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\begin{document}

\title{H\textsubscript{2} effect in Cr/PNP-catalyzed ethylene tetramerization:
a DFT study}



\author[1]{Fangqian Yin}%
\author[1]{Tingchun Zhu}%
\author[1]{Bin Li}%
\author[1]{Le Zhang}%
\affil[1]{Handan College}%


\vspace{-1em}



  
  \date{May 25, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
It is well noticed that hydrogen promotes catalyst activity in
Cr/PNP-catalyzed ethylene tetramerization, but the mechanism of this
boost is unclear. A density functional theory (DFT) study devoted to
exploring this effect was conducted, and conformation changes were
carefully taken into consideration to build a clear reaction pathway.
Three components in the catalytic cycle was examined in detail: the
production of 1-hexene from the metallacycloheptane, the production of
1-octene from metallacyclononane, and the formation of active center on
the catalyst. The result indicates that the formation of active center
on the catalyst becomes more favorable upon imposition of hydrogen,
where hydrogen function as a second ligand. This easing effect could be
the key factor leading to the outperformed catalyst activity.%
\end{abstract}%



\sloppy


H\textsubscript{2} effect in Cr/PNP-catalyzed ethylene tetramerization:
a DFT study

Fangqian Yin, Tingchun Zhu, Bin Li, and Le Zhang*

Hebei Key Laboratory of Heterocyclic Compounds Handan University Handan
056005, China E-mail: josephgo@sina.com

Supporting information for this article is given via a link at the end
of the document.

\textbf{Abstract:} It is well noticed that hydrogen promotes catalyst
activity in Cr/PNP-catalyzed ethylene tetramerization, but the mechanism
of this boost is unclear. A density functional theory (DFT) study
devoted to exploring this effect was conducted, and conformation changes
were carefully taken into consideration to build a clear reaction
pathway. Three components in the catalytic cycle was examined in detail:
the production of 1-hexene from the metallacycloheptane, the production
of 1-octene from metallacyclononane, and the formation of active center
on the catalyst. The result indicates that the formation of active
center on the catalyst becomes more favorable upon imposition of
hydrogen, where hydrogen function as a second ligand. This easing effect
could be the key factor leading to the outperformed catalyst activity.

\textbf{Keywords:} ethylene oligomerization * Cr-PNP catalyst * DFT
calculation * Hydrogen promoting effect * active center

Introduction

Driven by the emerging polyethylene, particularly the linear low-density
polyethylene (LLDPE) market, the demand for \selectlanguage{greek}\emph{α} -\selectlanguage{english}olefin proliferate
rapidly, especially the low carbon number components such as 1-butene,
1-hexene, and 1-octene\textsuperscript{{[}1{]}}. Compared to the fast
development of selective ethylene
trimerization\textsuperscript{{[}2{]}}. which first commercialized as
early as 2003 by Chevron Phillips Chemical Company
LP\textsuperscript{{[}3{]}}, the selective ethylene tetramerization
catalyst still suffer from relatively low activity and
selectivity\textsuperscript{{[}4{]}}. The first selective ethylene
tetramerization catalyst that has the potential to be commercialized was
reported by Sasol at 2004\textsuperscript{{[}5{]}}, using
methylaluminoxane(MAO)-activated Cr/PNP catalyst system to give a
1-octene selectivity up to 70\%, which is also the most studied catalyst
system up till today. It was noticed then that addition of 2.5 bar of
hydrogen to the system alleviated the polyethylene formation without
much compromise on selectivity and productivity, but the mechanism is
unclear. Further investigation regarding this hydrogen promoting effect
remained scarce until 2016 when Jiang \emph{et al.}
\textsuperscript{{[}6{]}} confirmed that there is a significant
improvement of PNP/Cr(III)/MAO catalyst activity on ethylene
tetramerization under hydrogen pressure ranging from 0.03 to 0.50 Mpa. A
DFT study of hydrogen effect on the Chevron-Phillips trimerization
system was conducted by Bahri-Laleh \emph{et al.} at
2017\textsuperscript{{[}7{]}}, in which hydrogen is believed to
participate into the reaction and leads to the formation of alkanes.
However, ethylene tetramerization experiments conducted by Jiang\emph{et
al.} showed little alkane product in the presence of hydrogen,
indicating further investigation is required. Liu \emph{et al.}
\textsuperscript{{[}8{]}} investigated the effects of hydrogen in PNP/Cr
catalytic system using DFT analysis at 2018, in which he proposed that
the increase of catalyst activity under hydrogen addition is due to the
lowered energy barrier to form metallacyclopentane. However, the energy
required for the oxidation addition from quartet bis(ethylene)Cr complex
to quartet heterocyclic Cr complex actually increases from 6.6 kcal/mol
to 7.0 kcal/mol upon addition of hydrogen, seemingly insufficient to
account for the significant increase of catalyst activity. Hydrogen
effect on the following reactions leading to the product was also
investigated where hydrogen function solely as a second ligand. Based on
these previous studies, here we compare competitive reactions from
metallacycloalkanes where hydrogen either participate into the reaction
to produce alkene, or function as a second coordinated ligand, with
conformation changes taken into consideration, to further explore how
hydrogen might have affect the ethylene oligomerization process using
DFT calculation. We also explore possible hydrogen effect outside the
catalytic cycle, namely the formation of catalyst active center to gain
the whole picture.

