Estimating pKa values for pentaoxyphosphoranes

Variations in proton transfer pathways and energetics on pristine and defect-rich quartz surfaces in water: Insights into the bimodal acidities of quartz

HYPOTHESIS

Understanding the mechanisms of proton transfer on quartz surfaces in water is critical for a range of processes in geochemical, environmental, and materials sciences. The wide range of surface acidities (>9 pKa units) found on the ubiquitous mineral quartz is caused by the structural variations of surface silanol groups. Molecular scale simulations provide essential tools for elucidating the origin of site-specific surface acidities.

SIMULATIONS

We used density-functional tight-binding-based molecular dynamics combined with rare-event metadynamics simulations to probe the mechanisms of deprotonation reactions from ten representative surface silanol groups found on both pristine and defect-rich quartz (101) surfaces with Si vacancies.

FINDINGS

The results show that deprotonation is a highly dynamic process where both the surface hydroxyls and bridging oxygen atoms serve as the proton acceptors, in addition to water. Deprotonation of embedded silanols through intrasurface proton transfer exhibited lower pKa values with less H-bond participation and higher energy barriers, suggesting a new mechanism to explain the bimodal acidity observed on quartz surface. Defect sites, recently shown to comprise a significant portion of the quartz (101) surface, diversify the coordination and local H-bonding environments of the surface silanols, changing both the deprotonation pathways and energetics, leading to a wider range of pKa values (2.4 to 11.5) than that observed on pristine quartz surface (10.4 and 12.1).

Probing the self-ionization of liquid water with ab initio deep potential molecular dynamics

The chemical equilibrium between self-ionized and molecular water dictates the acid-base chemistry in aqueous solutions, yet understanding the microscopic mechanisms of water self-ionization remains experimentally and computationally challenging. Herein, Density Functional Theory (DFT)-based deep neural network (DNN) potentials are combined with enhanced sampling techniques and a global acid-base collective variable to perform extensive atomistic simulations of water self-ionization for model systems of increasing size. The explicit inclusion of long-range electrostatic interactions in the DNN potential is found to be crucial to accurately reproduce the DFT free energy profile of solvated water ion pairs in small (64 and 128 H2O) cells. The reversible work to separate the hydroxide and hydronium to a distance [Formula: see text] is found to converge for simulation cells containing more than 500 H2O, and a distance of [Formula: see text] 8 Å is the threshold beyond which the work to further separate the two ions becomes approximately zero. The slow convergence of the potential of mean force with system size is related to a restructuring of water and an increase of the local order around the water ions. Calculation of the dissociation equilibrium constant illustrates the key role of long-range electrostatics and entropic effects in the water autoionization process.

Protonation of Strained Epoxy Resin under Wet Conditions via First-Principles Calculations Using the H+-Shift Method

A significant challenge in adhesive bonding is the accelerated breaking of stretched adhesives under wet conditions, which is known as cohesive failure. One group of commonly used adhesives consists of the amine-cured epoxy resins. Based on deprotonation free-energy calculations of the unstrained resin in water, it has recently been proposed that these adhesives can undergo failure through breakage originating at the protonated amine group under neutral or acidic conditions [J. Phys. Chem. B 2021, 125, 8989-8996]. In this study, we comprehensively investigated the degree of protonation of the amine group under both stretched and compressed conditions by devising a robust first-principles protonation calculation method applicable to strained materials. It was found that the amine group was partially protonated in neutral water at 298 K and that the amine group was protonated when the epoxy resin was stretched to a greater extent in water, and vice versa. These findings support the physicochemical cause of cohesive failure due to protonation of the amine group in the stretched amine-cured epoxy resins.

Modeling the Solvation and Acidity of Carboxylic Acids Using an Ab Initio Deep Neural Network Potential

Formic and acetic acid constitute the simplest of carboxylic acids, yet they exhibit fascinating chemistry in the condensed phase such as proton transfer and dimerization. The go-to method of choice for modeling these rare events have been accurate but expensive ab initio molecular dynamics simulations. In this study, we present a deep neural network potential trained using accurate ab initio data that can be used in tandem with enhanced-sampling methods to perform an efficient exploration of the free-energy surface of aqueous solutions of weak carboxylic acids. In particular, we show that our model captures proton dissociation and provides a good estimate of the pK_a, as well as the dimerization of formic and acetic acid. This provides a suitable starting point for applications in different research areas where computational efficiency coupled with the accuracy of ab initio methods is required.

Structural modifications as tools in mechanistic studies of the cleavage of RNA phosphodiester linkages

The cleavage of RNA phosphodiester bonds by RNase A and hammerhead ribozyme at neutral pH fundamentally differs from the spontaneous reactions of these bonds under the same conditions. While the predominant spontaneous reaction is isomerization of the 3',5'-phosphodiester linkages to their 2',5'-counterparts, this reaction has never been reported to compete with the enzymatic cleavage reaction, not even as a minor side reaction. Comparative kinetic measurements with structurally modified di-nucleoside monophosphates and oligomeric phosphodiesters have played an important role in clarification of mechanistic details of the buffer-independent and buffer-catalyzed reactions. More recently, heavy atom isotope effects and theoretical calculations have refined the picture. The primary aim of all these studies has been to form a solid basis for mechanistic analyses of the action of more complicated catalytic machineries. In other words, to contribute to conception of a plausible unified picture of RNA cleavage by biocatalysts, such as RNAse A, hammerhead ribozyme and DNAzymes. In addition, structurally modified trinucleoside monophosphates as transition state models for Group I and II introns have clarified some features of the action of large ribozymes.

