Multidimensional integration through Markovian sampling under steered function morphing: a physical guise from statistical mechanics

We present a computational strategy for the evaluation of multidimensional integrals on hyper-rectangles based on Markovian stochastic exploration of the integration domain while the integrand is being morphed by starting from an initial appropriate profile. Thanks to an abstract reformulation of Jarzynski's equality applied in stochastic thermodynamics to evaluate the free-energy profiles along selected reaction coordinates via non-equilibrium transformations, it is possible to cast the original integral into the exponential average of the distribution of the pseudo-work (that we may term "computational work") involved in doing the function morphing, which is straightforwardly solved. Several tests illustrate the basic implementation of the idea, and show its performance in terms of computational time, accuracy and precision. The formulation for integrand functions with zeros and possible sign changes is also presented. It will be stressed that our usage of Jarzynski's equality shares similarities with a practice already known in statistics as Annealed Importance Sampling (AIS), when applied to computation of the normalizing constants of distributions. In a sense, here we dress the AIS with its "physical" counterpart borrowed from statistical mechanics.Comment: 3 figures Supplementary Material (pdf file named "JEMDI_SI.pdf"

The roto-conformational diffusion tensor as a tool to interpret molecular flexibility

Stochastic modeling approaches can be used to rationalize complex molecular dynamical behaviours in solution, helping to interpret the coupling mechanisms among internal and external degrees of freedom, providing insight into reaction mechanisms and extracting structural and dynamical data from spectroscopic observables. However, the definition of comprehensive models is usually limited by (i) the difficulty in defining – without resorting to phenomenological assumptions – a representative reduced ensemble of molecular coordinates able to capture essential dynamical properties and (ii) the complexity of numerical or approximate treatments of the resulting equations. In this paper, we address the first of these two issues. Building on a previously defined systematic approach to construct rigorous stochastic models of flexible molecules in solutions from basic principles, we define a manageable diffusive framework leading to a Smoluchowski equation determined by one main tensorial parameter, namely the scaled roto-conformational diffusion tensor, which accounts for the influence of both conservative and dissipative forces and describes the molecular mobility via a precise definition of internal–external and internal–internal couplings. We then show the usefulness of the roto-conformational scaled diffusion tensor as an efficient gauge of molecular flexibility through the analysis of a set of molecular systems of increasing complexity ranging from dimethylformamide to a protein domain

Differential Dynamics at Glycosidic Linkages of an Oligosaccharide as Revealed by 13C NMR Spin Relaxation and Stochastic Modeling

Among biomolecules, carbohydrates are unique in that not only can linkages be formed through different positions but the structures may also be branched. The trisaccharide \uf062-D-Glcp-(1\uf0ae3)[\uf062-D-Glcp-(1\uf0ae2)]-\uf061-D-Manp-OMe represents a model of a branched vicinally disubstituted structure. A 13C site-specific isotopologue with labeling in each of the two terminal glucosyl residues enabled acquisition of high-quality 13C NMR relaxation parameters T1, T2 and heteronuclear NOE, with standard deviations of \uf0a3 0.5%. For interpretation of the experimental NMR data a diffusive chain model was used in which the dynamics of the glycosidic linkages is coupled to the global reorientation motion of the trisaccharide. Brownian dynamics simulations relying on the potential of mean force at the glycosidic linkages were employed to evaluate spectral densities of the spin probes. Calculated NMR relaxation parameters showed very good agreement with experimental data, deviating < 3%. The resulting dynamics is described by correlation times of 196 ps and 174 ps for the \uf062-(1\uf0ae2)- and \uf062-(1\uf0ae3)-linked glucosyl residues, respectively, i.e., different and linkage dependent. Notably, the devised computational protocol was performed without any fitting of parameters

Multiscale modeling of reaction rates: application to archetypal SN2 nucleophilic substitutions

