Conformational equilibrium isotope effects in glucose by 13C NMR spectroscopy and computational studies

Article abstract of DOI:10.1021/ja003291k

Anomeric equilibrium isotope effects for dissolved sugars are required preludes to understanding isotope effects for these molecules bound to enzymes. This paper presents a full molecule study of the α- and β-anomeric forms of D-glucopyranose in water using deuterium conformational equilibrium isotope effects (CEIE). Using 1D ¹³C NMR, we have found deuterium isotope effects of 1.043 ± 0.004, 1.027 ± 0.005, 1.027 ± 0.004, 1.001 ± 0.003, 1.036 ± 0.004, and 0.998 ± 0.004 on the equilibrium constant, ^H/DK_β/α, in [1-²H]-, [2-²H]-, [3-²H]-, [4-²H]-, [5-²H]-, and [6,6′-²H₂]-labeled sugars, respectively. A computational study of the anomeric equilibrium in glucose using semiempirical and ab initio methods yields values that correlate well with experiment. Natural bond orbital (NBO) analysis of glucose and dihedral rotational equilibrium isotope effects in 2-propanol strongly imply a hyperconjugative mechanism for the isotope effects at H1 and H2. We conclude that the isotope effect at H1 is due to n_p → σ* hyperconjugative transfer from O5 to the axial C1-H1 bond in β-glucose, while this transfer makes no contribution to the isotope effect at H5. The isotope effect at H2 is due to rotational restriction of OH2 at 160° in the α form and 60° in the β-sugar, with concomitant differences in n → σ* hyperconjugative transfer from O2 to CH2. The isotope effects on H3 and H5 result primarily from syn-diaxial steric repulsion between these and the axial anomeric hydroxyl oxygen in α-glucose. Therefore, intramolecular effects play an important role in isotopic perturbation of the anomeric equilibrium. The possible role of intermolecular effects is discussed in the context of recent molecular dynamics studies on aqueous glucose.

Full text of DOI:10.1021/ja003291k

J. Am. Chem. Soc. 2001, 123, 1327-1336
1327
13
Conformational Equilibrium Isotope Effects in Glucose by C NMR
Spectroscopy and Computational Studies†
Brett E. Lewis and Vern L. Schramm*,‡
Contribution from the Department of Biochemistry, Albert Einstein College of Medicine,
1300 Morris Park AVenue, Bronx, New York 10461
ReceiVed September 6, 2000. ReVised Manuscript ReceiVed NoVember 15, 2000
Abstract: Anomeric equilibrium isotope effects for dissolved sugars are required preludes to understanding
isotope effects for these molecules bound to enzymes. This paper presents a full molecule study of the R- and
â-anomeric forms of D-glucopyranose in water using deuterium conformational equilibrium isotope effects
(CEIE). Using 1D 13C NMR, we have found deuterium isotope effects of 1.043 ( 0.004, 1.027 ( 0.005,
1.027 ( 0.004, 1.001 ( 0.003, 1.036 ( 0.004, and 0.998 ( 0.004 on the equilibrium constant, H/DKâ/R, in
[1-2H]-, [2-2H]-, [3-2H]-, [4-2H]-, [5-2H]-, and [6,6′-2H2]-labeled sugars, respectively. A computational study
of the anomeric equilibrium in glucose using semiempirical and ab initio methods yields values that correlate
well with experiment. Natural bond orbital (NBO) analysis of glucose and dihedral rotational equilibrium
isotope effects in 2-propanol strongly imply a hyperconjugative mechanism for the isotope effects at H1 and
H2. We conclude that the isotope effect at H1 is due to np f σ* hyperconjugative transfer from O5 to the
axial C1-H1 bond in â-glucose, while this transfer makes no contribution to the isotope effect at H5. The
isotope effect at H2 is due to rotational restriction of OH2 at 160° in the R form and 60° in the â-sugar, with
concomitant differences in n f σ* hyperconjugative transfer from O2 to CH2. The isotope effects on H3 and
H5 result primarily from syn-diaxial steric repulsion between these and the axial anomeric hydroxyl oxygen
in R-glucose. Therefore, intramolecular effects play an important role in isotopic perturbation of the anomeric
equilibrium. The possible role of intermolecular effects is discussed in the context of recent molecular dynamics
studies on aqueous glucose.
Introduction
the anomeric effect may be the most discussed aspect of sugar
chemistry, it is by no means the only determinant of molecular
structure and energy. In fact, carbohydrates are complicated
molecules, and a number of experimental and theoretical
techniques have been brought to bear on their total molecular
structure and behavior. Raman and infrared spectroscopic studies
have been used to assign vibrational bands to specific bond
stretches, angle bends, and coupled motions.16-22 NMR studies
of glucose have been able to demonstrate differences in
extracyclic hydroxymethyl rotamer populations between the R-
and â-pyranose anomers,23 and a variety of chemical shift and
coupling constant data have been reported.24-32 Most recently,
Sugars are found as an important part of most aspects of
cellular structure and energy utilization. Nucleic acids, lectins,
most extracellular eukaryotic proteins and the substrates of
glycolysis, the pentose phosphate pathways, and others require
some participation by carbohydrate. The important roles of
sugars in biology have led to theoretical and experimental
investigations to understand the factors that affect their con-
formations, relative rotamer stabilities, and anomeric abun-
dances. The anomeric effect, first proposed by Lemieux1 and
arguably the most significant energetic stabilizing factor in sugar
chemistry, has been studied extensively in sugars and smaller
molecules both experimentally2-5 and theoretically.6-15 While
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69, 1-26.
† Supported by research grant GM41916 from the National Institutes of
Health.
‡ Telephone (718) 430-2813. Fax (718) 430-8565. E-mail vern@
aecom.yu.edu.
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10.1021/ja003291k CCC: $20.00 © 2001 American Chemical Society
Published on Web 01/24/2001

1328 J. Am. Chem. Soc., Vol. 123, No. 7, 2001
Lewis and Schramm
empirical relationships between homo- and heteronuclear cou-
pling constants and carbohydrate conformation24,33-38 and
several ab initio39,40 and molecular dynamics41-43 studies have
been used to explain the relative free energies of glucose
anomers and their rotamers.
Materials and Methods
Materials. [1-2H]Glucose was purchased from Sigma Chemical
Company (St. Louis, MO). [2-2H]-, [3-2H]-, [4-2H]-, [5-2H]-, and [6,6′-
2H2]glucose were obtained from Omicron Biochemicals (South Bend,
IN). Sugars were used without further purification. Methanol was from
Fisher Scientific (Pittsburgh, PA) and 5 mm NMR tubes and coaxial
inserts were from Wilmad Glass (Buena, NJ). Spectra were collected
on a 300 MHz Bruker instrument and quatronuclear probe.
Latitudinally, conformational equilibrium isotope effects have
been used to study molecular structure in a large number of
compounds. Methylpyridines,44,45 1,3-dioxanes,46 3-azabicyclo-
[3.2.2]nonanes,47 and cyclohexane derivates48-51 can each serve
as simple models for carbohydrates. In fact, hyperconjugation
and steric interactions contribute to equilibrium isotope effects
in these molecules in a well-understood way. However, whereas
previous studies employed singly substituted molecules to
analyze individual effects, no study to our knowledge has been
carried out on multiple substitutions in a single molecule to
demonstrate the interaction of effects. This has provided an
opportunity to explore the complete structure of glucose, the
central carbohydrate of biology, with a probe as well understood
as conformational equilibrium isotope effects.
