1. Study of hydrogen bonding in dihydroxyacetone
and glyceraldehyde using computational methods
S. Jalili *, H. Aghdastinat
Department of Chemistry, K. N. Toosi University of Technology, 322 West Mirdamad, P.O. Box 15875-4416, Tehran, Iran
Received 6 October 2007; received in revised form 12 January 2008; accepted 21 January 2008
Available online 2 February 2008
Abstract
The intramolecular hydrogen bonding in different conformers of dihydroxyacetone (DHA) and its isomer, glyceraldehyde (Gald) was
investigated using Density Functional Theory (DFT), second-order Møller–Plesset (MP2) method and ‘‘Atoms in Molecules” (AIM)
theory. The effect of intramolecular hydrogen bonding on the relative stability of conformers was studied. It was found that the stability
of different conformers depends on the size of the ring in which hydrogen bond is formed and the hybridization of the oxygen atom of
acceptor. The AIM analysis showed that some of the considered interactions are not real hydrogen bonds and therefore, there is no coop-
erativity in the considered conformers.
Ó 2008 Elsevier B.V. All rights reserved.
Keywords: Hydrogen bonding; Carbohydrate chemistry; Dihydroxyacetone; Cooperativity; Atoms in Molecules theory
1. Introduction
Carbohydrates are an important group of biological
molecules that have a large number of polar hydroxyl
groups which can form intramolecular hydrogen bonds
with each other and with carbonyl oxygen. These intramo-
lecular hydrogen bonds have a significant role in various
biological processes, such as the formation of condensed
phases, and the binding of carbohydrates by proteins in
biological events, like molecular recognition [1].
The strength of a hydrogen bond depends on the nature
of donor and acceptor groups such as electronegativity, net
atomic charge and chelate formation. Understanding the
electronic nature of hydrogen bonds is more difficult than
covalent and ionic bonds or Van der Waals forces. This
is because the term ‘‘hydrogen bonding” applies to a wide
range of interactions. Very strong hydrogen bonds resem-
ble covalent bonds, while very weak hydrogen bonds are
close to Van der Waals forces and the majority of hydrogen
bonds are distributed between these two extremes.
In this work, we have studied the intramolecular hydro-
gen bonding in different conformers of dihydroxyacetone,
and D-glyceraldehyde (Fig. 1). These trioses are formed
from the enzymatic breakdown of fructose 1-phosphate
and are very important in carbohydrate metabolism [2].
Dihydroxyacetone (DHA, 1) is a three-carbon achiral
ketose and provides the basis for the synthesis of other
monosaccharides, including glucose and fructose. D-Glyc-
eraldehyde (Gald, 2), which is an isomer of DHA is the
simplest aldose with a chiral center. The knowledge about
structures of DHA and Gald and their preferred conform-
ers is central for investigation of physical and chemical
properties of carbohydrates.
DHA and Gald have multiple hydrogen bonds in their
conformations. Experimental and theoretical studies show
that the most stable conformation of DHA is a bicyclic
structure in which two hydrogen bonds are formed between
OH groups and carbonyl oxygen [2–4]. In a study of DHA
and Gald using DFT and MP2 methods [5], it has been
shown that the stability of conformations depends on both
the ring size and hybridization of the acceptor atom
involved. They used geometrical and energetic criteria for
the existence of hydrogen bonds.
0166-1280/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.theochem.2008.01.026
*
Corresponding author. Tel.: +98 21 22853649; fax: +98 21 22853650.
E-mail address: sjalili@kntu.ac.ir (S. Jalili).
www.elsevier.com/locate/theochem
Journal of Molecular Structure: THEOCHEM 857 (2008) 7–12

2. Formation of intramolecular hydrogen bonds is an
important factor in the relative stability of conformers.
However, there is no general rule which help us to conclude
that a hydrogen bond really exists. There are a number of
geometrical criteria for the existence and stability of hydro-
gen bonds [6], but they are not so reliable, especially in the
case of weaker intramolecular hydrogen bonds. In 1995,
Popelier [7] showed in a study of CAHÁ Á ÁO hydrogen
bonds that the AIM theory of Bader [8] can be used to
characterize hydrogen bonds using a number of concerted
effects in the electron density. Since then, these AIM-based
criteria have been extensively used in the study of various
types of hydrogen bonds, including intramolecular [9] or
bifurcated [10] hydrogen bonds and intermolecular proton
transfer reactions [11,12]. In this paper, we have used these
effects to study hydrogen bonding in the considered model
systems.
