Dynamic solvent effects on the thermal cyclization of a hexadienone formed from a diphenylnaphthopyran: An example of a system with distinctly separate medium and chemical contributions to the overall reaction coordinate

Article abstract of DOI:10.1039/b212673g

Pressure effects on the rate of thermal fading of a colored hexadienone formed from 3,3-diphenyl-3 H-naphtho[2,1-b]pyran were measured at various temperatures in three highly viscous solvents, e.g., 2,4-dicyclohexyl-2-methylpentane, glycerol triacetate, and 2-methylpentane-2,4-diol, as well as in their chemically similar nonviscous counterparts, e.g., methyl acetate, ethanol, and methylcyclohexane. It was demonstrated that the medium and the chemical coordinate had to be treated separately. The experimental data and quantum-mechanical computations agreed with the formation of a cyclic activated complex. The dynamic solvent effects in the systems had to be described by a two-dimensional model that includes separately defined chemical and medium coordinates.

Full text of DOI:10.1039/b212673g

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Dynamic solvent effects on the thermal cyclization of a hexadienone
formed from a diphenylnaphthopyran: An example of a system with
distinctly separate medium and chemical contributions to the overall
reaction coordinatey
a
Yoshitaka Goto, Toru Takahashi, Yasushi Ohga, Tsutomu Asano,*
a
a
a
b
Michael Hildebrand and Noham Weinberg*
b
a
Department of Applied Chemistry, Faculty of Engineering, Oita University,
00 Dannoharu Oita 870-1192, Japan. E-mail: asano@cc.oita-u.ac.jp
Department of Chemistry, University College of the Fraser Valley, 33844 King Road,
Abbotsford, B.C., Canada V2S 7M9. E-mail: weinberg@sfu.ca
7
b
Received 3rd January 2003, Accepted 10th March 2003
First published as an Advance Article on the web 25th March 2003
Pressure effects on the rate of thermal fading of a colored hexadienone formed from 3,3-diphenyl-3
H-naphtho[2,1-b]pyran were measured at various temperatures in three highly viscous solvents, i.e., 2,4-
dicylohexyl-2-methylpentane, glycerol triacetate, and 2-methylpentane-2,4-diol, as well as in their chemically
similar nonviscous counterparts, such as methylcyclohexane, methyl acetate, and ethanol. Both experimental
data and quantum-mechanical calculations are in agreement with formation of a cyclic activated complex.
In the viscous solvents, high viscosities resulted in retardations of solvent thermal fluctuations which, in turn,
slowed down the cyclization. The analysis of experimental results unequivocally demonstrated that the dynamic
solvent effects in the present systems have to be described by a two-dimensional model that includes separately
defined chemical and medium coordinates. Predictions of an alternative one-dimensional model with a
diffusion-controlled reaction coordinate are not supported by the experimental data.
As we reported in our previous studies of the pressure effects
on the kinetics of Z/E-type isomerizations,
Introduction
6
–10
even relatively
3
ꢀ1
Transition state theory (TST) describes effects of pressure on
reaction rates in terms of a volume of activation, DV , related
slow reactions (k < 10 s ) demonstrated a significant depar-
ture from the TST and eqn. (1) in highly viscous media. The
observed viscosity dependence of the rate constant could not
be rationalized if we assumed that chemical transformations
are completely coupled with solvation changes. These two
components of solution reactions had to be treated as indepen-
dent coordinates, i.e., the chemical coordinate which described
atomic movements of a reactant molecule and the medium
coordinate which described solvation changes.
