An introduction to gravitational waves through electrodynamics: a quadrupole comparison

We present a pedagogical introduction to some key computations in gravitational waves via a side-by-side comparison with the quadrupole contribution of electromagnetic radiation. Subtleties involving gauge choices and projections over transverse modes in the tensorial theory are made clearer by direct analogy with the vectorial counterpart. The power emitted by the quadrupole moment in both theories is computed, and the similarities as well as the origins of eventual discrepancies are discussed. Finally, we analyze the stability of bound systems under radiation emission, and discuss how the strength of the interactions can be established this way. We use the results to impose an anthropic bound on Newton's constant of order G < 3×104 Gobs, which is on par with similar constraints from stellar formation.

Amyand David Buckingham. 28 January 1930—4 February 2021

David Buckingham was a chemical physicist and theoretical chemist who made fundamental contributions to the understanding of optical, electric and magnetic properties of molecules. Born in Australia, he was an undergraduate at the University of Sydney and the first PhD research student of John Pople (FRS 1961) at Cambridge, and there he made significant advances in the theory of intermolecular forces and nonlinear optics. He then moved to Oxford, where he and his group performed the first direct measurement of a molecular electric quadrupole moment. He was elected to the first chair of theoretical chemistry at the University of Bristol, where he wrote a particularly influential article on molecular moments, higher-order polarizabilities and intermolecular forces. His next appointment was at the University of Cambridge as the first holder of the 1968 Chair of Chemistry, and he was head of a distinguished department of theoretical chemistry for 28 years. With colleagues he pioneered experiment and theory on vibrational optical activity and developed a powerful model to predict the structures of weakly-bound molecules. A man of broad interests and achievements, he played first class cricket in the 1950s.

A Combined Experimental/Quantum-Chemical Study of Tetrel, Pnictogen, and Chalcogen Bonds of Linear Triatomic Molecules

Linear triatomic molecules (CO2, N2O, and OCS) are scrutinized for their propensity to form perpendicular tetrel (CO2 and OCS) or pnictogen (N2O) bonds with Lewis bases (dimethyl ether and trimethyl amine) as compared with their tendency to form end-on chalcogen bonds. Comparison of the IR spectra of the complexes with the corresponding monomers in cryogenic solutions in liquid argon enables to determine the stoichiometry and the nature of the complexes. In the present cases, perpendicular tetrel and pnictogen 1:1 complexes are identified mainly on the basis of the lifting of the degenerate ν 2 bending mode with the appearance of both a blue and a red shift. Van ′t Hoff plots of equilibrium constants as a function of temperature lead to complexation enthalpies that, when converted to complexation energies, form the first series of experimental complexation energies on sp1 tetrel bonds in the literature, directly comparable to quantum-chemically obtained values. Their order of magnitude corresponds with what can be expected on the basis of experimental work on halogen and chalcogen bonds and previous computational work on tetrel bonds. Both the order of magnitude and sequence are in fair agreement with both CCSD(T) and DFA calculations, certainly when taking into account the small differences in complexation energies of the different complexes (often not more than a few kJ mol−1) and the experimental error. It should, however, be noted that the OCS chalcogen complexes are not identified experimentally, most probably owing to entropic effects. For a given Lewis base, the stability sequence of the complexes is first successfully interpreted via a classical electrostatic quadrupole–dipole moment model, highlighting the importance of the magnitude and sign of the quadrupole moment of the Lewis acid. This approach is validated by a subsequent analysis of the molecular electrostatic potential, scrutinizing the σ and π holes, as well as the evolution in preference for chalcogen versus tetrel bonds when passing to “higher” chalcogens in agreement with the evolution of the quadrupole moment. The energy decomposition analysis gives further support to the importance/dominance of electrostatic effects, as it turns out to be the largest attractive term in all cases considered, followed by the orbital interaction and the dispersion term. The natural orbitals for chemical valence highlight the sequence of charge transfer in the orbital interaction term, which is dominated by an electron-donating effect of the N or O lone-pair(s) of the base to the central atom of the triatomics, with its value being lower than in the case of comparable halogen bonding situations. The effect is appreciably larger for TMA, in line with its much higher basicity than DME, explaining the comparable complexation energies for DME and TMA despite the much larger dipole moment for DME.

Approximate perfect fluid solutions with quadrupole moment

We investigate the interior Einstein’s equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational fields. Assuming that the deviation from spherically symmetry is small, we linearize the corresponding line element and field equations and find several classes of vacuum and perfect fluid solutions. We find some particular approximate solutions by imposing appropriate matching conditions.

Calculation of the Electric Quadrupole Moment of 6Li and 7Li in Shell Model and Cluster Model

In this paper, we have investigated electric quadrupole moment of (_^6)Li and (_^7)Li in both shell model and cluster model. In shell model, the nuclei (_^6)Li and (_^7)Li can be modeled as one core plus nucleons. Nucleons outside the closed shell can be considered as a two- and three-particle system. In cluster structure, we have selected alpha clusters and triton or deuteron in interaction with alpha cluster ((_^7)Li and (_^6)Li involving α+(_^3)H and α+(_^2)H, respectively). By solving Schrödinger equation and using suitable potential for interaction between particles by applying Nikiforov-Uvarov method, potential coefficients have been computed. Then, we have calculated the energy and wave function for nuclei(_^6)Li and (_^7)Li and compared the results obtained with experimental results. By having the wave function, we can obtain the quadrupole moment. These values are compared with predictions from shell-model and cluster-model calculations. Although the difference between them is small, the electric quadrupole moment results in the cluster model are in good agreement with experimental results. Keywords: Electric quadrupole moment, Shell-model, Cluster-model, Li isotopes, Non-relativistic equation.