We propose an approach to the evaluation of kinetic rates of elementary chemical reactions within Kramers\u2019 theory based on the definition of the reaction coordinate as a linear combination of natural, pseudo Z-matrix, internal coordinates of the system. The element of novelty is the possibility to evaluate the friction along the reaction coordinate, within a hydrodynamic framework developed recently [J. Campeggio et al., J. Comput. Chem. 2019, 40, 679\u2013705]. This, in turn, allows to keep into account barrier recrossing, i.e. the transmission coefficient that is employed in correcting transition state theory evaluations. To test the capabilities and the flaws of the approach we use as case studies two archetypal SN2 reactions. First, we consider to the standard substitution of chloride ion to bromomethane. The rate constant at 295.15 K is evaluated to k/c 96 = 2.7 7 10 126 s 121 (with c 96 = 1 M), which compares well to the experimental value of 3.3 7 10 126 s 121 [R. H. Bathgate and E. A. Melwyn-Hughes, J. Chem. Soc 1959, 2642\u20132648]. Then, the method is applied to the SN2 reaction of methylthiolate to dimethyl disulfide in water. In biology, such an interconversion of thiols and disulfides is an important metabolic topic still not entirely rationalized. The predicted rate constant is k/c 96 = 7.7 7 103 s 121. No experimental data is available for such a reaction, but it is in accord with the fact that the alkyl thiolates to dialkyl disulfides substitutions in water have been found to be fast reactions [S. M. Bachrach, J. M. Hayes, T. Dao and J. L. Mynar, Theor. Chem. Acc. 2002, 107, 266\u2013271]

Oxygen Reduction Reaction at Single-Site Catalysts: A Combined Electrochemical Scanning Tunnelling Microscopy and DFT Investigation on Iron Octaethylporphyrin Chloride on HOPG**

AbstractHere, we investigate the electrochemical activity of a highly oriented pyrolytic graphite (HOPG) supported iron octaethylporphyrin chloride film as a working electrode for the oxygen reduction reaction in 0.1 M HClO4 electrolyte. A voltammetric investigation indicated a quasi‐reversible electron transfer for the FeIII/FeII redox process, which turned out to be responsible for a "redox catalysis like" mechanism, in which the reduction of the metal center is first required to allow the O2 reduction. Here we proved that O2 is mostly reduced to H2O in a tetraelectronic process, as evidenced by a rotating ring‐disk electrode (RRDE). Furthermore, electrochemical scanning tunnelling microscopy (EC‐STM) is used as in operando technique for probing the electrode surface at the atomic level while the oxygen reduction reaction occurs, obtaining information on the molecule adlayer electronic and topographic structures. This allows us to follow the change in redox state from FeIII to FeII induced by the change of the electrode potential in O2 saturated electrolyte. The adsorption of O2 at the iron center was visualized and its depletion upon the application of a potential at which O2 can be reduced. The ORR process catalyzed by FeOEP adsorbed on HOPG was modelled by combining density functional theory, molecular dynamics, and thermodynamics data

flexibility at a glycosidic linkage revealed by molecular dynamics stochastic modeling and 13c nmr spin relaxation conformational preferences of α l rhap α 1 2 α l rhap ome in water and dimethyl sulfoxide solutions

Coupling between global reorientation and local motion is essential for reproducing NMR relaxation parameters of a flexible molecule

Advanced computational tools for the interpretation of magnetic resonance spectroscopies