2. Computational details
Ab initio calculations were carried out with the GAUSS-
IAN 03 program [13] and AIM analysis was performed
using AIM 2000 software [14]. The lowest energy confor-
mations of DHA and Gald were obtained using a potential
energy surface scan for rotation around single bonds. Sep-
arate conformers were distinguishable by unique values for
the dipole moments.
Four minimum-energy conformers were obtained for
each compound and their structures are shown in Fig. 2.
The geometries of these conformers were fully optimized
using the B3LYP/6-31++G(d,p) and MP2/6-31++G(d,p)
levels of theory. The frequency calculations were carried
out at same level of theory to characterize stationary struc-
tures and to include the zero point energy (ZPE) correc-
tions. ZPEs were scaled using suitable factors (0.9806 in
B3LYP method and 0.9814 in MP2 method). Single point
energy calculations were performed using the aug-cc-pVTZ
basis set. The wave functions required for AIM analysis
were obtained at the B3LYP/6-31++G(d,p) level of theory.
3. Results and discussion
3.1. Geometry and energy
Selected optimized parameters for DHA and Gald con-
formers are given in Tables 1 and 2, respectively. Depend-
ing on the orientation of hydroxyl groups, various
conformers may have different number of hydrogen bonds.
In 1a, the hydroxyl hydrogens are in a suitable position for
hydrogen bond formation with carbonyl oxygen. Two
intramolecular hydrogen bonds can form and as a result,
atoms are arranged in two five-membered rings. This is a
bifurcated hydrogen bond in which the carbonyl oxygen
is the common acceptor in two hydrogen bonds. The C4,
O8, H10, and H12 atoms are all in the same plane. As
shown in Table 1, this molecule is symmetric, and the
OAH, OÁ Á ÁH, and OÁ Á ÁO distances in two sides are exactly
equal. The OÁ Á ÁH and OÁ Á ÁO distances for two hydrogen
bonds are in the range corresponding to relatively strong
hydrogen bonds [15].
In 1b conformer of DHA, one of the hydroxyl hydro-
gens is outside rotated by 180° and can not form hydrogen
bond. Only one hydrogen bond and one ring are formed.
The O9AH10 bond length which participates in hydrogen
bonding is larger than O11AH12 length. This increase is
the result of charge transfer from acceptor orbitals to the
r* orbital of donor group [10]. The O9AH10, O8Á Á ÁH10,
and O8Á Á ÁO9 distances and the O8Á Á ÁH10AO9 angle are
relatively equal in 1a and 1b. This suggests that bifurcation
has not affected the hydrogen bond strength.
The 1c conformer has no opportunity for hydrogen
bond formation, because both of hydroxyl groups are out-
side rotated. This molecule is symmetric like 1a and its
Fig. 2. Different conformers of DHA (1a–1d) and Gald (2a–2d).
C
O
H2CHO CH2 OH CH CH CH2 OH
1 2O
OH
Fig. 1. The chemical structure of DHA (1) and Gald (2).
8 S. Jalili, H. Aghdastinat / Journal of Molecular Structure: THEOCHEM 857 (2008) 7–12

3. OAH bonds length are equal to (free) O11AH12 length in
1b.
Finally, in 1d, the molecule is rotated, such that the car-
bonyl group is out of access of hydroxyl groups. In this
molecule, two hydroxyl groups are arranged in a nonplanar
six-membered ring and form a hydrogen bond of the type
OAHÁ Á ÁOAH. The OÁ Á ÁH distance in 1d is less than 1a
and 1b and the OAHÁ Á ÁO angle is larger. Therefore, we
can conclude that this hydrogen bond is stronger than
OAHÁ Á ÁO@C hydrogen bond in 1a and 1b. The C@O bond
length is equal in 1c and 1d and increases from 1c to 1b to
1a, which is a result of the formation of zero, one and two
hydrogen bonds, respectively. The amount of increase for
C@O is smaller than OAH, because unlike the OAH bond,
C@O is a hydrogen bond acceptor.
