the two
major/characteristic ionization channels, i.e. for the Cl+ formation for
excitation from the diabatic ion-pair state (  2 ) to the HCl+ formation from the
diabatic Rydberg state (  1 ). Considering the general fact that Cl+ ion signals
via excitations to the ion-pair states and HCl+ ion signals via excitations to the
Rydberg states, signals are comparable or certainly of the same order of
magnitude (See Figs. 2-3) it is concluded that  should be somewhat close to
unity and certainly in the range 10-1 <  < 10.
By multiplying  and  (*) we get a measure of the actual rate of
formation of Cl+ via the diabatic Rydberg state (the “gateway channel”)
to that of its formation from the diabatic ion-pair state
This expression allows relative ion signal data to be fitted for known E
'
values using the variables  ,  and W12 as has been previously
accomplished40,41 and are here gathered together in Table 2.
Table 2: State interaction parameters.
State
max
W '12


*
f 32
0.4
0
4
0
3
1
0.7
0.002
0.5
0.001
g 3(1)
1.0
0.5
0.6
0.3
j 3(1)
2.7
0.004
3.5
0.014
-
0.031
2.1
0.065
f
j
3 (0+)
121
It is interesting to note that the * values are considerably different
between  and  states. There’s also a increase by an order of magnitude
between the g 3(1) state and the j 3(0+) and j 3(1) states. This opens
up the possibility that the values are characteristic for certain states and
could be used to assist in state assigments. Further experiments are
needed to determine this as no data exists for  states.
For instances of off-resonance interaction we can assume, to a first
approximation, that the ion intensity ratio is a sum of contributions due to
interactions from the ion-pair states to the Rydberg state. In such cases
common  and  parameters for I(Cl+)/I(HCl+) can be expressed as

 
2
2

I (Cl  )
   c 2,n (1   )   c 2,m (1   )




2
I ( HCl  )
(1  c 22,m )

 (1  c 2,n )




