Potential energy and free energy landscapes

Familiar concepts for small molecules may require reinterpretation for larger systems. For example, rearrangements between geometrical isomers are usually considered in terms of transitions between the corresponding local minima on the underlying potential energy surface, V. However, transitions between bulk phases such as solid and liquid, or between the denatured and native states of a protein, are normally addressed in terms of free energy minima. To reestablish a connection with the potential energy surface we must think in terms of representative samples of local minima of V, from which a free energy surface is projected by averaging over most of the coordinates. The present contribution outlines how this connection can be developed into a tool for quantitative calculations. In particular, stepping between the local minima of V provides powerful methods for locating the global potential energy minimum, and for calculating global thermodynamic properties. When the transition states that link local minima are also sampled we can exploit statistical rate theory to obtain insight into global dynamics and rare events. Visualizing the potential energy landscape helps to explain how the network of local minima and transition states determines properties such as heat capacity features, which signify transitions between free energy minima. The organization of the landscape also reveals how certain systems can reliably locate particular structures on the experimental time scale from among an exponentially large number of local minima. Such directed searches not only enable proteins to overcome Levinthal's paradox but may also underlie the formation of "magic numbers" in molecular beams, the self-assembly of macromolecular structures, and crystallization.     

Global energy minimization by rotational energy embedding

Given a sufficiently good empirical potential function for the internal energy of molecules, prediction of the preferred conformations is nearly impossible for large molecules because of the enormous number of local energy minima. Energy embedding has been a promising method for locating extremely good local minima, if not always the global minimum. The algorithm starts by locating a very good local minimum when the molecule is in a high-dimensional Euclidean space, and then it gradually projects down to three dimensions while allowing the molecule to relax its energy throughout the process. Now we present a variation on the method, called rotational energy embedding, where the descent into three dimensions is carried out by a sequence of internal rotations that are the multidimensional generalization of varying torsion angles in three dimensions. The new method avoids certain kinds of difficulties experienced by ordinary energy embedding and enables us to locate conformations very near the native for avian pancreatic polypeptide and apamin, given only their amino acid sequences and a suitable potential function.     

Relaxation of internal energy and collisional energy transfer

Using the exponential model for the collisional transition probability, it is shown that relaxation of average internal energy is a measure of bulk-average energy transfer ?ΔE?. This is a macroscopic property which is a complicated function of both time and initial excitation and is only distantly related to average energy transferred per collision ?ΔE?, a microscopic property.     

Ground state potential energy curve and dissociation energy of MgH

New high-resolution visible emission spectra of the MgH molecule have been recorded with high signal-to-noise ratios using a Fourier transform spectrometer. Many bands of the A 2Pi-->X 2Sigma+ and B' 2Sigma+-->X 2Sigma+ electronic transitions of 24MgH were analyzed; the new data span the v' = 0-3 levels of the A 2Pi and B'2Sigma+ excited states and the v'=0-11 levels of the X 2Sigma+ ground electronic state. The vibration-rotation energy levels of the perturbed A 2Pi and B' 2Sigma+ states were fitted as individual term values, while those of the X 2Sigma+ ground state were fitted using the direct-potential-fit approach. A new analytic potential energy function that imposes the theoretically correct attractive potential at long-range, and a radial Hamiltonian that includes the spin-rotation interaction were employed, and a significantly improved value for the ground state dissociation energy of MgH was obtained. The v'=11 level of the X 2Sigma+ ground electronic state was found to be the highest bound vibrational level of 24MgH, lying only about 13 cm(-1) below the dissociation asymptote. The equilibrium dissociation energy for the X 2Sigma+ ground state of 24MgH has been determined to be De=11104.7+/-0.5 cm(-1) (1.37681+/-0.00006 eV), whereas the zero-point energy (v'=0) is 739.11+/-0.01 cm(-1). The zero-point dissociation energy is therefore D0=10365.6+/-0.5 cm(-1) (1.28517+/-0.00006 eV). The uncertainty in the new experimental dissociation energy of MgH is more than 2 orders of magnitude smaller than that for the best value available in the literature. MgH is now the only hydride molecule other than H2 itself for which all bound vibrational levels of the ground electronic state are observed experimentally and for which the dissociation energy is determined with subwavenumber accuracy.     

Reversible energy transfer

Analysis of the transient and steady-state kinetics of reversible energy transfer shows that while the interpretation of lifetime measurements is difficult unless the donor and acceptor lifetimes are appreciably different, quantum yield measurements are relatively easy to interpret.

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Zusammenfassung Die Analyse der Kinetik der Übergangszustände und der stationären Zustände der reversiblen Energieübertragung zeigt, daß im Gegensatz zu einer schwierigen Interpretation der Messungen der Lebensdauer — es sei denn die Lebensdauer von Donor und Acceptor sind wesentlich voneinander verschieden — die Messungen der Quantumausbeute verhältnismäßig einfach zu interpretieren sind.

