Journal of Molecular Structure (Theochem) 594 (2002) 147–156
www.elsevier.com/locate/theochem
Theoretical molecular structures for partially bonded complexes of
trimethylamine with SO2 and SO3: ab initio and density functional
theory calculations
Jaebum Chooa, Sunghwan Kimb, Younghi Kwonb,*
a
Department of Chemistry, Hanyang University, Ansan 425-791, South Korea
Department of Chemistry, Hanyang University, Seoul 133-791, South Korea
b
Received 11 February 2002; accepted 5 April 2002
Abstract
The self-consistent reaction field (SCRF) method based on Onsager’s reaction field theory is applied to investigate the effect
of polar media on molecular structures of complexes of trimethylamime (TMA) with SOx ðx ¼ 2; 3Þ: The calculated SCRF N– S
bond lengths at the MPW1PW91/6-311 þ G(3df) level are in satisfactory agreement with the experimental N– S bond lengths
for the TMA – SOx upon crystallization. The results are enough to demonstrate the usefulness of the reaction field theory in
providing qualitative understanding of the medium effect on the partially bonded system such as TMA – SOx. q 2002 Elsevier
Science B.V. All rights reserved.
Keywords: Ab initio method; Density functional theory method; Self-consistent reaction field method; TMA– SOx complexes
1. Introduction
A chemical bond usually arises from electron-pair
sharing or ionic attraction, while a nonbonded
interaction occurs between chemically distinct entities. The former is significantly more energetic, while
the latter extends over a much longer range. Much less
familiar, however, are partially bonded interactions
that lie in the intermediate region between bonding
and nonbonding. Though some complexes of partially
formed bonds have been known in the crystallographic structures for decades [1], their experimental and theoretical investigation remains almost intact.
* Corresponding author. Fax: þ 82-2-2299-0762.
E-mail address: [email protected] (Y. Kwon).
The gas-phase zwitterion of sulfamic acid (þH3N –
SO2
3 ) is one of the examples of the partially bonded
molecules. Its N –S bond distance of 1.957 Å [2] lies
between the sum of the van der Waals radii (3.35 Å)
and the sum of the covalent radii (1.77 Å) for nitrogen
and sulfur [3]. This complex is unusual in that the N –
S bond length in the gas phase is remarkably longer
than that determined from X-ray and neutron diffraction methods on the solid [4 – 6]. Moreover, the
structural data indicate not only that the donor –
acceptor bond between nitrogen and sulfur is partially
formed in the isolated gaseous molecule but that the
process of crystallization drives the N – S bond length
essentially near to the magnitude of a hydrogen
bonding. The difference in the observed bond lengths
between the gas phase and solid state was explained
0166-1280/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 6 - 1 2 8 0 ( 0 2 ) 0 0 2 6 2 - 2
148
J. Choo et al. / Journal of Molecular Structure (Theochem) 594 (2002) 147–156
Fig. 1. Structures for TMA –SO2 and TMA–SO3. Hydrogen atoms of methyl group are not included.
theoretically using the ab initio calculations by Wong
et al. [7], which appears to be a general feature of
systems containing a partially formed bond [8].
Complexes of N(CH3)3 (trimethylamine, TMA)
with SOx ðx ¼ 2; 3Þ are another examples of partially
formed molecules. Both molecules have the structure
of a donor –acceptor complex as might have been
expected, with the nitrogen lone pair directed toward
the sulfur atom [9 –13]. The N – S bond lengths of SO2
and SO3 complexes in the gas-phase are 2.260 [9] and
1.912 Å [10], respectively. However, those partially
formed N –S bonds contract somewhat upon crystallization. What is more interesting here is that the
formation of crystalline TMA –SO3 drives the N – S
bond to contract strongly [9], while the formation of
crystalline TMA – SO2 does not [9,12]. In this paper,
applying the ab initio, density functional theory
(DFT), and self-consistent reaction field (SCRF)
methods [7,14,15] to the TMA – SOx system, we will
discuss the molecular structures and molecular
properties of the complexes TMA –SOx both in the
gas and condensed phases.
