Molecular Machanics of Water Monomer-Maple Code

This is the Maple code to support the molecular dynamics of a water monomer molecule, allowing investigation of the classical vibrations of this molecule.

Molecular Mechanics of Water Monomer

Simulation of the classical molecular dynamics of a water molecule can be useful in explaining normal modes of motion, Fourier Transforms, and fundamental frequencies of vibration, as illustrated herein.

CONFORMATIONAL DYNAMICS OF K-RAS AND H-RAS PROTEINS: IS THERE FUNCTIONAL SPECIFICITY AT THE CATALYTIC DOMAIN?

Ras proteins serve as crucial signaling modulators in cell proliferation through their ability to hydrolyze GTP and exist in a GTP “on” state and GTP “off” state. There are three different human Ras isoforms: H-ras, N-ras and K-ras (4A and 4B). Although their sequence identity is very high at the catalytic domain, these isoforms differ in their ability to activate different effectors and hence different signaling pathways. Much of the previous work on this topic has attributed this difference to the hyper variable region of Ras proteins, which contains most of the sequence variance among the isoforms and encodes specificity for differential distribution in the membrane. However, we hypothesize that sequence variation on lobe II of Ras catalytic domain alters dynamics and leads to differential preference for different effectors or modulators. In this work, we used all atom molecular dynamics to analyze the dynamics in the catalytic domain of H-ras and K-ras. We have also analyzed the dynamics of a transforming mutant of H-ras and K-ras and further studied the dynamics of an effectorselective mutant of H-ras. Collectively we have determined that wild type K-ras is more dynamic than H-ras and that the structure of the effector binding loop more closely resembles that of the T35S Raf-selective mutant, possibly giving us a new view and insight into the v mode of effector specificity. Furthermore we have determined that specific mutations at the same location perturb the conformational equilibrium differently in H-ras and K-ras and that an enhanced oncogenic potential may arise from different structural perturbations for each point mutation of a specific isoform.

Influence of termal fluctuations in radiation damage cascade production and defect dynamics in tungsten

The detailed study of the deterioration suffered by the materials of the components of a nuclear facility, in particular those forming part of the reactor core, is a topic of great interest which importance derives in large technological and economic implications. Since changes in the atomic-structural properties of relevant components pose a risk to the smooth operation with clear consequences for security and life of the plant, controlling these factors is essential in any development of engineering design and implementation. In recent times, tungsten has been proposed as a structural material based on its good resistance to radiation, but still needs to be done an extensive study on the influence of temperature on the behavior of this material under radiation damage. This work aims to contribute in this regard. Molecular Dynamics (MD) simulations were carried out to determine the influence of temperature fluctuations on radiation damage production and evolution in Tungsten. We have particularly focused our study in the dynamics of defect creation, recombination, and diffusion properties. PKA energies were sampled in a range from 5 to 50 KeV. Three different temperature scenarios were analyzed, from very low temperatures (0-200K), up to high temperature conditions (300-500 K). We studied the creation of defects, vacancies and interstitials, recombination rates, diffusion properties, cluster formation, their size and evolution. Simulations were performed using Lammps and the Zhou EAM potential for W

Stopping power dependence of nitrogen sputtering yields in copper nitride films under swift-ion irradiation: Exciton model approach

Nitrogen sputtering yields as high as 104 atoms/ion, are obtained by irradiating N-rich-Cu3N films (N concentration: 33 ± 2 at.%) with Cu ions at energies in the range 10?42 MeV. The kinetics of N sputtering as a function of ion fluence is determined at several energies (stopping powers) for films deposited on both, glass and silicon substrates. The kinetic curves show that the amount of nitrogen release strongly increases with rising irradiation fluence up to reaching a saturation level at a low remaining nitrogen fraction (5?10%), in which no further nitrogen reduction is observed. The sputtering rate for nitrogen depletion is found to be independent of the substrate and to linearly increase with electronic stopping power (Se). A stopping power (Sth) threshold of ?3.5 keV/nm for nitrogen depletion has been estimated from extrapolation of the data. Experimental kinetic data have been analyzed within a bulk molecular recombination model. The microscopic mechanisms of the nitrogen depletion process are discussed in terms of a non-radiative exciton decay model. In particular, the estimated threshold is related to a minimum exciton density which is required to achieve efficient sputtering rates.