Molecular Mechanism of Autodissociation in Liquid Water: Ab Initio Molecular Dynamics Simulations

Autodissociation in liquid water is one of the most important processes in various topics of physical chemistry, such as acid-base chemistry. Molecular simulations have elucidated most of the molecular mechanisms at the atomic level, yet quantitative analysis to compare with experiments using the potential of mean force (PMF) remains a hurdle, including the definition of reaction coordinates and the accuracy of liquid structures by ab initio molecular dynamics (AIMD) simulations with density functional theory (DFT) methods. Here, we perform AIMD simulations with the revPBE-D3 exchange-correlation functional to compute the PMF profiles of autoionization, or proton transfer (PT), in liquid water. For the quantitative analysis with physically meaningful reaction coordinates, we employ a PT coordinate, donor-acceptor (OH^--H₃O⁺) distance, and hydrogen (H)-bond number. The one-dimensional (1D) PMF profile along the PT coordinate shows no local minimum in the product state of PT (OH^- and H₃O⁺), which is necessary to accurately compute the acid dissociation constant (or pK_a). On the other hand, the 2D PMF profiles along the PT coordinate and donor-acceptor distance show local minima in the product state and reaction barriers, and the computed pK_w is comparable to the experiment. In addition, the 2D PMF profiles along the PT coordinate and the H-bond number reveal the molecular mechanism of the H-bond rearrangement concomitant with PT, in which the H-bond breaking before PT is slightly preferable. These findings indicate that an accurate evaluation of pK_a by MD simulations requires the donor-acceptor distance in addition to the conventional PT coordinate.

Investigation of the pKa of the Nucleophilic O2' of the Hairpin Ribozyme

Small ribozymes cleave their RNA phosphodiester backbone by catalyzing a transphosphorylation reaction wherein a specific O2' functions as the nucleophile. While deprotonation of this alcohol through its acidification would increase its nucleophilicity, little is known about the pK_a of this O2' in small ribozymes, in part because high pK_a's are not readily accessible experimentally. Herein, we turn to molecular dynamics to calculate the pK_a of the nucleophilic O2' in the hairpin ribozyme and to study interactions within the active site that may impact its value. We estimate the pK_a of the nucleophilic O2' in the wild-type hairpin ribozyme to be 18.5 ± 0.8, which is higher than the reference compound, and identify a correlation between proper positioning of the O2' for nucleophilic attack and elevation of its pK_a. We find that monovalent ions may play a role in depression of the O2' pK_a, while the exocyclic amine appears to be important for organizing the ribozyme active site. Overall, this study suggests that the pK_a of the O2' is raised in the ground state and lowers during the course of the reaction owing to positioning and metal ion interactions.

Stereoelectronic power of oxygen in control of chemical reactivity: the anomeric effect is not alone

Although carbon is the central element of organic chemistry, oxygen is the central element of stereoelectronic control in organic chemistry. Generally, a molecule with a C-O bond has both a strong donor (a lone pair) and a strong acceptor (e.g., a σ*_C-O orbital), a combination that provides opportunities to influence chemical transformations at both ends of the electron demand spectrum. Oxygen is a stereoelectronic chameleon that adapts to the varying situations in radical, cationic, anionic, and metal-mediated transformations. Arguably, the most historically important stereoelectronic effect is the anomeric effect (AE), i.e., the axial preference of acceptor groups at the anomeric position of sugars. Although AE is generally attributed to hyperconjugative interactions of σ-acceptors with a lone pair at oxygen (negative hyperconjugation), recent literature reports suggested alternative explanations. In this context, it is timely to evaluate the fundamental connections between the AE and a broad variety of O-functional groups. Such connections illustrate the general role of hyperconjugation with oxygen lone pairs in reactivity. Lessons from the AE can be used as the conceptual framework for organizing disjointed observations into a logical body of knowledge. In contrast, neglect of hyperconjugation can be deeply misleading as it removes the stereoelectronic cornerstone on which, as we show in this review, the chemistry of organic oxygen functionalities is largely based. As negative hyperconjugation releases the "underutilized" stereoelectronic power of unshared electrons (the lone pairs) for the stabilization of a developing positive charge, the role of orbital interactions increases when the electronic demand is high and molecules distort from their equilibrium geometries. From this perspective, hyperconjugative anomeric interactions play a unique role in guiding reaction design. In this manuscript, we discuss the reactivity of organic O-functionalities, outline variations in the possible hyperconjugative patterns, and showcase the vast implications of AE for the structure and reactivity. On our journey through a variety of O-containing organic functional groups, from textbook to exotic, we will illustrate how this knowledge can predict chemical reactivity and unlock new useful synthetic transformations.

Nuclear quantum effects on autoionization of water isotopologs studied by ab initio path integral molecular dynamics

In this study, we investigate the nuclear quantum effects (NQEs) on the acidity constant (pK_A) of liquid water isotopologs under the ambient condition by path integral molecular dynamics (PIMD) simulations. We compared simulations using a fully explicit solvent model with a classical polarizable force field, density functional tight binding, and ab initio density functional theory, which correspond to empirical, semiempirical, and ab initio PIMD simulations, respectively. The centroid variable with respect to the proton coordination number of a water molecule was restrained to compute the gradient of the free energy, which measures the reversible work of the proton abstraction for the quantum mechanical system. The free energy curve obtained by thermodynamic integration was used to compute the pK_A value based on probabilistic determination. This technique not only reproduces the pK_A value of liquid D₂O experimentally measured (14.86) but also allows for a theoretical prediction of the pK_A values of liquid T₂O and aqueous HDO and HTO, which are unknown due to their scarcity. It is also shown that the NQEs on the free energy curve can result in a downshift of 4.5 ± 0.9 pK_A units in the case of liquid water, which indicates that the NQEs plays an indispensable role in the absolute determination of pK_A. The results of this study can help inform further extensions into the calculation of the acidity constants of isotope substituted species with high accuracy.

