Gas-phase acidities of α- and α,α-SO2CF 3-substituted toluenes. Varying Resonance demand in the electron-rich system

Article abstract of DOI:10.1246/bcsj.20130052

The gas-phase acidities (GA) of aryl(trifluoromethylsulfonyl)methanes (ArCH₂SO₂CF₃; 1) and arylbis(trifluoromethylsulfonyl) methanes (ArCH(SO₂CF ₃)₂; 2) were determined by measuring proton-

Full text of DOI:10.1246/bcsj.20130052

© 2013 The Chemical Society of Japan
Bull. Chem. Soc. Jpn. Vol. 86, No. 7, 813-820 (2013)
813
Selected Papers
Gas-Phase Acidities of ¡- and ¡,¡-SO2CF3-Substituted Toluenes.
Varying Resonance Demand in the Electron-Rich System
Min Zhang,1 Md. Mizanur Rahman Badal,1 Ilmar A. Koppel,2 and Masaaki Mishima*1
1Institute for Materials Chemistry and Engineering, Kyushu University, Hakozaki, Higashi-ku, Fukuoka 812-8581
2Institute of Chemistry, University of Tartu, Ravila 14a Street, 50411, Tartu, Estonia
Received February 20, 2013; E-mail: mishima@ms.ifoc.kyushu-u.ac.jp
The gas-phase acidities (GA) of aryl(trifluoromethylsulfonyl)methanes (ArCH2SO2CF3; 1) and arylbis(trifluoro-
methylsulfonyl)methanes (ArCH(SO2CF3)2; 2) were determined by measuring proton-transfer equilibria. Substituent
effects for acidities of a series of ArCH(R1)R2 including 1 and 2 have been analyzed successfully in terms of the Yukawa-
¹
Tsuno equation. The resonance demand parameter r value was found to decrease linearly with increasing acidity of
¹
the GA values of the unsubstituted parent carbon acids, and the change of the r value was correlated with the acidifying
effect of the phenyl group (R = Ph) in the RCH2(R1)R2. In addition, the geometric features and natural charges of the
¹
conjugate anions calculated at B3LYP/6-311+G(d,p) were found to be correlated linearly with the r values. Such
¹
behavior of the resonance demand parameter in the electron-rich system, ArC (R1)R2, is completely consistent with that
observed for the electron-deficient system, ArC+(R1)R2, revealing that the resonance demand is contingent upon the
structure of carbanions and carbocations. Furthermore, it was found that the μ values also decreased with increasing
acidity of the GA values of the unsubstituted parent carbon acids. This would be related to the distribution of the charge
between the aromatic moiety and the C(R1)R2 moiety.
ꢁ þ
ꢁ þ
Gas-phase proton-transfer experiments have played a key
role for separating structural effects from medium effects
on organic reactivity, providing new insights into the intrin-
sic nature of the resonance demand in the substituent effect
which is one of the most important concepts in physical
organic chemistry.1-5 The substituent effects on the thermo-
dynamic stability (¦G° in kcal mol¹1) of benzylic carbocation,
XC6H4C+(R1)R2, were found to be described in terms of
the Yukawa-Tsuno eq 1 using a gas-phase set of substituent
constants of which values differ slightly from the standard
values determined in aqueous solution.6-11
where -·° and ꢂꢀ·R are sums for ·° and ꢀ·R of R1 and R2,
respectively, indicating that the change of the r+ value can be
related quantitatively with both field/inductive and resonance
effects of R1 and R2 substituents. These results suggest that
the degree of ³-delocalization in the benzylic carbocation
is determined by the intrinsic properties of the structure of
the unsubstituted parent carbocation. Similar correlations were
observed for the gas-phase basicities of benzoyl compounds,
ArCOR,12 and arylacetylenes, ArC¸CR,13-15 of which the
conjugate acids are benzylic carbocations, ArC+(OH)R and
ArC+=CHR, respectively. In addition, similar relationships
were observed for the substituent effects of electron affinities
of aromatic compounds, XC6H4R where R is a fixed sub-
stituent.16,17 Therefore, it is interesting to study whether the
resonance demand parameter in the substituent effect shows
similar behavior for the electron-rich system in which the
³-delocalization effect of para-³-acceptor should be exalted.
The gas-phase substituent effects in such electron-rich systems
themselves are important for understanding the intrinsic nature
of resonance effects because strong ³-acceptors such as NO2,
NO, and CHO groups at para-position in solution are signifi-
cantly influenced by specific hydrogen-bonding solvation,
i.e., substituent solvation assisted resonance (SSAR) effects
as noted by Taft et al.2-4 We thus decided to examine the effects
of ¡-substituents on the resonance demand for the gas-phase
acidity of ¡,¡-substituted toluene derivatives, ArCH(R1)R2,
as a measure of the thermodynamic stabilities of benzylic
carbanions. The gas-phase acidity values are known for several
series of benzylic carbon acids.18,19 In this study, the gas-phase
ꢁ
ꢁ
þ
ꢁ þ
ꢀ¤ꢀG ¼ μð· þ r ꢀ·R Þ
ð1Þ
ꢁ þ
where ·° and ꢀ·R are the normal substituent constant and
the resonance substituent constant, respectively, and r+ is the
resonance demand parameter representing the degree of the
³-delocalization of the positive charge into the aryl ³-system.
These correlation results revealed that the resonance demand
parameter (r+) varies significantly with the stability of the
unsubstituted parent carbocations (X = H), i.e., the r+ value is
correlated linearly as the following eq 2.11
rþ ¼ 0:026ꢀꢀGꢁðX=HÞ þ 1:00
ð2Þ
where ¦¦G°(X=H) is the stability of the unsubstituted parent
benzylic carbocation relative to ¡-cumyl cation. Furthermore,
the r+ value was described in terms of substituent constants for
fixed substituents, R1 and R2,
ꢁ
rþ ¼ 0:45ꢂ· þ 0:40ꢂꢀ·þR þ 1:28
ð3Þ
ꢁ
Published on the web April 13, 2013; doi:10.1246/bcsj.20130052

814
Bull. Chem. Soc. Jpn. Vol. 86, No. 7 (2013)
Gas-Phase Acidities of ¡- and ¡,¡-SO2CF3-Substituted Toluenes
¹
acidities of aryl(trifluoromethylsulfonyl)methanes 1 and aryl-
bis(trifluoromethylsulfonyl)methanes 2 (Chart 1) have been
determined to cover enough range of variation of the stability
of benzylic carbanions by measuring proton-transfer equilibria.
an appropriate reference conjugate anion (A ) of which acidity
is known.
