59 research outputs found
On the pseudo-Hermitian nondiagonalizable Hamiltonians
We consider a class of (possibly nondiagonalizable) pseudo-Hermitian
operators with discrete spectrum, showing that in no case (unless they are
diagonalizable and have a real spectrum) they are Hermitian with respect to a
semidefinite inner product, and that the pseudo-Hermiticity property is
equivalent to the existence of an antilinear involutory symmetry. Moreover, we
show that a typical degeneracy of the real eigenvalues (which reduces to the
well known Kramers degeneracy in the Hermitian case) occurs whenever a
fermionic (possibly nondiagonalizable) pseudo-Hermitian Hamiltonian admits an
antilinear symmetry like the time-reversal operator . Some consequences and
applications are briefly discussed.Comment: 22 page
Deconstructing dominant realities and the co-creation of hope at an HIV/AIDS baby sanctuary
The purpose of this research study is to describe emerging realities within an HIV/AIDS baby sanctuary using a social constructionist approach. The study is concerned with
the rediscovery of the value of human participation through the deconstruction of emerging problem narratives concerning HIV/AIDS. Co-research was used in which the researcher and the participants were actively involved in the research as coauthors. The study describes alternative realities that were uncovered at Cotlands Baby Sanctuary through the use of language, which was used as a symbolic tool of deconstruction. Through deconstructing the emerging problem narratives, stories of hope were uncovered. These stories of hope were highlighted throughout the research process.PsychologyM.A. (Counselling Psychology
Systematic Study of the Influence of Base-Step Parameters on the Electronic Coupling between Base-Pair Dimers: Comparison of A-DNA and B-DNA Forms
Modeling the Effect of the Electrolyte on Standard Reduction Potentials of Polyoxometalates
The electrochemistry of transition
metal oxide systems is gaining
much interest in the context of energy storage. Yet, predicting the
redox behavior of such systems remains very challenging for computational
chemistry. In this work, we examined instead a computational strategy
for related nano-sized molecular transition metal polyoxoanions, as
such polyoxometalates (POMs) can be treated at manageable computational
costs. As an example, we addressed the effects of an aqueous electrolyte
at the atomic scale for estimating the standard reduction potentials
MnÂ(IV/III) and MnÂ(III/II) of the tri-Mn-substituted W-based Keggin
ion. The electrolyte model involves explicitly solvated Li<sup>+</sup> counterions and accounts for the fluctuating aqueous medium, described
in first-principles molecular dynamics simulations. After equilibration,
the systems showed different local structures of the electrolyte around
the POM, depending on the oxidation state of the Mn centers. These
varying local structures affect the Mn reduction potentials differently
for the redox couples under study. Hybrid DFT calculations yield rather
accurate absolute redox potentials for Mn, in good agreement with
experiment, i.e., within 0.1 eV. This is in strong contrast to analogous
results from an implicit solvation model, where redox potentials were
notably underestimated, whereas models with counterions added, but
without explicit solvation, notably overestimated the redox potentials,
by up to 1 eV. Only by taking into account the full atomistic structure
of the multicomponent system, solute, and surrounding electrolyte
is one able to estimate the electrochemical properties of nanostructured
transition metal oxide systems with acceptable accuracy
Solvent Reorganization Energies in A-DNA, B-DNA, and Rhodamine 6G−DNA Complexes from Molecular Dynamics Simulations with a Polarizable Force Field
O<sub>2</sub> Activation and Catalytic Alcohol Oxidation by Re Complexes with Redox-Active Ligands: A DFT Study of Mechanism
As a contribution to understanding
catalysis by transition metal complexes with redox-active ligands
(here: catecholate – cat), we report a computational study
on the mechanism of a catalytic cycle where (i) O<sub>2</sub> is activated
at the metal center of the catecholate complex [Re<sup>V</sup>(O)Â(cat)<sub>2</sub>]<sup>−</sup> to yield [Re<sup>VII</sup>(O)<sub>2</sub>(cat)<sub>2</sub>]<sup>−</sup>, which (ii) subsequently is
applied to oxidize alcohols. We were able to identify the steps where
the redox-active ligands played a crucial role as e<sup>–</sup> buffer. For O<sub>2</sub> homolysis, a series of sequential 1e<sup>–</sup> steps leads to superoxo and bimetallic intermediates,
followed by facile cleavage of the bimetallic peroxo O–O linkage.
The <i>trans–cis</i> isomerization of <i>trans</i>-[Re<sup>V</sup>(O)Â(cat)<sub>2</sub>]<sup>−</sup> is the crucial
step of O<sub>2</sub> activation, with an absolute free energy barrier
of 16.8 kcal mol<sup>–1</sup> in methanol. Due to the ionic
character of intermediates, all reaction barriers of O<sub>2</sub> activation are significantly lowered in a polar solvent, thus rendering
O<sub>2</sub> homolysis kinetically accessible. With computational
results for the activation barriers of all elementary steps as well
as the calculated solvent effects, we are able to rationalize all
pertinent experimental findings. For catalytic alcohol oxidation,
we propose a novel cooperative mechanism that involves two units of
the metal complexes, ruling out the reaction via a seven-coordinated
active oxidant, as previously hypothesized. We present in detail calculated
energies and barriers for the reaction steps of the oxidation of methanol
as model alcohol as well as the energetics of crucial steps of the
experimentally studied oxidation of benzyl alcohol, both transformations
for methanol as solvent
Does the Preferred Mechanism of a Catalytic Transformation Depend on the Density Functional? Ethylene Hydrosilylation by a Metal Complex as a Case Study
For an extended set of density functionals
(BP86, BLYP, B3LYP,
B3PW91, PBE, PBE0, mPWPW, MPW1K, M06-L, M06, MPW3LYP, TPSS) we explored
the key steps of four mechanisms of ethylene hydrosilylation (Glaser–Tilley,
Chalk–Harrod, modified Chalk–Harrod, and σ-bond
metathesis) by a RhÂ(I) catalyst, previously studied at the B3LYP level.
