High resolution spectroscopy of methyltrioxorhenium: towards the observation of parity violation in chiral molecules.

Abstract

Originating from the weak interaction, parity violation in chiral molecules has been considered as a possible origin of biohomochirality. We have proposed the observation of molecular parity violation using the two-photon Ramsey fringes technique on a supersonic beam. As a first step in this direction, a detailed spectroscopic study of methyltrioxorhenium (MTO) has been undertaken. It is an ideal test molecule as the achiral parent molecule of chiral candidates for a parity violation experiment. For the (187)Re MTO isotopologue, a combined analysis of Fourier transform microwave and infrared spectra as well as ultra-high resolution CO(2) laser absorption spectra enabled the assignment of 28 rotational lines and 71 rovibrational lines, some of them with a resolved hyperfine structure. A set of spectroscopic parameters in the ground and first excited state, including hyperfine structure constants, was obtained for the ν(as) antisymmetric Re=O stretching mode of this molecule. This result validates the experimental approach to be followed once a chiral derivative of MTO is synthesized, and shows the benefit of the combination of several spectroscopic techniques in different spectral regions, with different set-ups and resolutions. The first high resolution spectra of jet-cooled MTO, obtained on a set-up being developed for the observation of molecular parity violation, are shown, which constitutes a major step towards the targeted objective.

Full text

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High resolution spectroscopy of methyltrioxorhenium: towards the
observation of parity violation in chiral molecules†

Clara Stoeffler1, Benoît Darquié1,*, Alexander Shelkovnikov1, Christophe Daussy1, Anne
Amy-Klein1, Christian Chardonnet1, Laure Guy2, Jeanne Crassous3, Thérèse R. Huet4, Pascale
Soulard5, Pierre Asselin5,*

1 Laboratoire de Physique des Lasers, UMR7538 Université Paris 13-CNRS, 99 av. J.-B.
Clément, F-93430 Villetaneuse, France
2Laboratoire de Chimie, UMR 5182 Ecole Normale Supérieure de Lyon-CNRS, 46 Allée
d’Italie, F-69364 Lyon 07, France
3Sciences Chimiques de Rennes, Campus de Beaulieu, UMR6226 Université de Rennes 1-
CNRS, 35042 Rennes Cedex, France
4Laboratoire de Physique des Lasers, Atomes et Molécules, UMR8523 Université Lille 1-
CNRS, F-59655 Villeneuve d’Ascq Cedex, France
5Laboratoire de Dynamique, Interactions et Réactivité, UMR7075 Université Pierre et Marie
Curie-CNRS, 4 Place Jussieu, F-75005 Paris, France
* to whom correspondence should be addressed: benoit.darquie@univ-paris13.fr,
pierre.asselin@upmc.fr
Abstract
Originating from the weak interaction, parity violation in chiral molecules has been
considered as a possible origin of the biohomochirality. It was predicted in 1974 but has never
been observed so far. Parity violation should lead to a very tiny frequency difference in the
rovibrational spectra of the enantiomers of a chiral molecule. We have proposed to observe
this predicted frequency difference using the two photon Ramsey fringes technique on a
supersonic beam. Promising candidates for this experiment are chiral oxorhenium complexes,
which present a large effect, can be synthesized in large quantity and enantiopure form, and
can be seeded in a molecular beam. As a first step towards our objective, a detailed
spectroscopic study of methyltrioxorhenium (MTO) has been undertaken. It is an ideal test
molecule as the achiral parent molecule of chiral candidates for the parity violation
experiment. For the 187Re MTO isotopologue, a combined analysis of Fourier transform
microwave and infrared spectra as well as ultra-high resolution CO2 laser absorption spectra
enabled the assignment of 28 rotational lines and 71 rovibrational lines, some of them with a
resolved hyperfine structure. A set of spectroscopic parameters in the ground and first excited
state, including hyperfine structure constants, was obtained for the νas antisymmetric Re=O
stretching mode of this molecule. This result validates the experimental approach to be
followed once a chiral derivative of MTO will be synthesized, and shows the benefit of the
combination of several spectroscopic techniques in different spectral regions, with different
set-ups and resolutions. First high resolution spectra of jet-cooled MTO, obtained on the set-
up being developed for the observation of molecular parity violation, are shown, which
constitutes a major step towards the targeted objective.

† Supplementary information available in the ancillary file: Measured and fitted transition frequencies as well as
spectroscopic constants.