Diabatic quantum gates

At present, several models for quantum computation have been proposed. Adiabatic quantum computation scheme particularly offers this possibility and is based on a slow enough time evolution of the system, where no transitions take place. In this work, a new strategy for quantum computation is provided from the opposite point of view. The objective is to control the non-adiabatic transitions between some states in order to produce the desired exit states after the evolution. The model is introduced by means of an analogy between the adiabatic quantum computation and an inelastic atomic collision. By means of a simple two-state model, several quantum gates are reproduced, concluding the possibility of diabatic universal faulttolerant quantum computation. Going a step further, a new quantum diabatic computation model is glimpsed, where a carefully chosen Hamiltonian could carry out a non-adiabatic transition between the initial and the sought final state.

MMonCa: A flexible and powerful new Kinetic Monte Carlo simulator

Kinetic Monte Carlo (KMC) is a widely used technique to simulate the evolution of radiation damage inside solids. Despite de fact that this technique was developed several decades ago, there is not an established and easy to access simulating tool for researchers interested in this field, unlike in the case of molecular dynamics or density functional theory calculations. In fact, scientists must develop their own tools or use unmaintained ones in order to perform these types of simulations. To fulfil this need, we have developed MMonCa, the Modular Monte Carlo simulator. MMonCa has been developed using professional C++ programming techniques and has been built on top of an interpreted language to allow having a powerful yet flexible, robust but customizable and easy to access modern simulator. Both non lattice and Lattice KMC modules have been developed. We will present in this conference, for the first time, the MMonCa simulator. Along with other (more detailed) contributions in this meeting, the versatility of MMonCa to study a number of problems in different materials (particularly, Fe and W) subject to a wide range of conditions will be shown. Regarding KMC simulations, we have studied neutron-generated cascade evolution in Fe (as a model material). Starting with a Frenkel pair distribution we have followed the defect evolution up to 450 K. Comparison with previous simulations and experiments shows excellent agreement. Furthermore, we have studied a more complex system (He-irradiated W:C) using a previous parametrization [1]. He-irradiation at 4 K followed by isochronal annealing steps up to 500 K has been simulated with MMonCa. The He energy was 400 eV or 3 keV. In the first case, no damage is associated to the He implantation, whereas in the second one, a significant Frenkel pair concentration (evolving into complex clusters) is associated to the He ions. We have been able to explain He desorption both in the absence and in the presence of Frenkel pairs and we have also applied MMonCa to high He doses and fluxes at elevated temperatures. He migration and trapping dominate the kinetics of He desorption. These processes will be discussed and compared to experimental results. [1] C.S. Becquart et al. J. Nucl. Mater. 403 (2010) 75