Aqueous pKa prediction for tautomerizable compounds using equilibrium bond lengths

The accurate prediction of aqueous pK_a values for tautomerizable compounds is a formidable task, even for the most established in silico tools. Empirical approaches often fall short due to a lack of pre-existing knowledge of dominant tautomeric forms. In a rigorous first-principles approach, calculations for low-energy tautomers must be performed in protonated and deprotonated forms, often both in gas and solvent phases, thus representing a significant computational task. Here we report an alternative approach, predicting pK_a values for herbicide/therapeutic derivatives of 1,3-cyclohexanedione and 1,3-cyclopentanedione to within just 0.24 units. A model, using a single ab initio bond length from one protonation state, is as accurate as other more complex regression approaches using more input features, and outperforms the program Marvin. Our approach can be used for other tautomerizable species, to predict trends across congeneric series and to correct experimental pK_a values.

First-Principles Calculation of Water pKa Using the Newly Developed SCAN Functional

Acid/base chemistry is an intriguing topic that still constitutes a challenge for computational chemistry. While estimating the acid dissociation constant (or pK_a) could shed light on many chemistry processes, especially in the fields of biochemistry and geochemistry, evaluating the relative stability between protonated and nonprotonated species is often very difficult. Indeed, a prerequisite for calculating the pK_a of any molecule is an accurate description of the energetics of water dissociation. Here, we applied constrained molecular dynamics simulations, a noncanonical sampling technique, to investigate the water deprotonation process by selecting the OH distance as the reaction coordinate. The calculation is based on density functional theory and the newly developed SCAN functional, which has shown excellent performance in describing water structure. This first benchmark of SCAN on a chemical reaction shows that this functional accurately models the energetics of proton transfer reactions in an aqueous environment. After taking Coulomb long-range corrections and nuclear quantum effects into account, the estimated water pK_a is only 1.0 pK_a unit different from the target experimental value. Our results show that the combination of SCAN and constrained MD successfully reproduces the chemistry of water and constitutes a good framework for calculating the free energy of chemical reactions of interest.

Determination of pKa Values via ab initio Molecular Dynamics and its Application to Transition Metal-Based Water Oxidation Catalysts

The p K a values are important for the in-depth elucidation of catalytic processes, the computational determination of which has been challenging. The first simulation protocols employing ab initio molecular dynamics simulations to calculate p K a values appeared almost two decades ago. Since then several slightly different methods have been proposed. We compare the performance of various evaluation methods in order to determine the most reliable protocol when it comes to simulate p K a values of transition metal-based complexes, such as the here investigated Ru-based water oxidation catalysts. The latter are of high interest for sustainable solar-light driven water splitting, and understanding of the underlying reaction mechanism is crucial for their further development.

Microscopic description of acid-base equilibrium

Acid-base reactions are ubiquitous in nature. Understanding their mechanisms is crucial in many fields, from biochemistry to industrial catalysis. Unfortunately, experiments give only limited information without much insight into the molecular behavior. Atomistic simulations could complement experiments and shed precious light on microscopic mechanisms. The large free-energy barriers connected to proton dissociation, however, make the use of enhanced sampling methods mandatory. Here we perform an ab initio molecular dynamics (MD) simulation and enhance sampling with the help of metadynamics. This has been made possible by the introduction of descriptors or collective variables (CVs) that are based on a conceptually different outlook on acid-base equilibria. We test successfully our approach on three different aqueous solutions of acetic acid, ammonia, and bicarbonate. These are representative of acid, basic, and amphoteric behavior.

Copper(ii)-mediated base pairing involving the artificial nucleobase 3H-imidazo[4,5-f]quinolin-5-ol

A highly stabilizing Cu(ii)-mediated base pair is introduced into DNA using a large artificial nucleobase.

Phosphodiester models for cleavage of nucleic acids

Nucleic acids that store and transfer biological information are polymeric diesters of phosphoric acid. Cleavage of the phosphodiester linkages by protein enzymes, nucleases, is one of the underlying biological processes. The remarkable catalytic efficiency of nucleases, together with the ability of ribonucleic acids to serve sometimes as nucleases, has made the cleavage of phosphodiesters a subject of intensive mechanistic studies. In addition to studies of nucleases by pH-rate dependency, X-ray crystallography, amino acid/nucleotide substitution and computational approaches, experimental and theoretical studies with small molecular model compounds still play a role. With small molecules, the importance of various elementary processes, such as proton transfer and metal ion binding, for stabilization of transition states may be elucidated and systematic variation of the basicity of the entering or departing nucleophile enables determination of the position of the transition state on the reaction coordinate. Such data is important on analyzing enzyme mechanisms based on synergistic participation of several catalytic entities. Many nucleases are metalloenzymes and small molecular models offer an excellent tool to construct models for their catalytic centers. The present review tends to be an up to date summary of what has been achieved by mechanistic studies with small molecular phosphodiesters.

