Open Journal of Physical Chemistry, 2011, 1, 37-44
doi:10.4236/ojpc.2011.12006 Published Online August 2011 (http://www.SciRP.org/journal/ojpc)
37
Theoretical Study on the Self, Water-Assisted and Au-
to-assisted Dimer Proton Transfer Reaction in the
N-Hydroxy-Methylen-Formamide
Rezika Larabi1, Yamina Belmiloud1,2, Meziane Brahimi1*
1Laboratoire de Ph ysico-Chimie Théorique et de Chimie Informatique, Faculté de Chimie, University of Sciences and
Technology Houari Boumediene, Alger, Algérie.
2Université M’Hamed Bouguerra, Rue de l’Indépendance, Boumerdes, Algérie.
Received May 11, 2011; revised June 17, 2011; accepted July 21, 2011
Abstract
The proton transfer in the isolated, mono and dehydrated forms, isolated dimers of N-Hydroxy Methylen
Formamide (NHMF) have been completely investigated in the present study using Density Functional The-
ory (DFT), Möller-Plesset perturbation (MP2) and Hartree-Fock (HF) methods with the 6-31G* and 6-311G*
basis sets. The barrier heights for both H2O-assisted and auto-assistance reactions are significantly lower
than that of the bare tautomerization reaction from NHMF to N-Formyl Formamide (NFF), implying the
importance of the superior catalytic effect of H2O in the monomer of NHMF and important role of
HOCH=N-COH for the intramolecular proton transfer.
Keywords: N-Hydroxy Methylen Formamide, Proton Transfer, HF, MP2 and DFT
1. Introduction
The importance of the amide functional group is demon-
strated by the fact that the amide peptide bond is the ba-
sic linkage in peptides and proteins. The NHMF (Figure
1) [1] is the smallest N-acyled Imidate which contains
the two amide and oximin forms of the formamide tauto-
meric equilibrium.
The internal coordinates optimization of the different
conformers: trans-trans, cis-cis and trans-cis lead to sta-
bles structures, respectively, of the same configuration
that the initial input and no imaginary frequencies were
found. The cis-trans optimization leads to a transition
state. The cis-cis structure is stabilized by intra-molecu-
lar hydrogen bond between H8 and O4. The hydrogen
bond generates in this conformer, on one hand the pla-
narity of the system at all theoretical levels and an other
hand an elongation of the double links C=N. The link C=
N and C=O are in the same plan. They do not constitute a
delocalized system. The lengths of the links C=N and C=
O, in the trans-cis conformer, correspond in all cases to
the localized links by comparing them to the experimen-
tal data that we met for C=N in the conjugated imines [2]
and the C=O in the formamide’s family [3,4]. This is
confirmed by the frequencies calculation which gives νC=N
= 1671.82 cm–1 and νC=O = 1718.75 cm–1 at MP2/6-31G*
level [1].
The conformational energy reaction cis-cis to trans-cis
is endothermic of 4.29 kcal/mol at B3LYP/6-31G* level.
The change of configuration passes by a transition state
which is situated at an energy barrier of 26.20 kcal/mol
at HF/6-31G* and 30.65 kcal/mol at B3LYP/6-31G* level
[1]. These energies correspond to a rotation around the
double bond C1=N2 and are, respectively, two and three
times larger than those we find in the literature for the
rotation around the bond C2-C3 in the butadiene (13.23
kcal/mol) [5]. These activation energies are high enough
to allow, in warm conditions, the passage from one to the
other of the two conformers. Thus, the two structures cis-
cis and trans-cis exist; the first one in the absence of the
other. The calculation of the electronic energy, corrected
energy at the zero point and thermal energy, leads for HF,
MP2 and B3LYP/6-31G* to the same order of stability:
Cis-cis > trans-cis > trans-trans > cis-trans.
In one hand the trans-cis form becomes strongly pre-
dominant in the polar solvent because of its high dipole
moment, which is much greater than that of cis-cis forms.
n fact, the dipole moment of the trans-cis structure of I

R. LARABI ET AL.
38
Figure 1. Different structures of the N-Hydroxy Methylen Formamide (NHMF) [1].
