RRKM modeling of collision activated reaction/collision induced dissociation experiments: Energy profile determination for phenylethyne incorporation on palladium (II)-phosphinous acid complex

Article abstract of DOI:10.1016/j.ijms.2012.05.002

We have recently reported a detailed ESI-collision activated reaction/collision activated reaction (ESI-CAR/CAR) and ESI-collision activated reaction/collision induced dissociation (ESI-CAR/CID) mass spectrometric investigation, combined with quantum chemistry calculations, to elucidate the reaction mechanism of [2 + 1] cycloaddition between alkyne and norbornadiene using a Pd(II) complex as catalyst. The coordination mode of alkyne on the metal was shown to be an essential preliminary step of the reaction, but mass spectrometric results were difficult to rationalize according to changes in the experimental conditions. In this work we present a detailed RRKM modeling of these experiments using MassKinetics software. We demonstrate how essential kinetic modeling is in order to interpret these experiments: both for phenomenological aspects (understand spectra and changes in their pattern due to energetic modifications) and as a link between quantum chemistry results and tandem MS experiments. Complete energy profile for isomerization and decomposition processes of [Pd[(t-Bu)(Ph)PO]₂H + PhCCH]⁺ complexes has been determined through kinetic modeling of experimental data. Detailed modeling procedure is presented; approximations discussed and validated for quantitative comparison with quantum chemistry calculations. Agreement between isomerization barriers determined with kinetic modeling of experimental data and those determined through quantum chemistry was found to be within few kcal/mol supporting the validity of the approach and assumptions made in the model.

Full text of DOI:10.1016/j.ijms.2012.05.002

International Journal of Mass Spectrometry 319–320 (2012) 31–39
Contents lists available at SciVerse ScienceDirect
International Journal of Mass Spectrometry
journal homepage: www.elsevier.com/locate/ijms
RRKM modeling of collision activated reaction/collision induced dissociation
experiments: Energy profile determination for phenylethyne incorporation on
palladium (II)–phosphinous acid complex
Denis Lesagea,∗, Antony Memboeufb,c, Yves Gimbertb, Jean-Claude Tabeta
a Institut Parisien de Chimie Moléculaire, UMR CNRS 7201 - FR 2769 UPMC univ Paris 06, 4 place Jussieu, 75005 Paris, France
b Department of Molecular Chemistry, DCM UMR 5250-ICMG FR 2607 CNRS-Université Joseph Fourier BP 53, 38041 Grenoble Cedex 9, France
c Université de Brest, UMR CNRS 6521, Laboratoire CEMCA, 6Av. Le Gorgeu, 29238 Brest Cedex 3, France
a r t i c l e i n f o
a b s t r a c t
Article history:
We have recently reported a detailed ESI-collision activated reaction/collision activated reaction
(ESI-CAR/CAR) and ESI-collision activated reaction/collision induced dissociation (ESI-CAR/CID) mass
spectrometric investigation, combined with quantum chemistry calculations, to elucidate the reaction
mechanism of [2 + 1] cycloaddition between alkyne and norbornadiene using a Pd(II) complex as catalyst.
The coordination mode of alkyne on the metal was shown to be an essential preliminary step of the reac-
tion, but mass spectrometric results were difficult to rationalize according to changes in the experimental
conditions. In this work we present a detailed RRKM modeling of these experiments using MassKinetics
software. We demonstrate how essential kinetic modeling is in order to interpret these experiments: both
for phenomenological aspects (understand spectra and changes in their pattern due to energetic modifi-
cations) and as a link between quantum chemistry results and tandem MS experiments. Complete energy
profile for isomerization and decomposition processes of [Pd[(t-Bu)(Ph)PO]2H + PhCCH]+ complexes has
been determined through kinetic modeling of experimental data.
Received 17 January 2012
Received in revised form 2 May 2012
Accepted 2 May 2012
Available online 11 May 2012
Keywords:
RRKM modeling
ESI
CAR
CID
Pd(II) complex
Cycloaddition
Detailed modeling procedure is presented; approximations discussed and validated for quantitative
comparison with quantum chemistry calculations. Agreement between isomerization barriers deter-
mined with kinetic modeling of experimental data and those determined through quantum chemistry
was found to be within few kcal/mol supporting the validity of the approach and assumptions made in
the model.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
chemistry field [5,6]. This technique, in combination with tan-
dem mass spectrometry (MS/MS), has played a major role to
Over the last decades, significant advances have been made
regarding the efficiency of transition-metal-mediated strategies for
the synthesis of organic compounds. However, gaining insight into
the structures and the reactivity of these complexes is still needed
to achieve significant improvements. The development of ESI has
dramatically expanded the areas to which mass spectrometric anal-
ysis can be applied and is rapidly becoming an important technique
for mechanistic studies of chemical reactions [1]. Additionally, ESI
has proven to be a soft ionization method that keeps intact weakly
bound ligands in a complex cluster ion. Indeed, energy deposited
during the ionization process mainly results in desolvation at the
skimmer [2–4]. With these advantages, ESI has become increas-
ingly popular as a key analytical tool in inorganic/organometallic
characterize metal complexes and to evaluate comparatively the
strengths of interaction between different ligands and a metal [7,8].
Recently, using triple quadrupolar-type instruments, collision acti-
vated reactions (CARs) of metal complex ions and organic ions with
neutral molecules have been employed to study mechanistic paths
of reactions [9–12]. This technique has been extensively used to
provide structural information often not directly accessible by col-
lision induced dissociation (CID). Note also that modified ion trap
mass spectrometers [13,14] and FT-ICR [15] are currently used for
organometallic reactivity studies.
In 2005, the synthesis and catalytic activity of Pd(II) complexes
by phosphinous acids was reported [16]. These Pd(II) complexes
catalyze a new [2 + 1] cycloaddition between alkyne and norborna-
diene derivatives (Scheme 1). However, the resulting cyclopropanic
compound is not the obvious standard outcome of Pd(II) complexes,
by comparison with structures observed using more classical coor-
dinated Pd(II) species [17–19].