Molecular electrostatic potential on the proton-donating atom as a theoretical descriptor of excited state acidity

Organic photoacids with enhanced acidities in the excited states have received much attention both experimentally and theoretically because of their applications in nanotechnology and chemistry. In this study, we investigate the excited-state acidities of 14 hydroxyl-substituted aromatic photoacids, with a focus on using theoretical molecular electrostatic potential (MEP) as an effective descriptor for photoacidity. For these model photoacids, we applied time-dependent density functional theory (TDDFT) at the ωB97X-D/6-31G(d) level to calculate the molecular electrostatic potentials of S₁ excited states and show that the molecular electrostatic potential on the proton-donating atom exhibits a linear relationship with the observed excited-state logarithmic acid dissociation constant (pK_a*). As a result, the molecular electrostatic potential on the proton-donating atom can be used to estimate the pK_a* values based on simple TDDFT calculations for a broad range of hydroxyl-substituted aromatic compounds. Furthermore, we explore the molecular electrostatic potential as a quantum descriptor for the photoacidities of cationic photoacids, and show a universal behavior of the pK_a*-MEP dependence. We also investigate the solvent effects on the photoacidity using TDDFT calculations with implicit solvent models. Finally, we discuss the physical insights implicated by the molecular electrostatic potential as a successful measure for photoacidity on the mechanism of proton transfer in the molecular excited states. This pK_a* descriptor provides an effective means to quantify the tendency of excited-state proton transfer with a relatively small computational cost, which is expected to be useful in the design of functional photoacids.

Origin of Acid-Base Catalytic Effects on Formaldehyde Hydration

The mechanisms of hydronium- and hydroxide-catalyzed formaldehyde hydrations were investigated by quantum mechanical/molecular mechanical molecular dynamics in combination with flexible coordinates. A stepwise bimolecular and a concerted termolecular mechanism were found with a hydronium catalyst. The latter is more favorable and better consistent with experiment. Structurally, a dipole-bound species initially arranges the nucleophile in a favorable configuration for both routes, significantly enhancing the reactive collisions. On the one hand, the hydronium catalyst also plays a role of a reactant in the bimolecular path. On the other hand, only a stepwise mechanism was found with a hydroxide catalyst. Overall, hydroxide is a stronger catalyst than a hydronium when it is in contact distance with formaldehyde.

'Dynamic Distance' Reaction Coordinate for Competing Bonds: Applications in Classical and Ab Initio Simulations

A versatile reaction coordinate, the "dynamic distance", is introduced for the study of reactions involving the rupture and formation of a series of chemical bonds or contacts. The dynamic distance is a mass-weighted mean of selected distances. When implemented as a generalized constraint, the dynamic distance is particularly suited for driving activated processes by controlled increase during a simulation. As a single constraint acting upon multiple degrees of freedom, the sequence of events along the resulting reaction pathway is determined unambiguously by the underlying energy landscape. Free energy profiles can be readily obtained from the mean constraint force. In this paper both theoretical aspects and numerical implementation are discussed, and the unique and diverse properties of this reaction coordinate are demonstrated using three examples:  In the framework of Car-Parrinello molecular dynamics, we present results for the prototypical double proton-transfer reaction in formic acid dimer and the photocycle of the guanine-cytosine DNA base pair. As a classical mechanical example, the opening of the binding pocket of the enzyme rubisco is analyzed.

Fundamentals of phosphate transfer

Historically, the chemistry of phosphate transfer-a class of reactions fundamental to the chemistry of Life-has been discussed almost exclusively in terms of the nucleophile and the leaving group. Reactivity always depends significantly on both factors; but recent results for reactions of phosphate triesters have shown that it can also depend strongly on the nature of the nonleaving or "spectator" groups. The extreme stabilities of fully ionised mono- and dialkyl phosphate esters can be seen as extensions of the same effect, with one or two triester OR groups replaced by O(-). Our chosen lead reaction is hydrolysis-phosphate transfer to water: because water is the medium in which biological chemistry takes place; because the half-life of a system in water is an accepted basic index of stability; and because the typical mechanisms of hydrolysis, with solvent H2O providing specific molecules to act as nucleophiles and as general acids or bases, are models for reactions involving better nucleophiles and stronger general species catalysts. Not least those available in enzyme active sites. Alkyl monoester dianions compete with alkyl diester monoanions for the slowest estimated rates of spontaneous hydrolysis. High stability at physiological pH is a vital factor in the biological roles of organic phosphates, but a significant limitation for experimental investigations. Almost all kinetic measurements of phosphate transfer reactions involving mono- and diesters have been followed by UV-visible spectroscopy using activated systems, conveniently compounds with good leaving groups. (A "good leaving group" OR* is electron-withdrawing, and can be displaced to generate an anion R*O(-) in water near pH 7.) Reactivities at normal temperatures of P-O-alkyl derivatives-better models for typical biological substrates-have typically had to be estimated: by extended extrapolation from linear free energy relationships, or from rate measurements at high temperatures. Calculation is free from these limitations, able to handle very slow reactions as readily as very fast ones, and capable of predicting rate constants with levels of accuracy acceptable to the experimentalist. We present an updated overview of phosphate transfer, with particular reference to the mechanisms of the reactions of alkyl derivatives and triesters. The intention is to present a holistic (not comprehensive!) overview of the reactivity of typical phosphate esters, in terms familiar to the working chemist, at a level sufficient to support informed predictions of reactivity for structures of interest.

