BAR-based multi-dimensional nonequilibrium pulling for indirect construction of QM/MM free energy landscapes: from semi-empirical to ab initio

2019 ◽  
Vol 21 (39) ◽  
pp. 21942-21959 ◽  
Author(s):  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Quantum Mechanics ◽  
Ab Initio ◽  
Molecular Mechanics ◽  
Indirect Method ◽  
Energy Landscapes ◽  
Free Energy Landscapes ◽  
Energy Simulations ◽  
Semi Empirical

The indirect method for the construction of quantum mechanics (QM)/molecular mechanics (MM) free energy landscapes provides a cheaper alternative for free energy simulations at the QM level.

BAR-Based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape: From Semi-Empirical to Ab Initio

2019 ◽  
Author(s):  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Indirect Method ◽  
Energy Simulation ◽  
Energy Landscapes ◽  
Time Step ◽  
Low Level ◽  
Free Energy Landscapes ◽  
High Level ◽  
Stiff Spring ◽  
Semi Empirical

<p>The indirect method for the construction of Quantum mechanics (QM)/ molecular mechanics (MM) free energy landscapes provides a cheaper alternative of free energy simulations at QM level. The indirect method features a direct calculation of the free energy profile at a relatively cheap low-level Hamiltonian and a low-level to high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. Often the indirect method can lead to about an order of magnitude speedup in free energy simulation. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. The method relies on bidirectional nonequilibrium pulling and bidirectional reweighting with the statistically optimal estimator. In the previous work, we focus on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM<->SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM<->QM corrections. The indirect nonequilibrium scheme is tested on a dihedral flipping case and a series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians, while AM1 and MNDO perform less well. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. The comparison between the indirect results from different SQM Hamiltonians could also provide some hints on the development of charge models. As AM1 can be corrected with the bond charge correction (BCC) to provide a cheap and accurate charge model, which is able to accurately reproduce the electrostatic potential (ESP) at HF level, PM6 would be able to do the same thing. Considering its higher similarity to the high-level Hamiltonians, the PM6-BCC model could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms. </p>

scholarly journals BAR-Based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape: From Semi-Empirical to Ab Initio

2019 ◽  
Author(s):  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Indirect Method ◽  
Energy Simulation ◽  
Energy Landscapes ◽  
Time Step ◽  
Low Level ◽  
Free Energy Landscapes ◽  
High Level ◽  
Stiff Spring ◽  
Semi Empirical

<p>The indirect method for the construction of Quantum mechanics (QM)/ molecular mechanics (MM) free energy landscapes provides a cheaper alternative of free energy simulations at QM level. The indirect method features a direct calculation of the free energy profile at a relatively cheap low-level Hamiltonian and a low-level to high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. Often the indirect method can lead to about an order of magnitude speedup in free energy simulation. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. The method relies on bidirectional nonequilibrium pulling and bidirectional reweighting with the statistically optimal estimator. In the previous work, we focus on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM<->SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM<->QM corrections. The indirect nonequilibrium scheme is tested on a dihedral flipping case and a series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians, while AM1 and MNDO perform less well. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. The comparison between the indirect results from different SQM Hamiltonians could also provide some hints on the development of charge models. As AM1 can be corrected with the bond charge correction (BCC) to provide a cheap and accurate charge model, which is able to accurately reproduce the electrostatic potential (ESP) at HF level, PM6 would be able to do the same thing. Considering its higher similarity to the high-level Hamiltonians, the PM6-BCC model could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms. </p>

scholarly journals BAR-Based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape: From Semi-Empirical to Ab Initio

2019 ◽  
Author(s):  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Indirect Method ◽  
Energy Simulation ◽  
Energy Landscapes ◽  
Time Step ◽  
Low Level ◽  
Free Energy Landscapes ◽  
High Level ◽  
Stiff Spring ◽  
Semi Empirical

<p>The indirect method for the construction of Quantum mechanics (QM)/ molecular mechanics (MM) free energy landscapes provides a cheaper alternative of free energy simulations at QM level. The indirect method features a direct calculation of the free energy profile at a relatively cheap low-level Hamiltonian and a low-level to high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. Often the indirect method can lead to about an order of magnitude speedup in free energy simulation. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. The method relies on bidirectional nonequilibrium pulling and bidirectional reweighting with the statistically optimal estimator. In the previous work, we focus on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM<->SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM<->QM corrections. The indirect nonequilibrium scheme is tested on a dihedral flipping case and a series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians, while AM1 and MNDO perform less well. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. The comparison between the indirect results from different SQM Hamiltonians could also provide some hints on the development of charge models. As AM1 can be corrected with the bond charge correction (BCC) to provide a cheap and accurate charge model, which is able to accurately reproduce the electrostatic potential (ESP) at HF level, PM6 would be able to do the same thing. Considering its higher similarity to the high-level Hamiltonians, the PM6-BCC model could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms. </p>

scholarly journals Seeding the Multi-dimensional Nonequilibrium Pulling for Hamiltonian Variation: Indirect QM/MM Free Energy Simulations