2. Computational details
There are two possible conformations for TMA –
SOx ðx ¼ 2; 3Þ; the staggered conformation and
eclipsed conformation as shown in Fig. 1. The
molecular geometries of staggered and eclipsed
conformers for each complex are fully optimized at
the various levels of theory using the GAUSSIAN 98
program [16]. During geometry optimizations, we
assumed that TMA – SO2 and TMA –SO3 have Cs
symmetry and C3v symmetry, respectively. In the
previous work for NH3 –SO3, which is an analogue of
TMA –SO3, the number of d-polarization function
sets on heavy atoms had a significant influence on the
calculated geometries [7]. Thus, we investigated the
effect of the d-polarization functions by using the 6311 þ G(d), 6-311 þ G(2d) and 6-311 þ G(3d) basis
sets. In addition to these basis sets, we used the 6311 þ G(2df) and 6-311 þ G(3df) basis sets in order
to investigate the effect of f-polarization functions.
We have carried out the geometry optimization at the
restricted Hartree – Fock (RHF) levels. The effects of
electron correlation on the geometry optimizations
have been taken into account intensively by the
second-order Moeller – Plesset perturbation (MP2)
method as well as the DFT method. Since weakly
bounded complexes are very difficult to handle with
the DFT methods [17–19], we pay attention to choose
proper functionals. In this work, we used Becke’s one
parameter hybrid functional with the modified Perdew–
Wang exchange-and-correlation (MPW1PW91) [20,
21]. According to Adamo and Barone, this functional
gives remarkable results both for covalent and noncovalent interactions [21]. To confirm this fact, we
tested some functionals by comparing the experimental
N–S bond lengths of TMA–SOx with computed ones
J. Choo et al. / Journal of Molecular Structure (Theochem) 594 (2002) 147–156
149
Table 1
Calculated N –S distance (Å) for TMA –SOx ðx ¼ 2; 3Þ in the gas phase at various calculational levels
TMA–SO2
RHF/6-311 þ G(3df)
B3LYP/6-311 þ G(3df)
BHandH/6-311 þ G(3df)
PW91PW91/6-311 þ G(3df)
B3PW91/6-311 þ G(3df)
BHandHLYP/6-311 þ G(3df)
MPW1PW91/6-311 þ G(3df)
MP2/6-311 þ G(3df)
Experiment
a
b
c
TMA–SO3
N–S
Da
N–S
Da
2.617
2.412
2.086
2.369
2.330
2.317
2.293
2.242
2.260(30)b
0.357
0.152
20.174
0.109
0.070
0.057
0.033
20.018
1.865
2.004
1.843
2.034
1.965
1.907
1.942
1.926
1.912(20)c
20.047
0.092
20.069
0.122
0.053
20.005
0.030
0.014
Deviation from the experimental value (the computed value minus the experimental value).
Ref. [9].
Ref. [10].
with the 6-311 þ G(3df) basis set. Five density
functionals were tested: (1) Becke’s three parameter
hybrid functional with the Lee–Yang–Parr correlation
functional (B3LYP) [22–24], (2) Becke’s three parameter hybrid functional with nonlocal correlation
provided by the Perdew 91 expression (B3PW91) [22,
25–27], (3) the Perdew–Wang’s exchange and correlation functionals (PW91PW91) [25–27], (4) Becke’s
half and half functional (BHandH) [28,29], and (5)
Becke’s half and half functional including Becke’s 1988
functional (BHandHLYP) [28,29]. As can be seen from
Table 1, MPW1PW91 functional gave the most reliable
results for both compounds, which can be best
comparable to the MP2 results.
