# Accelerations in the Lactonization of Trimethyl Lock Systems Are due to Proximity Orientation and not to Strain Effects

Authors: Rafik Karaman
Journal: Research Letters in Organic Chemistry
 (2009)

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## Abstract

DFT at B3LYP/6-31G(d,p) and HF at 6-31G and AM1 semiempirical calculations of thermodynamc
and kinetc parameters for the  trimethyl lock system (an important enzyme model) indicate that the
remarkable enhancement in the lactonizations is largely the result of a proximity orientation as opposed
to the currently advanced strain effect.


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## Body

## 1. Introduction

The study of enzyme mechanisms is of vast
importance and has become central to both bioorganic chemistry and
computational chemistry. Studies in this field by Bruice, Benkovic, Jencks, and
Bender over the past 40 years have contributed largely to understanding the
mode and scope by which certain enzymes achieve their catalytic activities [1]. These and studies of many others have been carried out in order to understand enzymatic catalysis which is characterized by high substrate specificity,
chemoselectivity, and stereospecificity along with large rate enhancements.
Among these are (1) the proximity model of Bruice [2, 3] on the
intramolecular cyclization of dicarboxylic semiesters, (2) the “orbital
steering” theory suggested by Koshland [4, 5], (3) the “spatiotemporal hypothesis”
devised by Menger [6–9] which describes the importance of the distance between
the two reactive centers in determining whether a reaction is inter- or
intramolecular, and (4) the gem-trimethyl lock (stereopopulation control)
proposal of Cohen [10–12].Reaction
models for mimicing enzyme catalysis usually fail to reach a desirable rate
enhancement due to a lack of a high degree of conformational restrictions
comparable to that existing in the enzyme-substrate complex [1]. In 1970, Cohen
studied the lactonization of a series of hydroxyhydrocinnamic acids and found
accelerations above 1015 when compared to the intermolecular
cyclization of the corresponding counterparts. He attributed this large
enhancement to what he called “stereopopulation control”  [10–12]. Cohen’s
interpretation of his data was criticized by various researchers who claimed
that the high rate enhancement results from relief in strain energy during the
lactonization of the hydroxyhydrocinnamic acid and not because of a
stereopopulation control within the trimethyl lock system [13–15].Recently, we have been engaged in exploring
the driving force(s) behind the remarkable acceleration rates in some
intramolecular reactions [16–19]. Using ab
initio molecular orbital at different levels, molecular mechanics, and
semiempirical molecular orbital methods, we studied the thermodynamic and
kinetic behavior of the lactonization of some hydroxy acids, the cyclization
reactions of Bruice’s di-carboxylic semiesters, the proton transfer reaction in
Menger’s system, and the cyclization of some ω-bromoalkanecarboxylate
anions. The results from these studies revealed the following main conclusions.
(1) Rate enhancement in intramolecular reactions can be driven by proximity
orientation which is due to strain effects or by proximity that is not related
to strain effects of a starting material and/or a corresponding transition
state. For example, our study on cyclization of Bruice’s dicarboxylic semiesters
reveals that the activation energy in these systems is dependent on the
difference in the strain energies of the transition states and the reactants,
and there is no relationship between the cyclization rate and the distance
between the nucleophile and the electrophile, and the reactivity extent of the
semiester system is linearly correlated with the strain energy difference
between the transition state and the reactant. On the other hand, acid
lactonization of hydroxy acids reveals that the enhancement in rates of the
lactonization in this system stems from the close proximity of the electrophile
to the nucleophile. Further, it shows that the rate of the lactonization
reaction is solely dependent on the ratio between the angle of attack of the
nucleophile and the distance between the two reacting centers. This is in accordance
with Menger’s “spatiotemporal hypothesis” that relates distance between the
nucleophile and the electrophile to the rate of the reaction. (2) Significant
rate enhancements in intramolecular reactions are due to both enthalpic and
entropic effects and not only due to enthalpic effects as was proposed by
Bruice. (3) The nature of the reaction (intermolecular or
intramolecular) is largely dependent on the distance between the two reacting
centers. For example, our ab initio
calculations on Menger’s system show that when the distance between the two
reacting centers is 2.4 Å, the reaction is intramolecular, whereas, when the
distance is 3 Å,
the reaction prefers the intermolecular process. Further, our study shows that
the proximity between the nucleophile and electrophile is largely dependent on
the strain energy of the system. For a strained system, the distance between
the two reacting centers is shorter than that in unstrained systems [16–19].In
this letter, we describe the DFT at B3LYP/6-31G (d,p) and the RHF at 6-31G levels,
as well as AM1 semiempirical calculations results (thermodynamics and kinetics)
for the acid-catalyzed and uncatalyzed lactonization reactions of the trimethyl
lock system. Our goal was to
establish the driving force behind the remarkable accelerations of the
intramolecular reaction in the tri-methyl lock system 1c in Figure
1.Figure 1
Hydroxyhydrocnnamc acids.