First we report complete data for the deuterium isotope effects
on the anomeric equilibrium of D-glucose in water. Then we
present conformational ensembles which are most likely to
compose these anomers in solution and which confirm the
experimental isotope effects. On the basis of these models and
calculations using gas-phase 2-propanol and methane, we are
able to explain these isotope effects in the context of the
anomeric effect, hydroxyl rotational restriction, and syn-diaxial
steric repulsion. These results are also discussed in terms of
some recent theoretical studies.
Peak Assignments. The 13C6 signals were assigned using their
longer transverse relaxation time. All other signals were unequivocally
assigned on the basis of 1H-13C heteronuclear spin correlation
spectroscopy and 2D INADEQUATE spectroscopy. 13C assignments
were further verified with 1D H-decoupled 13C spectra of deuterated
1
glucose.
Equilibrium NMR Spectroscopy. Individual peaks were better
resolved in 1D 13C as compared to 1D H spectra, and while 2D H-
COSY was capable of resolving the spectrum, we determined that
integrating in two dimensions could add unwanted complications.
Further, as we desired to acquire the isotope effect data in aqueous
solution, the utilization of 1D 1H NMR was ruled out because the H2O
peak (4.882 ppm) grossly interferes with the R-1H1 and â-1H1 peaks
(5.212 and 4.622 ppm, respectively) and because suppression of the
water signal could alter the observed integration ratio. Therefore, the
1
1
data reported here were acquired using inverse-gated 1H-decoupled 13
C
NMR with an interpulse delay of 8 times the longest carbon T1. All
samples were permitted to equilibrate to 25 °C in the instrument prior
to data acquisition. The solvent for sugars was H2O:methanol 9:1, and
spectra were collected in 5 mm tubes with D2O included within a coaxial
insert.
Spectral Analysis. The anomeric equilibrium constant, Kâ/R, was
calculated for unlabeled glucose by dividing the integral over â-13C1
by that over R-13C1 and also by dividing the integral for â-13C(5,3,2)
by that for R-13C(5,3,2). The Kâ/R values for deuterated glucose species
were calculated by taking the appropriate ratios of peaks which
contained no carbon splitting due to deuterium; for example, with [2-2H]-
glucose the 13C(5,3,2) signals were not used. Spectra were integrated
over a 1 ppm range centered on â- or R-13C1 and/or over a 2.6 ppm
range beginning 0.5 ppm downfield of the most shifted peak of the â-
or R-13C(5,3,2) clusters. Isotope effects and standard errors were
calculated by:
(26) Cussans, N. J.; Huckerby, T. N. Tetrahedron 1975, 31, 2719-26.
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DKâ/R ) 1Kâ/R/2Kâ/R
(34) Serianni, A. S.; Bondo, P. B.; Zajicek, J. J. Magn. Reson., Ser. B
1996, 112, 69-74.
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1998, 309, 145-52.
σmDK ) ((σm1K)2/(2K)2+ (1K)2(σm2K)2/(2K)4)1/2
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280, 177-186.
1
2
where Kâ/R and Kâ/R are mean values from separate spectra and σm
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Am. Chem. Soc. 1993, 115, 10863-70.
are the standard deviation of the mean for those measurements. In the
case of [4-2H]- and [6,6′-2H2]glucose, where two values of D
Kâ/R were
(38) Wu, J.; Bondo, P. B.; Vuorinen, T.; Serianni, A. S. J. Am. Chem.
Soc. 1992, 114, 3499-3505.
obtained, these were further averaged and the variance propagated
accordingly to yield the final values.
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1190-3.
Semiempirical and ab Initio Calculations. (A) Glucose. Theoreti-
cally, there can exist 12 rotamers of 4C1 glucose including two anomers,
three rotamers of the extracyclic hydroxymethyl, and two orientations
for intramolecular hydrogen bonds between the hydroxyl groups (Figure
1). It has been shown that the barriers to reorganization are large enough
to distinguish these ground states in the gas phase and probably in the
solution phase, although intramolecular hydrogen bonds are not likely
to be as important as glucose-water interactions. Geometry optimiza-
tions and frequency calculations were performed for each rotamer using
the Gaussian 94 software package.52
Geometry results and force constants in Cartesian coordinates were
used as input for the program QUIVER,53 which calculates “fraction-
ation factors” in isotopic exchanges for each species. QUIVER was
modified to permit specification of frequency correction factors (PM3,
0.9761, RHF/3-21G, 0.9085, and RHF/6-31G(d,p), 0.8992;54 DFT,
0.956155). Mole fractions for each species were calculated from the
Boltzmann distribution using final energies from the Gaussian 94
geometry jobs. Alternatively, extracyclic hydroxymethyl rotamer mole
fractions were taken as in Nishida et al.,23 and only the relative
(40) Ma, B.; Schaefer, H. F. III.; Allinger, N. L. J. Am. Chem. Soc. 1998,
120, 3411-22.
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97, 12093-9.
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Am. Chem. Soc. 1966, 88, 2520-5.
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1989, 30, 4585-88.
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1989, 30, 4593-6.
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(51) Williams, I. H. J. Chem. Soc., Chem. Commun. 1986, 627-8.

Equilibrium Isotope Effects in Glucose
J. Am. Chem. Soc., Vol. 123, No. 7, 2001 1329
Figure 2. 2-Propanol and HC-CC-O-HO dihedral (θ).
4
Figure 1. Rotamers of D-glucose in the C1 chair. Top row: three
low-energy staggered positions of the extracyclic hydroxymethyl group.
Bottom row: two orientations of gas-phase intramolecular hydrogen
bonds.
abundances of CW(+) and CCW(-) subsets were calculated from
Boltzmann distribution as above. These fractionation factors were
combined as shown in eq 1,
6
-1
)
øRi øâi
DK )
æ
æ
(1)
(
∑
Ri
âi
i ) 1
where æi are the fractionation factors and øi are the mole fractions for
rotamer i. This procedure was carried out using combinations of the
PM3, Hartree-Fock, and B3PW91 methods, the 3-21G and 6-31G**
basis sets, and the Onsager dipole solvation model (ꢀ ) 78.5). Energies
in kcal/mol due to electron delocalization were calculated by the NBO
extension56-59 of Gaussian 94.
(B) 2-Propanol. Using Gaussian 98,60 a gas-phase model of
2-propanol was minimized at the RHF/3-21G level of theory with
respect to all parameters except the torsional angle, θ, given by HC-
CC-O-HO (see Figure 2), which was held fixed at various positions.
Force constants in Cartesian coordinates were calculated for each
structure and transformed Via QUIVER into conformational equilibrium
Figure 3. Methane, methanol, methylamine and the p-type and sp-
type orbitals for ROH groups (clockwise from upper left).
(52) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;
Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G.
A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrezewski,
V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowki, J.; Stefanov, B. B.;
Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.;
Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.;
Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-
Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, ReVisions C.2, D.4;
Gaussian, Inc.: Pittsburgh, PA, 1995.
isotope effects. Energies due to hyperconjugative electron delocalization
and the populations of bonding and antibonding orbitals were calculated
by NBO in Gaussian 98.
