Cu(I)/ionic liquids promote the conversion of carbon dioxide into oxazolidinones at room temperature

Article abstract of DOI:10.3390/molecules24071241

Recently, the efficient chemical fixation of carbon dioxide (CO₂) into high value chemicals without using noble metal catalysts has become extremely appealing from the viewpoint of sustainable chemistry. In this work, a one-pot three component reaction of propargylic alcohols, anines and CO₂ that can proceed in an atom economy and environmentally benign manner by combination of CuI and tetrabutylphosphonium imidazol ([P₄₄₄₄][Im]) as a catalyst was described. Catalysis studies indicate that this catalytic system is an effective catalyst for the conversion of CO₂ into oxazolidinones at room temperature and ambient pressure without any solvent. The results provide a useful way to design novel noble metal-free catalyst systems for the transformation of CO₂ into other valuable compounds.

Full text of DOI:10.3390/molecules24071241

Article
Cu(I)/Ionic Liquids Promote the Conversion of
Carbon Dioxide into Oxazolidinones at
Room Temperature
1
1
1,
1
1
1,
Jikuan Qiu , Yue Zhao , Yuling Zhao *, Huiyong Wang , Zhiyong Li , Jianji Wang *
and Tiantian Jiao 2
1
Collaborative Innovation Center of Henan Province for Green Manufacturing of Fine Chemicals, Key
Laboratory of Green Chemical Media and Reactions, Ministry of Education, School of Chemistry and
Chemical Engineering, Henan Normal University, Xinxiang, Henan 453007, China;
qiujikuan001@163.com (J.Q.); zhaoyuechem@126.com (Y.Z.); whyhnxx@163.com (H.W.);
lizhiyong03@126.com (Z.L.)
2
College of Chemical and Environmental Engineering, Shandong University of Science and Technology,
Qingdao 266590, Shandong, China; jiaotiantian1988@163.com
*
Correspondence: jwang@henannu.edu.cn (J.W.); ylzhao@htu.cn (Y.Z.); Tel.: +86-373-3325805 (J. W.)
Received: 3 March 2019; Accepted: 28 March 2019; Published: 29 March 2019
Abstract: Recently, the efficient chemical fixation of carbon dioxide (CO ) into high value chemicals
2
without using noble metal catalysts has become extremely appealing from the viewpoint of
sustainable chemistry. In this work, a one-pot three component reaction of propargylic alcohols,
anines and CO
combination of CuI and tetrabutylphosphonium imidazol ([P4444][Im]) as a catalyst was described.
Catalysis studies indicate that this catalytic system is an effective catalyst for the conversion of CO
2
that can proceed in an atom economy and environmentally benign manner by
2
into oxazolidinones at room temperature and ambient pressure without any solvent. The results
provide a useful way to design novel noble metal-free catalyst systems for the transformation of
CO into other valuable compounds.
2
Keywords: carbon dioxide; ionic liquids; catalysis; oxazolidinones
1
. Introduction
With the global consumption of fossil fuels, the increasing concentration of CO in the
2
atmosphere could have a significant impact on the global climate [1,2]. Therefore, the development
of efficient strategies to reduce CO emissions has becoms an imperative task for scientific
researchers [3–5]. The chemical fixation and transformation of CO into valuable chemicals is an
ideal pathway for reducing CO emissions and fully utilize this cheap C source [6–10]. Thus,
considerable efforts have been devoted to the exploration of efficient strategy for chemical
utilization of CO to produce high-value chemical commodities [11–16].
2
2
2
1
2
Oxazolidinones are a class of nitrogen-containing heterocyclic compounds which have been
used as organic intermediates, chiral additives, antibacterial drugs and muscle relaxants, etc.
[
17–20]. The synthesis of oxazolidinones between propargyl alcohol, CO
important and atom-economic reaction for chemical utilization of CO [12,21]. However, the biggest
obstacle is the lack of an effective catalyst to facilitate its activation and conversion, since CO is a
highly oxidized and thermodynamically stable molecule [22]. In recent years, various metal catalysts
23–28] and metal-free catalysts [29,30] have been verified to be efficient for the reaction.
2
and an amine is an
2
2
[
Nevertheless, most of the catalytic systems usually required high temperatures, high pressures, toxic
organic solvents and noble metals. Therefore, a cheap, green and highly active catalyst is urgently
needed in order to make the reaction go smoothly at room temperature and atmospheric pressure.
Molecules 2019, 24, 1241; doi:10.3390/molecules24071241
www.mdpi.com/journal/molecules

