Accelerated Computation of Free Energy Profile at ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semi-Empirical Reference Potential. I. Weighted Thermodynamics Perturbation

Abstract

Free energy profile (FE Profile) is an essential quantity for the estimation of reaction rate and the validation of reaction mechanism. For chemical reactions in condensed phase or enzymatic reactions, the computation of FE profile at the ab initio (ai) quantum mechanical/molecular mechanics (QM/MM) level is still far too expensive. Although semiempirical (SE) method can be hundreds or thousands of times faster than the ai methods, the accuracy of SE methods is often unsatisfactory due to the approximations that have been adopted in these methods. In this work, we propose a new method termed MBAR +wTP in which the ai QM/MM free energy profile is computed by a weighted thermodynamic perturbation (TP) correction to the SE profile generated by the multistate Bennett acceptance ratio (MBAR) analysis of the trajectories from umbrella samplings (US). The weight factors used in the TP calculations are a byproduct of the MBAR analysis in the postprocessing of the US trajectories, which are often discarded after the free energy calculations. The raw ai QM/MM free energy profile is then smoothed using Gaussian process regression in which the noise of each datum is set to be inversely proportional to the exponential of the reweighting entropy. The results show that this approach can enhance the efficiency of ai FE profile calculations by several orders of magnitude with only a slight loss of accuracy. This method can significantly enhance the applicability of ai QM/MM methods in the studies of chemical reactions in condensed phase and enzymatic reactions.

Ab Initio Calculations of Free Energy of Activation at Multiple Electronic Structure Levels Made Affordable: An Effective Combination of Perturbation Theory and Machine Learning

“…Similar to our work, Shen et al 10 ) whose calculation has not been discussed in Refs. [10][11][12][13][14] In our work, we…”

“…[10][11][12][13][14] The machine learning (ML) based algorithms turn out to be a very useful in this respect as they allow for inexpensive calculations of energies of configurations, 6,10,13 acceleration of the configuration space sampling, 7,8,12 or improving the quality of results at the post-processing stage. 11 In this work we focus on calculations of free energy of activation. To this end, we propose an efficient simulation protocol combining concepts from free energy perturbation theory 15 (FEPT) and our recently introduced machine learning thermodynamic perturbation theory (MLPT) method 16 that allows to recompute the free energy difference determined at a certain level of theory (designated hereafter as a production method) at another level of theory (target method).…”

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

“…4). The simulation details have been introduced in our previous work, 24 and here we only provide a brief description. US window simulation, the system was optimized for 500 steps using the steepest decent optimization method followed by 500 steps of the conjugate gradient method.…”

“…However, if the target Hamiltonian is very different from the reference Hamiltonian, the convergence of the reweighting process can be troublesome, as discussed in our recent work. 24 Further smoothing of the free energy curve, for instance, using Gaussian process regression 35 is indispensable. The numerical instability comes from the exponential term, of which the ensemble average often shows random fluctuations with nonnegligible amplitude.…”

A Review : Aspek Termodinamika LiNO3 dalam Larutannya

“…Kedua gaya ini bekerja dalam arah yang berlawanan dan ion mencapai kecepatan akhir, yaitu kecepatan hanyut ion (s), jika gaya mempercepat F diimbangi oleh gaya perlambatan F ' . Gaya neto menjadi nol (F=F ' ) (195)(196)(197)(198)(199)(200) jika :…”