Lithium-Catalyzed anti-Markovnikov Intermolecular Hydroamination Reactions of Vinylarenes and Simple Secondary Amines

Article abstract of DOI:10.1002/cctc.201700043

Various β-arylethylamine derivatives were straightforwardly obtained by the lithium-catalyzed anti-Markovnikov selective intermolecular hydroamination reaction of secondary aliphatic amines with vinylarenes. The use of only 1.5 mol % LiCH₂TMS as a solid base in THF proved to be efficient to deliver the target products at room temperature with up to complete conversions. Both reaction partners were, moreover, used in equivalent amounts; thus, this protocol best respects the concepts of sustainable chemistry for the easy preparation of lead structures for pharmaceutically active compounds.

Full text of DOI:10.1002/cctc.201700043

Accepted Article
Title: Lithium-catalysed anti-Markovnikov intermolecular
hydroamination reactions of vinylarenes and simple secondary
amines
Authors: Stéphane Germain, Meije Lecoq, Emmanuelle Schulz, and
Jérôme Hannedouche
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10.1002/cctc.201700043
ChemCatChem
COMMUNICATION
Lithium-catalysed anti-Markovnikov intermolecular
hydroamination reactions of vinylarenes and simple secondary
amines
Stéphane Germain,[a] Meije Lecoq,[a] Emmanuelle Schulz,[a,b]* and Jérôme Hannedouche[a,b]*
Abstract: Various β-arylethylamine derivatives have been
straightforwardly obtained by lithium-catalysed anti-Markovnikov
selective intermolecular hydroamination reactions of secondary
aliphatic amines and vinylarenes. Use of as little as 1.5 mol %
LiCH2TMS as solid base in THF proved to be an efficient room-
temperature protocol for delivering the targeted products in up to
complete conversion. Both reaction partners were moreover used in
equivalent amounts, thus best respecting the concepts of
sustainable chemistry for the easy preparation of lead structures for
pharmaceutically active compounds.
efficiency and scope. It is in this context that we disclose herein
our studies towards the development of a convenient room-
temperature protocol for the direct anti-Markovnikov addition of
simple secondary aliphatic amines on vinylarenes using solely
solid trimethysilylmethyl lithium as a very efficient ligand-free
lithium-based (pre)catalyst in low loading (1.5 mol%) (Scheme 1).
The direct addition reaction of an amine across a carbon-carbon
double bond, the so-called hydroamination reaction, is one of
the most step- and atom- economical methodology for the
preparation of nitrogen-containing compounds from relatively
inexpensive and ubiquitous amines and olefins.[1] During the
past two decades, intense research activities have been
dedicated to the development of efficient catalytic systems for
the (stereo)selective intra- and intermolecular hydroamination of
olefins displaying Markovnikov regioselectivity.[1] In contrast, the
anti-Markovnikov regioselectivity remains poorly developed and
this despite the industrial importance of linear amine products.
Indeed, only sporadic catalytic systems based on organic
compounds,[2] late transition metals,[3] rare-earth elements,[4]
Scheme 1. State of the art in lithium-catalysed anti-Markovnikov
intermolecular hydroamination of vinylarenes and secondary amines.
A few years ago, our group has reported the first application of
chiral diaminobinaphthyl dilithium salts as easily available and
efficient alkali-metal based (pre)catalysts for the asymmetric
cyclohydroamination of amino-1,3-dienes with the highest
stereo- and enantioselectivites described to date (up to 93:7 dr
and 71 % ee).[9,10] The methodology was further extended to the
enantioselective intramolecular hydroamination of primary and
secondary amines tethered to alkenes at room temperature with
ee’s up to 58%.[9b,11] These efficient lithium-based catalysts were
in-situ prepared by a straightforward protocol resulting from the
combination of N-substituted (R)-(+)-1,1’-binaphthyl-2,2’-
diamines such as (R)-H2L1-3 (Figure 1) and LiCH2TMS in a 1:2.5
ratio. Analysis on the structure of the (pre)catalyst and control
experiments have clearly demonstrated that a small excess of
base (relative to the stoichiometry required to deprotonate the
diamines) was essential to the system reactivity.[9a] We describe
here our results concerning the ability of this specific catalytic
system to promote the more challenging intermolecular anti-
Markovnikov hydroamination reactions of vinylarenes and our
observations that lead to the development of a competent
ligand-free trimethysilylmethyl lithium-based (pre)catalyst for this
transformation.