Role of the active site guanine in the glmS ribozyme self-cleavage mechanism: quantum mechanical/molecular mechanical free energy simulations

The glmS ribozyme catalyzes a self-cleavage reaction at the phosphodiester bond between residues A-1 and G1. This reaction is thought to occur by an acid-base mechanism involving the glucosamine-6-phosphate cofactor and G40 residue. Herein quantum mechanical/molecular mechanical free energy simulations and pKa calculations, as well as experimental measurements of the rate constant for self-cleavage, are utilized to elucidate the mechanism, particularly the role of G40. Our calculations suggest that an external base deprotonates either G40(N1) or possibly A-1(O2'), which would be followed by proton transfer from G40(N1) to A-1(O2'). After this initial deprotonation, A-1(O2') starts attacking the phosphate as a hydroxyl group, which is hydrogen-bonded to deprotonated G40, concurrent with G40(N1) moving closer to the hydroxyl group and directing the in-line attack. Proton transfer from A-1(O2') to G40 is concomitant with attack of the scissile phosphate, followed by the remainder of the cleavage reaction. A mechanism in which an external base does not participate, but rather the proton transfers from A-1(O2') to a nonbridging oxygen during nucleophilic attack, was also considered but deemed to be less likely due to its higher effective free energy barrier. The calculated rate constant for the favored mechanism is in agreement with the experimental rate constant measured at biological Mg(2+) ion concentration. According to these calculations, catalysis is optimal when G40 has an elevated pKa rather than a pKa shifted toward neutrality, although a balance among the pKa's of A-1, G40, and the nonbridging oxygen is essential. These results have general implications, as the hammerhead, hairpin, and twister ribozymes have guanines at a similar position as G40.

The role of an active site Mg(2+) in HDV ribozyme self-cleavage: insights from QM/MM calculations

The hepatitis delta virus (HDV) ribozyme is a catalytic RNA motif embedded in the human pathogenic HDV RNA. It catalyzes self-cleavage of its sugar-phosphate backbone with direct participation of the active site cytosine C75. Biochemical and structural data support a general acid role of C75. Here, we used hybrid quantum mechanical/molecular mechanical (QM/MM) calculations to probe the reaction mechanism and changes in Gibbs energy along the ribozyme's reaction pathway with an N3-protonated C75H(+) in the active site, which acts as the general acid, and a partially hydrated Mg(2+) ion with one deprotonated, inner-shell coordinated water molecule that acts as the general base. We followed eight reaction paths with a distinct position and coordination of the catalytically important active site Mg(2+) ion. For six of them, we observed feasible activation barriers ranging from 14.2 to 21.9 kcal mol(-1), indicating that the specific position of the Mg(2+) ion in the active site is predicted to strongly affect the kinetics of self-cleavage. The deprotonation of the U-1(2'-OH) nucleophile and the nucleophilic attack of the resulting U-1(2'-O(-)) on the scissile phosphodiester are found to be separate steps, as deprotonation precedes the nucleophilic attack. This sequential mechanism of the HDV ribozyme differs from the concerted nucleophilic activation and attack suggested for the hairpin ribozyme. We estimate the pKa of the U-1(2'-OH) group to range from 8.8 to 11.2, suggesting that it is lowered by several units from that of a free ribose, comparable to and most likely smaller than the pKa of the solvated active site Mg(2+) ion. Our results thus support the notion that the structure of the HDV ribozyme, and particularly the positioning of the active site Mg(2+) ion, facilitate deprotonation and activation of the 2'-OH nucleophile.

Aqueous solutions: state of the art in ab initio molecular dynamics

The simulation of liquids by ab initio molecular dynamics (AIMD) has been a subject of intense activity over the last two decades. The significant increase in computational resources as well as the development of new and efficient algorithms has elevated this method to the status of a standard quantum mechanical tool that is used by both experimentalists and theoreticians. As AIMD computes the electronic structure from first principles, it is free of ad hoc parametrizations and has thus been applied to a large variety of physical and chemical problems. In particular, AIMD has provided microscopic insight into the structural and dynamical properties of aqueous solutions which are often challenging to probe experimentally. In this review, after a brief theoretical description of the Born-Oppenheimer and Car-Parrinello molecular dynamics formalisms, we show how AIMD has enhanced our understanding of the properties of liquid water and its constituent ions: the proton and the hydroxide ion. Thereafter, a broad overview of the application of AIMD to other aqueous systems, such as solvated organic molecules and inorganic ions, is presented. We also briefly describe the latest theoretical developments made in AIMD, such as methods for enhanced sampling and the inclusion of nuclear quantum effects.

Quantum mechanical/molecular mechanical free energy simulations of the self-cleavage reaction in the hepatitis delta virus ribozyme

The hepatitis delta virus (HDV) ribozyme catalyzes a self-cleavage reaction using a combination of nucleobase and metal ion catalysis. Both divalent and monovalent ions can catalyze this reaction, although the rate is slower with monovalent ions alone. Herein, we use quantum mechanical/molecular mechanical (QM/MM) free energy simulations to investigate the mechanism of this ribozyme and to elucidate the roles of the catalytic metal ion. With Mg²⁺ at the catalytic site, the self-cleavage mechanism is observed to be concerted with a phosphorane-like transition state and a free energy barrier of ∼13 kcal/mol, consistent with free energy barrier values extrapolated from experimental studies. With Na⁺ at the catalytic site, the mechanism is observed to be sequential, passing through a phosphorane intermediate, with free energy barriers of 2–4 kcal/mol for both steps; moreover, proton transfer from the exocyclic amine of protonated C75 to the nonbridging oxygen of the scissile phosphate occurs to stabilize the phosphorane intermediate in the sequential mechanism. To explain the slower rate observed experimentally with monovalent ions, we hypothesize that the activation of the O2′ nucleophile by deprotonation and orientation is less favorable with Na⁺ ions than with Mg²⁺ ions. To explore this hypothesis, we experimentally measure the pK_a of O2′ by kinetic and NMR methods and find it to be lower in the presence of divalent ions rather than only monovalent ions. The combined theoretical and experimental results indicate that the catalytic Mg²⁺ ion may play three key roles: assisting in the activation of the O2′ nucleophile, acidifying the general acid C75, and stabilizing the nonbridging oxygen to prevent proton transfer to it.

