Erratum: "On the meaning of Berry force for unrestricted systems treated with mean-field electronic structure" [J....

Intermolecular forces (IMF) are electrostatic attractions arising from charge-charge interactions between molecules. The strength of the intermolecular force is influenced by the distance of separation between molecules. The forces significantly affect the interactions in solids and liquids, where the molecules are close together. In gases, IMFs become important only under high-pressure conditions (due to the proximity of gas molecules). Intermolecular forces dictate the physical properties of...

Non-conservative forces are dissipative forces such as friction or air resistance. These forces take energy away from a system as it progresses. Unlike conservative forces, non-conservative forces do not have potential energy associated with them. This is because the energy is lost to the system and cannot be turned into useful work later.
Also unlike their conservative counterparts, they are path-dependent; where the object starts and stops does matter. For example, a grinding wheel applies a...

An applied magnetic field causes loosely bound π-electrons in organic molecules to circulate, producing a local or induced diamagnetic field over a large spatial volume. As the molecules tumble in solution, the field generated by π-electrons in spherical substituents results in a zero net field. However, the net field generated by π-electrons in non-spherical substituents is not zero. The effect of this induced field depends on the orientation of the molecule with respect to B0, resulting in...

In aromatic compounds, such as benzene, the circulation of (4n + 2) π-electrons sets up a diamagnetic or diatropic ring current around the perimeter of the molecule. This current induces a magnetic field that opposes the external field inside the ring and reinforces it on the outside. The protons in benzene are deshielded and exhibit high chemical shifts in the range 6.5–8.5 ppm. The shielding effect at the center of the ring is evident in complex aromatic molecules, such as annulenes. In...

Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...

A two-dimensional system in mechanical engineering involves the analysis of motion and forces in a plane. A two-dimensional force vector can be resolved into its components as: