Generating Converged Accurate Free Energy Surfaces for Chemical Reactions with a Force-Matched Semiempirical Model

Abstract

We demonstrate the capability of creating robust density functional tight binding (DFTB) models for chemical reactivity in prebiotic mixtures through force matching to short time scale quantum free energy estimates. Molecular dynamics using density functional theory (DFT) is a highly accurate approach to generate free energy surfaces for chemical reactions, but the extreme computational cost often limits the time scales and range of thermodynamic states that can feasibly be studied. In contrast, DFTB is a semiempirical quantum method that affords up to a thousandfold reduction in cost and can recover DFT-level accuracy. Here, we show that a force-matched DFTB model for aqueous glycine condensation reactions yields free energy surfaces that are consistent with experimental observations of reaction energetics. Convergence analysis reveals that multiple nanoseconds of combined trajectory are needed to reach a steady-fluctuating free energy estimate for glycine condensation. Predictive accuracy of force-matched DFTB is demonstrated by direct comparison to DFT, with the two approaches yielding surfaces with large regions that differ by only a few kcal mol.

Synthesis of RNA Nucleotides in Plausible Prebiotic Conditions from ab Initio Computer Simulations

“…In addition, we used the topological metric of Ref., 41 accurately tracking changes in the chemical bond network passing from reactants, through intermediates, until the products, particularly suited to chemical reactions in solution. [42][43][44] This metric comparing structure R(t) with reference…”

Synthesis of functionalized nitrogen-containing polycyclic aromatic hydrocarbons and other prebiotic compounds in impacting glycine solutions

“…Parameters for E BS and E Coul were taken from the mio-1-1 parameterization (available at http://www.db.org), a typical off-the-shelf parameter set for organic systems and biomolecules. 44,48,[53][54][55][56] It was previously shown that DFTB can recover DFT-level accuracy for systems under reactive conditions through tuning E Rep to DFT computed forces or training sets. [46][47][48]50,[57][58][59][60][61] Hence, most of the generic E Rep interactions in the mio-1-1 parameterization were replaced with force-matched ones (discussed below) that were determined specically for aqueous glycine chemistry.…”

“…Similar to previous work, we represented the repulsive energy by a pairwise ninth-order polynomial with linear coefficients determined through a forcematching procedure. 46,48 Force matching helps maximize the data from our DFT-MD simulations by tuning E Rep to the 3N forces available from each sampled MD conguration (where N is the number of atoms in the simulation). Potential functions for N-N, O-O, and N-O interactions were omitted from the t due to poor sampling, and repulsive energies from mio-1-1 were used here instead.…”

“…[37][38][39] However, DFT-MD simulations are too computationally intensive to probe beyond picosecond and nanometer time and length scales, whereas chemical equilibrium under these conditions can take nanoseconds or longer to be achieved. [40][41][42] Semi-empirical methods such as the density functional tight binding (DFTB) method [43][44][45][46][47][48] combine approximate quantum mechanics with empirical functions to offer an efficient alternative that is orders of magnitude less computationally intensive while retaining a high degree of accuracy. The computational efficiency of DFTB allows for initiating many independent simulations concurrently to generate trajectories that can approach chemical equilibrium timescales.…”

“…The computational efficiency of DFTB allows for initiating many independent simulations concurrently to generate trajectories that can approach chemical equilibrium timescales. [48][49][50][51] This relatively high throughput allows for running multiple independent MD simulations and gathering of ensemble statistics, which can inform the interpretation of noisy experimental results and validate coarse-grained models (e.g., equations of state) for large-scale simulations.…”