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I. Introduction: context and history
Chiral molecules have been identified as relevant candidates for the study of parity
violating effects arising from the exchange of virtual Z0 bosons between electrons and
constituents of the nuclei, a mechanism precisely described by standard electroweak theory. It
should lead to small energy differences between the two enantiomeric mirror image states of
chiral molecules1-3, but to date, no experiment has reached the sensitivity required to observe
this tiny difference. The weakness of the effect represents a very difficult experimental
challenge. There has been speculation that this minute difference could still be large enough
to trigger the observed homochirality in living organisms, the biochemistry showing, with
very few exceptions, a distinct preference for L-amino acids and D-monosaccharides over
their mirror images. The role of weak interaction in the origin of homochiral life is still a
subject of debate4-10, which is one motivation for an experimental observation of parity
violation (PV) in molecules that would enable to address this question quantitatively.
A number of experimental techniques have been proposed for the observation of PV in
molecular systems, including rovibrational11, electronic12-14, Mössbauer15 and NMR16
spectroscopy, as well as crystallization17 and solubility18 experiments, or optical activity
measurements19, but no unambiguous observation has so far been made. After the pioneering
work of Yamagata1, Rein2, and Gajzago and Marx3 who first suggested that weak interaction
is responsible for an energy difference in the spectrum of right- and left-handed chiral
molecules, Letokhov proposed in 1975 to observe PV effects in molecules as a
difference
RL
ννν−=∆
PV
in the rovibrational frequencies
of left and right enantiomers.11 After a first test on separated enantiomers of camphor in
197720, the most sensitive experiments to date following Lethokov’s proposal were performed
around 2000 by authors of this paper.21, 22 A CO2 laser-based spectrometer was developed to
probe a bromochlorofluoromethane (CHFClBr) transition around ν ~ 30 THz (10 µm or 1000
cm-1), using saturated absorption laser spectroscopy. The spectrum of each enantiomer was
simultaneously recorded in separate Fabry-Perot cavities, and the absorption frequencies were
compared at a 5×10-14 level. However, a residual pressure shift induced by impurities in the
samples was observed and found to limit the experimental sensitivity at 2×10-13 for the parity
violation effect (
8
<−
RL
νν
Hz), taking into account the respective enantiomeric excess of
56% and 72% for the R-(–) and S-(+) configuration samples. Later theoretical studies
predicted a PV difference for CHFClBr on the order of -2.4 mHz23, 24, corresponding to
17
PV
108
×−≈∆νν
. To go further, it was necessary to develop a new experiment in which,
among other improvements, collisional effects would be negligible.
A new generation of CO2 laser spectroscopy experiments based on the recording of
two-photon Ramsey fringes of chiral molecules in a supersonic jet is under development at
Laboratoire de Physique des Lasers (LPL).25-28 The experiment is adapted from an existing
Ramsey fringes set-up that enabled us to measure SF6 absolute frequencies with a sub-Hz (10-
14) accuracy.29, 30 In particular, it will benefit from the accurate control of the CO2 laser
frequency by comparison to a primary frequency standard. Besides we expect a strong
reduction of systematic effects for three reasons: (i) in such a supersonic jet set-up, collisions
are mainly due to background pressure, 4 to 5 orders of magnitude lower than in the CHFClBr
experiment, and the corresponding shift will be reduced accordingly; (ii) the same set-up will
be alternatively fed with right- and left-handed molecules which will cancel out a number of
systematic effects; (iii) the probed line width will be of the order of 100 Hz, instead of 60 kHz
for the CHFClBr experiment, which will reduce most systematic errors accordingly. With this
L
ν and
R
ν of the same transition
−

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set-up, a sensitivity of ~0.01 Hz (3×10-16) on the frequency difference between two
enantiomers seems accessible. For more details, the reader is advised to refer to 25.
The expected PV effect scales approximately as
most heavy nucleus).31, 32 Thus candidate molecules should preferably contain one or more
heavy atoms at or near the chiral centre. Lately, chiral selenium, tungsten, gold, mercury,
iridium, osmium and rhenium complexes have been calculated, by P. Schwerdtfeger, R. Bast
and coworkers, to be favourable candidates for PV observation.33-39 For instance, the rhenium
complex Re(η5-Cp*)(=O)(CH3)Cl (1) (Figure 1) presents a strong vibrational band in the 10
µm spectral region of the CO2 laser, and a large PV effect
(obtained from 4-component relativistic Hartree-Fock calculations) which we should detect
unambiguously with the new generation set-up.
The sensitivity of our experiment aiming at observing PV effects in molecules will
highly depend on the Ramsey fringes signal-to-noise ratio, the signal being proportional to the
molecular flux. Even if it is conceivable for synthetic chemists to produce chiral-at-metal
complexes similar as 1 in large quantity and with an enantiomeric excess of 100%, these
molecules are solid at room temperature, which constitutes a major difficulty for high
resolution molecular beam gas phase spectroscopy. Since methyltrioxorhenium (MTO) is an
oxorhenium complex known to sublimate easily, an interesting strategy is to study chiral
MTO derivatives. Parallel to the current development of appropriate chiral MTO derivatives
for PV observation, a detailed spectroscopic study of MTO has been undertaken and is
presented in this article. This work enabled us to validate our experimental approach and
develop the set-up dedicated to the PV observation. In section II, we briefly review the
families of oxorhenium complexes that were synthesized for our new PV test, and explain
why we foresee favourable molecules from achiral MTO. Section III describes a Fourier
Transform Microwave (FTMW) spectroscopy study of MTO and section IV reports on the
first rovibrational spectroscopic characterization of the νas antisymmetric Re=O stretching
mode of this molecule via Fourier Transform Infra Red (FTIR) spectroscopy. Room
temperature and jet-cooled spectra have been recorded. A list of observed lines were assigned
in J and K (and F for rotational transitions) and a list of calculated transition frequencies has
been proposed bringing to light a number of lines accessible to the CO2 laser. In section V,
ultra-high resolution CO2 laser saturated absorption spectroscopy of room temperature MTO
in a cell is described, giving credit to the previous analysis. A first relevant assignment of
fully resolved hyperfine transitions is proposed. First high resolution spectra of jet-cooled
MTO, obtained on the set-up dedicated to molecular PV effects observation, are shown,
which constitutes a major step towards the targeted test.
(is the nuclear charge of the
5
A
Z
A
Z
PV
ν∆
of 2.39 Hz (~10-13)35
II. Search of candidate molecules
The choice of the molecule is presently the most challenging issue since it needs to
fulfil a series of stringent conditions. A chiral molecule should have a strong absorption band
in the mid-infrared and a large PV effect in the rovibrational spectrum (i.e.
must be available in the two enantiopure forms and in large quantity (a few grams). It must
sublimate without decomposition in order to enable the production of a supersonic molecular
jet. In addition, we will prefer the simplest molecules with, if possible, no low-frequency
vibrational or internal rotation mode and the smallest possible number of hyperfine sublevels.
These are the conditions needed to obtain a favourable partition function, which has a direct
impact on the signal-to-noise ratio and thus the sensitivity of the experiment, since we probe a
single quantum level.
PV
ν∆
~ 1 Hz). It