(41)
where c22,n and c22,m are the fractional mixing contributions for the
interacting ion-pair states respectively.
122
7
Ionization of acetylene and
methyl bromide compared to HCl
It is interesting to compare the ionization mechanics of HCl on one hand
and of acetylene and methyl bromide on the other. As HCl has been well
covered in the previous parts of this dissertation, let us look at the organic
molecules a little closer.
The acetylene ion is formed by an ionization process similar to the
formation of HCl+, i.e. excitation of the acetylene molecule followed by
ionization. The formation of fragment ions are somewhat more
complex.12 However, they generally go through a rearrangement followed
by a predissociation of the parent molecule and a subsequent ionization of
the fragments, forming H+, C+, C2+, C2H+ and CH+.
For methyl bromide a similar story unfolds. Again the methyl bromide
ion is formed by an ionization process similar to the formation of
acetylene and HCl+, i.e. excitation of the methyl bromide molecule
followed by ionization. The formation of fragment ions is again much
more complex than of the parent molecule. In this case two rather
predominant predissociations occur forming CH3 and Br atoms on one
hand and C, H2 and HBr on the other, followed by ionization. Further
dissociation of the fragments can occur in addition to several other
ionization pathways.
To emphasise, for methyl bromide and acetylene this is a simplified
account of the ionization processes of the molecules. What is noteworthy,
however, is that in all these cases the formation of ion fragments goes
through a predissociation process of some sort. This would suggest that
predissociation plays a much more important role in spectroscopy than
hitherto believed.
For HCl, predissociation also plays a key part in the W12 model presented
above. It is interesting to note that it may be possible to use the  and 
values of uncharacterised states to assist in their assignment. 41 However,
more research is needed to ascertain a correlation between the  values of
known states and their assignment.
123
8
Unpublished work
8.1 C1-State
The C1 state of HCl is of interest due to its heavy predissociation. The
spectrum shown in Figure 18 has a typical form suggesting short
lifetimes due to predissociation. The mass spectrum analysis in Figure 19
confirms this theory as a much higher ratio of Cl+ is formed for all
rotational levels than expected for a Rydberg state. Most likely the HCl
molecule is predissociating into neutral H and Cl followed by a direct
three-photon ionization of Cl to Cl+.
1
C ' = 0, R
300
2
200
4
1
6
1
C ' = 0, S
C ' = 0, Q
1
2
C ' = 0, P
100
4
6
1
6
0
3
1
1
C ' = 0, O
-100
3
1
77300
77400
-200
-300
-400
77500
77600
77700
-1
[cm ]
Figure 18: (2+n) REMPI of C1 ←← X1+ (0,0) excitation. The figure shows a
diffused spectrum of the H35Cl isotopologue.
A mass spectrum also shows an interesting difference between mass peaks
belonging to the R and P series on the one hand and those belonging to the S
series on the other hand. The J’ = 4 peak of the S series diverges from the
almost linear mass ratios of the other rotational peaks. This divergence is
typically due to perturbation with an ion-pair state.
125
I(35Cl+)/I(H35Cl+) ratio
0.12
0.1
0.08
0.06
0.04
0.02
0
1
2
3
4
5
6
J'
Figure 19: I(Cl+)/I(HCl+) ratio for the C1 state ’=0. The white columns
represent the P-series, the black columns the R-series and the gray columns the
S-series. An increased I(Cl+)/I(HCl+)ratio is observed for the J’=4 rotational
level. A small increase in I I(Cl+)/I(HCl+) for the R-series at J’=4 is most likely
due to an overlap with the J’=2 peak of the S-series.
By using equation (40) it is possible to calculate the position of the J’=4
line of the ion-pair state. A comparison of this calculation with the ionpair states measured by Jacques and Barrow80 suggests however that this
cannot be as the energy difference between the rotational lines would
need to be much smaller.
This perturbation effect may therefore be due to a previously undetected state,
possibly a gateway state, as the increased ratio of I(Cl+)/I(HCl+)suggests.
8.2 E1-State
The E1 state of HCl is of interest due to its extended perturbation via off
resonance interaction. Figure 20 shows the I(Cl+)/I(HCl+)and
I(H+)/I(HCl+)ratio of individual rotational peaks for the E1 ←← X1+ (1,0)
excitation.
126
I(H+)/(HCl+) and I(Cl+)/(HCl+)
1,4
2,5
a)
b)
1,2
2
1
Cl+
Cl+
H+
1,5
0,8
H+
0,6
1
0,4
0,5
0,2
0
0
0
1
2
J´
3
4
5
0
