Structural Chemistry, Vol. 16, No. 3, June 2005 ( C2005)
Theoretical Investigation of Normal to Strong Hydrogen Bonds
Chaeho Pak,1Han Myoung Lee,1Jong Chan Kim,1Dongwook Kim,1and Kwang S. Kim1,2
Received May 13, 2004; revised August 11, 2004; accepted August 12, 2004
We review our theoretical work done on a variety of different chemical systems, which show different
H-bonding characteristics. The systems include water clusters, its interactions with polar molecules
and π-systems, organic nanotubes, enzymes, and ionophores/receptors. Special features of normal,
short, short strong, and π-type H-bonding interactions in these systems are discussed in terms of
structures, interaction energies, and spectra.
KEY WORDS: Hydrogen bond; ab initio calculations; water; ionophore; enzyme.
Nature is composed of a variety of different chem-
ical bonds. Life exists merely because there are atoms
and molecules, and intra and intermolecular forces gov-
erning them [1, 2]. One of the most vital forces, H-bond,
plays important roles both in chemistry and biology. For
instance, the most abundant and essential substance on
our planet, water, and the most important substance in
biosystems, proteins and DNA are held basically by net-
works of H-bonds. The H-bond energy ranges from 1
to 30 kcal/mol. Since H-bonds can be easily formed and
broken depending on the given environment, they are con-
sidered to have “on or off” functions in biology .
Although H-bond is one of the very important in-
termolecular forces, it is still poorly understood partially
due to their weak long-range interactions and their shal-
low, anisotropic, and anharmonic nature of potential en-
ergy surface. However, recent progress both in theoretical
and experimental methods has shown many new inter-
esting facts about the H-bonding. Then, these H-bond
interactions have been applied to the biological and ma-
terial chemistry [3–8]. H-bonds have often been used for
self-assembling macromolecular architecture such as cap-
sules, nanotubes, wires, etc. . The charge transfer (CT)
1National Creative Research Initiative Center for Superfunctional
Materials, Department of Chemistry, Division of Molecular and Life
Sciences, Pohang University of Science and Technology, San 31,
Hyojadong, Namgu, Pohang 790-784, Korea.
2To whom all correspondence should be addressed; e-mail: kim@
through the H-bonded networks of a wire form has been
chemically and biochemically explored . The charged
and ionic H-bond interactions have been applied to the
recognition of ions by receptors/ionophores . Many
biological systems such as proteins, membranes, RNA,
and DNA show functions related to multiply H-bonded
Among many different methods for studying
H-bonds, due to much progress in development of highly
efﬁcient computational algorithm, computer hardware,
and new theoretical models, ab initio molecular orbital
calculation has become probably the method of choice
for studying H-bonds. This is in part because theoretical
investigations make it easy to explore potential energy
surface in a variety of different conformations and deduce
different electronic energy components such as electro-
static, inductive, dispersive, charge transfer and repulsive,
as well as their inﬂuences on the structures, spectra, and in-
teraction energies. These energy components have differ-
ent physical origin, magnitude, and directionality. Electro-
static forces result from interactions between permanent
electric multipole moments of complex partners; induc-
tion forces result from interactions of permanent electric
multipole moment of one monomer with electric multi-
pole moment induced in the other monomer; dispersion
forces result from mutual polarization of electron densities
of two interacting monomers; charge transfer refers to
electron transfer between occupied orbitals and vacant
orbitals between different atoms; repulsive forces result
from the Pauli exclusion principle, which prevents the
electrons of one monomer from penetrating into the occu-
pied space of the other monomer. This exchange repulsion
2005 Springer Science+Business Media, Inc.
188 Pak, Lee, Kim, Kim, and Kim
increases with increasing overlap and is always destabiliz-
ing. Depending on the nature of H-bonds, it can have dif-
ferent proportions of these energy components. For exam-
ple, in the case of strong H-bond [F−HF], the charge
transfer accounts for more than 40% of the interaction
Even though it is tempting to cover all the aspects of
H-bonds, due to vast amount of materials, it is impractical
for this short review. Instead, interested readers can ﬁnd
many books [1, 2], and reviews [8, 9] concerning this
topic. In this review, we will summarize our theoretical
work done on many different chemical systems (gas phase
water clusters, organic nanotubes, enzymes, and recep-
tors), which exhibit wide variety of different H-bonding
characteristics such as normal, short, short strong, and π-
type H-bonds. Some of the pertinent issues which will be
addressed in the course of this review are the following:
(i) the changes in the interaction and binding energies due
to the cluster size on the example of water, (ii) the cooper-
ativity effect on molecular properties, (iii) the binding en-
ergies for charged H-bonds in enzymes and bio-receptors,
and (iv) normal versus strong hydrogen bonds.
H-BOND IN SMALL POLAR AND π-SYSTEMS
The H-bond interactions can be noted as X–
δ−Y, where X is a polar proton donor and Y a
proton acceptor or an electronegative ion with lone pairs
of electrons. Depending on the nature of X and Y, the
strength of H-bonds varies. For example, when X and
Y are a good proton donor and a good proton acceptor,
respectively, they form a very strong H-bond. Figure 1
shows interaction of water molecule with a variety of
different small polar (H2O, H2S, NH3,PH
Fig. 1. H-bonded dimers of neutral, charged, and σversus πH-bonds. W and NMHP
denotes for H2OandN-methyl-4-hydropyridine, respectively.
