Accelerated Computation of Free Energy Profile at Ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semiempirical Reference Potential. 3. Gaussian Smoothing on Density-of-States

Abstract

Calculations of free energy profile, aka potential of mean force (PMF), along a chosen collective variable (CV) are now routinely applied to the studies of chemical processes, such as enzymatic reactions and chemical reactions in condensed phases. However, if the ab initio QM/MM level of accuracy is required for the PMF, it can be formidably expensive even with the most advanced enhanced sampling methods, such as umbrella sampling. To ameliorate this difficulty, we developed a novel method for the computation of free energy profile based on the reference-potential method recently, in which a low-level reference Hamiltonian is employed for phase space sampling and the free energy profile can be corrected to the level of interest (the target Hamiltonian) by energy reweighting in a nonparametric way. However, when the reference Hamiltonian is very different from the target Hamiltonian, the calculated ensemble averages, including the PMF, often suffer from numerical instability, which mainly comes from the overestimation of the density-of-states (DoS) in the low-energy region. Stochastic samplings of these low-energy configurations are rare events. If a low-energy configuration has been sampled with a small sample size N, the probability of visiting this energy region is 1 /N (shall be exactly 1/N for a single ensemble), which can be orders-of-magnitude larger than the actual DoS. In this work, an assumption of Gaussian distribution is applied to the DoS in each CV bin, and the weight of each configuration is rescaled according to the accumulated DoS. The results show that this smoothing process can remarkably reduce the ruggedness of the PMF and increase the reliability of the reference-potential method. File list (2) download file view on ChemRxiv SI.pdf (487.66 KiB) download file view on ChemRxiv GaussianSmoothing.pdf (770.56 KiB)

Affordable Ab Initio Path Integral for Thermodynamic Properties via Molecular Dynamics Simulations Using Semiempirical Reference Potential

“…To ameliorate the numerical instability originated from incomplete sampling, the weights ω t (r n ) under the target Hamiltonian are scaled by Gaussian smoothing on the density of states. 47 In this work, we take U 0 as the PM6/MM 71 Hamiltonian and U t as the BLYP-D3/6-31G(d)/MM 72−74 level of theory. For simplicity, they will be labeled as the SQM and DFT levels of theory.…”

“…MsTP is a variant of the reference-potential method, in which the ensemble averages of any time-independent physical properties at a high level of theory are obtained indirectly from simulations at a lower level of theory. With further improvement, − this method is becoming more robust for the studies of chemical processes in the condensed phase. The idea of the reference-potential method has also been implemented by other groups. − …”

Accelerating ab initio QM/MM Molecular Dynamics Simulations with Multiple Time Step Integration and a Recalibrated Semi-empirical QM/MM Hamiltonian

“…In the reference potential method (i.e. indirect QM/MM simulations), 4,[39][40][41][42][43][44][45] the configurational sampling is carried out using a reference low-level potential energy, and then the low-level free energy results are corrected in a post-processing process using thermodynamical perturbation. 46 This correction can also be achieved through non-equilibrium work simulations.…”

Machine Learning Assisted Free Energy Simulation of Solution–Phase and Enzyme Reactions

“…To avoid such steep costs of direct ai-QM/MM free energy simulations, Gao, 19 Warshel 20 and others [21][22][23][24][25] developed indirect free energy simulations, where sampling is carried out using a reference semi-empirical QM/MM (se-QM/MM) potential and then the free energy result is corrected with a se-QM/MM !ai-QM/MM thermodynamic perturbation or with an interpolation between the two levels of potential, for example along the energy minimized reaction path. 26,27 Alternatively, one can adopt the multiple timestep simulation methodology from Tuckerman, [28][29][30][31] Schlick, 32,33 Nam, 34 Roux, 35 Rothslisberg, 36 and others, 37 where se-QM/MM trajectory propagation at regular/inner timesteps is coupled with ai-QM/MM trajectory corrections at outer timesteps.…”