As a part of our efforts to examine the limit of the validity
of this conclusion, we extended our measurements to yet
another unimolecular rate process, cyclization of a thermody-
namically unstable species 1 (R=Ph), photochemically gener-
6¼
to the pressure derivative of the observed rate constant, kobs
by equation
,
2
–4
ꢀ
ꢁ
ꢀ
ꢁ
6
6¼
DV
@
ln kobs
1
@DG
@P
¼
ꢀ
¼ ꢀ
RT
:
ð1Þ
@
P
RT
T
T
Defined as a difference between the partial molar volumes of
activated complex and the reactant(s), DV gives important
6
information on the structural changes that occur in the reac-
tion system as well as on the involvement of solvent molecules
in the reaction. However, the validity of eqn. (1) is essentially
restricted to the cases where an equilibrium between reactants
and activated complex is maintained in the course of reaction.
No information on the involvement of solvent molecules in the
dynamics of activation is thus contained in this equation.
High-pressure kinetics in highly viscous solvents is one of the
experimental ways to study how solvent molecules are involved
in the activation step. In highly viscous solvents, solvent visco-
ated in situ from 3,3-diphenyl-3H-naphtho[2,1-b]pyran 2, into
2
(Scheme 1). First, we discuss the nature of the chemical coor-
dinate on the basis of quantum-mechanical calculations of the
gas-phase potential energy surface (PES), then present kinetic
effects of pressure in nonviscous solvents and, finally, we
describe pressure effects in viscous solvents.
5
sity rapidly increases with increasing pressure and thermal
fluctuations become too slow to maintain thermodynamic
equilibrium between the initial state and the transition state
Gas-phase calculations
(
TS). Under such circumstances, the reaction rate is limited
by the rate of solvent thermal fluctuations and a so-called
dynamic solvent effect is observed.
To study the gas-phase reaction mechanism, AM1 and
B3LYP/6-31G** calculations were performed with Gaussian
1
1
9
8
for somewhat simplified models with R being either
CH or C(CH )=CH , and the second of the fused rings of
3
3
2
the naphthalene system removed. The results of calculations
indicate that the reaction coordinate is initially represented
by rotation around the single C–C bond of the exocyclic diene
y Preliminary results were presented at the 18th International Confer-
ence on High Pressure Science and Technology, July 23–27, 2001,
Beijing, China and published as a conference paper.
1
DOI: 10.1039/b212673g
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1825

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Scheme 1
system, tCC , followed by C–O bond formation along distance
kP
ln
¼ aP þ b lnð1 þ cPÞ
ð2Þ
ð3Þ
coordinate RCO (Scheme 1). A two-dimensional projection of
the AM1 PES on tCC–RCO coordinate subspace is shown in
Fig. 1 and relative B3LYP/6-31G** and B3LYP/6-31+G**
energies for reactants, TSs, and products are listed in Table 1.
k0:1
6¼
DVo ¼ ꢀða þ bcÞRT
ꢁ
The values at 25 C were ꢀ6.1 (c-HexMe), ꢀ6.3 (AcOMe) and
3
8.8 (EtOH) cm mol . These results are in agreement with
ꢀ1
ꢀ
the mechanism of Scheme 1. The product-like activated com-
plex has a smaller internal freedom of motion than the open-
chain reactant 1 and the volume of the reactant is expected
to decrease during the activation. This decrease in the free-
dom of motion in the activation step is also reflected in rela-
tively small preexponential factors which correspond to
activation entropies of ꢀ34 ꢂ ꢀ54 J K mol . The experi-
mental activation parameters are listed in Table 2. The activa-
tion energies are in reasonable agreement with the calculated
Experimental section
3
2
,3-Diphenyl-3H-naphtho[2,1-b]pyran 2 was prepared from
-naphthol and 1,1-diphenylprop-2-yn-1-ol as described in the
14
1
2
literature. The hexadienone 1 was photochemically generated
in situ from 2 and its decay was followed spectrophotometri-
cally. The experimental details were described elsewhere.