Theoretical Investigation of Normal to Strong Hydrogen Bonds 189
HBr, HI ) cationic (H3O+,NH
4+), anionic (F−,
−), and σversus π-systems (ace-
tone, imine, furan, pyridine, pyrrole, and N-methyl-4-
hydropyridine (NMHP) [9, 13]). There are also many sim-
ilar studies . Table I shows their interaction energies
[zero-point-energy (ZPE)-corrected energies: E0]using
the density functional theory employing Becke’s three
parameters with Lee–Yang–Parr functionals (B3LYP)/6–
311++G∗∗ and the Moller–Plesset second-order pertur-
bation theory (MP2)/aug-cc-pVDZ+(2s2p/2s) . The
interaction energies are reported as the median value of the
basis set superposition error (BSSE)-corrected and BSSE-
uncorrected values, which can be considered as the lower
and upper limits . Although the BSSE-corrected values
are more rigorous in theoretical viewpoint, the energy
obtained from incomplete basis sets is underestimated
due to the lack of insufﬁcient electron correlation energy,
which in most cases tends to be empirically compensated
partially by BSSE. In particular, it should be noted that
the BSSE-uncorrected H-bond distance is somewhat too
Tab l e I. MP2/aug-cc-pVDZ +(2s2p/2s) [B3LYP/6-311++G∗∗]
Zero-Point-Energy Corrected Interaction Energies (kcal/mol) of
Various Molecules with a Water Molecule
H2O2.56±0.42 [3.13 ±0.41]
H2S1.34±0.36 [1.39 ±0.28]
PH31.10 ±0.36 [0.95 ±0.19]
NH34.08 ±0.57 [4.60 ±0.38]
HF 6.26 ±0.59 [7.37 ±0.56]
HCl 4.20 ±0.52 [4.45 ±0.44]
HBr 3.51 ±0.60 [3.55 ±0.37]
HI 2.66 ±0.42 [2.03 ±0.26]
F−25.24 ±0.75 [27.40 ±0.55]
Cl−13.05 ±0.48 [13.51 ±0.15]
Br−11.55 ±0.70 [12.03 ±0.09]
I−9.43 ±0.63 [9.43 ±0.08]
218.56 ±0.71 [20.21 ±0.44]
OH−24.52 ±0.98 [26.65 ±0.43]
H3O+33.52 ±1.15 [35.83 ±0.72]
NH4+18.30 ±0.69 [20.14 ±0.42]
Acetone 3.60 ±0.52 [2.84 ±0.14]
Imine 4.82 ±0.59 [4.38 ±0.20]
Furan 2.55 ±0.51 [1.74 ±0.23]
Pyridine 5.82 ±0.70 [4.86 ±0.25]
σH-Pyrrole 4.74 ±0.58 [4.04 ±0.41]
πH-Pyrrole 4.65 ±0.92 [2.02 ±0.26]
πH-Benzene 2.86 ±1.13 [1.53 ±0.22]
πH-NMHP 5.51 ±1.14 [1.88 ±0.49]
Note.E0is the median value of BSSE-corrected and -uncorrected
binding energies with ZPE correction. The value added/subtracted by a
half BSSE is the upper and lower limits which are the BSSE-uncorrected
and -corrected binding energies, respectively. Values in brackets were
obtained at the B3LYP/6-311++G∗∗ level. NMHP denotes N-methyl-
short, so that the full BSSE correction underestimates
the binding energy due to the overestimated repulsion at
the distance (toward the hard wall region) shorter than
the optimal H-bond distance.
Ammonia has strong proton afﬁnity, thus has strong
H-bond interactions with the water monomer compared
with the interaction in the water dimer (4.08 kcal/mol
vs. 2.56 kcal/mol in E0). In NH3–H2O interaction, a
polarizable lone-pair electrons in NH3makes NH3better
H-accepting than H2O. H2S is a weaker proton acceptor
than H2O, and plays a role of H-donor in H2O–H2S inter-
action. The third elements P and S atoms have relatively
weak H-bond interactions due to large atomic radius.
In the hydrogen halide acid–water clusters , wa-
ter plays a role of H-acceptor, while in anion–water clus-
ters , water acts as H-donor as shown in Fig. 1. Good
acids provide protons more easily than stable anions. Their
properties are strongly related to the stabilization of chem-
icals and dissociated ions by the hydration effect. The
anionic systems have strong proton afﬁnity, which gives a
strong H-bond interaction. In the case of charged systems
[11, 12], the charge highly increases the strength of H-
bond interaction due to the strong electrostatic interaction.
In the protonated systems, the hydronium cation is a better
proton-donor than the ammonium cation , so hydro-
nium has stronger H-bond interaction than ammonium.
The positively charged systems have stronger H-bond in-
teractions than the negative-charged ones. The positively
charged atom can easily interact with the water O atom at
a shorter distance, while the negatively charged atom in-
teracts with only a few H atom without full coordination,
due to the presence of an excess electron that requires
a large vacant space around the anion for stabilization
as well as the repulsions between crowded H atoms of
Many electronegative atoms have different hy-
bridizations, which can have different effects on H-
bond interactions. The different hybridizations appear in
double and triple bonds, and in aromatic rings. Some
interesting N-containing aromatic rings were theoreti-
cally and experimentally investigated for their H-bond
interactions with water molecules. Pyridine, which has
sp2-hybridized nitrogen atom and resonance effect, has
stronger H-bonding interaction than those of ammonia–
water, imine–water, and furan–water systems. This is be-
cause the lone-pair electrons of pyridine are less-stabilized
and less-delocalized (“localization effect”) in the highest-
occupied molecular orbital (HOMO), while the lone-
pair electrons of furan are delocalized and stabilized at
the HOMO (π-electrons occupy carbon atom’s HOMO).
Pyridine is a good proton-acceptor and therefore plays
actively in the H-bond interaction. Pyrrole shows strong
190 Pak, Lee, Kim, Kim, and Kim
Fig. 2. The lowest-energy neutral water cluster structures (W2−12 at
0 K) and the thermodynamic energy changes (W2−8) depending on
σH-bond interactions with water due to resonance effect
and acidity, and also weak π-H bond interactions with
water molecules. In the latter case, the lone-pair electrons
are delocalized around the aromatic ring or resonating
ring by the resonance effect. The carbon π-electrons are
compatible with lone-pair electrons of water molecules.
The pictures of their π-type interactions with water show
the π-H interaction.
