One-electron Energy Research Articles

Fast method for quantum chemical calculations of large molecules with the approximation of the DFT Hamiltonian

The fundamentally new method NESE is proposed for quantum chemical calculations of large molecules, which employs the approximation of the Hamiltonian of the commonly used DFT method and is as fast as the AM1 and PM3 semi-empirical methods or the DFTB method. The parameters for the new method were chosen by the least-squares method based on the comparison of its matrix elements with the reference DFT/PBE Hamiltonian. The initial non-iterative version NESE-0 was computer-implemented and approved on many thousands of various molecules containing H, C, N, and O atoms. The NESE-0 method moderately outperforms the DFTB approach and is an order of magnitude better than the AM1, PM3, and PM6 levels in reproducing the one-electron energies calculated in terms of the DFT/PBE.

Influence of bulk inversion asymmetry on the magneto-optical spectrum of a HgTe topological insulator

The influence of bulk inversion asymmetry in [001] and [013] grown HgTe quantum wells is investigated theoretically. The bulk inversion asymmetry leads to an anti-crossing gap between two zero-mode Landau levels in a HgTe topological insulator, i.e., the quantum well with inverted band structure. It is found that this is the main contribution to the anti-crossing splitting observed in recent experimental magneto spectroscopic measurements. The relevant optical transitions involve different subbands, but the electron-electron interaction induced depolarization shift is found to be negligibly small. It is also found that the splitting of this anti-crossing only depends weakly on the tilting angle when the magnetic field is tilted away from the perpendicular direction to the quantum well. Thus, the strength of bulk inversion asymmetry can be determined via a direct comparison between the theoretical calculated one-electron energy levels and experimentally observed anti-crossing energy gap.

An approximate approach to calculate the potential acting on an electron in a molecule and construct the molecular face

The molecular face (MF) consists of all the classical turning points of electron movement in a molecule, and it is an iso-PAEM (the potential acting on an electron in a molecule) contour where PAEM (or one-electron energy) equals the negative value of ionization energy (-IE) of the molecule. It is the classical-forbidden region for an electron movement outside the MF, whereas it is the classical-permitted region enclosed by the MF. In this work, we developed an approximate method for quickly constructing the MF. To evaluate this method, we compared the MFs of the original and approximate methods for a series of molecules, such as some homologues, unsaturated hydrocarbons and haloalkanes. Furthermore, we showed the distributions of Fukui descriptors f+(r) and f−(r) on the MFs for haloalkanes, and heterocyclic compounds. Results showed that the approximate calculations are consistent with the exact calculations not only in representing molecular surface but also in predicting the ordering of activities. Armed with the new tool, the MFs of the isolated and stacked bases in DNA double helix were obtained for the first time. This work provides a new representation for indicating shape properties, frontier electron densities and chemical reactivities.

Theoretical Model on the Interplay of Disorder and Electron Correlations

In the present review paper we discuss a general theoretical treatment to investigate the interplay between the effects of disorder and electron-electron interaction in the Anderson-localized regime. In constructing the model Hamiltonian, the behaviour of Anderson-localized states with envelope function is explicitly taken into account. It is shown that, in the approximation of neglecting the interstate interactions, the rival effects of disorder and electron correlation can be described by two fundamental quantities: the average intrastate interaction energy and the distribution width of one-electron energies. On the basis of this model the spin susceptibility and electronic specific heat as well as density of states are calculated. It is shown that the intrastate interaction gives rise to the occurrence of singly-occupied states below the Fermi energy and that this results in a Curie-type spin susceptibility at low temperatures. It is shown that the configuration interaction which is one of the effects of interstate interactions gives rise to a kinetic type exchange interaction between singly-occupied states which favours spin-singlet states and that the competition between direct and kinetic exchanges leads to the spin pair model in which each localized spin of singly occupied state forms a ferromagnetic or antiferromagnetic pair with its nearest neighbour. Specific heat anomaly, in particular its magnetic field dependence, and magnetic susceptibility at very low temperatures are calculated by taking into account the coexistence of ferromagnetic and antiferromagnetic interactions within a spin pair model. It is shown that the experimental results on Si:P can be well explained by the present treatment. Finally the effects of electron-electron interactions on the magnetoresistance of the variable range hopping conduction are investigated. It is shown that magnetoresistance is positive as far as the change of localization length due to a magnetic field is neglected Taking into account the latter effect which is responsible for negative magneto-resistance, the total magnetoresistance is calculated for the systems of 1T-TaS2 and their observed peculiar features of magnetoresistance can be explained well by the present theory.

