Numerous novel catalysts and organic transformations are being developed nowadays,
but mechanistic studies on these organic reactions, which would certainly facilitate
a better understanding of the pathways and practical application of the reactions,
have been left behind. Although theoretical studies have proved to be powerful in
eliciting the mechanistic details of reactions,[1 ] experimental kinetic studies that provide details of the concentration dependence
of the reactants and catalysts and which give rate and equilibrium constants of the
reactions, thereby assisting in understanding the molecular-level behavior of the
reaction, are still essential and irreplaceable in mechanistic studies.[2 ]
Scheme 1 Chiral disulfonimide-catalyzed asymmetric cyanosilylation of 2-naphthaldehyde (2 )
The catalytic asymmetric addition of cyanide to carbonyl compounds to give enantioenriched
cyanohydrins is of great importance in organic synthesis, as chiral cyanohydrins are
versatile synthetic intermediates for many biologically important compounds, such
as α-hydroxy acids, α-amino acids and β-amino alcohols. A large variety of catalysts,
including enzymes,[3 ] metal-based Lewis acid catalysts,[4 ] organocatalysts,[5 ] and metal–organic frameworks,[6 ] have been developed in recent decades.[3 ]
[4 ]
[5 ]
[6 ]
[7 ] In 2016, List and co-workers reported efficient chiral disulfonimide organocatalysts
1a-H and 1b-H for the asymmetric cyanosilylation of aldehydes (Scheme [1 ]) at catalyst loadings down to 50 ppm (0.005 mol%) with yields of up to 98%, enantiomeric
ratios of up to 98:2, and reaction scales of up to 156 g.[8 ] Preliminary mechanistic investigations were conducted by in situ FTIR and NMR analysis,
revealing that the catalytically active species is actually a silylated disulfonimide
Lewis acid organocatalyst and that an interesting ‘dormant period’, induced mainly
by water, precedes the real catalytic cycle, as every free hydroxy group (in water
or the silanol) needs to be converted into the corresponding silyl ether before the
actual cyanosilylation starts. Although these studies provided a better understanding
of the precatalytic cycle, details of the actual catalytic cycle remain unknown.
Here, we report our detailed kinetic study on the cyanosilylation of 2-naphthaldehyde
(2 ) catalyzed by disulfonimide 1a-H , the results of which might contribute to an in-depth understanding of the reaction
mechanism and to future development of new catalysts and transformations.
Experimental kinetic studies were carried out by monitoring the progress of the reaction
by in situ FTIR [see Supporting Information (SI) for details]. To determine the reaction
orders of all components, several reactions were carried out under identical conditions
with various initial concentrations of reactants 2 and 3 and of catalyst 1a-H . From the results of the in situ FTIR measurements, time profiles for the concentration
of aldehyde [2 ] with various initial concentrations of TMSCN [3 ]0 were obtained, as shown in Figure [1a ]. Profiles of [2 ] vs time with various initial concentrations of aldehyde [2 ]0 and catalyst loadings [1a-H ]0 were also obtained (SI; Figures S13 and S16).
Figure 1 Evaluation of kinetic data by using the method of reaction progress kinetic analysis
(RPKA). (a) Concentration of 2 vs time profiles with various [3 ]0 ; (b) Rate vs [2 ] profiles with various [3 ]0 (y = rate, x = [2 ]); (c) Rate/[3 ]2 vs [2 ] profiles with various [3 ]0 (y = rate/[3 ]2 , x = [2 ]). Reaction conditions: 1a-H (0.01 mmol, 1.0 mol%), 20 °C, Et2 O (4.6 mL), initial concentration of aldehyde: [2 ]0 = 0.20 M, initial concentration of TMSCN: [3 ]0 = 0.24–0.56 M.
Reaction progress kinetic analysis (RPKA) is a method developed and formalized by
Blackmond and co-workers.[9 ] Compared with the classical kinetic approach (method of pseudo-zero-order), where
the concentration of one substrate is artificially fixed at a pseudo-constant high
value (usually tenfold), RPKA permits reactions to be carried out under synthetically
relevant conditions that are closer to standard reaction conditions and more reasonable.
A key point of RPKA is to determine the reaction orders by a trial-and-error procedure
by constructing graphical rate equations and attempting to find whether they overlay
by dividing the rate curves by the concentration of the substrate under study raised
to the power of the reaction order. We first evaluated our kinetic data by using the
RPKA method.
