Molecular Dynamics Driven by the Many-Body Expansion (MBE-MD)

We present a protocol for classical and nuclear quantum dynamics, in which the energies and forces are generated by the many-body expansion (MBE), and apply it to water clusters using the TTM2.1-F and MB-Pol interaction potentials at various temperatures. We carry out MBE-molecular dynamics (MD) classical and nuclear quantum dynamical simulations, in which the energies and forces of the full system are approximated by the two-, three-, and four-body terms of the MBE, and compare the average potential and the vibrational density of states with the full simulation, i.e., the one for which no MBE is used. Our results indicate that the thermally averaged potential energy from the MBE up to the four-body term converges with near-identical behavior to the one from the full simulation. The three-body makes a substantial contribution (∼20%) to the energy, whereas the four-body is necessary for obtaining quantitatively accurate energetics and forces, albeit making a small contribution to each (∼2%). We further show that the harmonic frequencies are reproduced to within a few wavenumbers (cm^–1) at the four-body level and that the slowest modes to converge with the MBE rank are those involving the strongest hydrogen bonds. Anharmonicity exacerbates this effect, so that a four-body description of the energies and forces is needed to achieve accurate anharmonic vibrational frequencies in the hydrogen-bonded OH-stretching region. We also discuss the asymptotic scaling of the MBE-MD protocol with respect to the cost of the underlying potential energy evaluation, suggesting that electronic structure methods that scale at least as N⁴, N being the size of the system, are needed to result in savings over the traditional full MD simulation. We anticipate that the MBE-MD protocol can evolve into a powerful and practical method, which will allow for highly accurate ab initio MD simulations on a much broader range of molecular systems than can be currently handled.