[5]
[6,7]
alkaline earth
or alkali
metals have exhibited such
regioselectivity mainly on vinylarenes to provide β-
arylethylamines as key synthons. To our knowledge, the anti-
Markovnikov selective hydroamination of amines and simple
aliphatic alkenes has not yet been reported, highlighting the
significant challenge with such development.[8] Although the field
of alkali metal-promoted hydroamination reaction emerged in the
early 1950s, most of the reported studies have been limited in
terms of scope to a few amine/olefin partners and have been
conducted under harsh reactions conditions. It is only recently
that the groups of Beller,[6c] and later Hultzsch,[6a] have truly
explored the scope of alkali-metal catalyzed anti-Markovnikov
hydroamination of vinylarenes with N-benzylpiperazine and
primary/secondary amines respectively, under gentler conditions
(Scheme 1). Beside the fact that these studies have provided
useful protocols for the preparation of a range of linear amine
products, there is still room for improvement in terms of catalyst
[a]
[b]
Dr S. Germain, M. Lecoq, Dr E. Schulz, Dr J. Hannedouche
Univ Paris-Sud, Institut de Chimie Moléculaire et des Matériaux
d’Orsay, UMR 8182, Bâtiment 420, Rue du doyen Georges, Orsay,
F-91405
emmanuelle.schulz@u-psud.fr, jerome.hannedouche@u-psud.fr
Dr E. Schulz, Dr J. Hannedouche
CNRS, Orsay, F-91405
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10.1002/cctc.201700043
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COMMUNICATION
as unchanged mixtures even after prolonged reaction time. Only
the use of pyrrolidine 2 in the presence of two equivalents of α-
methyl-styrene delivered the linear product 7 with a conversion
of 42 % after 5h of reaction (Table 2, entry 1). Extending the
reaction time to 24h did not improve the yield (Table 2, entry 2).
L1
R
(R)-H2 , R = CH2Ph
NH
L2
(R)-H2 , R = cyclopentyl
NH
R
(R)-H2L3, R = i-Pr
Figure 1. N-substituted (R)-(+)-1,1’-binaphthyl-2,2’-diamines H2L1-3
Table 2. Enantioselective intermolecular hydroamination of
and pyrrolidine 2 in [D6]benzene. [a]
α-methylstyrene
First efforts were thus drawn towards intermolecular
hydroamination reactions of styrene as a benchmark substrate.
The reaction of N-methylbenzylamine 1 (1 equiv.) and styrene (2
equiv) in the presence of our previously reported catalytic
system (R)-H2L1:LiCH2TMS in a 1:2.5 ratio delivered solely the
anti-Markovnikov product 4 with 92 % conversion in one hour
(Table 1, entry 1) at 100°C in benzene. Pyrrolidine 2 reacted
delightfully similarly under the same conditions, albeit
conversion could not exceed 81 %, even after prolonged
reaction time. Intermolecular hydroamination could also be
performed in the presence of a primary amine, since use of
benzylamine 3 delivered with the same regioselectivity the
mono-hydroamination product 6 in nearly complete conversion,
even if the reaction time dramatically increased for this reaction
(Table 1, entry 3). As far as we know, this specific selectivity has
until now not been observed in other reports for alkali salts
catalysed hydroamination reaction. Indeed, under a similar
excess of styrene, the reported LiN(TMS)2/TMEDA system (10
mol%) leads to the formation of bis(hydroamination) product as
side-product.[6a]
Entry
Ligand
Time [h]
NMR yield [%][b]
1
2
3
4
5
6
7
(R)-H2L1
5
42
24
24
24
24
24
6
43[c]
13[c]
8[c]
(R)-H2L2
(R)-H2L3
( )-H2L1
67[c]
78[c]
92[d]
-
-
[a] reaction was performed at 100°C in [D6]benzene allowing for NMR
conversion determination with ferrocene as internal standard. [b] racemic
product is observed. [c] prolonged reaction time to 120h does not improve the
yield. [d] at rt in [D8]THF.
