Molecules in confinement in clusters, quantum solvents and matrices: general discussion

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

A solvent is a substance, most often a liquid, that can dissolve other substances. Here, the substance being dissolved is called a solute. When a solvent and a solute combine, they form a solution - a homogenous mixture of both the solvent and the solute. Water is a universal biological solvent. Its polar structure allows it to dissolve many other polar compounds. The ability of water to dissolve is governed by a balance between water molecules binding to each other and binding to the solute.
A...

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

Most acid-base titrations are performed in an aqueous medium. In aqueous titrations, water competes with weaker acids or bases for proton donation or acceptance, leading to ambiguous endpoints in the titration curve. Water also affects the partial ionization of weak acids or bases. For example, water accepts a proton from acetic acid to form hydronium and acetate ions. The hydronium ion formed is a stronger acid than acetic acid, and the acetate ion is a stronger base than water. As a result,...

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...

After budding out from the ER membrane, some COPII vesicles lose their coat and fuse with one another to form larger vesicles and interconnected tubules called vesicular tubular clusters or VTCs. These clusters constitute a compartment at the ER-Golgi interface known as ERGIC (Endoplasmic Reticulum Golgi Intermediate Compartment). The ERGIC is a mobile membrane-bound cargo transport system that sorts proteins secreted from ER and delivers them to the Golgi.
With the help of motor proteins such...