Comparison of the experimental, semi-experimental and ab initio equilibrium structures of acetylene: Influence of relativisitic effects and of the diagonal Born-Oppenheimer corrections

The equilibrium structure of acetylene (also named ethyne) has been reinvestigated to resolve the small discrepancies noted between different determinations. The size of the system as well as the large amount of available experimental data provides the quite unique opportunity to check the magnitude and relevance of various contributions to equilibrium structure as well as to verify the accuracy of experimental results. With respect to pure theoretical investigation, quantum-chemical calculations at the coupled-cluster level have been employed together with extrapolation to the basis set limit, consideration of higher excitations in the cluster operator, inclusion of core correlation effects as well as relativistic and diagonal Born-Oppenheimer corrections. In particular, it is found that the extrapolation to the complete basis set limit, the inclusion of higher excitations in the electronic-correlation treatment and the relativistic corrections are of the same order of magnitude. It also appears that a basis set as large as a core-valence quintuple-zeta set is required for accurately accounting for the inner-shell correlation contribution. From a pure experimental point of view, the equilibrium structure has been determined using very accurate rotational constants recently obtained by a global analysis (that is to say that all non-negligible interactions are explicitely included in the Hamiltonian matrix) of rovibrational spectra. Finally, a semi-experimental equilibrium structure (where the equilibrium rotational constants are obtained from the experimental ground state rotational constants and computed rovibrational corrections) has been obtained from the available experimental ground-state rotational constants for ten isotopic species corrected for computed vibrational corrections. Such a determination led to the revision of the ground-state rotational constants of two isotopologues, thus showing that structural determination is a good method to identify errors in experimental rotational constants. The three structures are found in a very good agreement, and our recommended values are rCC 120.2958(7) pm and rCH 106.164(1) pm. © 2011 American Institute of Physics.

Plane wave and Coulomb asymptotics

A simple plane wave solution of the Schrodinger-Helmholtz equation is a quantum eigenfunction obeying both energy and linear momentum correspondence principles. Inclusion of the outgoing wave with scattering amplitude f asymptotic development of the plane wave, we show that there is a problem with angular momentum when we consider forward scattering at the point of closest approach and at large impact parameter given semiclassically by (l + 1/2)/k where l is the azimuthal quantum number and may be large (J. Leech et al., Phys. Rev. Lett. 88. 257901 (2002)). The problem is resolved via non- uniform, non-standard analysis involving the Heaviside step function, unifying classical, semiclassical and quantum mechanics, and the treatment is extended to the case of pure Coulomb scattering.

Marine reservoir corrections: St Helena, South Atlantic Ocean

We present the first marine reservoir age and Delta R determination for the island of St. Helena using marine mollusk radiocarbon dates obtained from an historical context of known age. This represents the first marine reservoir a.-c and Delta R determination in the southern Atlantic Ocean within thousands of kilometers of the island. The depletion of C-14 in the shells indicates a rather larger reservoir age for that portion of the surface Atlantic than models indicate. The implication is that upwelling old water along the Namibian coast is transported for a considerable distance, although it is likely to be variable on a decadal timescale. An artilleryman's button, together with other artifacts found in a midden, demonstrate association of the mollusk shells with a narrow historic period of AD 1815-1835.

Strong-field approximation for Coulomb explosion of H-2(+) and D-2(+) by short intense laser pulses

We present a simple quantum mechanical model to describe Coulomb explosion of H-2(+) and D-2(+) by short, intense infrared laser pulses. The model is based on the length gauge version of the molecular strong-field approximation and is valid when the process of dissociation prior to ionization is negligible. The results are compared with recent experimental data for the proton kinetic energy spectrum [Th. Ergler , Phys. Rev. Lett. 95, 093001 (2005); D. S. Murphy , J. Phys. B 40, S359 (2007)]. Using a Franck-Condon distribution over initial vibrational states, the theory reproduces the overall shape of the spectrum with only a small overestimation of slow protons. The agreement between theory and experiment can be made perfect by using a non-Frank-Condon initial distribution characteristic for H-2(+) (D-2(+)) targets produced by strong-field ionization of H-2 (D-2). For comparison, we also present results obtained by two different tunneling models for this process.