Many-body effects on the Rashba-type spin splitting in bulk bismuth tellurohalides

We report on many-body corrections to one-electron energy spectra of bulk bismuth tellurohalides---materials that exhibit a giant Rashba-type spin splitting of the band-gap edge states. We show that the corrections obtained in the one-shot $\mathit{GW}$ approximation noticeably modify the spin-orbit-induced spin splitting evaluated within density functional theory. We demonstrate that taking into account many-body effects is crucial to interpret the available experimental data.

Electronic properties of AlN crystal doped with Cr, Mn and Fe

The spin-resolved electronic energy band spectra, as well as partial and total density of electronic states of the crystal AlN, doped with Cr, Mn and Fe, have been evaluated within the projector augmented waves (PAW) approach by means of the ABINIT code. The Hartree-Fock exchange for correlated electrons is used to describe the correlated orbitals in the PAW framework. The calculated one-electron energies for electrons of spin up and down are very different. We have found that all the considered crystals are ferromagnetic.

Beryllium Atom from Weak to Strong Magnetic Fields

The energy levels involving the 10+, 1/3(−1)+, and 3(−1)− states of the beryllium atom in magnetic fields of 0–10 a.u. (1 a.u. corresponding to 4.7011 × 105 T) are investigated. To deal with the four-electron atomic system in magnetic fields, two related methods based on the anisotropic Gaussian basis set are applied. In the field region of 0 ≤ β < 0.5 a.u., owing to the relatively weak correlation between an inner core electron and an outer valence electron, we apply the freezing full-core method. In the field region of 0.5 ≤ β ≤ 10 a.u., we carry out the full-core-plus-correlation calculation, which has a better consideration about the additional correlations. Compared to the full configuration-interaction method, significant improvement on precision of energies of spin-singlet states is achieved. For spin-triplet states, energies of similar precision are attained using a smaller basis set. The corresponding one-electron ionization energies are presented and analyzed.

Photoelectron and electron momentum spectroscopy of 1-butene at benchmark theoretical levels

The results of experimental studies of the valence electronic structure of 1-butene employing photoelectron spectroscopy as well as electron momentum spectroscopy are interpreted on the ground of quantitative calculations of one-electron and shake-up ionization energies and of the related Dyson orbitals, using one-particle Green's function theory in conjunction with the third-order algebraic diagrammatic construction scheme (ADC(3)). Comparison is made with simulations of (e, 2e) electron momentum distributions obtained from standard (B3LYP) Kohn–Sham orbitals. Our analysis is based on highly quantitative determinations of the energy difference between the cis and gauche (C1) conformers, within ∼0.02 kcal mol−1 accuracy, and a thermostatistical evaluation thereby of conformer weights beyond the level of the rigid rotor harmonic oscillator approximation. Relative entropies are found to be particularly sensitive to hindered rotations. The shake-up onset is located at 15.9 eV, and the orbital picture of ionization breaks down completely at electron binding energies above 19 eV. If the available experimental momentum profiles demonstrate the dominance of the C1 conformer, they are in this case clearly not sensitive enough to the molecular conformation for evaluating conformer abundances with accuracies better than 10% due to the limited energy and momentum resolutions and likely physical complications.