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Following the relativistic calculations of Schwerdtfeger and Bast35, we have
considered chiral oxorhenium complexes (1, Figure 1) as appropriate molecules for a possible
experimental observation of PV in chiral molecules. Indeed, these molecules fulfil most of the
above requirements.
Since 2006, we have focused on different classes of compounds, i.e. chiral
oxorhenium complexes such as 2 bearing a hydrotris(1-pyrazolyl)borate (Tp) and a chiral
amino-alcohol as ligands, or “3+1 mixed” oxorhenium complexes such as 3, based on
sulfurated ligands (Figure 1).25 PV shifts of the order of 100 mHz have been calculated for
some of the sulfurated Re complexes.25, 40 Their synthesis in enantiopure form has been
studied. Diverse structural aspects have been investigated, among which their
stereochemistry and conformational analysis. High Performance Liquid Chromatography
(HPLC) separations over chiral stationary phases of these neutral complexes have revealed
themselves efficient for the preparation of pure enantiomers 40-42. However the sublimation of
all these complexes appeared difficult, preventing any possibility to efficiently prepare a
molecular jet.25
To circumvent this problem, we recently turned to MTO ((CH3)ReO3, 4 on Figure 1)
a molecule commercially available, known to sublimate very efficiently and at relatively low
temperature.25, 43 Therefore, our new target molecules are now chiral derivatives of MTO
such as molecule 5 having a tetrahedral chiral rhenium centre. A PV vibrational frequency
difference of 400 mHz (~10-14) has been recently estimated for this compound by T. Saue
and co-workers.25, 44 This molecule is thus an ideal prototype for the search of molecular PV.
As a first step we decided to study achiral MTO, the parent molecule of envisaged candidates
for the PV experiment. It is an ideal test molecule which will enable us to validate our
experimental approach and calibrate our set-up, via the study of the antisymmetric Re=O
stretching mode, that will exist in chiral derivatives even if the overall rovibrational spectrum
will be different.

N
NN
N
B
H
N
N
Re
O
O
H3CN
H3C
RRe,RO-C,SC-N-2
SPY-5-54-C-3
Re
O
S
S
S
SEt
Re
O
Cl
CH3
R-1
CH3
Re
O
O
O
4
R-5
CH3
Re
O
Se
S
(MTO)

Figure 1: Classes of chiral and achiral oxorhenium complexes that have been considered for
the experiment.
Once a candidate molecule is identified, there is most of the time very little
spectroscopic data available. This is the reason why our work involves experts in various
kinds of spectroscopies in order to acquire step-by-step a precise knowledge on spectral line
positions. A typical 10 MHz accuracy on the position of a rovibrational line is needed in order

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to be studied with the ultra-high resolution spectrometer at LPL. For this purpose, high
resolution rotational spectroscopy (section III) and rovibrational spectroscopy (section IV) of
MTO were examined.
MTO powder (from Strem Chemicals Inc., 98 % purity) has been used without
purification in all the experiments described in this paper.
III. Microwave rotational spectroscopy of MTO
The ground-state rotational constants of the two 187Re and 185Re isotopologues of
MTO have previously been determined using microwave spectroscopy by Sickafoose et al.45
MTO rotational spectroscopy has recently been re-investigated in T. Huet’s group (at
Laboratoire de Physique des Lasers, Atomes et Molécules, PhLAM) with a more sensitive
spectrometer in the 2-20 GHz range. The main characteristics of the spectrometer consists of
two large mirrors of diameter of 0.7 m, in order to maximise the signal-to-noise ratio at low
frequencies (diffraction losses), and an high signal acquisition repetition rate of 120 MHz.46
The MTO crystalline powder was heated at about 320 K and the vapour was mixed with neon
carrier gas at a backing pressure of 1.5 bar. The mixture was introduced into a Fabry-Perot
cavity at a repetition rate of 1.5 Hz. Molecules were polarized within the supersonic
expansion by a 2 µs microwave pulse and the free induction decay signal was detected and
digitized at a repetition rate of 120 MHz. After transformation of the signal from the time to
the frequency domain, molecular lines were observed as Doppler doublets, with a point every
0.46 kHz, resulting from the average of about 100 signals. The transition frequency was
deduced from the average of the two Doppler components with an uncertainty estimated to be
1 kHz for most of the lines. Compared to the previous work45, all the twenty-eight hyperfine
lines associated with the
01'
←≡← JJ
and
increasing by a factor of two the number of reported lines. Consequently a better uncertainty
could be obtained on several molecular vibrational ground state parameters. This new set of
values is reported in Table I (together with the previous set from Sickafoose et al) and will be
used for the present rovibrational analysis of the Re=O antisymmetric stretching vibrational
mode (section IV). The molecular parameters considered were the B rotational constant, the
DJ and DJK quartic centrifugal distortion parameters, the eQq quadrupole coupling constant
associated with the Re nuclear hyperfine quadrupole interaction, and the Caa and Cbb spin-
rotation parameters of the Re nucleus (because of the C3v symmetry, Cbb=Ccc).45 This set of
parameters was obtained for both the 185Re and 187Re MTO isotopologues using the SPFIT
program (developed by H. Pickett, Jet Propulsion Laboratory47), giving a root-mean-square
deviation on the difference between the observed and calculated transition frequencies (obs-
cal) of 2.7 kHz, for both species. The list of assigned lines is available in the ancillary file.


Table I : Molecular parameters of CH3187ReO3 and CH3185ReO3 in the ground state,
determined from microwave data. The parameter set from the pioneering microwave study of
Sickafoose et al45 is reported for comparison. The listed uncertainties are 1σ.
12 ← rotational transitions were recorded,


CH3
187ReO3 CH3
185ReO3

Ref. 45 This work Ref. 45 This work
A (MHz) - - - -

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B (MHz) 3466.964(2) 3466.96481(39) 3467.049(3) 3467.04957(39)
DJ (kHz) 0.7(2) 0.705(50) 0.6(4) 0.755(50)
DJK (kHz) 1.9(1.0) 2.208(118) 2.1(1.4) 1.971(118)
eQq (MHz) 716.546(17) 716.54005(192) 757.187(25) 757.18175(192)
Caa (kHz) -50(8) -52.22(37) -45(11) -50.66(37)
Cbb (kHz) -51.7(6) -51.464(92) -51.8(1.1) -51.165(92)