QM/MM simulation (B3LYP) of the RNase A cleavage-transesterification reaction supports a triester A(N) + D(N) associative mechanism with an O2' H internal proton transfer

The mechanism of the backbone cleavage-transesterification step of the RNase A enzyme remains controversial even after 60 years of study. We report quantum mechanics/molecule mechanics (QM/MM) free energy calculations for two optimized reaction paths based on an analysis of all structural data and identified by a search for reaction coordinates using a reliable quantum chemistry method (B3LYP), equilibrated structural optimizations, and free energy estimations. Both paths are initiated by nucleophilic attack of the ribose O2' oxygen on the neighboring diester phosphate bond, and both reach the same product state (PS) (a O3'-O2' cyclic phosphate and a O5' hydroxyl terminated fragment). Path 1, resembles the widely accepted dianionic transition-state (TS) general acid (His119)/base (His12) classical mechanism. However, this path has a barrier (25 kcal/mol) higher than that of the rate-limiting hydrolysis step and a very loose TS. In Path 2, the proton initially coordinating the O2' migrates to the nonbridging O1P in the initial reaction path rather than directly to the general base resulting in a triester (substrate as base) AN + DN mechanism with a monoanionic weakly stable intermediate. The structures in the transition region are associative with low barriers (TS1 10, TS2 7.5 kcal/mol). The Path 2 mechanism is consistent with the many results from enzyme and buffer catalyzed and uncatalyzed analog reactions and leads to a PS consistent with the reactive state for the following hydrolysis step. The differences between the consistently estimated barriers in Path 1 and 2 lead to a 10(11) difference in rate strongly supporting the less accepted triester mechanism.

Acidity constants of lumiflavin from first principles molecular dynamics simulations

DFT-based molecular dynamics simulations predict the acidity of lumiflavin in different redox states.

Proton affinity of the histidine-tryptophan cluster motif from the influenza A virus from ab initio molecular dynamics

Ab initio molecular dynamics calculations have been used to compare and contrast the deprotonation reaction of a histidine residue in aqueous solution with the situation arising in a histidine-tryptophan cluster. The latter is used as a model of the proton storage unit present in the pore of the M2 proton conducting ion channel. We compute potentials of mean force for the dissociation of a proton from the Nδ and Nε positions of the imidazole group to estimate the pKa's. Anticipating our results, we will see that the estimated pKa for the first protonation event of the M2 channel is in good agreement with experimental estimates. Surprisingly, despite the fact that the histidine is partially desolvated in the M2 channel, the affinity for protons is similar to that of a histidine in aqueous solution. Importantly, the electrostatic environment provided by the indoles is responsible for the stabilization of the charged imidazolium.

Intramolecular participation of amino groups in the cleavage and isomerization of ribonucleoside 3'-phosphodiesters: the role in stabilization of the phosphorane intermediate

A dinucleoside-3',5'-phosphodiester model, 5'-amino-4'-aminomethyl-5'-deoxyuridylyl-3',5'-thymidine, incorporating two aminomethyl functions in the 4'-position of the 3'-linked nucleoside has been prepared and its hydrolytic reactions studied over a wide pH range. The amino functions were found to accelerate the cleavage and isomerization of the phosphodiester linkage in both protonated and neutral form. When present in protonated form, the cleavage of the 3',5'-phosphodiester linkage and its isomerization to a 2',5'-linkage are pH-independent and 50-80 times as fast as the corresponding reactions of uridylyl-3',5'-uridine (3',5'-UpU). The cleavage of the resulting 2',5'-isomer is also accelerated, albeit less than with the 3',5'-isomer, whereas isomerization back to the 3',5'-diester is not enhanced. When the amino groups are deprotonated, the cleavage reactions of both isomers are again pH-independent and up to 1000-fold faster than the pH-independent cleavage of UpU. Interestingly, the 2'- to 3'-isomerization is now much faster than its reverse reaction. The mechanisms of these reactions are discussed. The rate accelerations are largely accounted for by electrostatic and hydrogen-bonding interactions of the protonated amino groups with the phosphorane intermediate.

