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Performance of 3D-space-based atoms-in-molecules methods for electronic delocalization aromaticity indices
Several definitions of an atom in a molecule (AIM) in three-dimensional (3D) space, including both fuzzy and disjoint domains, are used to calculate electron sharing indices (ESI) and related electronic aromaticity measures, namely, Iringand multicenter indices (MCI), for a wide set of cyclic planar aromatic and nonaromatic molecules of different ring size. The results obtained using the recent iterative Hirshfeld scheme are compared with those derived from the classical Hirshfeld method and from Bader's quantum theory of atoms in molecules. For bonded atoms, all methods yield ESI values in very good agreement, especially for C-C interactions. In the case of nonbonded interactions, there are relevant deviations, particularly between fuzzy and QTAIM schemes. These discrepancies directly translate into significant differences in the values and the trends of the aromaticity indices. In particular, the chemically expected trends are more consistently found when using disjoint domains. Careful examination of the underlying effects reveals the different reasons why the aromaticity indices investigated give the expected results for binary divisions of 3D spaceM.S. is grateful for the nancial help furnished by the
Spanish MICINN Project No. CTQ2008-03077/BQU and by the Catalan DIUE
through project No. 2009SGR63
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Wannier–Koopmans method calculations for transition metal oxide band gaps
The widely used density functional theory (DFT) has a major drawback of underestimating the band gaps of materials. Wannier–Koopmans method (WKM) was recently developed for band gap calculations with accuracy on a par with more complicated methods. WKM has been tested for main group covalent semiconductors, alkali halides, 2D materials, and organic crystals. Here we apply the WKM to another interesting type of material system: the transition metal (TM) oxides. TM oxides can be classified as either with d0 or d10 closed shell occupancy or partially occupied open shell configuration, and the latter is known to be strongly correlated Mott insulators. We found that, while WKM provides adequate band gaps for the d0 and d10 TM oxides, it fails to provide correct band gaps for the group with partially occupied d states. This issue is also found in other mean-field approaches like the GW calculations. We believe that the problem comes from a strong interaction between the occupied and unoccupied d-state Wannier functions in a partially occupied d-state system. We also found that, for pseudopotential calculations including deep core levels, it is necessary to remove the electron densities of these deep core levels in the Hartree and exchange–correlation energy functional when calculating the WKM correction parameters for the d-state Wannier functions
Solving the radial Dirac equations: a numerical odyssey
We discuss, in a pedagogical way, how to solve for relativistic wave
functions from the radial Dirac equations. After an brief introduction, in
Section II we solve the equations for a linear Lorentz scalar potential,
V_s(r), that provides for confinement of a quark. The case of massless u and d
quarks is treated first, as these are necessarily quite relativistic. We use an
iterative procedure to find the eigenenergies and the upper and lower component
wave functions for the ground state and then, later, some excited states.
Solutions for the massive quarks (s, c, and b) are also presented. In Section
III we solve for the case of a Coulomb potential, which is a time-like
component of a Lorentz vector potential, V_v(r). We re-derive, numerically, the
(analytically well-known) relativistic hydrogen atom eigenenergies and wave
functions, and later extend that to the cases of heavier one-electron atoms and
muonic atoms. Finally, Section IV finds solutions for a combination of the V_s
and V_v potentials. We treat two cases. The first is one in which V_s is the
linear potential used in Sec. II and V_v is Coulombic, as in Sec. III. The
other is when both V_s and V_v are linearly confining, and we establish when
these potentials give a vanishing spin-orbit interaction (as has been shown to
be the case in quark models of the hadronic spectrum).Comment: 39 pages (total), 23 figures, 2 table
Two--Electron Atoms in Short Intense Laser Pulses
We discuss a method of solving the time dependent Schrodinger equation for
atoms with two active electrons in a strong laser field, which we used in a
previous paper [A. Scrinzi and B. Piraux, Phys. Rev. A 56, R13 (1997)] to
calculate ionization, double excitation and harmonic generation in Helium by
short laser pulses. The method employs complex scaling and an expansion in an
explicitly correlated basis. Convergence of the calculations is documented and
error estimates are provided. The results for Helium at peak intensities up to
10^15 W/cm^2 and wave length 248 nm are accurate to at least 10 %. Similarly
accurate calculations are presented for electron detachment and double
excitation of the negative hydrogen ion.Comment: 14 pages, including figure
The two electron molecular bond revisited: from Bohr orbits to two-center orbitals
In this review we first discuss extension of Bohr's 1913 molecular model and
show that it corresponds to the large-D limit of a dimensional scaling
(D-scaling) analysis, as developed by Herschbach and coworkers.
In a separate but synergetic approach to the two-electron problem, we
summarize recent advances in constructing analytical models for describing the
two-electron bond. The emphasis here is not maximally attainable numerical
accuracy, but beyond textbook accuracy as informed by physical insights. We
demonstrate how the interplay of the cusp condition, the asymptotic condition,
the electron-correlation, configuration interaction, and the exact one electron
two-center orbitals, can produce energy results approaching chemical accuracy.
Reviews of more traditional calculational approaches, such as Hartree-Fock, are
also given.
The inclusion of electron correlation via Hylleraas type functions is well
known to be important, but difficult to implement for more than two electrons.
The use of the D-scaled Bohr model offers the tantalizing possibility of
obtaining electron correlation energy in a non-traditional way.Comment: 99 pages, 29 figures, review article, to appear in Advances in
Atomic, Molecular and Optical Physic
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