Classical methods

The Born-Oppenheimer approximation separated the motions of the nuclei and the electrons, due to the large difference in their size. This gives theoretical chemists two options for how to model a chemical system, and determine the potential energy:

  • Treat the nuclei as stationary and model the motions and interactions of the electrons using the Schrödinger equation
  • To integrate the motions of the electrons into the nuclei and model these particles as point charges Knowledge of the potential energy of a given atomic configuration means that is it possible to compare different configurations and determine the most probable.

The former is the basis for quantum mechanical calculations, such as density functional theory (DFT) methods. In these methods, the aim is to find an iterative solution to the Schrödinger equation. However, these methods are very computationally expensive and are therefore realistically limited to hundreds or thousands of atoms [1]. We will not discuss the details of quantum mechanical methods more than this, for more information, there are many great textbooks on the subject [2,3].

The latter uses methods that are known as classical methods. Classical methods involve the use of a potential model (sometimes called a force-field) to simulate chemical systems. Examples of simulations techniques that may leverage classical methods include molecular dynamics (which we will cover in this resource), Monte Carlo, Langevin dynamics, etc. A potential model uses mathematical functions to determine the potential energy of a given configuration of atoms. The use of mathematical functions to model the interactions of the particles is less computationally expensive than quantum mechanical methods meaning that it is possible to simulate larger systems.

An example of a classical method can be seen below where the particles have only a van der Waals interaction, which is a good model for argon gas. The number in the function is the temperature of the simulation in Kelvin. Click the “Interact” button at the top of this page to launch an interactive MyBinder page, you can then run the simulation at a series of different temperatures and see how the motions of the particles change.

import vdw
%matplotlib notebook
vdw.simulation(300)

References

  1. Erba, A.; Baima, J.; Bush, I.; Orlando, R.; Dovesi, R. J. Chem. Theory Comput. 2017, 13 (10), 5019–5027. 10.1021/acs.jctc.7b00687.
  2. Harvey, J. Computational Chemistry; Oxford University Press: Oxford, 2018.
  3. Atkins, P. W.; Friedmann, R. S. Molecular Quantum Mechanics, 5th ed.; Oxford University Press: Oxford, 2010.