ꢀ1
ꢀ1
1
3
To study the nonequilibrium effects of viscous solvents, we
used 2,4-dicyclohexyl-2-methylpentane (DCMP), glycerol tri-
acetate (GTA), and 2-methylpentane-2,4-diol (MPD) whose
viscosities at various temperatures and pressures were reported
ꢁ
gas-phase values of Table 1. Rate constants at 25 C and 0.1
MPa (0.143 in c-HexMe, 0.100 in AcOMe, and 0.0828 in
EtOH) clearly indicated the absence of a major polarity change
during the activation step as usually observed for electrocyclic
reactions. As can be seen from Table 2, the reaction barriers
were only marginally affected by the external pressure.
9
previously. In order to measure the equilibrium pressure effects,
similar measurements were also performed in nonviscous sol-
vents, such as methylcyclohexane (c-HexMe), methyl acetate
(
AcOMe), and ethanol (EtOH). No dynamic solvent effects were
observed in these solvents. At all conditions studied, the reaction
obeyed the first-order rate law and the rate constants could be
determined unequivocally.
Viscous solvents
The observed rate constants kobs in DCMP and GTA are
plotted against pressure in Figs. 3 and 4. The results in
1
MPD were qualitatively the same. For the sake of compari-
Experimental results and discussion
son, rate constants in less viscous media were also plotted in
ꢁ
these Figures for 25 C.
Nonviscous solvents
An increase in pressure resulted in similar magnitudes of
acceleration of the reaction at lower pressures. The activation
energies at 0.1 MPa (69.0 kJ mol for DCMP, 67.5 kJ mol
Pressure dependences of the first-order rate constant kobs in
methylcyclohexane are illustrated in Fig. 2. Similar pressure
dependences were also observed in methyl acetate and ethanol.
ꢀ1
ꢀ1
ꢀ
1
for GTA, and 66.1 kJ mol for MPD) were also very close to
the values in the corresponding nonviscous solvents (Table 2),
clearly indicating the validity of TST even in the viscous
solvents up to a few hundred MegaPascals (MPa). At higher
pressures and lower temperatures, however, pressure-induced
retardations were observed. Since these retardations were
observed only in viscous media, it is reasonable to assume
that TST became invalid for these systems because of high
viscosities at high pressures.
1
3
P
The results were fitted to eqn. (2) (k and k0.1 refer to the rate
constants at pressures P and 0.1 MPa, respectively) by adjust-
ing parameters a, b and c. The activation volume at zero
06
¼
pressure, DV , was then estimated from eqn. (3), that can
be obtained from eqn. (2) by differentiation with respect to
pressure.
Theoretical models
Two different models have been proposed to describe the
dynamic effects of medium in solution reactions. The first
1
model, proposed by Kramers and later modified by Grote
5
1
6,17
and Hynes (KGH model), describes the progress of a
reaction in terms of a single coordinate that represents a con-
Table 1 Relative B3LYP/6-31G** and B3LPY/6-31+G** (in
brackets) energies (kJ mol ) calculated for model reaction systems
ꢀ1
R:CH
3
R:C(CH
3 2
)=CH
Reactant, 1
TS
Product, 2
0
57.8[58.3]
0
70.6
Fig. 1 A 2D projection of the AM1 PES for the model reaction
)=CH
(
Scheme 1, the second ring removed, R:C(CH
10 kJ mol
3
2
). Energy grid
ꢀ76.4[ꢀ71.4]
ꢀ51.0
ꢀ1
–
.
1
826 Phys. Chem. Chem. Phys., 2003, 5, 1825–1830

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ꢀ1
Fig. 2 Pressure dependence of the cyclization rate constant (kobs/s
of 1 in methylcyclohexane at various pressures.
)
ꢀ1
Fig. 3 Pressure dependence of the cyclization rate constant (kobs/s
of 1 in DCMP at various temperatures.
)
certed Brownian motion of both the reaction system and the
solvent. Fig. 5 shows an example of a 2D PES for a typical
KGH-type system.
of high viscosity, the observed rate constant is represented by a
product of the TST rate constant kTST for the given physical
conditions by a transmission coefficient f(Z) that decreases as
Due to a strong coupling between the chemical and the
medium coordinate, the reaction cannot occur without
simultaneous restructuring of the solvation shell. All reaction
trajectories must therefore pass through the TS region.
