Carbon-13 NMR chemical shifts of dimeric model compounds of poly(propylene oxide): A proof of existence of the (C-H)-O attraction

Article abstract of DOI:10.1021/jp002923m

Conformational energies of poly(propylene oxide) (PPO) have been determined from ¹³C NMR chemical shifts of its six dimeric model compounds. The model compounds were prepared and fractionated by supercritical fluid chromatography into three com

Full text of DOI:10.1021/jp002923m

J. Phys. Chem. A 2001, 105, 3277-3283
3277
Carbon-13 NMR Chemical Shifts of Dimeric Model Compounds of Poly(propylene Oxide):
A Proof of Existence of the (C-H)‚‚‚O Attraction
Yuji Sasanuma,* Taisuke Iwata, Yasukazu Kato, and Haruhisa Kato
Department of Materials Technology, Faculty of Engineering, Chiba UniVersity, 1-33 Yayoi-cho, Inage-ku,
Chiba 263-8522, Japan
Takashi Yarita and Shinichi Kinugasa
Department of Analytical Chemistry, National Institute of Materials and Chemical Research (NIMC),
1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan
Robert V. Law
Department of Chemistry, Imperial College of Science, Technology and Medicine, London SW7 2AY, U.K.
ReceiVed: August 10, 2000; In Final Form: NoVember 27, 2000
Conformational energies of poly(propylene oxide) (PPO) have been determined from 13C NMR chemical
shifts of its six dimeric model compounds. The model compounds were prepared and fractionated by
supercritical fluid chromatography into three components: CH3OCH2CH(CH3)OCH2CH(CH3)OCH3 (head-
to-tail); CH3OCH2CH(CH3)OCH(CH3)CH2OCH3 (head-to-head); CH3OCH(CH3)CH2OCH2CH(CH3)OCH3 (tail-
to-tail). Carbon-13 NMR measurements using 1H broad-band decoupling and DEPT techniques were carried
out for the benzene solutions at 25 °C, and all observed NMR peaks were assigned to the methine, methylene,
pendant methyl, and terminal methoxy carbons. By the simulation based on the rotational isomeric state
(RIS) scheme and γ- and δ-substituent effects for the 13C NMR chemical shifts, the γ- and δ-effect parameters
and the conformational energies were optimized; the root-mean-square error between the calculated and
observed chemical shifts was minimized to 0.12 ppm. Values of the γ-anti effect (-2.6 ppm) of oxygen, the
γ-gauche effects of carbon (-4.9 ppm) and oxygen (-7.9 ppm), and the δ-effect (2.1 ppm) of oxygen for the
g+g- conformations were obtained to fall within the allowable ranges, as shown in the parentheses. The
conformational energies evaluated here are comparable to those determined for isotactic PPO in our previous
studies. These results confirm our interpretation of the gauche oxygen effect: The gauche stability of the
C-C bond in the main chain of PPO is due to the intramolecular (C-H)‚‚‚O hydrogen bonding.
1. Introduction
Recently, we have carried out the conformational analysis
of isotactic PPO and its monomeric model compound, 1,2-
dimethoxypropane (1,2-DMP), by ab initio molecular orbital
(MO) calculations and 1H and 13C NMR vicinal coupling
constants of 1,2-DMP and the RIS analysis of the characteristic
ratio and dipole moment ratio of isotactic PPO.6-9 Consequently,
we have found that the gauche stability of the CH2-CH bond
(the gauche oxygen effect)10 is due to the (C-H)‚‚‚O hydrogen
bonding formed in the g(g- conformation for the C-O/C-C
bond pairs, and presented the conformational energies of
isotactic PPO. The (C-H)‚‚‚O close contacts in, e.g., (R)-1,2-
DMP are illustrated in Figure 1, parts d, e, and f. The ω1
interaction is assigned to a second-order (C-H)‚‚‚O attraction,
with the C-C bond being in the g+ state and the ω2 interaction
to that with the bond in the g- state. Only the g+g+g+ conformer
is presumed to have an extra stabilization (ø). The energy
parameters thus obtained successfully reproduced all of the
experimental observations from both isotactic PPO and 1,2-
DMP. The interpretation for the gauche oxygen effect of PPO
has been supported from MO calculations using large basis
sets,11,12 and similar phenomena have been reported for poly-
(ethylene oxide) and its model compounds.13,14 Such weak
hydrogen bonds have been found in crystals.15,16 However, PPO
Poly(propylene oxide) (PPO) is prepared by the ring-opening
polymerization of propylene oxide. If both C-O bonds of the
monomer are cleaved, three kinds of linkages, head-to-tail
(H-T), head-to-head (H-H), and tail-to-tail (T-T), are formed
between the monomeric units, where H is the methine end and
T is the methylene end of the monomer unit. Propylene oxide,
having a chiral methine carbon, exists in either of two optical
forms, R and S. Therefore, the 13C NMR spectra observed from
atactic PPO are too complicated to be easily analyzed.1-3
The γ-substituent effects have often been utilized to predict
13C chemical shifts of polymers;4,5 the γ substituent, which is
separated from the observed carbon atom by three bonds, tends
to shield the carbon nucleus; the magnitude of the shielding
effect depends on the distance between the two atoms, thus being
sensitive to the conformation of the intervening bond. By this
method, the 13C NMR chemical shifts of a variety of polymers
have been successfully related to their microstructures.4,5 For
atactic PPO, the assignment of the chemical shifts has also been
attempted.1,4,5
* Author to whom correspondence should be addressed. E-mail ad-
dress: sasanuma@planet.tc.chiba-u.ac.jp. FAX number: +81 43 290 3394.