A-H þ Ao ꢀ Aꢀ þ AoH
ð4Þ
ꢀ
¹1
It was found that 1 is 45.6 kcal mol stronger acid than
Results and Discussion
toluene (GA = 373.7 kcal mol¹1 22) and 16 kcal mol stronger
¹1
Table 1 presents the gas-phase acidity (GA) values
(kcal mol¹1) derived from ¦G° values for the proton-transfer
equilibria between benzylic carbon acids 1 and 2 of interest and
than phenylacetone (344.522) and benzylnitrile (344.122), being
consistent with the order of the electron-withdrawing ability
of the ¡-substituent. That the gas-phase acidity of 2 is 73.7
¹1
kcal mol stronger than toluene indicates that the effect of
a second substitution by the SO2CF3 group on the acidity is
somewhat reduced compared to the first substitution. Such
nonadditive effects of second substitution on gas-phase acid-
ities were generally observed for multisubstituted methane
derivatives.19
H
C
SO2CF3
SO2CF3
CH2 SO2CF3
X
X
(1) R1 = H, R2 = SO2CF3
Chart 1.
(2) R1 = R2 = SO2CF3
The gas-phase acidity of 2 was found to strengthen from
¹1
300.0 to 292.7 kcal mol as the substituent changes from H
Table 1. GA Values (kcal mol¹1) Derived from ¦G° Values for the Proton-Transfer Equilibria between the Indicated Acid-Conjugate
Basea)
GA kcal mol–1
300.0g)
Acid
GA kcal mol–1
Acid
ΔG°
ΔG°
330.1b)
p-CF3C6H4OH
C6H5CHTf2
328.9b)
328.1
1.7
CH2(CN)2
2.0
299.0
(CF3)5C6OH
C6H5CH2Tf
p-FC6H4CH2Tf
0.9
1.5
1.7
m-FC6H4CHTf2
m-CF3C6H4CHTf2
298.1
2.8
1.2
2.6
0.5
1.3
326.1
4.0
296.4
325.3c)
324.9
p-CF3C6H4CO2H
p-ClC6H4CH2Tf
m-FC6H4CH2Tf
(CF3)3COH
3.4
2.1
1.0
0.0
296.0g)
295.8
C6F5SO2NHC6H4Cl-p
0.0
1.0
324.9
p-CF3C6H4CHTf2
1.0
0.2
324.0d)
323.6
3.1
CH3
m-ClC6H4CH2Tf
CF3COCH2COCH3
m-CF3C6H4CH2Tf
C6F5OH
294.8
292.7
H3C
OH
1.6
0.5
322.0e)
321.3
CH2CHTf2
3,5-(CF3)2C6H3CHTf2
CH2CHTf2
3.5
1.2
0.4
2.3
320.8e)
318.5
2.5
tBu
OH
291.3
290.2
p-CF3C6H4CH2Tf
CH2CHTf2
1.0
m-CNC6H4CH2Tf
3,5-(CF3)2C6H3CO2H
C6F5CO2H
1.2
317.5
Tf2CHCH2CHTf2
317.4f)
316.6e)
316.3e)
316.2
CF3CO2H
0.4
0.1
0.2
m-NO2C6H4CH2Tf
p-CNC6H4CH2Tf
C4F9SO2NH2
1.3
3.3
315.1
315.1e)
313.3
1.8
3,5-(CF)3C6H3CH2Tf
p-NO2C6H4CH2Tf
CH2(COCF3)2
0.6
2.3
312.6
310.3e)
a) Tf: SO2CF3. 1 cal = 4.184 J. b) Ref. 3. c) Ref. 2. d) Ref. 20, see also Ref. 22. e) Ref. 19. f) Ref. 21. g) Ref. 18.

M. Zhang et al.
Bull. Chem. Soc. Jpn. Vol. 86, No. 7 (2013)
815
Table 2. Relative Acidities of Benzylic Carbon Acids with Typical Substituents
¹1
R1, R2 in ArCH(R1)R2, ¹¤¦G°/kcal mol
Subst. in Ar
d)
d)
H, Ha)
H, CNb)
CN, CNc)
CF3, CF3
Cl, CF3
H, Tfe)
Tf, Tfe)
p-NO2
m-NO2
p-CN
m-CN
3,5-(CF3)2
p-CF3
m-CF3
p-Cl
28.5b)
15.7f)
20.4b)
20.8
13.2
16.2
11.8
14.8
11.3
19.0
15.5
11.9
13.0
10.6
14.8
9.6
6.8
3.2
4.5
3.2
14.6
9.9
19.5b)
13.9
11.7
6.9
6.8
5.5
16.3
11.3
8.6
7.3
4.2
3.6
11.2
8.8
5.6
6.6
7.3
5.3
5.5
8.5
3.9
5.3
3.8
4.5
m-Cl
m-F
4.1
1.9
p-F
1.3
1.7
¹0.1
¹0.9
0.0
(344.1)a)
2.0
m-Me
p-Me
H
¹0.2
¹1.1
0.0
(373.7)a)
¹1.0
¹1.7
0.0
(335.3)d)
¹1.4
0.0
(314.3)a),c)
0.0
(348.7)d)
0.0
(328.1)e)
0.0
(300.0)g)
(GA)
a) Ref. 22. b) Ref. 23. c) Ref. 19. d) Ref. 24. e) This work. f) Ref. 2. g) Ref. 18.
to 3,5-(CF3)2 while the corresponding change of 1 was 14.8
Table 3. Gas-Phase Substituent Constants Used for Corre-
lation Analysis Based on Yukawa-Tsuno Equation
¹1
kcal mol from 328.1 to 313.3 kcal mol¹1, indicating that the
magnitude of the substituent effect in 2 is significantly smaller
than 1. The relative gas-phase acidities of 1 and 2 are given in
Table 2 along with those for a series of benzylic carbon acids,
ArCH(R1)R2, which are available in the literature.2,18,19,22-24
ꢁ ꢀ b)
ꢀ·R
Subst.