1
2
3
J´
4
5
5
6
7
Figure 20: (2+n) REMPI of E1 ←← X1+ (1,0) and V1 ←← X1+ (14,0)
excitations. The figure shows the HCl+/Cl+ ratio of individual rotational peaks.
Table 3 shows the E values for the rotational peaks shown in figure 20.
Interestingly the mass ratio for E1 J’=0 and J’=1 appear to have reached
a perturbation “saturation” point as one would expect to see an increased
Cl+ formation for J’=0 compared with J’=1. Perturbation “saturation”
refers to a 50% mixture of the perturbed states.
Table 3: E values for the rotational peaks of the E 1 ←← X1+ (1,0) and V1
←← X1+ (14,0) excitations.
J’
E; [cm-1]
E1 (v’=1) ↔ V1(v’=14)
0
246.00
1
247.70
2
251.30
3
260.40
4
280.20
5
319.80
By assuming a 50% state mixing equation (34) can be used directly to
evaluate the W12 constant for this interaction. By doing so a value of
W12=124±2 cm-1 is found. For further studies it would be interesting to
use equation (41) to evaluate W12 using mass ratios and assuming a
considerable off reasonance interaction.
127
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Appendix A: Conference
presentations
Posters
(2+n) REMPI of Acetylene; Gerade Rydberg States and Photorupture
Channels.The 20th International Conference on High Resolution
Molecular Spectroscopy, Prague, Czech Republic, September 2-6, 2008.
MATTHIASSON K., KVARAN A., WANG V.H.
Two dimensional (2+n) REMPI of HCl; Photorupture Channels via the
F1 2 Rydberg state and Ab Initio; The 20th International Conference on
High Resolution Molecular Spectroscopy, Prague, Czech Republic,
September 2-6, 2008, MATTHIASSON K., KVARAN A., WANG V.H.
Two Dimensional (2+n) REMPI of HCl; Photorupture Channels via
Various Rydberg States; The 20th International Conference on High
Resolution Molecular Spectroscopy, Prague, Czech Republic, September
2-6, 2008, MATTHIASSON K., WANG H., KVARAN A.
HCl Photorupture Studies, Raunvísindaþing 2008, 14. og 15. mars í
Öskju, Náttúrufræðahúsi Háskóla Íslands, Kristján Matthíasson.
HCl Photorupture Studies, 4. ráðstefna Efnafræðifélags Íslands á Hótel
Loftleiðum, 2007; Kristján Matthíasson, Victor Huasheng Wang og
Ágúst Kvaran.
Rannsóknir á vetnistengdum sameindaþyrpingum: HF-þyrpingar.
Raunvísindaþing 2006, 3. og 4. mars í Öskju, Kristján Matthíasson,
Victor Huasheng Wang, Ómar F. Sigurbjörnsson og Ágúst Kvaran.
Three photon absobtion of open shell structured molecules. Annual NordForsk
Network Meeting 2005; Fundamental Quantum Processes in Atomic and
Molecular Systems, Sandbjerg, Denmark, 18. Agust – 22. August, 2005,
Kristján Matthíasson, Victor Huasheng Wang and Ágúst Kvaran.
Multiphoton absorption: LASER ionization and mass analysis, 3.
ráðstefna Efnafræðifélags Íslands á Nesjavöllum, 18. - 19. september,
2004; Victor Huasheng Wang, Kristján Matthíasson og Ágúst Kvaran.
135
Fjölljóseindagleypni
niturmonoxíð-sameindarinnar,
3.
ráðstefna
Efnafræðifélags Íslands á Nesjavöllum, 18. - 19. september, 2004;
Kristján Matthíasson, Victor Huasheng Wang og Ágúst Kvaran.
Multiphoton absorption: LASER ionization and mass analysis,
Raunvísindaþing 2004 í Öskju, Náttúrufræðahúsi Háskóla Íslands, 16. - 17.
apríl 2004; Victor Huasheng Wang, Kristján Matthíasson og Ágúst Kvaran.
Fjölljóseindagleypni niturmonoxíð-sameindarinnar, Raunvísindaþing
2004 í Öskju, Náttúrufræðahúsi Háskóla Íslands, 16. - 17. apríl 2004;
Kristján Matthíasson, Victor Huasheng Wang og Ágúst Kvaran.
Talks
Resonance enhanced multiphoton ionization and time of flight mass
analysis of C2H2, Annual NordForsk Network Meeting 2007;
Fundamental quantum processes in atomic and molecular systems,
Nesbúð, near Reykjavík, Iceland, 30. June – 2. July, 2007, Kristján
Matthíasson, Victor Huasheng Wang and Ágúst Kvaran.
Research on Hydrogen Bonded Molecular Clusters: HF-Clusters .Annual
NordForsk Network Meeting 2006; Fundamental quantum processes in
atomic and molecular systems, Petursburg, Russia.17-19 June 2006
Kristján Matthíasson, Victor Huasheng Wang and Ágúst Kvaran.
Research on Hydrogen Bonded Molecular Clusters: HF-Clusters
Raunvísindaþing 2006 í Öskju, Náttúrufræðahúsi Háskóla Íslands, 3. - 4.
mars. 2006; Kristján Matthíasson, Victor Huasheng Wang og Ágúst Kvaran
Resonance Enhanced Multiphoton Ionization and Time of Flight Mass
Analysis of C2H2, Annual NordForsk Network Meeting 2005;
Fundamental Quantum Processes in Atomic and Molecular Systems,
Sandbjerg, Denmark, 18. Agust – 22. August, 2005, Kristján
Matthíasson, Victor Huasheng Wang and Ágúst Kvaran.
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