H-BOND IN NEUTRAL WATER CLUSTERS
A water molecule has two lone pairs of electrons and
two positively charged hydrogen atoms. Therefore, a wa-
ter molecule favors four H-bond interactions. Neutral wa-
ter structures are determined mainly by the H-bond inter-
actions and strains between water molecules. Structures,
energetics, and electronic and spectroscopic properties
of small water clusters have been well investigated [18–
20]. In cluster-scale, water molecules can be classiﬁed as
“d,” “a,” “da,” “aa,” “daa,” “dd,” “dda” and “ddaa”-types,
where “d” and “a” indicate H-donor and H-acceptor, re-
The lowest-energy water clusters from water dimer
to dodecamer and their interaction energies are presented
in Fig. 2 and Table II. As the H-bond interaction is
weak and ﬂexible, their conformation and energetics
are temperature-dependent due to the entropy effect.
Figure 2 shows the interaction energies of water dimer to
octamer as a function of temperature. The water tetramer,
pentamer, and octamer are relatively stable with respect
to the water dimer, hexamer and heptamer. The dimer
to pentamer have global minimum energy structures
of cyclic ring conformation. However, as in Fig. 3, the
hexamer has ﬁve iso-energetic conformations. The high
level calculations show that the cage structure has the
lowest energy, followed by book, prism, cyclic, and bag
structures . The calculated interaction energies are
summarized in Table III. Indeed, the cage structure which
is most stable conformer of neutral water hexamer near 0
K, was experimentally observed . The nearly isoen-
ergetic conformer, book structure was recently observed
. In addition, the slightly higher energy conformer of
cyclic structure was observed in Ar matrix .
As the cluster size increases from the water dimer to
hexamer, the average O O distance of H-bonded water
cluster decreases with the increased H-bond strength. The
OH stretch modes of the non-cyclic water hexamer and
heptamer do not show further red-shifts with respect to
those of the water hexamer, because their O O distances
are almost the same as that of the cyclic hexamer. These
OO distances are useful for comparing their strengths
of H-bond interactions, and are also related to the red-
shifts of the stretch modes. The structures, energetics,
and spectra of the lowest energy water clusters from the
nonamer to dodecamer can be formed in our previous
Generally, single H-donor water molecules (“da” or
“daa” waters) have strong H-bond interactions in neutral
water clusters. This aspect appears in IR spectra for O H
stretching frequencies as strong red-shifts. Water trimer
to pentamers with cyclic mono-ring structures exhibit
strong H-bond interactions. The red-shifts of O H stretch
frequencies monotonically increase up to the hexamer
ring structure owing to the increase of the strength of
H-bond interaction by the decrease of bond angle strains
(Fig. 4 and Table IV). However, this H-bond strength
is saturated at the hexamer, and so the heptamer and
Theoretical Investigation of Normal to Strong Hydrogen Bonds 191
Table II. Interaction Energies (kcal/mol) of Neutral Water Clusters, (H2O)n=2−12
MP2/TZ2P++ MP2/aug-cc-pVDZ +(2s2p/2s)
nStructure #HB −Ee±BSSE/2 −E0−H298 −G50 −Ee±BSSE/2 −E0−H298 −G50
2 Linear 1 4.88 ±0.33 2.58 3.13 2.07 4.85 ±0.33 2.55 3.10 2.04
3 Ring 3 15.11 ±0.89 9.38 11.27 7.98 15.14 ±0.89 9.40 11.30 8.00
4 Ring 4 26.72 ±1.75 18.06 20.93 15.61 26.56 ±1.76 17.90 20.78 15.46
5 Ring 5 35.17 ±2.42 24.30 27.65 20.97 34.90 ±2.42 24.03 27.38 20.70
6 Cage 8 43.48 ±2.98 30.52 34.29 26.14 44.45 ±2.90 30.18 34.70 25.71
7 Prism34 10 55.24 ±3.66 37.89 43.39 32.35 55.85 ±3.66 38.50 44.00 32.96
2d 12 70.06 ±4.68 48.68 55.75 41.84 70.86 ±4.68 49.44 56.54 42.64
9aPrism45 9 79.14 ±5.39 55.69 63.27 48.05 82.00 ±5.39 57.96 65.55 50.26
10aPrism55 10 90.07 ±6.13 63.48 72.14 54.74 93.42 ±6.13 66.18 74.83 57.37
11aPrism56 11 98.67 ±6.82 69.66 78.99 59.98 102.14 ±6.82 72.40 81.73 62.65
12aPrism444 12 112.59 ±7.5 79.41 90.13 68.34 118.02 ±7.54 84.6 94.78 72.99
Note. The thermodynamic corrections were made using the B3LYP/6-311++G∗∗ values. For n≤8, all the geometries were fully optimized, while
for n≥9, the single-point energy calculations were carried out for MP2/TZ2P++ and MP2/aug-cc-pVDZ+(2s2p/2s) on the MP2/TZ2P optimized
octamer ring conformers have similar red-shifts. These
red-shifted values with respect to those of water monomer
reﬂect the strength of H-bond interactions between
water molecules. The cyclic pentamer cluster shows
∼540 cm−1red-shifted frequencies corresponding to “da”
water, while the hexamer-Cage and heptamer-Prism34
show ∼670 and ∼760 cm−1red-shifted frequencies, re-
spectively, corresponding to “daa”-type water (Fig. 4,
Table IV). The large shifts are due to the strong polar-
ization effect by the H-bonds.
HOH bending modes of neutral water clusters dis-
play blue shifts with respect to that of the pure water
monomer (Table IV). In going from “da” to “dda”-type
water, the blue-shift increases. For mono-cyclic ring struc-
tures, the maximum blue-shifts of HOH bending modes
Fig. 3. Five isoenergetic isomers of neutral water hexamer.
of “da” waters increase from the cyclic trimer to pen-
tamer; however, the hexamer to octamer show blue-shifts
similar to the pentamer. The “dda” waters in the cage
hexamer and cage heptamer and cubic D2d conformers
show the largest blue-shifts (∼120 cm−1) for the bending
The order of red-shifts of OH stretching frequen-
cies with respect to the average value of ν3and ν1of
the water molecule in the water dimer to dodecamer is
“da” (ν3)<“daa” (ν3)<“dda” (ν3)<“ddaa” (ν3)<
“ddaa” (ν1)≈<“dda” (ν1)<“da” (ν1)<“daa” (ν1). The
IR intensities of double proton donor-type waters (“dda”
and “ddaa”) in asymmetric OH stretching modes (ν3)are
strong, while the intensities of single donor-type waters
(“da” and “daa”) are strong in symmetric OH stretching
modes (ν1). The order of red-shifts of bending frequen-
cies with respect to that of monomer is “ddaa” >“dda” >
“daa” ≈“da.” In the cases of undecamer and dodecamer,
the ranges of −δν3and −δν1of “ddaa”-type are 209–299
and 245–496 cm−1, and that of δν2of “ddaa”-type is 93–
135 cm−1. The values of −δν3and −δν1of “dda”-type are
66–242 and 181–436 cm−1and that of δν2of “dda”-type
is 46–138 cm−1.
