Behavior of water dimer under the influence of external electric fields

advertisement
Indian Journal of Chemistry
Vol. 52A, Aug-Sept 2013, pp. 1056-1060
Behavior of water dimer under the influence of external electric fields
Arobendo Mondal, H Seenivasan, Sameer Saurav & Ashwani K Tiwari*
Department of Chemical Sciences, Indian Institute of Science Education and Research, Kolkata, Mohanpur Campus,
Krishivisyavidyalaya PO, Nadia, 741 252 West Bengal, India
Email: [email protected]
Received 3 April 2013; accepted 29 April 2013
A detailed quantum chemical study has been carried out at the CCSD(T) level of theory to understand the behavior of
water dimer under the influence of external electric fields. The energy values obtained at this level of theory follow the same
trend as observed with the DFT and MP2 levels of theory. Our calculations show that water dimer gets stabilized with
increase in the strength of electric field. A slight increase in the hydrogen bond distance and relatively larger decrease in the
hydrogen bond angle is found with the increase in the strength of electric field. The dipole moment and HOMO-LUMO
energy gap increase with the increase in the strength of electric field.
Keywords: Water dimer, Electric field, Coupled cluster methods, Dipole moments, HOMO-LUMO energy gap
Water clusters are group of water molecules (ranging
from two to a few) that are held together by hydrogen
bonds. Unlike atoms and molecules and solids, the
properties exhibited by the clusters under the
influence of external field are unique in many ways. It
is important to study water clusters in order to
understand properties of the bulk water, cloud and
ice formation, solution chemistry, electrochemical
and biochemical processes. To get an insight into
water clusters, it is necessary to know its behavior
under external influences, in particular, in the
presence of electric field. Various methods used
for understanding the interaction of water molecules
like new laser spectroscopy experiments, combined
with the global analysis of potential surfaces and
diffusion Monte-Carlo methods are explained in
the previous reports.1,2
Several attempts have been made by researchers to
understand the effect of external electric field on
water, both experimentally1-4 and theoretically.5-23 For
ease of understanding, the studies have been
segregated into two groups on the basis of the number
of water molecules involved. Water clusters (H2O)n in
which n ≤ 20 comprise one group and the ones
containing more than 20 water molecules fall in the
other. In the literature, we find that molecular
dynamics simulations have been carried out in order
to explain the bulk water and liquid water which
involve more than 20 molecules of water.10-15 On the
other hand, quantum chemical calculations16-19
employing very high level of theory have been
used to describe the interactions of small size clusters
(n < 20) to get accurate numbers for the observables
like stabilization energy, dipole moment, etc., which
further help in better understanding of the physics
involved.
Girardi and Figueiredo5 in their square model water
showed that the number of hydrogen bonds per molecule
is a monotonic decreasing function of the field
magnitude. In 1991, Zhu et al.6 studied the effect of an
intense laser field on liquid water using classical
molecular dynamics simulations using a water model
SPC-FP. They showed that both the liquid structure and
intramolecular geometry get distorted by forming a large
number of bifurcated hydrogen-bonds. Suresh et al.7
developed a theory based on reaction equilibria and
Boltzman distribution for studying hydrogen-bond
network of water in external electric field and predicted
that at practically attainable field strengths, the electric
field cannot disrupt the hydrogen-bond network.
However, weakening of the bonds is observed at higher
field strengths which cannot be attributed to the effect of
electric field alone. Very recently Saitta et al.8 studied
liquid water using ab initio molecular dynamics and
observed (i) significant modification in the hydrogenbond length and molecular orientation at low-tomoderate fields, and, (ii) dissociation and ionic current at
high fields (above 0.35 V/Å). A number of studies on
MONDAL et al.: WATER DIMER IN EXTERNAL ELECTRIC FIELDS
bulk water using molecular dynamics is available which
focus on structural modification by external electric
field.9-15 The molecular dynamics simulations, in
general, suggest that the structure of water (bulk, liquid
and clusters) changes after a particular threshold electric
field, which is higher for clusters when compared to that
for the bulk or liquid water.
