484 research outputs found
Total energy density as an interpretative tool
We present an unambiguous formulation for the total energy density within
density-functional theory. We propose that it be used as a tool for the
interpretation of computed energy and electronic structure changes during
structural transformations and chemical reactions, augmenting the present use
of electron density changes and changes in the Kohn-Sham local density of
states and Kohn-Sham energy density.Comment: 5 pages, 3 embedded figures, submitted to J. Chem. Phy
Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms
The random phase approximation (RPA) for the correlation energy functional of
density functional theory has recently attracted renewed interest. Formulated
in terms of the Kohn-Sham (KS) orbitals and eigenvalues, it promises to resolve
some of the fundamental limitations of the local density and generalized
gradient approximations, as for instance their inability to account for
dispersion forces. First results for atoms, however, indicate that the RPA
overestimates correlation effects as much as the orbital-dependent functional
obtained by a second order perturbation expansion on the basis of the KS
Hamiltonian. In this contribution, three simple extensions of the RPA are
examined, (a) its augmentation by an LDA for short-range correlation, (b) its
combination with the second order exchange term, and (c) its combination with a
partial resummation of the perturbation series including the second order
exchange. It is found that the ground state and correlation energies as well as
the ionization potentials resulting from the extensions (a) and (c) for closed
sub-shell atoms are clearly superior to those obtained with the unmodified RPA.
Quite some effort is made to ensure highly converged RPA data, so that the
results may serve as benchmark data. The numerical techniques developed in this
context, in particular for the inherent frequency integration, should also be
useful for applications of RPA-type functionals to more complex systems.Comment: 11 pages, 7 figure
Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets
The superposition of atomic potentials (SAP) approach has recently been shown
to be a simple and efficient way to initialize electronic structure
calculations [S. Lehtola, J. Chem. Theory Comput. 15, 1593 (2019)]. Here, we
study the differences between effective potentials from fully numerical density
functional and optimized effective potential calculations for fixed
configurations. We find that the differences are small, overall, and choose
exchange-only potentials at the local density approximation level of theory
computed on top of Hartree-Fock densities as a good compromise. The differences
between potentials arising from different atomic configurations are also found
to be small at this level of theory.
Furthermore, we discuss the efficient Gaussian-basis implementation of SAP
via error function fits to fully numerical atomic radial potentials. The guess
obtained from the fitted potentials can be easily implemented in any
Gaussian-basis quantum chemistry code in terms of two-electron integrals. Fits
covering the whole periodic table from H to Og are reported for
non-relativistic as well as fully relativistic four-component calculations that
have been carried out with fully numerical approaches.Comment: 12 pages, 8 figure
Time-dependent Density Functional calculation of e-H scattering
Phase shifts for single-channel elastic electron-atom scattering are derived
from time-dependent density functional theory. The H ion is placed in a
spherical box, its discrete spectrum found, and phase shifts deduced.
Exact-exchange yields an excellent approximation to the ground-state Kohn-Sham
potential, while the adiabatic local density approximation yields good singlet
and triplet phase shifts.Comment: 5 pages, 4 figures, 1 tabl
Exact-Exchange Kohn-Sham formalism applied to one-dimensional periodic electronic systems
The Exact-Exchange (EXX) Kohn-Sham formalism, which treats exchange
interactions exactly within density-functional theory, is applied to
one-dimensional periodic systems. The underlying implementation does not rely
on specific symmetries of the considered system and can be applied to any kind
of periodic structure in one to three dimensions. As a test system,
-polyacetylene, both in form of an isolated chain and in the bulk
geometry has been investigated. Within the EXX scheme, bandstructures and
independent particle response functions are calculated and compared to
experimental data as well as to data calculated by several other methods.
Compared to results from the local-density approximation, the EXX method leads
to an increased value for the band gap, in line with similar observations for
three-dimensional semiconductors. An inclusion of correlation potentials within
the local density approximation or generalized gradient approximations leads to
only negligible effects in the bandstructure. The EXX band gaps are in good
agreement with experimental data for bulk -polyacetylene. Packing
effects of the chains in bulk -polyacetylene are found to lower the band
gap by about 0.5 eV
Assessing the potential for postcopulatory sexual selection in elasmobranchs
This review highlights the potential role that post-copulatory sexual selection plays in elasmobranch reproductive systems and the utility of this group to further understanding of evolutionary responses to the post-copulatory processes of sperm competition and cryptic female choice. The growing genetic evidence for female multiple mating (polyandry) in elasmobranchs is summarized. While polyandry appears to be common in this group, rates of multiple paternity are highly variable between species suggesting that there is large variance in the strength of post-copulatory sexual selection among elasmobranchs. Possible adaptations of traits important for post-copulatory sexual selection are then considered. Particular emphasis is devoted to explore the potential for sperm competition and cryptic female choice to influence the evolution of testes size, sperm morphology, genital morphology and sperm storage organs. Finally, it is argued that future work should take advantage of the wealth of information on these reproductive traits already available in elasmobranchs to gain a better understanding of how post-copulatory sexual selection operates in this group
Scale-free memory model for multiagent reinforcement learning. Mean field approximation and rock-paper-scissors dynamics
A continuous time model for multiagent systems governed by reinforcement
learning with scale-free memory is developed. The agents are assumed to act
independently of one another in optimizing their choice of possible actions via
trial-and-error search. To gain awareness about the action value the agents
accumulate in their memory the rewards obtained from taking a specific action
at each moment of time. The contribution of the rewards in the past to the
agent current perception of action value is described by an integral operator
with a power-law kernel. Finally a fractional differential equation governing
the system dynamics is obtained. The agents are considered to interact with one
another implicitly via the reward of one agent depending on the choice of the
other agents. The pairwise interaction model is adopted to describe this
effect. As a specific example of systems with non-transitive interactions, a
two agent and three agent systems of the rock-paper-scissors type are analyzed
in detail, including the stability analysis and numerical simulation.
Scale-free memory is demonstrated to cause complex dynamics of the systems at
hand. In particular, it is shown that there can be simultaneously two modes of
the system instability undergoing subcritical and supercritical bifurcation,
with the latter one exhibiting anomalous oscillations with the amplitude and
period growing with time. Besides, the instability onset via this supercritical
mode may be regarded as "altruism self-organization". For the three agent
system the instability dynamics is found to be rather irregular and can be
composed of alternate fragments of oscillations different in their properties.Comment: 17 pages, 7 figur
The Antiquity and Evolutionary History of Social Behavior in Bees
A long-standing controversy in bee social evolution concerns whether highly eusocial behavior has evolved once or twice within the corbiculate Apidae. Corbiculate bees include the highly eusocial honey bees and stingless bees, the primitively eusocial bumble bees, and the predominantly solitary or communal orchid bees. Here we use a model-based approach to reconstruct the evolutionary history of eusociality and date the antiquity of eusocial behavior in apid bees, using a recent molecular phylogeny of the Apidae. We conclude that eusociality evolved once in the common ancestor of the corbiculate Apidae, advanced eusociality evolved independently in the honey and stingless bees, and that eusociality was lost in the orchid bees. Fossil-calibrated divergence time estimates reveal that eusociality first evolved at least 87 Mya (78 to 95 Mya) in the corbiculates, much earlier than in other groups of bees with less complex social behavior. These results provide a robust new evolutionary framework for studies of the organization and genetic basis of social behavior in honey bees and their relatives
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