Ramsey interferometry with a spin embedded in a Coulomb chain

We show that the statistical properties of a Coulomb crystal can be measured by means of a standard interferometric procedure performed on the spin of one ion in the chain. The ion spin, constituted by two internal levels of the ion, couples to the crystal modes via spatial displacement induced by photon absorption. The loss of contrast in the interferometric signal allows one to measure the autocorrelation function of the crystal observables. Close to the critical point, where the chain undergoes a second-order phase transition to a zigzag structure, the signal gives the behavior of the correlation function at the critical point.

‘Transforming justice’: challenges for restorative justice in an era of punishment-based corrections

Scholars of restorative justice have long debated its theoretical relationship with formal criminal justice. This analysis critically examines the range of sociostructural conditions in contemporary society that have halted the spread of restorative policies in practice and prevented them from realizing their transformative potential as an alternative system of justice. These factors are attributed largely to a punitive penal culture that is characterized by policy-making based on penal populism, the governance of risk and a managerialist criminal justice agenda; and the widespread co-optation of restorative programs by the state. This broad argument is explored in the context of two particular case studies – recent developments in youth justice and in sexual offending respectively in England and Wales and elsewhere. This examination ultimately highlights challenges for restorative justice in the current risk-driven penal climate and advocates a need to re-evaluate its relationship with formal state justice.

On the required shape corrections to the local density and generalized gradient approximations to the Kohn-Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies

It is well known that shape corrections have to be applied to the local-density (LDA) and generalized gradient (GGA) approximations to the Kohn-Sham exchange-correlation potential in order to obtain reliable response properties in time dependent density functional theory calculations. Here we demonstrate that it is an oversimplified view that these shape corrections concern primarily the asymptotic part of the potential, and that they affect only Rydberg type transitions. The performance is assessed of two shape-corrected Kohn-Sham potentials, the gradient-regulated asymptotic connection procedure applied to the Becke-Perdew potential (BP-GRAC) and the statistical averaging of (model) orbital potentials (SAOP), versus LDA and GGA potentials, in molecular response calculations of the static average polarizability alpha, the Cauchy coefficient S-4, and the static average hyperpolarizability beta. The nature of the distortions of the LDA/GGA potentials is highlighted and it is shown that they introduce many spurious excited states at too low energy which may mix with valence excited states, resulting in wrong excited state compositions. They also lead to wrong oscillator strengths and thus to a wrong spectral structure of properties like the polarizability. LDA, Becke-Lee-Yang-Parr (BLYP), and Becke-Perdew (BP) characteristically underestimate contributions to alpha and S-4 from bound Rydberg-type states and overestimate those from the continuum. Cancellation of the errors in these contributions occasionally produces fortuitously good results. The distortions of the LDA, BLYP, and BP spectra are related to the deficiencies of the LDA/GGA potentials in both the bulk and outer molecular regions. In contrast, both SAOP and BP-GRAC potentials produce high quality polarizabilities for 21 molecules and also reliable Cauchy moments and hyperpolarizabilities for the selected molecules. The analysis for the N-2 molecule shows, that both SAOP and BP-GRAC yield reliable energies omega(i) and oscillator strengths f(i) of individual excitations, so that they reproduce well the spectral structure of alpha and S-4.(C) 2002 American Institute of Physics.

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Shape corrections to the standard approximate Kohn-Sham exchange-correlation (xc) potentials are considered with the aim to improve the excitation energies (especially for higher excitations) calculated with time-dependent density functional perturbation theory. A scheme of gradient-regulated connection (GRAC) of inner to outer parts of a model potential is developed. Asymptotic corrections based either on the potential of Fermi and Amaldi or van Leeuwen and Baerends (LB) are seamlessly connected to the (shifted) xc potential of Becke and Perdew (BP) with the GRAC procedure, and are employed to calculate the vertical excitation energies of the prototype molecules N-2, CO, CH2O, C2H4, C5NH5, C6H6, Li-2, Na-2, K-2. The results are compared with those of the alternative interpolation scheme of Tozer and Handy as well as with the results of the potential obtained with the statistical averaging of (model) orbital potentials. Various asymptotically corrected potentials produce high quality excitation energies, which in quite a few cases approach the benchmark accuracy of 0.1 eV for the electronic spectra. Based on these results, the potential BP-GRAC-LB is proposed for molecular response calculations, which is a smooth potential and a genuine "local" density functional with an analytical representation. (C) 2001 American Institute of Physics.