H-BONDS IN HYDRATION AND
As shown in Fig. 5, a hydroxide ion forms tetra-
hydrated structure using three lone pairs. The tetra-
hydrated ﬂuoride ion has a surface state near 0 K, but
as temperature increases to the room temperature, it
can have nearly internal structure with tetrahedral co-
ordination using four lone pairs of electrons due to
192 Pak, Lee, Kim, Kim, and Kim
Table III. Interaction Energies (kcal/mol) of Five Isoenergetic Isomers of Neutral Water Hexamersa
Methods −ERing Book Bag Cage Prism
MP2/QZ(3df/2pd)++ −Ee43.34 44.04 43.40 44.21 44.23
MP2/HZ4P(2fg/2d)++ −Ee43.89 44.73 44.10 45.02 45.13
MP2/CBS −Ee44.8 45.6 — 45.8 45.9
MP2/aug-cc-pVDZ +(2s2p/2s)b−E029.75 30.25 29.95 30.17 30.08
MP2/TZ2P −E031.67 32.17 31.44 32.17 31.98
MP2/QZ(3df/2pd)++ −E029.64 30.00 29.34 29.94 29.65
MP2/HZ4P(2fg/2d)++c−E030.19 30.70 30.10 30.76 30.54
aAll data were from reference 18 except MP2/aug-cc-pVDZ+(2s2p/2s) cases.
bThe B3LYP/6-311++G∗∗ ZPEs were used for the ZPE correction.
cThe MP2(FC)/6-311++G∗∗ ZPEs were used for the ZPE correction.
the entropy effect . On the other hand, the tetra-
hydrated chloride ion has a surface bound state even at
room temperature . Strongly electronegative small
ions form strong H-bonds with water molecules, which
is larger than the water–water binding energy, due to
the strong electrostatic interactions. While a cation has
very strong electrostatic interaction, an anion has slightly
weaker electrostatic interaction because the presence of
an excess electron requires a large space for stabiliza-
tion (i.e., lowering the kinetic energy of the excess
COOPERATIVE EFFECT IN SHORT H-BOND
Although, in general sense, the cooperativity applies
to all intermolecular interactions, it is particularly impor-
Fig. 4. B3LYP/6-311++G∗∗ (in solid line) and MP2/DZP (in dotted
line) IR spectra for O H stretch frequency shifts with respect to the
average value of the free O H symmetric and asymmetric stretch fre-
quencies of the water monomer for the neutral water clusters, W1−8.
tant in H-bond interaction because of the relay effect of
hydrogen atoms. The H-bond distance tends to decrease
as cluster size increases. A number of books and articles
have been devoted to elucidate the cooperative effects in
hydrogen bond [1, 2]. The typical characteristics of coop-
erative effects are the shorter X–H distance, longer X H
distance, larger chemical shift, and red shifts of the O H
vibrational spectra. In the following section, after review-
ing previous work on linear hydrogen-bonded chains, we
will discuss the nature of recently synthesized calix 
hydroquinone (CHQ) nanotubes. Some of the questions
we would like to address are the following: (1) how sig-
niﬁcantly bond distances and bond energies change in
an inﬁnite linear hydrogen-bonded chain? (2) what is the
origin of these cooperativity? (3) what is the role of co-
operativity in determining the structures of organic and
Linear H-Bonded Chains
A number of studies have been devoted to investi-
gate the property of linear H-bonded chains such as HF,
HCN, and H2O systems. Mostly, the HF dimer has been
served as a hydrogen bond model. Experiments show that
the bent dimer and cyclic hexamer are stable in cluster
form. In crystalline hydrogen ﬂuoride, HF forms inﬁnite
chain structure by strong hydrogen bond (F···F distance
of 2.47 ˚
A which is ∼0.25 ˚
A shorter than the normal
F···F distance of 2.72 ˚
A in the ﬁnite system HF···HF)
. Guedes et al. have investigated the characteristics
of cyclic HF and HCl clusters , and showed that
hydrogen-bond cooperativity is related to electronic shar-
ing and delocalization through electron density difference.
