<I>A Special Section on</I> Computational Astrophysics

Abstract

Binary black holes occupy a special place in our quest for understanding the evolution of galaxies along cosmic history. If massive black holes grow at the center of (pre-)galactic structures that experience a sequence of merger episodes, then dual black holes form as inescapable outcome of galaxy assembly, and can in principle be detected as powerful dual quasars. But, if the black holes reach coalescence, during their inspiral inside the galaxy remnant, then they become the loudest sources of gravitational waves ever in the universe. The Laser Interferometer Space Antenna is being developed to reveal these waves that carry information on the mass and spin of these binary black holes out to very large look-back times. Nature seems to provide a pathway for the formation of these exotic binaries, and a number of key questions need to be addressed: How do massive black holes pair in a merger? Depending on the properties of the underlying galaxies, do black holes always form a close Keplerian binary? If a binary forms, does hardening proceed down to the domain controlled by gravitational wave back reaction? What is the role played by gas and/or stars in braking the black holes, and on which timescale does coalescence occur? Can the black holes accrete on flight and shine during their pathway to coalescence? After outlining key observational facts on dual/binary black holes, we review the progress made in tracing their dynamics in the habitat of a gas-rich merger down to the smallest scales ever probed with the help of powerful numerical simulations. N-Body/hydrodynamical codes have proven to be vital tools for studying their evolution, and progress in this field is expected to grow rapidly in the effort to describe, in full realism, the physics of stars and gas around the black holes, starting from the cosmological large scale of a merger. If detected in the new window provided by the upcoming gravitational wave experiments, binary black holes will provide a deep view into the process of hierarchical clustering which is at the heart of the current paradigm of galaxy formation. They will also be exquisite probes for testing General Relativity, as the theory of gravity. The waveforms emitted during the inspiral, coalescence and ringdown phase carry in their shape the sign of a dynamically evolving space-time and the proof of the existence of an horizon.

Mechanistic insights on the Pd-catalyzed addition of C–X bonds across alkynes – a combined experimental and computational study

“…In addition, analyzing the changes in bond lengths during the isomerization from cis - to trans -Pd( ii ) intermediate ( VIa to Va ) shows a slight elongation of the double bond and concomitant shortening of both C–Si and C–Pd bonds in the TS, suggesting a delocalization of positive charge between Pd, C and Si. 48 This corresponds with the calculated Mayer bond orders, 63,64 which indicate a decrease in bond order of the CC double bond during the TS for both R = TIPS and R = Mes, although more pronounced for the latter. At the same time, the C–R (R = TIPS or Mes) bond order increases during isomerization (indicating delocalization of charge into the R-substituent).…”

Pentavalent lanthanide nitride-oxides: NPrO and NPrO−complexes with NPr triple bonds

“…Herein, relativistic effects were taken into account through the zero-order regular approximation (ZORA) 22. Slater basis sets with the quality of triple-ζ plus two polarization functions (TZ2P)23 were used with the frozen core approximation and applied to the inner shells of [1s 2 –4d 10 ] for Pr, and [1s 2 ] for O and N. Kohn–Sham molecular orbital (MO) analysis and calculations of Mayer bond order indexes24 were also carried out using this program. Natural bond orbital analysis was carried out using NBO 6.0 in the Gaussian 09 program 25…”

The role of basis set superposition error in water addition reactions to Ln(III) cations

“…This result is consistent with the expected performance of large core pseudopotentials, which presumably overestimate the metal-ligand bond lengths due to poorer treatment of the core-valence correlation relative to the small core calculations. Note, however, that addition of a second solvation shell can alter the primary hydration LnOOH 2 bond lengths as a result of changes in the hydrogen bonding between ligands or deviations in electrostatic interactions [23,24].…”