(C) Methane, Methanol, and Methylamine. Various H-C-H,
H-C-O, and H-C-N angles were held fixed, and isotope effects
and NBO parameters were calculated as described above for 2-propanol.
Atoms are defined as in Figure 3.
(53) Saunders, M.; Laidig, K. E.; Wolfsberg, M. J. Am. Chem. Soc. 1989,
111, 8989-94.
(D) Cyclohexane. Calculations were also made on equitorial vs. axial
CH bonds in cyclohexane.
(54) Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502-13.
(55) Wong, M. W. Chem. Phys. Lett. 1996, 256, 391-9.
(56) Glendening, E. D.; Reed, A. E.; Carpenter, J. E.; Weinhold, F. NBO,
Version 3.0; Theoretical Chemistry Institute and Department of Chemistry,
University of Wisconsin: Madison, WI, 1994.
Results
Glucose 13C NMR. Sample NMR spectra are shown in Figure
(57) Foster, J. P.; Weinhold, F. J. Am. Chem. Soc. 1980, 102, 7211-8.
(58) Reed, A. E.; von Rague Schleyer, P. J. Am. Chem. Soc. 1987, 109,
7362-73.
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899-926.
1
4. Panel A shows a typical H spectrum of R/â-equilibrated
glucose in D2O. The anomeric signals flank the residual water
peak, and the remainder of the spectrum is sufficiently
complicated to rule out the integration of separate peaks. Panels
B and C represent 13C spectra of [U-1H]- and [3-2H]glucose,
respectively. Carbon signals at 96.3, 92.5, 76.25, 76.25, 74.6,
73.3, 71.9, and 71.8 ppm arise from C1â, C1R, C5â and C3â,
C2â, C3R, C5R, and C2R, respectively. This distribution made
it possible to integrate the C(5,3,2)â peaks in comparison with
the C(3,5,2)R peaks and also the C1â and C1R peaks. Whereas
(60) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Stratmann,
R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K.
N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi,
R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.;
Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.;
Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J.
V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.;
Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng,
C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.;
Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.;
Replogle, E. S.; Pople, J. A. Gaussian 98, ReVision A.6; Gaussian, Inc.:
Pittsburgh, PA, 1998.
1
with H observation it would have been impossible to acquire
the equilibrium constant for [1-2H]glucose, 13C NMR spectros-
copy permitted the acquisition of the complete set.

1330 J. Am. Chem. Soc., Vol. 123, No. 7, 2001
Lewis and Schramm
Table 2. Chemical Shifta and Observed Isotope Effect in Glucose
1H NMR (ppm)
13C NMR (ppm)
CEIEb
R
â
R
â
CH1
CH2
CH3
CH4
CH5
proR-CH6
1.043
1.027
1.027
1.001
1.036
5.09
3.41
3.61
3.29
3.72
3.72
4.51
3.13
3.37
3.30
3.35
3.75
92.9
72.5
73.8
70.6
72.3
96.7
75.1
76.7
70.6
76.8
0.998
61.6
61.7
proS-CH6
3.63
3.60
a Reference 28. b From Table 1.
Table 3. Calculated Anomeric Equilibrium Isotope Effects for
Glucose
gas phase
Onsager, e ) 78.8
Hartree-Fock
Hartree-Fock
label
expt PM3 3-21G 6-31G** B3PW91a 3-21G 6-31G**
[1-2H]
1.043 1.047 1.021 1.057
1.027 1.035 1.019 1.041
1.027 1.001 1.045 1.013
1.001 0.989 0.977 0.986
1.036 1.010 1.032 1.040
1.013 1.014 1.014
1.079
1.058
1.012
0.989
1.035
1.013
0.983
0.996
1.000
1.024
1.027
1.041
0.985
1.030
1.007
0.993
0.999
1.002
1.057
1.046
1.011
0.986
1.038
1.011
0.986
0.997
1.000
[2-2H]
[3-2H]
[4-2H]
[5-2H]
[6(S)-2H]
[6(R)-2H]
0.995 0.985 0.984
[6,6′-2H2] 0.998 1.008 0.998 0.998
[5-18O]
0.992 1.003 1.000
Hybrid-Calculated Isotope Effects Incorporating
Experimental Mole Fractionsb
[1-2H]
1.043 1.045 1.019 1.056
1.027 1.027 1.030 1.043
1.027 1.001 1.036 1.011
1.001 0.987 0.994 0.998
1.036 1.010 1.024 1.036
0.978 1.000 1.007
1.077
1.057
1.012
0.994
1.036
1.012
0.998
1.010
1.000
1.019
1.030
1.039
0.999
1.026
1.003
0.999
1.002
1.001
1.057
1.046
1.028
0.987
1.035
1.036
0.997
1.030
0.999
[2-2H]
[3-2H]
[4-2H]
[5-2H]
[6(S)-2H]
[6(R)-2H]
Figure 4. NMR spectra of D-glucose at equilibrium: (A) 1H NMR of
1.026 0.999 1.001
[6,6′-2H2] 0.998 1.004 0.999 1.008
1
glucose in D2O, 10% CD3OD; (B and C) H-uncoupled 13C NMR of
[5-18O]
a 6-31G**, no solvation. b Reference 23.
0.993 1.002 0.999
glucose and [3-2H]-glucose, respectively, in H2O, 10% CH3OH.
Table 1. Equilibrium Constant, Kâ/R, for Aqueous Glucose and
Isotope Effects Measured by 13C NMRa
and are therefore less shielded in the â-sugar. The converse is
true in the 1H spectrum. These relations are summarized in Table
2. Isotope effects on 13C chemical shift were also observed as
shown in Figure 4c.
equilibrium position,b Kâ/R
isotope effect,
label
(â/R)1
(â/R)2,3,5
n
DKâ/R
[U-1H]
[1-2H]
[2-2H]
[3-2H]
[4-2H]
[5-2H]
1.6104 ( 0.0047 1.5721 ( 0.0027 (15)
-
Calculations on Glucose. Comparison by Level of Theory
and Basis Set. The calculations performed at RHF/6-31G**
(Table 3a) best matched the 13C NMR data. These show the
largest effect at H1 followed by H2 and H5, with no effect at
H6. While the model yields different isotope effects for H2 and
H3 (1.046 and 1.011, respectively), the values are equidistant
from the experimental values of 1.027 for these atoms. Including
a solvent dielectric as in the Onsager dipole model contributed
little to the RHF/3-21G or RHF/6-31G** models. Isotope effects
at H1 and H2 were greatly exaggerated in the density functional
model (B3PW91/6-31G**), and the PM3 model performed well
except at protons H3 and H5. All models compute an inverse
isotope effect at H4, a different isotope effect between the two
extracyclic methylene protons, and, except for PM3, no
significant 18O isotope effect.
Hybrid Calculations: Experimental Mole Fractions. Where
the fractionation factors were combined according to the mole
fractions experimentally determined by Nishida et al.,23 the
results for each model were generally improved, particularly
for H3, H4, and H5 (Table 3b). The exceptions here are the
Onsager RHF/6-31G** calculations for the H6 protons, which
change from unity to one or three percent.