Rincon et al. also showed that the cooperative effect is re-
lated to electron delocalization between monomer units
through the analysis of the topology of electron density
. In addition, agreeing with the experimental result,
Theoretical Investigation of Normal to Strong Hydrogen Bonds 193
Tab l e IV. B3LYP/6-311++G∗∗ Vibrational Frequency Shifts (With Respect to the Monomer Frequencies ν3,ν1,andν2) and IR Intensities (Average
in Parentheses) of (H2O)n=2−8
nConformation “da” “daa” “dda” “dda” “da” “daa” “dda” “daa” “da”
2 Linear “a”: 8 (85) “d”: 30 (80) “a”: 3 (16) “d”: 112 (333) “d”: 26 (35) “a”: 10 (88)
3 Ring 27–33 (79) 188–257 (372) 49–21 (63)
4 Ring 37–38 (69) 310–442 (738) 79–29 (52)
5 Ring 32–39 (67) 339–488 (894) 94–39 (51)
6 Ring 36–37 (67) 344–499 (974) 95–35 (54)
Book 34–38 (68) 47 (77) 199 (398) 235 (320) 253–473 (1002) 552 (275) 115 (36) 79 (46) 60–26 (68)
Bag 28–45 (75) 47 (52) 257 (675) 200 (576) 176–539 (791) 611 (398) 116 (56) 70 (86) 99–29 (53)
Cage 26–45 (75) 39–43 (69) 176–208 (358) 143–226 (320) 295–342 (599) 385–617 (761) 106–93 (44) 73–57 (66) 38–32 (88)
Prism 26–37 (70) 38–41 (70) 147–190 (256) 122–260 (364) 275–639 (592) 123–75 (76) 51–28 (91)
7 Prism34 31 (64) 39–42 (70) 137–242 (387) 155–280 (367) 414 (623) 289–707 (787) 121–96 (51) 63–33 (67) 37 (151)
Ring 28–39 (66) 334–484 (984) 98–41 (54)
2d 44 (63) 230–275 (555) 185–204 (206) 519–604 (885) 122–75 (24) 48–36 (101)
Ring 29–30 (67) 323–472 (1006) 94–39 (55)
Note.Forn=1, ν3=3921 (57), ν1=3816(9), and ν2=1603 (67). Frequencies are in cm−1; IR intensities in km/mol. If δν1=δν3, it means that ν1is smaller than
ν3by 105 cm−1.
194 Pak, Lee, Kim, Kim, and Kim
Fig. 5. Structures of tetra-hydrated anions.
they showed that the cyclic hexamer is the most favorable
structure among cyclic clusters.
Hydrogen cyanide (HCN) has fully linear structure
as both a dimer complex and a solid state conformer.
Two different structures, cyclic and linear conformers,
have been conﬁrmed experimentally in the trimer cluster.
Karpfen investigated the structures, binding energies and
vibrational spectra of linear and cyclic HCN clusters, and
concluded that HCN clusters have weaker cooperativity
than HF .
Cooperative effects in H2O appears as gradual
shortening of hydrogen bond distance from dimer
A ) to liquid (∼2.8 ˚
A ) to ice (∼2.75 ˚
A ) .
Beside the studies of liquid water and ice, a lot of
theoretical studies have been devoted to water chains
[29–31]. Suhai calculated the bond distance and average
H-bond energy in inﬁnite water chain as 2.73 ˚
6.30 kcal/mol, respectively, which is comparable to
experimental results on ice (2.74 ˚
A , and 6.7 kcal/mol)
. Hermansson et al. investigated the polarization
of the individual water molecules in ﬁnite and inﬁnite
H-bonded chains, and showed that the induced dipole
moment in the middle of the long chain is about twice as
large as those at the ends. The additional dipole moments
are created by charge transfer from accepter to donor
. Masella et al. investigated the cooperative effects in
cyclic trimers comprised of water and methanol .
Short H-Bond in Organic Crystal
and Peptide Structures
The cooperativity of H-bond plays an important
role in determining the structures of molecular crystals
and biological molecules. Cyclohexane-1,3-dione forms
sheet, which has long chains of hydrogen bond with
most solvents (forms 6:1 cocrystal with benzene) .
Dannenberg et al.  explained this by comparing
asymptotic interaction energy of the inﬁnite chain and
cyclic hexamer. Comparing differences between urea
and 1,3-cyclohexanedione under external electric ﬁeld,
they found that the short distance in urea is reasonably
described by electrostatic interaction and polarization
effects, but 1,3-cyclohexanedione is not.
Fig. 6. Schematic of 1-D H-bonds relays. (a) 1-D H-bond relay of poly
1,2-ethanediols (diols). (b) 1-D H-bond relay of poly 1,3-propanedione
Cooperative effects in secondary protein structures,
helix and sheet have been reported . The linear chain
of formamide which resembles peptides, has large coop-
erativity in H-bond, which is 2.5 times as much as that of
formamide dimer. For the parallel and antiparallel sheet in
secondary protein structures, there was no cooperativity
in the parallel direction, while signiﬁcant cooperativity
exists in perpendicular direction. In methanol solvent sys-
tem, the cooperative effects were reduced, indicating that
the cooperativity is due to polarization effect.
Diol and Dione
We considered two different linear chainlike H-bond
relay, poly 1,2-ethanediols and 1,3-propanedione (Fig. 6)
. We have optimized the geometries on the plane up
to the decamer at the B3LYP/6-31G∗level, and up to hex-
amer at the MP2/6-31G∗level. We obtained the binding
energy of inﬁnite chain on the basis of the exponential
decay plot (Fig. 7).
In the case of the dimer, 1,3-propanedione has larger
H-bond energy (12.3 kcal/mol) than 1,2-ethanediol (5.9
kcal/mol) at the B3LYP level. Based on the exponential
decay plot, the H-bond energies in the inﬁnite chains
of 1,3-propanedione and 1,2-ethanediol are 24.4 and
9.8 kcal/mol, respectively, which increased by 12.0
and 3.9 kcal/mol, respectively, than those of the dimers
(Fig. 7). Also, bond distances are shortened by 0.07
and 0.15 ˚
A , respectively. MP2 results are comparable
with B3LYP results. Change of natural bond orbital
(NBO) atomic charge (Fig. 7) shows that the polarization
is mainly responsible for this cooperativity. H-bond
between diones is stronger with the larger cooperativity
effect than that of diols.
Short H-Bond for Organic Nanotubes
and the Solvent Effect
We recently synthesized calixhydroquinone
(CHQ) nanotubes, which are assembled by
Theoretical Investigation of Normal to Strong Hydrogen Bonds 195
Fig. 7. ZPE-uncorrected H-bond interaction energies (Ee), H···O distances (dH···O), and
atomic charges of H and O atoms of the central H-bond (qH,qO) in the 1-D H-bond relay
of 1,2-ethanediols and 1,3-propanediones. Reproduced by permission of American Chemical
Society: Reference  Suh, S. B.; Kim, J. C.; Choi, Y. C.; Yun, S.; Kim, K. S. J. Am. Ch em.
