Seeding the Multi-dimensional Nonequilibrium Pulling for Hamiltonian Variation: Indirect Nonequilibrium Free Energy Simulations at QM levels

04 October 2021, Version 2
This content is a preprint and has not undergone peer review at the time of posting.


The combination of free energy simulations in the alchemical and configurational spaces provides a feasible route to access the thermodynamic profiles under a computationally demanding target Hamiltonian. Normally, due to the significant differences between the computational cost of ab initio quantum mechanics (QM) calculations and those of semi-empirical quantum mechanics (SQM) and molecular mechanics (MM), this indirect method could be used to obtain the QM thermodynamics by combining the SQM or MM results and the SQM-to-QM or MM-to-QM corrections. In our previous works, a multi-dimensional nonequilibrium pulling framework for Hamiltonian variations has been introduced based on bidirectional pulling and bidirectional reweighting. The method performs nonequilibrium free energy simulations in the configurational space to obtain the thermodynamic profile along the conformational change pathway under a selected computationally efficient Hamiltonian, and uses the nonequilibrium alchemical method to correct or perturb the thermodynamic profile to that under the target Hamiltonian. The BAR-based method is designed to achieve the best generality and transferability and thus leads to modest (~20 folds) speedup. In this work, we explore the possibility of further accelerating the nonequilibrium free energy simulation by employing unidirectional pulling and using the selection criterion to obtain the initial configurations used to initiate nonequilibrium trajectories following the idea of adaptive steered molecular dynamics (ASMD). A single initial condition is used to seed the whole multi-dimensional nonequilibrium free energy simulation and the sampling is performed fully in the nonequilibrium ensemble. Introducing very short ps-length equilibrium sampling to grab more initial seeds could also be helpful. The ASMD scheme estimates the free energy difference with the unidirectional exponential average (EXP), but it does not follow exactly the requirements of the EXP estimator. Another deficiency of the seeding simulation is the inherently sequential or serial pulling due to the inter-segment dependency, which triggers some problems in the parallelizability of the simulation. Numerical tests are performed to grasp some insights and guidelines for using this selection-criterion-based ASMD scheme. The presented selection-criterion-based multi-dimensional ASMD scheme follows the same perturbation network of the BAR-based method, and thus could be used in various Hamiltonian-variation cases.


Nonequilibrium Pulling
Enhanced Sampling Simulation
Free Energy Perturbation
Steered Molecular Dynamics
Alchemical Free Energy Calculation
Unidirectional Pulling
Ordinary Average
Exponential Average
Gaussian Approximation
Gaussian Approximated Exponential Average
Free Energy Simulation
Indirect QM/MM Free Energy Simulation
Multi-dimensional Nonequilibrium Free Energy Simulation
Conformatinoal Change
Alchemical Transformation
Configurational Sampling
Multi-scale Treatment
Hamiltonian Variation
ab initio Quantum Calculations
Semi-empirical Quantum Calculations
Sample Size
Pulling Speed
Dihedral Flipping
Fast Growth
Slow Growth
Statistical Uncertainty
Initial Seed
Mean Absolute Error (MAE)
Adaptive Steered Molecular Dynamics
Selection Criterion
Jarzynski Theorem
Computational Cost
Statistical Inefficiency
Upper Bound


Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.