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Our previous work has revealed that metal salts combined with ionic liquid (IL) represent a
new hybrid catalyst that can be regarded as one of the most promising and efficient catalysts for
chemical transformations of CO
2
because of their remarkable synergistic catalysis mechanism [31].
For example, a Cu(I) salt/protic IL catalytic system can efficiently catalyze the cycloaddition of CO
2
with propargylic alcohols to produce α-alkylidene cyclic carbonates under mild conditions. Inspired
by these works, we now report that Cu(I) salt and the IL tetrabutylphosphonium
imidazol([P4444][Im]) act as a catalyst for the three component reaction of terminal propargyl
alcohols, CO and anines (Scheme 1). The results show that the CuI/[P4444][Im] catalyst system
2
exhibits excellent catalytic performance for the reaction with a wide range of substrates under
atmospheric pressure and room temperature conditions. In addition, the ionic liquid could be
recovered and reused at least five times without an obvious loss of catalytic activity and selectivity.
O
CuI(10%mol)
P4444Im(10%mol)
R3
R1
N
OH
3
O

CO2

R NH
2
2
R
30C, 1atm
R1
R2
1
2
3
Scheme 1. Cycloaddition reaction of propargyl alcohol and amines with CO .
2
2
. Result and Discussion
Owing to the unique catalytic performance of ILs in CO
2
conversion [32–34], several quaternary
phosphonium-based ILs and various copper (I) salts were selected to catalyze the reaction. Figure 1
shows the structures of the ILs.
N
O
N
N
P
F
F
P
P
F
N
O
N
[
P
4444][Im]
[P4444][Triz]
3
[P4444][CF COO]
P
N
N
P
[NO3]
P
[Br]
[
P4444][Ind]
[P4444][NO
3
]
[P4444][Br]
Figure 1. The structure and abbreviations of CO -reactive ILs employed in this work.
2
The synthesis of 1,3-oxazolidin-2-one 3a was carried out to systematically investigate the effect
o
of various parameters on the reaction. The reaction was performed at 30 C, 1 atm CO
2
, and 24 h, and
the results are shown in Table 1. As expected, the reaction did not occur in the absence of any
catalysts. The individual IL [P4444][Im] and CuI as a catalyst were ineffective for the reaction, giving a
low yield of product (Table 1, entries 2–3). To our delight, the yield of the product reached rose to
9
1% in the presence of CuI and [P4444][Im] (Table 1, entry 4). Encouraged by the result, we
investigated the effect of the type of anion on the yield of 3a in the reaction. The yield of 3a was
found to be 70%, 41%, 35%, 30%, and 28%, respectively, when CuI/[P4444][Triz], CuI/[P4444][Ind],
CuI/[P4444][CF
3
COO], CuI/[P4444][NO ] and [P4444][Br] were used as catalysts (Table 1, entries 5-9). The
3
significant differences in their catalytic activity may be ascribed to the different nucleophilicity of
these ILs as a result of their different basicity (Table S1). A larger IL pKa resulted in an improved
absorption capacity of CO
2
in the reaction system, which led to stronger reactivity between CO
2
with propargylic alcohol, amine and the catalyst, to afford a higher product yield [35]. The result
indicated that the ionic liquid anions play an important role in this conversion. Next, a variety of
copper (I) salts with [P4444][Im] were used for this reaction. The activity of these copper salts
followed the order: CuI > CuBr > CuCl (Table 1, entries 4, 10–11). Owing to the fact that among the
halogenated metal salts the iodide anion had a stronger dissociation capacity, the metal cation and

