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The N-representability problem places fundamental constraints on reduced density matrices (RDMs) that originate from physical many-fermion quantum states. Motivated by recent developments in functional theories, we introduce a hierarchy of ensemble one-body N-representability problems that incorporate partial knowledge of the one-body RDMs (1RDMs) within an ensemble of N-fermion states with fixed weights wi. Specifically, we propose a systematic relaxation that reduces the refined problem—where full 1RDMs are fixed for certain ensemble elements—to a more tractable form involving only natural occupation number vectors. Remarkably, we show that this relaxed problem is related to a generalization of Horn’s problem, enabling an explicit solution by combining its constraints with those of the weighted ensemble N-representability conditions. An additional convex relaxation yields a convex polytope that provides physically meaningful restrictions on lattice site occupations in ensemble density functional theory for excited states.

Computational Quantum Chemistry removes much of the mystery of modern computer programs for molecular orbital calculations by showing how to develop Excel spreadsheets to perform model calculations and investigate the properties of basis sets. Using the book together with the CD-ROM provides a unique interactive learning tool. In addition, because of the integration of theory with working examples on the CD-ROM, the reader can apply advanced features available in the spreadsheet to other applications in chemistry, physics, and a variety of disciplines that require the solution of differential equations.This book and CD-ROM makes a valuable companion for instructors, course designers, and students. It is suitable for direct applications in practical courses in theoretical chemistry and atomic physics, as well as for teaching advanced features of Excel in IT courses.

Hydroperoxymethyl thioformate (or HPMTF) is a compound relevant to the chemistry of sulfur in the marine atmosphere. The chemical cycling of this molecule in the atmosphere is still uncertain due in part to the lack of accurate knowledge of its photolytic behavior. Only approximations based on the properties of its chromophores are used in previous studies. In this work, we calculated the absorption spectra of the molecule in gas and aqueous phases using the Nuclear Ensemble Approach (NEA) and the CASPT2 method. Furthermore, we used such information to obtain relative photolysis rates. We found that the chromophore approximation overestimates the photolysis rates in the gas phase by twice the value obtained with the NEA-CASPT2 protocol. Furthermore, for the aqueous phase, we predict a lower role of photolysis as compared to the gas phase.