Variational reduced density matrix method in the doubly-occupied configuration interaction space using four-particle N-representability conditions: Application to the XXZ model of quantum magnetism.

This work deals with the variational determination of the two-particle reduced density matrix (2-RDM) and the energy corresponding to the ground state of N-particle systems within the doubly occupied configuration interaction (DOCI) space. Here, we impose for the first time up to four-particle N-representability constraint conditions in the variational determination of the 2-RDM matrix elements using the standard semidefinite programming algorithms. The energies and 2-RDMs obtained from this treatment and the corresponding computational costs are compared with those arisen from previously reported less restrictive variational methods [D. R. Alcoba et al., J. Chem. Phys. 149, 194105 (2018)] as well as with the exact DOCI values. We apply the different approximations to the one-dimensional XXZ model of quantum magnetism, which has a rich phase diagram with one critical phase and constitutes a stringent test for the method. The numerical results show the usefulness of our treatment to achieve a high degree of accuracy.

Buffer catalyzed cleavage of uridylyl-3',5'-uridine in aqueous DMSO: comparison to its activated analog, 2-hydroxypropyl 4-nitrophenyl phosphate.

Buffer catalysis of the cleavage and isomerization of uridylyl-3',5'-uridine (UpU) has been studied over a wide pH range in 80% aq. DMSO. The diminished hydroxide ion concentration in this solvent system made catalysis by amine buffers (morpholine, 4-hydroxypiperidine and piperidine) visible even at relatively low buffer concentrations (10-200 mmol L(-1)). The observed catalysis was, however, much weaker than what has been previously reported for the activated RNA model 2-hydroxypropyl 4-nitrophenyl phosphate (HPNP) in the same solvent system. In the case of morpholine, contribution of both the acidic and the basic buffer constituent was significant, whereas with 4-hydroxypiperidine and piperidine participation of the acidic constituent could not be established unambiguously. The results underline the importance of using realistic model compounds, along with activated ones, in the study of the general acid/base catalysis of RNA cleavage.

Biophysical modelling of phytoplankton communities from first principles using two-layered spheres: Equivalent Algal Populations (EAP) model.

There is a pressing need for improved bio-optical models of high biomass waters as eutrophication of coastal and inland waters becomes an increasing problem. Seasonal boom conditions in the Southern Benguela and persistent harmful algal production in various inland waters in Southern Africa present valuable opportunities for the development of such modelling capabilities. The phytoplankton-dominated signal of these waters additionally addresses an increased interest in Phytoplankton Functional Type (PFT) analysis. To these ends, an initial validation of a new model of Equivalent Algal Populations (EAP) is presented here. This paper makes a first order comparison of two prominent phytoplankton Inherent Optical Property (IOP) models with the EAP model, which places emphasis on explicit bio-physical modelling of the phytoplankton population as a holistic determinant of inherent optical properties. This emphasis is shown to have an impact on the ability to retrieve the detailed phytoplankton spectral scattering information necessary for PFT applications and to successfully simulate reflectance across wide ranges of physical environments, biomass, and assemblage characteristics.

On the measure of electron correlation and entanglement in quantum chemistry based on the cumulant of the second-order reduced density matrix.

In this paper we propose a functional of the many-body cumulant of the second-order reduced density matrix within the spin-free formalism of quantum chemistry which quantifies the idea of electron correlation and allows one to detect spin entanglement. Its properties are rigorously stated and discussed for spin-adapted pure states. Numerical determinations are performed for both equilibrium conformations and dissociation processes in molecular systems.

Correlated holes and their relationships with reduced density matrices and cumulants.

This paper describes a matrix formulation for the correlated hole theory within the framework of the domain-averaged model in many electron systems (atoms, molecules, condensed matter, etc.). General relationships between this quantity and one-particle reduced density matrices for any independent particle or correlated state functions are presented. This formulation turns out to be suitable for computational purposes due to the straightforward introduction of cumulants of two-particle reduced density matrices within the quantum field structure. Numerical calculations in selected simple molecular systems have been performed in order to determine preliminary correlated values for such a quantity.

Determination of atomic valence indices from population analyses at correlated level.

This work carries out a study of atomic valences within molecular systems based on Mulliken and topological population analyses at correlated level. The use of the unpaired electron densities leads to suitable relationships between valences, free valence indices, and bond indices, which turn out to be quite useful for computational purposes. The results arising from both methods at correlated and uncorrelated levels are compared in a large series of chemical compounds. Several interesting conclusions are drawn out and analyzed in detail.