The stability of DHA conformers is as 1a > 1d > 1b > 1c
(Table 3). It is clear that the hydrogen-bonded molecules
are more stable than 1c, which has no hydrogen bonds.
The most stable conformer is 1a with two hydrogen bonds.
1d and 1b conformers with one hydrogen bond are in next
positions. 1d is somewhat more stable than 1b, because it
has a stronger hydrogen bond, as concluded from their
geometries. The six-membered ring in 1d has lower strain
than five-membered ring of 1b. Moreover, the basicity of
acceptor atom in 1d (hydroxyl oxygen with sp3
hybrid) is
more than 1b (carbonyl oxygen, sp2
hybrid). Because of
these two factors, the hydrogen bond in 1d is stronger than
hydrogen bond in 1b. The values of dipole moments
increase stability decreasing.
Comparison of DFT and MP2 results show that the
MP2 values for geometrical parameters and dipole
moments are larger than DFT values and the MP2 energies
are less negative. The trends have not changed with the
change of calculation method and similar results are
obtained from two methods. This result is in agreement
with the previous studies on these systems [5].
Four conformers were considered for glyceraldehyde. In
2a, O8AH9 bond is oriented to carbonyl group side and is
capable to form an intramolecular hydrogen bond in a five-
membered ring. Moreover, the second hydroxyl group is in
a position close to O8AH9 bond and may form a hydrogen
bond of the type OAHÁ Á ÁOAH in a five-membered ring
arrangement. Such system of multiple hydrogen bonds that
forms the network A*AH* ? AAH ? B may be coopera-
tive [16], as predicted in other studies of glyceraldehyde [5].
Both OAH bonds are lengthened relative to free OAH (in
Table 1
Optimized parameters (angstroms and degrees) for dihydroxyacetone conformers
Parameter 1a 1b 1c 1d
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2
O9AH10 0.973 0.971 0.974 0.973 0.965 0.965 0.965 0.966
O11AH12 0.973 0.971 0.965 0.966 0.965 0.965 0.970 0.968
C4@O8 1.223 1.232 1.215 1.226 1.208 1.220 1.217 1.223
O8Á Á ÁH10 2.099 2.144 2.077 2.099 – – – –
O8Á Á ÁH12 2.099 2.144 – – – – – –
O8Á Á ÁO9 2.675 2.694 2.664 2.677 – – – –
O8Á Á ÁO11 2.675 2.694 – – – – – –
O9Á Á ÁH12 – – – – – – 2.046 2.062
O9Á Á ÁO11 – – – – – – 2.760 2.757
O8Á Á ÁH12AO11 116.19 114.39 – – – – – –
O8Á Á ÁH10AO9 116.20 114.40 116.91 116.45 – – – –
O9Á Á ÁH12AO11 – – – – – – 128.83 127.01
Table 2
Optimized parameters (angstroms and degrees) for glyceraldehyde conformers
Parameter 2a 2b 2c 2d
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2
O8AH9 0.974 0.974 0.973 0.973 0.968 0.970 0.966 0.970
O10AH11 0.969 0.969 0.965 0.965 0.965 0.966 0.971 0.966
C1@O12 1.216 1.229 1.215 1.228 1.208 1.222 1.216 1.229
O12Á Á ÁH9 2.107 2.087 2.101 2.086 – – – –
O8Á Á ÁO12 2.681 2.678 2.683 2.681 – – – –
O8Á Á ÁH11 2.390 2.329 – – – – – –
O8Á Á ÁO10 2.813 2.781 – – 2.788 2.767 – –
O10Á Á ÁH9 – – – – 2.320 2.283 – –
O12Á Á ÁH11 – – – – – – 2.165 2.166
O10Á Á ÁO12 – – – – – – 2.883 2.876
O12Á Á ÁH9AO8 116.33 117.40 116.71 117.77 – – – –
O8Á Á ÁH11AO10 105.83 107.62 – – – – – –
O10Á Á ÁH9AO8 – – – – 108.85 109.86 – –
O12Á Á ÁH11AO10 – – – – – – 129.68 128.93
S. Jalili, H. Aghdastinat / Journal of Molecular Structure: THEOCHEM 857 (2008) 7–12 9

4. 1c or 2b), but the amount of increase is larger for O8AH9
bond. The hydrogen bond distance is smaller for O9Á Á ÁH12
than for O8Á Á ÁH11 hydrogen bond. The hydrogen bond
angle is also larger in the O9Á Á ÁH12. Therefore, we can con-
clude that the OAHÁ Á ÁO@C hydrogen bond is stronger
than OAHÁ Á ÁOAH hydrogen bond in 2a. The reason is
that in the second hydrogen bond the acceptor has sp3
hybrid but forms a five-membered ring. This arrangement
is not favorable [5], because the tetrahedral atoms can
not minimize their strain in a five-membered ring.