Profiles for the concentration of aldehyde [2 ] vs time (Figure [1a ]) for various initial concentrations of TMSCN [3 ]0 were converted into rate vs [2 ] profiles (Figure [1b ]) that clearly indicated a positive reaction order in [3 ], as the rate significantly increased upon increasing the concentration of 3 . The rate vs [2 ] profiles (Figure [1b ]) were then converted into rate/[3 ] vs [2 ] profiles (SI; Figure S8); however, no sign of an overlay between these graphical
rate equations was observed. When the rate vs [2 ] profiles (Figure [1b ]) were further converted into rate/[3 ]2 vs [2 ] profiles, as shown in Figure [1c ], the graphical rate equations became much closer to each other, especially in the
middle range of the reaction progress ([2 ] = 0.075–0.15 M). However, it was still difficult to judge whether these graphical
rate equations overlaid one another or not. Although RPKA has proven to be a powerful
method[2 ]
[9 ] for deducing reaction orders (mainly integer numbers such as 0 or 1) of the components
participating in the reaction and for determining whether there is catalyst activation
or deactivation and substrate or product inhibition or acceleration, it does not work
as well when the reaction mechanism is more complex and the rate equation is more
complicated (the orders can be nonintegers or even negative if the overall rate expression
for the reaction is written in power-law form). As mentioned by Blackmond,[9a ] in some reactions, ‘it may be found that none of the plots of graphical rate equations
result in all the curves falling on top of one another.’ In 2016, Burés developed
a very simple and practical graphical method that uses a normalized time scale to
determine the order in catalyst.[10a ] However, this method is limited to the order in the catalyst concentration, which
is not a thermodynamic driving force of the reaction. Besides this quantity, the orders
of the reactants also need to be determined in most kinetic studies. Later, Burés
expanded his method and formalized the highly useful Variable Time Normalization Analysis
(VTNA), which allows determining the order of any component of a reaction.[10b ]
[c ]
Seeking to make full use of the kinetic data obtained from the steady-state catalytic
cycles of the entire reaction and to deduce the reaction orders of all components
in a more efficient and convenient way, we developed a novel method for treating the
kinetic data. Taking the determination of the order of TMSCN [3 ] as an example, the detailed procedures of this method are illustrated below (see
SI for details).
Step 1. Obtain the rate vs [reactant A] profiles. Several reactions were carried out under identical conditions, varying only the initial
concentration of reactant B, the order of which is to be determined [TMSCN (3 ) in this case]. The profiles of rate vs aldehyde concentration (Figure [1b ]; rate vs [2 ]) were obtained from the [2 ] vs time profiles, which were deduced from the data sets from the in situ FTIR measurements.
Step 2. Fit the rate vs [reactant A] profiles and get the functions. An accurate function (such as a high-order polynomial function) was used to fit the
curves of each reaction in the rate vs [2 ] profiles (Figure [2a ]; blue lines).
Step 3. Obtain the data sets of (rate, [reactant B]). A series of concentrations of 2 (reactant A) with a fixed interval (in this case 0.01 M) and within a selected range
(in this case 0.08–0.16 M) were used to calculate the instant progress rates from
the fitting functions and the instant concentrations of 3 (reactant B) corresponding to each [2 ]. The obtained data sets of (rate, [3 ]) are shown as red squares in Figure [2a ].
Step 4. Obtain the order of [reactant B] through a double log –arithmetic plot and by linear regression of the rate vs [reactant B] for each [reactant
A]. A profile of the log(rate) vs log[3 ] was plotted for each [2 ] (Figure. 2b; [2 ] = 0.16 M). Linear regression of this profile gave a function whose slope corresponded
to the order of [3 ] at this concentration of 2 . Thus, data sets of {(order of [3 ]), [2 ]} were obtained.
Step 5. Plot the profile of (order of [reactant B]) vs [reactant A]. The profile of (order of [3 ]) vs [2 ] was plotted (Figure [2c ]), which not only gave an approximate value for (order of [3 ]) but also indicated changes in the reaction order as a function of changing substrate
concentrations.
This method might look complicated when described in steps, but all the fitting and
data-processing steps can be easily done by using standard office software, such as
Microsoft Excel and Origin (OriginLab Corp., Northampton, MA). The average value for the order of [3 ] was calculated to be 1.94 (nearly second order). Thus, the apparent rate order of
3 in the form of a power-law reaction rate equation was obtained. The approximately
second-order kinetics in TMSCN suggests that two molecules of this substrate are involved
in a step that has a significant influence on the rate.