Aplicación de la física estadística a los medios granulares

Esta tesis se centra en el estudio de medios granulares blandos y atascados mediante la aplicación de la física estadística. Esta aproximación se sitúa entre los tradicionales enfoques macro y micromecánicos: trata de establecer cuáles son las propiedades macroscópicas esperables de un sistema granular en base a un análisis de las propiedades de las partículas y las interacciones que se producen entre ellas y a una consideración de las restricciones macroscópicas del sistema. Para ello se utiliza la teoría estadística junto con algunos principios, conceptos y definiciones de la teoría de los medios continuos (campo de tensiones y deformaciones, energía potencial elástica, etc) y algunas técnicas de homogeneización. La interacción entre las partículas es analizada mediante las aportaciones de la teoría del contacto y de las fuerzas capilares (producidas por eventuales meniscos de líquido cuando el medio está húmedo). La idea básica de la mecánica estadística es que entre todas soluciones de un problema físico (como puede ser el ensamblaje en equilibrio estático de partículas de un medio granular) existe un conjunto que es compatible con el conocimiento macroscópico que tenemos del sistema (por ejemplo, su volumen, la tensión a la que está sometido, la energía potencial elástica que almacena, etc.). Este conjunto todavía contiene un número enorme de soluciones. Pues bien, si no hay ninguna información adicional es razonable pensar que no existe ningún motivo para que alguna de estas soluciones sea más probable que las demás. Entonces parece natural asignarles a todas ellas el mismo peso estadístico y construir una función matemática compatible. Actuando de este modo se obtiene cuál es la función de distribución más probable de algunas cantidades asociadas a las soluciones, para lo cual es muy importante asegurarse de que todas ellas son igualmente accesibles por el procedimiento de ensamblaje o protocolo. Este enfoque se desarrolló en sus orígenes para el estudio de los gases ideales pero se puede extender para sistemas no térmicos como los analizados en esta tesis. En este sentido el primer intento se produjo hace poco más de veinte años y es la colectividad de volumen. Desde entonces esta ha sido empleada y mejorada por muchos investigadores en todo el mundo, mientras que han surgido otras, como la de la energía o la del fuerza-momento (tensión multiplicada por volumen). Cada colectividad describe, en definitiva, conjuntos de soluciones caracterizados por diferentes restricciones macroscópicas, pero de todos ellos resultan distribuciones estadísticas de tipo Maxwell-Boltzmann y controladas por dichas restricciones. En base a estos trabajos previos, en esta tesis se ha adaptado el enfoque clásico de la física estadística para el caso de medios granulares blandos. Se ha propuesto un marco general para estudiar estas colectividades que se basa en la comparación de todas las posibles soluciones en un espacio matemático definido por las componentes del fuerza-momento y en unas funciones de densidad de estados. Este desarrollo teórico se complementa con resultados obtenidos mediante simulación de la compresión cíclica de sistemas granulares bidimensionales. Se utilizó para ello un método de dinámica molecular, MD (o DEM). Las simulaciones consideran una interacción mecánica elástica, lineal y amortiguada a la que se ha añadido, en algunos casos, la fuerza cohesiva producida por meniscos de agua. Se realizaron cálculos en serie y en paralelo. Los resultados no solo prueban que las funciones de distribución de las componentes de fuerza-momento del sistema sometido a un protocolo específico parecen ser universales, sino que también revelan que existen muchos aspectos computacionales que pueden determinar cuáles son las soluciones accesibles. This thesis focuses on the application of statistical mechanics for the study of static and jammed packings of soft granular media. Such approach lies between micro and macromechanics: it tries to establish what the expected macroscopic properties of a granular system are, by starting from a micromechanical analysis of the features of the particles, and the interactions between them, and by considering the macroscopic constraints of the system. To do that, statistics together with some principles, concepts and definitions of continuum mechanics (e.g. stress and strain fields, elastic potential energy, etc.) as well as some homogenization techniques are used. The interaction between the particles of a granular system is examined too and theories on contact and capillary forces (when the media are wet) are revisited. The basic idea of statistical mechanics is that among the solutions of a physical problem (e.g. the static arrangement of particles in mechanical equilibrium) there is a class that is compatible with our macroscopic knowledge of the system (volume, stress, elastic potential energy,...). This class still contains an enormous number of solutions. In the absence of further information there is not any a priori reason for favoring one of these more than any other. Hence we shall naturally construct the equilibrium function by assigning equal statistical weights to all the functions compatible with our requirements. This procedure leads to the most probable statistical distribution of some quantities, but it is necessary to guarantee that all the solutions are likely accessed. This approach was originally set up for the study of ideal gases, but it can be extended to non-thermal systems too. In this connection, the first attempt for granular systems was the volume ensemble, developed about 20 years ago. Since then, this model has been followed and improved upon by many researchers around the world, while other two approaches have also been set up: energy and force-moment (i.e. stress multiplied by volume) ensembles. Each ensemble is described by different macroscopic constraints but all of them result on a Maxwell-Boltzmann statistical distribution, which is precisely controlled by the respective constraints. According to this previous work, in this thesis the classical statistical mechanics approach is introduced and adapted to the case of soft granular media. A general framework, which includes these three ensembles and uses a force-moment phase space and a density of states function, is proposed. This theoretical development is complemented by molecular dynamics (or DEM) simulations of the cyclic compression of 2D granular systems. Simulations were carried out by considering spring-dashpot mechanical interactions and attractive capillary forces in some cases. They were run on single and parallel processors. Results not only prove that the statistical distributions of the force-moment components obtained with a specific protocol seem to be universal, but also that there are many computational issues that can determine what the attained packings or solutions are.

Computational Study of the Fe(CN)(2)CO Cofactor and Its Binding to HypC Protein.

