[24]Pentaphyrin(2.1.1.1.1): A strongly antiaromatic pentaphyrin

Article abstract of DOI:10.1021/acs.joc.7b01998

[24]Pentaphyrin(2.1.1.1.1) 1 was synthesized by dehydrogenation of dihydropentaphyrin(2.1.1.1.1) 2 as the first example of vinylogous pentaphyrin. Pentaphyrin 1 takes a roughly planar structure and shows strong antiaromatic character, reflecting a 24π-con

Full text of DOI:10.1021/acs.joc.7b01998

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[24]Pentaphyrin(2.1.1.1.1): a Strongly Antiaromatic Pentaphyrin
Tomoki Yoneda, Tyuji Hoshino, and Saburo Neya
J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.7b01998 • Publication Date (Web): 19 Sep 2017
Downloaded from http://pubs.acs.org on September 20, 2017
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The Journal of Organic Chemistry
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[24]Pentaphyrin(2.1.1.1.1): a Strongly Antiaromatic Pentaphyrin
Tomoki Yoneda*, Tyuji Hoshino, Saburo Neya*
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Department of Physical Chemistry, Graduate School of Pharmaceutical Sciences, Chiba Unibersity. 1ꢀ8ꢀ1 Inohana Chuoꢀku,
Chiba, 260ꢀ8675, Japan, Eꢀmail: yoneda@chibaꢀu.ac.jp
Supporting Information Placeholder
CO2Et
CO2Et
ABSTRACT: [24]Pentaphyrin(2.1.1.1.1)
1
was synthesized by
N
H
N
C6F5
N
H
C6F5
dehydrogenation of dihydropentaphyrin(2.1.1.1.1) 2 as the first example of
vinylogous pentaphyrin. Pentaphyrin 1 takes a roughly planar structure and
shows strong antiaromatic character, reflecting 24πꢀconjugated circuit. In
spite of the antiaromatic character and the relatively small circuit, 1 is stable
under ambient conditions.
N
N
H
C6F5
[24]Pentaphyrin(2.1.1.1.1)
C6F5
Stable and Storongly Antiaromatic Vinylogous Expanded Porphyrin
Expanded porphyrins are conjugated macrocycles with
more than four pyrrole units, which have been demonꢀ
strated to realize various electronic states including Hückꢀ
el aromatic and antiaromatic, Möbius aromatic and antiꢀ
aromatic, and radical species.1 Among these, pentaphyrins
and their coreꢀmodified variants2 constitute a unique class
of conjugated macrocycles in light of the optical properꢀ
ties suitable for photodynamic therapy and lightꢀ
harvesting, and the intrinsic strain to take planar strucꢀ
tures.3 As the representative example, sapphyrins
([22]pentaphyrin(1.1.1.1.0)s) were first reported by
Woodward et al and extensively developed by Sessler et
al.4 Sapphyrins are planar 22π aromatic molecules conꢀ
sisting of two iminoꢀtype pyrroles and three aminoꢀtype
pyrroles. Pentakis(pentafluorophenyl)ꢀsubstituted penꢀ
taphyrin was formed as a Nꢀfused molecule presumably
Chart 2. Selected examples of porphyrinoids with vinylene
bridges at meso-positions.
as a consequence of its large steric strain.5 Recently, we
reported
the
synthesis
of
mesoꢀunsubstituted
[22]pentaphyrin(1.1.1.1.1), which existed as a planar nonꢀ
fused pentaphyrin with two intramolecular hydrogen
bonds.6 This pentaphyrin is spared the steric strain and
thus strongly aromatic. (Chart 1)
In the course of this work, we become interested in
[24]pentaphyrin(2.1.1.1.1) that possesses a vinylene
bridge along the conjugation circuit (Chart 1). While varꢀ
ious tetrapyrrolic macrocycles having vinylene bridges
such as porphycene (porphyrin(2.0.2.0)),7 corrphyꢀ
cene(2.1.0.1),8 homoporphyrin(2.1.1.1),9 hemiporphyrceꢀ
ne(2.1.1.0),10 and [20]porphyrin(2.1.2.1),11 were reported,
there are only a limited number of expanded porphyrins
possessing a vinylene bridge along the conjugation cirꢀ
cuit. As an interesting example, [26]ꢀ and
[28]hexaphyrin(2.1.1.0.1.1) were formed via transposition
of the mesoꢀcarbon during boron(III) insertion into
[28]hexaphyrin(1.1.1.1.1.1) (Chart 2).12 Some coreꢀ
modified vinyleneꢀbridged expanded porphyrins were
also reported.13 In this paper, we report the synthesis of
Chart 1. Skeletons of pentaphyrins. Their π-conjugation
circuits are shown in bold lines.