10.1021/jp002923m CCC: $20.00 © 2001 American Chemical Society
Published on Web 02/24/2001

3278 J. Phys. Chem. A, Vol. 105, No. 13, 2001
Sasanuma et al.
Figure 1. Intramolecular interactions of isotactic poly(propylene oxide)
(PPO) and its model compounds:6,7,9 the first-order interactions for (a)
bond 2, (b) bond 3, and (c) bond 4 (the illustration is based on H-T
(RR), see Figure 2a); the second-order interactions, (d) the ω1 interaction
found in the tg+g- conformation of the monomeric model, (R)-1,2-
dimethoxypropane ((R)-1,2-DMP), and (e) the ω2 interaction in the
g+g-t conformation of (R)-1,2-DMP; (f) the third-order ø interaction
in the g+g+g+ conformation of (R)-1,2-DMP. The dotted lines represent
the (C-H)‚‚‚O close contacts. In the present study, the intramolecular
interactions and the statistical weights of six dimeric model compounds
(see Figure 2) are represented by the corresponding capital letters: A,
B, Γ, ∆, Σ, Ω1, Ω2, and X.
and its oligomeric model compounds of interest here exist in
gas or liquid phase. It must be noted that the nonbonded
(C-H)‚‚‚O attractions influence the conformational preferences,
even when the molecules are in rapid motions.
In this study we have attempted to determine conformational
energies of six dimeric model compounds (Figure 2) of PPO
from their 13C NMR chemical shifts by a combined use of the
rotational isomeric state (RIS) scheme17 and the substituent
effects. The dimers may be the simplest compounds having
different regiosequences (H-T, H-H, and T-T) and stereo-
sequences (RR, RS, SR, and SS). Hereafter the compounds (and
molecules) with the H-T, H-H, and T-T linkages are,
respectively, referred to as H-T, H-H, and T-T. For each
linkage, four optical isomers RR, RS, SR, and SS, exist. However,
the RR and SS isomers and the RS and SR isomers are
indistinguishable by NMR. In this paper, therefore, the four
isomers are represented by RR and RS.
Figure 2. Schematic representation of the dimeric model compounds
of PPO: (a) H-T (RR), (b) H-T (RS), (c) H-H (RR), (d) H-H (RS),
(e) T-T (RR), and (f) T-T (RS) in their all-trans conformations. As
indicated, the atoms and bonds are numbered.
lecular interactions.18 By the analysis, we have determined the
conformational energies of the dimers and confirmed the
existence of the (C-H)‚‚‚O attractions.
2. Theoretical Section
According to the empirical additivity relationship,19,20 the
chemical shift of a carbon atom i is given by
The model compounds were prepared and separated for each
regiosequence by supercritical fluid chromatography (SFC). The
13C NMR spectra were measured for the benzene-d6 solution.
The chemical shifts were assigned to the methine, methylene,
pendant methyl, and terminal methoxy carbons and compared
with the theoretical calculations based on the γ- and δ-sub-
stituent effects and the RIS scheme, including the first-order
(between atoms or groups separated by three bonds), second-
order (by four bonds), and third-order (by five bonds) intramo-
nj,R
nj,â
ηj,γ
δ )
∆δ
+
∆δ
+
p ∆δη
+
∑
∑
∑ ∑
i
R,j
â,j
η
γ,j
nj,δ
j
j
η
j
p ∆δηê + S (1)
∑ ∑
ηê
δ,j
ηê
j

13C NMR of Dimeric Models of Poly(propylene oxide)
J. Phys. Chem. A, Vol. 105, No. 13, 2001 3279
where nj,R, nj,â, nj,γ, and nj,δ are the numbers of nonhydrogen
atoms j at the R, â, γ, and δ positions (separated by one, two,
three, and four bonds from the carbon i, respectively), ∆δR,j
and ∆δâ,j are the chemical shift increments due to the atoms at
SCHEME 1
the R and â positions, and ∆δηγ,j and ∆δηê are those due to the
δ,j
γ and δ atoms, with the intervening bond(s) being in the
η () t, g+, or g-) and ηê () tt, tg+... or g-g-) conformations,
respectively. Thus, the terms representing the γ- and δ-effects
include the conformational probabilities, pη and pηê, respectively.