Table 1. Intermolecular hydroamination of styrene and primary and
secondary amines in [D6]benzene.[a]
(R)-H2L1 (3.2 mol%)
NR1R2
LiCH2TMS (8 mol%)
NHR1R2
+
Unfortunately, 7 was recovered as a racemic mixture. The
same trend was observed in the presence of other chiral ligands
(R)-H2L2-3 (Table 2, entries 3-4). Fortunately, use of ligand ( )-
H2L1 as a racemic mixture allowed for an improved conversion
(67 % after 24h, Table 2, entry 5), that could be increased up to
78 % using 8 mol% of LiCH2TMS without any additional ligand
(Table 2, entry 6). We thus assume that the dramatic negative
influence of the presence of the ligands on the reaction rate is
due to the formation of inactive lithium amide aggregates, as
already observed by Beller et al..[6b] Delightfully, replacement of
[D6]benzene by [D8]THF permitted the reaction to be performed
at room temperature with 8 mol % of LiCH2TMS providing 7 with
a high conversion of 92 % in only 6h (Table 2, entry 7). This
more polar and coordinating solvent is indeed known to possibly
reduce the lithium derivatives aggregation state in solution.[12]
Ph
Ph
C6D6, 100 °C
( 2 equiv. ) ( 1 equiv. )
1 R1 = Bn, R2 = Me
2 R1, R2 = -(CH2)4-
3 R1 = Bn, R2 = H
4 R1 = Bn, R2 = Me
5 R1, R2 = -(CH2)4-
6 R1 = Bn, R2 = H
Entry
Amine
Product
Time [h]
NMR yield
[%]
1
2
3
1
2
3
4
5
6
1
92
0.75
48
81[b]
98[c]
[a] reaction was performed at 100°C in [D6]benzene allowing for NMR
conversion determination with ferrocene as internal standard. [b] maximal
conversion. [c] only mono-hydroamination anti-Markovnikov product is
observed.
According to the observed reactivity, disubstituted olefins
were then studied, and α- and β-methyl-styrene and trans-
stilbene were allowed to react with either N-methylbenzylamine
1 or pyrrolidine 2, under the same reactions conditions as
described above. Unfortunately, almost all reactions performed
were unsuccessful, and the engaged substrates were recovered
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n-BuLi (20 mol%) in THF at room temperature provides the
linear product in 80% yield after 24h of reaction.[6c,13]
Table 3. Intermolecular hydroamination of styrene and secondary amines
in [D8]THF.[a]
NR1R2
LiCH2TMS (1.5 mol%)
NHR1R2
+
Table 4. Intermolecular hydroamination of vinylarenes and N-
methylbenzylamine 1 or pyrrolidine 2 in [D8]THF.[a]
Ph
Ph
[D8]THF, 21 °C
( 1 equiv. ) ( 1 equiv. )
Amine
NR1R2
LiCH2TMS (1.5 mol%)
NHR1R2
+
Entry
Product
Time
[h]
NMR
yield
[%][b]
Ar
Ph
[D8]THF, 21 °C
( 1 equiv. ) ( 1 equiv. )
1 R1 = Bn, R2 = Me
2 R1, R2 = -(CH2)4-
1
1
>99 (82)
>99 (71)
1
2
Entry
Amine
Product
Time
[h]
NMR
yield
[%][b]
5
38
3
4
5
1
2
3
4
1
>99
>99
97
2
>99 (84)
>99
1
0.5
NMe
O
14
15
N
N
Ph
Ph
1
0.75
>99 (90)
6
0.25
>99
[a] reaction conditions : amine/styrene = 1/1, LiCH2TMS (1.5 mol %), Cp2Fe
(0.4 eq.), [D8]THF, 21°C. [b] NMR conversion determined against ferrocene
as internal standard and isolated yield in brackets.