Owing to the C3v symmetry of MTO, the A rotational constant cannot be determined
by microwave spectroscopy and we are not aware of any reliable gas phase value in the
literature. However, in reference48, Wikrent et al recorded rotational spectra of six
isotopologues of MTO and were able to determine a three-dimensional structure. Starting
from this geometry and imposing the C3v symmetry constraints, we calculated a value for A of
3849.81 MHz with an estimated uncertainty of the order of 10 MHz.
IV. FTIR spectroscopy of MTO
MTO in the gas phase is a prolate symmetric top with
vibrational modes.49 In the 1000 cm-1 region two stretching modes are infrared active: the
νas(E) and νs(A1) bands which correspond to the antisymmetric and symmetric vibrations of
the Re=O bond, whose band centres were measured at 959 and 998 cm-1 respectively in the
solid phase at room temperature.50
symmetry and 18
3v
C
A. Experimental results
Room temperature FTIR spectra have been recorded in an 85-cm static stainless steel
cell (described elsewhere51) at different instrumental resolutions ranging from 0.006 to 0.1
cm-1. Cold fundamental Re=O stretching and related hot bands of MTO could be observed
with the best signal-to-noise ratio, at 0.01 cm-1 instrumental resolution, as displayed on Figure
2 (A). Only one broad band is observed around 976 cm-1 (full width half maximum FWHM =
2 cm-1, 17 cm-1 away from the solid phase band centre) that we assign to the νas mode,
predicted to be 14 times more intense than the νs one.44 Such a spectrum doesn’t allow us to
extract reliable structural data on (CH3)ReO3, which justifies the need for supersonic jet high
resolution FTIR spectroscopy.
In a recent study of the urethane molecule (solid phase at room temperature, vapour
pressure < 0.1 mbar at 300 K)52, the Laboratoire de Dynamique, Interactions et Réactivité
(LADIR) acquired an experimental know-how in producing rare-gas supersonic jets seeded
with sublimated molecules. A glass container, filled here with MTO, and all the gas pipes all
the way to the nozzle exit are heated up to ~350 K to prevent recondensation of the
compound. The MTO vapour obtained is continuously seeded in a carrier gas to achieve
backing pressure conditions compatible with a supersonic expansion. In practice, MTO/argon
mixtures (backing pressure ~45 mbar) with an MTO molar dilution up to 13 % expand
through a circular nozzle of 1-mm diameter. Jet-cooled MTO is finally probed by the 16-pass
arrangement of the infrared beam of a Bruker IFS 120 HR interferometer equipped with a
bandpass optical filter centred at 980 cm-1 (FWHM = 100 cm-1) and focussed on a HgCdTe
photovoltaic detector (cut-off below 830 cm-1). In our conditions of supersonic expansion, 15

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g of crystalline MTO have been necessary to record the Fourier transform of 300 co-added
interferograms at 0.005 cm-1 instrumental resolution (0.0034 cm-1 boxcar apodized). A liquid
nitrogen trap positioned between the secondary and primary pumps enabled to retrieve ~50 %
of the initial MTO quantity.
The FTIR jet spectrum of the νas band recorded at 0.005 cm-1 instrumental resolution
is shown in Figure 2 (B). The argon moderate backing pressures and MTO high dilution used
for the supersonic expansion led to an efficient rovibrational cooling, as proved by the
absence of unresolved broad structure due to hot bands. The spectrum is composed of two
similar rovibrational contours centred at 975.98 cm-1 and 976.60 cm-1 respectively with a
10.5/6 intensity ratio. From the isotopic abundance of rhenium, 62.93 % for 187Re and 37.07
% for 185Re, we assign the lowest frequency band to the heaviest isotopologue, i.e.
(CH3)187ReO3 and the highest one to (CH3)185ReO3. Figure 3 (obs.) shows a zoom on the
187Re isotopologue band.
One first important conclusion of these experiments, obvious on Figure 2 and Figure 3
on which CO2 laser lines are labeled, is that the νas band of MTO should have transitions that
are compatible with the CO2 laser spectral window.


Figure 2: Room temperature cell (A) and jet-cooled (B) Fourier transform spectra of the νas
band of MTO recorded at respective instrumental resolution 0.01 and 0.005 cm-1. On the cell
spectrum, narrow lines marked by an asterisk belong to rovibrational transitions of gas phase
decomposition products of MTO. On the jet-cooled spectrum, the bands corresponding to the
two 187Re and 185Re isotopic species are well resolved. R(J) CO2 laser lines are labeled.


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B. Analysis of the jet-cooled ν νas spectrum of MTO

near the band centre, in a series of strong PQ(J,K) (∆K = -1, low frequency side) and RQ(J,K)
(∆K = +1, high frequency side) branches for which K is fixed. Each branch is composed of a
number of sub-bands of given J with
.
JK
≥
The energy terms for the ground state rotational structure are given by the following
expression:

22
) 1()() 1(),(
JJDKBAJ BJKJE
JJ
+−−++=

Higher order terms were neglected. Only the first order terms of the diagonal part of the
excited state vibration-rotation energy were used in our analysis:

2
as as
') 1('
KDKJJD
KKJK
−+−

where ζ is the first-order Coriolis constant for the degenerate vibration νas.