In addition, the counterpoise method [30] was
applied at the RHF/6-311 þ G(3df) and
MPW1PW91/6-311 þ G(3df) levels in order to correct the basis set superposition error (BSSE), which is
important to studies for the weak interaction such as
van der Waals interaction or hydrogen bonding. To
take into account the effect of polar media on
molecular structures, dipole moments, charge transfers, and vibrational spectra, we have employed the
self-consistent reaction field (SCRF) method [7,14,
15] at the RHF and MPW1PW91 levels. This method
is based on Onsager’s reaction field theory of the
electrostatic solute– solvent interaction [31]. In this
reaction field model, the solvent is represented by a
continuous dielectric, characterized by a given
dielectric constant (e ), and the solute is assumed to
be embedded into a spherical cavity, with radius (a0),
in the cavity. In the crystal, TMA –SO2 and TMA –
SO3 lie in the different surroundings: they have
different dielectric constants. However, according to
the Szafran et al., the method is very sensitive to the
choice of the solute radius, but not very sensitive to
the particular dielectric constants of polar solvents
[32]. Thus, in order to represent a polar medium, we
used a dielectric constant of 40.0, which was used in
the theoretical study of NH3 –SO3 [7]. Actually,
according to our preliminary calculation at the
MPW1PW91/6-311 þ G(3df) level for both compounds, the N – S distances calculated with e ¼ 60:0
are found to be slightly shorter than those calculated
with e ¼ 40:0 by around 0.001 Å.
3. Results and discussion
3.1. Molecular structures in the gas phase
The equilibrium geometries of TMA –SOx ðx ¼
2; 3Þ in the gas phase have been calculated at the RHF
levels as well as the MPW1PW91 and MP2 levels
using several basis sets. Our calculations show that,
for each compound, a staggered conformer is more
stable than the corresponding eclipsed conformer. It is
found that a staggered conformation corresponds to
the potential energy minimum, while an eclipsed
conformation is not at a local minimum which is at the
transition state.
Some key geometrical parameters for TMA – SO2
150
Table 2
Geometrical parameters for TMA–SO2 (Distances, Å; Angles, deg)
N1 –C2
N1 –C3
S5 –O6
/N1S5O6
/C2N1C3
/C3N1C4
/C2N1S5
/C3N1S5
/O6S5O7
a
Gas phase
RHF/6-311 þ G(2df)
RHF/6-311 þ G(3df)
RHF/6-311 þ G(3df) (BSSE)
MPW1PW91/6-311 þ G(d)
MPW1PW91/6-311 þ G(2d)
MPW1PW91/6-311 þ G(3d)
MPW1PW91/6-311 þ G(2df)
MPW1PW91/6-311 þ G(3df)
MPW1PW91/6-311 þ G(3df) (BSSE)
MP2/6-311 þ G(d)
MP2/6-311 þ G(2d)
MP2/6-311 þ G(3d)
MP2/6-311 þ G(2df)
MP2/6-311 þ G(3df)
Experimenta
2.613
2.617
2.585
2.319
2.329
2.295
2.297
2.293
2.257
2.380
2.323
2.279
2.251
2.242
2.260
1.450
1.449
1.449
1.454
1.451
1.451
1.451
1.450
1.451
1.459
1.456
1.456
1.457
1.455
1.468
1.449
1.448
1.448
1.453
1.451
1.451
1.452
1.450
1.451
1.459
1.456
1.456
1.457
1.455
1.461
1.404
1.399
1.400
1.465
1.453
1.449
1.451
1.445
1.446
1.476
1.471
1.467
1.464
1.458
1.444
95.1
95.1
95.2
96.0
96.0
96.2
96.1
96.2
96.3
95.2
95.4
95.5
95.8
95.7
95.9
111.9
111.8
111.8
112.7
112.7
112.7
112.7
112.7
112.6
112.1
112.4
112.3
112.4
112.3
111.8
112.1
112.0
112.0
113.4
113.3
113.2
113.3
113.2
113.1
113.0
113.1
113.0
113.0
113.0
112.6
104.1
104.5
104.5
102.6
102.8
103.3
103.1
103.2
103.7
102.2
102.8
103.3
103.6
103.6
104.3
108.2
108.2
108.1
107.3
107.3
107.1
107.1
107.1
107.0
108.4
107.7
107.6
107.4
107.4
107.9
117.2
117.5
117.5
116.1
116.3
116.4
116.0
116.4
116.2
116.9
117.0
116.9
116.4
116.8
116.9
80.2
80.1
79.9
78.7
78.6
78.2
78.4
78.2
78.0
80.1
79.7
79.4
79.0
79.0
78.5
Condensed media (e ¼ 40.0)
RHF/6-311 þ G(2df)
RHF/6-311 þ G(3df)
MPW1PW91/6-311 þ G(d)
MPW1PW91/6-311 þ G(2d)
MPW1PW91/6-311 þ G(3d)
MPW1PW91/6-311 þ G(2df)
MPW1PW91/6-311 þ G(3df)
Experimenta
2.170
2.157
2.217
2.222
2.193
2.194
2.183
2.046
1.460
1.460
1.457
1.455
1.455
1.455
1.455
1.468
1.463
1.462
1.461
1.458
1.458
1.459
1.458
1.478b
1.420
1.416
1.472
1.461
1.456
1.458
1.452
1.437b
98.1
98.1
98.1
97.9
98.0
98.0
98.0
98.9
111.5
111.4
112.4
112.4
112.3
112.4
112.3
111.3b
111.3
111.2
112.7
112.6
112.4
112.5
112.4
111.5
107.7
107.9
104.8
104.8
105.3
105.1
105.4
107.7
107.3
107.4
106.9
106.9
106.9
106.9
106.9
107.7b
114.8
115.0
114.7
115.0
115.1
114.7
115.1
113.7
74.9
74.8
74.9
75.2
74.9
75.0
74.9
73.6
a
b
Ref. [9].