\textbf{Results and Discussion}

The ethylene oligomerization process adopted into the calculation here
is based on a well-accepted metallacyclic mechanism, which was first
proposed by Manyik\textsuperscript{{[}9{]}} at Union Carbide at 1977.
The cycle starts with the oxidative coupling of two coordinated ethylene
to form a metallacyclopentane intermediate, followed by a \selectlanguage{greek}\emph{β} -\selectlanguage{english}H
transfer to a third coordinated ethylene, from which 1-hexene was
released. This mechanism was soon modified by
Briggs\textsuperscript{{[}10{]}} at 1989, proposing that a third
coordinated ethylene was inserted into the metallacyclopentane to give a
metallacycloheptane, from which \selectlanguage{greek}\emph{β} -\selectlanguage{english}H eliminate or \selectlanguage{greek}\emph{β}
-\selectlanguage{english}agostic 3,7-H shift take place to yield 1-hexene. This metallacyclic
mechanism was experimentally verified using deuterium labeling by Agapie
and coworkers\textsuperscript{{[}11{]}}, and applied to ethylene
tetramerization as well, which was also tested with isotopomers by
Sasol\textsuperscript{{[}12{]}}. The probing into the active center of
the catalysts, however, remained complicated because of the paramagnetic
nature of the various oxidation states of chromium formed during the
catalytic cycle\textsuperscript{{[}13{]}}, but there are more evidences
supporting Cr(I)/Cr(III) redox in the tetramerization catalytic
cycle\textsuperscript{{[}11a, 14{]}} using electron paramagnetic
resonance and X-ray absorption spectroscopy\textsuperscript{{[}15{]}},
or self-activating catalysts crystallization\textsuperscript{{[}16{]}},
so Cr(I)/Cr(III) redox cycle was applied in this study.

Based on the mechanism given before, the production of \selectlanguage{greek}\emph{α} -\selectlanguage{english}olefin
may occur via \selectlanguage{greek}\emph{β} -\selectlanguage{english}H eliminate or \selectlanguage{greek}\emph{β} -\selectlanguage{english}agostic 3,7-H shift
from the corresponding metallacycloalkane, through which hydrogen might
modify the energy barriers of the reactions only by coordination and not
necessarily involve into the reaction, as Liu stated in the previous
studies\textsuperscript{{[}8{]}}. However, we do believe it is possible
to include hydrogen into the reaction process that leads to the
production of alkene, in which hydrogen is inserted into the Cr-C bond,
offering an hydrogenolysis reaction to give an alkane chain, before
a\selectlanguage{greek}\emph{β} -\selectlanguage{english}H transfer to liberate \selectlanguage{greek}\emph{α} -\selectlanguage{english}olefin. The selectivity of
the catalyst depends on the relative equilibrium between decomposition
and ring expansion of the metallacycloalkane, so the energy required for
ring expansion is also calculated. Here we present the energy profiles
of these reactions on metallacycloheptane and metallacyclononane with or
without hydrogen, attempting to illustrate how hydrogen might affect the
reactions. All Gibbs free energies are relative to the starting material
plus the corresponding number of free ethylene molecules.