The R- and â-substituents induce the downfield shifts (i.e.,
∆δR,j > 0 and ∆δâ,j > 0), while the γ-substituent gives the
upfield shift (∆δηγ,j <0). The sign of ∆δηê is changeable with
the structure and conformation. The steric factor S is determined
by the extent of branching at the carbon i and its adjacent
carbons.
δ,j
to the other conformations have been assumed to be null:
tt
tg-
δ,C
g(t
δ,C
g(g(
δ,C
tt
tg-
δ,O
∆δ
∆δ ) ∆δ
) ∆δ
) ∆δ
) 0 ppm.
) ∆δ
) ∆δ
) ∆δ
)
δ,C
δ,O
g(t
g(g(
δ,O
δ,O
According to the RIS scheme,17 for example, the fractional
The above equation may be rewritten as
population fg
... of the conformation g+tg- ... can be
+tg-
calculated from statistical weight matrices Un’s (see Supporting
Information) according to
nj,γ
nj,δ
η
j
ηê
j
δi ) ∆δ0,i
+
p ∆δ
+
p ∆δ
(2)
∑ ∑
∑ ∑
η
ηê
γ,
δ,
J*[U′(g+)U′(g+t)U′(g+tg-) ...]J
η
j
ηê
j
2
3
4
fg tg- ... )
(3)
+
N-1
where ∆δ0,i is the summation of the first, second, and fifth terms
of eq 1 with respect to the observed carbon atom i. The ∆δ0,i
term, being independent of the conformation, may be given from
the molecule that has the same atoms at the R and â positions
as the compound of interest and only hydrogen atoms at the γ
positions. Such a molecule is designated the parent compound.
The parent compounds for the methine, methylene, pendant
methyl, and terminal methoxy carbons of the six model
compounds are 2-methoxy-1-propanol (CH3OCH(CH3)CH2OH),
1-methoxy-2-propanol (CH3OCH2CH(CH3)OH), 2-propanol
(CH3CH(CH3)OH), and dimethyl ether (CH3OCH3), respec-
tively. The individual carbon atoms have the same numbers and
kinds of R and â atoms (CH, 2 R-C, 1 R-O, 1 â-C, and 1 â-O;
CH2, 1 R-C, 1 R-O, 2 â-C, and 1 â-O; CH3, 1 R-C, 1 â-C, and
1 â-O; CH3O, 1 R-O and 1 â-C), irrespective of the linkage
and optical isomer. However, the â substituent groups are not
always common; e.g., for the methine carbons, 4CH of H-T, 1
â-CH2 and 1 â-O; 7CH of H-T, 1 â-CH3 and 1 â-O; 4CH and
J*[ U ]J
∏
n
n)2
where J* ) [100], J is the 9 × 1 column matrix of which
elements are unity, and N is the number of skeletal bonds. The
U′(g+) matrix can be obtained by filling the columns of the U2
2
matrix other than that corresponding to the g+ state with zero,
and the U′(g+t) matrix by filling the elements of the U3 matrix
3
other than that corresponding to the g+t conformation with zero,
etc. Strictly, the conformational energies may be defined for
each dimer. However, an outstanding advantage of the RIS
scheme is to allow us to calculate the conformation-dependent
and configuration-dependent properties using small number of
energy parameters. In this study, the same conformational
energies have been assumed to hold for the six dimers. To
distinguish the energy parameters from those established for
isotactic PPO,6,7,9 the interactions and statistical weights for the
dimers are represented by the corresponding capital letters: A,
B, Γ, ∆, Σ, Ω1, Ω2, and X.
3
7
6CH of H-H, 1 â-CH and 1 â-O, CH and CH of T-T, 1
â-CH3 and 1 â-O. Here the superscripts correspond to the carbon
numbers in Figure 2. On this basis, it is preferable that the ∆δ0,ú
(ú ) CH, CH2, CH3, or CH3O) value should be defined
according to the â-substituent group.
The conformational probability pη of the nth bond is given
as the sum of the fractional populations of conformers having
the η state in the nth bond, and pηê for the nth and (n + 1)th
bond pair as the sum of the populations of conformers having
the ηê conformation in the two bonds. The chemical shift δi
The γ-effect of carbon in the trans (antiperiplanar) position
is negligibly small, whereas the γ-anti effect (∆δtγ,O) of
oxygen is comparatively large (-2 to -3 ppm).19,20 In 13C NMR
studies on alkanes and their oxygenated derivatives, the
can be calculated from ∆δ0,ú’s, ∆δtγ,O, ∆δg( , ∆δg( , ∆δg(g-
,
γ,C
γ,O
δ,O
pη’s, and pηê’s.
