Use of classical forces

  One could immediately ask: how can we use Newton's law to move atoms, when everybody knows that systems at the atomistic level obey quantum laws rather than classical laws, and that Schrödinger's equation is the one to be followed?

A simple test of the validity of the classical approximation is based on the de Broglie thermal wavelength [17], defined as

$$\Lambda = \sqrt{\frac{2\pi\hbar^2}{M k_B T}}$$ (2)

where M is the atomic mass and T the temperature. The classical approximation is justified if $\Lambda \ll a$,where a is the mean nearest neighbor separation. If one considers for instance liquids at the triple point, $\Lambda/a$ is of the order of 0.1 for light elements such as Li and Ar, decreasing further for heavier elements. The classical approximation is poor for very light systems such as $\rm H_2$, He, Ne.

Moreover, quantum effects become important in any system when T is sufficiently low. The drop in the specific heat of crystals below the Debye temperature [18], or the anomalous behavior of the thermal expansion coefficient, are well known examples of measurable quantum effects in solids.

Molecular dynamics results should be interpreted with caution in these regions.