Electron and nuclear magnetic spectroscopies are powerful tools for studying molecular dynamics, being particularly sensitive to motions with relaxation times in the range of 10−9 - 10−6 s. This time window includes rigid body motions in fluids and ”soft” internal motions of molecules. Moreover, dynamics in this range comprehend proteins internal motions responsible for relevant chemical-physical properties, like substrate recognition, activity and folding. In a typical electron spin resonance (ESR) experiment molecular motions affect considerably the shape of the spectral line. In a nuclear magnetic resonance (NMR) experiment characteristic relaxations times of the spin magnetization, i.e. T1, T2 and NOE, are directly affected by internal mobility. The aim of this Ph.D. work is the implementation of integrated theoretical / computational methodologies for characterization of dynamical properties of molecules gathered from ESR and NMR measurements. The starting point is a ”time coarse-graining” procedure that leads to simplified models in which we introduce only dynamical characteristics that are relevant to the physical observables considered. In particular, stochastic models are employed, based on a number of structural parameters which are calculated. The idea is to treat these parameters at atomistic and / or mesoscopic level depending on their nature. Software packages have been developed, comprehending E-SpiReS (Electron Spin Resonance Simulation) for cw-ESR simulations, C++OPPS (COupled Probe Protein Smoluchowski) for NMR simulations and DITE (DIffusion TEnsor) for the evaluation of dissipative properties of molecules. These programs have been built as user-friendly tools targeted for use by experimentalists, as a kind of in silico extension of the laboratory equipment.Tecniche efficaci nello studio della dinamica molecolare sono le spettroscopie di risonanza elettronica e nucleare, essendo particolarmente sensibili a moti caratterizzati da scale dei tempi nell'intervallo da 10^-9 a 10^-6 s, nel quale rientrano sia i moti globali (di corpo rigido), sia le dinamiche interne di molecole in soluzione. E' da notare che questa finestra comprende anche la dinamica delle proteine, responsabile di proprieta' chimico-fisiche molto importanti, quali il riconoscimento del substrato, l'attivita' ed il folding. Tipicamente, in un esperimento di risonanza di spin elettronico (RSE) i moti molecolari sono responsabili dell'allargamento inomogeneo delle righe spettrali. Per quanto riguarda la risonanza magnetica nucleare (RMN), invece, la dinamica molecolare influisce sui rilassamenti T1, T2 e NOE. Lo scopo di questo lavoro e' l'implementazione di metodologie integrate teorico / computazionali per la caratterizzazione della dinamica molecolare a partire da misure RSE e RMN. In particolare, si proiettano i moti non importanti (''time coarse-graining''), ottenendo modelli per la dinamica relativamente semplici, che descrivono esclusivamente i moti rilevanti rispetto all'osservabile fisico in esame. In particolare, si impiegano modelli stocastici nei quali intervengono anche parametri strutturali che devono essere calcolati. Questi ultimi sono descritti a livello atomistico e / o mesoscopico in base alla loro natura. Sono stati sviluppati tre nuovi programmi: E-SpiReS (Electron Spin Resonance Simulation) per la simulazione di spettri RSE in onda continua, C++OPPS (COupled Protein Probe Smoluchowski) per simulazioni di misure di RMN e DITE (DIffusion TEnsor) per il calcolo di proprieta' dissipative di molecole con gradi di liberta' interni. Nell'implementazione dei programmi si e' fatto attenzione alla semplicita' d'uso, occupandosi anche dello sviluppo di interfacce grafiche, con l'obiettivo di affiancare i programmi alla strumentazione di laboratorio, come una sorta di estensione ''in silico'' della stessa

Computational Electron Paramagnetic Resonance SpectroscopyReference Module in Chemistry, Molecular Sciences and Chemical Engineering

In this article, we want to review computational approach to the interpretation of EPR observables. We shall limit our discussion only to cw-EPR spectroscopy, leaving out, by necessity, advanced EPR spectroscopies like time domain multiple-pulse spin echo and double resonance methods. Also, we shall address here only examples and systems for which a clear separation can be drawn between fast local motions of solvent-related properties and large-amplitude molecular relaxation processes. Within this hypothesis, which actually can be said to encompass most experimental situations, averaging of magnetic properties with respect to rapidly relaxing solvent local motions is allowed, thus implying that constant principal values of all involved magnetic tensors can be used in the SLE per se. A relevant exception is given by highly polar and protic solvents, like water and ethanol, where the presence of specific directional H-bonds may lead to a residual explicit dynamic dependence of the magnetic properties from local solvent coordinates (e.g., the average number of H-bonds) to be included in the SL

Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study

We illustrate how the Jarzynski equality (JE), which is the progenitor of non-equilibrium methods aimed at constructing free energy landscapes for molecular-sized fluctuating systems subjected to steered transformations, can be applied to derive equations of state for bulk systems. The key-step consists of physically framing the computational strategy of "total energy morphing'', recently presented by us as an efficient implementation of the JE [M. Zerbetto, A. Piserchia, D. Frezzato, J. Comput. Chem., 2014, 35, 1865-1881], in terms of build-up of the real thermodynamic state of a bulk material from the corresponding ideal state, in which the particles are non-interacting. In this context, the JE machinery yields the excess free energy versus suitably chosen controlled state variables, whose thermodynamic derivatives eventually lead to the equation of state. As an explanatory case study, we apply the methodology to derive the equation of state of gaseous methane by constructing the Helmholtz free energy versus the particle density (at fixed temperature) and then evaluating the thermodynamic derivative with respect to the volume. In our intent, this "old-style'' work on gaseous methane should open the way for the investigation of thermodynamics of extended systems via non-equilibrium methods