Variable temperature neutron diffraction analysis of a very short O-H;...O hydrogen bond in 2,3,5,6-pyrazinetetracarboxylic acid dihydrate: Synthon-assisted short Oacid-H...Owater hydrogen bonds in a multicenter array

Article abstract of DOI:10.1021/jp0476848

The occurrence of short hydrogen bonds in pyrazine di-, tri-, and tetracarboxylic acid dihydrates was analyzed. A very short O- H···O hydrogen bond was characterized in one of the tetracids. The synergy from resonance and polarization assistance in the finite, neutral array was found to be sufficient to result in short O-H···H hydrogen bonds when the carboxylic acid donor is activated. This synthon-assisted hydrogen-bond shortening phenomenon was postulated from the neutron-diffraction crystal structure.

Full text of DOI:10.1021/jp0476848

9406
J. Phys. Chem. A 2004, 108, 9406-9416
Variable Temperature Neutron Diffraction Analysis of a Very Short O-H‚‚‚O Hydrogen
Bond in 2,3,5,6-Pyrazinetetracarboxylic Acid Dihydrate: Synthon-Assisted Short
Oacid-H‚‚‚Owater Hydrogen Bonds in a Multicenter Array
Peddy Vishweshwar,† N. Jagadeesh Babu,† Ashwini Nangia,*,† Sax A. Mason,*,‡
Horst Puschmann,§ Raju Mondal,§ and Judith A. K. Howard*,§
School of Chemistry, UniVersity of Hyderabad, Hyderabad 500 046, India, Institut Laue-LangeVin
(6 rue Jules Horowitz) BP 156, 38042 Grenoble Cedex 9, France, and Department of Chemistry,
UniVersity of Durham, Durham DH1 3LE, U.K.
ReceiVed: May 28, 2004; In Final Form: August 13, 2004
Very short OsH‚‚‚O hydrogen bonds (O‚‚‚O ) 2.2-2.5 Å) usually occur when the H-bond is stabilized by
a negative or positive charge (OsH‚‚‚O-, O+sH‚‚‚O) or by resonance assistance (‚‚‚OdCsCdCsOsH‚‚‚).
We have characterized a very short intermolecular OacidsH‚‚‚Owater hydrogen bond in the title crystal structure,
1, by variable temperature neutron diffraction (O‚‚‚O ) 2.4751(11), 2.4765(10), 2.4807(12), and 2.4906(16)
Å at 20, 100, 200, and 293 K). The COOH donor is activated by π-cooperative hydrogen bonding
(OacidsH‚‚‚OdCacid), and the water-acceptor ability is enhanced by polarization assistance (σ-cooperative,
OwsH‚‚‚Oacid, OwsH‚‚‚Npyrazine). The absence of proton migration in the temperature range 20-293 K to
give ionic or tautomer forms rules out contribution from the charge- or resonance-assisted H-bonds in 1. The
shortening of the OacidsH‚‚‚Ow hydrogen bond through synergistic π- and σ-cooperativity in the finite, neutral
array I, named as a synthon-assisted hydrogen bond (SAHB), adds a new category to the current classification
of very short hydrogen bonds in three main types: negative charge-assisted H-bonds ((-)CAHBs), positive
charge-assisted H-bonds ((+)CAHBs), and resonance-assisted H-bonds (RAHBs). The very short hydrogen
bond in the X-ray crystal structure of 2,3,5-pyrazinetricarboxylic acid dihydrate, 5 (O‚‚‚O ) 2.4726(12) Å at
120 K), and the short hydrogen bonds in pyrazine dicarboxylic acids 2-4 (2.5513(11), 2.5269(12), and
2.5148(13) Å) validate the novel SAHB model. A comparison of the short OacidsH‚‚‚Ow hydrogen bond with
short OwsH‚‚‚Oacid distances in carboxylic acids with similar motifs, for example, 1 and 5 and 2 and 4,
shows that the activation of water oxygen by polarization assistance makes a significant contribution to the
SAHB. The behavior of the short OacidsH‚‚‚Ow bond in 1 is similar to short-strong CAHB/RAHB systems:
(1) quasi-covalent character of 0.27-0.30 valence units, (2) red shift in the OsH stretching frequency to
1200-1400 cm-1, and (3) hydrogen-bond energy of ∼16 kcal mol-1. Some examples retrieved from the
Cambridge Structural Database together with crystal structures from this study provide 21 cases of short
OacidsH‚‚‚Ow hydrogen bonds in multicenter synthons.
Introduction
of this important phenomenon.5,6 These studies show that strong
O-H‚‚‚O hydrogen bonds (O‚‚‚O ) 2.5-3.0 Å) have a
significant electrostatic character in the interaction and an
unsymmetrical potential such that the proton is confined to being
near the covalent atom. As the bond shortens (VSHB, O‚‚‚O )
2.2-2.5 Å), the interaction becomes stronger with increasing
covalent character. The decrease in the O‚‚‚O distance is
accompanied by a lengthening of the O-H bond and a
shortening of the H‚‚‚O bond until a symmetrical hydrogen bond
is reached at O‚‚‚O ≈ 2.40 Å. Very strong hydrogen bonds are
essentially three-center-four-electron covalent bonds. They have
been studied by infrared spectroscopy,7 valence bond analysis,8
bond order parameter analysis,9 NMR spectroscopy,10 and X-N
electron density measurements.11 There is great current interest
in the strongest types of hydrogen bonds because of their
significance in enzyme catalysis,12 chelating surfactants,13 proton
transfer,14 drug-receptor recognition/binding,15 and supramo-
lecular chemistry.16 They have been shown to exist in a high-
pressure phase of ice.17
A hydrogen bond, X-H‚‚‚A, arises from the attractive force
that exists between the donor covalent pair, X-H, in which a
hydrogen atom, H, is bound to the more electronegative atom,
X, and the other noncovalently bound nearest neighbor elec-
tronegative acceptor atom, A.1 Properties of hydrogen bonds,
methods of studying them, and their structural and functional
roles in proteins and other macromolecules, supramolecular
chemistry, and crystal engineering have been discussed in books
by Jeffrey and Saenger,1 Jeffrey,2 Scheiner,3 and Desiraju and
Steiner.4 Detailed studies by Emsley, Gilli, Huggins, Jeffrey,
Olovsson, Speakman, Steiner, Wilson, and others on the nature
and properties of very short hydrogen bonds (VSHBs,5a also
referred to as short-strong or low-barrier hydrogen bonds
(SSHBs or LBHBs)) have contributed to a better understanding
* Corresponding authors. E-mail: ansc@uohyd.ernet.in (A.N.); mason@
ill.fr (S.A.M.); j.a.k.howard@durham.ac.uk (J.A.K.H.). Phone/Fax: +91
40 23011338 (A.N.).
† University of Hyderabad.
OsH‚‚‚O hydrogen bonds (H-bonds) have been categorized
‡ Institut Laue-Langevin.
§ University of Durham.
by Gilli and co-workers18 on the basis of extensive neutron and
10.1021/jp0476848 CCC: $27.50 © 2004 American Chemical Society
Published on Web 09/30/2004

Synthon-Assisted Short Oacid-H‚‚‚Owater H-Bonds
J. Phys. Chem. A, Vol. 108, No. 43, 2004 9407
CHART 1: Different Categories of Hydrogen Bonds
Discussed in This Paper
X-ray crystallographic data (Chart 1). (1) Very strong H-bonds
are of three main types: (i) negative charge-assisted H-bonds
((-)CAHBs), OsH‚‚‚O-; (ii) positive charge-assisted H-bonds
((+)CAHBs), O+sH‚‚‚O; and (iii) resonance-assisted H-bonds
(RAHBs), or π-cooperative H-bonds, ‚‚‚OdCsCdCsOsH‚‚‚.
