"On-the-fly" Coupled Cluster Path Integral Molecular Dynamics

In this post, I'll show some supplementary details in addition to our "on-the-fly" coupled cluster path integral molecular dynamics paper [1].

In physical chemistry, there are many examples where molecular dynamics is used to sample atomistic systems. The electronic structure of such systems can be described with various methods. One very accurate ab initio method (i.e. one that does not require empirical parameters to describe the electronic structure), but also computationally expensive one is the coupled-cluster (CC) theory. In our paper, we used it to calculate the interatomic forces in a molecular dynamics simulation of the protonated water dimer [1]. We note in passing that this is to our knowledge first CC-based molecular dynamics simulation, which we will refer to also as the classical simulation in the following.

The forces have been calculated with cfour and the dynamics with a modified version of i-PI. To negotiate between cfour and i-PI, I wrote a wrapper that hands over the positions from i-PI to cfour and the forces from cfour back to i-PI. If anyone is interested in obtaining the wrapper, feel free to drop me a mail.

Here is a movie that depicts the classical point particles and the hopping of the proton between the two waters

Also the nuclei can be treated as quantum mechanically blurred particles. The path integral molecular dynamics (together with the Born-Oppenheimer approximation) provides an easy and (at least after a while) intuitively approach, where now each particle is replaced by a closed ring polymer with harmonic springs between the particles. In a pictographic way this would look like

where each of the two particles are represented by a closed P-bead ring polymer and the interatomic potential needs to be evaluated P times. In this case P has been chosen as 6, but it depends on the quantum nature of the system. Generally speaking, the nuclear quantum effects increase with decreasing temperature and particle masses.

The quantum simulation with quantum mechanically blurred particles and with P=32 now looks like

which is the to our knowledge first CC-based PIMD simulation.

For more details about the simulation, see the publication [1].

References:

[1] T. Spura, H. Elgabarty and T. D. Kühne, Phys. Chem. Chem. Phys., 2015, 17, 14355-14359 DOI: 10.1039/C4CP05192K