ꢀb
27
Z
(0 < b < 1) in the high viscosity limit:
kKGH ¼ kTSTf ðZÞ
ð4Þ
1
8,19
The second model, proposed by Agmon and Hopfield
AH model) and further developed by Sumi and Marcus,
2
0,21
(
Berezhkovskii et al.,
Since the value of f(Z) is solely determined by Z, the tem-
2
2–24
25,26
and by Basilevsky et al.,
assumes
perature dependence of kKGH must be identical with that of
kTST if viscosity is kept constant. An isoviscous Arrhenius plot
of kKGH should therefore give an isoviscous activation energy
that the two coordinates are independent of each other. As a
result, the reactant and product valleys are parallel to each
other, as illustrated in Fig. 6, and the reaction can occur simul-
taneously at various configurations of the solvent. The overall
reaction is thus represented in the AH model as an ensemble of
simultaneous reactions taking place along the chemical coordi-
nate at various configurations of the solvent. Therefore, reac-
tion trajectories can deviate substantially from the TS region.
As a result of the above differences, the two models make
totally different predictions about the viscosity dependence of
the activation energy. In the KGH model, the reactant particle
is pushed back and forth by solvent molecules while it gradu-
ally climbs up the energy barrier. The viscosity changes the
rate of diffusion of the system along the joint chemical–med-
ium coordinate, but it does not affect the height of the energy
barrier since all trajectories have to pass through the TS
region. As a result, the KGH model predicts that, in the limit
Ea,KGH,Z equal to Ea,TST,Z
.
ꢀ1
a
Table 2 Preexponential factors (A/s ) and activation energies (E /
ꢀ1
kJ mol ) for thermal ring closure of 1 in nonviscous solvents at
various pressures (P/MPa)
c-HexMe
AcOMe
EtOH
ꢀ
1
11
10 A/
ꢀ11
ꢀ1
ꢀ11
ꢀ1
P/
MPa
E
kJ mol
a
/
10 A/
s
E
kJ mol
a
/
10 A/
s
E
kJ mol
a
/
ꢀ
ꢀ1
ꢀ1
ꢀ1
s
0
1
3
4
6
.1
1.2
2.1
2.4
2.5
3.0
68.1
68.7
68.5
68.1
68.2
0.97
1.3
1.4
1.3
1.3
68.5
68.3
67.9
67.0
66.5
0.28
0.34
0.40
0.43
0.44
65.9
65.3
64.8
64.2
63.6
50
00
50
00
ꢀ1
Fig. 4 Pressure dependence of the cyclization rate constant (kobs/s
of 1 in GTA at various temperatures.
)
Phys. Chem. Chem. Phys., 2003, 5, 1825–1830
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Fig. 5 A 2D PES for a KGH-type model.
In the AH model, although the reaction can occur at a vari-
ety of different solvent configurations, usually only one confi-
guration gives the dominant contribution to the overall rate
constant. A balance between the rate of the diffusion-type sol-
vent reorganization along the medium coordinate and the rate
of barrier crossing along the chemical coordinate determines
this configuration. The situation is schematically illustrated
in Fig. 7.
The reaction starts from the lower left corner and the reac-
tant moves back and forth along the medium-coordinate valley
up to point 1* which gives the dominant contribution to the
overall rate constant. We do not have direct information on
the structure of the reactant at point 1*. However, since it is
in a solvation shell which stabilizes the activated complex, it
seems reasonable to speculate that 1* has a conformation with
a considerably smaller dihedral angle (Fig. 1). If 1* acquires
enough energy for surmounting the barrier, one fast movement
along the chemical coordinate brings it to the product valley as
shown by a long curly arrow. This movement is assumed to
take place in a frozen solvent cage. In other words, the move-
ment along the reaction coordinate is considered to be much
faster than thermal fluctuations of solvent molecules and the
solvent viscosity does not influence this transformation.