Soc. 2004,126, 2186.
one-dimensional (1-D) short hydrogen bond (SHB)
(Fig. 8) . Hydrogen bond length in CHQ is about
A , which is almost 0.2 ˚
A shorter than that of normal
Fig. 8. Longitudinal H-bond relay comprised of CHQs and water. (a)
Tubular polymer structure of a single nanotube obtained with X-ray
analysis for the heavy atoms and with ab initio calculations for the
H orientations (top and side views). (b) One of four pillar frames of
short H-bonds represents a 1-D H-bond relay composed of a series of
consecutive OH groups [hydroxyl groups ( OH) in CHQs and the OHs
in water molecules]. Reproduced by permission of American Chemical
Society: Reference  Suh, S. B.; Kim, J. C.; Choi, Y. C.; Yun, S.;
Kim, K. S. J. Am. Chem. Soc. 2004,126, 2186.
hydrogen bond. For cluster systems, we have carried
out B3LYP and MP2 calculations. To investigate the
periodic systems including solvent, we have carried out
plane wave density functional theory (PW-DFT) using
generalized gradient approximation (GGA) of Perdew
and Wang , and the Vanderbilt pseudopotentials .
One-dimensional SHB in CHQ nanotubes involve
three kinds of H-bond between hydroquinone (Qh) and
water (W). We denote the complex with a H-donor and a
H-acceptor as D >A. The W >Qh,Q
h>Qh, and Qh>
W in Fig. 9 have bond energies of 5.4, 6.3, 8.6 kcal/mol,
respectively (B3LYP/6-31G∗). These values are similar to
MP2/6-31G∗results of 5.6, 7.8, and 8.5 kcal/mol and PW-
DFT results of 5.6, 4.6, and 8.4 kcal/mol. Case Qh>W has
A shorter O···H bond distance and ∼3 kcal/mol
larger binding energy than case W >Qh. From orbital
interpretation of hydrogen bond, an H atom is likely to
stabilize the lone pair electrons of water oxygen atom
more than those of hydroquinone oxygen atom.
In order to investigate the effect of SHB in CHQ
nanotubes, we have performed calculations with the in-
creasing number of H-bonded clusters. On the basis of
exponential decay plot, the asymptotic H-bond energies
for W >Qh,Q
h>Qh, and Qh>W in inﬁnite H-bond
relay are estimated to be 11, 11, and 12 kcal/mol, re-
spectively. The average value of these H-bond energies is
196 Pak, Lee, Kim, Kim, and Kim
Fig. 9. Three types of H-bonding involved with 1-D H-bonds of CHQ
nanotubes. The H···O bond distances ( ˚
A ), atomic charges (qHand qO
in au) and their changes with respect to the values of the isolated systems
(qHand qOin au), and proton chemical shifts (δin ppm) are given
at the B3LYP/6-31G∗level.
11.3 kcal/mol, which is 4.5 kcal/mol higher than the nor-
We have calculated the average bond energy gain
in the inﬁnite SHB array (Eshb) and the solvent effect
in bond energy (Esol) using the partition scheme. In this
case, Eshb is −3.9 kcal/mol, and Esol is 1.2 kcal/mol. Thus
average HB energy per SHB in the presence of solvent
water molecule is 8.9 kcal/mol, which is 2.7 kcal/mol
larger than normal H-bond energy.
SHORT STRONG H-BOND IN
Short strong H-bond (SSHB) [38, 39] is char-
acterized by their large hydrogen bond energies
(>10 kcal/mol), short distances (<2.6 ˚
A ), and large
downﬁeld shift of NMR resonances (>15 ppm). In low di-
electric organic solvents, unusual physicochemical prop-
erties have been observed for a number of hydrogen bonds
between two partners with an equal pKa.
The proposal that SSHB plays a key role in the
enzymatic catalysis has been highly debated in recent
years . One of the examples for the role of SSHB
in enzymatic reaction can be found in 5-3-Ketosteroid
Isomerase (KSI) which is a paradigm for fast enzymatic
reactions . KSI catalyzes the conversion of β,γ-to
α,β-unsaturated steroidal ketones via a dienolate inter-
mediate at a nearly diffusion-controlled rate. During the
reactions, Asp38 serves as a base for abstracting the C4β-
proton of the steroid substrate, while Tyr14 (H-bonded by
Tyr55) and Asp99 serve as catalytic residues by providing
H-bonds to the oxyanion (C3 O or O3) of the dienolate
intermediate (Fig. 10).
The calculated results about energy proﬁle of the
wild-type system  indicates that the barriers for the
ﬁrst step (ES →TS1 →EI1; abstraction of the proton
from the substrate) and the third step (EI2 →TS3 →EP;
donation of the proton to the substrate) are very
similar and crucial in energy, while the second step
(EI1 →TS2 →EI2; rotation of Asp38) is not signiﬁ-
cant in energy so that total reaction is eventually two-step
mechanism. In the presence of Tyr14 or Asp99, the tran-
sition states TS1 and TS3 are lowered by ∼6 kcal/mol.
This result implies that the catalytic effect of the two
residues is almost equivalent. When Tyr14 and Asp99
were introduced simultaneously, TS1 and TS3 are low-
ered by ∼10 kcal/mol. Intermediate states (EIs: EI1 and
EI2) and TS2 are stabilized by ∼15 kcal/mol, suggesting
that the two functional groups contribute cooperatively to
the stabilization of EIs and TS2.
In the structure of the active sites in the complex with
the intermediate analogues, the hydrogen bond distances
between O3 and Tyr14 or Asp99 are ∼2.6 ˚
A, which is
slightly shorter than those (∼2.8 ˚
A ) of the structure in
complex with the product analogue  (Table V). NMR
spectroscopic investigations also indicate that in the D38N
mutant KSI, the H-bond between the catalytic residues and
equilenin exhibits a large downﬁeld shifted peak (>16
ppm) [41, 42].