[24]pentaphyrin(2.1.1.1.1)
1 as the first example of viꢀ
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view. Solvent molecules and mesoꢀpentafluorophenyl groups in
nylogous pentaphyrin. Curiously, pentaphyrin
1 is rather
1
2
3
4
5
6
7
8
side view are omitted. Thermal ellipsoids are shown in 50% probꢀ
ability.
Following our previous work,6b we employed a hybrid
synthetic protocol by using mesoꢀaryl tripyrrane and βꢀ
substituted dipyrrole. After reduction of 1,14ꢀ
stable under ambient conditions despite its distinct antiꢀ
aromatic character and relatively small size of the conjuꢀ
gation circuit.
C6F5
C6F5
C6F5
C6F5
OH
O
HO
O
NaBH4
pentafluorobenzoylꢀ5,10ꢀpentafluorophenyl tripyrrane
the obtained tripyrrane dicarbinol B14 and 1,2ꢀbis(3ꢀ
ethoxycarbonylꢀ4ꢀmethylpyrrolꢀ2ꢀyl)ethane
C8b,15 in
CH2Cl2 were treated with 0.3 equivalent of
A,
NH
NH
HN
HN
H
H
N
THF/MeOH
25 °C
N
C6F5
C6F5
C6F5
C6F5
1 h
p
ꢀ
9
toluenesulfonic acid under nitrogen atmosphere, and the
resulting mixture was oxidized with 2,3ꢀdichloroꢀ5,6ꢀ
dicyanoꢀ1,4ꢀbenzoquinone (DDQ). On a silica gel colꢀ
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A
B
CO2Et
EtO2C
NH
CO2Et
umn, dihydropentaphyrin(2.1.1.1.1)
band was separated (Scheme 1). Recrystallization with
hexane gave pure in 10% yield. Highꢀresolution elecꢀ
trospray ionization timeꢀofꢀflight mass spectroscopy (HRꢀ
2 eluted as a brown
EtO2C
HN
(1.0 eq)
1)
2
C
N
H
C6F5
N
H
C6F5
p-TsOH (0.30 eq)
ESIꢀTOF MS) indicated the parent ion peak of
2 at m/z
2) DDQ (2.0 eq)
=1240.1948 (calcd for C58H30N5F20O4 [M+H]+
=
N
+
N
1
CH2Cl2, 25 °C
1) 1.5 h, 2) 5 min
1240.1973). The H NMR spectrum of
2 showed two
N
H
C6F5
doublets at 6.82 and 6.55 ppm, and one singlet at 6.73
ppm due to the βꢀprotons, two singlets at 11.96 and 7.12
ppm due to the NH protons, a quartet and a triplet at 4.39
and 1.36 ppm due to the ethoxy groups, and a singlet due
to methyl groups at 2.11 ppm. These chemical shifts indiꢀ
cated nonaromatic character of its macrocycle. Additionꢀ
ally, a signal due to the four protons of the ethylene
bridge was observed as a singlet at 2.87 ppm (Figure 3a).
C6F5
2
10% for 2 steps
CO2Et
CO2Et
N
H
N
C6F5
N
Chloranil (10 eq)
C6F5
H
The structure of 2 has been confirmed by Xꢀray diffracꢀ
N
Toluene
120 °C
12 h
tion analysis to be a pentapyrrolic macrocycle, in which
an ethylene(ꢀCH2CH2ꢀ) unit bridges the pyrroles A and E
(Figure 1).16 The pyrrolic NH protons of the pyrroles A
and E are hydrogenꢀbonded with the pyrrolic nitrogen
atoms of the pyrroles B and D, respectively, while the
pyrrole C is pointing outward, similar structurally to the
monoꢀmesoꢀunsubstituted [22]pentaphyrin(1.1.1.1.1).6
N
H
C6F5
C6F5
1
78%
Scheme 1. Synthesis of dihydropentaphyrin
[24]pentaphyrin(2.1.1.1.1) 1.