As can be seen on Figure 3, each band contour of the νas perpendicular band53 consists,
422
) 1
+
(
KDKJJD
KKJK
−−
(1)
42
22
) 1
+
(''2) ''( ) 1
+
('),,,(
ν
JJDKlAKBAJJBlKJE
JJ
−−−++=
ζν
(2)
( , 1)
Q J
( , 1)
Q J
PP
( , 1)
Q J
( , 1)
Q J
R
R
( , 2)
Q J
( , 2)
Q J
R
R
( , 3)
Q J
( , 3)
Q J
R
R
( ,0)
( ,0)
RQ J
( , 2)
Q J
( , 2)
Q J
P
P
( , 3)
Q J
( , 3)
Q J
P
P
975.91975.91 975.92975.92 975.93975.93
0.0000.000
0.0020.002
0.0040.004
0.0060.006
0.0080.008
0.0100.010
R(20)R(20)
975.8975.8 975.9
Wavenumbers (cmWavenumbers (cm
976.0
-1)
976.1976.1
0.0100.010
0.012 0.012
0.0140.014
0.0160.016
0.0180.018
0.0200.020
0.0220.022
0.0240.024
0.026 0.026
0.0280.028
0.0300.030
0.0320.032
0.0340.034
calc.
with HFSwith HFS
calc.
without
HFS HFS
obs.obs.
CH3
CH3
187ReO3
Absorbance
RQ J
975.9976.0
-1)
calc.
calc.
without
187ReO3
Absorbance

Figure 3: Comparison between the jet-cooled FTIR spectrum (obs.) of the νas band of
(CH3)187ReO3 in the branch region and two simulations (see text) performed without
(calc.without HFS) or with (calc.with HFS) the contribution of the hyperfine structure (HFS).
The inset shows a simulated stick spectrum (before convolution with the boxcar response
function) of the PQ(J,2) branch, composed of sub-bands of given J with
HFS. The R(20) CO2 laser line is labeled.
=2, without
Q
JK
≥

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For a perpendicular band, transitions obey the rotational quantum number selection
;
1 , 0 ±=∆J
1
±=∆K
; ;
1
±=∆l
=−∆
lK
following combinations of parameters could be fitted:
Meanwhile, by fixing the value of either A or ζ, independent values of the other molecular
parameters can be determined.
Line intensities for such a symmetric top molecule perpendicular band can be
approximated under the form:


[
/),( exp),(
kThKJEgACKJI
KJKJ
−=ν

where J and K are the lower state quantum numbers,
lower state spin-rotation statistical weight, TR is the rotational temperature, ν is the transition
frequency, C is a factor depending on the induced electric dipole moment and on the partition
function, and h and k are the Planck and Boltzmann constants. The statistical weight
namely governed by the 2J+1 rotational degeneracy factor and the rules of nuclear spin
statistics for a C3v molecule with three identical atoms of nuclear spin 1 2 (H), outside the
axis of symmetry. Taking into account the selection rules for a perpendicular band associated
with a doubly degenerate upper state, the observed structure shows that the transitions from
vibrational ground state rotational levels with
K
to levels with
31
Kn
=± (n is an integer).
For the analysis we followed a three-step strategy. We first roughly simulated the band
contour of the, unresolved in J, PQ(J,K) and RQ(J,K) branches using formula (1) and (2),
neglecting at that step the hyperfine structure (HFS). We used A = 3849.81 MHz (as estimated
in section III) and other ground state parameters values obtained from microwave
spectroscopy (see Table I), and took excited-state centrifugal distortion constants DJJ’ and
DJK’ equal to those of the ground state. Then by manually adjusting νas, A’, B’, ζ and TR, we
simply tried to reproduce the frequency maxima of the Q branches (fourteen visible on
Figure 3 for 187Re MTO). Each calculated transition was convolved with the boxcar response
function at the instrumental resolution of 0.005 cm-1 FWHM. The excited-state parameter set
was obtained by manually minimizing the difference between experimental and simulated
frequency maxima of the
branches. For (CH3)187ReO3 our best agreement was obtained
with νas = 975.968 cm-1, A’ = 0.12811 cm-1, B’ = 0.11554 cm-1 and ζ = -0.0027. The
rotational temperature TR was estimated to 10 ± 3K. Figure 3 (obs. and calc. without HFS)
illustrates the good agreement, in the
branch region, between the jet FTIR spectrum of
(CH3)187ReO3 and the spectrum calculated with those parameters.
In a second step, we were able to assign 43 RR and 25 PP transitions of (CH3)187ReO3
on the jet-cooled FTIR spectrum. The list of these assigned lines, their experimental and
calculated frequencies, is available in the ancillary file.
For the less abundant 185Re MTO isotopologue, the same analysis led to the following
set of parameters: νas = 976.588 cm-1, A’ = 0.12808 cm-1, B’ = 0.11555 cm-1 and ζ = -0.0027.
A few RR and PP transitions of (CH3)185ReO3 were assigned, but a global fit could not be
performed. These results are not reported here.
Up to now, the HFS has not been taken into account in our analysis of the
antisymmetric Re=O vibrational mode. The strong quadrupole coupling strength eQq >700
MHz (see Table I) of the rhenium, similar in magnitude to the rotational constants, is
responsible for an important break-up of microwave rotational transitions into hyperfine
rules
0
. For the fundamental band, only the
'
as
A
ζν−
,
AA− '
,
) 1 ( '
A
ζ
−
.
R
]
(3)
KJ
A is the Hönl-London factor53,
KJ
g
the
KJ
g
is
3
n
=
are twice stronger than these associated
Q
Q

9

Page 10

components as observed in 45, 48 and will be responsible for large hyperfine splittings of the
transitions simulated in the previous rovibrational analysis. This HFS cannot be resolved
using FTIR jet spectroscopy but it is essential to fully include it in the rovibrational
simulation for two reasons: (i) evaluate the HFS impact on the recorded FTIR spectra at 100
MHz (0.0034 cm-1) instrumental resolution and on the corresponding rovibrational analysis,
(ii) propose a list of transition frequencies of the νas band assigned in
to reproduce and interpret the resolved hyperfine structures observed at LPL with ultra-high
resolution CO2 laser spectroscopy techniques (see section V).