5
6
0.25
8
>99
37
These softener reaction conditions were next applied to the
anti-Markovnikov selective hydroamination of styrene and
various secondary amine partners under lower catalyst loading
of base and an equimolar mixture of both reaction partners. Use
of only 1.5 mol% of LiCH2TMS at room temperature in [D8]THF
delivered regioselectively only anti-Markovnikov products. The
results obtained are gathered in Table 3. Hence, application of
these conditions to the reaction between N-methylbenzylamine 1
and styrene gave quantitatively benzyl-methyl-phenethyl-amine
4 in one hour (Table 3, entry 1) and the same result was
obtained with pyrrolidine 2 (Table 3, entry 2). Both products 4
and 5 were nicely isolated in high yields. Under similar
conditions of temperature, the reported LiN(TMS)2/TMEDA
system (10 mol%) affords 5 in 82% isolated yield after 107h,[6a]
highlighting the remarkable activity of our system comparatively
to the literature. Due to steric hindrance, transformation in the
presence of N-ethylbenzylamine 8 took place more slowly and
the targeted hydroamination product 12 was only formed in 38 %
yield after 5 h reaction (Table 3, entry 3) whereas diethylamine 9
reacted with a high rate producing diethyl-phenethyl-amine 13
with a complete conversion in only 2 h. N-methylpiperazine 10
7
8
96
96
59
58
98
(65)
9[c]
120
[a] reaction conditions : amine/styrene = 1/1, LiCH2TMS (1.5 mol %), Cp2Fe
(0.4 eq.), [D8]THF, 21°C. [b] NMR conversion determined against ferrocene as
internal standard and isolated yield in brackets. [c] LiCH2TMS (8 mol %).
Having these conditions in hands, the scope of the reaction
was extended to the use of N-methylbenzylamine 1 and
pyrrolidine 2 in intermolecular hydroamination reactions with
various arenes. Different substituents on styrene-based
derivatives were firstly investigated, and transformations were
then attempted in the presence of less activated alkene
derivatives (Table 4). Styrene derivatives diversely substituted
on the phenyl ring were firstly investigated and methylstyrene
compounds (with the methyl substituent located either in the
ortho or para-position) allowed the production of all targeted
compounds 16-18 with a complete conversion within one hour
and morpholine 11 underwent analogously
a
fast
hydroamination reaction with styrene giving rise to the targeted
products 14 and 15 in both high yield and short reaction time
(Table 3, entries 5-6). As a comparison, the addition of N-
benzylpiperazine (1 equiv.) and styrene (2 equiv.) catalysed by
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cold-recrystallisation of a 1M pentane solution of LiCH2TMS purchased
from Sigma-Aldrich. Bruker AM250, AV300, AV360 NMR spectrometers
operating at 250, 300, 360 MHz, respectively, were used to record the 1H
NMR spectra. Chemical shifts were referenced internally according to the
Me4Si resonance. Mass spectra were recorded by using a Bruker
MicrOTOF-Q spectrometer.
(Table 4, entries 1-3). Introduction of a methoxy substituent in
the ortho position proved also very efficient in terms of reaction
rate, whereas an important deceleration occurred with the
introduction of this donating group in para position (Table 4,
entries 4,5 vs.6). The reactivity difference between the ortho-
and para-position of the methoxy-substituent may be
rationalised by the favourable participation of the ortho-methoxy,
in contrast to the para-methoxy, to the coordination of the
carbon-carbon double bond to the reactive lithium intermediate.
This trend was previously noticed with yttrium-based catalytic
system.[4a] Unfortunately, 9-vinylanthracene did not react under
these reaction conditions and no transformation occurred when
it was introduced in stoichiometric quantity in the presence of
either N-methylbenzylamine 1 or pyrrolidine 2. α-Methyl-styrene
was then investigated as starting material and compounds 22
and 7 were delightfully obtained, albeit complete conversion
could not be reached even after prolonged reaction time of up to
4 days (Table 4, entries 7 and 8). However, α,β-disubstituted
olefins remained unreactive and no transformation could be
observed involving 1,2-dihydro-naphthalene, propenylbenzene,
cis- and trans-stilbene and neither secondary amines.
General procedure for anti-Markovnikov hydroamination of
vinylarenes in the presence of chiral ligand: A solution of LiCH2TMS
(3.5 mg, 37.5 µmol) in [D6]benzene or [D8]THF (200 µL) was added to a
solution of the appropriate ligand (15 µmol) in [D6]benzene or [D8]THF
(250 µL). The reaction mixture was allowed to stir for 5 min at r.t. before
being transferred to a vial containing the appropriate amine (0.45 mmol),
the styrene derivative (0.90 mmol) and ferrocene (33.5 mg, 0.18 mmol).
The reaction mixture was then introduced into a screw-tap or a J. Young-
tap NMR tube and the progress of the reaction was monitored by 1H
NMR spectroscopy using ferrocene as internal standard.