∗
Corresponding author. Tel.: +33 1 44 27 36 81; fax: +33 1 44 27 38 43.
E-mail address: denis.lesage@upmc.fr (D. Lesage).
1387-3806/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.ijms.2012.05.002

32
D. Lesage et al. / International Journal of Mass Spectrometry 319–320 (2012) 31–39
␩1) via a transition state TSacet (Scheme 2) prior to the coordination
of norbornadiene, yielding an insertion product.
To support this conclusion and make a quantitative compar-
ison between quantum chemical calculations and experimental
data, we have performed a detailed RRKM (Rice, Ramsperger, Kas-
sel, and Marcus) [21,22] modeling of the ESI-CAR/CID experiments
using MassKinetics software [23]. This dedicated software allows
for statistical modeling of out-of-equilibrium molecular systems
dissociating during tandem mass spectrometric experiments. It is
particularly suited to the treatment of multiple collisions to deter-
mine thermodynamic quantities, conditions that are more complex
(and thus less well controlled) than threshold CID measurements
[24,25]. Nevertheless, we demonstrate the reliability of the method
and the relevance of thermochemical results obtained. This is well-
illustrated by the good agreement obtained between experiments
and theoretical modeling. Approximations as well as the necessary
simplifications used in the model are tested and validated through a
sensitive analysis for the most critical variables. Note that we have
performed a detailed RRKM modeling of the ESI-CAR/CID experi-
ments previously published, without considering addition of new
experimental data. Using our approach, instead of a simple model,
a realistic molecular system is treated with a catalytic compound
in the form it is used in organic synthesis. So, the aim of this study
is first to report the ability to cross high energetic barrier under
rather special experimental conditions. Secondly, despite its high
complexity, this work proposes a methodological approach which
can be useful for the mass spectrometry community.
Scheme 1. Cyclopropanation between norbornadiene and phenylethyne with PAPd
phosphalladacycle precatalysts.
Scheme 2. Proposal of isomerization process from [a + PhCCH]+
␩1.
␩
to [aH + CCPh]+
2
2. Experimental
In
a
previous study, consecutive collision-activated
reaction/collision-activated reaction (CAR/CAR) and collision-
activated reaction/collision-induced dissociation (CAR/CID)
experiments were performed on a cationic Pd(II) complex (Pd[(t-
Bu)(Ph)PO]2H+ ion, denoted [a]+) [20]. These experiments were
useful for the identification of the coordination mode of alkyne
on the metal in the gas phase. On the basis of the results of
CAR/CAR experiments on this particular Pd(II) complex ion with
phenylethyne and norbornadiene, we demonstrated the essential
role of the order of addition of organic partners on the efficiency
to form the diadduct ion. This is key information to elucidate
and understand mechanistic aspects of this important reaction.
Theoretical calculations combined with mass spectrometry exper-
iments suggested a change in coordination mode of alkyne (␩2 into
2.1. Mass spectral analysis
Modifications of the mass spectrometer and experimental con-
ditions used to perform ESI-CAR/CID experiments have been
previously described [20]. However, to help following the details
in the modeling procedure, a brief recall of the necessary infor-
mation is given herein. All ESI mass spectra were recorded using
a modified Quattro I triple-quadrupole mass spectrometer (Micro-
mass, Manchester, UK). An illustration of the modified apparatus is
shown in Fig. 1.
The data were acquired using Masslynx software (version 3.4).
For complex ion desolvation, the ESI capillary voltage was main-
tained at 3.75 kV. Nitrogen was used as desolvation and nebulizing
Fig. 1. Schematic of the modified triple quadrupole mass spectrometer used to perform ESI-CAR/CID experiments. The different elements, their geometries and various
voltages applied, are indicated as well as corresponding MassKinetics (MK) parameters in the way they are used in the model.

D. Lesage et al. / International Journal of Mass Spectrometry 319–320 (2012) 31–39
33
gas. The source temperature was kept at 80 ◦C and other source
parameters were maintained constant throughout the complete set
of experiments except the cone voltage that was varied on purpose
between 5 and 50 V for our energetic study. In consecutive CAR/CID
experiments, theneutralreagentgassuchas phenylethyne(PhCCH)
or deuterated phenylethyne (PhCCD) was introduced into the H0
transfer hexapole, maintaining the pressure at 10−4 mbar (Penning
CP25-EK gauge). Note that for the reported CAR/CID experiments,
the micrometric valve of phenylethyne was entirely open and thus a
maximum possible pressure was used for the H0 transfer hexapole.
Adding nitrogen gas through a second introduction inlet did not
modify the formation yield of the complex. Recently, to increase
the pressure of the reagent gas in H0, the transfer hexapole was
changed into a closed cell by a home made modification. By an
opposite way the pressure was not reduced to be sure of a full
thermalization of the complexes formed under CAR conditions.
Keeping Q1 static, the precursor adduct ion of interest formed in
H0 was mass-selected by Q1 and allowed to decompose in H2 and
the product ion spectra were obtained by scanning Q3 (the colli-
sion voltage was varied from −5 to −50 V). Argon was used as the
collision target gas, and the collision cell pressure was maintained
at 10−4 mbar (Edwards PRL10 gauge). The pressure of H2 seems
to be an optimum value. Decreasing the pressure would facilitate
the treatment of multiple collision regimes but this would have
been at the expense of a broadening phenomenon of the peaks
because the ERMS curves would have been shifted to higher col-
lision voltage values. The effects of pressure varying from 1 to 100
relative values will be treated in detail in the future using proto-
nated leucine enkephalin as thermometer molecule (F. Ichou et al.,
to be published).