Averaged over crystallographically distinct values.
J. Choo et al. / Journal of Molecular Structure (Theochem) 594 (2002) 147–156
N1 –S5
J. Choo et al. / Journal of Molecular Structure (Theochem) 594 (2002) 147–156
151
Table 3
Geometrical parameters for TMA–SO3 (Distances, Å; Angles, deg)
N1 –S5
N1 –C2
S5 –O6
/N1S5O6
/C2N1C3
/C2N1S5
/O6S5O7
Gas phase
RHF/6-311 þ G(2df)
RHF/6-311 þ G(3df)
RHF/6-311 þ G(3df) (BSSE)
MPW1PW91/6-311 þ G(d)
MPW1PW91/6-311 þ G(2d)
MPW1PW91/6-311 þ G(3d)
MPW1PW91/6-311 þ G(2df)
MPW1PW91/6-311 þ G(3df)
MPW1PW91/6-311 þ G(3df) (BSSE)
MP2/6-311 þ G(d)
MP2/6-311 þ G(2d)
MP2/6-311 þ G(3d)
MP2/6-311 þ G(2df)
MP2/6-311 þ G(3df)
Experimenta
1.878
1.865
1.740
1.992
1.973
1.947
1.962
1.942
1.825
2.005
1.979
1.951
1.947
1.926
1.912
1.481
1.481
1.491
1.473
1.472
1.473
1.473
1.473
1.481
1.479
1.476
1.476
1.477
1.476
1.408
1.403
1.407
1.451
1.439
1.434
1.437
1.431
1.433
1.456
1.450
1.446
1.444
1.438
99.8
99.9
101.0
98.8
98.9
99.1
99.0
99.1
100.0
98.5
98.6
98.9
98.9
99.0
100.1
110.0
109.9
109.0
111.2
111.2
111.0
111.1
110.9
110.1
111.0
111.2
111.0
110.9
110.8
108.9
109.0
109.9
107.7
107.7
107.9
107.8
108.0
108.9
107.9
107.7
107.9
108.0
108.1
117.2
117.1
116.4
117.7
117.7
117.5
117.6
117.5
117.0
117.9
117.8
117.6
117.7
117.6
Condensed media (e ¼ 40.0)
RHF/6-311 þ G(2df)
RHF/6-311 þ G(3df)
MPW1PW91/6-311 þ G(d)
MPW1PW91/6-311 þ G(2d)
MPW1PW91/6-311 þ G(3d)
MPW1PW91/6-311 þ G(2df)
MPW1PW91/6-311 þ G(3df)
Experimentb
1.874
1.861
1.936
1.921
1.902
1.912
1.896
1.844
1.482
1.482
1.482
1.480
1.480
1.480
1.480
1.496
1.427
1.422
1.456
1.444
1.438
1.441
1.435
1.405
101.0
101.1
100.6
100.6
100.8
100.7
100.8
101.8
110.0
109.9
110.6
110.6
110.3
110.4
110.2
109.1
108.9
109.1
108.3
108.4
108.6
108.5
108.7
109.8
116.5
116.4
116.7
116.7
116.6
116.6
116.6
115.9
a
b
Ref. [10].