1.5076 ( 0.0059 (7) 1.043 ( 0.004
1.5681 ( 0.0068
1.5676 ( 0.0046
(8) 1.027 ( 0.005
(12) 1.027 ( 0.004
1.6196 ( 0.0054 1.5612 ( 0.0049 (3) 1.001 ( 0.003
1.5538 ( 0.0039
(3) 1.036 ( 0.004
[6,6-2H2] 1.6043 ( 0.0097 1.5838 ( 0.0068 (8) 0.998 ( 0.004
a In H2O, 10% MeOH. b From the ratio of integration of the C1(â/
R) peaks or the C2,3,5(â/R) peaks.
The isotope effects measured in this way are listed in Table
1. The equilibrium constant derived from the integrations (â/
R)1 and (â/R)5,3,2 are shown for each molecule. Significant
normal isotope effects can be seen at H1, H2, H3, and H5.
Effects of unity are seen at H4 and H6 (performed with [6,6′-
2H2]glucose). Whereas DKâ/R differed slightly between peak sets
in the case of [U-1H]-, [4-2H]-, and [6,6′-2H2]glucose, this was
assumed not to vary between the molecules.61 The CH bonds
which appear to differ vibrationally between R- and â-glucose
correspond precisely to those nuclei which have different
1
chemical shifts by H and 13C NMR. In other words, C1, C2,
C3, and C5 are downfield in â-glucose from their R counterparts
(61) As these signals arise from different sugars trace-labeled at either
C1, C2, C3, or C5, this difference could arise from a carbon anomeric
isotope effect. However, carbon effects never exceed 1%. Therefore, the
different choice of integration ranges is probably responsible.
Correlations with Isotope Effect in 6-31G** Calculations.
The RHF/6-31G**-Onsager dipole calculations were used to

Equilibrium Isotope Effects in Glucose
J. Am. Chem. Soc., Vol. 123, No. 7, 2001 1331
Table 4. Geometry and Electronic Changes in Representative Models of Glucose Anomersa
hyperconjugationc (kcal/mol)
orbital changesd
bond order
bond length (Å)
changeb
R
â
R
â
carbon
carbon
CH
CEIE
R
â
∆σ-σ*
σ f
f σ*
σ f
f σ* ∆Σ(â-R) hybrid. cont. (%) hybrid. cont. (%)
1
2
3
4
5
1.054
1.048
1.011
0.996
1.036
1.083
1.084
1.089
1.087
1.086
1.088
1.081
1.091
1.088
1.090
1.087
1.090
1.088
1.081
-0.00802 12.08
-0.00247 15.54
2.44
9.90
9.77e
5.15
5.18
0.49
0.14
0.51
0.26
-0.13
sp2.70
sp3.12
sp3.11
sp3.04
sp3.00
sp2.97
sp2.94
60.53
61.53
60.78
61.32
61.28
59.75
61.36
sp2.74
sp3.04
sp3.16
sp3.02
sp3.07
sp2.96
sp2.94
59.37
61.20
60.63
61.46
60.71
59.80
61.34
2.97 13.69
10.00f
-0.00072 12.42 10.27 12.99g 10.19
-0.00004 12.22 10.82 12.43
10.75
9.65h
10.49
2.18
-0.00215 11.61
9.23 11.70
6-proS 1.000
6-proR 1.000
-0.00027
6.39 10.31 6.47
-0.00027 11.07
2.16 10.92
a RHF/6-31G** Onsager dipole models R-gg(-) and â-gg(-) only. b Calculated by subtracting the number of electrons occupying the σ* orbital
from the number occupying the σ orbital and listed as the change between R- and â-glucose. c Sum of second-order perturbation contributions
calculated by NBO analysis. Cutoff ) 0.5 kcal/mol. d Hybridization of the carbon atom and contribution of the carbon atom to the bond in percent.
e-h Lp1 is the sp-type lone pair, and Lp2 is the p-type lone pair: eLp2(O5); fLp2,1(O2); gC2, C2-H2, and C2-O2 are better acceptors in â; hwhile
Lp2(O5) declines in â, Lp1(O5) increases by 1 kcal/mol.
into their respective σ* orbitals. The source of this electron
density for H1 is the p-type lone-pair of the ring oxygen, O5,
and for H2 it is mostly the p-type lone pair with some
contribution from the sp-type lone pair of O2. The energies
derived from these delocalizations are a full order of magnitude
greater than the corresponding differences for the H3 and H5
protons in R- and â-glucose. In the case of the latter protons,
the majority of delocalization energy derives from increased
overlap of the bonding σ orbital of C3-H3 with the antiperi-
planar C2-H2 and the C2-O2 antibonding σ* orbitals and from
a slightly increased donation by the p-type O5 ring oxygen lone
pair into the σ* orbital of C5-H5. The C4-H4 and C6-H6
bonds show no difference in electron delocalization.
Figure 5. Dihedral angle summary for hydroxyl groups in (A)
R-glucose and (B) â-glucose at RHF/6-31G** (Onsager dielectric ꢀ )
78.8). Backbone protons are all represented in the north position here
for comparison. The large circles, the vertices, and the line ends
represent the backbone carbons, the hydroxyl oxygens, and the hydroxyl
protons, respectively. The ends of identically labeled lines are connected
for clarity.
Whereas hyperconjugation is dominant for H1 and H2, steric
factors correlate with the isotope effects at H3 and H5. In
R-glucose, the 1-hydroxyl group is axial and might be expected
to interact sterically with the syn-diaxial H3 and H5 protons.
Examination of the same gg(-) models demonstrates that the
H3-O1 distance of 2.64 Å and the H5-O1 distance of 2.63 Å
are both inside the minimum radius expected for van der Waals
repulsion (2.72 Å). This strain is fully relieved in â-glucose
where the H3-H1 distance of 2.44 Å and the H5-H1 distance
of 2.54 Å are both outside the van der Waals radius expected
for two protons (2.40 Å). Comparison of the two models in
Figure 6 shows that in R-glucose the H3 and H5 protons are
strained away from the anomeric center. This strain is nonethe-
less insufficient to fully relieve the van der Waals radius
impingement. The same protons in â-glucose appear relaxed
and truly syn-diaxial with H1. These observations are mirrored
precisely in the RHF/3-21G calculations, in which this steric
interaction seems to be the dominant effect.
Conformational Equilibrium Isotope Effects in 2-Pro-
panol. 2-Propanol was selected as a small molecular model for
conformational isotope effects pertinent to glucose. We found
that varying the central HC-CC-O-HO dihedral angle in
2-propanol gives significant changes in the fractionation factor
for all protons and for H-C distances and C-C distances
(Figure 7). Reported here are properties for the central proton
HC and for the two antiperiplanar methyl protons HR and HL.
For every dihedral angle calculated, HR and HL minimized
precisely antiperiplanar to HC. Taking the dihedral angle of 59.9°
as the reference state (panel A), HC has a normal isotope effect
of 1.005 at 0° and an inverse isotope effect of 0.950 at 180°.
The other two protons, HR and HL, vary with each other and
inversely with respect to the central proton. Each experiences a
explore the anomeric differences since these proved superior
in predicting the atoms of largest and smallest isotope effect.
The calculations predict three major contributors (gg(-),
gt(-), and tg(-)) to the R-glucose population mixture and,
therefore, to its fractionation factor and two major contributors
(gg(-) and gt(-)) for â-glucose. We only present the data from
these major species.