g(
γ,C
g(
γ,O
γ-gauche effects of carbon and oxygen, ∆δ and ∆δ , have
3. Experimental Section
been found within the ranges of -4 to -6 ppm and -6 to -8
ppm, respectively.1,4,5 The δ-effects, which are typically smaller
in magnitude (e 0.5 ppm) than those of the R-, â-, and γ-effects,
have not been taken into account, except for the g(g-
conformations of the intervening bonds. In hydrocarbon poly-
mers, the g(g- conformations lead to a severe steric interaction
3.1. Sample Preparation. In the alcoholysis of propylene
oxide (PO), an acid catalyst yields a mixture of 2-alkoxy-1-
propanol and 1-alkoxy-2-propanol in approximately equal
amounts, while a base catalyst preferentially gives the latter
compound.21 The reactions provided all the six dimeric model
compounds, which were prepared as shown in Scheme 1.
Propylene oxide was initially reacted with methanol to yield a
mixture of 2-methoxy-1-propanol and 1-methoxy-2-propanol,
and these products were then further reacted with PO to produce
the dimerized alcohols. Then, two combinations of the catalysts
were used in the first and second steps: 1, NaOH and H2SO4;
2, H2SO4 and NaOH. The concentrations of the NaOH and H2-
SO4 catalysts were 0.3 and 1.3 mol%, respectively. The
individual products were treated with sodium hydride and
called the “pentane” effect,17 which results in these rarely
g(g-
δ,C
occurring. Thus, the δ-effect contribution (∆δ
) to the
chemical shift may be negligible in these cases. As stated in
the Introduction, however, the g(g- conformations for the C-O/
C-C bond pairs of PPO and its model compounds are stabilized
g(g-
by the (C-H)‚‚‚O hydrogen bonds. The ∆δ
values of 2 to
δ,O
g(g-
3 ppm have been estimated,19,20 whereas the ∆δ
effect
δ,O
may be negligible on the above basis. Here, the δ-effects related

3280 J. Phys. Chem. A, Vol. 105, No. 13, 2001
Sasanuma et al.
Figure 3. Supercritical fluid chromatograms of samples (a) 1 and (b)
2. The fractions A, B, C, and D were identified by GC/MS as 1,2-
DMP, H-H, H-T, and T-T, respectively.
Figure 4. 13C NMR spectra observed from the benzene solutions at
25 °C by using H broad-band decoupling: (a) T-T, (b) H-T, and
(c) H-H. The internal standard was tetramethylsilane.
1
iodomethane to yield mixtures of the model compound (referred
hereafter to as samples 1 and 2 in the order mentioned). All of
the chemicals were purchased from Wako Pure Chemical Ltd.
3.2. Supercritical Fluid Chromatography.22 The mobile
phase was carbon dioxide. A Shimadzu LC-6A pump was used
to deliver carbon dioxide. The pump head was cooled so as to
maintain a stable flow. A Shimadzu SLC-6A controller was
connected to the pump to regulate the mobile phase pressure.
The separation column of ODS-silica gel (250 mm × 4.6 mm)
was kept at a given temperature in a column oven of a Shimadzu
GC-7A system. A Rheodyne model 7125 sample injector with
a 20-µL sample loop, the FID detector attached to the Shimadzu
GC-7A system, and a Shimadzu C-R4A integrator were used.
The flow-rate of the mobile phase was controlled by a restrictor
of a capillary tube (400 mm × 50 µm i.d.).
respectively. Because PO was the racemic mixture, each fraction
includes RR and RS. As expected, sample 1 contains a large
amount of both H-T and H-H with a small amount of T-T,
whereas sample 2 includes a large amount of both T-T and
H-T and a small amount of H-H. Therefore, both samples
were mixed in equal quantities, dissolved in dichloromethane
at 10 wt%, and the retention behavior was investigated.
Consequently, the optimal conditions for the fractionation were
found as follows: the carbon dioxide pressure of 90 kg cm-2
,
the column temperature of 60 °C, and the injection of 8 µL.
Under these conditions, the fractionations were repeated ca. 250
times to acquire sufficient amounts of the three components
for the NMR measurements.
3.3. 13C NMR Measurements. Carbon-13 NMR spectra were
measured at 150.80 MHz on a JEOL JMS-GSX600 spectrometer
equipped with a variable-temperature controller. During the
measurement, the probe temperature was maintained at 25 °C
within a (0.1 °C fluctuation. The free induction decay signals
were accumulated ca. 128-1024 times by using the 1H broad-
band decoupling or the DEPT technique. In the former measure-
ment, the π/2 pulse width, the data acquisition time, and the
recycle delay were 6.2 µs, 0.8 s, and 2.2 s, respectively. Thus,
the recycle time was ca. 3 s, being 3-6 times the spin-lattice
relaxation times of PPO carbons.1 The digital resolution of the
spectra was 0.62 Hz. Benzene-d6 was used as the solvent, and
tetramethylsilane as the internal standard. The solute concentra-
tion was ca. 1 wt%.