Ref. [11].
and TMA – SO3 in the gas phase are summarized in
Tables 2 and 3, along with the values in the condensed
media. The calculated N – S bond lengths at the MP2
levels are in good agreement with the experimental
values of 2.260 and 1.912 Å, for TMA – SO2 and
TMA – SO3, respectively [9,10]. For both compounds,
the N –S bond lengths computed at the RHF level
show a large deviation from the experimental values.
They are also much different from the values
computed at the MP2 levels. On the other hand, the
values at the MPW1PW91 levels show a relatively
small deviation from the experimental values as well
as values computed at the MP2 levels. The N – S bond
lengths for both compounds are highly dependent on
the number of the d- or f-polarization functions
employed on heavy atoms. Generally, the N –S bond
lengths are shortened by adding more polarization
functions. Especially, the addition of f-polarization
functions gives the calculated N –S bond lengths for
both compounds closer to the experimental values.
Thus, considering the accuracy and efficiency of the
calculation, it appears that the MPW1PW91 method is
more appropriate for these systems than the RHF
method and that the f-polarization functions must be
employed on heavy atom in order to reproduce the
gas-phase geometry for both compounds.
The BSSE gives a significant effect on the N – S
bond length for each compound. The BSSE-corrected
N –S bond length of 2.257 Å for TMA – SO2 at the
MPW1PW91/6-311 þ G(3df) level is shorter by
0.036 Å than the non-BSSE corrected value, and
closer to the experimental value. However, the BSSEcorrected N – S bond length for TMA – SO 3 is
significantly shortened by 0.117 Å compared to the
non-BSSE-corrected value of 1.942 Å. The calculated
complexation binding energy for TMA –SOx is listed
in Table 4, along with the available experimental
values [33]. We can see that the BSSE-corrected
152
J. Choo et al. / Journal of Molecular Structure (Theochem) 594 (2002) 147–156
Table 4
Calculated binding energy in the gas phase and solvation energy (kcal/mol) for TMA–SOx ðx ¼ 2; 3Þ
TMA– SO2
RHF/6-311 þ G(2df)
RHF/6-311 þ G(3df)
RHF/6-311 þ G(3df) (BSSE)
MPW1PW91/6-311 þ G(d)
MPW1PW91/6-311 þ G(2d)
MPW1PW91/6-311 þ G(3d)
MPW1PW91/6-311 þ G(2df)
MPW1PW91/6-311 þ G(3df)
MPW1PW91/6-311 þ G(3df) (BSSE)
MP2/6-311 þ G(d)
MP2/6-311 þ G(2d)
MP2/6-311 þ G(3d)
MP2/6-311 þ G(2df)
MP2/6-311 þ G(3df)
Experiment
a
TMA–SO3
Binding energy
Solvation energy
Binding energy
Solvation energy
5.62
5.60
5.16
14.44
12.41
12.54
12.59
12.62
12.83
14.28
14.43
15.46
15.64
15.86
9.1(4)a
5.90
5.97
29.34
30.13
51.28
34.65
32.03
33.90
32.61
33.63
46.19
38.34
38.18
41.17
40.63
41.71
13.20
13.14
6.74
6.14
6.27
6.35
6.32
11.89
11.33
11.36
11.42
11.41
Ref. [33].
binding energy is much different from the non-BSSEcorrected value. In the counterpoise method, the
energies of monomer units are to be calculated with
the geometries they have in the complex. Free SO3 unit
in particular is a highly delocalized system with planar
structure. However, SO3 in TMA–SO3 is no longer
planar so that the delocalization in the SO3 unit in
TMA–SO3 is significantly weaker than that in free SO3.
As a result, the energy of the SO3 monomer increases,
and the complexation energy of TMA–SO3 deviates
significantly from the non-BSSE corrected value.
According to our calculation on monomeric SO2,
SO3 and TMA at the MPW1PW91/6-311 þ G(3df)
level, the S –O bond length and the /O –S – O bond
angle for free SO2 is 1.429 Å and 119.28, and, for free
SO3, 1.417 Å and 1208, respectively. The N – C bond
length for free TMA is 1.443 Å. It is clear that the N –
C and S – O bond lengths increase and the /O – S – O
bond angles decrease upon complexation. At all the
calculation levels, the calculated N – S bond lengths
for TMA –SO3 are shorter than those for TMA – SO2,
which means that SO3 is more strongly bound to TMA
than SO2.