(2) Moderate H-bonds consist of chains of polarization-assisted,
or σ-cooperative, H-bonds (PAHBs). (3) Weak, isolated H-bonds
(IHBs) are neither charge nor σ- or π-cooperative. Typical
examples of (-)CAHBs (O‚‚‚O ) 2.30-2.50 Å) are the well-
known Speakman salts5a with RCOOH‚‚‚RCOO- hydrogen
bonding, H-bonds between inorganic oxoacids and their con-
jugate bases (e.g., hydrogen phosphates and sulfates), and short,
intramolecular OsH‚‚‚O- H-bonds in dicarboxylic acids (e.g.,
hydrogen maleate and hydrogen phthalate). (+)CAHBs (O‚‚‚O
) 2.36-2.43 Å) are present in pseudo-hydrates, hydroxonium
ions, and protons donated to oxygen by strong acids. The
â-diketone enol fragment, formed by the conjugated ‚‚‚OdCs
CdCsOsH‚‚‚ group, is the most common example of a strong
RAHB (O‚‚‚O ) 2.39-2.55 Å).19 Thus, H-bond shortening in
(+)CAHBs is due to the electropositive donor hydrogen, that
in (-)CAHBs is due to the electronegative acceptor oxygen,
and that in RAHBs is due to π-delocalization in the heterodiene
fragment of the â-diketone enol group.5d Common examples
of PAHBs are σ-cooperative chain and ring motifs in crystals
of ice, alcohols, and phenols (2.65-2.75 Å). Isolated H-bonds
occur in the range 2.70-2.90 Å. In summary, very short (strong)
H-bonds are observed when either the donor or the acceptor is
charged or the H-bond is strengthened by synergism due to
increased π-delocalization, often in intramolecular situations.20
Vishweshwar et al.21 recently reported the low-temperature
(123 K) X-ray crystal structure of the title molecule (Figure 1)
with a very short intermolecular Oacid-H‚‚‚Ow hydrogen bond
(O‚‚‚O ) 2.4791(13) Å, H‚‚‚O ) 1.53 Å, O-H‚‚‚O )
171(2)°). Hydrogen-bond shortening in 2,3,5,6-pyrazinetetra-
carboxylic acid dihydrate, 1, was ascribed to the finite array of
π-cooperative H-bonds and the polarization of water oxygen
in motif I. As shown in Chart 2, the COOH donor is activated
because it accepts a hydrogen bond from another COOH group
(labeled #, π-cooperative assistance) and the acceptor ability
of oxygen is enhanced because the water donates H-bonds to
COOH and pyrazine N groups (polarization assistance, σ-co-
operative). The short Oacid-H‚‚‚Ow hydrogen bond in multi-
center motif I is in the CAHB/RAHB distance range of strong
H-bonds (O‚‚‚O ) 2.30-2.50 Å), but the shortening resembles
PAHBs of moderate strength (O‚‚‚O ) 2.65-2.75 Å). The short
Oacid-H‚‚‚Ow hydrogen bond in 1 does not appear to be of the
(-)CAHB, (+)CAHB, or RAHB type because there is no
evidence of ionic donor/acceptor groups and/or delocalization.21
Its shortness cannot be due to geometric compression because
the H-bond is intermolecular. We have now carried out variable
temperature neutron diffraction (VT-ND) on a single crystal of
Figure 1. Finite π-cooperative and σ-cooperative hydrogen-bond array
I in the X-ray crystal structure of pyrazine tetraacid 1 at 123 K. The
water molecule forms O-H‚‚‚O and O-H‚‚‚N hydrogen bonds with
the carboxylic acid and pyrazine groups. Molecules of the next layer
are shaded differently. Displacement ellipsoids are drawn at a 50%
probability level for non-hydrogen atoms. Metrics of the very short
Oacid-H‚‚‚Ow bond are shown.
CHART 2: π-Cooperative and σ-cooperative Hydrogen-
Bond Array I and the Related Motifs I′ and I′′ a
a Such motifs are categorized as a synthon-assisted hydrogen bond
in this paper. Synthons I or I′ are observed in the crystal structures of
1, 3, and 5.
1 at 20, 100, 200, and 293 K to examine the properties and
structural behavior of the very short Oacid-H‚‚‚Ow H-bond in
the neutral motif I. Hydrogen atom positions are determined
with limited accuracy by X-ray diffraction. The precise location
of hydrogen atoms in the crystal structure is of paramount
importance in hydrogen-bond studies.22 We sought to answer
some of the following questions with the neutron diffraction
crystal structure of 1: (1) Does the O-H bond lengthen with
decreasing H‚‚‚O distance? (2) Is there proton transfer in the
short O-H‚‚‚O H-bond to give ionic or resonant species? (3)
Does the very short O-H‚‚‚O bond have quasi-covalent
character, or is it largely electrostatic? The presence of a short
O-H‚‚‚O H-bond in a neutral array justifies detailed analysis
of this system. Although several very short and ionic Oacid
-
H‚‚‚O- H-bonds have been characterized by neutron diffrac-
tion,6c,f,23 there is only one neutron study of a very short and

9408 J. Phys. Chem. A, Vol. 108, No. 43, 2004
Vishweshwar et al.
TABLE 1: Neutron Diffraction Crystallographic Data of Pyrazine Tetracarboxylic Acid 1 (λ ) 0.83970 Å) at Different
Temperaturesa
123 Kb
293 K
200 K
100 K
20 K
empirical formula
fw
cryst syst
space group
a (Å)
b (Å)
c (Å)
C8H4N2O8‚(H2O)2
292.16
triclinic
C8H4N2O8‚(H2O)2
292.16
triclinic
C8H4N2O8‚(H2O)2
292.16
triclinic
C8H4N2O8‚(H2O)2
292.16
triclinic
C8H4N2O8‚(H2O)2
292.16
triclinic
P1h
P1h
P1h
P1h
P1h
5.4409(3)
6.4041(3)
8.6995(3)
98.572(3)
107.374(3)
105.519(3)
1
5.4950(10)
6.4410(10)
8.7670(10)
99.393(6)
107.565(7)
105.174(7)
1
5.4606(10)
6.4133(10)
8.7164(10)
98.962(5)
107.408(5)
105.348(5)
1
5.4385(10)
6.3885(10)
8.6809(10)
98.381(5)
107.406(5)
105.573(5)
1
5.4361(10)
6.3699(10)
8.6672(10)
97.911(5)
107.546(5)
105.718(5)
1
R (deg)
â (deg)
γ (deg)
Z
volume (Å3)
269.97(2)
1.797
275.44(8)
1.761
271.57(7)
1.785
268.72(7)
1.804
267.48(7)
1.813
D
calc (g/cm3)
T (K)
123(2)
293(1)
200(1)
100(1)
20(1)
a Full crystallographic data and structure refinement parameters are given in the Supporting Information. b X-ray data21 are given for comparison.
CHART 3: Short Hydrogen Bond in a Multicenter
Array in the Crystal Structure of the
Trypsin-CRA-10991 Complexa
a See ref 15 for details.