1-Methoxy-2-propanol and 2-propanol were also examined
by the NMR measurements, as purchased from Wako Pure
Chemical Ltd. without further purification. The chemical shifts
of 2-methoxy-1-propanol were determined by comparison
between the spectrum observed from 1-methoxy-2-propanol and
that from the mixture (prepared as above) of 1-methoxy-2-
propanol and 2-methoxy-1-propanol.
4.2. 13C NMR Spectra and Assignment. Figure 4 shows
13C NMR 1H broad-band decoupling spectra from benzene
solutions of T-T, H-T, and H-H at 25 °C. The peaks at 17-
18 ppm can be assigned to the pendant methyl carbons, and
those around 56-59 ppm to terminal methoxy carbons. The
signals around 74-78 ppm may be assigned to either methine
or methylene carbons by reference to the DEPT spectra. In
Figure 5, the methine and methylene parts of the DEPT(90)
and DEPT (135) spectra of H-T in benzene at 25 °C are
1
compared with the H broad-band decoupling spectrum. The
methylene signals are not observed by the DEPT(90) method
and are inverted in the DEPT(135) spectrum. In H-T, only two
methine and two methylene groups exist. However, four
doublets are observed; one of the doublets arises from RR and
the other from RS. The doublet spacing, corresponding to the
chemical shift difference between RR and RS, was found to
range from 0.00 to 0.14 ppm for H-T. The number of peaks
from H-H and T-T are smaller than that from H-T because
of the structural symmetry. The doublets from the H-H mixture
show comparatively large spacings; for CH and CH2, 0.27 ppm;
for CH3, 0.29 ppm; for CH3O, 0.02 ppm. For T-T, the doublet
was observed only from the methylene carbons at 75.61 and
75.66 ppm, probably owing to the influence of both nearby
chiral centers. The structural similarity between H-T and H-H
in atoms 1 to 5 and that between H-T and T-T in atoms 5 to
9 allow us to assign the peaks of H-T by reference to the
spectra of T-T and H-H.
4. Results and Discussion
4.1. Preparation, Characterization, and Purification of
Samples. Figure 3 shows the supercritical fluid chromatograms
of the samples 1 and 2. By GC/MS, the fractions A, B, C, and
D were identified as 1,2-DMP, H-H, H-T, and T-T,

13C NMR of Dimeric Models of Poly(propylene oxide)
TABLE 1: Conformational Energies:a Comparison of the Present with Previous Studies
isotactic PPOb (previous studies)
six dimeric models (present study)
J. Phys. Chem. A, Vol. 105, No. 13, 2001 3281
c
conformational energy
conformational energy
kcal mol-1
|∆(SD)/∆E|
kcal mol-1
ppm2 mol kcal-1
first-order interaction
ER
Eâ
Eγ
Eδ
Eσ
0.54 ( 0.03
0.83 ( 0.04
2.967
0.223
1.406
EA
EB
EΓ
E∆
EΣ
0.36
1.00
2.86
0.44
1.40
15.6
8.6
0.1
24.6
8.0
second-order interaction
Eω
-1.040
-1.753
EΩ
EΩ
-0.88
-1.53
26.9
2.7
1
1
2
Eω
2
third-order interaction
Eø
-0.908
EX
-0.93
9 × 10-4
a For the definition of the interactions, see Figure 1. b Determined from ab initio molecular orbital calculations for 1,2-DMP, H and 13C NMR
vicinal coupling constants of 1,2-DMP, and the RIS analysis of the experimental observations of the characteristic ratio and dipole moment ratio
of isotactic PPO. References 6, 7, and 9. c A measure of sensitivity of the calculated chemical shifts to each conformational energy. For the details,
see text.
1
â-O, and â-CH3O; ∆δ0,CH(3), R-CH2, R-CH3, R-O, â-O, and
â-CH), three ∆δ0,CH ’s (∆δ0,CH (1), R-O, R-CH, â-O, â-CH3,
2
2
â-CH3O; ∆δ0,CH (2), R-O, R-CH, â-O, â-CH3, â-CH; ∆δ0,CH (3),
2
2
R-O, R-CH, â-O, â-CH3, â-CH2), one ∆δ0,CH (∆δ0,CH (1),
3
R-CH, â-CH2, and â-O), and two ∆δ0,CH O’s (∆δ03,CH O(1), R-O
3
3
and â-CH2; ∆δ0,CH O(2), R-O and â-CH). As the initial values,
3
the conformational energies ER - Eø shown in Table 1,30 the
recommended values of ∆δtγ,O (-3.0 ppm),19 ∆δg( (-5.0
γ,C
g(
g(g-
δ,O
ppm),4,5 ∆δ (-7.0 ppm),4,5 and ∆δ
(2.0 ppm),19,20 and
γ,O
the chemical shifts of the parent compounds31 were employed.