Figure 2 Determination of the order of TMSCN [3 ] by using a novel method that makes use of the progress rates: (2a) Rate vs [2 ] profiles with various initial concentration of 3 (fitted with high-order polynomial functions, shown as blue lines) and the resulting
data sets of (rate, [3 ]) shown as red squares; (2b) Double logarithmic plot and linear regression of rate
vs [3 ] when [2 ] = 0.16 M (the deduced order of [3 ] corresponds to the slope, 1.8635); (2c) The profile of (order of [3 ]) vs [2 ] in the selected range of [2 ] (0.08–0.16 M). Reagents and conditions : 1a-H (0.01 mmol, 1.0 mol%), 20 °C, Et2 O (4.6 mL), initial concentration of aldehyde: [2 ]0 = 0.20 M, initial concentration of TMSCN: [3 ]0 = 0.24–0.56 M.
With the method described above, the average reaction order of aldehyde 2 was determined to be only 0.17, which is close to zero order. The average value for
the order of catalyst 1a-H was calculated to be 1.23 which is close to first order (see SI for details). Taking
the average reaction orders determined by our method, the power-law form of the rate
equation, which reflects the molecular-level behavior of the reaction as an empirical
approximation, can be stated as shown in Equation 1. The low reaction order in 2 suggests that the step involving its activation is significantly faster than the
addition of cyanide and that a catalyst species associated with aldehyde 2 is possibly involved in the rate-limiting step.
Rate = k ·[1a-H ]1.23 ·[2 ]0.17 ·[3 ]1.94 (Equation 1)
The temperature dependence of the reaction rates was studied in the range 273.15–303.15
K under otherwise identical conditions. The apparent activation energy of the reaction
was deduced to be 41 kJ·mol–1 (9.9 kcal·mol–1 ), according to the Arrhenius equation, by plotting ln(k ) vs 1/T (SI; Figures S20 and S21); this implies that the reaction is relatively sensitive
to temperature. The enthalpy of activation ΔH
‡ was deduced to be 39 kJ·mol–1 (9.3 kcal·mol–1 ) and the entropy of activation ΔS
‡ was deduced to be –81 J·mol–1 ·K–1 (–19 cal·mol–1 ·K–1 ) according to the Eyring equation by plotting ln(k /T ) vs 1/T . The Gibbs energy of activation ΔG
‡ was calculated to be 61 kJ·mol–1 (15 kcal·mol–1 ) at 273.15 K (SI; Figures S22–S24).
On the basis of these studies, we propose the catalytic cycle for the disulfonimide-catalyzed
asymmetric cyanosilylation of aldehydes shown in Scheme [2 ]. After a long period of dormancy[8 ] of up to several hours, the precatalytic cycle ends. The Brønsted acid precatalyst
1a-H then reacts with TMSCN to generate the catalytically active Lewis acid organocatalyst
1a-TMS as a mixture of O - and N -silylated species.[8 ] This interacts with the aldehyde 2 to generate activated species 5 . The low reaction order in 2 suggests possible saturation kinetics in [2 ], indicating that the formation of 5 is significantly faster than the reverse reaction or the addition of cyanide. Subsequently,
two molecules of TMSCN interact with 5 , possibly forming a new C–C bond through an aggregated cyclic transition state, as
shown in 6 , to produce species 7 with regeneration of one molecule of TMSCN, which is proposed to be the rate-determining
step. This is similar to the well-known Grignard reaction, which proceeds through
an aggregated six-membered-ring transition state bridged by a dimeric dication of
the Grignard reagent.[11 ] A study of the relationship between the enantiomeric excess of the product and the
enantiomeric excess of the catalyst revealed that there is no nonlinear effect[12 ] in this reaction (SI; Figure S27), which is consistent with the involvement of a
single catalyst molecule in the stereo-determining step. Finally, product 4 is quickly released from 7 and the active catalyst 1a-TMS is regenerated.
Scheme 2 Proposed catalytic cycle. Two molecules of TMSCN are possibly involved in the rate-determining
C–C bond-forming step.
In summary, a kinetic investigation of the disulfonimide-catalyzed cyanosilylation
of an aldehyde was conducted and the orders of the reactants and catalyst for a power-law
form of the rate equation were obtained. An aggregated cyclic transition state involving
two molecules of TMSCN was proposed. A novel and efficient method that makes use of
the progress rates to deduce the orders for both reactants and catalyst was developed
to treat kinetic data obtained from continuous monitoring of the progress of a reaction,
and this is expected to attract widespread attention. We predict that these studies
might not only facilitate an in-depth understanding of reaction mechanisms, but will
also benefit the future design and application of powerful organocatalysts (for example,
more-acidic chiral catalysts that could form aggregated cyclic transition states to
increase reactivity and also enhance enantioselectivity in reactions of other silylated
nucleophiles, such as silyl ketene acetals, enol silanes, TMSN3 or TMSCF3 ).[13 ]