2.2. Modeling details
Collision induced dissociation experiments were simulated
using MassKinetics Scientific Demo software [21] (version 1.11:
http://www.chemres.hu/ms/masskinetics/). Calculations were
done within the frame of RRKM theory. MassKinetics is a the-
oretical framework and an accompanying computer program
developed in order to describe reaction kinetics under statistical,
but non-equilibrium, conditions. Beside the parameters necessary
to solve numerically the master equation, a number of important
physical quantities can be varied simultaneously when performing
the kinetic modeling. Those can be intrinsic parameters of the
instrument (size of the mass spectrometer parts) or related to the
conditions in which the experiments were carried out (polariza-
tion of the multipoles, nature and pressure of the collision gas,
collision voltage in the ESI source or/and in H2). More critical are
the molecular parameters available: beside the fragmentation
parameters (activation energy E0 and entropy-related factor
ꢀS =/ ), which values constitute the main interest in this study,
there are also the collision energy transfer function, the initial
internal energy of ions, the number of fragmentation routes, the
collision efficiency of the collision partners and the geometrical
cross-section of the colliding analyte ions. All these parameters
are listed in Table 1 and intrinsic parameters of the instrument
indicated in Fig. 1. In the experiments performed a number of
parameters are fixed by definition or are intentionally maintained
constant (indicated in Fig. 1 as bold characters). Those which may
vary or which are intentionally modified are indicated as italic
characters in Table 1 and/or Fig. 1. To access the activation energies
(which is the main objective of this work), the energy-dependence
of the collision efficiency was described using the expression
proposed by Muntean and Armentrout [26]. The collision effi-
ciency, characterizing the amount of energy transferred within a
single collision in the center-of-mass frame, determines the shape
of the energy-dependence curve; the value of this parameter

34
D. Lesage et al. / International Journal of Mass Spectrometry 319–320 (2012) 31–39
Scheme 3. Three possible isomeric structures for Pd(II) complex ion with
phenylethyne.
Scheme 4. Energy diagram corresponding to the formation and ␩2–␩ isomeriza-
1
tion process from [a]+ + PhCCH as determined from quantum chemistry calculations.
2
Starting from the left of the diagram, barrier heights for the decomposition of ␩
as well as the average number of collisions (or gas pressure)
were adjustable parameters to fit experimental results and are
discussed in the next section. Frequency file models used for RRKM
modeling are reported in Supporting Material. Several molecular
parameters (entropy factor for the loose transition state and col-
lision efficiency) as well as ESI and H0 parameters (characteristic
temperature due to the ESI source and isomerization time) Table 1
were intentionally varied in order to evaluate the accuracy of the
activation energies determined during the fitting procedure.
1
complex [a + PhCCH]+ (barrier A: 16.7 kcal/mol), the ␩2–␩ isomerization process
(barrier B: 30.5 kcal/mol relative to ␩2) and of retro-isomerization ␩1–␩2 (barrier C:
1
17.9 kcal/mol) are indicated on the diagram. ␩ is 4.2 kcal/mol more stable than the
separated [a]+ and PhCCH reactants.
Table 2
Theoretical and experimental values for A, B and C energy barriers.
E0(A)
E0(B)
E0(C)
Theoretical (0 K) (kcal/mol)
Experimental RRKM modeling (kcal/mol)
16.7
15.5 4.5
30.5
31
17.9
15.9
7
2
2.3. Computational details
In this study we use quantum chemistry data previously gener-
ated and already published [20]. Briefly, the lanl2dz [27,28] electron
core potential (ECP) was used for all heavy atoms and polariza-
tion (d) orbitals were added to the basis set for nonmetallic heavy
atoms [29]. The coefficients for these orbitals were taken from
the D95(d) basis set. This level was used to freely optimize the
geometries of each complex using the Gaussian03 package [30].
All subsequent frequency calculations were done at the same level.
These energies were corrected for the zero-point energies and
the small BSSE (2.8 kcal/mol) when necessary. Additional neces-
sary files used for the modeling (e.g., frequency models, etc.) are
included as Supporting Material.
corresponding energy diagram, containing barrier heights for the
isomerization/retro-isomerization and decomposition processes of
1
2
␩
and ␩ is presented in Scheme 4 and Table 2.
Experimentally, the existence and formation of two isomeric
1
2
structures such as [aH + CCPh]+
␩ ␩ is high-
and [a + PhCCH]+
lighted by three evidences. First, using CAR/CID experiments, the
decomposition of the deuterated adduct ion leads to the compet-
itive release of PhCCH and PhCCD (Scheme 5b); this [aD + CCPh]+
precursor ion m/z 574 (108Pd) is formed by reaction of [a]+ + PhCCD.
+
We have reported that [ad1
]
m/z 472 ions (deuterated fragment
ions corresponding to the loss of PhCCH) exclusively come from the
␩
1 structure and their abundances depend on the cone voltage and
therefore on the initial internal energy deposited during the ioniza-
tion process. The ratio of deuterated over the sum of deuterated and
non-deuterated fragment ion peak intensities [ad1]+/([a]+ + [ad1]+)
(denoted D/(H + D)) is plotted as a function of the ESI source cone
voltage from 5 V up to 50 V keeping all other variables constant
(Fig. 2). A second evidence is illustrated by the surprising fact that
the Pd(II) complex formed between [a]+ and PhCCH at higher inter-
nal energy becomes more stable and, as a consequence, needs
more energy to decompose (Fig. 3). Note that the experimental
curve Fig. 2 is slightly different to that we previously published
[20] because we preferred to use data recorded the same day for
accurate comparison of Figs. 2 and 3; this prevents a shift in inter-
nal energy due to experimental artifacts like cone obstruction.
Finally, the existence of at least two structures is also shown by the
3. Results and discussion
To facilitate the discussion of the modeling procedure, quantum
chemical results are first summarized and the molecular problem
briefly discussed. Experimental results are then presented sequen-
tially with the corresponding kinetic modeling. Approximations are
discussed when used in the model; they are tested and validated
after the modeling has been completed.
