Koopmans' Analysis of Chemical Hardness with Spectral-Like Resolution

Three approximation levels of Koopmans' theorem are explored and applied: the first referring to the inner quantum behavior of the orbitalic energies that depart from the genuine ones in Fock space when the wave-functions' Hilbert-Banach basis set is specified to solve the many-electronic spectra of spin-orbitals' eigenstates; it is the most subtle issue regarding Koopmans' theorem as it brings many critics and refutation in the last decades, yet it is shown here as an irrefutable “observational” effect through computation, specific to any in silico spectra of an eigenproblem; the second level assumes the “frozen spin-orbitals” approximation during the extracting or adding of electrons to the frontier of the chemical system through the ionization and affinity processes, respectively; this approximation is nevertheless workable for great deal of chemical compounds, especially organic systems, and is justified for chemical reactivity and aromaticity hierarchies in an homologue series; the third and the most severe approximation regards the extension of the second one to superior orders of ionization and affinities, here studied at the level of chemical hardness compact-finite expressions up to spectral-like resolution for a paradigmatic set of aromatic carbohydrates.

TESTING THE INFLATIONARY NULL ENERGY CONDITION WITH CURRENT AND FUTURE COSMIC MICROWAVE BACKGROUND DATA

In some classes of inflationary models, a violation of the null energy condition (NEC) is expected during the phase of accelerated expansion. The most striking observational effect would be a "blue" spectrum of primordial gravitational waves with a spectral index nT larger than zero. In this brief paper, we first update the current constraints on the amplitude of a blue GW spectrum. We then forecast the ability of the ongoing Planck satellite mission to detect a violation of the NEC during inflation, showing that the detection of the GW background is substantially improved if the NEC is violated during inflation.