We observe in these gas-phase calculations that only the
2-hydroxyl changes significantly in dihedral angle between R-
and â-glucose (Figure 5). In R-glucose, the dihedral angle H2-
C2-O2-OH2 has a value of approximately 160° for all three
models, and in â-glucose, these have changed to about 60° for
both models. The respective angles permit intramolecular
hydrogen bonding to exist in the gas phase between the
2-hydroxyl and the 1-hydroxyl. The gg(-) models were taken
as representative for both R- and â-glucose and were therefore
examined by natural bond orbital analysis (Table 4). For all
protons in these models, CEIE correlates with bond length and
bond order changes. Bond lengthening and bond order decreases
in â-glucose yield normal equilibrium isotope effects. Further,
a decrease in the orbital coefficient of the sp3 orbital donated
by the carbon atom indicates bond polarization toward the
proton, and here this parameter is seen to correlate notably well
1
with CEIE and with the observed anomeric differences in H
and 13C chemical shift. Except for H1 and H2, carbon
hybridization also correlates with isotope effect.
(62) Summing with such a low cutoff energy may lead to errors since
some values will be within the errors expected for these calculations.
However, the use of higher cutoff values led to similar results (compare
Table S1, Supporting Information).
In summing over second-order perturbation energies above
the cutoff of 0.5 kcal/mol,62 it was observed that both H1 and
H2 benefit from a significant increase in electron delocalization

1332 J. Am. Chem. Soc., Vol. 123, No. 7, 2001
Lewis and Schramm
Figure 6. Syn-diaxial repulsion and relief in glucose. The protons H3 and H5 appear syn-diaxial with the anomeric substituent in the â-gg(-)
rotamer (right) and off-center in the R-gg(-) rotamer (left). These models at RHF/6-31G** Onsager resembled those at RHF/3-21G Onsager.
slight inverse effect of 0.997 at 0° and a much larger normal
effect of 1.025 at 180°. A normal isotope effect indicates a
vibrationally looser environment for the proton than it experi-
ences where the dihedral angle is minimized to 59.9°. As
expected, these isotope effects correlate well with C-H bond
length changes as a function of dihedral angle (panel B); the
central bond decreases from 1.0850 to 1.0785 Å and the HR
and HL lengths increase from 1.0825 to 1.0865 Å at 0° and
180°, respectively. The CC-CR and CC-CL distances (panel
C) also varied with central dihedral angle, from 1.528 to 1.532
Å at 0° and 180°, respectively. The bond lengths for HR and
HL and for CC-CR and CC-CR vary quite asymmetrically but
superimpose at 0° and 180° as expected. Finally, we observe a
significant change in the HC-CC-O angle with dihedral. Figure
7D shows this correlation overlaid with the angles and dihedrals
for the protons in glucose from the two most abundant rotamers
(R-gg(-) and â-gg(-)). As the dihedral is changed from 0° to
180°, HC-CC-O becomes more acute from 110.4° to 104.5°.
A concern in this type of study is that equilibrium isotope
effects may be improperly calculated if one part of the molecule
is held at a nonequilibrium position. In the present case,
visualization of the modes consisting primarily of HC-C stretch
and HC-CC-O-HO angle libration demonstrated complete
by increasing hyperconjugative overlap. But in the region 90°
to 0°, this overlap decreases but the isotope effects become even
larger. Remarkably, this is due to relief in this region of steric
impingement of the CC-HC bond by the bulky oxygen sp-type
and p-type lone pairs. The back lobe of the sp-type lone pair
which interacts with the CH bond at 0° is much smaller than
its main lobe or either p-type lobe visualized by NBO.
Calculations on Other Model Compounds. A brief analysis
of the data in Table 5 will assist in interpreting the calculations
on glucose below. Altering the normally 109.4° tetrahedral angle
of methane to 114° affects bond polarity, carbon hybridization,
and bond length. The two protons which were moved apart,
H1 and H4 in our model, are bonded to carbon hybrid orbitals
with less p-character than the remaining protons. The greater
s-character correlates with the shorter bonds, and the C-H1
and C-H4 bonds are also more polarized toward carbon. A
conformational equilibrium isotope effect calculation here yields
unity for exchange of H1 or H4 with either of the other protons.
The unperturbed symmetrical protons HL and HR of methanol
benefit from significant hyperconjugative charge transfer from
the p-type oxygen lone pair, paralleling the behavior of C-C
bonds in 2-propanol above, and consequently have longer CH
bonds and a significant CEIE of exchange (1.046) with HC (see
Figure 3 for atom lettering). These protons make a much larger
angle with the oxygen than does HC, a change that increases
the back-lobe overlap, and their bonds are more polarized toward
the carbon atom. The carbon hybrids paired with HL and HR
have less p-character as well. Decreasing this back-lobe overlap
by fixing HR-C-O at 108° affects the moved atom only with
a 2% inverse CEIE, decreased hyperconjugation by 2 kcal/mol
and increased carbon hybrid p-character. Increasing the HR-
C-HC angle by 5° to 112° alters the carbon hybrids toward all
three protons but effects barely a 1% inverse CEIE on H5. This
calculation was made holding HC-C-O-OH and HL-C-O-
OH fixed in order to isolate H5 movement. Finally, the nitrogen
lone pair in methylamine delocalizes into the σ* orbital of C-HC
with an associated energy of 11 kcal/mol, a longer, more carbon-
polarized CH bond, an increased HC-C-N angle, and a CEIE
of 1.041 for exchange of either HL or HR in place of HC.
In cyclohexane at RHF/3-21G, an axial CH bond benefits
from transfer (4 times 3.03 kcal/mol) donative to and receptive
from each of its two antiperiplanar partners, whereas an
equatorial CH bond benefits from a donative interaction (3.56
kcal/mol) and a receptive interaction (2.08 kcal/mol) with each
decoupling with respective frequencies of 2800 and 280 cm-1
.
This evidence, coupled with the smooth variation of 2H isotope
effects and bond lengths as dihedral is varied from 0° through
a global energy minimum at 60° and finally to 180°, is sufficient
to disqualify this concern.
Electron delocalization energies and population transfers were
observed to vary with the dihedral angle (Figure 8). Panel A
shows energy stabilization due to n f σ* hyperconjugation by
the oxygen lone pairs into the antibonding orbital of HC-CC.
The contribution due to the p-type (O) lone pair is greatest at
90° and that due to the sp-type lone pair (4) is greatest at 0°
and 180° with a nadir at 90°; these are precisely as expected
due to geometric overlap of the respective lone pairs with the
HC-CC bond. The total population of the antibonding σ* orbital
(panel B) directly follows the total energy (b) shown in panel
A and takes its dominant contribution from the p-type lone pair.
