Modelling Complex Bimolecular Reactions in a Condensed Phase: The Case of Phosphodiester Hydrolysis

Abstract

(1) Background: the theoretical modelling of reactions occurring in liquid phase is a research line of primary importance both in theoretical–computational chemistry and in the context of organic and biological chemistry. Here we present the modelling of the kinetics of the hydroxide-promoted hydrolysis of phosphoric diesters. (2) Method: the theoretical–computational procedure involves a hybrid quantum/classical approach based on the perturbed matrix method (PMM) in conjunction with molecular mechanics. (3) Results: the presented study reproduces the experimental data both in the rate constants and in the mechanistic aspects (C–O bond vs. O–P bond reactivity). The study suggests that the basic hydrolysis of phosphodiesters occurs through a concerted ANDN mechanism, with no formation of penta-coordinated species as reaction intermediates. (4) Conclusions: the presented approach, despite the approximations, is potentially applicable to a large number of bimolecular transformations in solution and therefore leads the way to a fast and general method to predict the rate constants and reactivities/selectivities in complex environments.

A Theoretical‐Computational Study of Phosphodiester Bond Cleavage Kinetics as a Function of the Temperature

“…For the same reasons, such a substrate was chosen by Wolfenden et al [22] to evaluate the rate constants of the uncatalyzed PÀ O cleavage reaction at high temperatures, i. e. where the reaction occurs on an accessible time scale. In a previous work, [21] we used a general statistical-mechanical approach based on a mixed quantum-classical method, the Perturbed Matrix Method (PMM), [26,27] to reconstruct the kinetics of HO -(the hydroxide ion) and Np 2 P À association and subsequent phosphodiester bond cleavage reaction at 300 K, obtaining results in very good agreement with the data of Wolfenden et al [22] extrapolated at that temperature from the experimental rate constants obtained at higher temperatures. Here, we extend our previously developed approach to model the reaction temperature dependence, describing in more details the physical-mathematical derivations, and briefly discuss its relation with the well established Eyring model corresponding to a special case of the presented general model.…”

“…Additionally, we can reasonably infer that the reaction events must occur through a specific and unique transition state (TS) whose mean traversing time is too short for any internal relaxation to occur, and thus no inversion of the TS traversing velocity can be present. Therefore, the corresponding reaction scheme is [21]…”

“…This coordinate uniquely defines the chemical states of the reference reactive centre (assuming a single reactive centre at infinite dilution) as R, TS, and P. In other words, it accurately describes the progression of the reaction process, as depicted in Figure 2. By defining with δ the narrow range of the reaction coordinate corresponding to the transition state (i. e., [x TS À d=2; x TS þ d=2�) and denoting with ξ m the minimum value of ξ corresponding to the minimum of the R chemical state range, we can express the partition functions Q R and Q TS in terms of the Landau free energy A, which is defined as follows: [21,28,29] A…”

“…[4,5] These observations inspired many research groups both in the development of synthetic catalysts able to cleave phosphodiester bonds [6][7][8][9][10][11][12][13][14] and in the theoretical modeling of key aspects affecting the kinetics of the cleavage. [15][16][17][18][19][20][21] For example, deciphering the mechanism of phosphate diester hydrolysis in solution in different conditions (e. g. temperature, pH, etc.) is crucial for a complete understanding the catalytic mechanisms of diesterases.…”

“…This substrate was chosen because can only react through the cleavage of the phosphorous -oxygen bond, instead of the carbon -oxygen bond as many other phosphoric diesters. [21,22] This is due to the steric hindrance provided by the t-butyl groups that favor the attack of the upcoming nucleophile to the phosphorous atom (see Figure 1).…”