CHART 4: Crystal Structures of Pyrazinecarboxylic
Acids 1-5 Discussed in This Paper
Figure 2. Oak Ridge thermal ellipsoid plot (ORTEP) of 2,3,5,6-
pyrazinetetracarboxylic acid dihydrate, 1, at 100 K by neutron diffrac-
tion. Atom numbering and displacement ellipsoids at a 50% probability
for all atoms are shown. The C8 carboxylic acid is coplanar with the
pyrazine ring (N7-C9-C8-O1 ) 9.31(7)°), and C11A is out of the
plane (N7-C10A-C11A-O5A ) 80.25(6)°).
in terms of the O-H versus H‚‚‚O distance function, the valence
bond order parameter, s, covalent versus electrostatic character,
and νs(O-H) in the IR spectrum.
Results and Discussion
neutral Oacid-H‚‚‚O bond.24 Recent reports15,25 of multicentered
short hydrogen-bond arrays (e.g., motif II, O‚‚‚O ) 2.50(04)
Å, Chart 3)15 in serine protease crystal structures imply that
the results of this study are relevant in drug design research on
enzyme catalysis and inhibitor potency.
Crystallization of 1 from 20% aqueous HCl gave diffraction-
quality millimeter-size crystals at room temperature after a few
weeks. A single crystal of 0.6 mm × 1.6 mm × 2.8 mm
(calculated volume, 3.65 mm3), obtained after multiple recrys-
tallizations, was selected from the mother liquor for neutron
diffraction. The D9 instrument at the Institut Laue-Langevin is
equipped with an 8° × 8° multiwire (32 × 32) position-sensitive
detector and is optimized for accurate neutron intensity mea-
surements at short wavelengths. At the chosen wavelength λ )
0.8397(1) Å from a Cu(220) monochromator in transmission,
the crystal was cooled slowly at 2° per minute to 20 K, while
monitoring a strong low-angle reflection. Data were collected
at 20 K, and the crystal was then warmed slowly to 100 K, to
200 K, and finally to 293 K, and the structure, redetermined at
each temperature (precision better than (1 K).27 Gratifyingly,
the dihydrate crystal did not become opaque, crack, or undergo
a phase transition during the week-long variable temperature
experiment. The neutron diffraction crystal structure of 1 is in
We discuss in this paper variable temperature neutron
diffraction of the very short O-H‚‚‚O hydrogen bond in
tetraacid 1. Similar neutral O-H‚‚‚O motifs (I and I′) with short
and very short H-bonds are identified in the X-ray crystal
structures of pyrazine di- and tricarboxylic acids 2-5 (Chart
4). The short hydrogen bonds in oxalic acid dihydrate crystal
structures (motif I′′) are compared with our results to highlight
their similarities. These crystallographic results provide evidence
of short O-H‚‚‚O hydrogen bonds in synergistic π- and
σ-cooperative neutral, finite arrays. We name this new hydrogen-
bond shortening model the synthon-assisted hydrogen bond
(SAHB, Chart 2) model and justify our terminology at the end
of this paper.26 The nature of the very short H-bond (VSHB) in
tetraacid 1 is compared with short-strong CAHB/RAHB bonds

Synthon-Assisted Short Oacid-H‚‚‚Owater H-Bonds
J. Phys. Chem. A, Vol. 108, No. 43, 2004 9409
Figure 3. π-Cooperative and σ-cooperative hydrogen-bond motif I in the crystal structure of pyrazine tetraacid 1 from variable temperature neutron
diffraction. Displacement ellipsoids are drawn at a 50% probability level for all atoms. (a) 293 K; (b) 200 K; (c) 100 K; (d) 20 K. Metrics of the
very short Oacid-H‚‚‚Ow hydrogen bond are indicated. Note the reduced thermal vibration of atoms at low temperature. All protons are fully
ordered (also see Figure 4). The synergy of π- and σ-cooperative H-bonds in motif I results in a synthon-assisted hydrogen bond (SAHB), discussed
in the text.
agreement with its X-ray structure21 (cell parameters, space
group, Table 1), so only the neutron structures are analyzed.
0.0167(5) Å2) is smaller than those of the other protons that
are engaged in short and moderate H-bonds at a given
temperature (0.0205(6), 0.0239(6), and 0.0236(6) Å2 at 20 K).
This confirms that the proton in the short-strong hydrogen bond
is sharply located and the quality of the neutron diffraction data
is satisfactory for a detailed analysis of hydrogen bonding.
Crystal Structure of 1 from Neutron Diffraction Data. The
crystal structure of 1 was solved (X-ray data) and refined
(neutron data) in the P1h space group. The molecule lies across
the inversion center (Z′ ) 0.5) with one carboxylic acid in the
plane of the pyrazine ring (torsion angle N7-C9-C8-O1 )
9.31(7)°) and the other one out of the plane (N7-C10A-
C11A-O5A ) 80.25(6)°), as shown in Figure 2. The coplanar
COOH group forms a very short O-H‚‚‚O hydrogen bond with
water (Figure 3). The Oacid-H‚‚‚Ow bond is within the VSHB
range (H‚‚‚O < 1.5 Å, O‚‚‚O < 2.5 Å)2,4,20 with H‚‚‚O distances
of 1.4430(20) and 1.4098(17) Å at 293 and 20 K, respectively.
There are no significant changes in the unit cell parameters
(∼1% compression in each dimension, ∼3% decrease in
volume), hydrogen-bond distances, and angles upon cooling the
crystal, except the usual shortening at low temperature (Tables
1 and 2). This means that there is no phase transition in the
temperature range 293-20 K. An important issue with very
short hydrogen bonds is how precisely the hydrogen atom is
located in the structure. Examination of Table 3 (and Figure 3)
shows that the mean square displacement of the proton in the
very short hydrogen bond is small. The average displacement
Dihydrate 1 has three categories of H-bonds: very short Oacid
-
H‚‚‚Ow, short Oacid-H‚‚‚Oacid, and moderate Ow-H‚‚‚Oacid and
Ow-H‚‚‚N. This trend of increasing hydrogen-bond distance
depending on the strength of donor/acceptor groups is typical
of carboxylic acid hydrates.28 Water is a good hydrogen-bond
acceptor but has moderate donor groups.
The polarization of a water molecule as an enhanced acceptor
group has been illustrated29 in an exceptionally short CsH‚‚‚
Ow H-bond (1.96 Å, 169.3°) in the complex (1,4-diethynyl-
benzene)‚(water)2‚(triphenylphosphine oxide)4. The donation of
water hydrogens to PdO groups (1.85 Å, 161°; 1.77 Å, 168°)
creates a more negative electrostatic potential around the oxygen
atom which results in a very short CsH‚‚‚O H-bond. In tetraacid
1, the donor COOH group of the very short H-bond is activated
because it accepts an OsH‚‚‚OdC hydrogen bond from another
COOH group (π-bond cooperativity). The basicity of the water
molecule is enhanced because the oxygen atom is polarized by
H-bond donation to the COOH and pyrazine groups. We have
of the proton that is involved in the very short H-bond (Ueq
)

9410 J. Phys. Chem. A, Vol. 108, No. 43, 2004
Vishweshwar et al.