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Résumé L'analyse de la cinétique de l'état transitoire et de l'état stationnaire du transfert réversible d'énergie montre que, si l'interprétation des mesures de durée de vie est difficile, à moins queles durées de vie du donneur et de l'accepteur soient très différentes, il est par contre relativement facile d'interpréter les mesures de rendement quantique.

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Dedicated to the memory of Professor K. H. Hansen.     

Bond energy, aromatic stabilization energy and strain in IPR fullerenes

Various models applied to DFT structures and energies of 2-D and 3-D aromatic molecules shed new light on the effects of strain and aromaticity in these systems. The cyclic pi electron delocalisation does not stabilize the fullerene C60 formation; and 5-6 and 6-6 CC bonds have near-identical bond stretch potentials.     

A three-dimensional He-NaH potential energy surface for rovibrational energy transfer studies

A three-dimensional potential energy surface for the He-NaH van der Waals complex is calculated at the coupled cluster singles-and-doubles with noniterative inclusion of connected triples [CCSD(T)] level of theory. Estimates of CCSD(T) interaction energies for an infinitely large basis set is obtained using a basis set extrapolation scheme. The He-NaH potential energy surface is much different than the He-LiH surface. In particular, the He-NaH system has a binding energy of De=19.73 cm(-1) in comparison to De=176.7 cm(-1) for He-LiH. These minima are at the theta=180 degrees linear geometry where the helium is located at the metal end of the metal hydride. The He-NaH and He-LiH potentials are very similar for the theta=0 degrees linear geometry. The He-NaH potential energy surface supports one vibrational bound state with E=-1.48 cm(-1). Since this energy is smaller than the accuracy of the potential energy surface, the existence of a bound He-NaH complex is questionable.     

Kinetic energy density study of some representative semilocal kinetic energy functionals

There is a number of explicit kinetic energy density functionals for noninteracting electron systems that are obtained in terms of the electron density and its derivatives. These semilocal functionals have been widely used in the literature. In this work, we present a comparative study of the kinetic energy density of these semilocal functionals, stressing the importance of the local behavior to assess the quality of the functionals. We propose a quality factor that measures the local differences between the usual orbital-based kinetic energy density distributions and the approximated ones, allowing us to ensure if the good results obtained for the total kinetic energies with these semilocal functionals are due to their correct local performance or to error cancellations. We have also included contributions coming from the Laplacian of the electron density to work with an infinite set of kinetic energy densities. For all but one of the functionals, we have found that their success in the evaluation of the total kinetic energy is due to global error cancellations, whereas the local behavior of their kinetic energy density becomes worse than that corresponding to the Thomas-Fermi functional.     

Empirical energy functions for energy minimization and dynamics of nucleic acids

An improved empirical energy function for energy minimization and dynamics calculations of nucleic acids is developed and evaluated by an examination of its representation of both static and dynamic properties of model systems. Among the properties studied and used for parameter optimization are base pairing interactions, sugar and phosphate energy surfaces, small crystal heats of sublimation, base, phosphate and sugar analogue vibration spectra, and the overall behavior of a DNA hexamer duplex in vacuum molecular dynamics simulations. The results obtained are compared with those from two other energy functions that have been used recently for nucleic acids. Parameters for two energy functions are given; one includes heavy atoms and only polar hydrogens and the other includes all atoms.     

Overview on conducting polymer in energy storage and energy conversion system

Polymer-based electrochemical devices such as supercapacitor, battery, and fuel cell have been developed and advanced for energy related application. In this regard, conducting polymers own several tunable characteristics for energy conversion and energy storage relevance. Consequently, efficient, reliable, low cost, conducting, stable, and environment friendly energy systems have been developed using conducting polymers. To enhance the efficiency and commercialization of energy systems, design, structure, composition, and fabrication technique used for conducting polymers and related composite have been focused. Challenges and future trend associated with current state of the art conducting polymer materials in supercapacitor, battery, and fuel cell are highlighted.     

Application of PCM thermal energy storage system to reduce building energy consumption

The building sector is known to make a large contribution to total energy consumption and CO₂ emissions. Phase change materials (PCMs) have been considered for thermal energy storage (TES) in buildings. They can balance out the discrepancies between energy demand and energy supply, which are temporally out of phase. However, traditional PCMs need special latent storage devices or containers to encapsulate the PCM, in order to store and release the latent heat of the PCM. The proper design of TES systems using a PCM requires quantitative information and knowledge about the heat transfer and phase change processes in the PCM. In Korea, radiant floor heating systems, which have traditionally been used in residential buildings, consume approximately 55% of the total residential building energy consumption in heating. This article reviews the development of available latent heat thermal energy storage technologies and discusses PCM application methods for residential building using radiant floor heating systems with the goal of reducing energy consumption.     

