On the single-electron local kinetic energy

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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.     

The Influence of the Exchange-Correlation Functional on the Non-Interacting Kinetic Energy and Its Implications for Orbital-Free Density Functional ApproximationsSCI北大核心CSCD

In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.     

Phase Space View of Ensembles of Excited States

The density functional theory and its extension to ensembles of excited states can be formalized as thermodynamics. However, these theories are not unique because one of their key quantities, the kinetic energy density,can be defined in several ways. Usually, the everywhere positive gradient form is applied; however, other forms are also acceptable, provided they integrate to the true kinetic energy. Recently, a kinetic energy density of the ground-state theory maximizing the information entropy has been proposed. Here, ensemble kinetic energy density, leading to extremum information entropy, is derived via constrained search. The corresponding ensemble temperature is found to be constant.     

Classical kinetic energy,quantum fluctuation terms and kinetic-energy functionals

We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson’s stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsäcker term and an (N?1)-electron kinetic correlation term. We further show that the Weizsäcker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. We then write the N-electron classical kinetic energy as the sum of the (one-electron) classical kinetic energy and another (N?1)-electron kinetic correlation term. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsäcker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase, and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases. Finally, we underline that, although our aim in this paper is conceptual rather than practical, our results are potentially useful for the construction of improved kinetic-energy functionals.     

The main beam correction term in kinetic energy release from metastable peaks

The correction term for the precursor ion signal width in determination of kinetic energy release is reviewed, and the correction term is formally derived. The derived correction term differs from the traditionally applied term. An experimental finding substantiates the inaccuracy in the latter. The application of the “T ‐value” to study kinetic energy release is found preferable to kinetic energy release distributions when the metastable peaks are slim and simple Gaussians. For electronically predissociated systems, a “borderline zero” kinetic energy release can be directly interpreted in reaction dynamics with strong curvature in the reaction coordinate.     

Mapping the ion kinetic energy in a helium microwave plasma orthogonal acceleration time-of-flight mass spectrometer.

The ion kinetic energy of a helium microwave plasma is studied using an orthogonal acceleration time-of-flight mass spectrometer. The ions produced in the plasma are extracted into the mass spectrometer in an 'off-cone' mode (i.e. the helium plasma plume is off the sampler cone), and enter the repelling zone in the x-direction, which is perpendicular to the flight tube. The information of ion initial kinetic energy was obtained from both theoretical calculations and experimental results. The potential influence of two x-direction steering plates (X-steering plates) on the ion energy and signal intensity was examined. The influence of gas composition on the ion kinetic energy was also investigated. The calculated results show that ions with different m/z have different velocity and kinetic energy when they enter the ion modulation zone, and lighter ions have higher velocity and lower kinetic energy. The experimental results obtained demonstrate that the ion signals of different m/z produced with an 'off-cone' sampling helium microwave plasma show similar trends as calculated with the potential difference of the X-steering plates, revealing their narrow kinetic energy distribution in the x-direction. Under typical operating conditions, the x-direction kinetic energy of ions detected mostly range from about 14.9 eV for (7)Li(+) to 16.8 eV for (208)Pb(+).     

立方体纳米氧化亚铜反应动力学的理论及实验研究

为了探究纳米多相反应过程的动力学行为,本文通过液相还原法可控合成了粒度为55 nm的立方体氧化亚铜（Cu₂O）。基于纳米与块体Cu₂O的区别,采用原位微量热技术获取Cu₂O体系与HNO₃反应过程的热动力学精细信息,结合热动力学原理及动力学过渡态理论计算得到Cu₂O反应动力学参数,并建立立方体动力学模型讨论并佐证动力学实验结果。结果表明,纳米Cu₂O的反应速率常数大于块体,而表观活化能、指前因子、活化焓、活化熵和活化Gibbs自由能均小于块体;随着温度的升高,纳米Cu₂O的反应速率常数和活化Gibbs自由能均增大。动力学模型表明影响反应动力学参数的主要因素为：偏摩尔表面焓影响表观活化能,偏摩尔表面熵影响指前因子,偏摩尔表面Gibbs自由能影响反应速率常数。本文为纳米材料多相反应动力学参数的获取和分析应用提供了一种普适的理论模型和实验方法。     