In Table 2, the calculated δi values are compared with the
corresponding experimental data. The overall root-mean-square
error (RMSEall) was minimized to 0.12 ppm, being comparable
with or less than the magnitudes of the δ-effects for conforma-
tions other than g(g-.19 These δ-effects have not been included
in the present calculations. The conformational energies, EA -
EX, determined here, differ slightly from those established for
isotactic PPO, ER - Eø. As a measure of sensitivity of the
calculated chemical shifts to each conformational energy E, the
|∆(SD)/∆E| ratio was estimated. Here the square deviation SD
is defined as SD (ppm2) ) ∑iI)1 (δav - δia,vobsd)2, where δai,vcalc
i,calc
and δai,vobsd are, respectively, the calculated and observed values
of the average chemical shift, I is the number of data. ∆E stands
for a small displacement in E from the optimum value.
Therefore, |∆(SD)| corresponds to the increase in SD induced
by ∆E. In the calculations, the other variables were set to the
optimum values. The |∆(SD)/∆E| ratios thus estimated are also
Figure 5. Methine and methylene parts of 13C NMR spectra of H-T
listed in Table 1. Of the energy parameters, EΩ is shown to be
1
1
in benzene at 25 °C: (a) H broad-band decoupling, (b) DEPT(90),
most effective on the calculated δi values. The E∆ and EA
parameters gave comparatively large |∆(SD)/∆E| values, whereas
the largest EΓ showed a small value of 0.1. This may be
explained as follows. The conformer populations are calculated
from the statistical weight matrices, of which elements are the
Boltzmann factors of the energy parameters; a large conforma-
tional energy gives a small statistical weight, thus being less
effective on conformer populations. The third-order interaction
X might be negligible in the chemical-shift calculation, because
and (c) DEPT(135) spectra. The internal standard was tetramethylsilane.
The 13C NMR chemical shifts of the parent compounds in
1
benzene at 25 °C, were determined from the H broad-band
decoupling and DEPT spectra.23-26
4.3. Calculations of Chemical Shifts by the RIS Scheme.
The statistical weight matrices for the six dimeric models are
shown in the Supporting Information.28 The simulation based
on eq 2 was carried out by the simplex method29 to achieve the
best agreement between the calculated and observed δi values.
Because of the uncertainty in the assignments to RR and RS
doublets, the simulation was performed using the average δi
value. The variables were as follows: eight conformational
|∆(SD)/∆EX| is as small as 9 × 10-4
.
From the conformational energies, EA - EX, the t, g+, and
g- fractions of the central C-C bond of 1,2-DMP can be
evaluated as 0.37 (0.34 ( 0.01), 0.47 (0.44 ( 0.01), and 0.16
(0.22 ( 0.01), respectively, where the values in the parentheses
were determined from NMR 1H-1H vicinal coupling constants
for the benzene solution at 26 °C.6 On the other hand, the energy
parameters, ER - Eø, optimized for isotactic PPO gave better
energies, one γ-anti effect (∆δtγ,O), two γ- gauche effect (∆δg(
γ,C
g(
g(g-
δ,O
and ∆δ ) and one δ-effect (∆δ
) parameters, and three
γ,O
∆δ0,CH’s (∆δ0,CH(1) including the effects of substituents, R-CH2,
R-CH3, R-O, â-O, and â-CH2; ∆δ0,CH(2), R-CH2, R-CH3, R-O,

3282 J. Phys. Chem. A, Vol. 105, No. 13, 2001
Sasanuma et al.
TABLE 2: Observed and Calculated Chemical Shifts of the
reasonable agreement between calculated and observed chemical
shifts of all the dimers. These facts indicate the existence of
the intramolecular (C-H)‚‚‚O attractions in the molecules
having the C-O-CH2 CH(CH3)O-C bond sequence and the
validity of the RIS scheme for the chemical-shift calculations.
Dimeric Model Compounds of PPO in Benzene at 25 °C
δi,a ppm
obsd
RR + RS
58.82 58.82 58.90 58.89 58.90
calcd c
carbon
no.b i
avg
RR
RS
avg
H-T
1
3
4
6
7
9
Acknowledgment. The statistical weight matrices (Support-
ing Information) were formulated when one (Y.S.) of us stayed
at Imperial College. We wish to thank Professor Julia Higgins’
group of Imperial College for hearty encouragement. This work
was supported in part by Grant-in-Aid for Scientific Research
(C) (No.11650920) of Japan Society for the Promotion of
Science and by the Royal Society, U.K.