·°a) ꢀ·R
ꢁ ꢀ b)
Subst.
·°a)
p-SO2CF3
p-NO2
p-NO
1.08
0.81
0.77
0.40
0.36
0.49
0.70
0.69
0.49
0.63
0.56
0.265
0.288
0.294
0.269
0.252
0.293
0.135
0.204
0.103
0.089
0.057
®
m-CN
m-SCF3
3,5-(CF3)2
3,5-Cl2
3,5-F2
m-CF3
m-Cl
p-Cl
m-F
p-F
m-Me
p-Me
0.67
0.59
0.98
0.77
0.54
0.50
0.36
0.30
0.26
®
®
®
®
®
®
®
®
®
®
®
®
®
®
0.00
R1
R1
R2
H
-
p-COCH3
p-CO2Me
p-CHO
p-CN
p-SO2Me
p-SOMe
p-SCF3
p-CF3
m-SO2CF3 0.99
m-NO2 0.73
m-COCH3 0.33
m-CHO 0.42
+
C
C
R2
X
R1
R2
δΔG
R1
R2
-
H
C
+
C
ð5Þ
X
ꢁ ꢀ
The gas-phase substituent constants, ·° and ꢀ·R , for typical
substituents are given in Table 3. Although the gas-phase
substituent effect is considered to be affected by substituent
polarizability in addition to the conventional resonance and
field/inductive effects,2,25,26 the polarizability effect is not
significant in the benzylic system because this effect is sharply
attenuated with a distance between the charged center and
the substituent.5 Therefore, we analyzed a series of substituent
effects for acidities of ArCH(R1)R2, in terms of the Y-T equa-
tion without polarizability effect in a similar manner to that
applied to the stabilities of benzylic carbocations in the gas
phase.7-15 Since para-³-acceptors are conjugated to the anionic
0.10
¹0.04
¹0.07
¹0.09
0.05
®
®
p-OMe
m-OMe
H
®
0.00
¹
a) Refs. 7 and 12. b) Determined from ·p
¹ ·°(g). The
(g)
¹
p
·
(g) values were derived from gas-phase acidities of phenols
¹
ꢁ ꢀ
where r = 1.00 by definition. The ꢀ·R values for meta sub-
stituents and para-³-donors are zero because of no direct
resonance interaction with the negative charge at the reaction
site.
ꢁ ꢀ
ꢁ þ
centers in the electron rich system, ꢀ·R instead of ꢀ·R was
used for the present systems.
¹
ꢁ
for the acidities of 1 is observed against · with an r of
ꢁ
ꢁ
ꢀ
ꢁ ꢀ
ꢀ¤ꢀG ¼ μð· þ r ꢀ·R Þ
ð6Þ
0.74 (squares, in Figure 2), indicating a somewhat smaller ³-
delocalization than that of phenol acidity.
The correlation parameters, μ and r , for a series of benzylic
ꢁ ꢀ
where ꢀ·R is the resonance substituent constant for ³-accep-
tor. The typical correlations are illustrated for R1 = R2 = H
and R1 = H, R2 = SO2CF3 in Figures 1 and 2, respectively.
Figure 1 shows that the substituent effect for acidities of
toluenes is not correlated with ·° (closed circles) and · (open
circles) but is excellently correlated with · with an r of 1.86
¹
¹
carbon acids are summarized in Table 4. The r value varies
significantly with the system from 1.86 for R1 = R2 = H to
0.16 for R1 = R2 = SO2CF3, indicating obviously that a degree
of ³-delocalization of the negative charge formed at the
benzylic carbon atom into the aromatic ³-system decreases
when R1 and R2 change to stronger electron-withdrawing
groups, i.e., the increasing acidity of the unsubstituted parent
¹
¹
ꢁ
¹
(squares). The r of 1.86 reveals a remarkably exalted ³-
delocalization of the negative charge at the benzylic carbon
atom of benzyl anion compared with that for phenoxide in gas-
¹
¹
phase (r = 1.00 by definition). Similarly, the best correlation
carbon acid. Indeed, the r values are correlated linearly with

816
Bull. Chem. Soc. Jpn. Vol. 86, No. 7 (2013)
p-SO2CF3
Gas-Phase Acidities of ¡- and ¡,¡-SO2CF3-Substituted Toluenes
Table 4. Y-T Correlation Results for Substituent Effects of
Gas-Phase Acidities
30
20
10
0
p-NO
p-NO2
¹
Carbon acids
μa)
r
R
SD
n
ArCH3
20.9 « 0.6 1.86 « 0.11 0.997 «0.3 22d)
b)
p-SO2Me
ArCH(CF3)2
ArCH(Cl)CF3
ArCH2CN
16.3 « 1.1
®
0.987 «0.3
8
9e)
p-CHO
p-COPh
p-COCH3
p-SOCH3
16.8 « 0.7 1.18 « 0.16 0.998 «0.5
17.1 « 0.2 1.36 « 0.08 0.999 «0.2 14f)
ArCH2SO2CF3 15.7 « 0.8 0.74 « 0.19 0.996 «0.6 12
15.0 « 0.5 0.60 « 0.13 0.999 «0.4
ArCH(SO2CF3)2 7.4 « 0.1 0.16 « 0.19c) 0.999 «0.1
p-CN
3,5-(CF3)2
m-NO2
p-CF3
ArCH(CN)2
9g)
5
m-CF3
¹1
ꢀ1 unit. b) No available data to determine the
value. c) Less reliable because of a limited data. d) Included
m-CHO
ꢁ
·
a) In kcal mol
p-Cl
m-F
¹
r
m-Cl
nine substituents other than data listed in Table 3, p-SO2CF3;
33.0, p-NO; 28.6, p-CHO; 21.3, p-COCH3; 18.8, p-CO2CH3;
18.3, p-COC6H5; 20.4, p-SO2CH3; 21.6, p-SOCH3; 14.4, m-
CHO; 9.6, taken from Refs. 2 and 23. e) Included 3,5-F2; 8.2.
f) Included m-OCH3; 1.4, p-OCH3; ¹0.9. g) Included p-OCH3;
¹1.1.
