Confined many-electron systems
TL;DR: In this article, the influence of spatial confinement on the physical and chemical properties of many quantum mechanical systems is discussed, including low-dimensional electron gas or impurity atoms in artificial mesoscopic scale semiconductor structures as well as atoms and molecules trapped in microscopic cavities like molecular zeolite sieves.
About: This article is published in Physics Reports.The article was published on 1996-06-01. It has received 348 citations till now. The article focuses on the topics: 1s Slater-type function & Mesoscopic physics.
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TL;DR: The variational method complemented with the use of explicitly correlated Gaussian basis functions is one of the most powerful approaches currently used for calculating the properties of few-body systems as mentioned in this paper.
Abstract: The variational method complemented with the use of explicitly correlated Gaussian basis functions is one of the most powerful approaches currently used for calculating the properties of few-body systems. Despite its conceptual simplicity, the method offers great flexibility, high accuracy, and can be used to study diverse quantum systems, ranging from small atoms and molecules to light nuclei, hadrons, quantum dots, and Efimov systems. The basic theoretical foundations are discussed, recent advances in the applications of explicitly correlated Gaussians in physics and chemistry are reviewed, and the strengths and weaknesses of the explicitly correlated Gaussians approach are compared with other few-body techniques.
278 citations
TL;DR: Phenomenological approaches on the basis of simple model potentials for the description of various situations where the atom is spacially confined, such as as atoms inside a C60-like environment or in impenetrable cavities of small radii are reviewed along with the trends in modifications in structure and photoionization of such confined atoms as mentioned in this paper.
202 citations
TL;DR: In this paper, the energy spectra of ground-state, ionized and excited multielectron atoms and ions of the 3d and 4d periods of the periodic table centred in impenetrable spherical confinement are detailed using Hartree-Fock configuration average calculations.
Abstract: The energy spectra of ground-state, ionized and excited multielectron atoms and ions of the 3d and 4d periods of the periodic table centred in impenetrable spherical confinement are detailed using Hartree-Fock configuration average calculations. It is shown explicitly for the first time that, owing to modifications in 3d and 4d orbital collapse, the filling of shells for the confined transition sequences becomes more regular than for free atoms with increasing confinement pressure, that s-d competition disappears, and that, for d-excited states, the crossings between inner-shell excited states and the double-ionization thresholds are altered. In general, the periodic table for confined (compressed) atoms can differ from that for free atoms. The importance of these findings for different branches of basic and applied physics and chemistry is indicated.
183 citations
TL;DR: The spherical confinement model leads to the ST values which satisfy the lower bound up to the limits of extreme confinements with the interesting new result displaying regions over which a set of upper and lower bounds to the information entropy sum can be locally prescribed.
Abstract: The Shannon information entropy of 1-normalized electron density in position and momentum space Sr and Sp, and the sum ST, respectively, are reported for the ground-state H, He+, Li2+, H-, He, Li+, Li, and B atoms confined inside an impenetrable spherical boundary defined by radius R. We find new characteristic features in ST denoted by well-defined minimum and maximum as a function of confinement. The results are analyzed in the background of the irreducible lower bound stipulated by the entropy uncertainty principle [I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975)]. The spherical confinement model leads to the ST values which satisfy the lower bound up to the limits of extreme confinements with the interesting new result displaying regions over which a set of upper and lower bounds to the information entropy sum can be locally prescribed. Similar calculations on the H atom in 2s excited states are presented and their novel characteristics are discussed.
156 citations
TL;DR: In this article, a hydrogen atom is embedded in an impenetrable spherical box and the dipole polarizability of the atom is evaluated at each confinement radius with respect to different plasma screening param- eters.
Abstract: Time dependent variation perturbation calculations have been performed for estimating the transition energies, os- cillator strengths and transition probability values for a few dipole allowed states of compressed hydrogen atom confined in a weakly coupled plasma. The compression is obtained by embedding the atom at the centre of an impenetrable spherical box. The dipole polarizability of the atom is evaluated at each confinement radius with respect to different plasma screening param- eters. The effect of pressure due to spatial confinement on the dipole polarizability and other atomic properties is analyzed. Results obtained are useful for the diagnostic determination of astrophysical and laboratory plasmas and for the calculation of collision rate coefficients needed for computing opacity of stellar envelopes - a quantity of importance in the context of stellar structure and pulsations.