Considering the energetic cost to break the POH–OP bond is suf-
ficiently important to preclude a possible rotation of the system
around Pd–P bond [31], only three different isomeric structures of
[a + PhCCH]+ can be envisioned (Scheme 3).
We recently published that two isomers are observed by CAR
experiments from complex [a]+ (formed in the ESI source) and
PhCCH (introduced into H0): an adduct with a classical coordina-
tion involving ␲ electrons of the acetylenic triple bond, yielding
a Pd(II) phenylethyne complex ([a + PhCCH]+ ␩2) and a Pd(II)
phenylethynyl complex ([aH + CCPh]+ ␩1) (Scheme 3) [20]. How-
ever, as mentioned above, a metallocarbene structure may also
be envisioned (structure on the right in Scheme 3, [a + CCHPh]+).
The corresponding structure was also computed and was found
to be 8.5 and 21.0 kcal/mol less stable than ␩ and ␩ respec-
tively with a transition state structure at 27.8 kcal/mol relative to
␩2. Consequently, for thermo-kinetic reasons we have considered
that the metallocarbene is not stable enough and easily decom-
poses in the source and/or in the H0–Q1 multipoles. Nevertheless,
it should be emphasized that such a metallocarbene intermedi-
ate is involved using Pt(II) complex instead of Pd(II) [31]. The
1
2
fact that ␩ species is much more reactive compared to ␩ struc-
ture under consecutive CAR/CAR experiments (using PhCCH/NBD
in H0/H2, respectively) [20]. Computations have shown that the
hetero diadduct ion formed [aH + CCPh ␩1 + NBD]+ 106Pd, m/z 663)
(
is not an association complex but has evolved to an advanced inser-
tion palladium complex (with C C bond formation).
For these multiple simulations two different models were used.
1
In a first model (called model A) the different species (␩ and ␩2)
1
2
are investigated from the end of H0 to the detector during CAR/CID
1
2
experiments. The fundamental assumption is that ␩ and ␩ com-
plexes are formed and thermalized in the H0 transfer hexapole at
80 ◦C manifold temperature and, relative abundances are modi-
fied due to ionization conditions. Using this kinetic model we were
2
able to determine the stability of the complex ion structure ␩ (A
value in Scheme 4), as well as the retro-isomerization barrier height

D. Lesage et al. / International Journal of Mass Spectrometry 319–320 (2012) 31–39
35
2
1
Scheme 5. Structures of fragment ions formed during CID decomposition of 108Pd(II) deuterated phenylethyne ␩ complex (a) and, of 108Pd(II) deuterated phenylethynyl ␩
complex (b).
Adapted with permission from Organometallics 28 (2009) 2735–2743 copyright 2009 American Chemical Society.
␩1–␩2 (barrier C). The question how these species are formed inside
H0 and the thermalization approximation are discussed using a sec-
ond model (called model B) with which we could determine the
3.1. E0(A) and E0(C) measurements (model A)
After reactive collision experiments (ESI-CAR) between [a]+, the
ionized 106Pd(II) complex, and phenylethyne present in H0, we
have mainly observed the formation of m/z 571 ions ([a]+ + PhCCH).
They correspond to one or several of the three complex ion struc-
tures presented in Scheme 3. When reactive collision experiments
were followed by dissociative collisions (ESI-CAR/CID), the loss of
PhCCH was always observed whatever experimental conditions
1
isomerization barrier ␩2–␩ (Table 1).
To assess this procedure, thermodynamic quantities (barrier
heights) derived from those two models are further combined
in a third model, model C that accounts for all processes simul-
taneously, namely the isomerization, retro-isomerization and
dissociation of the Pd(II) phenylethyne complex.
1
used. However, in the case of an ␩ structure formed prior to
the dissociation stage, the phenylethyne neutral loss requires one
Fig. 3. Cone voltage was varied from 5 to 50 V to produce a set of ERMS curves
from CAR/CID experiments. 10 V (H2) was applied during the dissociative collision
ꢀ
Fig. 2. [ad1]+/([a]+ + [ad1]+) ratio (denoted [D/(H + D)]) was obtained from CAR/CID
experiments and are plotted as a function of the cone voltage. [a]+ ions are formed
in the source and PhCCD is introduced into H0. The [a + PhCCD]+ complexes formed
stage. Survival yield is calculated using formula SY = I
2 /(I
+
IF ) where
1
1
2
␩
/␩
␩
/␩
intensity Iꢁ
corresponds to m/z 571 complex ions formed (106Pd(II)) in H0 during
1
2
/ꢁ
ꢀ
reactive collisions and
IF corresponds to fragment ions generated during the
into H0 (m/z 574, 108Pd(II)) are further decomposed by CID at 10 V collision volt-
CID stage in H2. Points are experimental results and curves are obtained by RRKM
simulations. For the sake of clarity curves that were obtained at 5 V and 45 V cone
voltages are not reported on the diagram, but follow the trend observed [20].
+
age in H2 to give either [ad1
]
(m/z 472) or [a]+ (m/z 471) fragment ions. CAR/CID
of [ad1 + PhCCH]+ ion (where labeled [ad1
]
is formed using deuterium oxide/d3-
+
acetonitrile (1:1, v/v) as ESI solvent mixture and PhCCH is introduced in H0) is also
proposed. Experimental values are presented as filled squares and circle and RRKM
simulations with full line.
Adapted with permission from Organometallics 28 (2009) 2735–2743 copyright
2009 American Chemical Society.

36
D. Lesage et al. / International Journal of Mass Spectrometry 319–320 (2012) 31–39
Table 3
1
1
Relative abundances of ␩ (compared to the sum ␩1 + ␩2), mean internal energies (ꢀEintꢁ) and characteristic temperatures of the complexes ␩2–␩ in the source (TChar(S)) as a
function of the cone voltage used.
