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, $trans$-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 $trans$-polyacetylene. Packing effects of the chains in bulk $trans$-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