New approximation to the third-order density : application to the calculation of correlated multicenter indices

In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro's, Nakatsuji's and Mazziotti's approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation

Inorganic Nanoparticles and the Immune System: Detection, Selective Activation and Tolerance

The immune system is the responsible for body integrity and prevention of external invasion. On one side, nanoparticles are no triggers that the immune system is prepared to detect, on the other side it is known that foreign bodies, not only bacteria, viruses and parasites, but also inorganic matter, can cause various pathologies such as silicosis, asbestosis or inflammatory reactions. Therefore, nanoparticles entering the body, after interaction with proteins, will be either recognized as self-agents or detected by the immune system, encompassing immunostimulation or immunosuppression responses. The nature of these interactions seems to be dictated not specially by the composition of the material but by modifications of NP coating (composition, surface charge and structure). Herein, we explore the use of gold nanoparticles as substrates to carry multifunctional ligands to manipulate the immune system in a controlled manner, from undetection to immunostimulation. Murine bone marrow macrophages can be activated with artificial nanometric objects consisting of a gold nanoparticle functionalized with peptides. In the presence of some conjugates, macrophage proliferation was stopped and pro-inflammatory cytokines were induced. The biochemical type of response depended on the type of conjugated peptide and was correlated with the degree of ordering in the peptide coating. These findings help to illustrate the basic requirements involved in medical NP conjugate design to either activate the immune system or hide from it, in order to reach their targets before being removed by phagocytes. Additionally, it opens up the possibility to modulate the immune response in order to suppress unwanted responses resulting from autoimmunity, or allergy or to stimulate protective responses against pathogens.