Molecules 2019, 24, 1241
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iodide anion could efficiently activate the substrates and promote the reaction in high yields [36].
The result suggested that the dissociation capacity of the anions acted a significant role in
determining the catalytic activity of the halogenated copper salts. In addition, Cu O and CuCN
2
could also catalyze the reaction, affording moderate yields (65% and 32%, respectively) (Table 1,
entries 12,13). Thus, CuI/[P4444][Im] was the best catalyst to further investigate this reaction.
o
Subsequently, the influence of catalyst amount on the yield of product was studied at 30 C and
1
atm CO with a reaction time of 24 h. As seen in Figure S1, the yield of 3a was strongly dependent
2
on the catalyst amount, and a maximum yield of 90% was obtained in the presence of 10 mol% CuI.
It was shown that the yield of 3a will slowly decrease with further increase of the catalyst loading.
Similar results were also obtained for the effect of IL amount in this reaction (Figure S2). Also, the
dependence of reaction time on the yield of 3a was studied and the results are shown in Figure 2.
The reaction was carried out at 30 °C, 1atm CO
catalyst. It is shown that a yield of 92% could be obtained after 24h, and the yield of 3a does not
improve with further prolonged reaction time. Moreover, the effect of CO pressure on the reaction
was studied. As shown in Table S2, the yield of 3a increased significantly with increasing pressure.
More CO could be dissolved in the liquid phase with further increasing pressure, which led to more
contact between CO with the substrates and the catalyst, and thus a higher yield of product was
obtained. From the above findings, the optimal reaction conditions for the reaction were:
CuI/[P4444][Im] as the catalyst, 30 °C, 24 h, and 1 atm CO
2
using CuI (10 mol%) and [P4444][Im] (10mol%) as
2
2
2
2.
Table 1. Reaction of 2-methyl-3-butyn-2-ol (1a), n-butylamine (2a) and CO
2
in various catalyst systems a.
O
CuI(10%mol)
P4444Im(10%mol)
n-Bu
N
OH
O

CO2

n-BuNH
2
30C, 1atm
1a
2a
3a
Entry
Catalyst
_c
IL
_d
Yield/ % b
1
2
3
4
5
6
7
8
9
0
_c
[P4444][Im]
_d
5
CuI
CuI
CuI
CuI
CuI
CuI
CuI
CuBr
CuCl
34
[P4444][Im]
[P4444][Triz]
[P4444][Ind]
91
70
41
[P4444][CF
3
COO]
35
[P4444]NO
3
30
[P4444]Br
28
1
1
1
1
0
1
2
3
[P4444][Im]
[P4444][Im]
[P4444][Im]
[P4444][Im]
IL
71
42
65
Cu O
2
CuCN
32
Entry
Catalyst
Yield/ % b
a
Reaction condition: 1a, 1.0 mmol, 2a, 1.0 mmol, catalyst, 0.1 mmol, CO (0.1 MPa, 99.999%), 24 h, 30
2
C; b Isolated yieid; Without copper salt; d Without IL.
c
°
The reactions of CO
under the optimized reaction conditions, and the results are listed in Table 2. It was shown that the
coupling reaction of different alkyl substituted propargylic alcohols with CO and anines proceeded
2
with different kinds of propargylic alcohols and amines were evaluated
2
smoothly, producing the corresponding oxazolidinones in good yields under mild conditions. It was
noted that a moderate yield of product was obtained for the propargylic alcohol with a cyclohexyl
group (3i), indicating the steric hindrance of the substituent seemed to hamper the reaction.
Furthermore, we also investigate the effect of amines with various substituents in this
transformation. It was clearly shown that most of alkyl-substituted amines were efficient substrates
3
to produce the corresponding oxazolidinones. However, when the R group of amines was a phenyl
group, no product was obtained (compound 3k), even after a prolonged reaction time of 36 h. This
phenomenon can be attributed to both the weak N-nucleophilicity and steric hindrance of the