At this juncture, we would emphasize on the
literature pertaining only to the clusters containing less
than 20 water molecules. Dykstra16 using a model
potential found that in a weak field, minor distortions
in trimer cyclic structure occurs, whereas at very high
field (~0.08 a. u.) the trimer ring opens since the field
overcomes the intermolecular interaction. A DFT based
study by Karahka and Kreuzer17 showed that for small
external electric fields the water whiskers polarize and
align along the field. The alignment of dipole moment
with the field is favoured because of the formation of
staggered conformation (in this case, helical) which is
usually lower in energy. At high fields, chargetransfer and re-hybridization leading to closing of the
HOMO-LUMO gap is observed which finally results
in fragmentation. Acosta-Gutiérrez et al.18 carried out
molecular dynamics simulation with TIP4P and
polarizable Dang-Chang potential to study the global
minimum structure, energy, dipole moment of water
cluster (n ≤ 20) in low and moderate electric fields
(E< 0.6 V/Å). They observed two distinct transitions
in the electric field: (i) field range of 0.1–0.3 V/Å, in
which the hydrogen bond reorganizes, and, (ii) field
range of 0.3–0.5 V/Å in which elongation of cluster in
direction of electric field occurs with enhanced dipole
moments. For large enough fields (0.6–1 V/Å), the
larger structures (n > 10) converges to helical
structures. Choi et al.19 have investigated small water
clusters (n = 3–5) in external electric field employing
DFT and concluded that with increasing electric field,
the clusters open up to form a linear chain along the
direction of the field. Their results compare well with
those of James et al.20, who showed the change of
structure of water clusters from compact to more
extended structures at higher fields, employing
classical rigid-body models of the TIPnP (n = 3–5)
family of effective pair potentials. Similar results are
reported for small methanol clusters, in terms of effect
of enhanced electric field on structure, although
threshold field is slightly higher for cyclic clusters of
methanol.21 Rai et al.22,23 have studied water clusters
for n = 6–8 and n = 9–20 using DFT and found that
due to applied electric field above a certain threshold
1057
value, the three-dimensional structure of clusters
opens up and forms linear, branched or net-like
structures such that dipolar water monomer align in
direction of electric field. Results for octamer are also
found to be consistent with those of James et al.20
In each case, the threshold values depend on size
of the cluster. Toledo et al.24 have investigated
the effect of external electric field on water clusters
n = 2–16 using DFT and noticed a change in
the number of hydrogen-bonds, thereby leading to
reduction in cluster sizes having stronger inter-cluster
hydrogen bonds.
From the available literature, Karahka and
Kaeuzer17 made some generalizations regarding the
field effects on water clusters, as follows: (a) at low
fields, only “physical effects” such as polarization of
the atoms and molecules occur, and, (b) the high
fields are responsible for the alterations in the
chemical characteristics of atoms and molecules.
In the present work, we explore and analyze
systematically the effect of external static electric
field on the electronic properties of water dimer in the
ground state using CCSD(T) level of theory25 which is
the “gold standard in quantum chemistry”.
Methodology
All calculations were performed using the
GAUSSIAN’03
package.26
The
structure
optimization, with and without electric field,
for water dimer were carried out under the second
order Moller-Plesset perturbation (MP2)27 level of
theory employing the 6-311++G** basis set. Then
the single point calculations for the MP2 theory
optimized geometries (with and without electric field)
were performed at the CCSD(T) level of theory.
Results and Discussion
The optimized geometries and the energy values
for the corresponding equilibrium geometries without
any external perturbation for the monomer, dimer,
trimer and its higher oligomers (4 ≤ n ≤ 20) calculated
at a higher levels of theory (MP2 and DFT) can be
found elsewhere.28-31 Herein we have calculated the
energies corresponding to the equilibrium geometries
of water dimer. The initial geometry is optimized in
the absence of field and this value is reported as the
energy at zero field or field-free energy. To study
the effect of electric field, the field is applied in the
OH–O hydrogen bond direction as shown in Fig. 1
and the structure of the dimer is optimized in the
1058
INDIAN J CHEM, SEC A, AUG-SEPT 2013
Fig. 1 – Direction of the applied external electric field is along
the O–H hydrogen bond between the two water molecules
(positive X direction).
Fig. 2 – Energy corresponding to the optimized geometries for
the increasing electric fields calculated at two levels of theory.
[1, MP2; 2, CCSD(T)].
increasing electric fields upto 100×10-4 a. u.
