Ground State Energy Of Electron Research Articles

Density dependence of excess electronic ground-state energies in simple atomic fluids

The ground-state energies of an excess electron E0 as a function of solvent density are computed using model electron–atom pseudopotentials in fluid helium, argon, and xenon. E0 is a lower bound to the experimentally measurable threshold to photoconductivity, V0. The nonuniqueness of the pseudopotential description of electron–molecule interactions is demonstrated. We find that when many-body polarization effects are included, our calculated E0 results are in close agreement with experimental V0 values indicating that the conduction-band energy lies close to the ground-state energy across a broad range of densities in these polarizable fluids. If the many-body nature of the polarization interaction is ignored the ground-state energies deviate significantly from the V0 results highlighting the importance of accurate treatment of many-body polarization interactions. It is shown that a mean-field theory of polarization gives substantial agreement with full many-body calculations. This allows us to introduce a mean-field, density-dependent pair potential which greatly simplifies such many-body calculations. In the more polarizable systems, it is found that the spatial extent of the ground-state wave function as a function of solvent density is correlated with the density dependence of both V0 and the electron mobility, and it becomes uniformly spread throughout our simulation cell as the electron mobility goes through its maximum value at intermediate solvent densities.

Quantum-confined Stark shift for differently shaped quantum wells

The quantum-confined Stark shift was calculated, using a numerical method, for eight differently shaped simple Al0.4Ga0.6As/AlxGa1-xAs quantum wells. The dependence of the electron and heavy-hole ground-state interband transition energy on external electric field, quantum well profile and its thickness was investigated. Calculations also include the excitation binding energy, the overlap of the electron and hole wavefunctions and their average spatial separation. A wider well has a larger Stark shift, independent of its shape. An extensive comparison was made of the field response to differently shaped wells having the same zero-field electron ground-state energy (78 meV). The thinnest was a 51 AA wide square well and the thickest a 261 AA asymmetric triangular well. The symmetric and asymmetric triangular wells were found to exhibit the largest Stark shifts but also had a larger reduction of the overlap and exciton binding energy. The square well, on the contrary, had the smallest Stark shift but also smaller variation of the overlap and exciton binding energy. Other wells exhibited characteristics between these two extreme cases.

Nonlocal exchange and kinetic-energy density functionals for electronic systems

The nonlocal weighted density approximation (WDA) to the exchange and kinetic-energy functionals of many electron systems proposed several years ago by Alonso and Girifalco is used to compute, within the framework of density functional theory, the ground-state electronic density and total energy of noble gas atoms and of neutral jellium-like sodium clusters containing up to 500 atoms. These results are compared with analogous calculations using the well known Thomas–Fermi–Weizsacker–Dirac (TFWD) approximations for the kinetic (TFW) and exchange (D) energy density functionals. An outstanding improvement of the total and exchange energies, of the density at the nucleus and of the 〈r−1〉 expectation values is obtained for atoms within the WDA scheme. For sodium clusters we notice a sizeable contribution of the nonlocal effects to the total energy and to the density profiles. In the limit of very large clusters these effects should affect the surface energy of the bulk metal. © 1992 John Wiley & Sons, Inc.

Electronic States in Quantum Wells with Interface Defects11The project supported by National Natural Science Foundation of China under granted No. 9687006-01 and 19004006

Effects of interface defects on electronic states in quantum wells (QWs) are investigated theoretically by introducing a coordinate transformation that transforms QWs with defective interfaces to those with planar interfaces plus an effective potential associated with interface defects. The interface defects are idealized as a cylindrical hollow protruding into the barrier materials on one of the interfaces. Electronic ground state energies are calculated variationally aa functions of the defect lateral sizes. For QWS with the well width d less than 150 Å, the changes in electronic energies due to interface defects will produce sizable effects on optical experiments, such as broadenings of excitation spectra of QWs. But our calculation predicts smaller spectrum broadenings than those predicated by the previous theory for the same interface disorder.