Prediction of Absolute Hydroxyl pKa Values for 3-Hydroxypyridin-4-ones

pKa values have been calculated for a series of 3-hydroxypyridin-4-one (HPO) chelators in aqueous solution using coordination constrained ab initio molecular dynamics (AIMD) in combination with thermodynamic integration. This dynamics-based methodology in which the solvent is treated explicitly at the ab initio level has been compared with more commonly used simple, static, approaches. Comparison with experimental numbers has confirmed that the AIMD-based approach predicts the correct trend in the pKa values and produces the lowest average error (∼0.3 pKa units). The corresponding pKa predictions made via static quantum mechanical calculations overestimate the pKa values by 0.3-7 pKa units, with the extent of error dependent on the choice of thermodynamic cycle employed. The use of simple quantitative structure property relationship methods gives prediction errors of 0.3-1 pKa units, with some values overestimated and some underestimated. Beyond merely calculating pKa values, the AIMD simulations provide valuable additional insight into the atomistic details of the proton transfer mechanism and the solvation structure and dynamics at all stages of the reaction. For all HPOs studied, it is seen that proton transfer takes place along a chain of three H2O molecules, although direct hydrogen bonds are seen to form transiently. Analysis of the solvation structure before and after the proton transfer event using radial pair distribution functions and integrated number densities suggests that the trends in the pKa values correlate with the strength of the hydrogen bond and the average number of solvent molecules in the vicinity of the donor oxygen.

Intracomplex general acid/base catalyzed cleavage of RNA phosphodiester bonds: the leaving group effect

The general acid/base catalyzed cleavage of a number of alkyl esters of uridine-3'- (and -5'-)phosphate has been studied by utilizing a cleaving agent, in which the catalytic moiety (a substituted 1,3,5-triazine) is tethered to an anchoring Zn(II):cyclen moiety. Around pH 7, formation of a strong ternary complex between uracil, Zn(II) and cyclen brings the general acid/base catalyst close to the scissile phosphodiester linkage, resulting in rate acceleration of 1-2 orders of magnitude with the uridine-3'-phosphodiesters. Curiously, no acceleration was observed with their 5'-counterparts. A β(lg) value of -0.7 has been determined for the general acid/base catalyzed cleavage, consistent with a proton transfer to the leaving group in the rate-limiting step.

Predicting the acidity constant of a goethite hydroxyl group from first principles

Accurate predictions of the acid-base behavior of hydroxyl groups at mineral surfaces are critical for understanding the trapping of toxic and radioactive ions in soil samples. In this work, we apply ab initio molecular dynamics (AIMD) simulations and potential-of-mean-force techniques to calculate the pK(a) of a doubly protonated oxygen atom bonded to a single Fe atom (Fe(I)OH(2)) on the goethite (101) surface. Using formic acid as a reference system, pK(a) = 7.0 is predicted, suggesting that isolated, positively charged groups of this type are marginally stable at neutral pH. Similarities and differences between AIMD and the more empirical multi-site complexation methodology are highlighted, particularly with respect to the treatment of hydrogen bonding with water and proton sharing among surface hydroxyl groups. We also highlight the importance of an electronic structure method that can accurately predict transition metal ion properties for goethite pK(a) calculations.

Binding affinity of a small molecule to an amorphous polymer in a solvent. Part 1: free energy of binding to a binding site

Crystallization is commonly used in a separation and purification process in the production of a wide range of materials in various industries. In industry, crystallization usually starts with heterogeneous nucleation on a foreign surface. The complicated mechanism of heterogeneous nucleation is not well understood; however, we hypothesize that there might be a possible correlation between binding affinity to a surface and enhancement of nucleation. Recent studies show that amorphous polymers can be used to control crystallization, selectively produce pharmaceutical polymorphs, and discover novel pharmaceutical polymorphs. To investigate the possible correlation between the binding affinity of one molecule to key binding sites (local binding) and heterogeneous nucleation activity as well as the possibility of using this binding affinity to help guide the selection of polymers that promote heterogeneous nucleation, we computed the free energy of binding of aspirin to four nonporous cross-linked polymers in an ethanol-water 38 v% mixture. These cross-linked polymers are poly(4-acryloylmorpholine) (PAM), poly(2-carboxyethyl acrylate) (PCEA), poly(4-hydroxylbutyl acrylate) (PHBA), and polystyrene (PS); all of them were cross-linked with divinylbenzene (DVB). These systems were used because their heterogeneous nucleation activities are available in literature, and the ranking is PAM > PCEA > PHBA ≈ PS. We generated three independent surfaces for each polymer and computed the free energy of binding of aspirin to the best binding site that we found on each surface. The average free energies of binding to the best sites of PAM, PCEA, PHBA, and PS are -20.4 ± 1.0, -16.7 ± 1.0, -14.4 ± 1.1, and -13.6 ± 1.1 kcal/mol, respectively. We found that the trend of the magnitudes of the average free energies of binding to the best sites is PAM > PCEA > PHBA ≈ PS. This trend is very similar to that of heterogeneous nucleation activity. Our results suggest the importance of the free energy of binding to key sites (local binding) and the possibility of using this quantity to help guide the selection of polymers that promote heterogeneous nucleation.

Free energy of binding of a small molecule to an amorphous polymer in a solvent

Crystallization is a commonly used purification process in industrial practice. It usually begins with heterogeneous nucleation on a foreign surface. The complicated mechanism of heterogeneous nucleation is not well understood, but we hypothesize that a possible correlation between binding affinity to a surface and nucleation enhancement might exist. Amorphous polymers have been used in controlling crystallization. However, to our knowledge, no attempt has been made to calculate the free energy of binding of a small molecule to an amorphous polymer in a solvent, and to characterize the binding sites/conformations of this system at a molecular level. We developed a two-step approach, first using Adsorption Locator to identify probable binding sites and molecular dynamics to screen for the best binding sites and then using the Blue-Moon Ensemble method to compute the free energy of binding. A system of ethylene glycol, polyvinyl alcohol (PVA), and heavy water (D(2)O) was used for validation, since experimental data exists on a related system. Looking at four independently constructed surfaces, we found that ethylene glycol binds to an indentation on the surface or in a hole beneath the surface. We focused on the indentation binding sites because they are easily accessible and do not have large free energy barriers. The closest system for which experimental data on binding energetics exists is ethylene glycol on PVA in aqueous solutions/gels, and the magnitudes of the free energy of binding to the three best indentation binding sites are close to the experimental value, 0.4-3.7 kcal/mol higher. Our approach offers a way to compute the free energy of binding and characterize the binding sites/conformations, and is general enough to apply to other small molecule/amorphous polymer/solvent systems.