At low viscosities, diffusion along the medium coordinate is
relatively fast so that point 1* opposes the true saddle point of
the PES. Under these conditions, the major contribution to the
overall rate constant comes from the TS flux and the reaction
Fig. 7 A reaction trajectory in the AH model.
rate can be described by the TST. As the viscosity increases,
the rate of diffusion decreases which reduces the TS flux. How-
ever, in contrast with the case of the KGH model where the TS
flux is the sole contributor to the overall rate constant, in the
AH model the overall process is represented by an array of
parallel fluxes crossing the ridge at different points. Therefore,
as the TS flux ‘‘dries out’’, the location of point 1* where the
dominant flux originates shifts down to the starting point 1
along the bottom of the reactant valley. This alleviates the
negative impact of viscosity on the overall rate and thus the
viscosity dependence of the AH rate constant kAH is expected
to be weaker than that of kKGH
.
The isoviscous temperature dependence of kAH should also
be different from that of kKGH . Under isoviscous conditions
the rate of diffusion along the reactant valley would demon-
strate a much weaker temperature dependence than the rate
of the barrier crossing. Therefore, an increase in temperature
will shift point 1* further towards the starting point 1. As a
result, the direct positive effect of the temperature on kAH will
be partly compensated by the negative effect of the increase in
the barrier height and the overall effect of temperature on kAH
will be weaker than that on kTST , i.e. the isoviscous activation
energy for Ea,AH,Z is expected to be lower than Ea,TST,Z . Thus,
comparing the observed isoviscous activation energies to
the Ea,TST,Z values should allow one to discriminate between
KGH- and AH-type behavior.
Isoviscous activation energies
If viscosity could be manipulated without affecting other phy-
sico-chemical properties of the system, the isoviscous Ea,TST,Z
would be the same as the isobaric Ea,TST . However, in reality,
viscosity change is inevitably accompanied by changes in other
physical and chemical properties, i.e., if temperature and vis-
cosity are chosen as independent parameters, pressure becomes
a function of these parameters: P ¼ P(T, Z). If activation ener-
gies are determined from the Arrhenius plots, an isobaric E
a
and an isoviscous Ea,Z can be defined as derivatives
ꢀ
ꢁ
ꢀ
ꢁ
@
ln k
@ ln k
@T
2
2
Ea ¼ RT
and Ea;Z ¼ RT
:
@
T
Fig. 6 A 2D PES for an AH-type model.
P
Z
1
828
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Since P ¼ P(T, Z),
ꢀ
ꢁ
ꢀ
ꢁ ꢀ
ꢁ
@
ln k
@ ln k
@P
@P
@T
2
2
Ea;Z ¼ RT
þ RT
:
@
T
Z
T
Z
a
The first term in the right-hand side of this equation is E ,
6¼
the isothermal pressure derivative of k is related to DV by
eqn. (1), and
ꢀ
ꢁ
ꢀ
ꢁ ꢂꢀ
ꢁ
@
@
P
T
@Z
@T
@Z
@T
¼
ꢀ
:
Z
P
T
Therefore,
Ea;Z ¼ Ea þ DV T
ꢀ
ꢁ ꢂꢀ
ꢁ
@
Z
@Z
@P
6¼
:
ð5Þ
@
T
P
T
Thus, both Ea,obs,Z and Ea,TST,Z values contain effects of the
activation volume.