In the intricate maturation process of [NiFe]-hydrogenases, the Fe(CN)2CO cofactor is first assembled in a HypCD complex with iron coordinated by cysteines from both proteins and CO is added after ligation of cyanides. The small accessory protein HypC is known to play a role in delivering the cofactor needed for assembling the hydrogenase active site. However, the chemical nature of the Fe(CN)2CO moiety and the stability of the cofactor–HypC complex are open questions. In this work, we address geometries, properties, and the nature of bonding of all chemical species involved in formation and binding of the cofactor by means of quantum calculations. We also study the influence of environmental effects and binding to cysteines on vibrational frequencies of stretching modes of CO and CN used to detect the presence of Fe(CN)2CO. Carbon monoxide is found to be much more sensitive to sulfur binding and the polarity of the medium than cyanides. The stability of the HypC–cofactor complex is analyzed by means of molecular dynamics simulation of cofactor-free and cofactor-bound forms of HypC. The results show that HypC is stable enough to carry the cofactor, but since its binding cysteine is located at the N-terminal unstructured tail, it presents large motions in solution, which suggests the need for a guiding interaction to achieve delivery of the cofactor.

Multiscale modeling of the plastic behaviour in single crystal tungsten: from atomistic to crystal plasticity simulations

En una planta de fusión, los materiales en contacto con el plasma así como los materiales de primera pared experimentan condiciones particularmente hostiles al estar expuestos a altos flujos de partículas, neutrones y grandes cargas térmicas. Como consecuencia de estas diferentes y complejas condiciones de trabajo, el estudio, desarrollo y diseño de estos materiales es uno de los más importantes retos que ha surgido en los últimos años para la comunidad científica en el campo de los materiales y la energía. Debido a su baja tasa de erosión, alta resistencia al sputtering, alta conductividad térmica, muy alto punto de fusión y baja retención de tritio, el tungsteno (wolframio) es un importante candidato como material de primera pared y como posible material estructural avanzado en fusión por confinamiento magnético e inercial. Sin embargo, el tiempo de vida del tungsteno viene controlado por diversos factores como son su respuesta termo-mecánica en la superficie, la posibilidad de fusión y el fallo por acumulación de helio. Es por ello que el tiempo de vida limitado por la respuesta mecánica del tungsteno (W), y en particular su fragilidad, sean dos importantes aspectos que tienes que ser investigados. El comportamiento plástico en materiales refractarios con estructura cristalina cúbica centrada en las caras (bcc) como el tungsteno está gobernado por las dislocaciones de tipo tornillo a escala atómica y por conjuntos e interacciones de dislocaciones a escalas más grandes. El modelado de este complejo comportamiento requiere la aplicación de métodos capaces de resolver de forma rigurosa cada una de las escalas. El trabajo que se presenta en esta tesis propone un modelado multiescala que es capaz de dar respuestas ingenieriles a las solicitudes técnicas del tungsteno, y que a su vez está apoyado por la rigurosa física subyacente a extensas simulaciones atomísticas. En primer lugar, las propiedades estáticas y dinámicas de las dislocaciones de tipo tornillo en cinco potenciales interatómicos de tungsteno son comparadas, determinando cuáles de ellos garantizan una mayor fidelidad física y eficiencia computacional. Las grandes tasas de deformación asociadas a las técnicas de dinámica molecular hacen que las funciones de movilidad de las dislocaciones obtenidas no puedan ser utilizadas en los siguientes pasos del modelado multiescala. En este trabajo, proponemos dos métodos alternativos para obtener las funciones de movilidad de las dislocaciones: un modelo Monte Cario cinético y expresiones analíticas. El conjunto de parámetros necesarios para formular el modelo de Monte Cario cinético y la ley de movilidad analítica son calculados atomísticamente. Estos parámetros incluyen, pero no se limitan a: la determinación de las entalpias y energías de formación de las parejas de escalones que forman las dislocaciones, la parametrización de los efectos de no Schmid característicos en materiales bcc,etc. Conociendo la ley de movilidad de las dislocaciones en función del esfuerzo aplicado y la temperatura, se introduce esta relación como ecuación de flujo dentro de un modelo de plasticidad cristalina. La predicción del modelo sobre la dependencia del límite de fluencia con la temperatura es validada experimentalmente con ensayos uniaxiales en tungsteno monocristalino. A continuación, se calcula el límite de fluencia al aplicar ensayos uniaxiales de tensión para un conjunto de orientaciones cristalográticas dentro del triángulo estándar variando la tasa de deformación y la temperatura de los ensayos. Finalmente, y con el objetivo de ser capaces de predecir una respuesta más dúctil del tungsteno para una variedad de estados de carga, se realizan ensayos biaxiales de tensión sobre algunas de las orientaciones cristalográficas ya estudiadas en función de la temperatura.-------------------------------------------------------------------------ABSTRACT ----------------------------------------------------------Tungsten and tungsten alloys are being considered as leading candidates for structural and functional materials in future fusion energy devices. The most attractive properties of tungsten for the design of magnetic and inertial fusion energy reactors are its high melting point, high thermal conductivity, low sputtering yield and low longterm disposal radioactive footprint. However, tungsten also presents a very low fracture toughness, mostly associated with inter-granular failure and bulk plasticity, that limits its applications. As a result of these various and complex conditions of work, the study, development and design of these materials is one of the most important challenges that have emerged in recent years to the scientific community in the field of materials for energy applications. The plastic behavior of body-centered cubic (bcc) refractory metals like tungsten is governed by the kink-pair mediated thermally activated motion of h¿ (\1 11)i screw dislocations on the atomistic scale and by ensembles and interactions of dislocations at larger scales. Modeling this complex behavior requires the application of methods capable of resolving rigorously each relevant scale. The work presented in this thesis proposes a multiscale model approach that gives engineering-level responses to the technical specifications required for the use of tungsten in fusion energy reactors, and it is also supported by the rigorous underlying physics of extensive atomistic simulations. First, the static and dynamic properties of screw dislocations in five interatomic potentials for tungsten are compared, determining which of these ensure greater physical fidelity and computational efficiency. The large strain rates associated with molecular dynamics techniques make the dislocation mobility functions obtained not suitable to be used in the next steps of the multiscale model. Therefore, it is necessary to employ mobility laws obtained from a different method. In this work, we suggest two alternative methods to get the dislocation mobility functions: a kinetic Monte Carlo model and analytical expressions. The set of parameters needed to formulate the kinetic Monte Carlo model and the analytical mobility law are calculated atomistically. These parameters include, but are not limited to: enthalpy and energy barriers of kink-pairs as a function of the stress, width of the kink-pairs, non-Schmid effects ( both twinning-antitwinning asymmetry and non-glide stresses), etc. The function relating dislocation velocity with applied stress and temperature is used as the main source of constitutive information into a dislocation-based crystal plasticity framework. We validate the dependence of the yield strength with the temperature predicted by the model against existing experimental data of tensile tests in singlecrystal tungsten, with excellent agreement between the simulations and the measured data. We then extend the model to a number of crystallographic orientations uniformly distributed in the standard triangle and study the effects of temperature and strain rate. Finally, we perform biaxial tensile tests and provide the yield surface as a function of the temperature for some of the crystallographic orientations explored in the uniaxial tensile tests.