Band offset determination from conduction band filling in InGaAs/GaAs quantum wells

Conduction band filling experiments are performed on InGaAs/GaAs quantum well samples under intense optical excitation. The Quasi-Fermi level pinning at the quantum well edge and the well luminescence saturation is used to measure the electron ground state energy relative to the quantum well edge. The conduction band offset calculated using this energy value is found to be independent of the In fraction and equal to 0.6.

Density dependence of the ground-state energy of excess electrons in liquid methane

The ground-state energy (V0) of excess electrons in liquid methane is calculated as a function of liquid density. In the calculation, we use a high-precision molecular potential which satisfactorily describes the scattering of low-energy electrons in the gas phase. Our results are found to reproduce very well the experimental V0 values.

Ground state correlation energy of the Be-sequence forZ=4?20 in MCDF approximation

The ground state (J=0) electronic correlation energy of the 4-electron Be-sequence is calculated in the Multi-Configuration Dirac-Fock approximation forZ=4–20. The 4 electrons were distributed over the configurations arising from the 1s, 2s, 2p, 3s, 3p and 3d orbitals. Theoretical values obtained here are in good agreement with experimental correlation energies.

Cluster method for the calculation of the electronic density and the ground-state energy of an insulator: Application to solid helium

We propose a new method based on small clusters with the constraint of periodic symmetry to compute electron density and ground-state electronic energy of solids. Calculations are carried out on h.c.p. solid helium, and the Hartree-Fock density is shown to differ from the sum of atomic densities. The correlation energy is responsible for the existence of a small attractive energy per atom, which depends on the lattice parameters. The binding energy per atom cannot be expressed as the sum of two-atom interatomic potentials, but interatomic interactions to higher order must be included. Their effect is to decrease the Van der Waals attraction and to increase the hard-core repulsion.

Notes on the theory of atom/molecule-surface scattering

The aim of this lecture is to discuss in as pedagogic a fashion as possible and from the point of view of theory some aspects of collision phenomena at surfaces. These phenomena can be very complicated. In particular collisions that result in chemical reaction – e.g., dissociation of molecules – are complex in the sense that the adiabatic approximation, where the electrons are assumed to adapt instantaneously to the motion of the nuclei, is invariably suspect and often manifestly irrelevant. The theoretical problem posed by such collisions is therefore rather intractable and only very simple model systems can be treated [1]. I restrict myself of mechanical collisions characterized by a single potential energy surface V(rp, {ri}), where rp, {ri} are the coordinates of the particle, P, and the lattice nuclei, respectively. V is the electronic ground-state energy with the nuclear coordinates held fixed. This restriction simplifies the problem, which, however, remains far from trivial. We are still left with a many-body-problem involving a potentially infinite number of particles that has been solved only numerically and in the classical limit. If we want more than this, we have to pick away at the problem as best we can using intuition and taking guidance from experiment.

Strongly correlated electron ground-state energy approximations for Anderson-like models

We report preliminary results of convergence properties for nonperturbative resolvent approximations to Anderson-like models of magnetic ions in metals. Our study is initially focused on the spin- 1/2 Anderson model for magnetic impurities, but the methods studied can include multiplet and crystal-field effects which are needed for more accurate descriptions of real systems. We will compare the nonperturbative Lanczos method (tridiagonalization) and similar truncation schemes to exact ground-state energies for the impurity model and assess the efficacy of these nonperturbative approaches to understanding the Anderson lattice, heavy fermions, and other strongly interacting electronic systems.