General procedure for anti-Markovnikov hydroamination of
vinylarenes and primary and secondary amines catalysed by ligand
free- LiCH2TMS: A solution of LiCH2TMS (0.6 mg, 6 µmol) in [D8]THF
(400 µL) was transferred to a vial containing the appropriate amine (0.4
mmol), the appropriate vinylarene (0.4 mmol) and ferrocene (0.08 mmol).
The reaction mixture was then introduced into a screw-tap or a J. Young-
tap NMR tube and the progress of the reaction was monitored by 1H
NMR spectroscopy using ferrocene as internal standard. The reaction
mixture was quenched with ethanol and the product was purified on a
preparative TLC plate.
Fortunately, pyrrolidine
2
reacted in the presence of
allylbenzene (8 mol % LiCH2TMS), and compound 23 was
isolated in 65% yield after a complete conversion.[6d] Simple less
reactive olefins such as pent-1-ene or oct-1-ene failed to
undergo the hydroamination reaction with pyrrolidine 2 and only
double bond isomerisation could be observed. Attempts to use
more reactive substrates, such as norbornene or
cyclohexadiene have not been successful either and 2-vinyl- or
4-vinylpyridine underwent only fast polymerization under these
conditions.
N-Benzyl-N-methyl-2-phenylethanamine (4): Rf=0.48 (pentane/EtOAc
75:25); colorless oil (83 mg, 0.37 mmol, 82%); 1H NMR (300 MHz,
CDCl3, 294 K): δ=2.34 (s, 3 H), 2.64–2.77 (m, 2 H), 2.83–2.95 (m, 2 H),
3.62 (s, 2 H), 7.20–7.39 ppm (m, 10 H); 13C{1H} NMR (75 MHz, CDCl3,
294 K): δ=34.1, 42.3, 59.4, 62.3, 126.1, 127.1, 128.4, 128.5, 128.9,
129.2, 139.1, 140.7 ppm; MS (EI): m/z (%):134.0 (78), 90.9 (100); HRMS
(ESI): m/z: calcd for C16H20N (226.1590): [M+H]+; found 226.1587. These
data are in agreement with previously published data.[6a]
To conclude, we have described a mild procedure allowing
for
lithium-catalysed
intermolecular
hydroamination
of
vinylarenes and simple secondary aliphatic amines.
Comparatively to preceding reports, use of LiCH2TMS as base
permitted for the reaction to be run at room temperature and
with low catalyst amount (1.5 mol %). Under these conditions,
various β-arylethylamines were rapidly obtained in high yields
from diverse styrene derivatives and secondary amines. Further
1-Phenethylpyrrolidine (5): Rf=0.09 (pentane/EtOAc 75:25); yellow oil
(50 mg, 0.29 mmol, 71%); 1H NMR (300 MHz, CDCl3, 294 K): δ=1.75–
1.94 (m, 4 H), 2.55–2.68 (m, 4 H), 2.68–2.78 (m, 2 H), 2.83–2.91 (m, 2
H), 7.16–7.37 ppm (m, 5 H); 13C{1H} NMR (90 MHz, CDCl3, 294 K):
δ=23.7, 35.9, 54.4, 58.5, 126.3,128.6, 128.8, 140.5 ppm; MS (EI): m/z
(%): 83.9 (100); HRMS (ESI): m/z: calcd for C12H18N (176.1434): [M+H]+;
found 176.1433. These data are in agreement with previously published
data.[6a]
efforts are still needed to allow for
a control of the
stereoselectivity of the newly formed stereogenic centres what
remains highly challenging in anti-Markovnikov intermolecular
hydroamination promoted by chiral lithium salts.[14]
N,N-diethyl-2-phenylethanamine (13): Rf = 0.51 (DCM/MeOH 90:10);
colorless oil (60 mg, 0.34 mmol, 84%); 1H NMR (360 MHz, CDCl3, 294 K)
δ=1.04 (t, 6 H), 2.41 (q, 4 H), 2.64-2.74 (m, 2 H), 2.81-2.90 (m, 2 H),
7.16-7.37 ppm (m, 5H). 13C{1H} NMR (90 MHz, CDCl3, 294 K) δ=12.5,
36.7, 51.6, 58.2, 126.6, 128.7, 128.9, 140.8 ppm; HRMS (ESI): m/z:
calcd for C12H20N (178.1590): [M+H]+; found 178.1591. These data are in
agreement with previously published data.[16]
Experimental Section
General. All manipulations were performed under an Ar atmosphere by
using standard Schlenk or glovebox techniques. [D6]Benzene and
