Training machine learning potentials for reactive systems: A Colab tutorial on basic models.

In the last several years, there has been a surge in the development of machine learning potential (MLP) models for describing molecular systems. We are interested in a particular area of this field - the training of system-specific MLPs for reactive systems - with the goal of using these MLPs to accelerate free energy simulations of chemical and enzyme reactions. To help new members in our labs become familiar with the basic techniques, we have put together a self-guided Colab tutorial (https://cc-ats.github.io/mlp_tutorial/), which we expect to be also useful to other young researchers in the community. Our tutorial begins with the introduction of simple feedforward neural network (FNN) and kernel-based (using Gaussian process regression, GPR) models by fitting the two-dimensional Müller-Brown potential. Subsequently, two simple descriptors are presented for extracting features of molecular systems: symmetry functions (including the ANI variant) and embedding neural networks (such as DeepPot-SE). Lastly, these features will be fed into FNN and GPR models to reproduce the energies and forces for the molecular configurations in a Claisen rearrangement reaction.

Free Energy Profile Decomposition Analysis for QM/MM Simulations of Enzymatic Reactions.

In enzyme mechanistic studies and mutant design, it is highly desirable to know the individual residue contributions to the reaction free energy and barrier. In this work, we show that such free energy contributions from each residue can be readily obtained by postprocessing ab initio quantum mechanical molecular mechanical (ai-QM/MM) free energy simulation trajectories. Specifically, through a mean force integration along the minimum free energy pathway, one can obtain the electrostatic, polarization, and van der Waals contributions from each residue to the free energy barrier. Separately, a similar analysis procedure allows us to assess the contribution from different collective variables along the reaction coordinate. The chorismate mutase reaction is used to demonstrate the utilization of these two trajectory analysis tools.

Shikonin promotes hypertrophic scar repair by autophagy of hypertrophic scar-derived fibroblasts.

PURPOSE: To investigate the Shikonin (SHI) induce autophagy of hypertrophic scar-derived fibroblasts (HSFs) and the mechanism of which in repairing hypertrophic scar. METHODS: This study showed that SHI induced autophagy from HSFs and repaired skin scars through the AMPK/mTOR pathway. Alamar Blue and Sirius red were used to identify cell activity and collagen. Electron microscopy, label-free quantitative proteomic analysis, fluorescence and other methods were used to identify autophagy. The differences in the expression of autophagy and AMPK/mTOR pathway-related proteins after SHI treatment were quantitatively analyzed by Western blots. A quantitative real-time polymerase chain reaction assay was used to detect the expression of LC3, AMPK and ULK after adding chloroquine (CQ) autophagy inhibitor. RESULTS: After treatment with SHI for 24 hours, it was found that the viability of HSFs was significantly reduced, the protein expression of LC3-II/LC3-I and Beclin1 increased, while the protein expression of P62 decreased. The expression of phosphorylated AMPK increased and expression of phosphorylated mTOR decreased. After the use of CQ, the cell autophagy caused by SHI was blocked. The key genes LC3 and P62 were then reexamined by immunohistochemistry using a porcine full-thickness burn hypertrophic scar model, and the results verified that SHI could induce autophagy in vivo. CONCLUSIONS: These findings suggested that SHI promoted autophagy of HSFs cells, and the potential mechanism may be related to the AMPK/mTOR signal pathway, which provided new insights for the treatment of hypertrophic scars.

Visualization of Electron Density Changes Along Chemical Reaction Pathways.

We propose a simple procedure for visualizing the electron density changes (EDC) during a chemical reaction, which is based on a mapping of rectangular grid points for a stationary structure into (distorted) positions around atoms of another stationary structure. Specifically, during a small step along the minimum energy pathway (MEP), the displacement of each grid point is obtained as a linear combination of the motion of all atoms, with the contribution from each atom scaled by the corresponding Hirshfeld weight. For several reactions (identity SN2, Claisen rearrangement, Diels-Alder reaction, [3+2] cycloaddition, and phenylethyl mercaptan attack on pericosine A), our EDC plots showed an expected reduction of electron densities around severed bonds (or those with the bond-order lowered), with the opposite observed for newly-formed or enhanced chemical bonds. The EDC plots were also shown for copper triflate catalyzed N2O fragmentation, where the N-O bond weakening initially occurred on a singlet surface, but continued on a triplet surface after reaching the minimum-energy crossing point (MECP) between the two potential energy surfaces.