77.11, 77.13 77.12 77.54 77.42 77.48
75.27, 75.34 75.31 75.28 75.33 75.31
73.50, 73.64 73.57 73.54 73.62 73.58
76.55, 76.62 76.59 76.59 76.65 76.62
56.65, 56.66 56.66 56.83 56.81 56.82
10, 11d 17.17, 17.25 17.38 17.40 17.53 17.53
17.52, 17.56
17.58 17.59
e
RMSEH-T 0.16
H-H
1
3
4
6
7
9
10
11
58.82, 58.84 58.83 58.83 58.74 58.79
77.48, 77.75 77.62 77.55 77.29 77.42
73.06, 73.33 73.20 73.21 73.13 73.17
73.06, 73.33 73.20 73.21 73.13 73.17
77.48, 77.75 77.62 77.55 77.29 77.42
58.82, 58.84 58.83 58.83 58.74 58.79
18.35, 18.64 18.50 18.24 18.50 18.37
18.35, 18.64 18.50 18.24 18.50 18.37
Supporting Information Available: The statistical weight
matrices of the six dimeric model compounds H-T (RR), H-T
(RS), H-H (RR), H-H (RS), T-T (RR), and T-T (RS) dimers.
This information is available free of charge via the Internet at
http://pubs.acs.org.
References and Notes
e
RMSEH-H 0.12
T-T
1
3
4
6
7
9
10
11
56.64
76.27
56.64 56.57 56.57 56.57
76.27 76.24 76.27 76.26
(1) Schilling, F. C.; Tonelli, A. E. Macromolecules 1986, 19, 1337.
(2) Heatley, F.; Luo, Y. Z.; Ding, J. F.; Mobbs, R. H.; Booth, C.
Macromolecules 1988, 21, 2713.
(3) Miura, K.; Kitayama, T.; Hatada, K.; Nakata, T. Polym. J. 7, 685,
697.
(4) Tonelli, A. E. NMR Spectroscopy and Polymer Microstructure: The
Conformational Connection; VCH Publishers: New York, 1989.
(5) Bovey, F.; Mirau, P. NMR of Polymers; Academic Press: New
York, 1996.
(6) Sasanuma, Y. J. Phys. Chem. 1994, 98, 13486.
(7) Sasanuma, Y. Macromolecules 1995, 28, 8629.
(8) Law, R. V.; Sasanuma, Y. J. Chem. Soc., Faraday Trans. 1996,
92, 4885.
(9) Law, R. V.; Sasanuma, Y. Macromolecules 1998, 31, 2335.
(10) Abe, A.; Hirano, T.; Tsuruta, T. Macromolecules 1979, 12, 1092.
(11) Smith, G. D.; Borodin, O.; Bedrov, D. J. Phys. Chem. A 1998,
102, 10318.
(12) Smith, G. D.; Jaffe, R. L.; Yoon, D. Y. Chem. Phys. Lett. 1998,
289, 480.
(13) Tsuzuki, S.; Uchimaru, T.; Tanabe, K.; Hirano, T. J. Phys. Chem.
1993, 97, 1346.
(14) Jaffe, R. L.; Smith, G. D.; Yoon, D. Y. J. Phys. Chem. 1993, 97,
12745.
75.61, 75.66 75.64 75.61 75.64 75.63
75.61, 75.66 75.64 75.61 75.64 75.63
76.27
56.64
17.07
17.07
76.27 76.24 76.27 76.26
56.64 56.57 56.57 56.57
17.07 17.03 17.08 17.06
17.07 17.03 17.08 17.06
e
RMSET-T 0.04
RMSEall
f
0.12
a Relative to the chemical shift of tetramethylsilane. b See Figure 2.
c The optimized parameters are as follows: ∆δtγ,O ) -2.6 ppm,
g(
γ,C
g(
γ,O
g(g-
) 2.1 ppm,
δ,O
∆δ
) -4.9 ppm, ∆δ
) -7.9 ppm, ∆δ
∆δ0,CH(1) ) 76.12 ppm, ∆δ0,CH(2) ) 77.33 ppm, ∆δ0,CH(3) ) 77.87
ppm, ∆δ0,CH2(1) ) 79.87 ppm, ∆δ0,CH2(2) ) 79.60 ppm, ∆δ0,CH2(3) )
77.73 ppm, ∆δ0,CH3(1) ) 25.35 ppm, ∆δ0,CH3O(1) ) 59.17 ppm, and
∆δ0,CH3O(2) ) 61.09 ppm. For the definition of these parameters, see
text. The conformational energies obtained are listed in Table 1. d The
signals from carbons 10 and 11 of H-T were not distinguishable. e The
root-mean-square error (RMSE) is defined as RMSE (ppm) )
[∑Ii)1(δav - δai,vobsd)2/I]1/2, where I is the number of data. f The RMSE
(15) Jeffrey, G. A. An Introduction to Hydrogen Bonding; Oxford
University Press: New York, 1997.
(16) Desiraju, G., Steiner, T., Eds. The Weak Hydrogen Bond: Ap-
plications to Structural Chemistry and Biology; Oxford University Press:
New York, 1999.