Cone voltage (V)
5
10
15
20
25
30
35
40
45
50
1
Model Aa
␩
abund. (%)
0
1.69
411
0
2.28
482
2
2.86
547
13
3.44
608
40
4.02
664
63
4.61
718
79
5.19
770
80
5.77
821
73
6.35
870
63
6.94
917
Model Bb ꢀEintꢁ (eV) Eq. (2)
TChar(S) (K)
a
1
Measured at the end of H0 hexapole after partial ␩2–␩ isomerization and thermalization.
b
1
Initial values determined near the cone before ␩2–␩ isomerization and thermalization in H0 hexapole.
2
stability of ␩ and ␩1, a ratio D/(H + D) close to 0.4 instead of 0.25
of the two alcoholic hydrogen to be transferred back to form a
phenylethyne group. Therefore, using deuterated phenylethyne
(PhCCD) and according to Scheme 5, the formation of an inter-
would be expected.
Concerning the E0(C) measurement, the tight transition state
(rearrangement cleavage) and associated frequencies were defined
by quantum chemistry (ꢀS =/ (t) = −5.5 cal/(mol K), see Supporting
1
mediate ␩ structure would lead to both non-deuterated [a]+ and
+
deuterated [ad1
␩
]
ions, whereas [a]+ ions only are generated from
structures. The ratio [ad1]+/([a]+ + [ad1]+) (denoted D/(H + D)),
2
Material). In a first approximation (to be verified later), the ␩1–␩
2
pathway is followed by a total decomposition of ␩2, leading to
was then monitored as a function of the cone voltage as presented
in Fig. 2 (filled squares). Under these CAR/CID experimental con-
the separated compounds [a]+ and PhCCH, without possible ␩2–␩
1
1
ditions, ␩ abundance that depends on the cone voltage, cannot
retro-isomerization. The best simultaneous fit of the D/(H + D) ratio
(Fig. 2) and ERMS curves (Fig. 3) was obtained considering C.
Eff. = 0.17 0.05 as collision efficiency coefficient for the Muntean
and Armentrout energy transfer function. The 0.05 uncertainty for
this collision efficiency coefficient will be discussed later.
Thanks to the E0(A) and E0(C) measurements, from the extreme
points of the curves Figs. 2 and 3, it is now possible to determine
the abundance of ␩ for the different cone voltage values. Results
be directly deduced from the D/(H + D) ratio presented in Fig. 2.
1
2
This is due to the fact that the two species ␩ and ␩ are not
completely decomposed at 10 V CID collision and, increasing the
collision energy to higher values than 10 V prevents, on our instru-
ment, accurate measurements of the D/(H + D) ratio due to peak
broadening. In spite of these limitations, one readily notices the ten-
dency to an increase of the deuterated fragment ions when the cone
voltage is increased up to approximately 40 V. When the applied
voltage is higher, deuterated fragment ions are less abundant. An
important point is that below 15 V, no deuterated fragment ions are
observed. This suggests that under these low cone voltages there is
an exclusive PhCCH release. Hence, solely the ␩2 complex is formed
inside H0 and transferred into the collision cell H2.
1
are shown in Table 3.
When computing the D/(H + D) ratio, Fig. 2, the value of the bar-
rier height for atom-transfer was considered invariant with respect
to the nature of the atom. A RRKM modeling of isotopic effect is not
proposed herein because the ꢀS =/ (l) = 10 12 of the direct cleav-
age is estimated (not calculated) with a large inaccuracy and thus
the expected isotopic effects would be certainly masked and not
properly evaluated. Nevertheless, as previously reported [20], the
reversed labeling reaction was also performed using deuterium
oxide/d3-acetonitrile (1:1, v/v) as ESI solvent mixture. Thus, CAR
processes using unlabeled phenylethyne allow the formation of
the [ad1 + PhCCH]+ ion m/z 574 which are consecutively decom-
posed under CID processes. Taking into account the reproducibility
of the curves, mentioned in the text, we can conclude that low or
no kinetic effects take place for the formation and decomposition
of the deuterated species. Thus, the 0.5 expected D/(D + H) ratio is
not achieved because of retro isomerization processes occurring at
high collision voltages rather than isotopic effects.
2
While maintaining the cone voltage at 10 V (␩ complex ions
only are formed in H0), we have plotted ERMS curve (filled squares
in Fig. 3) by the monitoring of the survival yield (SY) ratio as a
function of the collision voltage applied in the H2 collision cell.
The survival yield is usually defined by the following relationship:
SY = I(p+)/[I(p+) + ꢂI(f+)] where I(p+) is the abundance of the parent
ion signal and ꢂI(f+) is the sum of the abundances of the fragment
ions observed. RRKM simulations were performed to fit this exper-
imental curve using model A. The unfavored “direct” isomerization
␩2–␩1 under CID is first neglected and not considered in the kinetic
modeling. This way, it is possible to fit the “10 V” curve (denoted
Exp. 10 V) in Fig. 3 taking into account the E0(A) energy value only.
2
In this model, ␩ isomers are the only parent ions present. They
are considered to be thermalized in H0 at 353 K and to travel into
3.2. E0(B) energy measurement (model B)
H2 where they are decomposed after collisional activation with Ar
´
gas. The geometrical cross-section was fixed at C.S. = 100 A2 and the
˚
The question of the formation of ␩ complex in H0 is now
1
1
collision gas pressure was fitted (these variables are strongly linked
as they essentially determine the number of collisions experienced
by the mass-selected ions). The E0(A) value, which corresponds to
studied using model B (Table 1). The relative abundance of ␩
species (Table 3), obtained from simultaneous fit of Figs. 1 and 2,
are reported in Fig. 4. In the latter figure, normalized population
of “transitory” precursor complex ion ([a]+ + PhCCH) =/ , containing
potentially enough energy to cross the barrier “B” to form the ␩
species, are presented as a function of the ESI source cone voltage
(indicated with continuous lines). At low cone voltage, the abun-
2
the ␩ dissociation energy, was determined at 15.5 4.5 kcal/mol,
assuming a transition state ꢀS =/ (l) = 10 12 cal/(mol K) (direct
cleavage or loose TS). The reported error bars will be discussed later
in the text.
