Communication: Improved ab initio molecular dynamics by minimally biasing with experimental data

Abstract

Accounting for electrons and nuclei simultaneously is a powerful capability of ab initio molecular dynamics (AIMD). However, AIMD is often unable to accurately reproduce properties of systems such as water due to inaccuracies in the underlying electronic density functionals. This shortcoming is often addressed by added empirical corrections and/or increasing the simulation temperature. We present here a maximum-entropy approach to directly incorporate limited experimental data via a minimal bias. Biased AIMD simulations of water and an excess proton in water are shown to give significantly improved properties both for observables which were biased to match experimental data and for unbiased observables. This approach also yields new physical insight into inaccuracies in the underlying density functional theory as utilized in the unbiased AIMD.

Absolute proton hydration free energy, surface potential of water, and redox potential of the hydrogen electrode from first principles: QM/MM MD free-energy simulations of sodium and potassium hydration

“…For the cluster-continuum calculations, error sources include the selection of the clusters (sampling), their small sizes (smooth trends and fast convergence being required for a meaningful extrapolation 117 ), the estimation of the cluster entropy, 118-120 the choice of a cluster permittivity in the CE calculation, and the problems associated with a QM-CE boundary (surface definition, atomic radii). For the CPMD/BOMD calculations, error sources include the shortcomings of DFT methods in terms of electron correlation (including dispersion), affecting both bulk water properties [121][122][123][124][125][126][127][128][129][130] and ion-water interactions, 66,67,105,131 the small system sizes considered (resulting in a high weight for the approximate finite-size correction term), the very limited sampling times, the ambiguity in defining the appropriate reference potential within DFT water, 21,112,[132][133][134][135][136] and the numerical problems (see, e.g., footnotes 42 and 45 in Ref. 111) associated with creating a species or injecting electrons when applying computational alchemy in a QM framework [137][138][139][140][141][142][143] (see, however, Refs.…”

Coarse-Grained Directed Simulation

“…7 The way that the pre-factor η t is adjusted corresponds to a learning rate rule, that is, how much trust to ascribe to the step size coming from the other λ -dependent terms. For example, Bussi and coworkers use 9 : $${\eta }_i^t=\frac{A_i}{1+\frac{t}{{\tau }_i}}$$ while White and Voth use 8, 10–11 : $${\eta }_i^t=\frac{A_i}{\sqrt{true{\sum }_{j=1}^t{\left({\delta }_i^t\right)}^2}}$$For the linear bias, the gradient term is a matrix with entries given by: $${\left(\frac{\partial \mathrm{bold-italic\Delta }}{\partial {\mathit{\lambda }}^t}\right)}_{ij}=-{false\langle f_i{f}_{j}false\rangle }_t+{false\langle f_{i}false\rangle }_t{false\langle f_{j}false\rangle }_t,$$ so, the gradient is proportional to the covariance of the two observables on iteration t : $$\left(\frac{\partial \mathrm{bold-italic\Delta }}{\partial {\mathit{\lambda }}^t}\right)=-{\text{Cov}}^{t}false(f_i,f_{j}false)\equiv \overline{\stackrel{false¯}{J}}$$…”

Recent advances in maximum entropy biasing techniques for molecular dynamics

“…The bottom plot shows how each value ofr corresponds to a unique biasing strength. A more sophisticated system which demonstrates the capabilities of improving dynamic observables is the recent work on EDS ab initio molecular dynamics (AIMD) simulations of water [10]. DFT water with the BLYP exchange functional poorly represents water structure as seen in Figure 3 (black line).…”

“…A number of unrelated observables improved as well, including RDFs and the water self-diffusion coefficient, which increased to 0.06±Å 2 /ps. White et al [10] further demonstrated that the EDS bias could be transferred to excess proton-water simulations and that when combined with DFT dispersion corrections [28], the agreement further improves. The accuracy improvement with the dispersion corrections shows that EDS is general in its applicability to DFT methods.…”

“…The key results from EDS have been to improve thermodynamic observables and indirectly improve dynamic observables. For example, EDS was recently used to create a state-of-the-art DFT water model that gives near perfect agreement with X-ray scattering results, water diffusivity, and proton-hopping behavior by improving only the water oxygen-oxygen coordination number [10].…”