The maximum field strength considered in this
study is approximately equal to 0.5142 V/Å
(1 a.u. = 51.4220652 V/Å). MP2 was used to optimize
the structures and CCSD(T) was used to obtain the
single point energy of the optimized structures. As
can be seen in Fig. 2, the energy values calculated at
MP2 and the CCSD(T) levels of theory follow the
same (decreasing) trend for the different electric fields
considered. We observed a small decrease in energy
at the CCSD(T) level which shows that the obtained
energy is close to the true ground state energy which
is expected when a more accurate level of theory is
used. It was also observed that the energy of the dimer
decreases with increasing electric field (Fig. 3a). This
shows that the water dimer attains a more stable
structure with the increasing electric field. Earlier
researchers also observed similar phenomena in their
studies.18-20 Acosta-Gutiéuez et al.18 suggested that
this decrease in energy is not a particularly effective
Fig. 3 – (a) Plot of total energy of the system as a function of
hydrogen bond distance with the increasing electric field
calculated at the CCSD (T) level of theory, and, (b) Change in the
dissociation energy of the dimer with the increasing electric field.
diagnostic for structural changes as the electric field
intensity changes. Toledo et al.24 in their study argued
that the small cluster becomes stronger with the
increase in electric field which confirms the findings
of this study. Change in dissociation energy of the
dimer with the increasing field strength is plotted in
Fig. 3b. We find a steady increase in the dissociation
energy up to 0.008 a.u. (0.4114 V/Å) followed by a
decrease at higher fields.
The hydrogen bond distance plotted against the
electric field shows an overall increase in the
hydrogen bond length up to 0.008 a.u. and an
appreciable decrease thereafter (Fig. 4). On close
scrutiny, we find that there are oscillations in the
value of the H-bond distances and the observed
increase is not perfectly linear. It is worth mentioning
MONDAL et al.: WATER DIMER IN EXTERNAL ELECTRIC FIELDS
Fig. 4 – Variation of OH—O angle and OH bond distance of
dimer with increasing electric field. [1, O–H bond distance;
2, OH—O bond angle].
Fig. 5 – Change in the orientation of the water molecule with the
electric field showing the increase in the O—H bond distance and
the change in orientation angle.
here that H-bond length increases over a very small
range (1.951–1.963 Å) and at this range such
oscillations are expected. Acosta-Gutiéuez et al.18
attributed this increase to reorganization of hydrogen
bonds whereas James et al.20 concluded that the
higher fields favor a more extended structure which
can align with the field in a more effective way.
Profound decrease in the OH–O bond angle was
observed with increasing electric field. Change in the
OH–O bond angle and the O–H bond distances with
the electric field are illustrated with a series of dimer
geometries (Fig. 5). It is apparent from Fig. 5 that
the second H2O molecule tries to align itself in
order to minimize the energy and maximize the
interaction of the dipole with the field. It has been
proposed that there exists a second energy channel to
minimize the interaction energy.9 The synergistic
action of increase in dipole moment along with the
increase in hydrogen bond length and the decrease in
the O–H–O hydrogen bond angle leads to decrease
in the energy of the system.
1059
Fig. 6 – Change in the values of dipole moment and the HOMOLUMO energy gap for the water dimer with the increasing electric
field. [1, HOMO-LUMO gap; 2, dipole moment].
The plot of dipole moment and HOMO-LUMO
energy gap versus electric field is shown in Fig. 6. We
see that the dipole moment of the water dimer
increases with the increasing electric field. There is a
steep increase in the very low field strength region
(up to 0.0045 a.u.) after which the increase appears
to be slower. This increase in dipole moment is
due to the contributions from the individual
polarizability of the water dimers. As the electric
field increases, the dimers are more polarized and
they try to align in the direction of the field. Similar
results related to the orientation of dipole moments of
water along the field taking place in such low electric
field (0.1 – 0.2 V/Å) has been reported.17,18 The
increase in the HOMO-LUMO energy gap with the
increase in the field is evident from Fig. 6. This
increase attains a threshold value at 0.008 a. u. after
which it starts decreasing. Similar behavior was
exhibited by a trimer in a previous study wherein it
was found additionally that the energy gap closes at
the point of dissociation. We may also expect such
behavior for the dimers in very high field strengths.
The above discussion shows that the field strength
of 0.008 a.u. corresponds to some physical
phenomena which are yet unclear. With the help of
available literature we may assume it might that the
rearrangement of hydrogen bond takes place prior to
the threshold field strength. Increase in the field
strength beyond this point may lead to dissociation
of the dimer, which requires further detailed
investigations.