1
The determination of E0(C) = 15.9 2 kcal/mol, for the retro-
isomerization barrier, was obtained through RRKM simulation by
the simultaneous fit of the “35 V” curve shown in Fig. 3, and of the
dance of this transitory complex may be superimposed to estimated
1
␩
abundance using a barrier E0(B) equal to 31 7 kcal/mol.
At high cone voltage, it is obvious that the ion population hav-
ratio value D/(H + D) = 0.25 (Fig. 2) which is characteristic of the
ing enough energy to form the high energy isomer ␩1 (Fig. 4) tends
to be 100%. Clearly, increasing the ESI source cone voltage is shift-
ing the whole internal energy distribution of transitory precursor
ions above the appearance energy of isomerization Eapp = E0(B) + KS,
where KS relates to the kinetic shift. The kinetic shift is the excess
energy above the critical energy required to observe dissociation
1
␩
abundance for 35 V cone voltage. This ratio of 0.25 is the point
1
where the abundance of ␩ species reaches almost its maximum
value. Thus, using MassKinetics model, an abundance of 79% for ␩
1
allowed the simultaneous fit of the “35 V” curve and led to a cal-
culated ratio D/(H + D) equal to 0.25. Note that, assuming a similar

D. Lesage et al. / International Journal of Mass Spectrometry 319–320 (2012) 31–39
37
transfer hexapole is estimated to be 80 ␮s by considering a con-
stant velocity of the ions and despite the multiple collision regime.
For comparison, the mean residence time of the ions during CAR
experiments in H2 (characterized by a closed cell and, as a con-
sequence, a higher pressure) had been experimentally measured
equal to 1–3 ms, using a quick neutral loss scan [9]. This shorter
reaction time in H0, compared to H2, is also revealed by the lower
reactivity [20].
The initial internal energy of the transitory ([a]+ + PhCCH) =/ pre-
cursor complex ion is calculated considering that only the [a]+ ion
is heated near the cone area and a colder neutral (PhCCH) is added
[Eq. (2)], leading to a stabilizing effect on the resulting adduct ion.
By successive collisions with the reagent gas, ␩1 and ␩2 complexes
formed are either stabilized or broken. Note that phenylethyne
(characterized by a DOF = 36) allows a more efficient cooling com-
pared to monoatomic or diatomic collision gases usually used [32].
1
2
After many collisions, thermalized ␩ and ␩ species are obtained
at the exit of H0 (hypothesis of model A). Overall, the agreement
between experimental (RRKM) and computational is very good,
2
1
reinforcing the idea of a rapid thermalization of ␩ and ␩ com-
plex ions. The shape of the curve superimposed to the experimental
points until 50% of ␩1 abundance is also an argument for the validity
of this model.
1
Fig. 4. ␩
abundance vs. cone voltage calculated from Eq. (2) using
1
E0(B) = 31 kcal/mol (continuous line) and
␩
abundance vs. cone voltage used
for ERMS simulations (Fig. 2) and for [ad1]+/([a]+ + [ad1]+) ratio simulations (Fig. 3)
(open dots).
It should be emphasized that, considering ([a]+ + PhCCH) =/ tran-
sitory complex is heated near the cone [Eq. (3)], the mean internal
energy and characteristic temperature values do not change signif-
icantly (less than 4%).
within an experimental time frame defined by the mass spectrom-
eter geometry. The fact that experimental abundance of ␩1 reaches
a maximum at 40 V (80% of ␩1) is due to retro-isomerization (␩1–␩
2
1
ꢀEint
,
in eVꢁ = (0.1165Vc + 0.966) + 0.144
(2)
followed by decomposition) during the formation of ␩ in H0. This
For [a]+ ion, DOF = 156, T = 353 K, Etherm(353 K) = 0.966 eV and for
PhCCH neutral, DOF = 36, Etherm(353 K) = 0.144 eV: considering that
[a]+ ion is heated near the cone and a neutral PhCCH at 353 K is
added to form the transitory ([a]+ + PhCCH) =/ precursor complex
ion (note that for this estimation, sole the mean internal energies
are added but no convolution of internal energy distributions are
used).
is even more pronounced at higher energy values according to
the decrease of the curve above 40 V cone voltage. As soon as all
these complex formation/decomposition and isomerization/retro-
isomerization processes have occurred during the reactive stage,
we hypothesize that all ions are thermalized within the H0 cell,
hence “freezing” the distribution of ions between the three differ-
1
ent forms (decomposed, ␩ or ␩2).
For this RRKM simulation, the initial internal energy deposited
during the ionization process on the transitory ([a]+ + PhCCH) =/
precursor complex ion was estimated using the following calibra-
tion formula which has been previously determined for the ESI
source used [3]:
ꢀEint
,
in eVꢁ = 0.1094Vc + 1.28
[a + PhCCH]+
ion,
considering
(3)
For
DOF = 198,
that
T = 353 K,
transitory
Etherm(353 K) = 1.281 eV:
([a]+ + PhCCH) =/ precursor complex ion is heated near the
cone.
ꢀEintꢁ = [405 × 10−6 − 480 × 10−9 DOF]VcT + Etherm(T)
(1)
For this empirical equation (Eq. (1)), the mean internal energy
(ꢀEintꢁ, in eV) depends on the cone voltage (Vc, in V), the source tem-
perature (T, in K), the number of degrees of freedom (DOF = 3N − 6
normal modes of vibration, where N is the number of atoms) and the
internal energy due to the source temperature at 0 V cone voltage
(Etherm(T), in eV).