Bulk and Surface Polarons in Photoexcited Anatase TiO2

Using hybrid functional electronic structure calculations, we have investigated the structure and energetics of photogenerated electrons and holes in the bulk and at the (101) surface of anatase TiO2. Excitons formed upon UV irradiation are found to become self-trapped, consistent with the observation of temperature-dependent Urbach tails in the absorption spectrum and a large Stokes shift in the photoluminescence band of anatase. Electron and hole polarons are localized at Ti3+ and O– lattice sites, respectively. At the surface, the trapping sites generally correspond to undercoordinated Ti3+5c and O–2c surface atoms or to isolated OH species in the case of a hydroxylated surface. The polaron trapping energy is considerably larger at the surface than in the bulk, indicating that it is energetically favorable for the polarons to travel from the bulk to the surface. Computed one-electron energy levels in the gap and hyperfine coupling constants compare favorably with oxidation potential and EPR measurements.

Electronic structure, chemical bonding, and oxidation numbers of first-row transition metals in [MePIm2 ] complexes and their cations

The qualitative structures of the upper one-electron energy levels of imidazole-coordinated first-row transition metal porphyrin [MePIm2] complexes established in the present study have shown that the second oxidation number of the first-row transition metals in the neutral complexes do not change in their cations and double cations. It was found that occupied orbitals of the density functional theory method obtained with B3LYP functional are not correctly ordered. Therefore, they cannot be used in investigations of the orbital structure of the upper molecular orbitals. A qualitative analysis of density functional theory method wave functions in terms of Mulliken and natural charges of atoms, together with an analysis of electrostatic potentials of the neutral [MePIm2] complex, its single and double cations, demonstrates that the highest occupied orbitals of these complexes are mainly formed by atomic orbitals of the porphyrin ring atoms. Therefore, transition metal atoms are not active in chemical reactions with these complexes unless the 3d electrons of transition metal atoms are excited, for example by light. A mechanism of an electron transfer reaction that occurs between a heme cytochrome and Fe-oxide mineral surface is discussed in the light of the obtained results. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Electron Momentum Spectroscopy of pyrimidine at the benchmark ADC(3) level

An extensive study of the valence electronic structure, ionization spectrum and electron momentum distributions of pyrimidine is presented, on the ground of accurate calculations of one-electron and shake-up ionization energies and of the related Dyson orbitals, using one-particle Green’s Function theory in conjunction with the third-order Algebraic Diagrammatic Construction scheme [ADC(3)]. Comparison is made with results obtained from standard (B3LYP) Kohn–Sham orbitals and recent measurements employing Electron Momentum Spectroscopy. Quantitative insights into the experimental momentum distributions are amenable without resorting to any empirical rescaling of pole strengths, provided band overlaps and relaxation effects are properly accounted for.

Electron Momentum Spectroscopy of Norbornadiene at the Benchmark ADC(3) Level

An extensive study, throughout the valence region, of the electronic structure, ionization spectrum, and electron momentum distributions of norbornadiene is presented, on the ground of accurate calculations of valence one-electron and shake-up ionization energies and of the related Dyson orbitals, using one-particle Green's function (1p-GF) theory in conjunction with the so-called third-order algebraic diagrammatic construction scheme [ADC(3)]. Comparison is made with results obtained from standard (B3LYP) Kohn-Sham orbitals and measurements employing electron momentum spectroscopy, taking into account the contamination of inner- and outer-valence spectral bands by numerous shake-up states. Four relatively intense shake-up lines at 12.1, 16.4, 17.6, and 17.8 eV are found to yield recognizable spectral fingerprints in the EMS experiments. Valence bands at electron binding energies larger than 20 eV are subject to a complete breakdown of the orbital picture of ionization.

A new confinement potential in spherical quantum dots: Modified Gaussian potential

A new confinement potential for spherical quantum dots, called the modified Gaussian potential (MGP), is studied. In the present work, the following problems are investigated within the effective-mass approximation: (i) the one-electron energy spectra, (ii) wave functions, (iii) the problem of existence of a bound electron state, and (iv) the binding energy of center and off-center hydrogenic donor impurities. For zero angular momentum ( l = 0 ) , the new confinement potential is sufficiently flexible to obtain analytically the spectral energy and wave functions. The results obtained from the present work show that (i) the new potential is suitable for predicting the spectral energy and wave functions, and (ii) the geometrical sizes of the quantum dot play the important roles on the energy levels, wave functions, the binding energy, and the existence of a bound electron state.