H
p-F
p-Me
0.0
0.4
0.8
1.2
1.6
σ ,σ , σ(r- = 1.86)
°
Figure 1. Y-T plot for gas-phase acidities of toluenes
(R1 = R2 = H), closed circle; ·°, open circle; · , square;
¹
2.0
¹
ꢁ
· at r = 1.86.
H,H
p-NO2
H,CN
1.5
16
12
8
r-
Cl,CF3
3,5-(CF3)2
m-NO2
m-CN
p-CN
1.0
CN,CN
H,SO2CF3
p-CF3
0.5
0.0
m-CF3
m-Cl
m-F
Increasing acidity
360 380
SO2CF3, SO2CF3
320 340
4
0
p-Cl
300
acid(X=H)/kcal mol-1
p-F
ΔG°
H
¹
Figure 3. Plot of the resonance demand parameter (r )
against gas-phase acidities of unsubstituted parent carbo-
nacids, C6H5CH(R1)R2.
0.0
0.2
0.4
°
0.6
0.8
1.0
1.2
σ , σ , σ(r- = 0.74)
Figure 2. Y-T plot for gas-phase acidities of ¡-SO2CF3-
substituted toluenes (R1 = H, R2 = SO2CF3), closed circle;
¹
¹
Since the acidifying effect of the phenyl group can be regarded
as a measure of the degree of the ³-delocalization of the
negative charge formed at the benzylic carbon atom into
the phenyl group, the existence of such a linear relationship
between both quantities suggests again that the negative charge
formed at the benzylic carbon atom is stabilized competitively
by the aryl group and ¡-substituents. In fact, the stabiliza-
tion effect of the phenyl substitution in the strongest acid,
RCH(SO2CF3)2, is nearly zero, being consistent with a negli-
ꢁ
·°, open circle; · , square; · at r = 0.74.
the GA values of the unsubstituted parent benzylic compounds
as shown in Figure 3.
rꢀ ¼ 0:023ꢀGA ꢀ 6:57 ðR ¼ 0:984Þ
ð7Þ
This linear relationship indicates that the degree of the ³-
delocalization of the negative charge formed at the benzylic
carbon atom into the aryl ³-system decreases with the
increasing stability of the carbanions. In addition, it is found
¹
gibly small r value of 0.16. In conclusion, the effect of the
aryl group on the stability of the carbanion is compensated
with the electronic effects of R1 and R2.
¹
that the r values are correlated linearly with the acidifying
¹
effect of the phenyl group (¦¦G°Ph) that is given by the
difference in GA values between unsubstituted parent benzylic
carbon acid, PhCH(R1)R2, and the corresponding methane
derivative, CH2(R1)R2 (Table 5 and Figure 4).
Such changes of the r values are expected to relate to the
geometric features and the charge distributions of their conju-
gate anions. Therefore, theoretical calculations have been con-
ducted for the conjugate anions of the unsubstituted parent
¹
carbon acids, C6H5C (R1)R2, at the B3LYP/6-311+G(d,p)
rꢀ ¼ 0:050ꢀꢀGꢁPh þ 0:11 ðR ¼ 0:971Þ
ð8Þ
level of theory. The results are given in Table 5 (also Table S1).

M. Zhang et al.
Bull. Chem. Soc. Jpn. Vol. 86, No. 7 (2013)
817
Table 5. Gas-Phase Acidities of PhCH(R1)R2 and CH2(R1)R2, Acidifying Effects of the Phenyl
Group, Natural Charges of the Phenyl Group, and Selected Bond Distance of the Conjugate Anions
¹1
GA/kcal mol
a)
R1
R2
¦¦G°ph
-q(Ph)b)
C1C7/¡c)
PhCH(R1)R2
CH2(R1)R2
H
Cl
H
CF3
H
H
CF3
CN
CF3
SO2CF3
CN
SO2CF3
373.7d)
348.7e)
344.1d)
335.3e)
328.1g)
314.3h)
300.0i)
409.9d)
®
365.2d)
348.7f)
339.8h)
328.9d)
300.6i)
36.2
®
¹0.618
¹0.377
¹0.362
¹0.241
¹0.223
¹0.197
¹0.035
1.391
1.416
1.421
1.454
1.441
1.452
1.490
21.1
13.4
11.7
14.6
0.6
CN
SO2CF3
a) ¦¦G°ph = GA[CH2(R1)R2] ¹ GA[PhCH(R1)R2]. b) Group natural charges of the phenyl moiety
obtained by natural population analysis at B3LYP/6-311+G(d,p)// B3LYP/6-311+G(d,p). c) Bond
length of C1C7. Numbering of atoms given in Table S1. d) Ref. 22. e) Ref. 24. f) Determined in this
¹1
¹1
study, 1.0 kcal mol stronger than nitromethane (GA = 349.7 kcal mol¹1 d)) and 1.0 kcal mol weaker
than 1,1,1,2,3,3,3-heptafluoropropane (GA = 347.8 kcal mol¹1, unpublished). g) This work. h) Ref. 19.
i) Ref. 18.
22
H,H
H,H
2.0
1.5
20
18
16
14
12
10
8
H,CN
(CF3)2
H,SO2CF3
H,CN
Cl, CF3
r-
(CN)2
ρ
1.0
H,SO2CF3
(CN)2
0.5
(SO2CF3)2
Increasing acidity
(SO2CF3)2
10
0
0
6
20
30
40
300 320 340 360 380
ΔΔG°Ph/kcal mol-1
ΔG°(X=H)/kcal mol-1
¹
Figure 4. Plot of the resonance demand parameter (r )
against the stabilization effect of the phenyl group.
¦¦G°Ph = GA[CH2(R1)R2] ¹ GA[C6H5CH(R1)R2].
Figure 5. Plot of the μ values against gas-phase acidities of
unsubstituted parent carbonacids, C6H5CH(R1)R2.