Molecules 2019, 24, 1241
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substrates, which further hamper the reaction [37]. From the above analysis, the catalyst system
reported here is more favorable for alkyl amines than aromatic amines.
90
60
30
0
0
5
10
15
20
25
30
Reaction time (h)
Figure 2. Effect of reaction time on the product yield over CuI and [P4444][Im]; Reaction conditions:
a, 1.0 mmol, 2a, 1.0 mmol, CuI, 0. mmo, [P4444][Im], 0.1 mmol, CO (1 atm), 30 °C. The yield was
isolated yield.
1
2
Table 2. Three-component reactions of propargylic alcohols(1), amines(2) and CO under optimized
2
conditions a.
1
2
3
3
a (87%) b
e (81%) b
3b (81%) b
3f (70%) b
3c (82%) b
3g (75%) b
3k (0) c
3d (85%) b
3h (73%) b
3
3
i (71%) b
3j (54%) b
a
Reaction conditions: 1, 1.0 mmol, 2, 1.0 mmol, CuI, 0.1 mmol, [P4444][Im], 0.1 mmol, CO (1atm),
2
b
c
within 24 h, 30 °C. Isolated yieid. The reaction time is prolonged to 36 h.
To gain insight into the reaction mechanism, the catalytic role of [P4444][Im]/CuI with CO
2
and
the substrates were elucidated by H-NMR and C-NMR spectroscopy. In the H-NMR spectrum of
the mixture of [P4444][Im]/CuI with 1a and n-BuNH (Figure 3), the OH signal became broad and
shifted from 5.28 to 5.57, which indicated the formation of a hydrogen bond between [P4444][Im] and
1
13
1
2
1
3
1
a [35]. In addition, the C-NMR signal assigned to the C1, C2, and C3 sites could be attributed to
the interaction between CuI with the C≡C bond, leading to the activation of propargylic alcohol
Figure 4). These analysis suggested that the -OH and C≡C bond on the substrate 1a were
(
synergistically activated by [P4444][Im] and CuI. Moreover, several additional control experiments
were performed and the results are shown in Scheme 2. It was shown that the CuI/[P4444][Im] catalyst
could efficiently catalyze the reaction of 1a with CO to form cyclic carbonate 4a with a yield of 70%.
2

Molecules 2019, 24, 1241
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In addition, 4a reacted with n-butylamine to afford 3a smoothly without any catalyst. Therefore, the
reaction of propargylic alcohols, anines and CO
pathway [37].
2
can be assumed to go through the cyclic carbonate
OH
+
n-BuNH2 + [P4444][Im] + CuI
5
.57
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
ppm
OH
5
.28
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5 ppm
Figure 3. 1H-NMR spectra of propargylic alcohol, n-BuNH
2
with and without CuI/[P4444][Im]
catalyst.
O H
+
n-B uNH 2
+
[P4444][Im ]
+
C uI
6
4.09
6
5.47
8
6.16
115 110 105 100 95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
ppm
O H
C1
C3
63.44
1.62
C2
7
0.67
9
C2
C
C3
115 110 105 100 95
90
85
80
1
75
70
65
60
55
50
45
40
35
30
25
20
15
10
ppm
Figure 4. 13C-NMR spectra of propargylic alcohol, n-BuNH
2
with and without CuI/[P4444][Im]
catalyst.
O
O
CuI (10 mol%)
[P4444][Im] (10 mol%)
O
OH + CO
2
3
0 oC, 16 h
1a
1 atm
4a, 70%
O
O
N
O
O
Catalyst-free
O
+
NH
2
3
0 oC, 12h
4
a
2a
3a, 90%
Scheme 2. Control experiments.