Transferable orthogonal tight-binding parameters for ZnS and CdS

Calculations of Slater–Koster (SK) parameters appearing in the tight-binding method usingsp3d5 basis sets for both the cationic and anionic species are presented for ZnS and CdS. We haveadjusted these parameters to match the band structures obtained from the full potentiallinear augmented plane wave method. This operation has been carried out for a variety ofstructures namely zinc blende, wurtzite, rocksalt, CsCl and for a wide range ofnear-neighbor distances. The SK parameters have slightly different values for the samenear-neighbor distance in different structures. Therefore, a least-squares fitting has beenperformed separately for each parameter as a function of only the near-neighbor distance toguarantee the transferability of these parameters to different structural environments. Thefitted parameters are then used to calculate the electronic structure of small-sizedclusters of ZnS and CdS in given geometries and the results are compared with ab initio results. A fairly good agreement found in the one-electron energy spectrumand total energy confirms transferability of the parameters to different lengthscales. A detailed account of the calculation procedure and calibration results isgiven in the present paper. These parameters can be used to study the electronicstructure of large-sized clusters where first-principles methods are computationallydemanding. It may be mentioned that the SK parameters do not satisfy theR − (l + l′ + 1) Harrison scaling law for larger values of the near-neighbor distanceR.

Simulation of the structure and electronic configuration of Pd n (C60) m complexes

The structure and electronic configuration of Pd(C60)2, Pd2(C60)2, Pd3(C60)3, and Pd6(C60)3 complexes have been simulated in terms of the density functional theory within the Perdew—Burke—Ernzerhof (PBE) approximation. The results of the calculation of the Pd6(C60)3 trimer have been used to simulate the structure of the quasi-one-dimensional polymer [C60Pd3]n molecule. For this macromolecule, the oneelectron energy levels have been calculated. It has been found that the band gap is 0.6 eV. The calculations have been performed using the crystal orbital method in the extended Huckel approximation. The possibility of using the obtained results for evaluating the catalytic properties of the studied complexes has been discussed.

Simulation of pure and defective wurtzite-type ZnO

Changes in the structural and electronic properties of zinc oxide (ZnO) due to the O vacancy and F-centre were studied using a semi-empirical quantum-chemical approach based on Hartree–Fock theory. A periodic supercell of 128 atoms was exploited throughout the study. The semi-empirical parameters for the Zn atom are obtained by reproducing the main properties of the ZnO crystal as well as the first three ionization potentials of the Zn atom. The perturbation imposed by the defect leads to atomic relaxation, which is computed and discussed in detail. It is found that electron density redistribution in the vicinity of defects plays an important role in the determination of atomic movements. The introduction of an oxygen vacancy generates a local one-electron energy level placed below the conduction band while the presence of an F-centre produces a local energy level just above the upper valence band of the material. The deep situation of the local energy level corresponding to the F-centre implies that the F-centre cannot serve as a source of unintentional n-type electrical conductivity in ZnO. Changes in the chemical bonding are observed, showing that it becomes slightly more covalent because of oxygen-vacancy-type defects.

Lifetimes of quantum well states and resonances in Pb overlayers on Cu(111)

We present results of calculations of the lifetimes of excited electrons (holes) in quantum well states and quantum well resonances in Pb overlayers supported on Cu(111). Many-body decay via inelastic energy relaxation and one-electron decay via energy-conserving one-electron transfer into the substrate are considered. One-electron energies and wave functions have been computed for different coverages of the Pb overlayer (from 1 to 18 monolayers) by using a one-dimensional pseudopotential for the entire overlayer-substrate system in the framework of density functional theory within the local density approximation. The elastic (energy-conserving resonant electron transfer) contribution to the total lifetime broadening of quantum well resonances has been calculated within the wave packet propagation method. The inelastic electron-electron (many-body) contribution to the lifetime broadening of both occupied and unoccupied quantum well states has been evaluated using $GW$ approximation. The decay mechanisms of both quantum well states and quantum well resonances in thick overlayers are discussed.