2
and
Figure 2. XꢀRay crystal structure of pentaphyrin 1 obtained from
chlorobenzene/nonane solution. a) Top view and b) side view.
Figure 1. XꢀRay crystal structure of dihydropentaphyrin 2 obꢀ
tained from acetonitrile/water solution. a)Top view and b)side
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Solvent molecules and mesoꢀpentafluorophenyl groups in side
able for Xꢀray diffraction analysis were obtained by diffuꢀ
sion of ꢀnonane into its chlorobenzene solution with one
drop of water. In the unit cell, two different structures
were found. Thus, we used averaged values in the followꢀ
1
2
view are omitted. Thermal ellipsoids are shown in 30% probabilꢀ
ity. One of two similar molecules in the symmetrical unit is
shown.
n
3
4
5
6
7
8
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ing discussion. The structure of
a roughly planar pentaphyrin(2.1.1.1.1). The formed C25ꢀ
C26 double bond showed ꢀstereochemistry with a bond
length of 1.34 Å. The largest dihedral angle was 18.9(17)°
and the mean plane deviation (MPD) of the main penꢀ
1 has been revealed to be
E
taphyrin skeleton of
1
2
was calculated to be 0.269 Å (Figꢀ
, the hydrogen bonding interaction
ure 2).17 Similar to
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25
25
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20
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5
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5
0
0
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between the pyrrolic NH protons of the pyrroles A and E
with the nitrogen atoms of the pyrroles B and D is imꢀ
portant to keep the planar structure. The strong antiaromaꢀ
ticity of its 24π conjugation circuit of
1 is indicated by its
1H NMR spectrum that displays signals at 4.48 and 4.04
ppm due to the outer β protons, a singlet at 17.68 ppm due
to the inner β protons, two singlets at 26.11 and 2.86 ppm
due to outer and inner NH protons, and a quartet and a
triplet at 3.77 and 1.00 ppm due to the ethoxy groups
1
(Figure 3b). The H signal of the transꢀvinylene bridge
was observed as a singlet at 11.57 ppm, indicating free
rotation of the vinylene bridge at room temperature. At –
90 °C in CD2Cl2, the signal of
1 was significantly broadꢀ
ened, suggesting that the rotation was considerably
slowed down but not frozen (Figure 3c). The rotation of
vinylene group is indicated to be faster than that of porꢀ
phyrin(2.1.2.1).11
1
Figure 3. H NMR spectra of a) 2 in CDCl3 at room temperature
and 1 b) in CDCl3 at room temperature and c) in CD2Cl2 at −90
°C. * indicates residual solvent peaks.
The UV/vis absorption spectrum of
2 exhibits a relatively
12
10
8
sharp absorption band at 508 nm and a weak absorption
band at 787 nm. These absorption bands are derived from
the noncyclic conjugated pentapyrrolic unit. The absorpꢀ
tion spectrum of
1 is totally different from that of 2, disꢀ
playing a broad Soret band at 498 nm and a very weak
absorption up to about 1700 nm (Figure 4). The weak
absorption can be ascribed to the presence of lowꢀenergy
dark states, which are characteristic of antiaromatic porꢀ
phyrinoids.18
6
Cyclic voltammetry (CV) measurements for
2 revealed
4
reversible oxidation waves at 0.18 and 0.51 V and an irreꢀ
versible reduction wave at ꢀ1.08 V versus a ferroꢀ
2
cene/ferrocenium ion couple. On the other hand,
1 indiꢀ
cated reversible oxidation waves at 0.08 and 0.38 V and
reduction waves at –0.90 and –1.11 V (see SI). The elecꢀ
0
300 500 700 900 1100 1300 1500 1700 1900
trochemical HOMO–LUMO gaps were 1.26 eV for
0.98 eV for . The smaller HOMO–LUMO gap of
that of
To obtain further insight into the physical properties of
and , we performed DFT calculations (B3LYP/6ꢀ31G(d)
2
and
1
1
than
2
was consistent with its antiaromatic character.
1
Figure 4. UV/Vis absorption spectra of 2(black) and 1(red) in
CH2Cl2. *Vibration bands of solvent.