As expected, as the acidity of the unsubstituted parent carbon
acids increases, the bond distance C1C7 lengthens and the sum
of the natural charges in the phenyl moiety obtained by natural
population analysis decreases, revealing the weakened ³-
interaction between the phenyl group and the negative charge at
Furthermore, it is interesting to note that a slope of 0.023 in
Figure 3 is surprisingly similar to that of 0.026 observed for
the benzylic carbocation system though this agreement may be
ꢁ þ
ꢁ ꢀ
accidental. This similarity suggest that ꢀ·R and ꢀ·R values
may have a common scale in the degree of ³-delocalization
although both parameters are determined by different defini-
¹
the benzylic carbon atom. The r values are indeed correlated
ꢁ þ
ꢁ ꢀ
ꢁ
linearly with the bond length of the C1C7 and with the natural
charge of the phenyl moiety of the corresponding carbanion,
tions, ꢀ·R ¼ ·þ ꢀ · and ꢀ·R ¼ ·ꢀ ꢀ ·ꢁ.
It is also noteworthy that the magnitude of μ value as a
measure of electron demand of the system also tends to
decrease with the increasing acidity of the unsubstituted parent
carbon acid. Excluding R1 = R2 = SO2CF3, the μ values are
correlated linearly with the GA values of the unsubstituted
parent acids as shown Figure 5.
¹
-qPh in PhC (R1)R2, following eqs 9 and 10, respectively
(Figures S1 and S2).
rꢀ ¼ ꢀ17:8dðC1C7Þ þ 26:5 ðR ¼ 0:981Þ
ð9Þ
ð10Þ
rꢀ ¼ ꢀ3:03ꢂqPh þ 0:062 ðR ¼ 0:990Þ
These results suggest that the resonance demand parameter
is an intrinsic property of molecular structure. The present
results on the resonance demand in the electron-rich system are
completely consistent with that observed for the effects on the
resonance demand parameter r+ for ³-donor substituents in the
electron-deficient, benzylic carbocations.11,12,15
μ ¼ 0:098ꢀGAðX=HÞ ꢀ 16:3 ðR ¼ 0:956Þ
ð11Þ
This result suggests that the μ value is also influenced by the
electronic effect of R1 and R2. On the other hand, until now we
did not pay much attenttion to the μ value for the carbocation
system, ArC+(R1)R2, because the variation in μ caused by R1

818
Bull. Chem. Soc. Jpn. Vol. 86, No. 7 (2013)
Gas-Phase Acidities of ¡- and ¡,¡-SO2CF3-Substituted Toluenes
and R2 substituents is very small, i.e., ¹13.0 for R1 = R2 = Me
to ¹14.5 for R1 = H, R2 = CF3. The present obtained μ values
for the electron-rich system forces us to reexamine the previous
results for a series of benzylic carbocations for a comparison
with the present observation. A careful examination reveals
that the μ value for the benzylic carbocation tends to decrease
with the increasing stability of a carbocation. The μ values are
correlated linearly with the stability of the unsubstituted parent
benzylic carbocation in a similar manner to the present benzylic
carbanion system (Figure S3),27 indicating that the μ value for
the carbocation system is also dependent on the thermodynamic
stability of unsubstituted parent cabocation.
intrinsic properties arising from the structure of carbanions
or carbocations. In addition, it was found that the μ values also
decreased with increasing acidity of the GA values of the
unsubstituted parent carbon acids. This would be due to the
varying distribution of the charge in the molecuar skeleton
caused by the R1 and R2 groups.
Experimental
Melting points were measured on a YanaCO MP-J3
apparatus and are reported uncorrected. The NMR spectra
were recorded on a JEOL JNM-EX400 or ECA-500 FT-NMR
spectrometer in CDCl3 and chemical shifts are reported in
¤ value downfield from the internal standard tetramethylsilane
(TMS).
μ ¼ ꢀ0:069ꢀꢀGꢁðX=HÞ ꢀ 13:1 ðR ¼ 0:975Þ
ð12Þ
where ¦¦G°(X=H) is the thermodynamic stability of benzylic
carbocation, C6H5CH+(R1)R2, relative to that of ¡-cumyl
cation (R1 = R2 = CH3). Such variation of the μ value would
be interpreted by the charge distribution in a molecular
framework of interest. In the thermodynamically more stable
carbanions with strong electron-withdrawing groups R1 and R2,
the negative charges formed at the benzylic carbon atom by
deprotonation are located at the C(R1)R2 moiety rather than the
aromatic moiety. For example, in the conjugate anion of 2 a
total natural charge of the phenyl moiety is only ¹0.035 and
the rest of the charge is localized at the C(SO2CF3)2 moiety
while in the benzyl anion (R1 = R2 = H) the group natural
charges of the phenyl moiety is ¹0.618 as seen in Table 5. That
is, the center of the charge would be far from the substituent
on the benzene ring in the conjugate anion of 2, resulting in a
small μ value. The same situation must be held in the benzylic
carbocations.
Chemicals. Preparation of (m,p-substituted phenyl)methyl
trifluoromethyl sulfones (1).31 General procedure: A mixture of
benzylic halide (10 mmol) and CF3SO2Na (2.0 g, 13 mmol) in
propionitrile (30 mL) was heated at reflux temperature. While
disappearance of the starting halide was monitored by TLC,
the mixture was cooled, the salts were removed by filtration
and the filtrate was concentrated under reduced pressure. The
residue was purified by column chromatography using a linear
EtOAc gradient in hexane to give the targeted products 1 as
solids. Phenylmethyl trifluoromethyl sulfone: mp 81-83 °C.
1H NMR (CDCl3): ¤ 4.48 (s, 2H), 7.38-7.46 (m, 5H). 3-Fluoro-
1
phenylmethyl trifluoromethyl sulfone: mp 88-89 °C. H NMR
(CDCl3): ¤ 4.47 (s, 2H), 7.16-7.46 (m, 4H). 4-Fluorophenyl-
methyl trifluoromethyl sulfone: mp 103-105 °C. 1H NMR
(CDCl3): ¤ 4.46 (s, 2H), 7.13-7.16 (m, 2H), 7.40-7.43 (m,
2H). 3-Trifluoromethylphenylmethyl trifluoromethyl sulfone:
mp 80-81 °C. 1H NMR (CDCl3): ¤ 4.54 (s, 2H), 7.59-7.76 (m,
4H). Anal. Calcd for C9H6F6O2S: C, 36.99; H, 2.07%. Found:
C, 36.45; H, 2.21%. 4-Trifluoromethylphenylmethyl trifluoro-
methyl sulfone: mp 110-112 °C. 1H NMR (CDCl3): ¤ 4.54
(s, 2H), 7.58 (d, J = 8.0 Hz, 2H), 7.72 (d, J = 8.0 Hz, 2H).
