Classical Force-Fields which Reproduce Equilibrium Quantum Distributions

Personal hero and noted banjo enthusiast Bill Miller often poses the following thought experiment to critique classical MD:

The zero point energy in the ~3000 wavenumber modes of water is more than 20 times larger than Kb*T at room temperature. If you gave these degrees of freedom their ZPE in classical MD that ZPE would leak into other modes, at the very least resulting in a high effective temperature.

In protein simulations this isn’t an immediate problem because high-frequency oscillators are frozen out by the SHAKE algorithm (to allow for large integrator timesteps) and given no zero point energy. Clearly it would be nicer to treat the quantum effects in the MD. People in this field know there are many, many ways to do this, usually based on some scheme to approximately integrate the path integral, but nothing as simple as running CHARMM or CPMD.

In this pre-print Ryan Alan and I propose an alternative: generate an effective force field which reproduces the density of the quantum system under the laws of classical statistical mechanics. We show such a potential exists, and that the map between the physical potential and the fictitious effective potential is unique. You can think of this like DFT for quantum MD, it takes a simulation which is easy to perform (classical MD/MC) and gives you the exact density. The catch is that you need to come up with this mapping that contains all the information about the difference between the quantum and classical effective potentials. (something like the problem of knowing the exact functional). We also numerically inverted that map for some low dimensional systems.


McClean’s Clock Variational Principle

In the time between finishing my post-doc and beginning the group I’ve been indulging my appetite for random quantum ideas outside of the electronic structure realm. Jarrod McClean came up with this pretty wild adaptation of quantum computing’s ancilla concept to do quantum dynamics. The approach (which we cast as a version of the quantum time-dependent variational principle) has some interesting features, and we eventually managed to do parallel in time dynamics with it. (arXiv)


Welcome to Summer Student Triet Nguyen!

Triet S. Nguyen comes from Dallas where she studied nanotubes for drug delivery as an undergraduate in the Lab of Prof. Steven O. Nielsen with the assistance of Dr. Udayana Ranatunga. She originally hails from Saigon, and is interested studying quantum aspects of energy transport. Her summer study is supported by generous fellowship funding from The Department of Chemistry at Notre Dame, and she can be temporarily found in COMSEL devouring online coursework and filling Notre Dame CRC queue with chemical simulations. Welcome Triet.