The major distinction between the eclipsed conformer and the corresponding staggered conformer is
that the N – S bond length of the eclipsed conformer is
about 0.1 Å longer than that of the staggered
conformer, which implies that TMA and SOx monomers in the eclipsed conformation for each complex
are bound more weakly to each other than in the
staggered conformation.
3.2. Molecular structures in condensed media
According to the previous experiments, the N – S
bond length upon crystallization is contracted by
0.214 Å for TMA –SO2 and 0.068 Å for TMA – SO3
[9 –11]. Previous workers suggested that this contraction might be due to the close interatomic contact
between hydrogen and oxygen atoms in the crystal or
the stabilization by effect of the media [9,10]. In order
to take into account the effect of the media, we have
employed the SCRF method based on Onsager’s
reaction field theory. As can be seen in Tables 2 and 3,
the N – S bond lengths in condensed media calculated
at the MPW1PW91/6-311 þ G(3df) level are 2.183 Å
for TMA –SO2 and 1.896 Å for TMA – SO3. The bond
length differences between the gas phase and the
condensed media are 0.110 and 0.046 Å, for TMA –
SO2 and TMA –SO3, respectively. Thus, it is clear that
the contraction of the N –S bond length upon crystallization is primarily due to the medium effect of the
surroundings although the magnitudes of N –S bond
contractions for both compounds are not remarkable
J. Choo et al. / Journal of Molecular Structure (Theochem) 594 (2002) 147–156
153
Table 5
Dipole moments (Debye) for TMA–SOx ðx ¼ 2; 3Þ
TMA– SO2
RHF/6-311 þ G(2df)
RHF/6-311 þ G(3df)
MPW1PW91/6-311 þ G(d)
MPW1PW91/6-311 þ G(2d)
MPW1PW91/6-311 þ G(3d)
MPW1PW91/6-311 þ G(2df)
MPW1PW91/6-311 þ G(3df)
MP2/6-311 þ G(d)
MP2/6-311 þ G(2d)
MP2/6-311 þ G(3d)
MP2/6-311 þ G(2df)
MP2/6-311 þ G(3df)
Experiment
a
b
TMA–SO3
Gas phase
Condensed media
Gas phase
Condensed media
3.51
3.46
5.27
4.99
5.06
5.11
5.06
4.73
4.75
4.92
5.12
5.09
4.800a
7.05
7.09
7.54
7.19
7.27
7.32
7.30
7.85
7.84
7.19
7.07
7.10
7.11
7.12
7.10
7.08
7.15
7.22
7.22
7.111b
9.91
9.90
9.82
9.58
9.60
9.62
9.62
Ref. [9].
Ref. [10].
compared to the experimental bond lengths. However,
our calculations assure the experimental fact that the
formation of crystalline TMA –SO3 drives the N – S
bond nearly to 1.77 Å, the sum of the covalent radii of
nitrogen and sulfur, whereas the formation of crystalline TMA –SO2 does not.
When we apply the SCRF method, the /N – S – O
bond angle for TMA – SO3 increases by 2 – 38, which
means that the interaction between the monomers
TMA and SO3 is enhanced. In the reaction field, the
angle a between the N –S bond and SO2 plane
decreases by about 58, which also implies some
increase in the interaction between the monomers.
This is because there is the maximum overlap between
the nitrogen lone pair which is the highly occupied
molecular orbital (HOMO) of TMA, and the 3p – 3d
hybridized orbital of sulfur which is the lowest
unoccupied molecular orbital (LUMO) of SO2 when
the angle a is 558 [12]. For both complexes, the N –C
and S – O bond lengths slightly increase, while the
bond angles /C – N –C and /O –S – O decrease. This
fact indicates that the interaction between TMA and
SOx is increased by medium effect.