The distances between Oresidue and O3 (d[OrO3])
along the reaction path (Table V)  indicates that even
though normal H-bonds are formed between residues and
substrate at the starting and ending point of reaction, they
are converted to short strong one during the reaction where
d[OrO3] is reduced by ∼0.2 ˚
A , in accordance with the
The comparison of π-type H-bond interaction and
traditional water-water σ-type H-bond interaction should
be very interesting. The interaction energies of ethylene–
water π-H bond and water–water σ-H bond interac-
tions were calculated to be 2.84 ±0.59 and 4.89 ±0.41
kcal/mol at the MP2/aug-cc-pVDZ level, where the lower
and upper limits are the BSSE-corrected and -uncorrected
values, respectively. In order to analyze the interaction
energy component, the symmetry-adapted perturbation
theory (SAPT)  calculations were performed using
the same basis set and geometries. SAPT have been used
to analyze the interaction energies as the terms of elec-
trostatic, induction, dispersion, and exchange interaction
Theoretical Investigation of Normal to Strong Hydrogen Bonds 197
Fig. 10. Schematic representation of reaction mechanism of KSI.
elst is the electrostatic interaction energy of the
monomers with the unperturbed electron distribution,
exch their ﬁrst-order valence repulsion energy due to
the Pauli exclusion principle, E(2)
ind stands for the second-
order energy gain resulting from the induction interaction,
exch−ind represents the repulsive exchange interaction
due to the electronic cloud deformation, E(2)
the second-order dispersion energy, E(2)
exch−disp denotes the
second-order correction for a coupling between the ex-
change repulsion and the dispersion interaction, and δHF
includes the higher-order correction for the induction and
the exchange interactions.
For the ethene–water and water–water SAPT inter-
action energies without ZPE correction (Ee;−2.0 and
−4.1 kcal/mol, respectively), the electrostatic components
are −3.9 and −8.4 kcal/mol, the ﬁrst-order exchange com-
ponents are 5.5 and 8.5 kcal/mol, the second-order induc-
tion terms are −2.7 and −2.9 kcal/mol, and the second-
order dispersion energies are −2.4 and −2.3 kcal/mol,
respectively. The electrostatic interaction is dependent on
Tab le V. Distances ( ˚
A ) Between Oresidue and O3 Along the Reaction
Path (Fig. 10) in Wild-Type of KSI
Residue ES TS1 EI1 TS2 EI2 TS3 EP
Tyr14 2.68 2.64 2.55 2.51 2.55 2.61 2.67
Asp99 2.75 2.66 2.60 2.55 2.58 2.65 2.71
the electronegativity difference between H-bond compo-
nent atoms, which is available in the water–water H-bond
interaction. The πsystems have low energy lowest-energy
unoccupied molecular orbitals (LUMOs) and polarizable
πelectrons occupied in the higher energy molecular π
orbitals. The πsystems can play a role of good electron-
donating group. Therefore, with respect to the electrostatic
interaction energy of πH-bond interaction, the exchange
component is highly repulsive. While the exchange com-
ponent of water–water H-bond interaction is in the magni-
tude similar to the electrostatic interaction, the induction
energy of π-H-bond interaction has relatively large energy
component. The dispersion interaction is also relatively
large due to the diffuse and polarizable πelectron density
in the π-H bond interaction.
H-BOND IN RECEPTORS/IONOPHORES
Host–guest complexes play an important role in
biological processes, and H-bonds play a crucial role
in the molecular recognition phenomena. In this con-
text, by utilizing hydrogen bond interaction, various
ionophores/receptors with selective binding afﬁnity of
speciﬁc ions have been designed, and demonstrated by
experiments [6, 13, 44–46]. Usually, H-bonds in those
receptors are in competition with the interaction of polar
solvent with ions. Therefore, the most important strat-
egy in designing receptors/ionophores is to know how
198 Pak, Lee, Kim, Kim, and Kim
Fig. 11. Relative afﬁnities (kcal/mol) of various ammonium receptors
for NH4over K+.Esol for selected receptors in CHCl3solution were
obtained using the IPCM method.
to optimize the H-bond between receptor and ion in the
presence of solvent molecules.
H-Bond in the Selective Receptor for Ammonium
Ion (NH4+) Over Potassium Ion (K+)
The recognition of NH4+has attracted lots of interest
since ammonium-containing compounds are very impor-
tant in chemical, biological, and physiological molecular
system . One of the major problems in the selective
recognition of NH4+over K+arises from their nearly
equivalent sizes. Since the pKaof NH4+is 9.0, the subunit
to recognize NH4+should be strong proton-withdrawing
to strengthen the charged H-bonds . Figure 11 shows
the interaction energies in the gas phase and CH3Cl3so-
lution for the tripodal receptor with various subunits to
selectively recognize NH4+over K+. The interaction en-
ergy in solvent was calculated using the static isodensity
surface polarized continuum model (IPCM) method.
Apart from the recognition efﬁcacy in solvent, the
receptors need to possess solvent access-blocking groups
(such as Me). In this way, the coordination number of the
receptors is limited to no more than 4. Since NH4+and
K+favor the coordination numbers of 4 and 6, respec-
Fig. 12. Schematics of tripodal receptors for halide ions.
tively , the optimally solvated NH4+in the presence
of receptors is more energetically favored than the under-
Ionic H-Bonds in Receptors for Anions
With an aid of supramolecular chemistry, recogniz-
ing and sensing anionic species have recently emerged as
a key research ﬁeld [6, 13, 44–46]. In particular, the de-
velopment of receptors capable of selectively recognizing
a speciﬁc anion is quite intriguing. To enhance the sensing
efﬁcacy and selectivity of anions in solvent, strong ionic
H-bond has been frequently harnessed. In this vein, sev-
eral selective receptors utilizing charged H-bonds will be
Recently, we have designed the tripodal receptors
(1–3) with 1,3-disubstituted imidazolium ring subunit
which can form (C–H)+···X−hydrogen bonds with
anions  (Fig. 12), in contrast with the common practice
that most positively charged anion receptors were
designed to form N H···X−hydrogen bonds. 1HNMR
titration experiment was performed to investigate anion
binding properties of hosts. Upon addition of chloride
anion to host 1, signiﬁcantly large down ﬁeld shifts (δ
>0.94 ppm) were observed for the proton of C(2) which
is in between two N atoms of imidazolium subunit. This
suggests complexation of the anion by CH hydrogen
bonds. Although both hosts 1and 2show higher afﬁnities
for the chloride anion than bromide, the afﬁnity and the
selectivity of host 1for halide anions are much higher
than those of host 2(Table VI). This is a consequence
of stronger (C H)+···X−hydrogen bonds by more
electron-deﬁcient imidazolium moieties as well as more
enhanced charge-dipole interaction by the NO2group.