Bridging semiempirical and ab initio QM/MM potentials by Gaussian process regression and its sparse variants for free energy simulation.

Free energy simulations that employ combined quantum mechanical and molecular mechanical (QM/MM) potentials at ab initio QM (AI) levels are computationally highly demanding. Here, we present a machine-learning-facilitated approach for obtaining AI/MM-quality free energy profiles at the cost of efficient semiempirical QM/MM (SE/MM) methods. Specifically, we use Gaussian process regression (GPR) to learn the potential energy corrections needed for an SE/MM level to match an AI/MM target along the minimum free energy path (MFEP). Force modification using gradients of the GPR potential allows us to improve configurational sampling and update the MFEP. To adaptively train our model, we further employ the sparse variational GP (SVGP) and streaming sparse GPR (SSGPR) methods, which efficiently incorporate previous sample information without significantly increasing the training data size. We applied the QM-(SS)GPR/MM method to the solution-phase SN2 Menshutkin reaction, NH3+CH3Cl→CH3NH3++Cl-, using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. For 4000 configurations sampled along the MFEP, the iteratively optimized AM1-SSGPR-4/MM model reduces the energy error in AM1/MM from 18.2 to 4.4 kcal/mol. Although not explicitly fitting forces, our method also reduces the key internal force errors from 25.5 to 11.1 kcal/mol/Å and from 30.2 to 10.3 kcal/mol/Å for the N-C and C-Cl bonds, respectively. Compared to the uncorrected simulations, the AM1-SSGPR-4/MM method lowers the predicted free energy barrier from 28.7 to 11.7 kcal/mol and decreases the reaction free energy from -12.4 to -41.9 kcal/mol, bringing these results into closer agreement with their AI/MM and experimental benchmarks.

Perspective: Reference-Potential Methods for the Study of Thermodynamic Properties in Chemical Processes: Theory, Applications, and Pitfalls.

In silico investigations of enzymatic reactions and chemical reactions in condensed phases often suffer from formidable computational costs due to a large number of degrees of freedom and enormous important volume in phase space. Usually, accuracy must be compromised to trade for efficiency by lowering the reliability of the Hamiltonians employed or reducing the sampling time. Reference-potential methods (RPMs) offer an alternative approach to reaching high accuracy of simulation without much loss of efficiency. In this Perspective, we summarize the idea of RPMs and showcase some recent applications. Most importantly, the pitfalls of these methods are also discussed, and remedies to these pitfalls are presented.

Machine learning based implicit solvent model for aqueous-solution alanine dipeptide molecular dynamics simulations.

Inspired by the recent work from Noé and coworkers on the development of machine learning based implicit solvent model for the simulation of solvated peptides [Chen et al., J. Chem. Phys., 2021, 155, 084101], here we report another investigation of the possibility of using machine learning (ML) techniques to "derive" an implicit solvent model directly from explicit solvent molecular dynamics (MD) simulations. For alanine dipeptide, a machine learning potential (MLP) based on the DeepPot-SE representation of the molecule was trained to capture its interactions with its average solvent environment configuration (ASEC). The predicted forces on the solute deviated only by an RMSD of 0.4 kcal mol-1 Å-1 from the reference values, and the MLP-based free energy surface differed from that obtained from explicit solvent MD simulations by an RMSD of less than 0.9 kcal mol-1. Our MLP training protocol could also accurately reproduce combined quantum mechanical molecular mechanical (QM/MM) forces on the quantum mechanical (QM) solute in ASEC environment, thus enabling the development of accurate ML-based implicit solvent models for ab initio-QM MD simulations. Such ML-based implicit solvent models for QM calculations are cost-effective in both the training stage, where the use of ASEC reduces the number of data points to be labelled, and the inference stage, where the MLP can be evaluated at a relatively small additional cost on top of the QM calculation of the solute.

