Dynamic Computational Chemistry

Computational chemistry of molecules in the form of its work horse Density Functional Theory DFT based on the Schrödinger equation of quantum mechanics, typically computes end states of kernel/electron configurations from energy minimisation, and not the dynamics of the formation of a molecule. This is understandable since electron configurations appear as probability densities expressed by a wave function, and dynamics of probability distributions can appear to be difficulty to capture.  There are methods of molecular dynamics to handle this like Car-Parrinello based on DFT as a mixture of classical mechanics for kernels and quantum mechanics for electrons, but they require heavy computation.

We meet the same situation in statistical thermodynamics focussed on equilibrium states of increasing  entropy, and not the actual dynamics leading from one state to the other. But it is possible to follow the dynamics by computing solutions to the Euler equations for compressible flow, as shown in Computational Thermodynamics.  

In a similar spirit Real Quantum Mechanics RealQM describes the dynamics of molecule formation based on a new type of Schrödinger equation in the form of classical deterministic continuum mechanics geared to simulate dynamics without the above split into classical and non-classical mechanics, with a prospect of more reasonable computational cost. The establishing of the free boundary in RealQM can also be seen as a dynamic process of shifting electron densities to reach continuity. The precise shift of electron densities in a radiating atom is open to simulation of RealQM.

Here you can yourself run RealQM code for the dynamical formation of the first molecule in the early Universe from a Helium atom capturing a proton to form the cation He+H.