The use of the hartree-fock-slater eigenvalues to estimate excitation and ionization energies in sulfur-nitrogen compounds

Total statistical energy differences for electronic excitation energies and ionization potentials are expanded in a McLaurin series leading to one-electron energy terms plus correction terms. The different nature of the correction to the one-electron values for the above properties in the Hartree–Fock–Slater scheme as compared to the Hartree–Fock method is commented on. Examples are provided comparing excitation energies and ionization potentials from experiment, transition state method, total statistical energy differences, and one-electron estimates for several sulfur nitrides.

Microscopic origin of magnetism and magnetic interactions in ferropnictides

One year after their initial discovery, two schools of thought have crystallized regarding the electronic structure and magnetic properties of ferropnictide systems. One postulates that these are itinerant weakly correlated metallic systems that become magnetic by virtue of spin-Peierls type transition due to near-nesting between the hole and the electron Fermi surface pockets. The other argues these materials are strongly or at least moderately correlated, the electrons are considerably localized and close to a Mott-Hubbard transition, with the local magnetic moments interacting via short-range superexchange. In this paper we argue that neither picture is fully correct. The systems are moderately correlated, but with correlations driven by Hund's rule coupling rather than by the on-site Hubbard repulsion. The iron moments are largely local, driven by Hund's intra-atomic exchange. Superexchange is not operative and the interactions between the Fe moments are considerably long-range and driven mostly by one-electron energies of all occupied states.

The self-consistent field for crystals

Exchange in isolated atoms and ions is investigated, to throw light on the approximate exchange to be used in crystals. An intercomparison, carried out by the author, J. B. Mann, J. H. Wood, and T. M. Wilson, for the case of Cu+ is described in detail. Here five different values of exchange are used: VXHF, the Hartree-Fock value; VXS, a free-electron exchange suggested by Kohn, Sham, and Gaspar, in which the exchange correct for a free-electron gas at the Fermi energy is assumed; VXLSW, a modification of an exchange recently suggested by Liberman, proposed by the writer and Wood, in which we use an energy-dependent exchange suggested by the free-electron gas theory; and VXa, in which the exchange VXS is multiplied by such a factor α that the total energy of the atom is minimized. Of these, VXLSW and VXα both give orbitals which are good approximations to the Hartree-Fock and VXLSW also gives eigenvalues agreeing well with the Hartree-Fock. The VXα method, however, gives eigenvalues numerically smaller than the Hartree-Fock, by amounts which increase as we go to the inner electrons. In spite of this, the eigenvalues of the VXα method empirically prove to form very good one-electron energies to use in the energy-band problem. The reason for this is then examined. A method for studying atoms with partially filled shells, such as the 3d transition atoms, is described. We call it the Hyper-Hartree-Fock method, since it deals with an average energy over many electronic states, rather than a single state as in the HF method. The criterion for minimum energy is shown to be the equality of one-electron energies E'i of two shells such as 3d and 4s, which can interchange electrons, where E'i differs from the ordinary eigenvalue of the Hartree-Fock method. The latter represents the energy difference between an atom and an ion lacking an electron; the modified energy E'i is the derivative of the energy with respect to the occupation number. It is shown that these E'i's are the energies which should be used in an energy-band calculation, not the ordinary HF energies. The two sets of energies differ by a considerable amount in the transition elements, but the quantities E'i agree well with the eigenvalues of the method using the exchange VXα. This appears to explain the success of the latter method for energy-band calculations, and suggests that it is better than a Hartree-Fock calculation, even if the latter could be carried out. It is pointed out that the quantities E'i are closely related to the electronegativities used by the chemists, and also to one-particle energies met in the theory of the Fermi liquid.