2
level).19 The HOMO–LUMO gap for
2 was calculated to
be 1.75 eV and scarce electron density on its two sp3 carꢀ
bons was observed in its HOMO and LUMO orbitals. On
In the next step, we examined the dehydrogenation of
Attempted dehydrogenation of with excess DDQ led to
2.
the other hand, the HOMO–LUMO gap of
ed to be relatively small 1.33 eV. The πꢀorbitals derived
from the vinylene bridge of was clearly observed in its
1 was calculatꢀ
2
its serious decomposition. After numerous experiments,
we found that ethyleneꢀselective dehydrogenation proꢀ
ceeded efficiently with 10 equiv. of
at 120 C to give [24]pentaphyrin(2.1.1.1.1)
yield (Scheme 1). To our delight, pentaphyrin
1
HOMO and LUMO. The nucleusꢀindependent chemical
p
ꢀchloranil in toluene
in 78%
was very
shift (NICS) values20 at the center of the macrocycles
̊
1
(NICS(0)) were calculated to be –2.50 ppm for
+19.60 ppm for , supporting nonaromatic and strongly
antiaromatic characters for and , respectively. We also
calculated the rotational barrier of the vinylene bridge of
to be ca. 10.1 kcal/mol. In the optimized structure of
2 and
1
1
stable in the solid state and in solution indefinitely even in
the aerobic conditions. HRꢀESIꢀTOF MS indicated the
2
1
parent ion peak of
1
at m/z =1236.1697 (calcd for
C58H26N5F20O4 [MꢀH] – = 1236.1671). Crystals of
1
suitꢀ
–
1
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transition state (1-TS), the bond length of C25–C26 is
NMR(CDCl3, 298 K)
7.12(brs, 1H, outer NH), 6.82(d, J = 4.8 Hz, 2H,
ꢀH), 6.55(d, J = 4.8 Hz, 2H, ꢀH), 4.39(q, J = 6.8 Hz, 4H, ꢀ
OCH2CH3), 2.87(s, 4H, ethylene), 2.11(s, 6H, ꢀCH3), 1.36(t, J =
6.8 Hz, 6H, ꢀOCH2CH3): 19F NMR(CDCl3, 298 K)
(ppm) =
δ
(ppm) = 11.96(brs, 2H, inner NH),
1
2
3
4
5
6
7
8
1.341 Å and those of adjacent C24–C25 and C26–C1
bonds are 1.467 and 1.465 Å. Therefore, the C25–C26
vinylene group is rotating about C24–C25 and C26–C1
single bonds keeping its character of C25–C26 double
bond. (see SI)
β
ꢀH), 6.73(s, 2H,
β
β
β
δ
−137.01(d, J = 18.0 Hz, 4F, oꢀF), −140.05(d, J = 18.0 Hz, 4F, oꢀ
F), −152.18(d, J = 20.9 Hz, 2F, pꢀF), −152.86(d, J = 20.9 Hz, 2F,
pꢀF), −164.26(t, J = 17.9 Hz, 2F, mꢀF), −164.87(t, J = 17.9 Hz,
In summary, we synthesized [24]pentaphyrin(2.1.1.1.1)
as the first example of vinylogous pentaphyrin via dehyꢀ
drogenation of nonconjugated dihydropenꢀ
taphyrin(2.1.1.1.1) . Pentaphyrin was certainly stable
1
2F, mꢀF): 13C NMR(CDCl3, 298 K)
δ (ppm) = 164.9, 159.2,
154.1, 148.3, 146.5, 137.4, 131.5, 130.8, 130.7, 124.2, 118.6,
118.1, 98.4, 60.3, 29.3, 14.4, 12.3 (The signals for mesoꢀ
pentafluorophenyl carbons were not observed clearly because of
2
1
9
under ambient conditions despite its strongly antiaromatic
character and relatively small conjugation circuit. Further
exploration of vinylogous expanded porphyrins bearing
mesoꢀaryl and βꢀalkyl substituents is now ongoing in our
laboratory.
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their complicated 13CꢀF coupling); UV/Vis (CH2Cl2):
λmax[nm]
(ε[M–1cm–1])= 385(36000), 433(46000), 508(11600), and
787(34000). HRMS(ESIꢀTOF, positive mode) m/z [M+H]+
Calced for C58H30F20N5O4+ 1240.1973; Found 1240.1948.