The water-membrane interface as a substrate for H+-H+ superflow

Mobile protons in water bound at the interface with the membrane are analogous in a number of respects to the conduction electrons in a thin layer of metal spread on the surface of a dielectric. The hypothesis analyzed in this paper is that such mobile hydrogen bonds may be paired by propagating electronic oscillations in polar side groups of the membrane. The model is dual to the BCS theory of electronic superconductivity in that (1) the mobile H+ bonds play the role of conduction electrons and (2) the pairing interaction has its origin in electronic excitations rather than lattice vibrations. The pairing mechanism is similar to that in Little's proposed room temperature organic superconductor, except that it involves transient alterations in ground state energies of polarizable electrons in a colorless membrane rather than polarization of dye-like side groups. Numerical estimates based on formulae applicable to metallic superconductors show that condensation of proton pairs would be feasible in small connected domains on the membrane surface if the water structure is closely packed and the effective mass of the protons sufficiently reduced (though significant disanalogies between the bound water and metal cases make the quantitative applicability of these formulae unlikely). Some of the factors that favor a superfluid transition are high salt concentration, polarizable macromolecules on the membrane that increase the three-dimensionality of the interaction, and the presence of proton donors and acceptors other than oxygen. The dynamic order inherent in a proton superflow could provide the basis for a wide variety of highly ordered motions in biological systems.

Generation of ground electronic state haloalkyl radicals in the gas phase

Gaseous haloalkyl radicals were prepared by the photolysis of iodohaloalkanes in Pyrex vessels containing mercury (I) halides. Cleavage of the carbon-iodine bond gave mercury (II) halide and a radical which was subsequently shown to react on the ground state electronic energy surface. The usefulness of this method for chemical activation rate constant studies is illustrated by measurement of unimolecular rate constants for decomposition of CH2ClCH2Cl and CF3CH3. Possible mechanisms for photodecomposition of iodoalkanes in the presence of mercury (I) halides are discussed.

Dimensional interpolation for two-electron atoms

The ground-state electronic energy of helium-like atoms is calculated by interpolating between exact solutions for the limiting cases of one-dimensional and infinite-dimensional systems. In suitably scaled coordinates, the D=1 limit corresponds to replacing the Coulombic potentials by delta functions. With another choice of scaling, the D=∞ limit reduces to a classical electrostatic problem; the electrons take fixed positions that correspond to replacing wave functions with delta functions. The ground-state energy for arbitrary dimension D and nuclear charge Z can be represented as εD=ε∞[1+c1/D+c2/D2+F(D,Z)/D3]. The first three terms are obtained from a perturbation expansion about D=∞; these correspond, respectively, to the limiting rigid electronic structure (envisioned by G. N. Lewis!) and to harmonic and anharmonic vibrations about that structure. The interpolation function F(D,Z) is approximated as a geometric series, determined by fitting the accurately known energies for the D=1 limit and for D=5. This procedure yields an accuracy of 2 parts in 105 or better for D=3 and Z≥2. Study of the Z dependence reveals that at D=1 the perturbation expansion in powers of 1/Z has a self-similar structure. Also, for each D there exists a critical nuclear charge Z*, with magnitude near 12, for which F(D,Z*)=0; the first three terms of the expansion about D=∞ then give the exact energy.

The parity violating energy differences between the enantiomers of α-amino acids

The parity-violating weak neutral current perturbation of the groundstate electronic energy has been calculated, using ab initio methods, for the series of α-amino acids glycine, alanine, valine, serine and aspartic acid. It is found that the WNC energy shifts for these fundamental biomolecules consistently favour the existence of the natural L-enantiomers in preference to the unnatural mirror image D-enantiomers for the molecular conformations preferred in aqueous media. The parity violating energy differences between enantiomers are small, of the order 10-14 J mol-1, and highly sensitive to molecular conformation. The significance of the energy difference between enantionmers arising from the electroweak interactions with reference to the transition from a prebiotic racemic geochemistry to the terrestrial homochiral biochemistry is discussed.

Thermodynamic properties of bcc crystals at high temperatures: The transition metals.