124 citations
Cites background from "Confined many-electron systems"
...Basically the problem is similar to that of studying the spectra of compressed atoms like that trapped in zeolite, fullerenes or under high pressure (Jaskolski 1996; Connerade 2000; Gupta 1982)....
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46,339 citations
TL;DR: In this article, the authors proposed a truncated icosahedron, a polygon with 60 vertices and 32 faces, 12 of which are pentagonal and 20 hexagonal.
Abstract: During experiments aimed at understanding the mechanisms by which long-chain carbon molecules are formed in interstellar space and circumstellar shells1, graphite has been vaporized by laser irradiation, producing a remarkably stable cluster consisting of 60 carbon atoms. Concerning the question of what kind of 60-carbon atom structure might give rise to a superstable species, we suggest a truncated icosahedron, a polygon with 60 vertices and 32 faces, 12 of which are pentagonal and 20 hexagonal. This object is commonly encountered as the football shown in Fig. 1. The C60 molecule which results when a carbon atom is placed at each vertex of this structure has all valences satisfied by two single bonds and one double bond, has many resonance structures, and appears to be aromatic. Before 1985, it was generally accepted that elemental carbon exists in two forms, or allotropes: diamond and graphite. Then, Kroto et al. identified the signature of a new, stable form of carbon that consisted of clusters of 60 atoms. They called this third allotrope of carbon 'buckminsterfullerene', and proposed that it consisted of polyhedral molecules in which the atoms were arrayed at the vertices of a truncated icosahedron. In 1990, the synthesis of large quantities of C60 [see Nature 347, 354–358 (1990)] confirmed this hypothesis.
13,394 citations
Book•
01 Jan 1978
TL;DR: This book presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines as well as specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.
Abstract: This book is based on the author's experience with calculations involving polynomial splines. It presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines. After two chapters summarizing polynomial approximation, a rigorous discussion of elementary spline theory is given involving linear, cubic and parabolic splines. The computational handling of piecewise polynomial functions (of one variable) of arbitrary order is the subject of chapters VII and VIII, while chapters IX, X, and XI are devoted to B-splines. The distances from splines with fixed and with variable knots is discussed in chapter XII. The remaining five chapters concern specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting. The present text version differs from the original in several respects. The book is now typeset (in plain TeX), the Fortran programs now make use of Fortran 77 features. The figures have been redrawn with the aid of Matlab, various errors have been corrected, and many more formal statements have been provided with proofs. Further, all formal statements and equations have been numbered by the same numbering system, to make it easier to find any particular item. A major change has occured in Chapters IX-XI where the B-spline theory is now developed directly from the recurrence relations without recourse to divided differences. This has brought in knot insertion as a powerful tool for providing simple proofs concerning the shape-preserving properties of the B-spline series.
10,258 citations
TL;DR: In this paper, free standing Si quantum wires can be fabricated without the use of epitaxial deposition or lithography using electrochemical and chemical dissolution steps to define networks of isolated wires out of bulk wafers.
Abstract: Indirect evidence is presented that free‐standing Si quantum wires can be fabricated without the use of epitaxial deposition or lithography. The novel approach uses electrochemical and chemical dissolution steps to define networks of isolated wires out of bulk wafers. Mesoporous Si layers of high porosity exhibit visible (red) photoluminescence at room temperature, observable with the naked eye under <1 mW unfocused (<0.1 W cm−2) green or blue laser line excitation. This is attributed to dramatic two‐dimensional quantum size effects which can produce emission far above the band gap of bulk crystalline Si.
7,393 citations
TL;DR: In this paper, the electronic properties of inversion and accumulation layers at semiconductor-insulator interfaces and of other systems that exhibit two-dimensional or quasi-two-dimensional behavior, such as electrons in semiconductor heterojunctions and superlattices and on liquid helium, are reviewed.
Abstract: The electronic properties of inversion and accumulation layers at semiconductor-insulator interfaces and of other systems that exhibit two-dimensional or quasi-two-dimensional behavior, such as electrons in semiconductor heterojunctions and superlattices and on liquid helium, are reviewed. Energy levels, transport properties, and optical properties are considered in some detail, especially for electrons at the (100) silicon-silicon dioxide interface. Other systems are discussed more briefly.
5,638 citations