[D8]THF were dried with sodium benzophenone ketyl, transferred under
vacuum, and stored over activated 3 Å molecular sieves. Ligand H2L1-3
were prepared according to a reported procedure.[15] All amines and
vinylarenes were dried with calcium hydride and transferred under
vacuum. 9-vinylanthracene was dried under vacuum. All amines and
vinylarenes were further dried for at least 2 h with 3Å molecular sieves
with a few drops of solvent prior to use. (R)-(+)-1,1’-binaphthyl-2,2’-
diamine was purchased from Sigma-Aldrich and used without any further
purification. Ferrocene was purchased from Sigma-Aldrich and was
purified by sublimation prior to use. Solid LiCH2TMS was obtained by
N-(2-phenethyl)morpholine (15): Rf
= 0.48 (DCM/MeOH 90:10);
1
colorless oil (69 mg, 0.36 mmol, 90 %); H NMR (300 MHz, CDCl3, 294
K) δ=2.36-2.72 (m, 6 H), 2.79-2.87 (m, 2 H), 3.92-4.02 (m, 4 H), 7.12-
7.33 ppm (m, 5 H); 13C{1H} NMR (75 MHz, CDCl3, 294 K) δ=46.3, 52.6,
58.4, 66.9, 126.2, 128.7, 128.9, 140.0 ppm; HRMS (ESI): m/z: calcd for
C12H18NO (192.1382): [M+H]+; found 192.1385. These data are in
agreement with previously published data.[17]
N-(2-phenypropyl)pyrrolidine (23): Rf = 0.10 (EtOAc/pentane 75:25);
colorless oil (55 mg, 0.29 mmol, 65 %); 1H NMR (250 MHz, [D8]THF, 294
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10.1002/cctc.201700043
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COMMUNICATION
K) δ=0.90(d, J=6.0 Hz, 3 H), 1.61-1.73 (m, 4 H), 2.39 (dd, J=9.3, 12.8 Hz
1 H), 2.46-2.70 (m, 5 H), 2.99 (dd, J=3.8, 12.8 Hz, 7.01-7.38 (m, 5 H);
13C{1H} NMR (62.5 MHz, [D8]THF, 294 K) δ=16.4, 23.6, 41.1, 50.1, 59.6,
125.1, 127.4, 128.8, 139.9; HRMS (ESI): m/z: calcd for C13H20N
(190.1590): [M+H]+; found 190.1596. These data are in agreement with
previously published data.[18]
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Acknowledgements
The authors are thankful to MENSR, CNRS and the Groupe de
Recherche International (GDRI) “Homogeneous Catalysis for
Sustainable Development” for their support to this work.
[7]
[8]
For an excellent review on base-catalysed hydroamination of
unactivated olefins including the early developments of the field: J.
Seayad, A. Tillack, C. G. Hartung, M. Beller, Adv. Synth. Catal. 2002,
344, 795.
For efficient strategies to control the regioselectivity: a) Y. Xi, T. W.
Butcher, J. Zhang, J. F. Hartwig, Angew. Chem. Int. Ed. 2016, 55, 776;
b) reference 3a; c) Y. Yang, S.-L. Shi, D. Niu, P. Liu, S. L. Buchwald,
Keywords: Intermolecular hydroamination • Lithium • Anti-
Markovnikov addition • Secondary amines • Vinylarenes
Science 2015, 349, 62; d) S. Zhu, S. L. Buchwald, J. Am. Chem. Soc.
2014, 136, 15913.
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10.1002/cctc.201700043
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Stéphane Germain, Meije Lecoq,
Emmanuelle Schulz,* and Jérôme
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Lithium-catalysed anti-Markovnikov
intermolecular hydroamination
reactions of vinylarenes and simple
secondary amines
Various β-arylethylamine derivatives have been straightforwardly obtained by
lithium-catalysed anti-Markovnikov selective intermolecular hydroamination
reactions of vinylarenes and secondary aliphatic amines. Use of as little as 1.5
mol % LiCH2TMS as solid base in THF proved to be an efficient room-temperature
protocol for delivering the targeted products in up to complete conversion and under
stoichiometric partner conditions.
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