TABLE 2: Geometrical Parameters of Hydrogen Bonds in Pyrazine Tetraacid 1 (Neutron Diffraction)
H-bond
T (K)
r (Å)
d (Å)
D (Å)
θ (deg)
Oacid-H‚‚‚Ow
20
100
200
1.0721(15)
1.0720(13)
1.0640(16)
1.0550(20)
0.96
0.9861(17)
0.9871(14)
0.9895(19)
0.9839(19)
0.91
0.9670(18)
0.9670(14)
0.9652(20)
0.9607(19)
0.89
0.9690(20)
0.9699(18)
0.9630(20)
0.9560(20)
0.85
1.4098(17)
1.4113(14)
1.4233(18)
1.4430(20)
1.53
1.7393(18)
1.7365(14)
1.7370(19)
1.7490(20)
1.81
1.8174(19)
1.8151(14)
1.8231(20)
1.8450(20)
1.90
1.9982(19)
2.0050(17)
2.0300(20)
2.0600(20)
2.14
2.4751(11)
2.4765(10)
2.4807(12)
2.4906(16)
2.4791(13)
2.6919(12)
2.6931(9)
2.6996(14)
2.7080(15)
2.7010(12)
2.7794(12)
2.7781(10)
2.7836(14)
2.8001(15)
2.7811(12)
2.9256(12)
2.9340(9)
171.45(15)
171.46(11)
171.60(16)
171.35(17)
171.0
161.28(18)
162.14(13)
163.28(19)
163.70(20)
163.3
172.80(20)
173.51(17)
173.03(21)
172.70(30)
172.0
159.56(17)
159.70(12)
159.90(17)
160.28(18)
157.6
293
123 (XRD)a
Oacid-H‚‚‚Oacid
Ow-H‚‚‚Oacid
Ow-H‚‚‚N
20
100
200
293
123 (XRD)a
20
100
200
293
123 (XRD)a
20
100
200
2.9534(13)
2.9777(14)
2.9393(16)
293
123 (XRD)a
a X-ray data21 are given for comparison.
TABLE 3: Mean Square Displacement (Ueq, Å2) of Protons
CHART 6: (a) The Continuous Array of Partial Positive
and Negative Charges on the Donor and Acceptor
Groups in the Cooperative, Neutral Motif I; (b) Proton
Transfer Can Result in Resonance (Ia) and/or Ionic (Ib-
d) Tautomersa
in Pyrazine Tetraacid 1 (ND Data)
proton
20 K
100 K
200 K
293 K
Oacid-H‚‚‚Ow
0.0167(5) 0.0218(3) 0.0291(6) 0.0379(6)
Oacid-H‚‚‚Oacid 0.0205(6) 0.0265(4) 0.0404(7) 0.0515(8)
Ow-H‚‚‚Oacid
Ow-H‚‚‚N
0.0239(6) 0.0306(4) 0.0415(7) 0.0554(9)
0.0236(6) 0.0256(4) 0.0348(7) 0.0434(7)
0.0166(5) 0.0236(3) 0.0326(6) 0.0427(6)
a
Oacid-H‚‚‚Ow
a Displacement of the hydrogen atom along the O-H‚‚‚O H-bond.
CHART 5: Hydrogen-Bonded Complexes
AcOH‚H2O‚pyrazine IIIa and AcOH‚H2O‚AcOH IIIb
Showing the Polarization of Water Oxygen through
Spartan Calculations
confirmed this computationally in model hydrogen-bonded
complexes, that is, acetic acid‚water‚pyrazine and acetic acid‚
water‚acetic acid (Chart 5), that resemble the polarization of
water in hydrogen-bond array I. The negative electrostatic
potential (ESP) at the water oxygen (Spartan,30 RHF 6-31G*)
increases from -46.2 kcal mol-1 in free water to -64.4 and
-65.2 kcal mol-1 in complexes IIIa and IIIb, respectively (see
the Supporting Information for ESP plots). The negative ESP
of the hydrogen-bonded water oxygen is comparable to that for
PdO oxygen, a very strong H-bond-acceptor group. In effect,
synergy of a finite π-bond cooperative array and polarization-
assisted H-bonds is able to shorten the OsH‚‚‚O bond into the
very short distance range (O‚‚‚O ) 2.30-2.50 Å).
Proton migration in phenol‚pyridine and carboxylic acid‚
pyridine cocrystals (OsH‚‚‚N h O‚‚‚H‚‚‚N h O‚‚‚HsN) has
been studied by variable temperature neutron diffraction.31 The
absence of proton transfer in pyrazine tetraacid 1 is crucial to
the proposed π- and σ-cooperative hydrogen-bond shortening.
If there is proton transfer in I to one or more of the motifs Ia,
Ib, Ic, and Id (Chart 6),32 or a delocalized hybrid structure,
then H-bond shortening could well be a result of ionic donor/
acceptor groups and/or resonance assistance, that is, CAHB/
RAHB. OsH and H‚‚‚O distances in the neutron diffraction
a The absence of motifs Ia-d in the crystal structure rules out
contributions from charge and resonance assistance to the neutral
synthon I.
crystal structure of 1 at different temperatures (Table 2) indicate
the absence of ionic and resonance forms Ia-d. Furthermore,
the CdO and CsO bond distances in the COOH group and
the CsNdC angle in the pyrazine ring (Table 4) are in
agreement with these hydrogen-bonding groups being present
in a neutral form rather than as ionic/resonant species.33 The
unambiguous location of the hydrogen atom in the OacidsH‚‚‚Ow
bond and the absence of disorder/delocalization/proton transfer

Synthon-Assisted Short Oacid-H‚‚‚Owater H-Bonds
J. Phys. Chem. A, Vol. 108, No. 43, 2004 9411
participates in the VSHB through the H-bond array I, similar
to the crystal structure of tetraacid 1. The OacidsH‚‚‚Ow bond
in 5 (O4‚‚‚O8 ) 2.4726(12) Å) is stabilized by the synergy
from π-cooperative and polarization assisted H-bonds (Figure
6). The other H-bonds in synthon I have short to moderate
distances, similar to tetraacid 1. The third carboxylic acid (C6)
forms the centrosymmetric hydrate motif IV with the second
water molecule (O5‚‚‚O7 ) 2.5137(13) Å). The OacidsH‚‚‚Ow
H-bond of motif IV is short, akin to diacid 4, while the other
OsH‚‚‚O/N H-bonds are of moderate length (Table 6). The
crystal structure of triacid 5, analyzed as a combination of
H-bond motifs in tetraacid 1 and diacid 4, contains H-bonds of
increasing distance from very short and short OacidsH‚‚‚Ow
bonds to short and moderate OacidsH‚‚‚Oacid, OwsH‚‚‚Oacid, and
OwsH‚‚‚N interactions. Before closing the X-ray crystal
structure discussion, we emphasize that all the protons in 2-5
are located in difference electron density maps and the neutral
form of the COOH group is concluded from CdO and CsO
bond distances and NsCdN angles33 (Table 4).
Figure 4. Fourier map (Fobs) calculated from the 20 K neutron
diffraction crystal structure of 1. The projection is perpendicular to
the plane of O1, O14, and H2. The contours are at a nuclear scattering
density of 1 fm Å-3, and dashed lines indicate negative contours.
Contours are shown at intervals of 3 units from -21 (minimum,
-21.71) to +42 (maximum, +42.70). The nuclear density is localized
on the hydrogen atom, and there is no evidence of disorder.
Hydrogen-bonding trends in acids 1-5 are now discussed.