The Chalk–Harrod and the σ-bond metathesis mechanisms
were determined to be preferred for all these functionals. The preference
among these two mechanisms and the corresponding highest relative
barriers (6.6–11.8 kcal·mol<sup>–1</sup>) depend
on the functional. To a certain extent, the differences in the description
of the reaction can be traced back to the correlation part of the
functionals. For the most notable functional-dependent barrier, similar
values were calculated when the LYP correlation functional and the
functionals M06-L and M06 were employed, but distinctively different
values resulted from the functionals PBE, PW91, and TPSS
Metal-Supported Metal Clusters: A Density Functional Study of Pt<sub>3</sub> and Pd<sub>3</sub>
The geometric, energetic, and electronic properties of
metal-supported
metal clusters were examined computationally by applying a method
based on density functional theory to model systems. To explore lattice
strain effects on these systems, Pt<sub>3</sub> and Pd<sub>3</sub> clusters adsorbed on Au(111) and Cu(111) were studied. The geometric
and electronic properties of these small metal-supported clusters
were found to differ from the corresponding overlayer system. The
d-band centers of the adsorbed clusters on Au(111) were calculated
to be very similar to those of the adsorbed clusters on Cu(111), indicating
that the support has only a minor effect on the d-band center of the
adsorbed clusters. In contrast, the gap between the local d-band centers
of Pt and Pd overlayers and the Fermi energy is reduced from −2.41
eV (Pt) and −2.10 eV (Pd) on Cu(111) to −1.41 eV (Pt)
and −1.22 eV (Pd) on Au(111)
Toward a Reliable Energetics of Adsorption at Solvated Mineral Surfaces: A Computational Study of Uranyl(VI) on 2:1 Clay Minerals
We
developed an efficient computational protocol for studying adsorption
at solvated solid surfaces by a quantum mechanical method. We combine
first-principles molecular dynamics at low temperature with simulated
annealing and optimization steps to allow relaxation of the solvent
structure without strongly perturbing the geometry of adsorption complexes.
On the example of uranylÂ(VI) adsorption at the (110) edge surface
of smectite minerals we show by density functional calculations using
periodic slab models that our approach yields more reliable energies
than direct optimization. In this way we were able to identify the
preferred adsorption complex at this smectite surface. By decomposing
the complex formation energies into deprotonation energies of the
surface and adsorption energies as well as by a charge analysis of
the adsorption sites, we rationalize this result as well as the composition
and the structures of less stable adsorbed species. Our computational
results are compatible with available experimental structural data
of uranylÂ(VI), adsorbed at montmorillonite
O<sub>2</sub> Activation and Catalytic Alcohol Oxidation by Re Complexes with Redox-Active Ligands: A DFT Study of Mechanism
As a contribution to understanding
catalysis by transition metal complexes with redox-active ligands
(here: catecholate – cat), we report a computational study
on the mechanism of a catalytic cycle where (i) O<sub>2</sub> is activated
at the metal center of the catecholate complex [Re<sup>V</sup>(O)Â(cat)<sub>2</sub>]<sup>−</sup> to yield [Re<sup>VII</sup>(O)<sub>2</sub>(cat)<sub>2</sub>]<sup>−</sup>, which (ii) subsequently is
applied to oxidize alcohols. We were able to identify the steps where
the redox-active ligands played a crucial role as e<sup>–</sup> buffer. For O<sub>2</sub> homolysis, a series of sequential 1e<sup>–</sup> steps leads to superoxo and bimetallic intermediates,
followed by facile cleavage of the bimetallic peroxo O–O linkage.
The <i>trans–cis</i> isomerization of <i>trans</i>-[Re<sup>V</sup>(O)Â(cat)<sub>2</sub>]<sup>−</sup> is the crucial
step of O<sub>2</sub> activation, with an absolute free energy barrier
of 16.8 kcal mol<sup>–1</sup> in methanol. Due to the ionic
character of intermediates, all reaction barriers of O<sub>2</sub> activation are significantly lowered in a polar solvent, thus rendering
O<sub>2</sub> homolysis kinetically accessible. With computational
results for the activation barriers of all elementary steps as well
as the calculated solvent effects, we are able to rationalize all
pertinent experimental findings. For catalytic alcohol oxidation,
we propose a novel cooperative mechanism that involves two units of
the metal complexes, ruling out the reaction via a seven-coordinated
active oxidant, as previously hypothesized. We present in detail calculated
energies and barriers for the reaction steps of the oxidation of methanol
as model alcohol as well as the energetics of crucial steps of the
experimentally studied oxidation of benzyl alcohol, both transformations
for methanol as solvent
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