Shikonin promotes hypertrophic scar repair by autophagy of hypertrophic scar-derived fibroblasts

Purpose: To investigate the Shikonin (SHI) induce autophagy of hypertrophic scar-derived fibroblasts (HSFs) and the mechanism of which in repairing hypertrophic scar. Methods: This study showed that SHI induced autophagy from HSFs and repaired skin scars through the AMPK/mTOR pathway. Alamar Blue and Sirius red were used to identify cell activity and collagen. Electron microscopy, label-free quantitative proteomic analysis, fluorescence and other methods were used to identify autophagy. The differences in the expression of autophagy and AMPK/mTOR pathway-related proteins after SHI treatment were quantitatively analyzed by Western blots. A quantitative real-time polymerase chain reaction assay was used to detect the expression of LC3, AMPK and ULK after adding chloroquine (CQ) autophagy inhibitor. Results: After treatment with SHI for 24 hours, it was found that the viability of HSFs was significantly reduced, the protein expression of LC3-II/LC3-I and Beclin1 increased, while the protein expression of P62 decreased. The expression of phosphorylated AMPK increased and expression of phosphorylated mTOR decreased. After the use of CQ, the cell autophagy caused by SHI was blocked. The key genes LC3 and P62 were then reexamined by immunohistochemistry using a porcine full-thickness burn hypertrophic scar model, and the results verified that SHI could induce autophagy in vivo. Conclusions: These findings suggested that SHI promoted autophagy of HSFs cells, and the potential mechanism may be related to the AMPK/mTOR signal pathway, which provided new insights for the treatment of hypertrophic scars.

Computational Investigation of Substituent Effects on the Fluorescence Wavelengths of Oxyluciferin Analogs.

Oxyluciferin, which is the light emitter for firefly bioluminescence, has been subjected to extensive chemical modifications to tune its emission wavelength and quantum yield. However, the exact mechanisms for various electron-donating and withdrawing groups to perturb the photophysical properties of oxyluciferin analogs are still not fully understood. To elucidate the substituent effects on the fluorescence wavelength of oxyluciferin analogs, we applied the absolutely localized molecular orbitals (ALMO)-based frontier orbital analysis to assess various types of interactions (i.e. permanent electrostatics/exchange repulsion, polarization, occupied-occupied orbital mixing, virtual-virtual orbital mixing, and charge-transfer) between the oxyluciferin and substituent orbitals. We suggested two distinct mechanisms that can lead to red-shifted oxyluciferin emission wavelength, a design objective that can help increase the tissue penetration of bioluminescence emission. Within the first mechanism, an electron-donating group (such as an amino or dimethylamino group) can contribute its highest occupied molecular orbital (HOMO) to an out-of-phase combination with oxyluciferin's HOMO, thus raising the HOMO energy of the substituted analog and narrowing its HOMO-LUMO gap. Alternatively, an electron-withdrawing group (such as a nitro or cyano group) can participate in an in-phase virtual-virtual orbital mixing of fragment LUMOs, thus lowering the LUMO energy of the substituted analog. Such an ALMO-based frontier orbital analysis is expected to lead to intuitive principles for designing analogs of not only the oxyluciferin molecule, but also many other functional dyes.

Facilitating ab initio QM/MM free energy simulations by Gaussian process regression with derivative observations.

In combined quantum mechanical and molecular mechanical (QM/MM) free energy simulations, how to synthesize the accuracy of ab initio (AI) methods with the speed of semiempirical (SE) methods for a cost-effective QM treatment remains a long-standing challenge. In this work, we present a machine-learning-facilitated method for obtaining AI/MM-quality free energy profiles through efficient SE/MM simulations. In particular, we use Gaussian process regression (GPR) to learn the energy and force corrections needed for SE/MM to match with AI/MM results during molecular dynamics simulations. Force matching is enabled in our model by including energy derivatives into the observational targets through the extended-kernel formalism. We demonstrate the effectiveness of this method on the solution-phase SN2 Menshutkin reaction using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. Trained on only 80 configurations sampled along the minimum free energy path (MFEP), the resulting GPR model reduces the average energy error in AM1/MM from 18.2 to 5.8 kcal mol-1 for the 4000-sample testing set with the average force error on the QM atoms decreased from 14.6 to 3.7 kcal mol-1 Å-1. Free energy sampling with the GPR corrections applied (AM1-GPR/MM) produces a free energy barrier of 14.4 kcal mol-1 and a reaction free energy of -34.1 kcal mol-1, in closer agreement with the AI/MM benchmarks and experimental results.

Accelerating Ab Initio Quantum Mechanical and Molecular Mechanical (QM/MM) Molecular Dynamics Simulations with Multiple Time Step Integration and a Recalibrated Semiempirical QM/MM Hamiltonian.