11,16,21,26-tetrakis(pentafluorophenyl)-3,8-
bis(ethoxycarbonyl)-2,9-dimethyl pentaphyrin(2.1.1.1.1) 1.
Dihydropentaphyrin 2 (37.2 mg, 0.30 mmol) was stirred with
chloranil (73.8 mg, 10 eq) in toluene (6 mL) at 120 °C. After 12 h,
the reaction mixture was extracted with ethyl acetate and washed
five times with saturated NaHCO3 solution. The organic phase
was washed again with water and brine and dried over anhydrous
Na2SO4. The solvent was evaporated to dryness under reduced
pressure. The residue was dissolved again to CH2Cl2 and passed
through a short silicaꢀgel column followed by evaporation of solꢀ
vent under reduced pressure. Recrystallization with hexane gave
EXPERIMENTAL SECTION
Materials and Methods. All reagents were of the commerꢀ
cial grade and were used without further purification except where
noted. The spectroscopic grade dichloromethane was used as a
solvent for all spectroscopic studies. Silica gel column chromatogꢀ
raphy was performed on Wakogel Cꢀ200. Thinꢀlayer chromatogꢀ
raphy (TLC) was carried out on aluminum sheets coated with
silica gel 60 F254 (Merck 5554). UV/Visible absorption spectra
1
were recorded on a Shimadzu UVꢀ3600PC spectrometer. H and
19F NMR spectra were recorded on a JEOL ECZꢀ400 spectromeꢀ
1
1
pure [24]pentaphyrin(2.1.1.1.1) 1 (28.8 mg, 0.23 mmol, 78%). H
ter (operating as 399.78 MHz for H, 376.13 MHz for 19F, and
100.53 MHz for 13C) using tetramethylsilane(TMS) as the internal
NMR (CDCl3, 298 K):
17.68(s, 2H, inner ꢀH), 11.57(s, 2H, ꢀCH=CHꢀ), 4.48(d, J = 4.4
Hz, 2H, outer ꢀH), 4.04 (d, J = 4.4 Hz, 2H, outer ꢀH), 3.77(q, J
= 6.8 Hz, 4H, ꢀOCH2CH3) 2.86(s, 1H, outer NH), 1.56(s, 6H,
CH3), 1.00(t, J = 6.8 Hz, 6H, ꢀOCH2CH3); 19F NMR(CDCl3, 298
K): (ppm) = −135.58(d, J = 18.1 Hz, 4F, oꢀF), −140.88(d, J =
δ (ppm) = 26.11(brs, 2H, inner NH),
1
reference for H and 13C (
δ
= 0 ppm). Hexafluorobenzene for 19F
β
β
β
(δ = –162.9 ppm) was employed as external references. Highꢀ
β
ꢀ
resolution electrosprayꢀionization timeꢀofꢀflight mass spectroscoꢀ
py (HRꢀESIꢀTOFꢀMS) was recorded on a JEOL AccuTOF model
using positive mode for methanol solutions of samples. Data for
single crystal Xꢀray diffraction analyses were collected on a
Rigaku RꢀAXIS RAPID diffractometer using a graphite monoꢀ
chromator with CuKα radiation (λ = 1.54187 Å). Data collection
and reduction were performed using RAPID AUTO. The strucꢀ
tures for crystallography were solved by direct methods using
SHELXL97, and were refined using SHELXL97 on YadokariꢀXG
program.
δ
17.7 Hz, 4F, oꢀF), −152.90(t, J = 24.1 Hz, 2F, pꢀF), −153.00(t, J =
17.7 Hz, 2F, pꢀF), 160.9ꢀ−161.2(m, 8F, mꢀF) 13C NMR(CDCl3,
298 K)
δ (ppm) = 165.7, 163.1, 153.2, 151.1, 150.7, 138.7, 139.3,
138.5, 136.7, 130.5, 127.1, 123.4, 121.9, 121.5, 60.1, 13.9, 10.2
(The signals for mesoꢀpentafluorophenyl carbons were not obꢀ
served clearly because of their complicated 13CꢀF coupling);.
UV/Vis (CH2Cl2):
λmax[nm] (ε
[M–1cm–1]) = 498(63000) and
1050(1000). HRMS(ESIꢀTOF, negative mode): m/z: [M–H]–,
Calcd for C58H26F20N5O4– 1236.1671; Found 1236.1697.
