Theoretical Analysis of Kinetic Isotope Effects on Proton Transfer Reactions between Substituted α-Methoxystyrenes and Substituted Acetic Acids

Abstract

Primary kinetic isotope effects (KIEs) on a series of carboxylic acid-catalyzed protonation reactions of aryl-substituted α-methoxystyrenes (X-1) to form oxocarbenium ions have been computed using the Kleinert variational second-order perturbation theory (KP2) in the framework of Feynman path integrals (PI) along with the potential energy surface obtained at the B3LYP/6-31+G(d,p) level. Good agreement with the experimental data was obtained, demonstrating that this novel computational approach for computing KIEs of organic reactions is a viable alternative to the traditional method employing Bigeleisen equation and harmonic vibrational frequencies. Although tunneling makes relative small contributions to the lowering of the free energy barriers for the carboxylic acid catalyzed protonation reaction, it is necessary to include tunneling contributions to obtain quantitative estimates of the KIEs. Consideration of anharmonicity can further improve the calculated KIEs for the protonation of substituted α-methoxystyrenes by chloroacetic acid, but for the reactions of the parent and 4-NO2 substituted α-methoxystyrene with substituted carboxylic acids, the correction of anharmonicity overestimates the computed KIEs for strong acid catalysts. In agreement with experimental findings, the largest KIEs are found in nearly ergoneutral reactions, ΔGo ≈ 0, where the transition structures are nearly symmetric and the reaction barriers are relatively low. Furthermore, the optimized transition structures are strongly dependent on the free energy for the formation of the carbocation intermediate, i.e., the driving force ΔGo, along with a good correlation of Hammond shift in the transition state structure.

Developing a Systematic Approach for Ab Initio Path-Integral Simulations

“…We have thus derived the analytical closed forms of Eq. (41) up to P20 Wong 2008;Wong and Gao 2008;Wong, Richard et al 2009;Wong, Gu et al 2012). Consequently, the W as a function of an arbitrary Ω can be promptly obtained.…”

“…This complexity is a major factor limiting applications of the KP theory beyond KP1, the original FK approach. Wong 2008;Wong and Gao 2008;Wong, Richard et al 2009;Wong, Gu et al 2012). Hence the multidimensional V effectively reduces to 3N one-dimensional potentials along each normal mode coordinate.…”

“…(39)] iteratively for different trial values of Ω by Monte Carlo multi-dimensional numerical integrations. In fact, after the interpolating potential along each instantaneous normal-mode coordinate is determined, there is little computational cost for obtaining the W. Thereby, high level ab initio or densityfunctional (DFT) methods can be used to evaluate the potential energy function for ab initio path-integral calculations (Wong, Richard et al 2009;Wong, Gu et al 2012). …”

“…Furthermore, in contrast to Car-Parrinello MD (CPMD) which is limited to potential energy derived from DFT (Car and Parrinello 1985), our method is independent of how the potential energy functions being constructed. Therefore, by combining it with our novel automated integration-free path-integral (AIF-PI) method together (See Section 5; Wong and Gao 2008;Wong, Richard et al 2009;Wong, Gu et al 2012), we will also be able to compute free-energy barriers, changes of binding energy, pK a values, and isotope effects at an ab initio path integral level (see Section 6).…”

“…theoretical method that combines our novel systematic free-energy expansion approach, based on Zwanzig's free-energy perturbation theory, with our recently developed automated integration-free path-integral method, based on Kleinert's variational perturbation theory, Wong and Gao 2008;Wong, Richard et al 2009;Wong, Gu et al 2012) to perform ab initio path-integral simulations for realistic macromolecules at an affordable computational cost. Since in this new method, we can progressively choose computationally affordable levels of theory, now important physical quantities, e.g., free-energy barrier, change of binding energy, pK a value, and isotope effect, can all be computed at an ab initio path-integral level.…”