Molecular dynamics (MD) simulations employing ab initio quantum mechanical and molecular mechanical (ai-QM/MM) potentials are considered to be the state of the art, but the high computational cost associated with the ai-QM calculations remains a theoretical challenge for their routine application. Here, we present a modified protocol of the multiple time step (MTS) method for accelerating ai-QM/MM MD simulations of condensed-phase reactions. Within a previous MTS protocol [Nam J. Chem. Theory Comput. 2014, 10, 4175], reference forces are evaluated using a low-level (semiempirical QM/MM) Hamiltonian and employed at inner time steps to propagate the nuclear motions. Correction forces, which arise from the force differences between high-level (ai-QM/MM) and low-level Hamiltonians, are applied at outer time steps, where the MTS algorithm allows the time-reversible integration of the correction forces. To increase the outer step size, which is bound by the highest-frequency component in the correction forces, the semiempirical QM Hamiltonian is recalibrated in this work to minimize the magnitude of the correction forces. The remaining high-frequency modes, which are mainly bond stretches involving hydrogen atoms, are then removed from the correction forces. When combined with a Langevin or SIN(R) thermostat, the modified MTS-QM/MM scheme remains robust with an up to 8 (with Langevin) or 10 fs (with SIN(R)) outer time step (with 1 fs inner time steps) for the chorismate mutase system. This leads to an over 5-fold speedup over standard ai-QM/MM simulations, without sacrificing the accuracy in the predicted free energy profile of the reaction.

Oxymatrine promotes hypertrophic scar repair through reduced human scar fibroblast viability, collagen and induced apoptosis via autophagy inhibition.

Scars are common complications of burns and trauma, resulting in mental trauma, physical pain, and a heavy financial burden for patients. Specific and effective anti-scarring drugs are lacking in clinical practice. Phytochemicals are easily accessible, low in toxicity, and have various biological and pharmacological properties. Oxymatrine is a phytochemical that regulates autophagy networks. Autophagy is closely related to the maintenance, activity, differentiation, and life-death of skin fibroblasts during wound repair, which results in pathological scars. We hypothesised that oxymatrine may promote hypertrophic scar repair by inhibiting fibroblast autophagy. In vitro studies showed that inhibition of autophagy by oxymatrine decreased viability and collagen metabolism, and increased apoptosis of human scar fibroblasts (HSFs). In vivo studies showed that inhibition of autophagy by oxymatrine promoted scar repair, resulting in a significantly improved final outcome of the hypertrophic scars, a smaller scar area, decreased epidermal and dermal thickness, and a significant downregulation of CK10, P63, collagen I, α-SMA, and TGF-ß1. In summary, oxymatrine promoted hypertrophic scar repair by decreasing HSF viability and collagen, and inducing apoptosis via autophagy inhibition. This study provides a new perspective on the mechanism of hypertrophic burn scar formation, as well as key scientific data for the application of the phytochemical oxymatrine as a new method for the prevention and treatment of hypertrophic scars.

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

Path integral molecular dynamics (PIMD) is becoming a routinely applied method for incorporating the nuclear quantum effect in computer simulations. However, direct PIMD simulations at an ab initio level of theory are formidably expensive. Using the protonated 1,8-bis(dimethylamino)naphthalene molecule as an example, we show in this work that the computational expense for the intramolecular proton transfer between the two nitrogen atoms can be remarkably reduced by implementing the idea of reference-potential methods. The simulation time can be easily extended to a scale of nanoseconds while maintaining the accuracy on an ab initio level of theory for thermodynamic properties. In addition, postprocessing can be carried out in parallel on massive computer nodes. A 545-fold reduction in the total CPU time can be achieved in this way as compared to a direct PIMD simulation at the same ab initio level of theory.

