2. Nanoscale modeling

When we speak of atoms, ions or electrons, we're talking about the quantum world, one of whose basic concepts is wave-particle duality, i.e. all objects in this world simultaneously exhibit wave and particle properties. In quantum mechanics, the trajectory of a particle is replaced by a time-dependent state characterized by a wave function that depends on both the particle's position r and time t: ψ(r, t). This wave function, in itself, has no physical significance, but it can be interpreted as a probability amplitude, its square ψ*.ψ = |ψ (r, t)| ² then representing the probability density of the particle's presence at a given point in space, at a given time.

It is this electron density that nanoscopic or atomistic methods seek to determine.

This gives rise to two main classes of methods:...