3.3. Binding energies and related molecular
properties
The calculated complexation binding energies for
both compounds in the gas phase are tabulated in
Table 4 with the solvation energies in the condensed
media, which are the electronic contribution to the
free energy of solvation. In order to estimate the
solvation energies in the condensed media with
the dielectric constant e ¼ 40:0; we applied the
SCRF method to the each TMA complex. As can be
seen in Table 5, the binding energies in the gas phase
at the MPW1PW91/6-311 þ G(3df) level are computed to be 12.67 and 33.63 kcal/mol for TMA – SO2
and TMA – SO3, respectively.
In Onsager’s reaction field model, the permanent
dipole moment of the solute will induce a dipole in the
surrounding medium, which in turn will interact with
molecular dipole to lead to stabilization. Thus, it is the
dipole moment that is one of the most important
molecular properties. The calculated dipole moments
for TMA – SOx are listed in Table 5. The calculated
gas-phase dipole moments for each compound at
the MPW1PW91 and MP2 levels are closer to the
corresponding experimental values than those at the
RHF level. Since TMA – SO3 has a rather larger dipole
moment than TMA – SO2, we would expect that the
TMA –SO3 is more stabilized by the reaction field
than the TMA – SO2. As can be seen from Table 4, the
solvation energy for TMA –SO3 is almost twice of
that of TMA –SO2. At any rate, both complexes are
stabilized in the condensed media by the effect of
154
J. Choo et al. / Journal of Molecular Structure (Theochem) 594 (2002) 147–156
Table 6
Charge transfer from TMA to SOx ðx ¼ 2; 3Þ
TMA –SO2
RHF/6-311 þ G(2df)
RHF/6-311 þ G(3df)
MPW1PW91/6-311 þ G(d)
MPW1PW91/6-311 þ G(2d)
MPW1PW91/6-311 þ G(3d)
MPW1PW91/6-311 þ G(2df)
MPW1PW91/6-311 þ G(3df)
MP2/6-311 þ G(d)
MP2/6-311 þ G(2d)
MP2/6-311 þ G(3d)
MP2/6-311 þ G(2df)
MP2/6-311 þ G(3df)
Experiment
a
b
TMA–SO3
Gas phase
Condensed media
Gas phase
Condensed media
0.05
0.07
0.14
0.22
0.25
0.22
0.25
0.12
0.22
0.24
0.25
0.26
0.2 –0.3a
0.32
0.29
0.27
0.35
0.35
0.35
0.37
0.58
0.60
0.26
0.43
0.51
0.47
0.53
0.28
0.45
0.51
0.51
0.56
0.58b
0.70
0.71
0.40
0.55
0.60
0.60
0.64
Ref. [9].
Ref. [10].
media. It is also found that the dipole moments in the
condensed media for both compounds increase due to
the effect of polar media. The increased dipole
moment in the condensed media for TMA – SOx is
closely related to the redistribution of charge in the
complex, that is, the charge transfer from TMA to SOx
Table 7
Some calculated vibrational frequencies for TMA–SOx ðx ¼ 2; 3Þ at
the MPW1PW91/6-311 þ G(3df) level
Free SOx
TMA–SOx
Gas phase
Condensed
media
Exptl.a
Calcd.
Exptl.b
Calcd.
TMA–SO2
nas(SO2) 1419.4
ns(SO2)
1215.7
d(SO2)
529.7
n(N –S)
1362
1151
518
1336.1
1170.5
547.8
140.2
1270
1120
550
1291.5
1148.2
554.4
162.6
TMA–SO3
nas(SO3) 1444.6
ns(SO3)
1113.5
das(SO3)
535.1
ds(SO3)
510.8
n(N –S)
1390
1065
530
498
1375.9
1093.2
557.0
595.7
264.3
1330
1076
556
605
Calcd.
a
b
c
1346.4
1087.4
559.1
603.0
284.9
Ref. [38].
Ref. [35] for TMA–SO2 and Ref. [36] for TMA–SO3.
Ref. [37].