(17) Flory, P. J. Statistical Mechanics of Chain Molecules; Inter-
science: New York, 1969.
(18) Xu, J.; Song, X.; Zhou, Z.; Yan, D. J. Polym. Sci., Polym. Phys.
Ed. 1991, 29, 877.
i,calc
for all the data.
agreement with experiment; the t, g+, and g- fractions were
0.34, 0.43, and 0.23, respectively.7,9 The γ- and δ-effect
parameters were evaluated as follows: ∆δtγ,O ) -2.6 ppm
(-2 to -3 ppm),19,20 ∆δγg(,C ) -4.9 ppm (-4 to -6 ppm),1,4,5
g(
g(g-
δ,O
∆δ ) -7.9 ppm (-6 to -8 ppm),1,4,5 and ∆δ
) 2.1
(19) Pihlaja, K.; Kleinpeter, E. Carbon-13 NMR Chemical Shifts in
Structural and Stereochemical Analysis; VCH Publishers: New York, 1994.
(20) Barfield, M. J. Am. Chem. Soc. 1995, 117, 2862.
(21) Chitwood, H. C.; Freure, B. T. J. Am Chem. Soc. 1946, 68, 680.
(22) Yarita, T.; Nomura, A.; Abe, K.; Takeshita, Y. J. Chromatogr. A
1994, 679, 329.
γ,O
ppm (2 to 3 ppm).19,20 All of these parameters fall within the
allowable ranges shown in the parentheses. The optimized values
of the other parameters are given in the footnote c of Table 2.
(23) 13C NMR of 2-methoxy-1-propanol 1CH3O2CH(3CH3)4CH2OH
(C6D6, 25 °C, δ): 56.19 (C-1), 78.04 (C-2), 15.60 (C-3), 66.16 (C-4). The
superscripts in the chemical formula represent the carbon numbers. The
internal standard was tetramethylsilane.
5. Concluding Remarks
In the previous studies,7-9 the gauche oxygen effect of PPO
has been interpreted as follows: the gauche stability of the C-C
bond in the main chain is due to the (C-H)‚‚‚O hydrogen
bonding formed in the g(g- conformations for the C-O/C-C
bond pairs. We determined the conformational energies of
isotactic PPO from ab initio molecular orbital calculations at
3
(24) 13C NMR of 1-methoxy-2-propanol 1CH3O2CH2 CH(4CH3)OH
(C6D6, 25 °C, δ): 58.64 (C-1), 78.86 (C-2), 66.32 (C-3), 19.26 (C-4).
2
(25) 13C NMR of 2-propanol 1CH3 CH(CH3)OH(C6D6, 25 °C, δ): 25.43
(C-1), 63.87 (C-2).
(26) The boiling point (-24.8 °C) of dimethyether 1CH3OCH3 is lower
than the freezing point (-11 °C) of benzene-d6. The chemical shift (59.4
in δ) of C-1 was taken from ref 27.
the MP2/6-31+G*//HF/6-31G* level and H and 13C NMR
1
(27) Stothers, J. B. Carbon-13 NMR Spectroscopy; Academic Press:
New York, 1972; Chapter 5.
(28) For H-H and T-T, the molecular symmetry is not perfectly
expressed in the statistical weight matrices. In the calculations, therefore,
the following pairs of bond conformations were averaged: for RR, pn,t and
vicinal coupling constants of 1,2-DMP and the RIS analysis of
the characteristic ratio and dipole moment ratio of isotactic
PPO.7,9 Each of the six dimeric model compounds treated here
differs in regiosequence and stereosequence. Nevertheless, the
minor modification of the above energy parameters gave the
p
N+1-n,t, pn,g+ and pN+1-n,g+, and pn,g- and pN+1-n,g-; for RS, pn,t and pN+1-n,t
,
pn,g+ and pN+1-n,g-, and pn,g- and pN+1-n,g+, where n is the bond number,

13C NMR of Dimeric Models of Poly(propylene oxide)
J. Phys. Chem. A, Vol. 105, No. 13, 2001 3283
N is the number of bonds () 8), and pn,η (η ) t, g+, or g-) is the bond
conformation of the η state of the bond n.
constants of 1,2-DMP in benzene,6 dipole moment ratios of isotactic PPO
in benzene,9 and ab initio MO calculations including the self-consistent
reaction field effect for 1,2-DMP in benzene,7 were used here as the initial
values.
(31) 78.04 ppm for the methine, 78.86 ppm for the methylene, 25.43
ppm for the pendant methyl, and 59.4 ppm for the terminal methoxy carbons.
(29) Nelder, J. A.; Mead, R. Computer J. 1965, 7, 308.
(30) The conformational energies of isotactic PPO and 1,2-DMP were
shown to exhibit large solvent dependence.6,7 The energy parameters ER -
Eø shown in Table 1, determined from NMR 1H-1H vicinal coupling