NHMF is 2.48, 2.52 (2.42) Debye in B3LYP and MP2
(HF//6-31G*). In another hand, these two forms in the
cis-cis tautomeric equilibrium are identical. All these
facts explain our choice of the equilibrium tautomer
study of the trans-cisforms of the NHMF molecule which
contain in the same time the amide and imidic forms of
the formamide molecules.
The formamide-formamidic tautomerization has been
used to a model in large basic linkage in peptides and
proteins. Several theoretical studies on the monohydrated
(bi-hydrated) formamide-water complex have deter-
mined that the preferred mechanism for proton transfer
to form formamidic acid proceeds via stable cyclic dou-
ble or triple hydrogen bonded transition state [6-11].
The energy barrier for the formamide→formamidic
acid isomerization was estimated by Wang et al. [8] to be
48.9 kcal/mol in the gas phase. But in the same article it
was shown that a single H2O molecule directly assists the
tautomerization of formamide lowers the barrier to 22.6
kcal/mol.
The present work has two purposes: 1) To perform the
same studies with the NHMF molecules and to compare
theses results; 2) To discuss the possibility that NHMF
dimers may be involved in an effecting tautomerization.
2. Computational Methods
In this work, all computations were carried out by means
of the Gaussian 03W [12]. All the geometries of local
minima and transition state structures were optimized
without symmetry restrictions (C1 symmetry was as-
sumed) by the gradient procedure initially at the HF level
and subsequently at the second order of closed shell
Möller-Plesset perturbation theory [13].
The results have been compared with those obtained
from the Functional Density Theory (DFT) by using the
function of exact exchange of Becke (B3) [14] and the
function of the gradient correction of Lee Yang Parr
(LYP) [15]. The characteristics of local minima and
transition states were verified by establishing that the
matrices of the energy second derivatives (Hessians)
have zero and one negative eigenvalues, respectively at
all level of theory.
3. Results and Discussion
The structures and frequencies of the equilibrium ge-
ometry were discussed briefly in the introduction of this
work and in detail by Brahimi et al. at the HF, post-HF
(MP2) and density functional theory levels for the iso-
lated NHMF [1].
3.1. Self, Water-Assisted and Self-assisted
Proton Transfer Reaction in the NHMF
Molecules
3.1.1. Geometries
Both formamide and formamidic forms to the tautomeric
equilibrium of formamide molecules are present in the
smallest N-acyled imidate NHMF (Figure 1) [1]. The
self-proton transfer from O7-H8 to N2 in the NHMF gives
the N-Formyl Formamide (NFF) molecules. Figure 2
shows the geometries of the reactants, transition states
and products involved in the self, H2Oassisted, (H2O)2-
assisted and self-assisted NHMF proton transfer reac-
tions obtained at HF, MP2 and DFT/B3LYP levels with
6-311G* basis.
For the self mechanism (NHMF TS NFF), the transi-
tion state appears to hold a co-planar four-membered-
ring. When we exam the structural changes from reactant
to product, it can be seen that the C=N-C=O dihedral
angle fluctuate according to the theoretical level used,
this angle worth 0.0(9.4) at the HF, 28.2(32.7) at the
MP2 and 23.8(27.9) degrees at the B3LYP//6-31G* (6-
311G*), and the C=O bond length does not vary from
reactant to product via transition state. This proves once
more that the C-N bond length corresponds well to a
imple bond and the C=N and C=O are not conjugated in s

R. LARABI ET AL.
39
(a)
(b)

40 R. LARABI ET AL.
(c)
(d)
Figure 2. The optimized st ructures of the reactant s, transition states and pro ducts of the (a) Self, (b) H2O-assisted, (c) (H2O)2-
assisted and (d) auto-assisted tautomeric process. Th e bond lengths are in Å and bond angles in degree.

R. LARABI ET AL.
41
the NHMF molecules. Also we can see, the N2C1O7 bond
angle is compressed by 13.7(13.3) degrees for the transi-
tion state at the MP2//6-31G* (6-311G*) level. The C=N
bond to lengthen of 1.283(1.279) to 1.394(1.395) Å and
the C-N bond to contract of 1.413(1.414) to 1.388(1.389)
Å to attain the NFF structure at the MP2//6-31G* (6-
311G*) level. In all cases, we remark that the C=O bond
narrowed when the C=N to stretch out. The geometrical
parameters, calculated with the DFT/B3LYP level, are in
good agreement with those obtained with the MP2 level.