Absolute partial cross sections and kinetic energy analysis for the electron impact ionization of ethylene

We present absolute partial electron impact ionization cross sections for ethylene in the electron energy range between threshold and 1000 eV measured with a two sector field double focusing mass spectrometer. Ion kinetic energy distribution functions have been measured at all electron energies by applying a deflection field method. Multiplication of the measured relative cross sections by the appropriately determined discrimination factors lead to accurate relative partial cross sections. Normalization of the sum of the relative partial cross sections to an absolute total cross section gives absolute partial cross section values. The initial kinetic energy distributions of several fragment ions show the presence of two or more contributions that exhibit different electron energy dependencies. Differential cross sections with respect to the initial kinetic energy of the ions are provided and are related to specific ion production channels. The electron threshold energies for the direct and numerous other dissociative ionization channels are determined by quantum chemical calculation and these allow the determination of the total kinetic energy release and the electron energy loss for the most prominent dissociative ionization channels.     

Photoelectron spectroscopy of naphthacene and perylene crystals by the rare gas emission lines

The energy distribution curves (EDC's) of the photoelectrons emitted from naphthacene (C₁₈H₁₂) and perylene (C₂₀H₁₂) crystals were measured using the rare gas resonance emission lines (He 21.22 eV, Ne 16.85 and 16.67 eV and Ar 11.83 and 11.62 eV). The peaks in the higher kinetic energy regions agree well with the peaks obtained from molecular photoelectron spectroscopy studies if constant energy shifts are assumed. In the lower kinetic energy regions, however, fixed kinetic energy peaks are found which are independent of the incident photon energies.     

Gradient corrections in the energy density functional

It is shown, by calculations in He and Ne with HF densities, that the improvement obtained when gradient corrections are added to the local approximation to the kinetic energy, arises from a detailed improvement in the kinetic energy density.     

Interatomic interactions in momentum space. Momentum density and kinetic energy in chemical bonding

On the basis of the virial theorem for a uniform scaling process of a polyatomic system, the total energy and its gradient are quantitatively related with the behavior of the electron density in momentum space through the kinetic energy of the system. For attractive and repulsive interactions, the behavior of the momentum density distribution and its effect on the stabilization energy and the interatomic force are examined. Some guiding principles are deduced for their interrelation. The results are used to clarify the role of kinetic energy in chemical bonding. Possible energy partitioning in this approach is also mentioned.     

The elimination of carbon monoxide from molecular ions of phenol and other [C6H6O]+˙ isomers

Phenol and five acyclic isomeric compounds have been investigated using electron impact and field ionization techniques, mass analysed ion kinetic energy spectrometry and collision induced dissociation mass analysed ion kinetic energy spectrometry. The kinetic energy release data corresponding to the elimination of carbon monoxide from the molecular ions show that at least two structures of the reactant ion are involved. The electron impact and field ionization collision induced dissociation mass analysed ion kinetic energy spectra indicate that under electron impact conditions, the phenol ion partially isomerizes to another ion structure. An isomerization of about 40% to the structure of cis-2-hexen-4-yn-1-al is in good accordance with the spectral data.     

Imaging ion-molecule reactions: charge transfer and C-N bond formation in the C(+) + NH3 system

The velocity mapping ion imaging method is applied to the ion-molecule reactions occurring between C(+) and NH(3). The velocity space images are collected over the relative collision energy range from 1.5 to 3.3 eV, allowing both product kinetic energy distributions and angular distributions to be obtained from the data. The charge transfer process appears to be direct, dominated by long-range electron transfer that results in minimal deflection of the products. The product kinetic energy distributions are consistent with a process dominated by energy resonance. The kinetic energy distributions for C-N bond formation appear to scale with the total available energy, providing strong evidence that energy in the [CNH(3)](+) precursor to products is distributed statistically. The angular distributions for C-N bond formation show pronounced forward-backward symmetry, as expected for a complex that resembles a prolate symmetric top decaying along its symmetry axis.     