Molecules 2019, 24, 1241
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Based on the above results, a plausible mechanism for the reaction catalyzed by CuI/[P4444][Im]
as depicted in Scheme 3 is proposed. Firstly, the hydroxyl group of the propargyl alcohol is activated
by IL [P4444][Im], then it reacts with CO to generate a zwitterionic carbamate species 1. Meanwhile,
2
the C≡C triple bond of the propargyl alcohol was activated by CuI, and then the intermediate 2 was
obtained. Then the intermediate cyclic carbonate 3 was formed by an intramolecular ring-closing
reaction with the release of the catalyst. Finally, the cyclic carbonate undergoes a nucleophilic attack
by a primary amine to generate the product oxazolidinone 5.
O
O
O
R1
O
O
IL
H
R1
R2
O
O
IL
CO
2
H
R2
R1 R2
CuI
CuI
2
IL H
1
IL
[P4444][Im]
O
R3
O
R1
O
N
H
O
3
R3 NH2
R2
O
O
R1
R2
N R3
OH
O
R1
R2
5
4
IL
CuI
+
Scheme 3. The proposed mechanism for the reaction of propargyl alcohol, CO and an amine
2
catalyzed by [CuI]/[P4444][Im].
3
. Experimental Section
3
.1. Chemicals
Propargylic alcohols, amines, CuI, Cu
Company Limited (Beijing, China). The ILs [P4444][CF
purchased from Lanzhou Greenchem ILs (Lanzhou, Gansu, China). Other ILs such as [P4444][Triz],
2O, CuCl, CuBr, CuCN were obtained from J&K Scientific
3COO], [P4444][NO3] and [P4444][Br] were
[P
4444][Ind] and [P4444][Im] were synthesized by the ion exchange method [38].
3
.2. General Procedures for the Synthesis of Oxazolidinones
Typically, propargylic alcohol 1a (1.0 mmol), n-butylamine (2a, 1.0 mmol) and CuI (0.1
mmol)/[P4444][Im] (0.1 mmol) were mixed in a 10 mL Schlenk flask. Then the reaction mixture was
stirred at 30 °C for 24 h in the pressure of 0.1 MPa CO . After the reaction was completed, water (5
2
mL) was added into this mixture, and the organic phase was purified through column
chromatography. The ionic liquid was collected and reused without further treatment by removing
any water under vacuum.
3
.3. Characterization of the Products
The products were confirmed by using H-NMR analysis on Avance NEO 400 spectrometer
Bruker, Beijing, China) and Avance III HD 600 spectrometer (Bruker, Beijing, China). All of the
1
(
products matched well with the previously reported experimental results [26].
1
3
-butyl-5,5-dimethyl-4-methyleneoxazolidin-2-one (3a), orange oil; H-NMR (CDCl
3
, 400 MHz does not
match above) δ: 4.07 (d, J = 4.0 Hz, 1 H), 3.98 (d, J = 4.0 Hz, 1 H), 3.44 (t, J = 8.0 Hz, 2 H), 1.61–1.52 (m, 2
H), 1.49 (s, 6 H), 1.37–1.29 (m, 2 H), 0.95 (t, J = 7.2 Hz, 3 H) ppm.
1
3
-butyl-5-isobutyl-5-methyl-4-methyleneoxazolidin-2-one (3b), orange solid; H-NMR (CDCl
3, 600 MHz)
δ: 4.09 (s, 1 H), 3.93 (s, 1 H), 3.51-3.38 (m, 2 H), 1.80–1.43 (m, 8 H), 1.40–1.31 (m, 2 H), 1.02–0.89 (m, 9
H) ppm.