In spite of the enhanced afﬁnity for halide anions, the
recognition of F−was not accomplished through charged
H-bond with host 1, because of the nucleophilic reaction
of F−on C(2). For the complex of host 2and F−,ab
Theoretical Investigation of Normal to Strong Hydrogen Bonds 199
Tab l e VI . Association Constants (Ka) and Binding Free Energies
(G0) for 1:1 Complexes of Host 1–3 (Fig. 12) with Anions in
DMSO-d6at 298 K
Hosts Anions Ka(M−1)−G0298
Note. Estimated errors <10%. Anions used in this assay were in the
form of their tetrabutylammonium salts. −G0298 is in kcal/mol.
initio calculations predicted that F−forms shorter and
more linear H-bond with host 2than Cl−or Br−,so
that F−shows higher binding energies both in the gas
and polar solvent phases. In polar solvent with dielec-
tric constant of acetonitrile (ε=36.64), the calculated
binding energies of 2with F−and Cl−decrease to only
∼20 kcal/mol, while they are larger than 200 kcal/mol
in the gas phase. This indicates that the cationic imida-
zolium receptor interacts with polar solvent so that its
effective charges on C(2) diminish, and its ability of form-
ing charged H-bond with anions decreases. This trend is
conﬁrmed again in the experimental results in 1:1 mix-
ture of DMSO-d6and acetonitrile-d3or DMSO-d6sol-
vent. In these highly polar solvent, F−interacts mod-
erately with host 3, while the butyl groups block the
direct interaction of F−with solvent molecules and re-
duce the micro-environmental polarity around the binding
Recently, by extending this approach, a receptor
of anthracene derivative with two imidazolium moieties
which show selective binding afﬁnity for H2PO4−over
other halide anions and anion-induced changes in ﬂuo-
rescence was reported (host 4in Fig. 13) . However,
further investigation shows that F−forms 2:1 complex
with receptor on each charged H-bonding site. In addition
to (C H)+···F−bonding (1.63 ˚
A ), due to the high ﬂex-
ibility of the receptor site of host 4, the hydrogen atom
connecting CH2between the anthracene and imidazolium
moiety also interacts with F−at a distance of 2.29 ˚
the other hand, host 5favors H2PO4−over F−in polar
acetonitrile solvent. For both hosts 4and 5systems, their
H2PO4−···(H C)+distances are almost same, and so are
F−···(H C)+distances (1.7 and 1.6 ˚
A , respectively).
In the case of host 5, however, F−···(H2C) interaction
becomes negligible (>3˚
A ). Consequently, the greater
rigidity of host 5enhances the binding selectivity towards
Fig. 13. Molecular system (model A) designed for the recognition of
H2PO4−. Reproduced by permission of American Chemical Society:
Reference [46(b)] Yoon, J.; Kim, S. K.; Singh, N. J.; Lee, J. W.; Yang
Y. J.; Chellappan, K.; Kim, K. S. J. Org. Chem . 2004,69, 581.
H-Bond in Amphi-Ionophores
Cyclic polypeptides  can interact with both
cations through C O moieties and anions through N H
moieties (Fig. 14). In structures 6and 7, both carbonyl
and amide groups are nearly on the same cylindrical
surface, i.e., nearly parallel to the principal axis. Upon
complexation with an ion, the cyclic peptides are found
to have two types of binding: one at center (n·Iwhere
ndenotes the cyclic peptides and Idenotes an ion) and
the other above the molecular plane (n·I). In the pres-
ence of cation, carbonyl dipole moieties tend to point
Fig. 14. Selected structures of cyclic peptides (glycine) and their ion
complexes. Reproduced by permission of American Chemical Society:
Reference [49(a)] Kim, K. S.; Cui, C.; Cho, S. J. J. Phys. Chem. B 1998,
200 Pak, Lee, Kim, Kim, and Kim
inward (toward the cation), while, in the presence of an
anion, amide dipole moieties point inward, forming H-
bond. The type of binding is decided by the size of ions
and the cavity of cyclic peptides. If an ion is small and the
cyclic peptides is sufﬁciently large, then n·I-type complex
is formed. Otherwise, n·I-type complexation is observed.
When 7binds with F−, it prefers n·I-type binding. In the
case of Cl−, however, the complex changes its geometry
−···H distances are 2.57 ˚
three H atoms and 2.68 ˚
A for the remaining three H
atoms with supplementary angle, φ, equal to 30 and 37◦,
The most simplest and abundant atom in the universe,
hydrogen atom is involved in one of the most complex and
ﬂexible bonding in both chemical and biological systems,
giving its special features including wide range interaction
energies, cooperativity effect, proton exchange through
the H-bonds, self assembly of molecular tubes and layers,
and functional geometries of multiply H-bonded frames
in biological molecules. We have illustrated how a variety
of different chemical systems have different H-bonding
characteristics, and how each energy component plays
in these bonds. Normally, the good proton-accepting and
proton-donating capability and the dipole give combinato-
rially strong H-bond interactions. Many N-containing H-
bond interaction systems in biochemical systems should
be considered more in regard to biochemical-solvation
phenomena. The studies of these weak interaction sys-
tems could be applied to the developments of available
functional molecular systems. Indeed, utilizing the co-
operative versus competitive effect of hydrogen bonds,
we have been successful in designing various hydrogen-
bonded ionophores, receptors, supramolecules, nanoma-
terials, and nanodevices . Therefore, we hope that
the present review of the H-bonding would be useful for
understanding the role of H-bonding in molecular and
This research was supported by KOSEF(CRI) and
partly by BK21.
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