3-Nitrophenylmethyl trifluoromethyl sulfone: mp 84-85 °C.
1H NMR (CDCl3): ¤ 4.59 (s, 2H), 7.67-7.82 (m, 2H), 8.33-
8.37 (m, 2H). Anal. Calcd for C8H6F3NO4S: C, 35.69; H,
2.25; N, 5.20%. Found: C, 36.45; H, 2.21; N, 5.47%. 4-
Nitrophenylmethyl trifluoromethyl sulfone: mp 101-102 °C.
1H NMR (CDCl3): ¤ 4.58 (s, 2H), 7.66 (d, J = 8.0 Hz, 2H),
8.32 (d, J = 8.8 Hz, 2H). Anal. Calcd for C8H6F3NO4S: C,
35.69; H, 2.23; N, 5.20%. Found: C, 35.85; H, 2.20; N, 5.37%.
3-Chlorophenylmethyl trifluoromethyl sulfone: mp 88-89 °C.
1H NMR (CDCl3): ¤ 4.45 (s, 2H), 7.23-7.47 (m, 4H). Anal.
Calcd for C8H6ClF3O2S: C, 37.14; H, 2.32%. Found: C, 37.01;
H, 2.32%. 4-Chlorophenylmethyl trifluoromethyl sulfone: mp
Finally, it should be noted that the μ value of 7.4 for 2 is
remarkably smaller than the expected value from the linear
relationship shown in Figure 5. The reason for the small μ
value is not clear at the present stage. Similar small μ values as
well as the r+ value were observed for the solvolysis of ¡,¡-
di-t-butylbenzyl p-nitrobenzoates28 and 4-methylbenzo[2.2.2]-
bicycloocten-1-yl triflates29 in which the vacant p-orbital of
carbocation intermediates is significantly twisted from the
benzene ³-orbital plane.30 The calculated geometry of the
conjugate anion of 2 shows that the S-C-S plane of the
¹
C (SO2CF3) moiety is also twisted from the benzene plane by
61.3°, suggesting that there may be some common reasons for
a reduced μ value in a highly congested system. Further study
is obviously needed to answer this question.
Conclusion
Substituent effects for acidities of a series of ArCH(R1)R2,
have been analyzed successfully in terms of the Y-T equation
using substituent parameters in gas the phase. The resultant
103-105 °C. H NMR (CDCl3): ¤ 4.45 (s, 2H), 7.39 (d, J =
1
8.4 Hz, 2H), 7.44 (d, J = 8.8 Hz, 2H). 3-Cyanophenylmethyl
trifluoromethyl sulfone: mp 75-77 °C. 1H NMR (CDCl3): ¤
4.41 (s, 2H), 7.58-7.79 (m, 4H); 13C NMR (CDCl3): ¤ 55.17,
113.85, 117.58, 120.89, 125.07, 130.23, 133.64, 134.56,
135.47. Anal. Calcd for C9H6NF3O2S: C, 43.37; H, 2.41; N,
5.62%. Found: C, 43.44; H, 2.36; N, 5.87%. 4-Cyanophenyl-
methyl trifluoromethyl sulfone: mp 123-125 °C. 1H NMR
(CDCl3): ¤ 4.53 (s, 2H), 7.57 (d, J = 8.4 Hz, 2H), 7.76
(d, J = 8.0 Hz, 2H). 3,5-Bis(triluoromethyl)phenylmethyl tri-
¹
resonance demand parameter r value decreased linearly with
increasing acidity of the GA values of the unsubstituted parent
¹
carbon acids, and the change of the r value was found to be
related with the geometric parameters and natural charges of
the conjugate carbanions calculated at B3LYP/6-311+G(d,p).
Such behavior of the resonance demand in the electron-
¹
rich system, ArC (R1)R2, is completely consistent with that
observed for the electron-deficient system, ArC+(R1)R2, sug-
gesting that the resonance demand must be determined by the
fluoromethyl sulfone: mp 86-87 °C. H NMR (CDCl3): ¤ 4.60
1
(s, 2H), 7.91 (s, 2H), 8.00 (s, 1H).

M. Zhang et al.
Bull. Chem. Soc. Jpn. Vol. 86, No. 7 (2013)
819
Preparation of substituted arylbis(triflyl)methanes.31 General
procedure: To a solution of 1 (0.5 mmol) in dry diethyl ether
(3 mL) was added t-BuLi (0.34 mL, 0.55 mmol, 1.6 M solution
in hexane) dropwise at ¹78 °C, and the resulting mixture
was stirred for 20 min. Triflic anhydride (92 mL, 0.28 mmol)
was then added, and the resulting mixture was allowed to warm
to room temperature over a period of 1 h. After the reaction
mixture was cooled to ¹78 °C, t-BuLi (0.34 mL, 0.55 mmol,
1.6 M in hexane) was added dropwise, and the resulting mix-
ture was stirred for 20 min. Triflic anhydride (0.28 mmol) was
then added, and the resulting mixture was allowed to reach
room temperature over a period of 1 h before the reaction was
quenched with water. The resultant mixture was neutralized and
washed with hexane. The aqueous phase was acidified with 4 M
aqueous HCl and extracted with ether twice. The organic layers
were dried over magnesium sulfate, filtered and concentrated
under reduced pressure. The residue was recrystallized using
2:1 hexane to ethylacetate to give desired products 2. 3-Fluoro-
phenylbis(triflyl)methane: mp 51-53 °C. 1H NMR (CDCl3):
¤ 5.87 (s, 1H), 7.21-7.58 (m, 4H). MS (FAB): Calcd for [M]+
C9H5O4F7S2: m/z 373.9518. Found: m/z 373.9518. 3-Tri-
time for the establishment of equilibrium was between 500 ms
and 50 s, depending upon the pressure and molecular structure
of neutrals. In the case of highly delocalized carbanions, the
achievement of equilibrium took a very long time ca. 30-50 s.