,
J
K and , in order
F
(6, 0)
(6, 0)
R
R
R
R
(6, 2)
(6, 2)
R
R
R
R
(6,1)
(6,1)
R
R
R
R
(6, 3)
(6, 3)
R
R
R
R
(6, 4)
(6, 4)
R
R
R
R
(6, 5)
(6, 5)
R
R
R
R
(6, 6)
(6, 6)
R
R
R
R
(7, 5)
(7, 5)
P
P
R
R
(7, 4)
(7, 4)
P
P
R
R
(7, 3)
(7, 3)
P
P
R
R
977.60
977.60
977.65
Wavenumbers (cm
Wavenumbers (cm
977.70
-1)
977.75
977.75
0.000
0.000
0.002
0.002
0.004
0.004
0.006
0.006
0.008
0.008
0.010
0.010
calc.
calc.
obs.
obs.
Absorbance
977.65977.70
-1)
Absorbance

Figure 4: Comparison between observed jet-cooled FTIR and the calculated (with Set 2 of
Table II) stick spectra of seven RR(6,K) assigned transitions (with K=0-6) of the νas band of
(CH3)187ReO3.
Thus, in a third step, we added the HFS with the help of the SPFIT/SPCAT suite of
programs of H. Pickett47, to the analysis of the 187Re MTO. We fitted the energy levels with a
Hamiltonian containing the spin-rotation interaction terms Caa and Cbb, and more important,
the rhenium quadrupole coupling constant
187Re isotopologue of MTO, we included in the fit: (i) the assigned rotational lines used in
the microwave study of section III, (ii) the assigned PP(J,K) and RR(J,K) lines recorded by
FTIR spectroscopy, and (iii) the HFS of the RQ(20,0) line recorded at ultra-high resolution at
LPL, and the high resolved RQ(19,0) and PQ(12,1) lines recorded in a jet apparatus at LPL, as
described in the next section, that could all be assigned over the course of this analysis (see
section V for more details). The complete set of assigned lines used in this analysis is
available in the ancillary file. The fit led to an rms value of (obs-cal) of 0.0017 cm-1 (51
MHz) and the values obtained for the molecular parameters are presented in Table II together
with their error bars. For this fit, centrifugal distortion constants (except DKK) and the spin-
in both the ground and excited states. For the
eQq

10

Page 11

rotation interaction Caa were fitted but constrained to the same value in the ground and
excited states. At a first stage (Set 1 in Table II), we constrained the value of the A constant
at 3849.81 MHz (value estimated in section III), and obtained ζ = -0.0011(3)<<1. At a
second stage (Set 2 in Table II), we neglected the first-order Coriolis contribution, to be able
to fit both effective A and A’ rotational constants. The A value stays within the predicted
uncertainty (section III). Both sets of parameters are equivalent.
Figure 3 illustrates the good agreement, in the Q branch region, between the jet FTIR
spectrum of (CH3)187ReO3 and the spectrum calculated with Set 2 of Table II. Compared to
the rough simulation of the first step, adding the HFS contribution does not practically
change the position of the maxima of the Q branches but has for consequence to smooth
their overall line shape due to the unresolved structure of the rovibrational transitions. Figure
4 displays a comparison between jet-cooled and calculated (with Set 2 of Table II) stick
spectra of seven RR(6,K) assigned transitions (K from 0 to 6) of the νas band of (CH3)187ReO3.
The HFS contribution is clearly illustrated on this figure. The order of magnitude of HFS
splitting is ~100 MHz (~3×10-3 cm-1) for low J values. It decreases when J increases, and
increases with K.
Table II : Ground- and excited-state (vas = 1) parameters of the isotopologue CH3187ReO3.
Microwave (section III) and Infrared data, both from FTIR (section IV) and high resolution
CO2 laser absorption experiments (section V), were used. The listed uncertainties are 1σ.
Both sets of values are equivalent (see text).

Set 1 Set 2
A (MHz) 3849.81 a 3854.01(1.27)
B (MHz) 3466.96481(39)
0.705(50) b
2.208(118) b
3466.96481(39)
0.705(50) b
2.208(118) b
DJ (kHz)
DJK (kHz)
eQq (MHz) 716.54005(192)
-52.22(37) b
716.54005(192)
-52.22(37) b
Caa (kHz)
Cbb (kHz)
νas (cm-1)
-51.464(92) -51.464(92)
975.9665(3) 975.9667(3)
A’ (MHz) 3847.14(34) 3851.35(1.12)
B’ (MHz) 3463.4362(224)3463.4362(224)
ζ
-0.0011(4)
0.705(50) b
2.208(118) b
0.0 a
DJ ’ (kHz) 0.705(50) b
2.208(118) b
DJK ’ (kHz)
eQq’ (MHz) 694.779(44)
-52.22(37) b
694.779(44)
-52.22(37) b
Caa’ (kHz)
Cbb’ (kHz) -53.005(149) -53.005(149)
(a) Fixed value
(b) Fitted and constrained to the corresponding ground state/excited state value