The population of the σ bonding orbital of the HC-CC bond
also demonstrates angular dependence, with its maximum loss
at 180°, corresponding to maximum overlap with the σ* orbital
of an antiperiplanar O-HO bond. As the angle is changed from
180° to 90°, it is clear that the isotope effect can be explained

Equilibrium Isotope Effects in Glucose
J. Am. Chem. Soc., Vol. 123, No. 7, 2001 1333
Figure 8. Hyperconjugative effects in the HC-CC bond vary with
CC-O dihedral angle in 2-propanol: (A) delocalization energy in kcal/
mol due to overlap of the p-type oxygen lone pair (O), the sp-type
oxygen lone pair (4), and the sum of these (b) with the antibonding
σ* orbital; (B) variance of electron population in σ orbital (O) and σ*
orbital (b) with dihedral angle.
demonstrate the opposite trend for these parameters. The pure
p-type oxygen lone pair causes C-HL(R) to become more p-like
than expected to increase overlap, the hyperconjugative popula-
tion of σ* for these CH bonds lengthens them instead, and we
see that the CH bonds are less carbon-polarized where there is
more delocalization. Comparison with the sp6-hybridized ni-
trogen lone pair of methylamine illustrates that target bond
rehybridization is acutely sensitive to lone pair composition. In
this case, the difference in p-character between methyl protons
is double that in methanol, indicating that the diluted p-character
of this lone pair is not as effective in offsetting the increased
s-character of the hybrid due to linear angle increase.
Discussion
Isotope Effects at H1 and H2. The experimental equilibrium
isotope effects with glucose can be explained fully in terms of
phenomena observed in gas-phase models. A significant normal
isotope effect of 1.043 is observed at H1. Simple axial-
equatorial isotope effects are already well documented. Deu-
terium isotope effect studies in cyclohexane have reported an
observed value63 of 1.060 at -88 °C and a calculated value51
of 1.039 at the same temperature. These values translate to free
energy differences of 91 and 59 J/mol and isotope effects of
1.037 and 1.024 at 25 °C, respectively. All of these values favor
deuterium equatorially, similar to the preference in glucose. This
is consistent with previous work25 which concluded from the
∼10 Hz greater coupling constant 1JC1H1 of R-glucose in solution
that the C1-H1 bond is longer64 when axial in â-glucose than
when it is equatorial in R-glucose. However, a closer look at
the difference in structure between cyclohexane and glucose
rules out these axial-equatorial differences as dominant in the
Figure 7. C-O dihedral angle effects in gas-phase 2-propanol at RHF/
3-21G: (A) CEIE for HC (b), HR (O), and HL (4) from reference point
of 60°; (B) bond lengths for protons in (A); (C) CC-CL (O) and CC-
CR (b) bond length versus dihedral angle; (D) HC-CC-O angle (b)
also varies with dihedral angle; overlaid are R-H2 (O), â-H2 (O), R-H6
(2), â-H6 (9), and other backbone protons (b) from the glucose
models.
of two antiperiplanar CC bonds. Therefore, in cyclohexane an
axial CH bond is loosened by a net 1 kcal/mol over the
equatorial bond, consistent with the conclusions drawn previ-
ously in the same system.6,51 The same NBO analysis shows
differences in carbon hybridization for axial (sp3.20) and equato-
rial (sp3.04) bonds with corresponding bond length differences.
Several associations can be made from these models. First,
unperturbed hyperconjugation causes a much larger isotope
effect than the structural perturbations illustrated here. Second,
hyperconjugative delocalization yields the dominant effects on
electronic configuration. In methanol, the larger HL(R)-C-O
angles should be accompanied by much less p-character and
much shorter and more carbon-polarized bonds. The results
(63) Ayden, R.; Gunther, H. Angew. Chem., Int. Ed. Engl. 1981, 20,
985.
(64) Maciel, G. E.; McIver, J. W. J.; Ostlund, N. S.; Pople, J. A. J. Am.
Chem. Soc. 1970, 92, 11-18.

1334 J. Am. Chem. Soc., Vol. 123, No. 7, 2001
Lewis and Schramm
Table 5. Reflection of Distortion in Electronic Parameters of Diastereomeric Protons of Model Compoundsa
compound
H
H-C-X angleb
C hybrid.
CH length (Å)
C cont %
hyperconj. (kcal/mol)c
CEIE
CH4
1,4
2,3
HL,HR
HC
HR
HC
HL
HR
HC
114.1
108.4
112.2
107.3
108.0
107.8
112.7
110.9
106.6
111.7
114.9
109.3
sp2.89
sp3.11
sp2.83
sp2.87
sp2.89
sp2.79
sp2.76
sp2.81
sp2.75
sp2.90
sp2.91
sp3.02
1.082
1.085
1.088
1.081
1.088
1.081
1.087
1.088
1.080
1.089
1.092
1.085
61.09
60.98
59.14
60.16
59.12
60.19
59.20
59.13
60.24
59.08
59.48
60.50
n/a
1.001d
MeOH
8.4+1.8
2.3
6.8+1.8
2.2
8.8+1.4
7.5+1.9
2.2
8.6+1.5
11.21
1.50
1.046d
MeOH(HR-C-Of108°)
MeOH(HR-C-HCf112°)
CH3NH2
0.981e
1.001e
0.999e
0.993e
0.996e
1.000e
1.041d
HL
HC
HL,HR
a For models in Figure 3 calculated at RHF/6-31G**. b In methane, X ) H (the other in pair). For other models, X ) O,N. c Sums represent
p-type plus sp-type. Single values indicate p-type contribution only. d Exchange. e With respect to the same proton in MeOH.
Figure 9. Ring-oxygen lone-pair electron delocalization in glucose anomers. The anomeric effect in R-glucose (left) is the result of np f σ*
hyperconjugation to the axial anomeric hydroxyl. In â-glucose (right) the same hyperconjugative effect loosens the axial C1-H1 bond but gives
only a minor contribution to the C5-H5 bond.
latter molecule. The equatorial CH1 in R-glucose would be
expected to benefit more from its antiperiplanar relationship with
the C2-C3 and O5-C5 bonds than the CH1 in â-glucose,
which possesses only an antiperiplanar relationship with CH2.
This is confirmed in the R-sugar; the equatorial CH1 is loosened
much more by C2-C3 (donative, 3.60 kcal/mol; receptive 2.21)
and by O5-C5 (donative, 5.15; receptive, 1.59) than the axial
CH1 is loosened by CH2 (donative, 3.22; receptive, 3.89). Thus,
a tightening effect at â-H1 is due to a loss of an antiperiplanar
bond partner. However, the axial CH1 in â-glucose benefits
from interaction with the lone pairs of ring oxygen O5 (receptive
from p-type, 8.01; receptive from sp-type, 1.76). There is a
greater delocalization of the same lone pair in R-glucose (the
anomeric effect), but its target is the axial C1-O1 bond,
stabilizing the otherwise much less favorable R-sugar (Figure
9). The isotope effect at H1 is the superposition of two effects,
the unfavorable loss of antiperiplanar overlap energy in the
â-sugar combined with the favorable increased overlap with the
p-type lone pair of O5. The C1-H1 bond in â-glucose
experiences a net delocalization of 5.15 kcal/mol, consistent with
conclusions drawn previously in the same system.6,51
Our models show the gas-phase preference in R-glucose for
a torsional angle of 160° compared to 60° in â-glucose, in
agreement with past work.15 According to our calculations of
2-propanol, a 160° to 60° change would result in a normal
isotope effect at H2 of approximately 5%. This is more than
sufficient to account for our measured isotope effect of 2.7%,
and the discrepancy leaves room both for level-of-theory
dependency and for incomplete rotational restriction in solution,
which would tend to dilute a larger effect toward unity. These
results strongly imply that in solution the 2-hydroxyl of each
anomer at least partially prefers a different angle. The correlation
of linear angle and torsional angle for H2 protons with those in
2-propanol (Figure 7D) implies further that the same mechanism
is at work.
