The present work presents three second-order perturbative developments from a complete active space (CAS) zero-order wave function, which are strictly additive with respect to molecular dissociation and intruder state free. They differ by the degree of contraction of the outer-space perturbers. Two types of zero-order Hamiltonians are proposed, both are bielectronic, incorporating the interactions between electrons in the active orbitals, therefore introducing a rational balance between the zero-order wave function and the outer-space. The use of Dyall’s Hamiltonian, which puts the active electrons in a fixed core field, and of a partially contracted formalism seems a promising compromise. The formalism is generalizable to multireference spaces which are parts of a CAS. A few test applications of the simplest variant developed in this paper illustrate its potentialities.

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Small- and medium-core pseudopotentials representing [Ar]3d10- and [Kr]-like cores, respectively, have been adjusted for the In atom, supplementing the energy-consistent three-valence-electron large-core ([Kr]4d10 core) pseudopotential of the Stuttgart group. The performance of these potentials is tested against those of other groups and against experiment, in calculations for the ground-state potential curves of InH, InF, and InCl, both at the self-consistent-field and correlated levels. The role of the core size is discussed, and systematic errors of large- and medium-core pseudopotentials are analyzed.

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Atmospheric compositions can provide powerful diagnostics of formation and migration histories of planetary systems. We investigate constraints on atmospheric abundances of H 2 O, Na, and K, in a sample of transiting exoplanets using latest transmission spectra and new H 2 broadened opacities of Na and K. Our sample of 19 exoplanets spans from cool mini-Neptunes to hot Jupiters, with equilibrium temperatures between ∼300 and 2700 K. Using homogeneous Bayesian retrievals we report atmospheric abundances of Na, K, and H 2 O, and their detection significances, confirming 6 planets with strong Na detections, 6 with K, and 14 with H 2 O. We find a mass-metallicity trend of increasing H 2 O abundances with decreasing mass, spanning generally substellar values for gas giants and stellar/superstellar for Neptunes and mini-Neptunes. However, the overall trend in H 2 O abundances, from mini-Neptunes to hot Jupiters, is significantly lower than the mass-metallicity relation for carbon in the solar system giant planets and similar predictions for exoplanets. On the other hand, the Na and K abundances for the gas giants are stellar or superstellar, consistent with each other, and generally consistent with the solar system metallicity trend. The H 2 O abundances in hot gas giants are likely due to low oxygen abundances relative to other elements rather than low overall metallicities, and provide new constraints on their formation mechanisms. The differing trends in the abundances of species argue against the use of chemical equilibrium models with metallicity as one free parameter in atmospheric retrievals, as different elements can be differently enhanced.

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Control of near-degeneracy effects and dynamical correlation in atoms and molecules is within sight, thanks to an economical method that mixes configuration interaction ͑CI͒ and density functional theory ͑DFT͒. The influence of the size of the configuration-space has been studied for light systems including elements of the first and second period of the Periodic Table.

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