The second-neighbor central-force model of a bcc crystal, previously used in lowest-order anharmonic perturbation theory to calculate the thermodynamic properties of the alkali metals, is here applied to the transition metals V, Nb, Ta, Mo, and W. The limitations of the model are apparent in the thermal-expansion results, which fall away from the experimental trend above about 1800 K. The specific heat similarly fails to exhibit the sharp rise that is observed at higher temperatures. A static treatment of vacancies cannot account for the difference between theory and experiment. The electrons have been taken into account by using a model that specifically includes d-band effects in the electron ground-state energy. The results thus obtained for the bulk moduli are quite satisfactory. In the light of these results, we discuss the prerequisites for a better treatment of metals when the electrons play an important role in determining the thermodynamic properties.

One-electron diatomics in momentum space. I. Implication of first iterated solutions for the ground state

For one-electron diatomic systems, an iterative solution of the momentum-space Schrödinger equation is examined using the Fock transformation which enables us to expand the kernel of the integral equation by the four-dimensional spherical harmonics. Starting from the united atom (UA) and simple LCAO approximations, first iterated solutions are derived and their properties are analyzed. The corresponding approximate energy eigenvalues are also obtained as a function of the internuclear distance R. The result from the LCAO starting function is found to be reliable semiquantitatively: in the range of 0≤R≤20, the maximum errors of the ground-state electronic energy are 4.7% and 1.7%, respectively, for the H+2 and HeH2+ systems, when compared with the exact values.

Analysis of low-energy electron transmission experiments through thin solid xenon films in the elastic scattering region.

In this paper, we derive a relation between the current ${I}_{t}$ transmitted by a thin dielectric film as a function of incident electron energy E and the electronic energy-band structure of the film, with application to solid xenon. The analysis of ${I}_{t}$(E) in the elastic scattering region allows one to determine the electronic conduction-band density of states and to calculate the electron mean free path as a function of energy. It provides also a useful tool for determining the quasi-free electron ground-state energy ${V}_{0}$ of the solid.

The electroweak origin of biomolecular handedness

The parity-violating weak neutral current perturbation of the ground-state electronic energy has been calculated by ab initio methods for glycine over a range of chiral conformations, for L-alanine, L-α-aminopropionitrile, and for the peptide residue of polypeptides in the α-helix and the β-sheet conformation. It is found that L-alanine in its preferred conformation in aqueous solution and the L-peptides in the α-helix and the β-sheet conformation, have a lower ground-state energy than the corresponding D-enantiomers, because of the electroweak interaction. The enantiomer energy difference is small, of the order of 10 -14 J mol -1 , corresponding to an enantiomeric excess of 10 6 molecules of L-alanine or the L-peptide in one mole of the corresponding racemic mixture in thermodynamic equilibrium at ambient temperature. The significance of the energy difference between enantiomers arising from the electroweak interaction for the transition from racemic geochemistry to homochiral biochemistry in terrestrial evolution is discussed.

The parity-violating energy difference between enantiomeric molecules

The parity-violating weak neutral current perturbation of the groundstate electronic energy has been calculated, by ab initio methods, for the (S)-isomer of hydrogen peroxide, over a range of standard Gaussian basis sets. The STO-N-31G, but not the STO-NG, sets give energy shifts E pv which converge with increasing N towards the corresponding E pv value given by an extended basis. Calculations for α-amino acids, peptides, model helical systems, with the STO-6-31G basis, or with an analogous set for corre-sponding sulphur analogues, show that the E pv shift is sensitive in sign and magnitude to the molecular conformation generally. It is found that L-alanine and the L-peptides in the α-helix and the β-sheet conformation have a lower ground state energy than the corresponding D-enantiomers due to the WNC interaction. The energy shift E pv only approximates to an expected Z 5 proportionality, and it does not correlate consistently in sign with the handedness of a helical system.

Ground state energy of the fractional quantised Hall system

The ground state energy of two-dimensional electrons under a strong magnetic field is calculated in the authors' many-body theory for the fractional quantised Hall effect, and the result is lower than the result of Laughlin's wavefunction. The presence of the energy gap at fractional fillings provides a downward cusp in the correlation energy which makes those states stable to produce quantised Hall steps. The ground state has a broken symmetry and no pinning.