11

Page 12

V. Ultra-high resolution absorption spectroscopy of MTO
In the context of molecular PV observation, the highest resolution spectroscopy
techniques are needed and an experimental set-up based on the powerful method of Doppler-
free two-photon Ramsey fringes in a supersonic molecular beam was proposed.25-28 It was
thus necessary to check whether a complex molecule such as MTO which has spectroscopic
properties similar to the chiral derivatives that we consider for such a test, is suitable for this
kind of spectroscopy and optimize the supersonic beam apparatus accordingly. The first steps
in this direction are exposed in the following paragraphs.
A. The spectrometer
The ultra-high resolution laser spectrometer used for the experiment dedicated to the
PV observation is based on the combination of two CO2 lasers which can operate in the 8-12
µm range (already described elsewhere29, 30). Frequency stability and tunability are important
issues for this experiment. In order to probe lines of the νas band of MTO, found to be centred
around 976 cm-1, the two lasers are set on one same laser line of the CO2 10.2-µm R branch.
The first is locked to an OsO4 rovibrational line. The frequency stabilization scheme is
described in 54: a sideband generated with a tunable electro-optic modulator (EOM) is
stabilized on an OsO4 saturated absorption line (FWHM ~20 kHz) detected in transmission of
a 1.6-m long Fabry-Perot cavity. The laser spectral width measured from the Allan deviation
of the beat note between two independent lasers shows a typical frequency instability below 1
Hz after 100 s.54 For data collection and averaging (see section C), frequency stability is
however also required over longer times of a few tens of minutes, after which the typical
frequency instability is ~100 Hz.54 This system can achieve a frequency accuracy better than
100 Hz.54
The second laser, whose beam is used to probe MTO, is phase locked to the first with
a tunable radio frequency (RF) offset. The first laser sets the frequency stability and accuracy,
while the second enables frequency tunability under computer control of the synthesizer
delivering the RF offset. In these conditions, tunability is however limited to the laser gain
curve width, i.e. ~80 MHz. By allowing, or not, the second laser beam to be frequency shifted
by up to two acousto-optic modulators (AOMs), tunability around each CO2 line could be
increased to a spectral window of [-280 MHz, +280 MHz]. Both AOMs, of respective fixed
frequencies 40 and 80 MHz, were set up in double pass, either on the +1 or -1 diffraction
order.
B. Saturated absorption spectroscopy in a cell
In this section, we describe saturated absorption spectroscopy of MTO at 300 K in a
cell.25 These experiments constitute a first step towards jet spectroscopy (much more
molecule-consuming). Less than 1 g of MTO was enough to perform this study. They were
carried out to confirm results of section IV analysis predicting that lines were observable with
our CO2 laser spectrometer, and to try to identify predicted rovibrational transitions.
A 58-cm long and 45-mm diameter cylindrical glass cell, ended with anti-reflective
coated ZnSe windows, was filled with a vapour of MTO at a pressure of about 10-3 mbar
much below the vapour pressure of a few 10-1 mbar at room temperature. The laser beam was
sent in the cell (pump beam), retroreflected with a simple mirror (probe beam) and focused on
an HgCdTe photodetector. The power ratio between pump and probe beam could be

12

Page 13

controlled by placing optical attenuators between the mirror and the cell. The beam waist
inside the cell was 5 to 10 mm. To reduce the effect of laser amplitude noise, the saturated
absorption signal is detected after frequency modulation at 5 kHz. The modulation is applied
on piezoelectric transducers that control the length of the laser cavity. A locking amplifier
enables second harmonic detection in order to strongly flatten the baseline induced by the
laser gain curve. Spectra are recorded by scanning the laser frequency through computer
control of the phase-lock loop RF offset.

Wavenumbers/cm-1
Saturated absorption amplitude
-15-10-505 10
Frequency/MHz offset by 29 257 658.53 MHz
975.9308975.9306975.9304975.9302975.9300
-10.2 -10.1 -10.0 -9.9
100 kHz
3×10
-6 cm
-1

41/2
39/2
43/2
37/235/2
45/2

Figure 5: Saturated absorption spectrum of MTO in a cell at 300 K (experimental conditions:
3000 points, 100 ms integration time per point, average of 2 back-and-forth sweeps, 200 kHz
of modulation depth (modulation index of 40), 0.002 mbar of MTO pressure, pump (resp.
probe) beam power of 95 µW (resp. 12 µW)). The offset corresponds to the R(20) CO2 laser
line frequency. The inset is a zoom on a single intense line (experimental conditions: 200
points, 100 ms integration time per point, single back-and-forth sweep, 50 kHz of modulation
depth (modulation index of 10), 0.002 mbar of MTO pressure, pump (resp. probe) beam
power of 24 µW (resp. 3 µW)). Assigned ∆F=0 six most intense hyperfine components
associated with the RQ(20,0) line of 187Re MTO are labelled with their F quantum number.

Saturated absorption spectra were recorded with MTO pressures typically ranging
from 10-4 to 10-2 mbar, pump beam power ranging from 5 µW to 2.5 mW and pump to probe
beam power ratio ranging from 1 to 8. The first laser is locked on an R(67) line of 192OsO4.55
Figure 5 displays a spectrum recorded over 30 MHz around the R(20) CO2 laser line (origin of
the frequency axis), where we expect to find several MTO lines from the previous
rovibrational study (section IV). The hyperfine structure of MTO is responsible for such a

13

Page 14

dense spectrum. The inset zooms on a single intense line, recorded over 400 kHz. This line is
well fitted by the 2nd derivative of a Lorentzian of half width at half maximum (HWHM) of
94 kHz, and is centred at 29 257 648.504(2) MHz (975.93010508(4) cm-1). By reducing
pressure (~10-4 mbar), modulation depth (30 kHz) and laser intensity (~µW), HWHM line
widths smaller than 50 kHz (~10-6 cm-1) were obtained. Such a residual line width can not be
explained only by transit time broadening (~5 kHz) and residual Doppler broadening induced
by an angle between the two counter-propagating beams (<20 kHz), but is fully compatible
with an unresolved magnetic hyperfine structure due to the spins of Re and H nuclei. This
particular line was assigned as the ∆F=0, F=43/2 quadrupolar component of the RQ(20,0)
rovibrational line (see below).
Ultra-high resolved dense signals such as the one on Figure 5, were observed in the
probed [-200 MHz, +270 MHz] spectral window around the R(20) CO2 laser line. Less dense
spectra of smaller amplitude were observed in spectral windows of ~50 MHz around R(18)
and R(18)-160 MHz, R(22) and R(22) -160 MHz, R(24) and R(24) -160 MHz (with the first
laser respectively locked on the
line of
conclusions of our analyses of section III and IV. From the set of parameters obtained in the
analysis including HFS, we simulated a 300 K spectrum. In the spectrum displayed on Figure
5, we managed to identify the ∆F=0 six most intense hyperfine components associated with
the RQ(20,0) line of 187Re MTO, and probably components of either higher J lines or 185Re
MTO unidentified signals. The measured frequencies of the six identified hyperfine
components of the RQ(20,0) line, which are labelled with their F quantum number on Figure
5, were actually included in the analysis with HFS, as mentioned in section IV.B, with a 10
kHz experimental uncertainty. Their assigned frequencies are available in the ancillary file
with the complete set of assigned lines used in section IV.B analysis. Additionally, a list of
187Re MTO simulated (from Set 2 of Table II) lines that are potentially observable in the 560
MHz spectral region that can be explored around the R(18), R(20), R(22) and R(24) laser lines
is given in Table III. The simulated frequency uncertainties σf given by the fitting procedure
were taken into account to build up this table. We noticed that σf roughly follows σf ~ 0.016
J2+0.328 K2 MHz (with however lower σf for J ~ 20, as a consequence of the assignment of
the RQ(20,0) hyperfine components with a very good experimental uncertainty). In contrast to
the signal observed around R(18) and R(20) laser lines, which can potentially originate from
lots of lines, the situation is much simpler around R(22) which is expected to coincide with
only one simulated rovibrational line, RR(4,3). No 187Re MTO line is expected around R(24).
However the observed signal is compatible with the simulated RR(7,1) line of 185Re MTO as
deduced from the rougher analysis of this isotopologue (section IV). Note that we expect
185Re MTO to also contribute to the signal observed around the other CO2 laser lines.
Higher-order terms, namely the non-diagonal contributions from the l-type doubling
interactions, should be included in the model to fully reproduce the ultra high-resolution
spectrum. It would then be possible to propose new assignments with estimated uncertainties.
In the near future, the identification in the saturation spectra of more simulated lines (in
particular the two isolated lines expected around R(22) and R(24)) should lead to a refined set
of molecular parameters. This work is currently under progress. However, the resolution is
not good enough for a complete study of magnetic hyperfine interactions. This could only be
performed by using our 18-m long absorption cell56 or by observing Ramsey fringes on a
molecular beam.29
line of
190OsO4, and and
192OsO4
55). Those observations correlated rather well with the
)() 59(
3
1−
AR
)() 74(
0
1−
AR
)() 80(
2
1−
AR