Ionophores and receptors using cation-π interactions: Collarenes

Cation-π interactions are important forces in molecular recognition by biological receptors, enzyme catalysis, and crystal engineering. We have harnessed these interactions in designing molecular systems with circular arrangement of benzene units that are capable of acting as ionophores and models for biological receptors. [n]Collarenes are promising candidates with high selectivity for a specific cation, depending on n, because of their structural rigidity and well-defined cavity size. The interaction energies of [n]collarenes with cations have been evaluated by using ab initio calculations. The selectivity of these [n]collarenes in aqueous solution was revealed by using statistical perturbation theory in conjunction with Monte Carlo and molecular dynamics simulations. It has been observed that in [n]collarenes the ratio of the interaction energies of a cation with it and the cation with the basic building unit (benzene) can be correlated to its ion selectivity. We find that collarenes are excellent and efficient ionophores that bind cations through cation-π interactions. [6]Collarene is found to be a selective host for Li+ and Mg2+, [8]collarene for K+ and Sr2+, and [10]collarene for Cs+ and Ba2+. This finding indicates that [10]collarene and [8]collarene could be used for effective separation of highly radioactive isotopes, 137Cs and 90Sr, which are major constituents of nuclear wastes. More interestingly, collarenes of larger cavity size can be useful in capturing organic cations. [12]Collarene exhibits a pronounced affinity for tetramethylammonium cation and acetylcholine, which implies that it could serve as a model for acetylcholinestrase. Thus, collarenes can prove to be novel and effective ionophores/model-receptors capable of heralding a new direction in molecular recognition and host-guest chemistry.