The short Oacid-H‚‚‚Ow H-bond is longer in 2, 3, and 4
compared to 1 for two reasons. The carboxylic acid group is a
stronger H-bond donor than water, so the role of finite π-bond
cooperativity is enhanced in 1 compared to 2-4 (motif I vs
motif I′). The carboxylic acid donor in tetraacid 1 is stronger
than diacids 2-4 because more electron-withdrawing groups
are loaded on the pyrazine ring. In addition to these factors,
the more important reason for H-bond shortening in array I is
the polarization of the water molecule. We say this because the
VSHB is shorter in triacid 5 (O‚‚‚O ) 2.4726(12) Å at 120 K)
compared to tetraacid 1 (2.4791(13) Å at 123 K, XRD data
from Tables 2 and 6), even though the COOH donor is
marginally stronger in 1 because of an extra electron-withdraw-
ing group. Incidentally, the short O‚‚‚O distance in 5 at 120 K
is comparable to the distance in 1 at 20 K. That this shortening
of Oacid-H‚‚‚Ow is due to an increase in the acceptor strength
of water oxygen by polarization-assisted hydrogen bonding is
evident from the comparison of Ow-H‚‚‚Oacid and Ow-H‚‚‚N
distances. These σ-cooperative H-bonds, which polarize the
water oxygen, are shorter in 5 compared to 1 (O‚‚‚O )
2.7461(12) Å (5), 2.7811(12) Å (1); O‚‚‚N ) 2.8947(13) Å (5),
2.9393(16) Å (1); XRD data from Tables 2 and 6). A similar
correlation between the shortness of the Oacid-H‚‚‚Ow bond and
the stronger polarization of water oxygen through Ow-H‚‚‚Oacid
in the cooperative synthon IV is observed for diacids 2 and 4
too (Figure 5, Table 6). All this shows that the polarization of
the water oxygen acceptor through σ-cooperatiVe hydrogen
bonding makes a significant contribution to H-bond shortening
in neutral array I, with auxiliary support coming from
π-cooperative H-bonding. These results illustrate that stronger
donor and acceptor groups in motif I shorten (strengthen) the
Oacid-H‚‚‚Ow bond, similar to the behavior of very short and
short (very strong and strong) hydrogen bonds in well-studied
CAHB/RAHB categories.2,5,18 Such graded effects show that
H-bond shortening in motif I is due to chemical (electrostatic)
reasons, that is, the strengthening of donor and acceptor groups,
and not a chance consequence of geometric compression, steric
congestion, or crystal packing effects. This synergistic π- and
σ-cooperative H-bond shortening in a neutral multicenter array
contributes to the growing number of studies toward under-
standing these interactions in terms of a unified electrostatic-
covalent hydrogen-bond model,5d,18e which represents a con-
tinuum in energy from weak interactions to strong H-bonds and
from very strong H-bonds to covalent bonds.37
TABLE 4: CsO and CdO Bond Lengths in the COOH
Group and CsNdC Bond Angles in the Pyrazine Ring of
Acids 1-5 (Taken from X-ray Experiments)
acid
CsO (Å)
CdO (Å)
CsNdC (deg)
1
1.3113(17)
1.2957(16)
1.3115(13)
1.3143(13)
1.3067(16)
1.3078(14)
1.3064(14)
1.2997(14)
1.2022(15)
1.2174(14)
1.2119(13)
1.2122(13)
1.2140(15)
1.2009(14)
1.2124(14)
1.2149(14)
117.63(11)
2
3
4
5
117.85(9)
118.53(9)
116.86(11)
117.51(10)
116.86(9)
in the multicenter H-bond array are confirmed by the Fourier
map of 1 from neutron diffraction data (Figure 4).
Very Short and Short Hydrogen Bonds in Pyrazine Di-
and Triacids 2-5. The X-ray crystal structures of 2,3-
pyrazinedicarboxylic acid dihydrate, 2 (123 K),34 5,6-dimethyl-
2,3-pyrazinedicarboxylic acid dihydrate, 3 (123 K),21 and 2,5-
pyrazinedicarboxylic acid dihydrate, 4 (153 K),35 were analyzed
(Table 5).36 These three diacids crystallize as dihydrates, akin
to tetraacid 1, and contain similar hydrogen-bond motifs except
that a water molecule replaces the COOH donor that initiates
the H-bond array (#COOH in I, motif I′). The water oxygen is
polarized through H-bonds with the COOH and pyrazine groups
as before. The Oacid-H‚‚‚Ow H-bond shortens progressively
from 2 to 3 to 4 (O‚‚‚O ) 2.5513(11), 2.5269(12), and
2.5148(13) Å, Table 6), but these distances are longer than the
short H-bond in 1. Diacids 2 and 4 aggregate through the
cooperative, cyclic H-bond motif IV (Chart 7), whereas
molecules of 3 are connected in a catemer arrangement via motif
I′ (Figure 5).
2,3,5-Pyrazinetricarboxylic acid dihydrate, 5,36 was crystal-
lized from 20% aqueous HCl. The asymmetric unit has one acid
molecule and two water molecules because the triacid molecule
is devoid of an inversion center. In contrast, diacids 1-4 with
a C2 axis or inversion symmetry reside on the special position.
Two COOH groups of 5 are roughly coplanar with the pyrazine
ring, and the third COOH group is out of the plane (N1sC3s
C6sO5 ) 10.45(14)°, N2sC2sC5sO4 ) 4.29(14)°, and N1s
C1sC4sO1 ) 81.02(14)°). The in-plane COOH group (C5)

9412 J. Phys. Chem. A, Vol. 108, No. 43, 2004
Vishweshwar et al.
TABLE 5: X-ray Crystallographic Data of Pyrazine Di- and Triacids 2-5 (λ ) 0.71073 Å)a
2b
3c
4d
5b
empirical formula
fw
cryst syst
space group
a (Å)
b (Å)
c (Å)
C6H4N2O4‚(H2O)2
204.14
monoclinic
C2/c
5.3470(2)
13.0286(4)
11.7443(4)
90
99.036(1)
90
C8H8N2O4‚(H2O)2
232.19
orthorhombic
Pbcn
12.6454(3)
9.0812(3)
8.8800(3)
90
C6H4N2O4‚(H2O)2
204.14
triclinic
P1h
5.2101(2)
6.8261(2)
6.8713(2)
119.144(2)
99.808(2)
99.927(2)
1
C7H4N2O6‚(H2O)2
248.15
triclinic
P1h
5.2830(3)
6.6497(3)
13.8423(7)
93.064(2)
90.513(2)
103.009(2)
2
R (deg)
â (deg)
γ (deg)
Z
90
90
4
4
volume (Å3)
Dcalc (g/cm3)
T (K)
808.00(5)
1.678
123(2)
1019.74(5)
1.512
123(2)
200.85(1)
1.688
153(2)
473.02(4)
1.742
120(2)
a Full crystallographic data and structure refinement parameters are given in the Supporting Information. b This paper. c Reference 21. d Reference
35.