\selectlanguage{greek}\textbf{Hydrogen effect on \emph{α}-olefin production from
metallacycloalkanes}\selectlanguage{english}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1.} Relative Gibbs free energy profiles (kcal/mol) to
produce 1-hexene from metallacycloheptane without hydrogen

Starting from the metallacycloheptane (M0), there are three possible
developments presented in Figure 1, from which two leads to the
formation of 1-hexene. 1-hexene could be produced via a one-step\selectlanguage{greek}\emph{β}
-\selectlanguage{english}agostic interaction (M-TS0-1) due to ring flexibility with an energy
barrier of 13.1 kcal/mol, or via a two-step \selectlanguage{greek}\emph{β} -\selectlanguage{english}H transfer
incorporated with a conformation change, overcoming energy barriers of
12.4 kcal/mol (M-TS0-2) and 15.9 kcal/mol (M-TS2'-3) for each step. The
ring-expansion involves ethylene coordination from M0 to M4, followed by
insertion of ethylene to the M-C bond via M-TS4-5 with an energy barrier
of 17.1 kcal/mol. Note that both ethylene coordination and ring
expansion are endergonic, hence the overall energy barrier for ring
expansion without hydrogen should be the sum of the two, namely 17.4
kcal/mol.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2.} Relative Gibbs free energy profiles (kcal/mol) to
produce 1-hexene from metallacycloheptane with hydrogen.

When hydrogen is introduced into the system, an additional pathway is
included into the calculation, and all energies are referred to
M0-H\textsubscript{2}, the Gibbs free energy of which is set to 0 for
analysis convenience. The one-step \selectlanguage{greek}\emph{β} -\selectlanguage{english}agostic interaction via
M-TS0'-1-H\textsubscript{2} to liberate 1-hexene has an energy barrier
of 9.8 kcal/mol, but an endergonic conformation change of 6.1 kcal/mol
from M0-H\textsubscript{2} to M0'-H\textsubscript{2} is necessary to
enable the reaction, thus the overall energy barrier rise to 15.9
kcal/mol, which is actually higher than that without hydrogen (13.1
kcal/mol). The two-step \selectlanguage{greek}\emph{β} -\selectlanguage{english}H transfer occur via two transition
states M-TS0-4-H\textsubscript{2} and M-TS4'-5-H\textsubscript{2},
overcoming energy barriers of 13.7 kcal/mol and 16.9 kcal/mol
respectively. The hydrogenolysis occur via M-TS0-2-H\textsubscript{2} to
give an alkane chain, overcoming an energy barrier of 15.8 kcal/mol. An
exergonic conformation change from M2-H\textsubscript{2} to
M2'-H\textsubscript{2} occurred to enable further \selectlanguage{greek}\emph{β} -\selectlanguage{english}H transfer
to liberate 1-hexene via M-TS2'-3-H\textsubscript{2}, with an energy
barrier of 11.8 kcal/mol. The ring expansion occur through first an
endergonic ethylene coordination of 2.4 kcal/mol, followed by an
ethylene insertion of 17.6 kcal/mol, both figures higher than those
without hydrogen, indicating a higher overall energy barrier.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3.} Relative Gibbs free energy profiles (kcal/mol) to
produce 1-octene from metallacyclononane without hydrogen.