14

Page 15

Table III: Calculated lines of 187Re MTO potentially observable in the 560 MHz spectral
region around R(18), R(20), R(22) and R(24) CO2 laser lines. The (J,K) quantum numbers are
listed in the third column. Already experimentally assigned lines are indicated in bold
PQ
(45,45), (46,45), (47,44), (47,45), (47,46), (48,44), (48,46), (48,45), (49,43),
(49,44), (49,45), (50,43), (50,44), (50,45), (51,42), (51,43), (51,44), (52,42),
(52,43), (52,44), (52,43), (53,41), (53,42), (53,43), (54,41), (54,42), (55,40),
(55,41), (55,42), (56,40), (56,41), (57,39), (57,40), (57,41), (58,40), (59,38),
(59,39), (59,40), (60,38), (60,39), (61,37), (61,38), (62,36), (62,37), (62,38),
(62,36), (63,37), (64,35), (64,36), (65,35), (65,36), (66,34), (66,35), (67,33),
(67,34), (68,34), (68,33), (69,32), (69,33), (70,31), (70,32), (71,31), (71,32),
(72,30), (72,31), (73,30), (74,30), (75,28), (75,29), (76,28), (77,27), (79,25),
(79,26), (80,25), (84,22), (85,21), (73,29), (74,29), (76,27), (77,26), (78,26),
(80,24), (81,23), (81,24), (82,23), (83,22), (84,21), (85,20), (86,19), (86,20),
(87,19), (88,18), (89,17), (90,16), (91,15), (91,16), (92,14), (92,15), (94,12),
(95,12), (98,9)
R(18)
RP
(6,1)
PQ
(2,2), (3,2), (4,2), (5,2), (6,2), (7,2), (11,1), (12,1) a, (13,1), (14,1), (15,1),
(16,1)
(18,0), (19,0) a, (20,0) b, (21,0), (24,1), (25,1), (26,1), (28,2), (29,2), (30,2),
(31,3), (32,3), (33,3), (35,4), (36,4), (39,5), (38,5), (41,6), (42,6), (43,7), (44,7),
(46,8), (47,8), (48,9), (49,9), (50,10), (51,10), (52,11), (53,11), (54,12), (55,12),
(56,13), (57,13), (58,14), (59,14), (60,15), (61,15), (62,16), (63,16), (63,17),
(64,17), (65,18), (66,18), (67,19), (68,19), (68,20), (69,20), (70,21), (71,21),
(71,22), (72,22), (73,23), (74,23), (74,24), (75,24), (76,25), (77,25), (77,26),
(78,26), (78,27), (79,27), (80,28), (81,28), (81,29), (82,29), (82,30), (83,30),
(84,30), (84,31), (85,31), (85,32), (86,32), (86,33), (87,33), (87,34), (88,34),
(89,34), (89,35), (90,35), (90,36), (91,36), (93,39), (94,39), (95,39)
R(20)
RQ
R(22)
RR
(4,3)
R(24)
Ø
(a) assigned lines in the jet-cooled linear absorption spectrum of Figure 6
(b) assigned line in the 300 K saturated absorption spectrum of Figure 5
C. Molecular jet spectroscopy
In this section, we detail the first high resolution but still Doppler broadened (~MHz
line width) spectra of jet-cooled MTO. They were obtained on the set-up currently under
development for molecular PV observation, and constitute a significant advance towards the
ultimate test, likely to be performed on chiral derivatives of MTO.
The molecular jet apparatus is 3-m long with two vacuum chambers pumped by
diffusion pumps. Supersonic expansion occurs through a circular nozzle in a first chamber
(pressure of 10-5-10-4 mbar under working conditions) separated from the second one
(pressure of 10-6-10-5 mbar under working conditions) by a skimmer. The nozzle-to-skimmer
distance is adjustable between 2 and 25 mm. To produce a supersonic jet of MTO, our
strategy (like in section IV) consisted in heating MTO contained in a reservoir (stainless steel)
and seeding its vapour in a carrier gas (helium). Extensive studies of the MTO-seeded jet
characteristics (MTO dilution and flux, longitudinal velocity, translational temperature,…) as
a function of reservoir temperature, backing He pressure, nozzle-to-skimmer distance, nozzle

15