For H2O-assisted tautomerization (NHMF(H2O)→
TS(H2O)→FF(H 2O)), the most stable geometry of reac-
tant NHMF(H2O) is the cyclic double-hydrogen bonded
structure. The two hydrogen bonding distances are 2.205
(2.253) Å and 1.833 (1.814) Å, respectively, at HF//6-31G*
(6-311G*) levels. These results are in good agreement
with those obtained by Ai-Ping-Fu and Col. in the study
of proton transfer in the formamide [11].
In the NFF(H2O) product, it is also a double hydrogen
bonded system with the two hydrogen bonds and are
2.044 (2.014) Å and 2.132 (2.168) Å, respectively, at
HF/6-31G*(6 -311G*) level. In comparison with the self-
tautomerization, the obvious difference is that the N2C1O7
angle has to be compressed by only 1.2 degrees at
MP2/6-311G* level (for NHMF→NFF is 13.3˚). The
passage of isolated NHMF tautomeric form to the hy-
drated ones leads a net variation of the C1N2C3O4 dihe-
dral angle. On DFT/B3LYP level, its value (23.8 without
H2O) becomes (4.7 with H2O) degrees with 6-31G* basis
and (27.9) becomes 11.3 degrees with 6-311G* basis. On
MP2 level, its value passes from 28.2 to 12.6 degrees
with 6-31G* basis and from 32.7 to 21.2 degrees with 6-
311G* basis. On HF level, its value passes from 0 to 2.8
degrees with 6-31G* basis and from 9.4 to 2.9 degrees
with 6-311G* basis. Thus, the introduction of one water
molecule has an effect on the planarity of the system but
not the delocalization for the π electrons. In fact, the
C1=N2 and C3=O4 bonds correspond, in all cases, to a
localized bonds. In the NFF structure, the solvent effect
is practically vanished.
Similar to the H2O-monomer assisted process, the
(H2O)2-catalyzed mechanism, the reactions also started
by the formation of the NHMF (H2O)2 which involves a
co-planar eight membered-ring due to the formation of
the hydrogen bonds. In the reaction process, two H2O
molecules involve in assisting the passage of the proton
from NHMF to NFF. As discussed above, from Figure 2
we can see the framework of NHMF monomer change
greatly in TS than that TS (H2O) and TS (H2O)2 . In ad-
dition, ∠NHO is 102.7˚ at MP2//6-311G* in TS, while
∠NHO and ∠OHO are 143.7˚ and 154.5˚ respectively
at MP2//6-311G* in TS(H2O), whereas ∠NHO, ∠OHO
et OHO are all closed to 180˚ in TS(H2O)2 (168.2˚,
164.5˚ and 173.8˚ at MP2/6-311G*). This quasi-linear
structure causes the proton easier to transfer in proceed-
ing of NHMF(H2O)2→TS(H2O)2→NFF(H2O)2 than in
proceeding of NHMF(H2O)→TS(H2O)→NFF(H2O) and
NHMF→TS→NFF. So the intimate involvement of wa-
ter can assist the proton transfer. The two H2O molecules
make easy the proton transfer from O7 towards N2.
For the NHMF self-assisted mechanism, the optimized
geometries of the stationary points, transition state at HF,
MP2 and DFT/B3LYP levels with 6-311G* are also il-
lustrated in Figure 2 being similar to the water-catalyzed
reactions, the reactant of the NHMF dimer also forms a
co-planar eight membered-ring via two equivalent hy-
drogen bonding. The hydrogen bond distance is 1.872
and 1.629 Å, respectively at HF and B3LYP//6-311G*
level. Similarly, NFF dimmer also appears to be a cyclic
double hydrogen bonded structure with the hydrogen
bond distance is 2.006 and 1.889 Å, respectively at HF
and B3LYP//6-311G* level. In NHMFdimer, the NHO
angle is quasi-linear (179.9 at B3LYP//6-311G* level)
causing the proton easier to transfer from the oxygen
atoms towards the nitrogen ones. In all cases, the two
forms NHMF-dimmer and NFF-dimer exhibit a plan
structures.