Exptl.c
unit. The TMA –SOx ðx ¼ 2; 3Þ complex is a charge
transfer complex in which the nitrogen electron lone
pair of TMA might be donated to the LUMO of the
sulfur atom of SOx. Since the N – S bond length for
TMA –SO3 is shorter than that of TMA –SO2, we
expect that the charge transfer in TMA –SO3 would be
stronger than that of TMA – SO2. We have calculated
the magnitude of the charge transfer for both
complexes by Mulliken population analysis [34]. As
shown in Table 6, the charge transfers calculated at
the RHF levels are smaller than those at the
MPW1PW91 and MP2 levels. When electron correlation is included, the computed values are approaching very close to the experimental values. It is also
found that the charge transfer is pronounced in the
condensed media. This means that the interaction
between TMA and SOx unit is somewhat increased by
medium effect.
3.4. Vibrational spectra
1293.0
1054.0
540.0
566.0
According to Sass and Ault [35,36], asymmetric
stretching frequencies of the SOx ðx ¼ 2; 3Þ subunit
are shifted in a smooth fashion to somewhat lower
frequencies upon complexation with stronger bases.
In other words, they decrease as the interaction
between SOx and bases increases. In TMA – SOx, the
interaction between two monomers somewhat
J. Choo et al. / Journal of Molecular Structure (Theochem) 594 (2002) 147–156
increases in the condensed media compared with the
gas phase. Thus, we can expect that a similar
frequency shift would be found for these complexes
in the condensed media. Some vibrational frequencies
calculated at the MPW1PW91/6-311 þ G(3df) level
for SOx and its TMA complexes are listed in Table 7,
with available experimental data [35 – 38]. As can be
seen from Table 7, asymmetric stretching modes of
SOx unit for both compounds are shifted to lower
frequencies in the condensed media. The symmetric
stretching modes also decrease. The red shift of the
calculated stretching modes is in accord with our
expectation. The difference in the magnitude of the
red shift for each compound is consistent with the
difference in the magnitude of contraction of the N – S
bond length. According to our calculation in the
condensed media, the bending modes of SOx for both
compounds exhibit a different behavior, shifting to
higher frequencies. In the condensed media, the
bending mode of SO2 for TMA – SO2 and the
symmetric bending mode of SO3 for TMA – SO3 are
slightly shifted to higher frequencies by around
7 cm21. However, the computed asymmetric bending
mode of SO3 for TMA –SO3 is almost unchanged.
Those bending behaviors of SOx in TMA – SOx are
consistent with the fact that the bending mode of SOx
would be shifted to somewhat higher frequencies as
the interaction between SOx and methylamine derivatives increases [35,36]. The stretching mode nN – S
increases in the condensed media by around 20 cm21,
which means that the N – S bond is a little strengthened in the condensed media.
155
somewhat smaller than the experimental ones. As
suggested by the previous workers [9,10], it is
believed that the bond contraction might be due to
either the effect of condensed media or the interatomic
contact with neighboring molecules in the crystal.
Since our calculations considered only the medium
effect, some deviation between the calculated and
experimental contractions might be ascribed to the
neglect of interatomic contact in the crystal. However,
our calculations gave a qualitative confirmation of the
fact that the formation of crystalline TMA – SO3
would drive the N –S bond nearly to the covalent
bonding while the formation of crystalline TMA – SO2
would not. In the condensed media, the dipole
moments and the binding energies for both complexes
increase, and the charge transfer from TMA to SOx
unit is enhanced. The vibrational frequencies are also
affected by the reaction field. These results are enough
to demonstrate the usefulness of the reaction field
theory in providing qualitative understanding of the
medium effect on the partially bonded system such as
TMA –SOx. Considering the accuracy and efficiency
of the calculation, the MPW1PW91 levels in the
SCRF method might be appropriate for our purpose.
Acknowledgment
This work was supported by Korea Research
Foundation Grant 2001-015-DP0248.
References
4. Conclusions
In this paper, we have applied SCRF method based
on Onsager’s reaction field theory to investigate the
effect of media on molecular structures, binding
energies, dipole moments, charge transfers, and
vibrational spectra of partially bonded complexes
TMA – SO x ðx ¼ 2; 3Þ: At the MPW1PW91/6311 þ G(3df) level, the N – S bond lengths for
TMA – SOx upon crystallization can be nearly reproducible. The bond length differences between the gas
phase and condensed media are 0.110 and 0.046 Å for
TMA – SO2 and TMA – SO3, respectively. The calculated bond contractions for both compounds are
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