## 2. Methods

The DFT, HF, and
AM1 calculations were carried out using the quantum chemical package
Gaussian-98 [20]. The MM2
molecular mechanics strain energy calculations were performed using Allinger’s
MM2 program installed in Chem 3D Ultra 8.0 [21]. The starting geometries of all the
molecules in this study were obtained using the Argus Lab program [22].  The calculations were carried out based on the
restricted Hartree-Fock (RHF) method with full optimization of all geometrical
variables (bond lengths, bond angles, and dihedral angles) [23]. To avoid results with local minima
optimization, the keyword Freq Opt = (Z-matrix, MaxCycle = 300, CalcAll) GFINPUT
IOP(6/7 = 3) was used in the input files of the starting geometries.  The geometry optimizations included
estimations of second derivatives (Hessian matrix) for each of the 3n−6 parameters in each species (2n−3 for planar structures) [24]. DEP analytical gradients were used
throughout the optimization.  Geometries
were optimized in internal coordinates and were terminated when Herbert’s test
was satisfied in the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.An energy minimum (a stable
compound or a reactive intermediate) has no negative vibrational force
constant. A transition state is a saddle point which has only one negative
vibrational force constant [25].The
transition state structures were verified by their only one negative frequency.
The verification was accomplished by viewing the frequency results via the Molden program [26]. The “reaction coordinate method”  [27–29] was
used to calculate the activation energy for the lactonization processes of hydroxyl
acids 1a–1d. In this method, the
value of one bond is limited for the appropriate degree of freedom while all
other variables are optimized. The activation energy values for the cyclization
reactions were calculated from the difference in the energies of the global
optimum structures for the reactants 1a–1d
and the derived transition states of the cyclization reactions. The transition
state structures for the cyclization reactions of 1a–1d were obtained from the decrease in the distance between the
phenolic oxygen (O10) and the carbonyl carbon (C1) in increments of 0.1 Å. Full optimization
of the transition states was accomplished after removing the constrains imposed
while executing the energy profile. The frequency results obtained from the
optimization were viewed by Molden program and it was found that all the
transition state structures, studied here, have only one negative frequency. The
DFT at B3LYP/ 6-31G (d,p) and HF at 6-31G levels of the reactions of 1a–1d were calculated with and without
the inclusion of solvent (water, dielectric constant =  78.39). The keywords SCF = Tight
and SCRF =  Dipole were used in the input files when calculating energies with
the incorporation of a solvent.