Each measurement was performed at several ratios of partial
pressures and at different overall pressures. The pressures of the
neutral reactants were measured by means of a Bayard-Alpert
ionization gauge with appropriate correction factors being
applied to convert the gauge readings to relative intensities of
the various compounds.33,34 A solid probe equipped with a
small glass vessel was also used for some strong acids which
were easily decomposed on the surface of a stainless steel inlet
tube. Arithmetic mean values of K were used to calculate ¤¦G°
¹1
(= ¹RT ln K) with an average uncertainty of «0.2 kcal mol
in most cases. Ion-eject experiments were also carried out to
ensure that proton-transfer reactions occurred. The gas-phase
acidity values for the reference compounds were taken from
the literature.18-20 Although the measurement of each proton-
transfer equilibrium was carried out at 323 K, the acidity values
obtained can be regarded as the values at 298 K, because the
entropy term is relatively small in proton-transfer equilibria in
the gas phase and because the acidities of reference compounds
are compiled at 298 K.
Calculations. DFT calculations were carried out using the
Gaussian 09 program.35 The geometries were fully optimized at
the B3LYP/6-311+G(d,p) level of theory. Vibrational normal
mode analyses were performed at the same level to ensure that
each optimized structure was a true minimum on the potential
energy surface. Natural population analysis was also carried out
to compute the charges.
1
fluoromethylphenylbis(triflyl)methane: mp 60-61 °C. H NMR
(CDCl3): ¤ 5.97 (s, 1H), 7.74-7.95 (m, 4H). MS (FAB):
¹
Calcd for [M] C10H4O4F9S2: m/z 422.9407. Found m/z
422.9411. 4-Trifluoromethylphenylbis(triflyl)methane: mp 76-
1
77 °C. H NMR (CDCl3): ¤ 5.97 (s, 1H), 7.83-7.85 (m, 4H).
¹
MS (FAB): Calcd for [M] C10H4O4F9S2: m/z 422.9407.
Found: m/z 422.9434. 3,5-Bis(trifluoromethyl)phenylbis(tri-
1
flyl)methane: mp 71-73 °C. H NMR (CDCl3): ¤ 6.04 (s, 1H),
¹
7.91-8.18 (m, 3H). MS (FAB): Calcd for [M] C11H3O4F12S2:
m/z 490.9281. Found: m/z 490.9276.
Gas-Phase Acidity Measurement. The gas-phase acidity
measurements were performed on an Extrel FTMS 2001 Fourier
transform ICR spectrometer equipped with an IonSpec Data
station. Most of the experimental techniques used for the mea-
surements of the equilibrium constants of the proton-transfer
reactions (eq 16) are the same as the general procedures in the
literature.3,32 Equations 13-16 describe the sequence of reac-
tions which occur in a typical experiment, where AH and AoH
are the measured acid and the reference acid, respectively.
We are indebted to the Joint Project of Chemical Synthe-
sis Core Research Institutions, the Ministry of Education,
Culture, Sports, Science and Technology, Japan for financial
support. I. A. K. thanks the Estonian Centre of Excellence
HIGHTECHMAT SLOKT117T; and targeted financing of
the Ministry of Education and Science SF0180089s08, and
Estonian Science Foundation project 8162. The authors are
grateful to Professor T. Taguchi and Professor H. Yanai (Tokyo
Univ. Pharm. Life Sci.) for gifts of 1,1,3,3-tetrakis(trifluoro-
methanesulfonyl)propane, 2-(2,2-bis(trifluoromethylsulfonyl)-
ethyl)-4,6-dimethylphenol, and 2,6-bis(2,2-bis(trifluoromethyl-
sulfonyl)ethyl)-4-tert-butylphenol.
MeONO þ eꢀ ! MeOꢀ þ NO
MeOꢀ þ AoH ! Aoꢀ þ MeOH
MeOꢀ þ AH ! Aꢀ þ MeOH
Aoꢀ þ AH ꢀ Aꢀ þ AoH
ð13Þ
ð14Þ
ð15Þ
ð16Þ
Supporting Information
¹
An experiment is initiated by a 5-ms pulse of a low-energy
electron beam (0.3 to 0.5 eV) through the ICR cell. The elec-
trons are captured by methyl nitrite at a partial pressure of
Optimized geometries, plots of the r vs. the bond length
C1C7 and natural charge of aromatic moiety, and plot of the μ
vs. the relative stability of the unsubstituted benzylic carboca-
tions. This material is available free of charge on the Web at:
http://www.csj.jp/journals/bcsj/.
¹
1-2 © 10¹7 Torr and CH3O is produced (eq 13). The acids
¹
AH and AoH react with CH3O to yield M ¹ 1 negative ions
(eqs 14 and 15). For the measurements of arylbis(trifluoro-
methylsulfonyl)methanes methyl nitrite was not needed be-
cause strongly acidic substrates were deprotonated easily only
by electron-ionization. The partial pressures of the neutrals
were maintained at lower than 4 © 10¹7 Torr. The equilibrium
constant K for reaction (eq 16) was evaluated from the expres-
References
1
R. W. Taft, Protonic Acidities and Basicities in the Gas
Phase and in Solution: Substituent and Solvent Effects in Progress
in Physical Organic Chemistry, John Wiley & Sons, Inc., 1983,
Vol. 14, p. 247. doi:10.1002/9780470171936.ch6.
¹
¹
sion K = [Ao /A ][AH/AoH]. The relative abundances of ions
2
R. W. Taft, R. D. Topsom, The Nature and Analysis
¹
¹
A and Ao were determined by the relative intensities of ICR
mass spectra signals when the equilibrium was attained. The
of Substitutent Electronic Effects in Progress in Physical
Organic Chemistry, John Wiley & Sons, Inc., 1987, Vol. 16,

820
Bull. Chem. Soc. Jpn. Vol. 86, No. 7 (2013)
Gas-Phase Acidities of ¡- and ¡,¡-SO2CF3-Substituted Toluenes
p. 1. doi:10.1002/9780470171950.ch1.
M. Fujio, R. T. McIver, Jr., R. W. Taft, J. Am. Chem. Soc.
1981, 103, 4017.
168, 141.
3
22 J. E. Bartmess, in Negative Ion Energetics Data, ed. by
W. G. Mallard, P. J. Linstrom, NIST Chemistry WebBook, NIST
Standard Reference Database Number 69, National Institute of
Standards and Technology, Gaithersburg MD, 2005, 20899, http://
webbook.nist.gov.