A molecular level picture of the stabilization of A-DNA in mixed ethanol–water solutions

Advances in computer power, methodology, and empirical force fields now allow routine “stable” nanosecond-length molecular dynamics simulations of DNA in water. The accurate representation of environmental influences on structure remains a major, unresolved issue. In contrast to simulations of A-DNA in water (where an A-DNA to B-DNA transition is observed) and in pure ethanol (where disruption of the structure is observed), A-DNA in ≈85% ethanol solution remains in a canonical A-DNA geometry as expected. The stabilization of A-DNA by ethanol is likely due to disruption of the spine of hydration in the minor groove and the presence of ion-mediated interhelical bonds and extensive hydration across the major groove.

Molecular switch in signal transduction: Reaction paths of the conformational changes in ras p21

Conformational changes in ras p21 triggered by the hydrolysis of GTP play an essential role in the signal transduction pathway. The path for the conformational change is determined by molecular dynamics simulation with a holonomic constraint directing the system from the known GTP-bound structure (with the γ-phosphate removed) to the GDP-bound structure. The simulation is done with a shell of water molecules surrounding the protein. In the switch I region, the side chain of Tyr-32, which undergoes a large displacement, moves through the space between loop 2 and the rest of the protein, rather than on the outside of the protein. As a result, the charged residues Glu-31 and Asp-33, which interact with Raf in the homologous RafRBD–Raps complex, remain exposed during the transition. In the switch II region, the conformational changes of α2 and loop 4 are strongly coupled. A transient hydrogen bonding complex between Arg-68 and Tyr-71 in the switch II region and Glu-37 in switch I region stabilizes the intermediate conformation of α2 and facilitates the unwinding of a helical turn of α2 (residues 66–69), which in turn permits the larger scale motion of loop 4. Hydrogen bond exchange between the protein and solvent molecules is found to be important in the transition. Possible functional implications of the results are discussed.

Cross-validated maximum likelihood enhances crystallographic simulated annealing refinement

Recently, the target function for crystallographic refinement has been improved through a maximum likelihood analysis, which makes proper allowance for the effects of data quality, model errors, and incompleteness. The maximum likelihood target reduces the significance of false local minima during the refinement process, but it does not completely eliminate them, necessitating the use of stochastic optimization methods such as simulated annealing for poor initial models. It is shown that the combination of maximum likelihood with cross-validation, which reduces overfitting, and simulated annealing by torsion angle molecular dynamics, which simplifies the conformational search problem, results in a major improvement of the radius of convergence of refinement and the accuracy of the refined structure. Torsion angle molecular dynamics and the maximum likelihood target function interact synergistically, the combination of both methods being significantly more powerful than each method individually. This is demonstrated in realistic test cases at two typical minimum Bragg spacings (dmin = 2.0 and 2.8 Å, respectively), illustrating the broad applicability of the combined method. In an application to the refinement of a new crystal structure, the combined method automatically corrected a mistraced loop in a poor initial model, moving the backbone by 4 Å.

Progress toward chemical accuracy in the computer simulation of condensed phase reactions.

We describe a procedure for the generation of chemically accurate computer-simulation models to study chemical reactions in the condensed phase. The process involves (i) the use of a coupled semiempirical quantum and classical molecular mechanics method to represent solutes and solvent, respectively; (ii) the optimization of semiempirical quantum mechanics (QM) parameters to produce a computationally efficient and chemically accurate QM model; (iii) the calibration of a quantum/classical microsolvation model using ab initio quantum theory; and (iv) the use of statistical mechanical principles and methods to simulate, on massively parallel computers, the thermodynamic properties of chemical reactions in aqueous solution. The utility of this process is demonstrated by the calculation of the enthalpy of reaction in vacuum and free energy change in aqueous solution for a proton transfer involving methanol, methoxide, imidazole, and imidazolium, which are functional groups involved with proton transfers in many biochemical systems. An optimized semiempirical QM model is produced, which results in the calculation of heats of formation of the above chemical species to within 1.0 kcal/mol (1 kcal = 4.18 kJ) of experimental values. The use of the calibrated QM and microsolvation QM/MM (molecular mechanics) models for the simulation of a proton transfer in aqueous solution gives a calculated free energy that is within 1.0 kcal/mol (12.2 calculated vs. 12.8 experimental) of a value estimated from experimental pKa values of the reacting species.