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

Despite recent advances in the development of machine learning potentials (MLPs) for biomolecular simulations, there has been limited effort on developing stable and accurate MLPs for enzymatic reactions. Here we report a protocol for performing machine-learning-assisted free energy simulation of solution-phase and enzyme reactions at the ab initio quantum-mechanical/molecular-mechanical (ai-QM/MM) level of accuracy. Within our protocol, the MLP is built to reproduce the ai-QM/MM energy and forces on both QM (reactive) and MM (solvent/enzyme) atoms. As an alternative strategy, a delta machine learning potential (ΔMLP) is trained to reproduce the differences between the ai-QM/MM and semiempirical (se) QM/MM energies and forces. To account for the effect of the condensed-phase environment in both MLP and ΔMLP, the DeePMD representation of a molecular system is extended to incorporate the external electrostatic potential and field on each QM atom. Using the Menshutkin and chorismate mutase reactions as examples, we show that the developed MLP and ΔMLP reproduce the ai-QM/MM energy and forces with errors that on average are less than 1.0 kcal/mol and 1.0 kcal mol-1 Å-1, respectively, for representative configurations along the reaction pathway. For both reactions, MLP/ΔMLP-based simulations yielded free energy profiles that differed by less than 1.0 kcal/mol from the reference ai-QM/MM results at only a fraction of the computational cost.

[Study on the correlation between the content of bone morphogenetic protein 2 in demineralized bone matrix and its osteogenic activity in vitro and in vivo].

OBJECTIVE: To investigate the correlation between the content of bone morphogenetic protein 2 (BMP-2) in demineralized bone matrix (DBM) and its osteogenic activity in vitro and in vivo, in order to choose a simple and convenient method to evaluate the osteogenic activity of DBM. METHODS: The left mid-femoral tissues of 9 donors were taken, and DBMs (S1-S9) were prepared by dynamic decalcification process, and inactivated DBM (control group) was prepared at the same time. Protease inhibitor method, collagenase method, guanidine hydrochloride/ethylene diamine tetraacetic acid (EDTA) method, and RIPA lysate method were used to extract BMP-2 in S1-S9 and inactivated DBMs. The BMP-2 content was measured and the differences between DBMs were compared. Then the S1-S9 and inactivated DBMs were co-cultured with mouse embryonic osteoblasts MC3T3-E1, respectively. The cell proliferation was detected by MTT method and fluorescence staining, and alkaline phosphatase (ALP) activity was detected at the same time. Thirty BALB/c male nude mice were divided into 10 groups, namely S1-S9 DBM groups (S1-S9 groups) and inactivated DBM group (control group), with 3 mice in each group. Muscle pockets of the middle thighs were prepared on both hindlimbs of mice in each group, and implanted corresponding DBM materials. At 4 weeks after operation, the samples were taken for HE staining observation and semi-quantitative evaluation, and the new bone formation score was calculated. RESULTS: The BMP-2 content of DBM derived from different donor bones was distinct. The BMP-2 content obtained by different extraction methods for DBM prepared from the same donor bone was also different, and the extraction efficiency of the guanidine hydrochloride/EDTA method was the highest. In vitro cell experiments, MTT test displayed that cell proliferations and ALP activity were significantly higher in S4 and S6 groups than in other groups at each time point after co-cultivation ( P<0.05). Moreover, the cell proliferation of S4 group was the most significant at 7 days ( P<0.05); fluorescence staining demonstrated that the osteoblasts of each group was in good condition, but the osteoblasts of S1, S2, S3, S4, and S6 groups were significantly more than other groups. In vivo ectopic osteogenesis experiments, the cartilage and new bone formation could be seen in the bone graft area of S1-S6 groups at 4 weeks after operation, and with the increase of BMP-2 content, the more new bone formation induced by the material, the higher the score of new bone formation of the material ( P<0.05). Among them, S4 and S6 groups contained a large number of chondrocytes and osteoblasts in the osteogenesis area. CONCLUSION: The osteogenic activity of DBM can be evaluated through BMP-2 quantitative detection combined with in vitro osteoblast proliferation and differentiation experiments.

Accelerated Computation of Free Energy Profile at Ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semiempirical Reference Potential. 4. Adaptive QM/MM.

Although quantum mechanical/molecular mechanics (QM/MM) methods are now routinely applied to the studies of chemical reactions in condensed phases and enzymatic reactions, they may experience technical difficulties when the reactive region is varying over time. For instance, when the solvent molecules are directly participating in the reaction, the exchange of water molecules between the QM and MM regions may occur on a time scale comparable to the reaction time. To cope with this situation, several adaptive QM/MM schemes have been proposed. However, these methods either add significantly to the computational cost or introduce artificial restraints to the system. In this work, we developed a novel adaptive QM/MM scheme and applied it to the study of a nucleophilic addition reaction. In this scheme, the configuration sampling was performed with a small QM region (without solvent molecules), and the thermodynamic properties under another potential energy function with a larger QM region (with a certain number of solvent molecules and/or different levels of QM theory) are computed via extrapolation using the reference-potential method. Our simulation results show that this adaptive QM/MM scheme is numerically stable, at least for the case studied in this work. Furthermore, this method also offers an inexpensive way to examine the convergence of the QM/MM calculation with respect to the size of the QM region.

