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.     

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.     

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.     

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.     

Partitioning of atomization energy

The present work provides a technique for partitioning the atomization energy of a molecule into diatomic contributions. The method is largely based on the redistribution of the kinetic energy term in Mayer's energy partitioning and uses free‐atom energies as a reference. The comparison of Mayer's original method, the alternative Ichikawa–Yoshida approach, and the new atomization energy partitioning (AEP) shows that the new approach has advantages in describing trends in diatomic energies in molecules with triple bonds, as well as for hydrogen bonds. The proposed AEP is a viable alternative to Mayer's energy partitioning method. © 2007 Wiley Periodicals, Inc. Int. J. Quantum Chem, 2008     

Strain energy of phenanthrene

The strain energy of phenanthrene was derived to be (4.9 ± 2.8) kJ · mol⁻¹, on the basis of the latest standard enthalpies of formation of polycyclic aromatic hydrocarbons. This strain energy agrees well with those estimated from a semi-empirical calculation and from the basicity in hydrogen fluoride solution. The calculation again confirmed the standard enthalpy of formation of phenanthrene, Δ_fH⁰(g)=(201.7±2.9) kJ · mol⁻¹ at T=298.15 K, which was determined by Nagano (J. Chem. Thermodyn. 34 (2002) 377–383). The coupling constant J_4,5 in ¹H-n.m.r. spectrum of phenanthrene in CDCl₃ solution was determined to be 0.55 Hz, which indicates no significant through-space coupling between the 4- and 5-hydrogens.     

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.     

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.     

Reactive domains of energy hypersurfaces and the stability of minimum energy reaction paths

Special properties of the Riemannian metric for energy hypersurfaces, defined within the framework of the Born-Oppenheimer approximation, are utilized in devising a partitioning scheme for domains of nuclear coordinates. The chemically important coordinate domains are distinguished from domains of lesser importance by their curvature properties. Conditions are derived for the stability of minimum energy reaction paths, and the effects of instability regions are investigated. Instability domains along minimum energy paths may allow small vibrational perturbations to alter the outcome of the chemical reaction.     

Correlation energy extrapolation by intrinsic scaling. V. Electronic energy, atomization energy, and enthalpy of formation of water

The method of correlation energy extrapolation by intrinsic scaling, recently introduced to obtain accurate molecular electronic energies, is used to calculate the total nonrelativistic electronic ground state energy of the water molecule. Accurate approximations to the full configuration interaction energies are determined for Dunning's [J. Chem. Phys. 90, 1007 (1989)] correlation-consistent double-, triple- and quadruple-zeta basis sets and then extrapolated to the complete basis set limit. The approach yields the total nonrelativistic energy -76.4390+/-0.0004 hartree, which compares very well with the value of -76.4389 hartree derived from experiment. The energy of atomization is recovered within 0.1 mh. The enthalpy of formation, which is obtained in conjunction with our previous calculation of the dissociation energy of the oxygen molecule, is recovered within 0.05 mh.     

Valence energy in variational Monte Carlo: CuH dissociation energy

We show how to estimate the dissociation energy of CuH using the variational Monte Carlo method. The techniques involved are (i) an all-electron approach, (ii) a diffusion-only Metroplis algorithm which is well-suited for sampling the nodal regions properly, and (iii) a core-valence partitioning scheme such that the dissociation energy is estimated from the valence energies of CuH and Cu only. This approach avoids several of the approximations inherent in pseudopotential methods. Using relatively crude wave functions, we obtain an estimate of the dissociation energy and dipole moment with an accuracy on par with much more elaborate calculations in the literature. © 1996 John Wiley & Sons, Inc.     

Calculation of the size dependence of the ionization energy and autoionization energy of Hg-clusters

To study the transition from van der Waals to metallic bonding we calculate the size dependence of the ionization energy and 5d→6p autoionization energy of Hg _n -clusters using a parametrized LCAO model. Our results are in good qualitative agreement with experiment. Comparison with experimental results suggests that electron correlations play an important role for the transition from localized (van der Waals-like) to delocalized (covalent or metallic) electronic states occuring in Hg _n atn?13–19.     

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.     

An ab initio potential energy surface and vibrational energy levels of ZnH2

A three‐dimensional potential energy surface of the electronic ground state of ZnH₂ (${X}^1\sum _g^ +$ ) molecule is constructed from more than 7500 ab initio points calculated at the internally contracted multireference configuration interaction with the Davidson correction (icMRCI+Q) level employing large basis sets. The calculated relative energies of various dissociation reactions are in good agreement with the previous theoretical/experimental values. Low‐lying vibrational energy levels of ZnH₂, ZnD₂, and HZnD are calculated on the three‐dimensional potential energy surface using the Lanczos algorithm, and found to be in good agreement with the available experimental band origins and the previous theoretical values. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A model for the free energy of adsorption on low energy surfaces.

In constructing a generalized thermodynamics for the fluid-vapor-solid equilibrium in poorly wetted systems the specific free energy of adsorption at saturation vapor pressure is a basic and elusive term. If the adsorbed phase is modeled as a two dimensional gas, systems for which a complete spectrum of data is available can serve as an empirical basis for constructing and testing adsorption-contact angle relationships. From the extension of such relationship other often inassessible terms can be estimated. Such a construct is reported here and extended to the estimation of the excess adsorption entropy at saturation vapor pressure in non-wetting systems     

Theoretical study on the potential energy surface and vibrational energy levels of HXeI

The potential energy surface for the electronic ground state of the HXeI molecule is constructed by using the internally contracted multi-reference configuration interaction with the Davidson correction（icMRCI＋Q）method and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces.The three-body dissociation channel is found to be the dominate dissociation channel for HXeI.Based on the obtained potentials,vibrational energy levels of HXeI are calculated using the Lanczos algorithm.Our theoretical results are in excellent agreement with the available observed values.