Kinetic energy release in ionic fragmentations: Use as an ion structure probe

The kinetic energy released in unimolecular reactions, as measured from the width of the corresponding metastable peak, shows only a small dependence on such parameters as source temperature, ion-source residence time and ion acceleration voltage. Similarly, fragmenting ions generated from different members of an homologous series of molecular ions have been found to release the same kinetic energy and hence do not exhibit a degrees-of-freedom effect analogous to that for metastable abundances. In general, molecular ions formed by electron-impact have been found to release slightly less kinetic energy on fragmentation than the corresponding ions formed via a fragmentation sequence. These observations suggest that kinetic energy release is a useful method of structural characterization of metastable ions; while increase in the average internal energies of the ions sample lead to larger energy releases, this effect is usually small. The use of a very narrow energy resolving (β) slit and a procedure in which the metastable peak width is extrapolated to zero slit width has been found to improve the accuracy of measurement of the kinetic energy release, particularly when the metastable and main beam peak widths are of comparable magnitude.     

Quantum dynamics of the CH3 fragment: a curvilinear coordinate system and kinetic energy operators

A curvilinear coordinate system for AB(3) fragments is given. The corresponding exact kinetic energy operator is derived and a series of simpler, progressively more approximate kinetic energy operators are suggested. The operators are tailored for quantum dynamics simulations using the multiconfigurational time-dependent Hartree approach. It is outlined how these fragment coordinates can be utilized to set up coordinate systems for larger systems such as AB(3)C or AB(3)CD. Calculations of the vibrational levels of CH(3) and quantum dynamics studies investigate the accuracy of the different kinetic energy operators suggested.     

Electron kinetic energies from vibrationally promoted surface exoemission: evidence for a vibrational autodetachment mechanism

We report kinetic energy distributions of exoelectrons produced by collisions of highly vibrationally excited NO molecules with a low work function Cs dosed Au(111) surface. These measurements show that energy dissipation pathways involving nonadiabatic conversion of vibrational energy to electronic energy can result in electronic excitation of more than 3 eV, consistent with the available vibrational energy. We measured the dependence of the electron energy distributions on the translational and vibrational energy of the incident NO and find a clear positive correlation between final electron kinetic energy and initial vibrational excitation and a weak but observable inverse dependence of electron kinetic energy on initial translational energy. These observations are consistent with a vibrational autodetachment mechanism, where an electron is transferred to NO near its outer vibrational turning point and ejected near its inner vibrational turning point. Within the context of this model, we estimate the NO-to-surface distance for electron transfer.     

The interaction of slow positrons with organic moecules above and below positronium formation thresholds

A review is given of the ionization of organic moecules by monoenergetic positrons having energies in the range of 0.5–15 eV. Two mechanisms, unique to positrons, are described. If the kinetic energy of the positron is above the positronium formation threshold, such that electrons can be removed from the molecules to form free positronium atoms, the ionization/fragmentation behavior can be explained qualitatively by a modification of the Ore gap theory. To explain how positrons can ionize and fragment molecules when their kinetic energies are below the positronium formation threshold, it is necessary to assume that energy is transferred to the molecule by the annihilation process. Ionization cross sections for positrons having kinetic energies below the positronium formation threshold are sensitive to molecular size, structure and bond types. Continuing work involves a search for positronium compound formation and measurements of the kinetic energy distributions of ions.     

Study of the kinetic energy densities of electrons as applied to quantum dots in a magnetic field

There are three expressions for the kinetic energy density t( r ) expressed in terms of its quantal source, the single-particle density matrix: t _A( r ) , the integrand of the kinetic energy expectation value; t _B( r ) , the trace of the kinetic energy tensor; t _C( r ) , a virial form in terms of the ‘classical’ kinetic field. These kinetic energy densities are studied by application to ‘artificial atoms‘ or quantum dots in a magnetic field in a ground and excited singlet state. A comparison with the densities for natural atoms and molecules in their ground state is made. The near nucleus structure of these densities for natural atoms is explained. We suggest that in theoretical frameworks which employ the kinetic energy density such as molecular fragmentation, density functional theory, and information-entropic theories, one use all three expressions on application to quantum dots, and the virial expression for natural atoms and molecules. New physics could thereby be gleaned.