Isotope Effects at H3 and H5. Scaling the 2-propanol
calculations to match the CEIE at H2 results in an inverse
contribution of approximately 1.3% to the experimental isotope
effects at H1 and H3. Each of these isotope effects would then
result from a combination of the effect secondary to the
2-hydroxyl torsional change and a larger normal contribution
due to some other effect. While both sites experience significant
isotope effects, neither C3-O3 nor C5-O5 torsional angles
undergo any real change in geometry between the anomeric
ensembles, and the anomeric difference in hyperconjugative
energies experienced by the respective bonds are an order of
magnitude smaller than those for H1 and H2. Although our
calculations on geometry perturbations of hyperconjugated
protons in methanol showed that a 5° H-C-O angle increase
can yield a 2% isotope effect, neither H3 nor H5 in R-glucose
appears to move in this most sensitive direction. The H-C-
C(O) angles for these protons remain very similar between
anomers. Instead we propose that these isotope effects result
from hindered angle bending motions by the axial O2 in
R-glucose. In this anomer, both protons are within the minimum
O-H van der Waals radius of 2.72 Å. In the â-anomer, H1
instead is syn-diaxial with H3 and H5 and all three protons are
Stereochemically, CH2 shares an antiperiplanar relationship
with different partners in R- and â-glucose and consequently
experiences different hyperconjugative energies in the two
anomers. In R-glucose, CH2 is loosened by C1-O1 (donative,
4.89; receptive, 1.51) whereas in the â-sugar, CH2 is loosened
by CH1 (donative, 3.89; receptive, 3.22). These energies predict
a slight (0.71 kcal/mol) net effect to loosen the CH1 bond in
the â-sugar, but the majority of the isotope effect arises from
the difference in orientation of OH2. In the â-sugar, there is
significant donation from the lone pairs of O2 (p-type, 6.84;
sp-type, 3.16) into σ*-C2-H2. The same bond in the R-sugar
interacts only with the O2-OH2 bond (donative, 3.82; receptive,
3.37). Hence another 3 kcal/mol comes from this difference in
hydroxyl orientation, leaving the CH2 bond in â-glucose with
a net loosening interaction of about 4 kcal/mol.

Equilibrium Isotope Effects in Glucose
J. Am. Chem. Soc., Vol. 123, No. 7, 2001 1335
outside the H-H van der Waals radius of 2.40 Å. Deuterium
atoms favor the more vibrationally restricted conformation,44,45,65
since deuterium atoms are effectively smaller than protons in
CH bonds.50
also, possibly including some changes in angle preference. We
favor the latter interpretation of those authors’ results as
indicative merely of angle preferences and make note that neither
our data nor our theoretical models comment on the presence
of intramolecular hydgrogen bonds in aqueous solution. Even
whether they may be more important for one of the anomers
cannot be established from the present results.
Solvation. In their simulations, Molteni and Parrinello42 found
there to be a tighter hydration shell around the anomeric
hydroxyl for the R-sugar in solution. This shell would neces-
sarily be accompanied by tighter hydrogen bonds. Gawlita et
al.68 have shown in 2-propanol that the R-proton is highly
sensitive to hydrogen bond strength, benefiting from an increase
in σ* population when the oxygen atom more strongly shares
its proton with another heteroatom. This effect can be balanced
to unity by a counteracting H-bond reception. However, as the
precise lattice structure of H2O around either anomer is
unknown, it is not possible to tell at this time whether to expect
H-bond donative or receptive interactions to be favored by
hydration shell tightening.
The hyperconjugative advantage in â-glucose comes from
increased antiperiplanar overlap in its less-strained structure;
the increased planarity of H5-C5-O5 sp-type and H3-C3-
C2-H2 in â-glucose is slightly offset by decreased planarity
of 1° between each pair and C4-H4. This different combination
of effects at H3 and H5 could account for the different isotope
effects. The latter hyperconjugative effects would also contribute
in the correct direction to the bond polarity changes seen at
these protons but are insufficient on their own to be the sole
cause of the observed isotope effects. It is also interesting to
note that hyperconjugation plays no larger a role at C5 than at
C3. It is expected that the p-type lone pair of O5 would have a
higher reduction potential since it does not participate in the
anomeric effect, and therefore it would tend to delocalize more
into the antibonding orbital σ* of C5-H5. Instead, as mentioned
above, the increased hyperconjugation at H5 in the â-anomer
is probably mostly geometrically driven.
Isotope Effects at H6. The magnetic nonequivalence of the
methylene protons observed by Nishida in glucose mirrors
similar results in aqueous and DMSO solutions of nucleosides66
and clearly implies some restricted motion about the C5-C6
or C6-O6 bonds. That this nonequivalence is mainly preserved
between anomers implies that there is no anomeric effect on
this rotational restriction. The latter statement is consistent with
our findings of no overall anomeric isotope effect at C6.
However, the more telling experiment here involves measuring
the anomeric isotope effect of the stereospecifically labeled
compounds; as Nishida reports, there is some change in chemical
shift for each proton between anomers. Whether this would
translate into an observable isotope effect outside the error range
of our measurements remains a question.
γ-Substituent Effect. Finally, is it possible that the γ-sub-
stituent effect69-71 may contribute to the isotope effect and
chemical shift change at both C3 and C5? Chemical shift studies
in substituted cyclohexanes, dioxanes, and steroids have shown
that a γ-anti electronegative atom will cause an upfield or more
shielded 13C shift71-74 unless the carbon serves as a bridgehead
atom, where the trend is reversed.71 A γ-gauche electronegative
substituent will cause a downfield shift.72 The axial 1-hydroxyl
of R-glucose is gauche to both C3 and C5, while the equatorial
hydroxyl is γ-anti in the â-anomer. Since the change from
R-glucose to â-glucose is equivalent to a change from γ-gauche
to γ-anti, the chemical shift of C3 and C5 would be expected
to move upfield. Instead, we observe a downfield shift in
1
â-glucose. Furthermore, H and 13C shifts vary together with
increasing electronegativity of the γ-anti atom,74 whereas in
â-glucose C3 and C5 are less shielded while the corresponding
protons H3 and H5 are more shielded. Thus, we conclude that
the classic γ-substituent effect plays no role in glucose.
Bond Polarizations and Chemical Shifts. Previous studies
have demonstrated significant lone-pair geometry effects on
vicinal C-H bond lengths and strengths.2,3,5,7,47 We propose
that the shielding differences observed in the NMR studies are
due to a hyperconjugative cause at CH1 and CH2 but not CH3
or CH5. For the latter protons, we suggest that the increased
polarity toward carbon in the R-anomer is the result of electronic
repulsion by the electron-rich axial oxygen.
Curiously, the gg(-) models which we have presented in this
report demonstrate the opposite difference in chemical shift to
that observed by Nishida. Since greater carbon atom p-orbital
character corresponds to longer bonds and greater shielding and
more H-polarized CH bonds also correspond to greater proton
shielding, we would expect the 6-proS proton to shift at a higher
field than the 6-proR proton, contrary to Nishida’s findings.