Similar analysis was conducted on metallacyclononane and presented in
Figure 3 and Figure 4. The production of 1-octene through one-step
agostic interaction via N-TS0-1 requires an energy barrier of 15.8
kcal/mol. The two-step \selectlanguage{greek}\emph{β} -\selectlanguage{english}H transfer occur via N-TS0-2 and
N-TS-2-3, with energy barriers of 13.9 kcal/mol and 17.5 kcal/mol
respectively. Further ring expansion leads to the formation of
byproducts and is neglected in this calculation,\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 4.} Relative Gibbs free energy profiles (kcal/mol) to
produce 1-octene from metallacyclononane with hydrogen

Upon addition of hydrogen, one-step agostic interaction via
N-TS0''-5-H\textsubscript{2} requires an energy barrier of 7.8 kcal/mol.
The overall energy barrier required for this agostic interaction
includes the necessary conformation change from N0-H\textsubscript{2} to
N0''-H\textsubscript{2,} and thus rise to 10.7 kcal/mol, which is still
significantly lower than that without hydrogen (15.8 kcal/mol). The
two-step \selectlanguage{greek}\emph{β} -\selectlanguage{english}H transfer starts with an exergonic conformation
change from N0-H\textsubscript{2} to N0'-H\textsubscript{2}, enabling
the transfer via transition state N-TS0'-3-H\textsubscript{2} and
N-TS3-4-H\textsubscript{2} with energy barriers of 12.8 kcal/mol and
19.8 kcal/mol respectively. It is difficult to compare how hydrogen
affects this two-step reaction, as one step becomes more favorable yet
the other more unfavorable, but since the agostic interaction is
generally easier to occur, the reaction might well proceed via the
one-step agostic route. The pathway of \selectlanguage{greek}\emph{β} -\selectlanguage{english}H transfer after
hydrogenolysis is also calculated on metallacyclononane. The hydrogen
insertion from N0-H\textsubscript{2} to N1-H\textsubscript{2} via
N-TS0-1-H\textsubscript{2} requires 8.9 kcal/mol, and the
following\selectlanguage{greek}\emph{β} -\selectlanguage{english}H transfer via N-TS1'-2-H\textsubscript{2} after an
endergonic conformation change of 4.1 kcal/mol has an energy barrier of
15.8 kcal/mol.

The energy required for conformation change and coordination is
necessary to take into consideration, especially when the transformation
is endergonic, as the reaction needs the overcoming of these barriers to
occur. Here we present the relevant energy barrier figures with or
without hydrogen in Table 1, in which endergonic conformation change are
labeled in brackets.

\textbf{Table 1.} \selectlanguage{greek}Δ\selectlanguage{english}G of the reactions calculated regarding
metallacycloheptane and metallacyclononane with and without hydrogen,
figures in brackets indicate energy required for necessary conformation
change or ethylene coordination\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
& metallacycloheptane & metallacycloheptane & metallacyclononane &
metallacyclononane\tabularnewline
\midrule
\endhead
& Without hydrogen & With hydrogen & Without hydrogen & With
hydrogen\tabularnewline
\selectlanguage{greek}\emph{β}-\selectlanguage{english}agostic interaction & 13.1 & (6.1) 9.8 & 15.8 & (2.9)
7.8\tabularnewline
Two-step \selectlanguage{greek}\emph{β}-\selectlanguage{english}H elimination & 12.4, 15.9 & 13.7, 16.9 & 13.9, 17.5 &
12.8, 19.8\tabularnewline
Hydrogenolysis and \selectlanguage{greek}\emph{β}-\selectlanguage{english}H elimination & - & 15.8, 11.8 & - & 8.9,
(4.1) 15.8\tabularnewline
Ring expansion & (0.3) 17.1 & (2.4) 17.6 & - & -\tabularnewline
\bottomrule
\end{longtable}