TABLE 6: Geometrical Parameters of the Hydrogen Bonds
Synthon-Assisted Hydrogen Bonds. A survey of the Cam-
bridge Structural Database41 for COOH‚‚‚OH2 hydrogen bonds
in the distance range O‚‚‚O ) 2.30-2.50 Å and O-H‚‚‚O )
160-180° provided two examples42 of neutral carboxylic acids
(Chart 8), other than the title tetraacid and oxalic acid. The
COOH group in CACTUW is activated as an alkyne carboxylic
acid, and the pyrone ring in ZZZSSY02 is sufficiently electron
withdrawing to shorten the O-H‚‚‚O bond (motif I′′). The
Oacid-H‚‚‚Ow bond in ZZZSSY02 is the shortest hydrogen bond
in a neutral array (Figure 7), possibly because the COOH donor
group is attached to a doubly activated electron-withdrawing
position (R to O and â to enone) on the pyrone ring. The reason
for H-bond shortening in a neutral array may therefore be
generalized as follows. If an actiVated carboxylic acid donor
(pKa 1-3) hydrogen bonds to a water molecule that is in turn
H-bonded to O/N acceptors, then the Oacid-H‚‚‚Ow H-bond can
be Very short because the H-bond donor is strengthened by
π-cooperatiVity, or resonance assistance, and the water oxygen
acceptor strength is enhanced by σ-cooperatiVity, or polarization
assistance. We name this novel hydrogen-bond shortening
phenomenon, a result of synergy from finite RAHB and PAHB
(π- and σ-bond cooperative motifs in Chart 1), synthon-assisted
hydrogen bonding. All the hydrogen bonds of the multicenter
SAHB motif I, Oacid-H‚‚‚Oacid, Ow-H‚‚‚Oacid, and Ow-H‚‚‚
in Pyrazine Acids 2-5
acid
H-bond
d (Å)
D (Å)
θ (deg)
2
Oacid-H‚‚‚Ow
Ow-H‚‚‚Oacid
Ow-H‚‚‚N
C-H‚‚‚O
1.61
2.10
1.95
2.44
1.57
2.03
2.08
2.62
2.72
1.57
2.03
1.99
2.60
1.50
1.64
1.83
1.92
1.99
2.06
2.06
2.60
2.5513(11)
2.8993(11)
2.8143(12)
3.3121(13)
2.5269(12)
2.8747(12)
2.8963(13)
3.4980(14)
3.6459(14)
2.5148(13)
2.8024(12)
2.8492(16)
3.4524(16)
2.4726(12)
2.5137(13)
2.7193(12)
2.7461(12)
2.7802(13)
2.8810(14)
2.8947(13)
3.4238(14)
168.0
156.9
166.4
150.5
167.4
163.4
156.5
147.5
159.1
171.0
155.0
166.6
147.9
170.0
168.0
163.9
172.0
156.5
162.8
160.6
142.3
3
Oacid-H‚‚‚Ow
Ow-H‚‚‚Oacid
Ow-H‚‚‚N
C-H‚‚‚O
C-H‚‚‚O
4
5
Oacid-H‚‚‚Ow
Ow-H‚‚‚Oacid
Ow-H‚‚‚N
C-H‚‚‚O
a
b
Oacid-H‚‚‚Ow
Oacid-H‚‚‚Ow
a
Oacid-H‚‚‚Oacid
a
Ow-H‚‚‚Oacid
b
Ow-H‚‚‚Oacid
Ow-H‚‚‚N b
Ow-H‚‚‚Na
C-H‚‚‚O
a Motif I. b Motif IV.
CHART 7: Cyclic Hydrogen-Bond Motif IV in the
Crystal Structures of 2, 4, and 5
Npyr/Oacid, contribute to the shortening of the Oacid-H‚‚‚Ow bond.
Moreover, while the RAHB and PAHB hydrogen bonds in
carboxylic acids and alcohols/phenols have typical O‚‚‚O
distances of 2.50-2.70 Å, the combination of these motifs in a
cooperative array can lead to further shortening of the hydrogen
bond (O‚‚‚O < 2.50 Å). Thus, hydrogen-bond shortening results
from the extended synthon and not from a single interaction.
In this respect, SAHBs are different from the two-center CAHBs
in which shortening is ascribed either to the electropositive donor
hydrogen or to the electronegative acceptor atom. Three variants
of SAHBs are illustrated in synthons I, I′, and I′′ (Chart 2).
There is a pronounced preference in pyrazine di- and higher
acids for crystallization with the inclusion of water, whereas
pyrazine monocarboxylic acids aggregate via the robust acid‚
‚‚pyridine heterosynthon.35 Pyrazine acids with two or more
COOH groups are rich in H-bond acceptors, and the water
molecule, with two donors and one acceptor, compensates for
this difference to give a saturated hydrogen-bond adduct.38 The
number of hydrogen-bond synthons in crystal structures 1-5
with varying numbers of COOH groups is essentially two:
H-bond synthons I and IV. The analysis of crystal structures in
terms of a limited number of supramolecular synthons39
(recurring motifs) is the first step toward crystal engineering,40
the rational design of solid-state architectures from functional-
ized molecules.
The low-temperature X-ray crystal structures of oxalic acid
dihydrate 6 have a very short Oacid-H‚‚‚Ow H-bond in motif
I′′. A plot of O‚‚‚O distance versus O-H(D)‚‚‚O angle in oxalic
acid 6 (and its perdeuterated dihydrate),43 tetraacid 1, triacid 5,
CACTUW, and ZZZSSY02 is shown in Figure 7. This
distance-angle scatter plot of 21 neutron and/or X-ray crystal
structures shows that we have characterized a very short Oacid
-
H‚‚‚Ow hydrogen bond by variable temperature neutron dif-
fraction. Even though the oxalic acid dihydrate crystal structures
have been investigated extensively,43 the shortening of the
hydrogen bond through a synthon-assisted hydrogen bond, or
synergy from π- and σ-cooperative H-bonds, is not mentioned

Synthon-Assisted Short Oacid-H‚‚‚Owater H-Bonds
J. Phys. Chem. A, Vol. 108, No. 43, 2004 9413
Figure 6. X-ray crystal structure of 2,3,5-pyrazinetricarboxylic acid,
5. (a) ORTEP with displacement ellipsoids drawn at a 50% probability
for non-hydrogen atoms. The dihedral angles of the carboxylic acid
groups with the pyrazine ring are N1-C3-C6-O5 ) 10.45(14)°, N2-
C2-C5-O4 ) 4.29(14)°, and N1-C1-C4-O1 ) 81.02(14)°. (b)
Metrics of the Oacid-H‚‚‚Ow hydrogen bond in motifs I and IV are
indicated. Tricarboxylic acid 5 has the shortest Oacid-H‚‚‚Ow hydrogen
bond (O‚‚‚O ) 2.4726(12) Å) in this family of structures. The crystal
structure of triacid 5 is analyzed as a combination of H-bonds in
tetraacid 1 and diacids 2 and 4.
Figure 5. Short Oacid-H‚‚‚Ow hydrogen bond in the X-ray crystal
structures of (a) 2,3-pyrazinedicarboxylic acid dihydrate, 2, (b) 2,5-
pyrazinedicarboxylic acid dihydrate, 4, and (c) 5,6-dimethyl-2,3-
pyrazinedicarboxylic acid dihydrate, 3. Diacids 2 and 4 have the dimer
motif IV, and diacid 3 has the catemer arrangement via motif I′. The
shorter Oacid-H‚‚‚Ow hydrogen bond in 4 compared to 2 correlates with
a shorter Ow-H‚‚‚Oacid hydrogen bond in the former structure,
highlighting the importance of polarization assistance toward hydrogen-
bond shortening. See the text and Table 6 for details. Displacement
ellipsoids are drawn at a 50% probability for non-hydrogen atoms.
CHART 8: CSD Refcodes of Crystal Structures with a
Synthon-Assisted Short OAcid-H‚‚‚Ow Hydrogen Bond
in the earlier publications.42-44 The occurrence of short synthon-
assisted hydrogen bonds with similar extended motifs in diverse
crystal structures justifies the proposal for adding the new SAHB
category to the existing classification of CAHBs and RAHBs.
Other Characteristics of Synthon-Assisted Short H-Bonds
in 1. The nature of the very short O-H‚‚‚O hydrogen bond in
1 was examined by a few other parameters to compare its
behavior with conventional CAHB/RAHB very short or short-
strong hydrogen bonds.