While these trends are reverse in gt(-) models (for structures
see Supplemental Listing 1), this should be insufficient to
account for the discrepancy because Nishida finds the gg
rotamers to dominate by 10%.
Intramolecular Hydrogen Bonds. At this point we wish to
distinguish that intramolecular hydrogen bonds are not a
prerequisite to preferred hydroxyl angles in solution. The role
of intramolecular hydrogen bonds in aqueous solutions has been
debated. Dais and Perlin67 concluded that the terminal hydroxyls
of D-fructose in D2O are more intramolecularly hydrogen bonded
in the R-furanose form than in either the â-furanose or
â-pyranose forms, indicating that some conformers show
intramolecular hydrogen bonding even in aqueous solutions,
but Molteni and Parrinello42 report finding no evidence of
intramolecular bonding in their MD study of aqueous glucose.
Simmerling et al.43 observe in their molecular dynamics studies
the existence of preferred hydroxyl torsional angles in solution
for the R-anomer of glucose. While those authors do not present
data for the â-anomer, we would expect similar results here
Summary. A summary of the anomeric equilibrium effects
is given in Table 6. Excluding the <1 kcal/mol anomeric
difference in the antiperiplanar partner, the only effect experi-
enced at H2 is the preferential orientation of OH2 at 60° in
â-glucose and 160° in R-glucose. Scaling our results in
2-propanol to fit the experimental isotope effect of 1.027 implies
the impact of this effect on both H1 and H3 to be 0.987.
(68) Gawlita, E.; Lantz, M.; Paneth, P.; Bell, A.; Tonge, P.; Anderson,
V. J. Am. Chem. Soc. 2000, 122, 11660-11669.
(69) Grutzner, J. B.; Jautelat, M.; Dence, J. B.; Smith, R. A.; Roberts, J.
D. J. Am. Chem. Soc. 1970, 92, 7107-20.
(70) Rao, V. S.; Perlin, A. S. Carbohyd. Res. 1981, 22, 141-8.
(71) Forrest, T. P.; Webb, J. G. K. Org. Magn. Reson. 1979, 12, 371-
5.
(72) Lambert, J. B.; Vagenas, A. R. Org. Magn. Reson. 1981, 17, 270-
7.
(73) Eliel, E. L.; Bailey, W. F.; Kopp, L. D.; Willer, R. L.; Grant, D.
M.; Bertrand, R.; Christensen, K. A.; Dalling, D. K.; Duch, M. W.; Wenkert,
E.; Schell, F. M.; Cochran, D. W. J. Am. Chem. Soc. 1975, 97, 322-30.
(74) Wiberg, K. B.; Barth, D. E.; Pratt, W. E. J. Am. Chem. Soc. 1977,
99, 4286-9.
(65) Bartell, L. S. J.Am. Chem. Soc. 1961, 83, 3567-71.
(66) Hruska, F. E.; Wood, D. J.; McCaig, T. N.; Smith, A. A.; Holy, H.
Can. J. Chem. 1974, 52, 497-508.
(67) Dais, P.; Perlin, A. S. Carbohyd. Res. 1987, 169, 159-169.

1336 J. Am. Chem. Soc., Vol. 123, No. 7, 2001
Lewis and Schramm
Table 6. Summary of Contributors to Isotope Effects in Glucose
phenomenon and effect
anomeric
effect
hydroxyl
freezing
steric
repulsion
solvation
difference
γ-subst.
effect
CH2
restriction
H
antiperiplanar
total
1
2
3
4
5
6
1.100
0.987
1.027
0.987
0.961
1.000
1.010
?
?
1.043
1.027
1.022
1.000
1.035
1.000
1.025
1.025
1.000
1.000
1.010
1.000
Assuming that these phenomena combine as products in isotope
effects, the intrinsic isotope effect at H1 due to a combination
of a normal isotope effect caused by overlap with the p-type
lone pair of O5 and an inverse isotope effect due to loss in
antiperiplanar partners would have to be 1.057. On the basis of
the NBO analysis and the isotope effect at H2, estimating the
isotope effect per kcal/mol at 1% would give a 10% normal
isotope effect at H1 due to the 10 kcal/mol advantage of p-type
lone pair overlap and an inverse 3.9% effect due to the loss in
antiperiplanar partner for that bond. A roughly 3.5% combined
isotope effect due to steric restriction of angle bending modes
and minor electron delocalization at H3 and H5 would be
required to give approximately the correct results at these
positions. We estimate the antiperiplanar hyperconjugation at
approximately 10% of the anomeric effect due to our NBO
analysis of the glucose anomers, leaving an isotope effect of
1.025 due to the steric repulsion of the axial 1-hydroxyl in
R-glucose. The γ-substituent effect plays no role at H3 and H5,
but a difference in solvation is certainly very likely to have
some effect nearest the anomeric center. While the magnetic
nonequivalence of the H6-proR and H6-proS methylene protons
implies restricted motion and intramolecular interactions, these
are apparently unchanged by anomeric configuration and do not
give an observed isotope effect. We do not rule out solvation
difference as a possible contributor. It seems most likely to play
a role at OH1 and OH2, but presently the magnitude or direction
of its contribution has not been assessed.
Other Isotope Effect Studies. The equilibrium isotope effects
with glucose are necessary to interpret enzymatic kinetic isotope
effects in terms of modeling transition state structure and for
studies of equilibrium isotope effects in enzyme-ligand binding
equilibria. Our demonstration of significant anomeric equilib-
rium isotope effects raises the possibility that solution conform-
ers which do not undergo chemical transformation during
reaction studies or do not participate in binding reactions may
seriously bias observed isotope effects. This is of particular
concern in studies of secondary 3H-kinetic isotope effects since
the anomeric effects observed here are similar in magnitude to
those expected in kinetic studies. Tritium binding isotope effect
studies may be similarly affected, as they depend on the
magnitude of the equilibrium isotope effect, the equilibrium
constant itself, and the relative binding affinities of the various
solution conformers. The values reported here permit investiga-
tors to provide corrections for equilibrium deuterium or tritium
isotope effects on glucose interactions with proteins.
Conclusion
We have found significant conformational equilibrium isotope
effects on the anomeric equilibrium constant for glucose in
aqueous solution. The results provide correction factors for the
use of isotope effects to probe transition states and enzyme-
ligand binding reactions. We have also been able to draw from
the gas-phase calculations some conclusions about the energetics
and conformations of glucose and the interplay of phenomena
underlying conformational equilibrium isotope effects. Four of
seven protons experience a less vibrationally constrained
environment in â-glucose; two of these, H1 and H2, may be
explained in hyperconjugative terms and two, H3 and H5,
require some combination of steric repulsion and hyperconju-
gation. We consider the application of natural bond orbital
analysis to a whole-molecule isotope effect study to be a
significant advance toward understanding the forces which
determine molecular structure.
Acknowledgment. We would like to express thanks to Drs.
Sean Cahill and Mark Girvin for their important assistance with
practical aspects of the 13C NMR studies and Dr. Frank
Weinhold for advice regarding NBO analysis.
Supporting Information Available: Natural bond orbital
analysis of electron delocalization with a cutoff value of 0.9
kcal/mol, fractionation factors and calculations of ensemble
isotope effects, and the geometries of minimized glucose models.
This material is available free of charge via the Internet at
http://pubs.acs.org.
JA003291K