4
M. Mashima, R. R. McIver, Jr., R. W. Taft, F. G. Bordwell,
W. N. Olmstead, J. Am. Chem. Soc. 1984, 106, 2717.
5
R. W. Taft, J. L. M. Abboud, F. Anvia, M. Berthelot, M.
Fujio, J.-F. Gal, A. D. Headley, W. G. Henderson, I. Koppel, J. H.
Qian, M. Mishima, M. Taagepera, S. Ueji, J. Am. Chem. Soc. 1988,
110, 1797.
23 I. A. Koppel, J. Koppel, V. Pihl, I. Leito, M. Mishima,
V. M. Vlasov, L. M. Yagupolskii, R. W. Taft, J. Chem. Soc., Perkin
Trans. 2 2000, 1125.
6
Y. Tsuno, M. Fujio, Adv. Phys. Org. Chem. 1999, 32, 267;
Y. Tsuno, M. Fujio, Chem. Soc. Rev. 1996, 25, 129.
M. Mishima, S. Usui, H. Inoue, M. Fujio, Y. Tsuno, Nippon
Kagaku Kaishi 1989, 1262.
24 H. F. Koch, J. C. Biffinger, M. Mishima, Mustanir, G.
Lodder, J. Phys. Org. Chem. 1998, 11, 614.
25 J. I. Brauman, L. K. Blair, J. Am. Chem. Soc. 1968, 90,
5636.
7
8
M. Mishima, H. Nakamura, K. Nakata, M. Fujio, Y. Tsuno,
26 W. J. Hehre, C.-F. Pau, A. D. Headley, R. W. Taft, R. D.
Topsom, J. Am. Chem. Soc. 1986, 108, 1711.
Chem. Lett. 1994, 1607.
¹1
ꢁ ꢀ1
unit) for the sub-
9
M. Mishima, K. Arima, H. Inoue, S. Usui, M. Fujio, Y.
27 Revised μ values (in kcal mol
·
Tsuno, Bull. Chem. Soc. Jpn. 1995, 68, 3199.
10 M. Mishima, H. Inoue, S. Itai, M. Fujio, Y. Tsuno, Bull.
Chem. Soc. Jpn. 1996, 69, 3273.
11 M. Mishima, H. Inoue, M. Fujio, Y. Tsuno, Bull. Chem.
Soc. Jpn. 1997, 70, 1163.
stituent effect on the gas-phase stability benzylic carbocations,
ArC+(R1)R2: ¹13.0 (R1, R2 = Me, Me), ¹13.0 (Me, Et), ¹13.6
(H, Me), ¹14.0 (H, H), ¹14.0 (Me, CF3), ¹14.5 (H, CF3).
28 M. Fujio, T. Miyamoto, Y. Tsuji, Y. Tsuno, Tetrahedron
Lett. 1991, 32, 2929.
12 M. Mishima, Mustanir, M. Fujio, Y. Tsuno, Bull. Chem.
Soc. Jpn. 1996, 69, 2009.
29 M. Fujio, K. Nakashima, E. Tokunaga, Y. Tsuji, Y. Tsuno,
Tetrahedron Lett. 1992, 33, 345.
13 T. Matsumoto, K. Koga, S. Kobayashi, M. Mishima, Y.
Tsuno, Z. Rappoport, Gazz. Chim. Ital. 1995, 125, 611.
14 M. Mishima, T. Ariga, T. Matsumoto, S. Kobayashi, H.
Taniguchi, M. Fujio, Y. Tsuno, Z. Rappoport, Bull. Chem. Soc.
Jpn. 1996, 69, 445.
15 T. Matsumoto, S. Kobayashi, M. Mishima, Y. Tsuno, Int. J.
Mass Spectrom. Ion Processes 1998, 175, 41.
16 M. Mishima, C. Huh, H. W. Lee, H. Nakamura, M. Fujio,
Y. Tsuno, Tetrahedron Lett. 1995, 36, 2265.
17 C. Huh, C. H. Kang, H. W. Lee, H. Nakamura, M.
Mishima, Y. Tsuno, H. Yamataka, Bull. Chem. Soc. Jpn. 1999, 72,
1083.
18 I. Leito, E. Raamat, A. Kütt, J. Saame, K. Kipper, I. A.
Koppel, I. Koppel, M. Zhang, M. Mishima, L. M. Yagupolskii,
R. Y. Garlyauskayte, A. A. Filatov, J. Phys. Chem. A 2009, 113,
8421.
19 I. A. Koppel, R. W. Taft, F. Anvia, S.-Z. Zhu, L.-Q. Hu,
K.-S. Sung, D. D. DesMarteau, L. M. Yagupolskii, Y. L.
Yagupolskii, N. V. Ignat’ev, N. V. Kondratenko, A. Y. Volkonskii,
V. M. Vlasov, R. Notario, P.-C. Maria, J. Am. Chem. Soc. 1994,
116, 3047.
20 R. W. Taft, I. A. Koppel, R. D. Topsom, F. Anvia, J. Am.
Chem. Soc. 1990, 112, 2047.
21 C. Jinfeng, R. D. Topsom, A. D. Headley, I. Koppel, M.
Mishima, R. W. Taft, S. Veji, J. Mol. Struct.: THEOCHEM 1988,
30 K. Nakata, M. Fujio, Y. Saeki, M. Mishima, Y. Tsuno, K.
Nishimoto, J. Phys. Org. Chem. 1996, 9, 573.
31 A. Hasegawa, T. Ishikawa, K. Ishihara, H. Yamamoto, Bull.
Chem. Soc. Jpn. 2005, 78, 1401.
32 Md. M. R. Badal, M. Mishima, Bull. Chem. Soc. Jpn. 2010,
83, 58.
33 J. E. Bartmess, R. M. Georgiadis, Vacuum 1983, 33, 149.
34 K. J. Miller, J. Am. Chem. Soc. 1990, 112, 8533.
35 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria,
M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B.
Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P.
Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg,
M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida,
T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A.
Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd,
E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi,
J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S.
Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene,
J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo,
R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi,
C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G.
Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich,
A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski,
D. J. Fox, Gaussian 09 (Revision B.01), Gaussian, Inc., Wallingford
CT, 2010.