Empirical Bond Order of a Hydrogen Bond. A quantitative
measure of the covalent character in a hydrogen bond is the
valence or bond order, s, which measures the sharing of electron
density between the X-H and H‚‚‚A bonds.9 The bond orders,
s values, for the very short and short O-H‚‚‚O bonds in 1 were
calculated from the empirically derived equations listed in the
footnotes of Table 7. Values of sO-H ) 0.691 and sH‚‚‚O ) 0.295
for the Oacid-H‚‚‚Ow H-bond (r ) 1.0721(15) Å and d )
1.4098(17) Å at 20 K) mean that the hydrogen atom has bonded
∼70% of the valence unit to the covalent bond and ∼30% to
the hydrogen bond. The O-H‚‚‚O interaction in 1 therefore is
well within the quasi-covalent regime defined for interanion

9414 J. Phys. Chem. A, Vol. 108, No. 43, 2004
Vishweshwar et al.
Figure 8. Plot of d(H‚‚‚O) vs r(O-H) (Å) in pyrazine tetraacid 1
from neutron diffraction data (Table 2). The points for the Oacid-H‚‚
‚Ow, Oacid-H‚‚‚Oacid, and Ow-H‚‚‚Oacid bonds overlay nicely on the
solid curve for the equation, rX-H ) r0 - b ln{1 - exp[(r0 - rH‚‚‚X)/
b]}. The solid line is the curve from experimentally derived parameters
from neutron diffraction data, r0,OH ) 0.925, bOH ) 0.397. The dashed
Figure 7. Distance-angle scatter plot of the very short Oacid-H‚‚‚Ow
hydrogen bond in 21 crystal structures with synthon-assisted hydrogen
bonds (SAHBs). Pyrazine tetraacid 1 is represented by filled squares
(9), oxalic acid 6 is represented by filled circles (b), the deuterated
oxalic acid structures are represented by open circles (O), triacid 5 is
represented by a filled triangle (2), ZZZSSY02 is represented by a
filled diamond ([), and CACTUW is represented by a bold dash (s).
Tetraacid 1: ND (red filled square) 20 K, (magenta filled square) 100
K, (yellow filled square) 200 K, (light blue filled square) 293 K; XRD
(maroon filled square) 123 K. Triacid 5: (light green filled triangle)
120 K. Oxalic acid: XRD (light green filled circle) 15 K, (dark blue,
dark green, and maroon filled circles) 100 K, (black and olive green
filled circles) 130 K, (red, magenta, and yellow filled circles) 170 K,
(pink and purple filled circles) 225 K. Deuterated oxalic acid: (red
open circle) 15 K, (dark blue open circle) 100 K. ZZZSSY02: (orange
filled diamond) 161 K. CACTUW: (orange bold dash) 150 K.
line is interpolated from gas-phase electron diffraction values, r0,OH
)
0.96, bOH ) 0.346. The dispersion of points in 1 along the solid curve
is comparable to the conventional CAHB/RAHB short O-H‚‚‚O bonds,
shown in Figure 5 of ref 18c.
bond order of ∼0.3 valence units. The quantum chemical
approach to the calculation of covalent bond orders and atomic
valence indices46 is not used in this paper.
Hydrogen-Bond Potential Energy Well. The hydrogen-bond
potential energy function can have one of these three forms:
(i) an unsymmetrical double-well potential such that the proton
lies in a sufficiently deep minimum and is covalently bonded,
O-H‚‚‚O; (ii) a shallow, symmetrical double-well potential such
that the proton has sufficient vibrational energy to tunnel through
the small activation barrier, O-H‚‚‚O h O‚‚‚H-O; or (iii) a
single well minimum with the proton centered between the two
oxygen atoms, O‚‚‚H‚‚‚O. Usually, short-strong hydrogen bonds
lie in a potential well that resembles function ii or iii. The
electrostatic-covalent character increases toward a quasi-
covalent nature as the H-bond shortens and the potential function
changes from i to ii to iii. The potential energy well in tetraacid
1 is unsymmetrical (like case i) because the hydrogen atom is
covalently bonded to the COOH group and there is no proton
migration to H2O at all the temperatures studied. Proton transfer
is a characteristic of short-strong hydrogen bonds with potential
function ii. SSHBs are present when ∆pKa ≈ 0 (e.g., COOH,
COO-) because the covalent bond and hydrogen bond can
lengthen and shorten, respectively, thereby increasing the
strength of the hydrogen bond.6f,12h,31a Proton transfer is not
observed in 1 because the donor and acceptor groups do not
have an acid-conjugate base relationship. The migration of a
proton from COOH to H2O is unlikely even in the strongest
H-bonds because of the large difference in their pKa values
(COOH, ∼2; H2O, ∼15). There are examples in biochemistry
wherein pKa matching is not really necessary, for example, short
hydrogen bonds in enzyme-inhibitor crystal structures of serine
proteases.12g,15,25 We demonstrate from this study that short
hydrogen bonds are possible in multicenter, neutral arrays even
if the pKa values are far apart because the network of hydrogen
bonds activates both the donor group and the acceptor group,
thereby stabilizing the short H-bond. Interestingly, the donor
and acceptor functional groups involved in the short hydrogen
bonds discussed in this paper (synthon I and related motifs)
and those in protease-inhibitor complexes (synthon II and other
motifs in ref 15) have similar pKa values. A systematic survey
of the protein crystal structure database will possibly reveal more
examples of short-strong, neutral hydrogen bonds akin to the
SAHB array.
TABLE 7: Bond Order,a,b s, of Hydrogen Bonds in Pyrazine
Tetraacid 1 (from ND Data)
H-bond
T (K)
rO-H (Å)
sO-H
dH‚‚‚O (Å)
sH‚‚‚O
Oacid-H‚‚‚Ow
20
100
200
293
20
100
200
293
1.0721(15) 0.691 1.4098(17) 0.295
1.0720(13) 0.691 1.4113(14) 0.293
1.0640(16) 0.704 1.4233(18) 0.285
1.0550(20) 0.721 1.4430(20) 0.271
0.9861(17) 0.857 1.7393(18) 0.128
0.9871(14) 0.855 1.7365(14) 0.129
0.9895(19) 0.850 1.7370(19) 0.129
0.9839(19) 0.862 1.7490(20) 0.125
Oacid-H‚‚‚Oacid
a Calculated using the equations s ) exp[(r0 - r)/b] and rX-H ) r0
- b ln{1 - exp[(r0 - rH‚‚‚X)/b]}, with r0,OH ) 0.925 and bOH ) 0.397.
b Σ s ) sX-H + sH‚‚‚A ) 1 according to hydrogen-bond order conserva-
tion. See ref 9 for details.