In 2b, only one hydroxyl group is in a suitable position
for hydrogen bond formation. A hydrogen bond of the
type OAHÁ Á ÁO@C is formed, which is a part of a five-mem-
bered ring. The O8AH9, C@O, and H9Á Á ÁO12 distances
and the value of O8AH9Á Á ÁO12 angle are equal in 2a and
2b. This is incompatible with a cooperative interaction
for 2a.
In 2c, two hydroxyl groups are close to each other and
can form an OAHÁ Á ÁOAH hydrogen bond in a five-mem-
bered ring, but like in 2a, this interaction is not so strong.
However, the values of OÁ Á ÁH distance and OAHÁ Á ÁO
angle show that this interaction is somewhat stronger than
the interaction in 2a. This evidence is also against the coop-
erativity in 2a, because we expect that the cooperativity
leads to an enhanced interaction in 2a.
The 2d conformer has only one possibility for hydrogen
bond formation. This is an OAHÁ Á ÁO@C hydrogen bond
which forms a nonplanar six-membered ring. The
H11Á Á ÁO12 distance in 2d is larger than the H9Á Á ÁO12 dis-
tance in 2b, but the OAHÁ Á ÁO angle is larger in this case. So
we can not compare the strength of these hydrogen bonds
based on geometrical data. The O8AH9 bond length is
consistent with a hydrogen bond-free hydroxyl group.
The C@O length is like 2a and 2b, but larger than 2c.
The energy values for Gald conformers are given in
Table 4. According to these data, the most stable con-
former is 2a which has two interactions. The next stable
conformers are 2d, 2b, and 2c. The fact that 2d is more sta-
ble than 2b shows that probably the ring size is a more
important factor in the stability of hydrogen bonds than
the hybridization. Based on MP2 energies however, the
order of 2d and 2b changes, which is in agreement with
the hypothesis that a hydrogen bond with sp2
-hybridized
acceptor atom is more stable in a five-membered ring
arrangement.
In general, each keto conformer is more stable than its
corresponding enol tautomer. The CH2OH group in the
vicinity of carbonyl group of DHA is an electron donor
and increases the basicity of carbonyl oxygen. The only
exception is for 1c and 2c, possibly because there is no
intramolecular interaction in 1c.
The loss of cooperativity on the basis of geometrical and
energetic data raises a question about the nature of interac-
tions in 2a and 2c. On the next section we will answer this
question using the AIM theory.
3.2. AIM analysis
Bader’s AIM theory helps us to investigate hydrogen-
bonded systems using the properties of electron density
q(r). The diagonalization of the Hessian matrix of q(r)
yields to three eigenvalues k1, k2, and k3. Two important
properties are calculated from these eigenvalues: the Lapla-
cian of electron density, k1 + k2 + k3 = $2
q(r) and the ellip-
ticity, e = (k1/k2) À 1. The ellipticity describes the
symmetry of the electron density distribution along the
bond path. It is found that closed-shell interactions such
as ionic bonds, hydrogen bonds and Van der Waals’ inter-
actions should have a positive $2
q and a relatively small
value of q.