The mean internal energies ꢀEintꢁ, and corresponding character-
istic temperatures TChar(S) (assuming a thermal-like internal energy
distribution), are reported in Table 3. A characteristic temperature
is a hypothetic untruncated Boltzmann internal energy distribution
of the activated precursor ion prior to decomposition [2]. It is differ-
ent from the effective temperature (Teff) which is not a Boltzmann
distribution and which is related to the decomposing precursor ion
population. This TChar is currently used to define the ESI source
internal energy distribution and Teff is usually used to describe
decomposition into a collision cell for instance using the kinetic
method. Note that before crossing the barrier of isomerization
the internal energy deposited on the transitory ([a]+ + PhCCH) =/
ion is equal to (TChar(S) + E0(A)) which corresponds to the internal
3.3. Kinetic modeling considering the whole energy profile
(model C)
The knowledge of E0(A), E0(C) and E0(B) barriers allows to pro-
pose a more complex MassKinetics model considering the return
energy barriers (previously neglected) for the simultaneous fit
of Figs. 2 and 3 curves. Thus, it is possible to verify that under
2
1
CID processes the [a + PhCCH]+
␩ ␩ is
formed from [aH + CCPh]+
immediately decomposed without retro-isomerization. In fact, the
1
formation of ␩ species is exclusively possible in H0 due to the
presence of phenylethyne reagent gas under “relaxing” collision
2
1
regime and do not originate from direct ␩ to ␩ isomerization.
It is therefore obvious that the use of a more complex model in
MassKinetics, which considers the return energies, does not change
the simulations of Figs. 2 and 3.
2
For these two figures, the relative ␩1–␩ abundances and the
decomposition of these species were discussed without question-
ing how they were formed (model A). By opposition, the question
1
of possible formation of [aH + CCPh]+
␩
species in H0 is partially
energy due to the cone voltage and the source temperature plus
answered Fig. 4 (model B). This formation is due to the possi-
ble relaxation of the formed complex (hot ion + colder neutral).
Nevertheless, this phenomenon may be reinforced considering the
possible contribution of a third collision partner occurring at high
2
the [a + PhCCH]+
␩
stabilization energy.
For this calculation, the mean residence time is estimated to be
300 ( 200) ␮s. Note that the minimum residence time in the H0

38
D. Lesage et al. / International Journal of Mass Spectrometry 319–320 (2012) 31–39
pressure. This suggests that the lifetime of the transitory complex
([a]+ + PhCCH) =/ is longer compared to the frequency of collisions.
Thus, the 3-body collision allows the removal of part of the internal
energy with the neutral. In fact, this question is partially answered
because sole the available population that potentially has enough
energy to form ␩1 is accessed. Because of this internal energy relax-
4 kcal/mol) due to a defined transition state (accessed by theoret-
ical chemistry, by opposition to E0(A)).
The E0(B) value is determined with a very large uncertainty. This
uncertainty is mainly linked to the empirical internal energy cali-
bration of the ESI source (at least about 20%, due to the inaccuracy
of thermochemical data of the reference molecules used for the cal-
ibration [3]) and is also due to the estimated isomerization time
(t(H0) = 300 ( 200) ␮s).
2
ation, the retro-isomerization process leading to ␩ from ␩1, and
occurring during the formation of ␩1, cannot be easily described
and is not modeled. However, this process certainly explains the
Note that the existence of a third species (metallocarbene
[a + CCHPh]+, Scheme 3) in competition with ␩1, had also been con-
sidered. Its formation in H0 is thermodynamically favored due to a
lower barrier (11.1 kcal/mol, compared to 13.7 kcal/mol, measured
above the starting partners) [20]. However, MassKinetics simula-
tions show that thermalized metallocarbene species cannot survive
during its transfer through Q1 (less than 0.1%) due to the low
reverse energy barrier (6.8 kcal/mol) and due to the endothermicity
of its formation. As a consequence, this species is never accessible
by CID in H2. It is logical to assume that this metallocarbene com-
plex ion is also easily formed and broken in H0 leading back to the
reaction products [a]+ and PhCCH before formation of [a + PhCCH]+
1
decrease of the ␩ relative abundance for the highest cone voltage
values (up to 80% for 40 V). Indeed, the ␩1 population characterized
by the highest energy may be broken before its thermalization.
1
It should be noted that the reported
␩
abundances
(Figs. 2 and 3) were discussed at the exit of H0 hexapole. Thus,
1
2
in this model A, thermalized ␩ and ␩ complexes were partly
decomposed (2% and 53%, respectively) in the first analyzer Q1
(25 cm long) before entering the collision cell H2. This phenomenon
is taken into account for the simulations. This also explains why
the complexes are decomposed at 5 V collision voltage whatever
the cone voltage used (Fig. 3). The [a]+ fragment ions formed in
Q1 are not detected but, due to truncated internal energy distri-
butions of the precursor ions at the entrance of H2 collision cell,
part of the survivor ions have almost enough energy to decom-
pose. Thus, without considering metastable decompositions, a low
increase in internal energy by collision processes will shift one part
of the internal energy distribution to values higher than the appear-
ance energy (E0 + KS) leading to decomposition. This phenomenon
2
1
␩
and [aH + CCPh]+
␩ thermalized complex ions. By opposition
2
1
these ␩ and ␩ species (transferred at 47% and 98% through Q1,
respectively) are characterized by higher reverse energy barriers
(16.7 and 17.9 kcal/mol, respectively). The loss of internal energy
occurring during the formation of the metallocarbene [a + CCHPh]+
species is not taken into account for the calculation of the curve
Fig. 4. Indeed, the formation and the decomposition of metallocar-
bene complex ion in H0 would be accompanied by a loss of internal
2
is reinforced for ␩ structure because the ion population near the
appearance energy is more abundant compared to that of ␩1.
energy and, as a consequence, by a lower abundance of ␩ ion.