Absolute pKa Values and Solvation Structure of Amino Acids from Density Functional Based Molecular Dynamics Simulation

Absolute pKa values of the amino acid side chains of arginine, aspartate, cysteine, histidine, and tyrosine; the C- and N-terminal group of tyrosine; and the tryptophan radical cation are calculated using a revised density functional based molecular dynamics simulation technique introduced previously [ Cheng , J. ; Sulpizi , M. ; Sprik , M. J. Chem. Phys. 2009 , 131 , 154504 ]. In the revised scheme, acid deprotonation is considered as a dissociation rather than a proton transfer reaction, and a correction term for treating the proton as a hydronium ion is suggested. The acidity constants of the amino acids are obtained from the vertical energy gaps for removal or insertion of the acidic proton and the computed solvation free energy of the proton. The unsigned mean error relative to experimental results is 2.1 pKa units with a maximum error of 4.0 pKa units. The estimated mean statistical uncertainty due to the finite length of the trajectories is ±1.1 pKa units. The solvation structures of the protonated and deprotonated amino acids are analyzed in terms of radial distribution functions, which can serve as reference data for future force field developments.

Cleavage of RNA phosphodiester bonds by small molecular entities: a mechanistic insight

RNA molecules participate in many fundamental cellular processes either as a carrier of genetic information or as a catalyst, and hence, RNA has received increasing interest both as a chemotherapeutic agent and as a target of chemotherapy. In addition the dual nature of RNA has led to the RNA-world concept, i.e. an assumption that the evolution at an early stage of life was based on RNA-like oligomers that were responsible for the storage and transfer of information and as catalysts maintained primitive metabolism. Accordingly, the kinetics and mechanisms of the cleavage of RNA phosphodiester bonds have received interest and it is hoped they will shed light on the mechanisms of enzyme action and on the development of artificial enzymes. The major mechanistic findings concerning the cleavage by small molecules and ions and their significance for the development of efficient and biologically applicable artificial catalysts for RNA hydrolysis are surveyed in the present perspective.

Kinetic isotope effects for RNA cleavage by 2'-O- transphosphorylation: nucleophilic activation by specific base

To better understand the interactions between catalysts and transition states during RNA strand cleavage, primary (18)O kinetic isotope effects (KIEs) and solvent D(2)O isotope effects were measured to probe the mechanism of base-catalyzed 2'-O-transphosphorylation of the RNA dinucleotide 5'-UpG-3'. The observed (18)O KIEs for the nucleophilic 2'-O and in the 5'-O leaving group at pH 14 are both large relative to reactions of phosphodiesters with good leaving groups, indicating that the reaction catalyzed by hydroxide has a transition state (TS) with advanced phosphorus-oxygen bond fission to the leaving group ((18)k(LG) = 1.034 +/- 0.004) and phosphorus-nucleophile bond formation ((18)k(NUC) = 0.984 +/- 0.004). A breakpoint in the pH dependence of the 2'-O-transphosphorylation rate to a pH independent phase above pH 13 has been attributed to the pK(a) of the 2'-OH nucleophile. A smaller nucleophile KIE is observed at pH 12 ((18)k(NUC) = 0.995 +/- 0.004) that is interpreted as the combined effect of the equilibrium isotope effect (ca. 1.02) on deprotonation of the 2'-hydroxyl nucleophile and the intrinsic KIE on the nucleophilic addition step (ca. 0.981). An alternative mechanism in which the hydroxide ion acts as a general base is considered unlikely given the lack of a solvent deuterium isotope effect above the breakpoint in the pH versus rate profile. These results represent the first direct analysis of the transition state for RNA strand cleavage. The primary (18)O KIE results and the lack of a kinetic solvent deuterium isotope effect together provide strong evidence for a late transition state and 2'-O nucleophile activation by specific base catalysis.

Redox potentials and pKa for benzoquinone from density functional theory based molecular dynamics

The density functional theory based molecular dynamics (DFTMD) method for the computation of redox free energies presented in previous publications and the more recent modification for computation of acidity constants are reviewed. The method uses a half reaction scheme based on reversible insertion/removal of electrons and protons. The proton insertion is assisted by restraining potentials acting as chaperones. The procedure for relating the calculated deprotonation free energies to Brønsted acidities (pK(a)) and the oxidation free energies to electrode potentials with respect to the normal hydrogen electrode is discussed in some detail. The method is validated in an application to the reduction of aqueous 1,4-benzoquinone. The conversion of hydroquinone to quinone can take place via a number of alternative pathways consisting of combinations of acid dissociations, oxidations, or dehydrogenations. The free energy changes of all elementary steps (ten in total) are computed. The accuracy of the calculations is assessed by comparing the energies of different pathways for the same reaction (Hess's law) and by comparison to experiment. This two-sided test enables us to separate the errors related with the restrictions on length and time scales accessible to DFTMD from the errors introduced by the DFT approximation. It is found that the DFT approximation is the main source of error for oxidation free energies.