1060
INDIAN J CHEM, SEC A, AUG-SEPT 2013
Conclusions
A detailed quantum mechanical study at the
CCSD(T) level of theory has been carried out to
understand the influence of electric field on water
dimer. Our calculations show that electric field has
negligible effect on hydrogen bond distance but has a
large effect of hydrogen bond angle. It has also been
found that dipole moment and HOMO-LUMO energy
gap increase with increase in the strength of electric
field. It is also important to note that the results
obtained in our study agree qualitatively with
previous DFT and MP2 studies, while however,
the energy computed by CCSD(T) method are quite
different from the above mentioned methods.
References
1
2
Liu K, Cruzen J D & Saykally R J, Science, 271 (1996) 929.
Keutsch F N & Saykally R J, Proc Natl Acad Sci, 98 (2001)
10533.
3
Kumarappan V, Krishnamurthy M & Mathur D, Phys Rev A,
67 (2003) 063207.
4
Moro R, Rabinowitch R, Xia C & Kresis V V, Phys Rev Lett,
97 (2006) 123401.
5
Girardi M & Figueiredo W, J Chem Phys, 125 (2006)
094508.
6
Zhu S -B, Zhu J–B & Robinson G W, Phys Rev B, 44 (1991)
2602.
7
Suresh S J, Satish A V & Choudhary A, J Chem Phys, 124
(2006) 074506.
8
Marco Saitta A, Saija F & Giaquinta P V, Phys Rev Lett, 108
(2012) 207801.
9
Sutmann G, J Electroanal Chem, 450 (1998) 289.
10 Vegiri A, J Mol Liq, 112 (2004) 107.
11 Schevkunov S V & Vegiri A, J Mol Struct THEOCHEM,
574 (2002) 27.
12 Schevkunov S V & Vegiri A, J Mol Struct THEOCHEM,
593 (2002) 19.
13 Vegiri A, J Chem Phys, 116 (2002) 8786.
14 Vegiri A & Schevkunov S V, J Chem Phys, 115 (2001) 4175.
15 Jung D H, Yang J H & Jhon M S, J Chem Phys, 244 (1999)
331.
16 Dykstra C E, Chem Phys Lett, 299 (1999) 132.
17 Karahka M & Kreuzer H J, Phys Chem Chem Phys, 13
(2011) 11027.
18 Acosta-Gutiéuez S, Hernández-Rojas J, Bretòn J, Gomez
Lorente J M & Wales D J, J Chem Phys, 135 (2011) 124303.
19 Choi Y C, Pak C & Kim K S, J Chem Phys, 124 (2006)
094308.
20 James T, Wales D J & Rojas J H, J Chem Phys, 126 (2007)
054506.
21 Rai D, Kulkarni A D, Gejji S P & Pathak R K, J Chem Phys,
135 (2011) 024307.
22 Rai D, Kulkarni A D, Gejji S P & Pathak R K, J Chem Phys,
128 (2008) 034310.
23 Rai D, Kulkarni A D, Gejji S P, Bartolotti L J & Pathak R K,
J Chem Phys, 138 (2013) 044304.
24 Toledo E J L, Custodio R, Ranalho T C, Eugenia M, Porto G
& Magriotis Z M, J Mol Struct THEOCHEM, 915 (2009)
170.
25 (a) Coester F, Nucl Phys 1 (1958) 421; (b) Coester F &
Kümmel H, Nucl Phys, 17 (1960) 477; (c) Čížek J, J Chem
Phys, 45 (1966) 4256; (d) Čížek J, Adv Chem Phys, 14 (1969)
35; Paldus J, (e) Čížek J & Shavitt I, Phys Rev A, 5 (1972) 50;
(f) Bartlett R J & Purvis III G D, Int J Quantum Chem 14
(1978) 561; (g) Purvis III G D, Phys Sci, 21 (1980) 225;
(h) Bishop R F & Lührmann K H, Phys Rev B, 17 (1978)
3751.
26 GAUSSIAN 03, (Gaussian Inc., Pittsburgh, PA) 2004.
27 Møller C & Plesset M S, Phys Rev, 46 (1934) 618.
28 Kim K & Jordan K D, J Phys Chem, 98 (1994) 10089.
29 Nielsen I M B, Seidl E T & Janssen C L, J Chem Phys, 110
(1999) 9435.
30 Qian P, Sog W, Lu L & Yang Z, Int J Quant Chem, 110
(2010) 1923.
31 Maheshwary S, Patel N, Sathyamurthy N, Kulkarni A D &
Gadre S R, J Phys Chem A, 105 (2001) 10525.
Download