Molecules 2019, 24, 1241
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1
3
-cyclohexyl-5,5-dimethyl-4-methyleneoxazolidin-2-one (3c), orange solid; H-NMR (CDCl
3, 600 MHz) δ:
4
.19 (d, J = 3.0 Hz, 1 H), 3.97 (d, J = 3.0 Hz, 1 H), 3.55 (t, J = 12.0 Hz, 1 H), 1.86-1.66 (m, 13 H), 1.25–1.14
(m, 4 H) ppm.
1
3
-isobutyl-5,5-dimethyl-4-methyleneoxazolidin-2-one (3d), colorless oil; H-NMR (CDCl
3
, 600 MHz) δ:
4
.27 (s, 1 H), 3.11–3.04 (m, 1 H), 2.96–2.89 (m, 1 H), 1.99-1.92 (m, 1 H), 1.51 (s, 3 H), 1.43. (s, 2 H), 1.34
(
d, J = 12 Hz, 2 H), 0.92–0.87 (m, 6 H) ppm.
-hexyl-5,5-dimethyl-4-methyleneoxazolidin-2-one (3e), colorless oil; H-NMR (CDCl
d, J = 2.4 Hz, 1 H), 3.97 (d, J =3 Hz, 1 H), 3.43 (t, J = 7.8 Hz, 2 H), 1.63–1.58 (m, 2 H), 1.49 (s, 1 H),
1
3
3
, 600 MHz) δ: 4.07
(
1
.32–1.30 (m, 6H), 0.89–0.88 (m, 3H) ppm.
1
5
4
7
-ethyl-3-isobutyl-5-methyl-4-methyleneoxazolidin-2-one (3f), colorless oil; H-NMR (CDCl , 600 MHz) δ:
3
.10 (d, J = 3 Hz, 1 H), 3.92 (d, J = 3 Hz, 1 H), 3.30–3.19 (m, 2 H), 1.85–1.80 (m, 1 H), 1.48–1.45 (d, J =
.2 Hz, 5 H), 1.02 (t, J = 7.8 Hz, 2 H), 0.93–0.90 (m, 6 H), 0.89 (s, 1 H)ppm.
1
3
4
0
,5-diisobutyl-5-methyl-4-methyleneoxazolidin-2-one (3g), orange solid; H-NMR (CDCl
3, 600 MHz) δ:
.09 (s, 1 H), 3.93 (s, 1 H), 3.28–3.23 (m, 2 H), 2.14–2.04 (m, 1 H), 1.51 (s, 1 H), 1.04–0.98 (m, 2 H),
.97–0.91 (m, 12 H) ppm.
1
3
-cyclohexyl-5-isobutyl-5-methyl-4-methyleneoxazolidin-2-one (3h), orange solid; H-NMR (CDCl
3
, 600
MHz) δ: 4.24 (s, 1 H), 3.93 (s, 1 H), 3.64–3.53 (m, 1 H), 2.15–1.45 (m, 12 H), 1.34–1.15 (m, 4 H),
0
.94–0.91 (m, 6 H) ppm.
1
3
-cyclohexyl-5-ethyl-5-methyl-4-methyleneoxazolidin-2-one (3i), orange solid; H-NMR (CDCl , 600
3
MHz) δ: 4.25 (d, J = 3.0 Hz, 1 H), 3.93 (d, J = 3.0 Hz, 1 H), 3.62–3.55 (m, 1 H), 1.66–1.47 (m, 11 H),
1
.35–1.18 (m, 4 H), 0.88 (t, J = 7.8 Hz, 3 H) ppm.
-Butyl-4-methylene-1-oxa-3-azaspiro[4.5]decan-2-one (3j), orange oil; H-NMR (CDCl
.07 (d, J = 3.0 Hz, 1 H), 3.95 (d, J = 2.4 Hz, 1 H), 3.43 (t, J = 7.8 Hz, 2 H), 1.76–1.65 (m, 5 H), 1.61–1.50
1
3
3, 600 MHz) δ:
4
(m, 7 H), 1.40–1.31 (m, 2 H), 0.94 (t, J = 7.2 Hz, 3 H) ppm.
4
. Conclusions
In conclusion, we have developed an excellent and cost-competitive catalytic process catalyzed
by the CuI/[P4444][Im] system for the transformation of CO to form oxazolidinones. The reaction can
2
proceed efficiently under room temperature and atmospheric pressure conditions to give high yields
of product. A wide range of propargylic alcohols and amines has been employed, which confirmed
the versatility of the catalyst system for the synthesis of oxazolidinones. Preliminary mechanistic
studies suggest that the reaction of propargylic alcohols, anines and CO
carbonate pathway. This work reveals the great potential of ionic liquids combined with metal salts
as an efficient type of catalysts for CO conversion under mild conditions.
2
could involve the cyclic
2
Supplementary Materials: The following are available online.
Author Contributions: Organic synthesis and compound characterization, J.Q. and Y.Z (Yue Zhao); NMR
spectroscopy, Y.Z. (Yue Zhao); writing—original draft preparation, J.Q.; writing-review and editing, Y.Z.
(Yuling Zhao), J.W., Z.L., H.W.; project administration, Z.L. and H.W.; formal analysis, T.J.
Funding: This work was supported by the National Natural Science Foundation of China (Grant No. 21773058,
U1704251, 21733011), National Key Research and Development Program of China (2017YFA0403101), Project
funded by China Postdoctoral Science Foundation (No. 2017M622349), and the 111 Project (No. D17007). This
work was also supported by the High Performance Computing Center of Henan Normal University.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
P4444][Im]
Tetrabutylphosphonium imidazole
[
[
[
P
4444][CF
3
COO
Tetrabutylphosphonium 2,2,2-trifluoroacetic acid
Tetrabutylphosphonium 1,2,4-triazole
Tetrabutylphosphonium indazole
P4444][Triz
4444][Ind
P

Molecules 2019, 24, 1241
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[
P
4444][Br]
4444][NO
Tetrabutylphosphonium bromide
Tetrabutylphosphonium nitrate
[P
3
]
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Sample Availability: Samples of the compounds of 3a–3j are available from the authors.
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