1
Thus a lower E0(B) barrier is expected. For all these reasons, the
measurement of E0(B) = 31 7 kcal/mol, although very close to the
theoretical value E0(B) = 30.5 kcal/mol, should be considered with
caution. Nevertheless, an important conclusion is that, in spite of
the reactive cooling due to the low internal energy of phenylethyne
as compared with the Pd-complex ion, enough internal energy may
be deposited on the transitory precursor ion near the source to cross
a barrier of E0(Bꢂ) around 10 kcal/mol above the starting partners.
Uncertainty related to the initial internal energy of ions at
the end of H0 (assumed to follow a thermal distribution, model
A) is not taken into account. Nevertheless, without considering
thermalization processes inside H0, for 10 V cone voltage the char-
acteristic temperature of the “transitory” ([a]+ + PhCCH) =/ complex
ion should be estimated equal to 482 K (Eq. (2)) when leaving the
H0 hexapole. Using this high temperature the entire “10 V” curve
cannot be fitted Fig. 3, whatever the collision parameters used
(pressure and efficiency of collision). Moreover, it is not possible
to explain why the ERMS curves recorded at 5 V (not reported)
10 V and 15 V cone voltages (Fig. 3) are very close, considering
different initial internal energies (TChar(s) = 411 K, 482 K and 547 K,
respectively). These observations support the idea of the forma-
tion of thermalized species, at least for low cone voltage values.
For a higher cone voltage value, this assumption is more difficult to
verify.
3.4. Uncertainties in the evaluations of E0(A), E0(C) and E0(B)
The estimation of uncertainties was made by using the esti-
mated uncertainties of the molecular parameters (especially the
loose TS) and the uncertainties of energy deposited on the ions (into
the source and during the CID processes). The effect of the variation
of the different parameters used to fit the experimental curves was
also studied for a reasonable estimation of uncertainties (Table 1).
The large uncertainty of E0(A) = 15.5 4.5 kcal/mol is first due to
the fact that the transition state, corresponding to the [a + PhCCH]+
␩
2 decomposition, could not be isolated by theoretical chemistry. A
loose transition state ꢀS =/ (l) = 10 12 cal/(mol K) was used for the
simulations leading to an uncertainty of 3 kcal/mol for E0(A). The
ꢀS =/ and its related uncertainty were calculated as follow. When
considering a loose TS, vibrational frequencies of separated prod-
ucts were used. Five transitional frequencies (those that become
rotations and translations of the dissociated products) were identi-
fied from missing frequencies in the [a + PhCCH]+ ␩2 initial complex
(see Supporting Information). These five added frequencies were
reduced by a factor of 1/3 to estimate reasonable TS. This scaling fac-
tor was intentionally varied from 1 to 1/10 to estimate the amount
of uncertainty generated [33]. This large variation of scaling fac-
tors, used to describe transition states, allows to obtain realistic TS
but at the expense of a large inaccuracy. On the other hand, part of
the E0(A) uncertainty is also linked to the use of estimated collision
parameters (pressure, energy transfer function, etc.) [23,26]. The
deposited energy distribution model used is that recently described
by Muntean and Armentrout [26], implemented in MassKinetics,
which consists in two exponential-type functions with a unique
parameter to determine, namely the collision efficiency. The latter
parameter has been optimized at C.Eff. = 0.17 0.05 which leads
to an additional source of error of 1.4 kcal/mol for the E0(A)
energy value (see Supporting Information for efficiency value vary-
ing from 0.12 to 0.22). It should be remembered that, as discussed
by Vékey, a value higher than 0.3 is unrealistic [23]. The uncertainty
of E0(C) measurement is estimated close to 2 kcal/mol (instead of
4. Conclusion
Considering the number of parameters that are out of precise
control or that are difficult to describe accurately (in particular
the pressure of the collision gas, and various molecular parame-
ters listed in Table 1), it is quite encouraging to observe such a
good agreement for the determination of energy profile between
quantum chemistry and RRKM kinetic modeling of those com-
plex experiments. Obviously, according to our discussion of the
accuracy achieved, simplification of the complex physico-chemical
processes to the model developed in this paper is facilitated by

D. Lesage et al. / International Journal of Mass Spectrometry 319–320 (2012) 31–39
39
the compensation of errors between different parameters of the
model that are strongly correlated (e.g., collision gas pressure and
geometrical collision cross-section).
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43 (2008) 447–455.
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Journal of Mass Spectrometry 40 (2005) 1–8.
The quantum chemistry provided the support for the existence
of three isomers; however, kinetic modeling can explain changes
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in the spectra when modifying experimental conditions consid-
2
ering two isomers [a + PhCCH]+
␩
and [aH + CCPh]+ ␩1. On the
other hand, the proposed model is particularly complex due to the
coexistence of two equilibrated forms in H0, whose abundances
depend on the source conditions. This model shows that it is possi-
ble to explain the experimental results, especially the coexistence
2
of these two species ([a + PhCCH]+
␩
and [aH + CCPh]+ ␩1). How-
1
2
ever, it is also likely that the large stability difference of ␩ and ␩
species is not related to a large stabilization energy difference but is
rather due to entropic effects (direct and rearrangement cleavages
2
for ␩ and ␩1, respectively). These simulations also show that it is
possible under these CAR conditions to form such species, through
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1071–1075.
collisional cooling, even though the formation of [aH + CCPh]+
␩
1 is
characterized by a large energy barrier; around 10 kcal/mol higher
than the started partners [a]+ and PhCCH.
[19] A. Tenaglia, L. Giordano, G. Buono, Organic Letters 8 (2006) 4315–4318.
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219–241.
We are grateful to the CNRS and ANR project “SPOs Preligands”
(contract no. BLAN07-1 190839) for financial support. This work
was supported by the computing facilities of the CRCMM, “Centre
Régional de Compétences en Modélisation Moléculaire de Mar-
seille”, and the CECIC-UJF.
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Appendix A. Supplementary data
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the online version, at http://dx.doi.org/10.1016/j.ijms.2012.05.002.
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