3.1.2. Energetic
Figure 3 shows the energetic diagrams of the reactants,
transition states and products involved in the 1) self, 2)
H2O-assisted, 3) (H2O)2-assisted and 4) self assisted
NHMF proton transfer reactions obtained at HF, MP2
and DFT/B3LYP levels with 6-311G* basis.
It appears that the NHMF→NFF energy reaction, with
ZPE correction, is exothermic of 17.35, 17.61 and 17.17
kcal/mol. at the HF, MP2 and DFT/B3LYP//6-311G*
level, respectively, thus the NFF form is the most stable
than that NHMF one.
The NHMF→NFF reaction passes through out a transi-
tion state situated at an energy barrier of 44.26, 44.32 and
of f 19.16 Kcal/mol. at the HF, MP2 and B3LYP//6-311G*
level, respectively. We think that the great barrier energy
at the gas phases involve the simultaneous existence of
the two NHMF and NFF molecules.
In one hand, Figure 3 shows that the NHMF (H2O)→
NFF(H2O) is also exothermic. We note that the two
NHMF and NFF hydrated molecules are slightly stabi-
lized comparing to the isolated molecules. The energetic
gap from the two reactions, hydrated and isolated, is re-
duced by 1.32(1.47), 1.12(1.27) and 3.25(3.23) kcal/mol.
at the HF, MP2 and DFT/B3LYP//6-31G* (6-311G*) level,
respectively. We note also that the solvent effect decrease
the barrier of the activation energy. The gap energy is
23.13(24.30), 22.37(23.83) and 8.80(10.15) kcal/mol. at
he HF, MP2 and DFT/B3LYP//6-31G*(6-311G*) level, t

R. LARABI ET AL.
42
(a)
(b)
(c)
(d)
Figure 3. The optimized struct ures of the reactant s, transi tion states and products of the (a) Self, (b) H2O-assisted, (c) (H2O)2-
assisted and (d) auto-assisted tautomeric process. Th e bond lengths are in Å and bond angles in degree.

R. LARABI ET AL.
43
respectively and the 6-31G* to 6-311G* basis extension
increase slightly the activation barrier energy.
In another hand, the results, obtained at the different
level of theory (with ZPE correction), show that the
NHMF (H2O)2→NFF(H2O)2 is exothermic by 16.97, 17.26
and 12.82 kcal/mol at the HF, MP2 and B3LYP//6-311G*
level, respectively. These energies barriers are the same
with those obtained for the NHMF (H2O)→NFF(H2O)
reaction for the proton transfer when we use one water
molecule. The DFT/B3LYP level, conduce to the small-
est energy barrier, see 3.85 kcal/mol. This proves that the
second water molecule addition doesn’t have an effect on
all the different energetic value.
The NHMF-dimer→NFF-dimer reaction is exothermic
of 32.72, 32.46 and 26.56 kcal/mol. at the HF, MP2 and
DFT/B3LYP//6-311G* level, respectively. The transition
state, compared to the reactant one, is located at 5.55,
4.29 kcal/mol. at the HF, MP2//6-311G*, respectively
and –2.56 kcal/mol. at the DFT/B3LYP//6-311G* level.
The latter value is probably due to a spontaneous NHMF
NFF reaction. In the NHMF-dimer tautomerization, the
energy barrier decreases about 90% in comparison with
the self-NHMF tautomerization. According to this study,
we conclude that the NHMF→NFF reaction is au-
to-assisted by the NHMF-dimer proton transfer with the
smallest barrier and a good structural arrangement that
favoured the proton transfer mechanism.
4. Conclusions
The introduction of one or more water molecules has not
a great effect of the NFF geometrical parameters con-
trary to the NHMF ones. The water molecule restores the
planarity of the systems without affecting the no-conju-
gaison of the two C=N and C=O double bonds.
In all cases, the NFF molecules are more stable then
the NHMF ones.
All theoretical levels, in aqueous environments, tend
to decrease the energy barrier and the energy tautomeri-
zation compared to the gas phases. The HF and MP2
results promote the existence of the two NHMF and NFF
separate molecules in the gas phase and hydrated ones.
DFT leads a lower barrier energy compared with those
obtained at the HF and MP2 levels.
Thus this method provides the simultaneous existence
of the both molecules in the both environments. Finally,
the NHMF→NFF reaction is established on a self-as-
sisted NHMF dimmer with low barrier energies.
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