## 3. Results and
Discussion

In
order to determine whether stereopopulation control, suggested by Cohen et al. [10–12] or conventional relief of strain
energy, proposed by Winans and Wilcox [13] and supported by a
theoretical study by Houk et al. [15]  is the driving force for the enzyme-like
accerelation in 1c,  we have
calculated the AM1 thermodynamic properties for the lactonization of
hydroxyhydrocinnamic acids 1a–1d
(Figure 1) using Gaussian 98 version 3.0 [20] available at our Al-Quds computer center.
These thermodynamic calculations were performed (the calculated data is depicted
in Tables S1 and S2, Supplementary Material,  available at  doi:10.1155/2009/240253) in order to prove that rates of
reactions cannot be predicted from free energy changes (MM2 strain energy,
thermodynamic parameter) as was previously reported by Winans and Wilcox [13].The
AM1 calculations of the enthalpic and entropic energies of the lactonization
processes of hydroxy acids having a trimethyl lock (1c) and lacking the trimethyl lock (1a) (see Table1) reveal that
the difference in  the free energy values between the lactonization reactions of
the two systems (ΔΔG) is 9.7 kcal/mol (ΔΔG   =   ΔG tetrahedral
intermediate-ΔG hydroxyl acid).
Based on this value, the calculated rate enhancement of the lactonization of 1c
compared to that of 1a should be 1.1 × 107,  which is 104-fold
less than the experimentally determined value (see Table 1) [10–12]. Further,
the MM2 calculated difference in strain energies (ΔEs3,1=Es3−Es1,  for the
numbering see Figure 1) in the two systems 1a and 1c is about 7 kcal/mol, which
is equal to 1.2 × 105 (106-fold less than the
experimentally value). This result excludes the notion that the remarkable rate
enhancement in the lactonization of 1c is solely accommodated by conventional
relief of strain as was reported by the groups of Houk and Wilcox  [13–15].Table 1
AM1 and MM2 calculated thermodynamic properties of hydroxyhydrocinnamic
acid derivatives. (All values were calculated by AM1 method except for the
values ofEs which were calculated by MM2 method.)
StructureΔΔHf3,1TΔS3,1ΔEs3,1ΔΔG3,1logkexpbPAAa−1.95−4.8214.272.87−10.0001a−5.25−3.9610.54−1.29−5.2261b−4.82−1.779.95−3.05−5.2061c−12.10−1.083.49−11.035.7711d−9.39−1.777.35−7.62−1.581aPAA Stands for the bimolecular reaction
of phenol and acetic acid.bTaken from reference [10–12]. The numbers 1 and 3
refer to structures 1 and 3 (see Figure 1).To
test whether the conformational restriction plays an important role in the rate
accerelation of the lactonization processes of hydroxy acids 1a and 1c,
calculations of the rotational barrier around the C2–C3 bond were executed.
Note that the C1–O10 distance in hydroxyhydrocinnamic acids is dependent upon
the C1/C2/C3/C4 dihedral angle. This C1–O10 distance should be crucial for
enhancing the lactonization rate according to the stereopopulation control
(conformational locking) suggested by Cohen [10–12]. When plotting the C1–O10
distance in 1a and 1c against the heats of formation of the resulting
conformations (see Figure 2), an important result emerges.  In 1c,
the shortest C1–O10 distance values correspond to the most stable conformations,
whereas for 1a the shortest
distance values correspond to the highest energy conformations.(2a) a plot of energy versus dihedral angle C1C2C3C4 in 2a and 2c.
(2b) a plot of energy versus C1–O10 distance in 2a and 2c.
(a)(b)Further, calculations of the thermodynamic
parameters (ΔG,  ΔH and S) of each
of the energetically most stable conformers in 1a, as well as those for the conformer with the shortest C1–O10
distance, reveal that for 1a to
reside in the most productive position to react intramolecularly requires a  ΔG  = 10.73 kcal/mol (composed of  ΔH = 4.91 kcal/mol
and -
TΔS = 5.82 kcal/mol).  In contrast, 1c requires  ΔG = 3.93 kcal/mol
(ΔH = 1.85 kcal/mol
and-TΔS = 2.08 kcal/mol)
in order to fulfill the same task (see Table S3,
Supplementary Material, available at doi:10.1155/2009/240253). The roughly 7 kcal/mol difference in
ground-state free energy for the two systems is equivalent to about 1.4 ×  106 in rate enhancement of 1c over 1a.
Again, the calculations show clearly that the conformational locking is not the
critical factor in the rate accerelation seen with 1c (comprising only a calculated 106 value versus an
experimental 1011 value) [10–12].In
light of the results of the AM1 calculations that show neither the steric
effects suggested by Winans and Wilcox [13] nor the conformational locking suggested by
Cohen [10–12] are
the main driving force for the enhancement in the lactonization of 1c, we have calculated, using the “reaction coordinate”  method, the activation energy values (ΔΔG‡) for the formation
and the collapse of the tetrahedral intermediate involved in the lactonization
process. The DFT at B3LYP/6-31G
(d,p) and HF/6-31G levels as well as the AM1 activation energy values were
calculated with and without the inclusion of solvent (water,  dielectric
constant 78.39) and the results obtained indicate that the effect of water on
the relative rate values is negligible (1.2–1.8 kcal/mol for the three