short O-H‚‚‚O bonds; for example, the O-H‚‚‚O- H-bond in
potassium hydrogen oxalate has values of sO-H ) 0.73 and sH‚
‚‚ ) 0.26.6c In comparison, the strong hydrogen bonds in 1
O
have a less covalent and more electrostatic character (for Oacid
-
H‚‚‚Oacid, sO-H ) 0.857, sH‚‚‚O ) 0.128, r ) 0.9861(17) Å, and
d ) 1.7393(18) Å at 20 K). Bond order, s, is meaningful only
when calculated from accurate neutron diffraction crystal
structures and at short H‚‚‚O distances (d < 1.8 Å).5e
A plot of dH‚‚‚O versus rO-H displays the expected inverse
relation for the very short and short O-H‚‚‚O hydrogen bonds
in 1 (Figure 8). Experimental values of r and d in 1 fit perfectly
the continuous solid curve derived from neutron diffraction
crystal structures when due allowance is made for the usual
dispersion of H-bond data. The three clusters of the four VT
measurements at d ) 1.41-1.44, 1.74-1.75, and 1.81-1.84 Å
(Table 2) lie on the solid curve with about the same scatter as
the points from the CAHB and RAHB crystal structures reported
by Gilli et al.18c,45 Thus, the synthon-assisted short H-bond in
1 exhibits characteristics similar to conventional short H-bonds
in terms of an inverse O-H distance relation and a hydrogen-

Synthon-Assisted Short Oacid-H‚‚‚Owater H-Bonds
J. Phys. Chem. A, Vol. 108, No. 43, 2004 9415
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Red Shift in the O-H Infrared Stretching Vibration. In
accordance with the covalent O-H bond lengthening in short-
strong H-bonds, the stretching frequency ,νs, of the COOH group
in 1 shows a red shift in the IR spectrum (KBr). The O-H
stretching vibrations of Oacid-H‚‚‚Ow in solid 1 appear at 1454,
1386, 1338, 1277, 1213, 1174, and 1134 cm-1. The broad peaks
at 3462 and 3219 cm-1 arise from the O-H stretching vibrations
of the COOH and water groups (see the Supporting Informa-
tion). These IR frequencies match the empirical νs(O-H) versus
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O‚‚‚O distance relation.7b,47 The hydrogen-bond energy of Oacid
-
H‚‚‚Ow (O‚‚‚O ) 2.49 Å, νs(O-H) ) 1350 cm-1) is estimated
as EHB ≈ 16 kcal mol-1 through comparison with a closely
related crystal structure.48 Differential scanning calorimetry and
thermal gravimetric analysis confirm the phase purity and
stoichiometry of tetraacid dihydrate 1 (Tonset H2O release at 144
°C; Tonset melting at 207 °C, decomposes).
Conclusions
We report the occurrence of short hydrogen bonds in pyrazine
di-, tri-, and tetracarboxylic acid dihydrates 1-5. A very short
O-H‚‚‚O hydrogen bond is characterized in tetraacid 1 and
triacid 5, and short O-H‚‚‚O hydrogen bonds are analyzed in
diacids 2, 3, and 4. The variable temperature neutron diffraction
analysis of dihydrate 1 and low-temperature X-ray diffraction
of dihydrates 2-5 provide an in-depth understanding of the short
hydrogen bond in multicenter synthons I and I′. The synergy
from resonance and polarization assistance in the finite, neutral
array is sufficient to result in short (strong) O-H‚‚‚O hydrogen
bonds when the carboxylic acid donor is activated. This novel
synthon-assisted hydrogen-bond shortening phenomenon is
postulated from the neutron diffraction crystal structure of 1,
verified through the X-ray structures of 2-5, and examples
retrieved from the Cambridge Structural Database (CSD) that
obey SAHB. The present study shows that not only charge and
resonance assistance but also polarization assistance can lead
to very short intermolecular O-H‚‚‚O hydrogen bonds (O‚‚‚O
) 2.4-2.5 Å). This is the first study of a very short Oacid-H‚
‚‚Ow hydrogen bond by variable temperature neutron diffraction
and, in general, a systematic analysis of short O-H‚‚‚O
hydrogen bonds in neutral arrays. The similarity of hydrogen-
bonded synthons discussed in this paper to multicenter short
H-bonds in enzyme-inhibitor crystal structures extends these
results to structure-based drug design. Tetraacid 1 and its amide
have potential in the crystal engineering of square network
architectures.
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Acknowledgment. A.N. thanks the Department of Science
and Technology (SR/S5/OC-02/2002) for research funding. P.V.
and N.J.B. thank the CSIR and UGC for fellowships. University
of Hyderabad acknowledges financial support from the UPE
program. J.A.K.H. thanks the EPRSC for a Senior Research
Fellowship and support to H.P. R.M. thanks the ORS for
support. We thank Dr. M. T. Kirchner (University of Hyderabad)
for discussion.
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Supporting Information Available: Synthesis of pyrazine
acids 1, 3, and 5, neutron diffraction and X-ray diffraction
experimental details, tables of crystal data, crystallographic files
of neutron and X-ray structures (cif format), electrostatic surface
potential maps of water, difference Fourier maps of 1, and IR
spectra of 1 (KBr and Nujol). This material is available free of
charge via the Internet at http://pubs.acs.org.
References and Notes
(1) Jeffrey, G. A.; Saenger, W. Hydrogen Bonding in Biological
Structures; Springer-Verlag: Berlin, 1991.

9416 J. Phys. Chem. A, Vol. 108, No. 43, 2004
Vishweshwar et al.
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short and strong for the Oacid-H‚‚‚Ow hydrogen bond on the basis of an
earlier usage,5a its hydrogen-bond energy of ∼16 kcal mol-1, and other
characteristics of this interaction studied in this paper. Another reason for
describing the Oacid-H‚‚‚Ow hydrogen bond as Very short (O‚‚‚O ) 2.30-
2.50 Å) is to distinguish it from short (2.50-2.75 Å) and moderate (2.75-
3.00 Å) hydrogen bonds present in the same crystal structure. Weak
hydrogen bonds are those with carbon acid donors or phenyl ring acceptors,
for example, C-H‚‚‚O, C-H‚‚‚N, and O-H‚‚‚π (3.00-4.00 Å).
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These values are taken from the 1,2,4,5-benzenetetracarboxylic acid‚4,4′-
bipyridine cocrystal.31b Carboxylic acid proton order/disorder can be
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are given in the Supporting Information.
(28) See ref 2, Table 4.6, pp 61-63.
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(44) See ref 2 (p 99) and ref 19c for π-bond cooperative H-bond
shortening in carboxylic acids and amides.
(45) We have plotted r and d distances in 1 to compare their scatter
plot with the CAHB/RAHB data in Figure 5 of ref 18c. The scatter of points
in 1 along the solid curve is comparable to conventional short H-bonds.
(46) AÄ ngya´n, J. G.; Loos, M.; Mayer, I. J. Phys. Chem. 1994, 98, 5244.
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(47) The O-H stretching frequency, νs, of tetraacid 1 is derived from
the empirical O‚‚‚O (Å) versus νs(O-H) (cm-1) function (ref 7). Very short
Oacid-H‚‚‚Ow H-bond, νs ) 1350 cm-1 (O‚‚‚O ) 2.49 Å at 293 K, ND);
moderate Oacid-H‚‚‚Oacid and Ow-H‚‚‚Oacid bonds, νs ) 3180 and 3390
cm-1 (O‚‚‚O ) 2.70 and 2.80 Å).
(48) See ref 18d. The Cambridge Structural Database (CSD) Refcode
DETSBR01 with O‚‚‚O ) 2.465 Å and νs ∼1200 cm-1 has an EHB value
of 15.5 kcal mol-1. The empirical correlation of O‚‚‚O with νs and EHB is
approximate. We mention these values to show that the numbers for tetraacid
1 are similar to strong RAHB systems.
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(33) Typical CsO and CdO distances in carboxylic acid groups are
1.312(2) and 1.219(2) Å, respectively, whereas the two values are closer
to each other in carboxylate or disordered carboxylic acid groups (1.284(2)
and 1.235(2) Å). The mean CsNdC angles for the pyridine ring in the
protonated and unprotonated forms are 121.4(9) and 116.3(16)°, respectively.