The introduction of hydrogen modifies the energy barriers of these
reactions, albeit in different directions. For metallacycloheptane, the
energies required for possible reactions are generally raised upon
addition of hydrogen. The energy required for the agostic 3,7-H shift
seems to be reduced from 13.1 kcal/mol to 9.8 kcal/mol, but a
conformation change of 6.1 kcal/mol is required, making the overall
energy barrier higher than that without hydrogen. It is difficult to
determine exactly which pathway is applied to produce 1-hexene without
hydrogen, as the energy requirements of the two pathways are similar,
but it is clear that \selectlanguage{greek}\emph{β} -\selectlanguage{english}agostic 3,7-H shift becomes more
favorable among the three possible reaction pathways in the presence of
hydrogen. For metallacyclononane, the formation of 1-octene via \selectlanguage{greek}\emph{β}
-\selectlanguage{english}agostic hydrogen shift becomes much more favorable as the energy
barrier is greatly reduced from 15.8 kcal/mol to 10.7 kcal/mol with the
introduction of hydrogen, but the formation of metallacyclononane itself
becomes more difficult as the energy required for the ring expansion of
metallacycloheptane rises from 17.4 kcal/mol to 20.0 kcal/mol, making
hydrogen's full significance to the reaction hard to ascertain.Thus, we
turned to explore how hydrogen might affect the formation of the active
center on the catalyst in hopes of finding a more conclusive influence.

\textbf{Hydrogen effect in the formation of active center on the
catalyst}

Upon addition of MAO, the chromium pre-catalyst is believed to undergo
methylation and reduction to form an active center capable to coordinate
at least two ethylene in order to form the key intermediate
metallacyclopentane\textsuperscript{{[}17{]}}. A proposed mechanism is
used based on previous works by Sasol\textsuperscript{{[}18{]}}, in
which two ethylene molecules both coordinate onto the metal center
axially to achieve minimal steric around the active center. Figure 5
shows the Gibbs free energy profiles for the activation process, all
figures relative to the starting molecule A0 where two ethylene
molecules are just coordinated onto the metal center.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 5.} Relative Gibbs free energy profiles (kcal/mol) for
the formation of active center on Cr/PNP catalyst, where ethylene
coordinated both axially.

The process starts with the insertion of one ethylene into the M-C bond
via A-TS0-1, overcoming an energy barrier of 5.9 kcal/mol, followed by a
conformation change (A1 to A1') of 5.7 kcal/mol and reduction
elimination of 8.7 kcal/mol via A-TS1'-2 to give an active species A2.
Note that this conformation change is necessary to bring \selectlanguage{greek}\emph{β} -\selectlanguage{english}H
from propyl group close to methyl group to enable further reaction, and
both the conformation change from A1 to A1' and the reaction over
A-TS1'-2 are endergonic, hence the overall energy required for the
formation of active center without hydrogen could be regarded as the sum
of the two, namely 14.4 kcal/mol.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Figure 6.} Relative Gibbs free energy profiles (kcal/mol) for
the formation of active center on Cr/PNP catalyst with hydrogen, with
hydrogen coordinated onto the metal center opposite the ethylene
molecule