Eight concerted effects within the AIM formalism have
been considered as the suitable criteria for hydrogen bond-
ing [7]. The first three of them are: (1) the existence of a
bond path, containing a bond critical point (BCP) between
the donor hydrogen atom and the acceptor, (2) the value of
density q(r) at the BCP, and (3) the value of the Laplacian
Table 3
Energy values for DHA conformers
Conformer Absolute energy (a.u.) Relative energy (kcal/mol) Dipole moment (D)
B3LYP MP2 B3LYP MP2 B3LYP MP2
1a À343.62862 À342.93465 0.00 0.00 1.87 2.20
1b À343.62061 À342.92711 5.03 4.73 4.58 5.01
1c À343.61113 À342.91783 10.98 10.56 5.84 6.50
1d À343.62088 À342.92734 4.86 4.59 3.67 3.90
Table 4
Energy values for Gald conformers.
Conformer Absolute energy (a.u.) Relative energy (kcal/mol) Dipole moment (D)
B3LYP MP2 B3LYP MP2 B3LYP MP2
2a À343.62086 À342.93465 0.0 0.0 1.51 1.96
2b À343.61648 À342.92711 2.75 4.73 3.05 3.53
2c À343.61295 À342.91783 4.96 10.56 4.78 5.30
2d À343.61683 À342.92576 2.53 5.58 2.75 3.22
10 S. Jalili, H. Aghdastinat / Journal of Molecular Structure: THEOCHEM 857 (2008) 7–12

5. ($2
q) of the density at the BCP. These three criteria
together with ellipticity and distance to a ring critical point
(RCP) will be referred to as ‘‘BCP” criteria.
Molecular graphs for DHA and Gald conformers are
depicted in Fig. 3. The bond paths are shown along with
BCPs and RCPs. It is clear that all the predicted hydrogen
bonds for DHA conformers are obtained from AIM anal-
ysis. 1a has two hydrogen bonds, characterized with two
critical points between O8Á Á ÁH10 and O8Á Á ÁH12 atoms.
Two RCPs are observed for two five-membered rings. In
2b, only one hydrogen bond is formed. 1c does not have
any hydrogen bond and 1d has a six-membered ring
formed by OAHÁ Á ÁOAH hydrogen bond.
The situation is different for Gald conformers. We can
see that only OAHÁ Á ÁO@C hydrogen bonds are predicted
from AIM theory and there is no OAHÁ Á ÁOAH hydrogen
bond in 2a or 2c. The interaction between hydroxyl groups,
although changes the geometry of the molecule to some
extent does not fulfill the requirements of a ‘‘hydrogen
bonding” interaction. The reason is probably that the ori-
entation of acceptor orbitals does not facilitate hydrogen
bond formation in a five-membered ring. Therefore, there
is no additional hydrogen bond and no cooperativity in
2a, in spite of previous findings based on geometrical crite-
ria [5].
The critical point properties for various covalent and
hydrogen bonds in DHA and Gald conformers are given
in Tables 5 and 6, respectively. The charge density (q)
and the Laplacian of charge density ($2
q) at hydrogen
BCPs are all in the proposed range of 0.002–0.034 a.u.
and 0.024–0.139 a.u., respectively [7]. The charge density
at BCP for hydrogen bonds is an order of magnitude smal-
ler than for the corresponding covalent bonds. The Lapla-
cian of charge density, $2
q is positive for H-bonds, in
contrast to covalent bonds.
We can compare the strength of hydrogen bonds based
on a number of criteria [10]. One criterion is related to
ellipticity. Larger ellipticity corresponds to a weaker inter-
action. Table 5 shows that for 1a, all properties are equal
for two hydrogen bonds and the molecule is symmetric.
For 1d, the ellipticity of O9Á Á ÁH12 BCP is one order of
magnitude smaller than the O8Á Á ÁH12 ellipticity in 1a and
1b. Therefore, the hydrogen bond in 1d is stronger than
in 1a and 1b, as predicted from geometric data. For Gald,
the ellipticity of H11Á Á ÁO12 hydrogen bond in 2d is much
smaller than the H9Á Á ÁO12 ellipticity in 2a and 2b. There-
Fig. 3. Molecular graphs of DHA and Gald conformers showing all BCP and RCP.