2021 ◽  
Author(s):  
Zhaoxi Sun ◽  
Qiaole He
Keyword(s):  
Free Energy ◽  
Quantum Mechanics ◽  
Computational Cost ◽  
Selection Criterion ◽  
Energy Difference ◽  
Energy Simulation ◽  
Computationally Efficient ◽  
Free Energy Difference ◽  
Energy Simulations ◽  
Semi Empirical

<p>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 is often applied to obtain the QM thermodynamics by combining the SQM or MM thermodynamics 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 fold) 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. 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 consequence 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. Therefore, some tests are required to grasp some insights and guidelines for using this selection-criterion-based ASMD scheme. The ASMD method is tested thoroughly on a dihedral flipping model system and encouraging numerical results are obtained. The selection-criterion-based multi-dimensional ASMD framework follows the same perturbation framework of the BAR-based method, and thus could be used in various Hamiltonian-variation cases.</p>

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

2021 ◽  
Author(s):  
Zhaoxi Sun ◽  
Qiaole He
Keyword(s):  
Free Energy ◽  
Quantum Mechanics ◽  
Computational Cost ◽  
Selection Criterion ◽  
Energy Difference ◽  
Energy Simulation ◽  
Computationally Efficient ◽  
Free Energy Difference ◽  
Energy Simulations ◽  
Semi Empirical

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.

scholarly journals BAR-based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscapes: Varying the QM Region

2021 ◽  
Author(s):  
Zhaoxi Sun ◽  
Zhirong Liu
Keyword(s):  
Free Energy ◽  
Main Idea ◽  
Thermodynamic Cycle ◽  
Basis Set ◽  
Energy Landscapes ◽  
Computationally Efficient ◽  
Feasible Alternative ◽  
Free Energy Landscapes ◽  
Energy Simulations ◽  
High Level

<div><p>The indirect construction of the free energy landscape at Quantum mechanics (QM)/ molecular mechanics (MM) levels provides a feasible alternative to the direct QM/MM free energy simulations. The main idea under the indirect method is constructing a thermodynamic cycle, exploring the configurational space at a computationally efficient but less accurate low-level Hamiltonian, and performing an alchemical correction to obtain the thermodynamics at an accurate but computationally demanding high-level Hamiltonian. In our previous works, we developed a multi-dimensional nonequilibrium free energy simulation framework to obtain QM/MM free energy landscapes indirectly. Specifically, we considered obtaining semi-empirical QM (SQM) results by combining the MM results and the MM-to-SQM correction and obtaining the QM results by combining the SQM results and the SQM-to-QM correction. In this work, we explore the possibility of changing the region for electronic structure calculations in the multi-scale QM/MM treatment, which could also be considered as a change of the level of theory. More generally, the multi-dimensional nonequilibrium Hamiltonian-variation/perturbation framework could be used to obtain transformations between different Hamiltonians of interest, such as changing the QM theory, the size of the QM region, and the basis set simultaneously. </p> <p> </p></div>

scholarly journals BAR-Based Multi-Dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape

2019 ◽  
Author(s):  
Xiaohui Wang ◽  
Qiaole He ◽  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Thermodynamic Cycle ◽  
Simulation Method ◽  
Collective Variable ◽  
Energy Simulation ◽  
Energy Landscapes ◽  
One Dimensional ◽  
Free Energy Landscapes ◽  
Energy Simulations

<p>Construction of free energy landscapes at Quantum mechanics (QM) level is computationally demanding. As shown in previous studies, by employing an indirect scheme (i.e. constructing a thermodynamic cycle connecting QM states via an alchemical pathway), simulations are converged with much less computational burden. The indirect scheme makes QM/ molecular mechanics (MM) free energy simulation orders of magnitude faster than the direct QM/MM schemes. However, the indirect QM/MM simulations were mostly equilibrium sampling based and the nonequilibrium methods were merely exploited in one-dimensional alchemical QM/MM end-state correction at two end states. In this work, we represent a multi-dimensional nonequilibrium pulling scheme for indirect QM/MM free energy simulations, where the whole free energy simulation is performed only with nonequilibrium methods. The collective variable (CV) space we explore is a combination of one alchemical CV and one physically meaningful CV. The current nonequilibrium indirect QM/MM simulation method can be seen as the generalization of equilibrium perturbation based indirect QM/MM methods. The test systems include one backbone dihedral case and one distance case. The two cases are significantly different in size, enabling us to investigate the dependence of the speedup of the indirect scheme on the size of the system. It is shown that the speedup becomes larger when the size of the system becomes larger, which is consistent with the scaling behavior of QM Hamiltonians. </p>

Sign in / Sign up

Export Citation Format

Share Document