Nanostructured energy materials for electrochemical energy conversion and storage: A review

Nanostructured materials have received tremendous interest due to their unique mechanical/electrical properties and overall behavior contributed by the complex synergy of bulk and interfacial properties for efficient and effective energy conversion and storage. The booming development of nanotechnology affords emerging but effective tools in designing advanced energy material. We reviewed the significant progress and dominated nanostructured energy materials in electrochemical energy conversion and storage devices, including lithium ion batteries, lithium–sulfur batteries, lithium–oxygen batteries, lithium metal batteries, and supercapacitors. The use of nanostructured electrocatalyst for effective electrocatalysis in oxygen reduction and oxygen evolution reactions for fuel cells and metal–air batteries was also included. The challenges in the undesirable side reactions between electrolytes and electrode due to high electrode/electrolyte contact area, low volumetric energy density of electrode owing to low tap density,and uniform production of complex energy materials in working devices should be overcome to fully demonstrate the advanced energy nanostructures for electrochemical energy conversion and storage. The energy chemistry at the interfaces of nanostructured electrode/electrolyte is highly expected to guide the rational design and full demonstration of energy materials in a working device.     

Binding free energy, energy and entropy calculations using simple model systems

Free energy differences are calculated for a set of two model host molecules, binding acetone and methanol. Two active sites of different characteristics were constructed based on an artificially extended C60 fullerene molecule, possibly functionalised to include polar interactions in an otherwise apolar, spherical cavity. The model host systems minimise the necessary sampling of conformational space while still capturing key aspects of ligand binding. The estimates of the free energies are split up into energetic and entropic contributions, using three different approaches investigating the convergence behaviour. For these systems, a direct calculation of the total energy and entropy is more efficient than calculating the entropy from the temperature dependence of the free energy or from a direct thermodynamic integration formulation. Furthermore, the compensating surrounding–surrounding energies and entropies are split off by calculating reduced ligand-surrounding energies and entropies. These converge much more readily and lead to properties that are more straightforwardly interpreted in terms of molecular interactions and configurations. Even though not experimentally accessible, the reduced thermodynamic properties may prove highly relevant for computational drug design, as they may give direct insights into possibilities to further optimise ligand binding while optimisation in the surrounding–surrounding energy or entropy will exactly cancel and not lead to improved affinity.     

Self-charging power system for distributed energy: beyond the energy storage unit

Power devices for the smart sensor networks of Internet of things (IoT) are required with minimum or even no maintenance due to their enormous quantities and widespread distribution. Self-charging power systems (SCPSs) refer to integrated energy devices with simultaneous energy harvesting, power management and effective energy storage capabilities, which may need no extra battery recharging and can sustainably drive sensors. Herein, we focus on the progress made in the field of nanogenerator-based SCPSs, which harvest mechanical energy using the Maxwell displacement current arising from the variation in the surface-polarized-charge-induced electrical field. Prototypes of different nanogenerator-based SCPSs will be overviewed. Finally, challenges and prospects in this field will be discussed.

Recent progresses and future prospects on nanogenerator-based self-charging power systems (SCPSs) are discussed with this perspective.     

Mapping potential energy surfaces

A recently proposed dynamical method [A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)] allows us to globally sample the free energy surface. This approach uses a coarse-grained non-Markovian dynamics to bias microscopic atomic trajectories. After a sufficiently long simulation time, the global free energy surface can be reconstructed from the non-Markovian dynamics. Here we apply this scheme to study the T=0 free energy surface, i.e., the potential energy surface in coarse-grained space. We show that the accuracy of the reconstructed potential energy surface can be dramatically improved by a simple postprocessing procedure with only minor computational overhead. We illustrate this approach by conducting conformational analysis on a small organic molecule, demonstrating its superiority over traditional unbiased approaches in sampling potential energy surfaces in coarse-grained space.     

Topology of energy hypersurfaces

Some of the basic notions of chemistry, associated with an energy function of several variables, are shown to be of topological character. Properties of potential energy hypersurfaces, structural relations, models for interconversion processes and transformations between such models suggest a topological theory (reaction topology) for the analysis of potential energy hypersurfaces. By introducing appropriate topologies into the nuclear configuration spaceR and equivalent topologies on the energy hypersurfaceE, rigorous definitions are given for fundamental chemical concepts such asmolecular structure andreaction mechanism. These definitions are based on the properties of the expectation value of energy, a quantum mechanical observable. Topologies based on curvature, structural and energetic relations of the energy hypersurface are proposed for a theoretical interpretation of molecular processes.