Table 5
Critical point properties for DHA conformers
Interaction q $2
q k1 k2 k3 e
1a O9AH10 0.3553 À2.041 À1.8193 À1.7708 1.5496 0.0274
O11AH12 0.3553 À2.041 À1.8193 À1.7708 1.5496 0.0274
O8Á Á ÁH10 0.0219 0.0856 À0.0251 À0.0144 0.1251 0.7315
O8Á Á ÁH12 0.0219 0.0856 À0.0251 À0.0144 0.1251 0.7315
1b O9AH10 0.3539 À2.029 À1.8105 À1.7626 1.5476 0.0271
O11AH12 0.3654 À2.074 À1.8347 À1.7871 1.5480 0.0266
O8Á Á ÁH10 0.0230 0.0870 À0.0269 À0.0171 0.1311 0.5675
1c O9AH10 0.3659 À2.073 À1.8340 À1.7861 1.5468 0.0267
O11AH12 0.3659 À2.073 À1.8338 À1.7861 1.5468 0.0267
1d O9AH10 0.3638 À2.080 À1.8429 À1.7964 1.5590 0.0259
O11AH12 0.3601 À2.084 À1.8514 À1.8053 1.5724 0.0255
O9Á Á ÁH12 0.0225 0.0724 À0.0267 À0.0259 0.1251 0.0327
S. Jalili, H. Aghdastinat / Journal of Molecular Structure: THEOCHEM 857 (2008) 7–12 11

6. fore, this hydrogen bond is stronger, the result obtained
from B3LYP energies, but violated based on MP2 energies.
The second criterion is distance of a BCP from the clos-
est RCP. Fig. 3 shows that this distance is larger for 1d and
2d. Thus, these hydrogen bonds are stronger than the
hydrogen bonds in other conformers. From the above-
mentioned criteria, we can conclude that 1d has a stronger
hydrogen bond than 2d.
In summary, the results of geometry, energy, and AIM
calculations show that the first factor that influences the
strength of a hydrogen bond is ring size. Six-membered
rings are more stable than five-membered rings. The other
important factor is the hybridization of acceptor atom. The
basicity of a sp3
-hybridized atom is more than a sp2
-
hybridized one, leading to a better interaction.
4. Conclusion
The quantum mechanical calculations showed that
hydrogen bonding is an important factor in the relative
stability of carbohydrate conformers. The strength of a
hydrogen bond depends on size of the ring formed as a
result of hydrogen bonding, and the hybridization of the
acceptor atom and the first factor is shown to be more
important than the second. AIM analysis of model systems
rejected some of the considered hydrogen bonds based on
geometrical parameters. These interactions, although have
some effects on the structure of molecules cannot be classi-
fied as hydrogen bonds.
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Table 6
Critical point properties for Gald conformers
Interaction q $2
q k1 k2 k3 e
2a O8AH9 0.3535 À2.0339 À1.8141 À1.7680 1.5482 0.0260
O10AH11 0.3615 À2.0703 À1.8333 À1.7871 1.5501 0.0258
O12Á Á ÁH9 0.0217 0.0853 À0.0248 0.0140 0.1242 0.7394
2b O8AH9 0.3553 À2.0331 À1.8119 À1.7645 1.5433 0.0268
O10AH11 0.3658 À2.0768 À1.8394 À1.7896 1.5522 0.0277
O12Á Á ÁH9 0.0267 0.0858 À0.0250 À0.0141 0.1250 0.7725
2c O8AH9 0.3612 À2.0735 À1.8360 À1.7907 1.5532 0.0252
O10AH11 0.3646 À2.0779 À1.8398 À1.7927 1.5546 0.0262
2d O8AH9 0.3646 À2.0731 À1.8355 À1.7894 1.5518 0.0257
O10AH11 0.3592 À2.0779 À1.8438 À1.7989 1.5649 0.0249
O12Á Á ÁH11 0.0180 0.0564 À0.0206 À0.0194 0.0966 0.0588
12 S. Jalili, H. Aghdastinat / Journal of Molecular Structure: THEOCHEM 857 (2008) 7–12