When hydrogen is introduced into the system, the reduction elimination
could originate from the \selectlanguage{greek}\emph{β} -\selectlanguage{english}H on the alkyl group, or from the
hydrogen molecule, thus enable other possible scenarios to occur. Figure
6 presents the Gibbs free energy profiles with hydrogen adsorbed axially
onto the metal center. In this case direct reduction from hydrogen
adsorbed onto the metal center to liberate methane off could occur via
A-TS0 -1-H\textsubscript{2} with an energy barrier of 3.6 kcal/mol. The
other methyl group could be eliminated in the same way via
A-TS1-2-H\textsubscript{2} with an energy barrier of 13.3 kcal/mol.
Similar as before, ethylene could insert into the M-C bond via
A-TS0-3-H\textsubscript{2} with an energy barrier almost the same as
that without hydrogen (5.8 kcal/mol), from which the \selectlanguage{greek}\emph{β} -\selectlanguage{english}H
eliminate could occur via A-TS3'-4-H\textsubscript{2} after endergonic
conformation change from A3-H\textsubscript{2} to
A3'-H\textsubscript{2}to bring the propyl group close to the methyl
group, this time overall energy barrier reduced to 12.2 kcal/mol. This
pathway is exactly the same as when hydrogen is absent, in which
hydrogen function as a ligand and does not participate into the
reaction. The energy barrier is reduced from 14.4 kcal/mol to 12.2
kcal/mol upon introduction of hydrogen. A third possible route would be
a combination of the two developments, in which elimination from
hydrogen occur after ethylene insertion to release first methane and
then propane. However, this reduction via A-TS3-8-H\textsubscript{2} has
an exceptionally high energy barrier of 33.4 kcal/mol, hence unlikely to
happen. It is also possible that after ethylene insertion, another
ethylene is adsorbed onto the available site of the metal center to give
A5-H\textsubscript{2}, from which another insertion occurs via
A-TS5-6-H\textsubscript{2} to form two alkyl chain. A \selectlanguage{greek}\emph{β} -\selectlanguage{english}H
eliminate via A-TS6'-7-H\textsubscript{2} would produce the active
center, but a conformation change bringing two propyl group close to
each other is required, which is sterically unfavorable, as is showed in
the high energy barrier (20.7 kcal/mol required to change from
A6-H\textsubscript{2} to A6'-H\textsubscript{2}).

Judging from energy profile present in Figure 6, two pathways are
energetically more favorable among these possible developments:
elimination from the hydrogen molecule adsorbed onto the metal center,
and ethylene insertion followed by conformation change and \selectlanguage{greek}\emph{β} -\selectlanguage{english}H
elimination, namely the same pathway without hydrogen. Either way, the
imposition of hydrogen reduced the energy barrier to form the active
center (3.6 kcal/mol, 13.3 kcal/mol; or 5.8 kcal/mol, 12.2 kcal/mol;
compared to 5.9 kcal/mol, 14.4 kcal/mol without hydrogen), the only
difference would be whether hydrogen participate into the reaction, or
function as a second ligand. From the calculations we tested, this
reduction of energy barrier is the only compartment to demonstrate an
unquestionable easing effect, hence we propose that the formation of
active center is a key factor regarding catalyst activity, thus coincide
with the assumption raised by Jiang \emph{et al.} in
2016\textsuperscript{{[}6{]}} that hydrogen might play an important role
in the generation of active centers. In this case, hydrogen reduces the
energy barrier to generate active centers on the catalyst, hence more
active centers are available for reaction, leading to the significant
increase of catalyst activity.

\textbf{Conclusion}

Herein we investigated the effect of hydrogen posed over Cr-PNP
catalyzed ethylene oligomerization process using DFT calculation.
Multiple pathways were tested and compared. The introduction of hydrogen
modified the energy barriers during the oligomerization, but the exact
effect is debatable and unclear. However, hydrogen do reduce the energy
barrier to form the active center on the catalyst, enabling
proliferation of active centers. Hence, we propose that hydrogen
promotes catalyst activity by easing the formation of active centers on
the catalyst.

\textbf{Experimental Sector}

Computation details: All DFT calculations were accomplished with
Gaussian 09\textsuperscript{{[}19{]}} program package using B3LYP
functional. 6-31G* basis set were used for all atoms except for Cr,
which was described with LANL2DZ (ECP) basis
set\textsuperscript{{[}20{]}}. The Gaussian View 6.0 program was used to
build the structures. Monovalent cations with quartet spin states were
considered in theoretical models for the DFT
study\textsuperscript{{[}21{]}}. Vibrational frequencies were checked
for all minima and transition states. Intrinsic reaction coordinate
calculations were carried out to verify connections between transition
states and different conformations. The model chosen was
Cr/Me\textsubscript{2}PN(C\textsubscript{5}H\textsubscript{9})PMe\textsubscript{2}with
a cyclopentyl group attached to N, and the formation of active cationic
Cr(I) specie includes reduction implication of cocatalyst from Cr(III).
The Gibbs free energy collected under default conditions, and the
solvent used in the calculation is methylcyclohexane.

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