A simplified charge projection scheme for long-range electrostatics in ab initio QM/MM calculations.

In a previous work [Pan et al., Molecules 23, 2500 (2018)], a charge projection scheme was reported, where outer molecular mechanical (MM) charges [>10 Å from the quantum mechanical (QM) region] were projected onto the electrostatic potential (ESP) grid of the QM region to accurately and efficiently capture long-range electrostatics in ab initio QM/MM calculations. Here, a further simplification to the model is proposed, where the outer MM charges are projected onto inner MM atom positions (instead of ESP grid positions). This enables a representation of the long-range MM electrostatic potential via augmentary charges (AC) on inner MM atoms. Combined with the long-range electrostatic correction function from Cisneros et al. [J. Chem. Phys. 143, 044103 (2015)] to smoothly switch between inner and outer MM regions, this new QM/MM-AC electrostatic model yields accurate and continuous ab initio QM/MM electrostatic energies with a 10 Å cutoff between inner and outer MM regions. This model enables efficient QM/MM cluster calculations with a large number of MM atoms as well as QM/MM calculations with periodic boundary conditions.

Li1.2Mn0.54Ni0.13Co0.13O2 nanosheets with porous structure as a high-performance cathode material for lithium-ion batteries.

The morphological and structural optimizations of electrode materials are efficient ways to enhance their electrochemical performance. Herein, we report a facile co-precipitation and subsequent calcination method to fabricate Li1.2Mn0.54Ni0.13Co0.13O2 nanosheets consisting of interconnected primary nanoparticles and open holes through the full thickness. By comparing the nanosheets and the agglomerated nanoparticles, the effects of the morphology and structure on the electrochemical performance are investigated. Specifically, the nanosheets exhibit a discharge capacity of 210 mA h g-1 at 0.5C with a capacity retention of 85% after 100 cycles. The improved electrochemical performance could be attributed to their morphological and structural improvements, which may facilitate sufficient electrolyte contacts, short diffusion paths and good structural integrity during the charge/discharge process. This work provides a feasible approach to fabricate lithium-rich layered oxide cathode materials with 2D morphology and porous structure, and reveals the relationships between their morphology, structure and electrochemical performance.

Controllable preparation of one-dimensional Li1.2Mn0.54Ni0.13Co0.13O2 cathode materials for high-performance lithium-ion batteries.

Lithium-rich layered oxides are attractive candidates of high-energy-density cathode materials for high-performance lithium ion batteries because of their high specific capacity and low cost. Nevertheless, their unsatisfactory rate capability and poor cycling stability have strongly hindered commercial applications in lithium ion batteries, mainly due to the ineffectiveness of the complicated synthesis techniques to control their morphologies and sizes. In this work, the Li1.2Mn0.54Ni0.13Co0.13O2 cathode materials with a one-dimensional rod-like morphology were synthesized via a facile co-precipitation route followed by a post-calcination treatment. By reasonably adding NH3·H2O in the co-precipitation reaction, the sizes of the metal oxalate precursors could be rationally varied. The electrochemical measurements displayed that the Li1.2Mn0.54Ni0.13Co0.13O2 short rods delivered a high capacity of 286 mA h g-1 at 0.1C and excellent capacity retention of 85% after 100 cycles, which could be contributed to the improvement of the electrolyte contact, Li+ diffusion, and structural stability of the one-dimension porous structure.

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.

Calculations of the free energy profile, also known as potential of mean force (PMF), along a chosen collective variable (CV) are now routinely applied in the studies of chemical processes, such as enzymatic reactions and chemical reactions in condensed phases. However, if the ab initio quantum mechanical/molecular mechanics (QM/MM) level of accuracy is required for the PMF, it can be formidably demanding 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 the 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, and some low-energy conformations may get oversampled in simulations of a finite length. 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.