Quantum free energy landscapes from ab initio path integral metadynamics: Double proton transfer in the formic acid dimer is concerted but not correlated

Abstract

With the goal of computing quantum free energy landscapes of reactive (bio)chemical systems in multi-dimensional space, we combine the metadynamics technique for sampling potential energy surfaces with the ab initio path integral approach to treating nuclear quantum motion. This unified method is applied to the double proton transfer process in the formic acid dimer (FAD), in order to study the nuclear quantum effects at finite temperatures without imposing a one-dimensional reaction coordinate or reducing the dimensionality. Importantly, the ab initio path integral metadynamics technique allows one to treat the hydrogen bonds and concomitant proton transfers in FAD strictly independently and thus provides direct access to the much discussed issue of whether the double proton transfer proceeds via a stepwise or concerted mechanism. The quantum free energy landscape we compute for this H-bonded molecular complex reveals that the two protons move in a concerted fashion from initial to product state, yet world-line analysis of the quantum correlations demonstrates that the protons are as quantum-uncorrelated at the transition state as they are when close to the equilibrium structure.

Free‐Energy Landscape and Proton Transfer Pathways in Oxidative Deamination by Methylamine Dehydrogenase

“…[89]) and is found in single, [90] multiple [56] as well as excited-state [91] proton transfer processes in the gas phase buta lso in condensed phases.I nt he case of MADH,t he averagec arbon-oxygen distance decreases from 3.38 AE .011 in the reactantw ell to 2.65 AE 0.06 at the TS if the protoni st ransferred to OD1 and from 3.05 AE 0.07 to 2.65 AE 0.06 in case of transfer to OD2. Such contraction of the donor-acceptor distance upon protont ransfer along hydrogen bonds, being directly linked to al oweringo f the (free) energy barrier to transfer,i sw ell known as ag eneral phenomenon (see, for example, Section 2.2 in Ref.…”

“…[55]) or an activation free energy of 14.4 kcal mol À1 (quoted from the abstract of Ref. [56]). However,t he purpose of this study is not to produce aq uantitative description of the barrier in the first place, or even to most accurately reproduce experimental data, but to analyze the two possible transfer pathways relative to each other using am ore general sampling approach than before.…”

“…[56] This technique, which combines the path integral formalism to quantizet he nuclear degrees of freedom with acceleratedm etadynamics sampling, has the capability,i fi ntegrated with QM/MM interactions, to produce complementary insights into hydrogen tunneling in enzymatic reactions. [56] This technique, which combines the path integral formalism to quantizet he nuclear degrees of freedom with acceleratedm etadynamics sampling, has the capability,i fi ntegrated with QM/MM interactions, to produce complementary insights into hydrogen tunneling in enzymatic reactions.…”

“…In MADH, one oxygen atom acceptsahydrogen bond from the backbone NH group of TRP,w hereas the other oxygen atom interacts with Thr122b via as trong hydrogen bond. [56] Computer simulation of hydrogen transfer mechanisms with tunneling can offer detailed, atomic insight into such processes, but incorporating nuclear quantum effects into the simulation of biological systems is challenging due to the complex natureo ft he environment in combination with the inherently multidimensionaln atureo ft unneling. Initially,b ased on its positioni na vailable crystal structures,O D2 had been suggested to act as the proton acceptor, but later,s everalc omputer simulations [16,47,48,54,55] provided substantial evidence that the more distant OD1 atom could also be av iable protona cceptor.T hese computational studies increasingly suggest,m oreover, that the huge kinetic differences between MADH and AADH are related to mechanistic differences concerning the immediate proton acceptor.…”

“…[48,55] Moreover,f or AADH, the simulation study by Masgrau et al [47] indeed found proton transfer to the more distant oxygen atom, O2 (corresponding to OD1 in MADH), to be the dominant channel in the AADH-TA system,i nc ontrastt ow hat as imple crystal structure analysis would suggest.L ast but not least,w ith respectt oc omputed tunneling corrections to thermalr eaction rates and thus to computed KIEs, it is known that these depend exquisitely on the particular reactionp athway.F or all these reasons it is mandatoryt oc larify first the issue of the acceptors ite for proton transfer within MADH including hydrogen bonding upon movingf rom the reactantt ot he product complex before being able, in subsequent steps, to address the intricate issue of proton tunneling atroom temperature in fluctuating protein environments using, for instance, accelerated ab initio path integrals ampling techniques to map the multidimensionalquantum free-energy landscapes. [56] Computer simulation of hydrogen transfer mechanisms with tunneling can offer detailed, atomic insight into such processes, but incorporating nuclear quantum effects into the simulation of biological systems is challenging due to the complex natureo ft he environment in combination with the inherently multidimensionaln atureo ft unneling. [53] Severalg roups have used computational methods to model the key proton transfer step in the reaction of MA with MADH.…”