different lactonization processes of 1a,
1c, and 1d). This is in accordance with previously reported studies of
Houk et al. on lactonization of hydroxy acids, that indicate that
the solvation effect more-or-less cancels out when comparing reactivities
of species having the same structural features (even though the absolute rate
constants cannot be evaluated) [13–15]. Thus, reaction rates were computed from the
activation energy results for both the acid-catalyzed and uncatalyzed
lactonization processes of hydroxy acids 1a–1d. The calculated rates are linearly related to the experimentally
determined rate values, the correlations which are shown in (1) (for the
acid-catalyzed process) and in (2) (for the un-catalyzed process). The AM1
calculations results of the activation energy values for the lactonization
processes of hydroxy acids 1a–1d
were correlated very well with the values obtained using the ab initio method at the DFT
B3LYP/6-31G (d,p) and RHF/6-31G, and the correlation results are depicted in (3)-(4), respectively:
(1)log(k1xk1a)calc=0.9911logkexp−0.1238,R=0.99,
where  k1x is the cyclization rate of hydroxy acid 1b-1d, and k1a is the cyclization rate of hydroxy acid 1a;
(2)log(k2xk2a)calc=0.9768logkexp−0.6725,R=0.99,
where k2x is the cyclization rate of protonated hydroxy acid 2b-2d, and k2a is the cyclization rate of protonated hydroxyl acid 2a;
(3)ΔΔG‡(HF)=0.9216ΔΔG‡(AM1)+13.68,R=0.99,
where    ΔΔG‡ (HF) and    ΔΔG‡ (AM1) are the
calculated activation energy values by RHF/6-31G and AM1 methods, respectively;
(4)ΔΔG‡(B3LYP)=1.1878ΔΔG‡(AM1)+0.9788,R=0.99,
where    ΔΔG‡  (B3LYP) is the
calculated activation energy values by B3LYP/6-31G (d,p).The calculated rate values of the
lactonization processes of 1a and 1c
using (2) are 104 and 1014, respectively. This gives a
predicted rate enhancement of about 1010 which is in good agreement
with the experimentally determined value (1011). Our calculations
also reveal that the rate-limiting step is formation rather than collapse of
the tetrahedral intermediate [16–19], in opposition to the conclusions reported by
Houk et al. [15].It
is accepted that strain-accelerated reactions occur for compounds that, by
necessity, are rigid with high bond-rotation barriers that exceed those
required for the reaction. Further, such compounds have distorted bond
distances or/and bond angles when compared to strain-free compounds [1]. Our theoretical
calculations indeed predict distortion of bond angles and bond distances in the
phenyl ring of 1c which is supported by the X-ray crystal structure of the
corresponding alcohol [30]. However, the same distortions with the
same magnitude are observed with 1b and
to some extent with the corresponding tetrahedral intermediates 3c and 3b. If the acceleration is due
to strain relief, we should see comparable rates for 1c and 1b,  but actually the lactonization rate
of 1c is 1010 times
faster than that of 1b. This
suggests no significant strain relief upon the lactonization of 1c.The
second convincing point excluding strain as the main driving force for the rate
acceleration is that in 1c the rotation
barrier around C2-C3 is found to be 3 kcal/ mol smaller than that of 1a.  This surprising conclusion arises from the
fact that 1c has a stronger intramolecular carboxyl/hydroxyl hydrogen-bonding
than does 1a.  If  Winans and Wilcox were
correct [13]  and the rate acceleration is indeed due to strain-relief, then the
C2-C3 bond in 1a should be more affordable to rotation than that of 1c.
In other words, if strain-accelerated reactions occur in compounds that are
rigid with high bond rotation barriers, then the rate comparison between 1a and
1c cannot be due to strain effects.For
a better understanding the lactonization process, we conducted reaction-coordinate
calculations for 1a and 1c (when the C1–O10 distance is in the range of2.5–1.5 Å) by calculating the change
in energy as a function of the  O10/C1/C2
attack angle (α) and the C1–C10
distance between the two reacting centers (r).
An excellent correlation was observed between the entalpic energy E and α/r the ratio between the attack angle and the distance. Further,
it was found that the slope (S)
follows the order  S(1a)>S(1d)>S(1c). This result suggests that the energy needed to increase the
value of angle α to reach the
optimal value for formation of the transition state is less in the case of 1c
when compared to 1a. This in turn indicates that the approach of the hydroxyl
group to the carbonyl carbon in the case of 1c is much easier than in the case of 1a.


## 4. Conclusions

The combined results
indicate that the driving force in the first and second stages of the approach
(C1–O10 =4–2.5 Å, and 2.5–1.5 Å), is due to a proximity effect.  Hydroxy acids that are rigid in the organized
state have lower activation energies (such as 1c) than those with less rigidity (such as 1a).  It is worthy to note
that Mengerhas advocated abandoning thermodynamic models involving
entropy in favor of distance effects on rate, and in fact he has derived an
equation relating rate and distance [31, 32].



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