Viscosity increases with pressure and decreases with tem-
perature, therefore the ratio of derivatives in the second term
in the right-hand side of eqn. (5) is negative. Since at low vis-
6¼
cosities the DV values are negative for the present reaction, the
isoviscous activation energies are expected to be larger than
the isobaric ones in the TST-valid region. At high viscosities,
6
however, the apparent values of DV become positive (kobs
decreases with pressure) and the isoviscous activation ener-
Fig. 9 Viscosity dependence of the cyclization rate constant (kobs
/
ꢀ1
gies are expected to be smaller than the isobaric ones. Figs.
and 9 illustrate the viscosity dependence of kobs at various
s
) of 1 in GTA at various temperatures.
8
temperatures in DCMP and GTA, respectively. From these
plots, rate constants at a constant viscosity were estimated
for different temperatures by fitting kobs to cubic equations
of Z and isoviscous Arrhenius plots were constructed. The
activation energies thus obtained are listed in Table 3 for
all the three viscous solvents studied.
listed in Table 4. As can be seen from the data of Tables 3
and 4, Ea,obs,Z are smaller than Ea,TST,Z at viscosities where
TST is expected to fail, which is consistent with the prediction
of the AH model. Since Ea,KGH,Z is expected to be equal to
Ea,TST,Z at any viscosities, all of these observations strongly
For comparison, we need the corresponding values of
suggest that the AH model describes the present system better
than the KGH model.
As expected, the Ea,obs,Z values show a clear tendency to
Ea,TST,Z which can be obtained from isoviscous Arrhenius plots
for kTST . The necessary values of kTST are not immediately
available for the entire pressure range, as the TST fails at
higher viscosities. However, as mentioned above, even in the
viscous solvents, the TST is valid at low pressures. The rate
constants obtained for this TST-valid pressure region were
fitted to eqn. (2) and the resultant equation was then used to
estimate kTST and the activation parameters for the entire pres-
sure range. The activation energies Ea,TST,Z thus obtained are
decrease with increasing Z in DCMP and GTA, whereas the
Ea,TST,Z values increase with increasing viscosity.
Conclusions
Slow thermal rate process study at highly viscous conditions
again unequivocally demonstrated that the medium and the
chemical coordinate have to be treated separately. In order
to obtain the information on the extent of coupling between
these coordinates, further analyses based on the theoretical
models are in progress and the results will be reported shortly.
Table 3 Isoviscous activation energies obtained from kobs (Ea,obs,Z/kJ
ꢀ
1
mol ) for the cyclization of 1 in viscous solvents at various viscosities
Z/Pa s)
(
ꢀ
1
0
1
2
3
4
5
6
Z
10
10
10
74
76
76
10
72
71
76
10
69
64
10
65
56
10
58
10
50
DCMP
GTA
MPD
77
76
74
Table 4 Isoviscous activation energies obtained from kTST (Ea,TST,Z
/
ꢀ1
kJ mol ) for the cyclization of 1 in viscous solvents at various viscos-
ities (Z/Pa s)
ꢀ1
0
1
2
3
4
5
6
Z
10
73
77
74
10
74
78
77
10
74
81
79
10
74
83
81
10
75
85
83
10
75
87
86
10
75
90
88
10
76
92
91
DCMP
GTA
MPD
Fig. 8 Viscosity dependence of the cyclization rate constant (kobs
/
ꢀ1
s
) of 1 in DCMP at various temperatures.
Phys. Chem. Chem. Phys., 2003, 5, 1825–1830
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Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V.
Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C.
Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala,
Q. Cui, K. Morokuma, N. Rega, P. Salvador, J. J. Dannenberg,
D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman,
J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu,
A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L.
Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A.
Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W.
Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-
Gordon, E. S. Replogle, J. A. Pople, Gaussian 98, Revision
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Acknowledgements
Financial supports by the Ministry of Education, Science,
and Culture (08454204), Japan Society for Promotion of
Science and Culture (13440191), and the Natural Sciences
and Engineering Research Council of Canada are gratefully
acknowledged.
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9
0
1
1
1
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27 Simple Kramers model predicts b ¼ 1.
15
1
830
Phys. Chem. Chem. Phys., 2003, 5, 1825–1830