11,16,21,26-tetrakis(pentafluorophenyl)-3,8-
bis(ethoxycarbonyl)-2,9-dimethyl
5,6-
dihydropentaphyrin(2.1.1.1.1) 2. 5,10ꢀbis(pentafluorophenyl)ꢀ
1,14ꢀbis(pentafluorobenzoyl)tripyrrane A (940 mg, 1.0 mmol)
was reduced with NaBH4 (378 mg, 20 eq) in a 10:1 mixture soluꢀ
tion of THF and methanol (110 mL). After 1 h, the reaction was
quenched with water and the products were extracted with ethyl
acetate. The organic phase was washed with brine and dried over
anhydrous Na2SO4. The solvent was removed under reduced presꢀ
sure to yield diꢀcarbinol B quantitatively, which was unstable at
ambient temperature and hence had to be used immediately. The
diꢀcarbinol was added to a solution of 1,2ꢀbis(3ꢀethoxycarbonylꢀ
4ꢀmethylpyrrolꢀ2ꢀyl)ethane C (341 mg, 1.0 mmol) in CH2Cl2 (200
mL). After the resultant solution was stirred in N2 atmosphere for
5 min, pꢀtoluenesulfonic acid monohydrate (57.6 mg, 0.30 eq)
was added and stirring was continued for 1.5 h. DDQ (454 mg,
2.0 eq) was added and the resulting solution was stirred for further
5 min. The reaction mixture with 100 mL of ethyl acetate was
passed through a basic alumina column with followed by evaporaꢀ
tion of solvent under reduced pressure. The residue was purified
by silica gel chromatography using 1:10 mixture of
EtOAc/Hexane. After collection of the brown band, recrystallizaꢀ
tion with hexane afforded pure 2, (118 mg, 0.033 mmol, 10%). 1H
ASSOCIATED CONTENT
The Supporting Information is available free of charge on the
ACS Publications website.
Xꢀray crystallographic data for compound 1 and 2 (CIF)
1H, 19F and 13C NMR spectra of compounds; Cyclic voltamꢀ
mograms; detailed XꢀRay crystallographic data; and calculated
data (PDF)
AUTHOR INFORMATION
Corresponding Author
*Eꢀmail: yoneda@chibaꢀu.jp
*Eꢀmail: sneya@faculty.chibaꢀu.jp
ORCID
Tomoki Yoneda: 0000ꢀ0002ꢀ9804ꢀ0240
Tyuji Hoshino: 0000ꢀ0003ꢀ4705ꢀ4412
Saburo Neya: 0000ꢀ0002ꢀ2203ꢀ5760
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The Journal of Organic Chemistry
(13) (a) Gopalakrishna, T. Y.; Reddy, J. S.; Anand, V. G. Angew.
Chem., Int. Ed. 2013, 52, 1763. (b) Gopalakrishna, T. Y.; Anand, V.
G. Angew. Chem. Int. Ed. 2014, 53, 6678.
Notes
1
The authors declare no competing financial interest.
2
3
4
5
6
7
8
9
(14) Anand, V. G.; Saito, S.; Shimizu, S.; Osuka, A. Angew. Chem.
Int. Ed. 2005, 44, 7244.
(15) (a) Fischer, H.; Scheyer, H. Justus Liebigs Ann. Chem. 1924,
439, 185. (b) Chen, Q.ꢀQ.; Yan, F.; Ma, J. S.; Jin, S. Chinese Chem.
Lett. 1993, 4, 567.
ACKNOWLEDGMENTS
This work was supported by JSPS KAKENHI for young
scientist Number 210I0153(B) and the Program to Dissemiꢀ
nate Tenure Tracking System from MEXT of Japan. We
thank Dr. T. Tanaka and Prof. Dr. A. Osuka (Kyoto Univerꢀ
sity) for Xꢀray crystallography and cyclic volutammetry
measurements.
(16) Crystal data for 2, C58H29F20N5O4·3(acetonitrile)
(Mr=1363.03), Monoclinic, space group P21/n (No. 14), a =
22.5153(9), b = 8.3136(3), c = 32.1163(13) Å,
β = 100.0015(18), V =
5901.1(4) Å3, Z = 4, calcd = 1.534 gcmꢀ3, T = 93(2) K, R1 = 0.0736 (I
ρ
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