The generalized molecular fractionation with conjugate caps/molecular mechanics method for direct calculation of protein energy

Fault-tolerant quantum chemical calculations with improved machine-learning models

Easy and effective usage of computational resources is crucial for scientific calculations. Following our recent work of machine-learning (ML) assisted scheduling optimization [J. Comput. Chem. 2023, 44, 1174], we further propose (1) the improved ML models for the better predictions of computational loads, and as such, more elaborate load-balancing calculations can be expected; (2) the idea of coded computation, that is, the integration of gradient coding, in order to introduce fault tolerance during the distributed calculations; and (3) their applications together with re-normalized exciton model with time-dependent density functional theory (REM-TDDFT) for calculating the excited states. Illustrated benchmark calculations include P38 protein, and solvent model with one or several excitable centers. The results show that the improved ML-assisted coded calculations can further improve the load-balancing and cluster utilization, owing primarily profit in fault tolerance that aims at the automated quantum chemical calculations for both ground and excited states.

Noncovalent binding of carbofuran to acetylcholinesterase from Homo sapiens, Danio rerio, Apis mellifera and Caenorhabditis elegans: Homology modelling, molecular docking and dynamics, and quantum biochemistry description

Although various regulatory agencies have banned or severely restricted the use of carbofuran (CAR), recent reports indicate the presence of CAR residues in both cultivated and wild areas. This pesticide is a potent inhibitor of acetylcholinesterase (AChE), which acts by preventing the hydrolysis of acetylcholine (ACh). Given the critical role of AChE::ACh in the proper functioning of the nervous system, we thought it appropriate to investigate the binding of CAR to AChEs from Homo sapiens, Danio rerio, Apis mellifera, and Caenorhabditis elegans using homology modelling, molecular docking, molecular dynamics, and quantum biochemistry. Molecular docking and dynamics results indicated peculiar structural behavior in each AChE::CAR system. Quantum biochemistry results showed similar affinities for all complexes, confirming the description of carbofuran as a broad-spectrum pesticide, and have a limited correlation with IC50 values. We found the following decreasing affinity order of AChE species: H. sapiens > A. mellifera > C. elegans > D. rerio. The computational results suggest that CAR occupies different pockets in the AChEs studied. In addition, our results showed that CAR binds to hsAChE and ceAChE in a very similar manner: it has high affinities for the same subsites in both species and forms hydrogen bonds with residues (hsTYR124 and ceTRP107) occupying homologous positions in the peripheral site. This suggests that this nematode is a potential model to evaluate the toxicity of carbamates, even though the sequence identity between them is only 41 %. Interestingly, we also observed that the catalytic histidines of drAChE and amAChE exhibited favorable contacts with carbofuran, suggesting that the non-covalent binding of carbofuran to these proteins may promote faster carbamylation rates than the binding modes to human and worm acetylcholinesterases. Our computational results provide a better understanding of the binding mechanisms in these complexes, as well as new insights into the mechanism of carbamylation.

Polarizable Embedding Potentials through Molecular Fractionation with Conjugate Caps Including Hydrogen Bonds

Polarizable embedding (PE) refers to classical embedding approaches, such as those used in quantum mechanics/molecular mechanics (QM/MM), that allow mutual polarization between the quantum and classical regions. The quality of the embedding potential is critical to provide accurate results, e.g., for spectroscopic properties and dynamical processes. High-quality embedding-potential parameters can be obtained by dividing the classical region into smaller fragments and deriving the parameters from ab initio calculations on the fragments. For solvents and other systems composed of small molecules, the fragments can be individual molecules, while a more complicated fragmentation procedure is needed for larger molecules, such as proteins and nucleic acids. One such fragmentation strategy is the molecular fractionation with conjugate caps (MFCC) approach. As is widely known, hydrogen bonds play a key role in many biomolecular systems, e.g., in proteins, where they are responsible for the secondary structure. In this work, we assess the effects of including hydrogen-bond fragmentation in the MFCC procedure [MFCC(HB)] for deriving the embedding-potential parameters. The MFCC(HB) extension is evaluated on several molecular systems, ranging from small model systems to proteins, directly in terms of molecular electrostatic potentials and embedding potentials and indirectly in terms of selected properties of chromophores embedded in water and complex protein environments.

Toward an extreme-scale electronic structure system

Electronic structure calculations have the potential to predict key matter transformations for applications of strategic technological importance, from drug discovery to material science and catalysis. However, a predictive physicochemical characterization of these processes often requires accurate quantum chemical modeling of complex molecular systems with hundreds to thousands of atoms. Due to the computationally demanding nature of electronic structure calculations and the complexity of modern high-performance computing hardware, quantum chemistry software has historically failed to operate at such large molecular scales with accuracy and speed that are useful in practice. In this paper, novel algorithms and software are presented that enable extreme-scale quantum chemistry capabilities with particular emphasis on exascale calculations. This includes the development and application of the multi-Graphics Processing Unit (GPU) library LibCChem 2.0 as part of the General Atomic and Molecular Electronic Structure System package and of the standalone Extreme-scale Electronic Structure System (EXESS), designed from the ground up for scaling on thousands of GPUs to perform high-performance accurate quantum chemistry calculations at unprecedented speed and molecular scales. Among various results, we report that the EXESS implementation enables Hartree-Fock/cc-pVDZ plus RI-MP2/cc-pVDZ/cc-pVDZ-RIFIT calculations on an ionic liquid system with 623 016 electrons and 146 592 atoms in less than 45 min using 27 600 GPUs on the Summit supercomputer with a 94.6% parallel efficiency.

A simple and consistent quantum-chemical fragmentation scheme for proteins that includes two-body contributions

The Molecular Fractionation with Conjugate Caps (MFCC) method is a popular fragmentation method for the quantum-chemical treatment of proteins. However, it does not account for interactions between the amino acid fragments, such as intramolecular hydrogen bonding. Here, we present a combination of the MFCC fragmentation scheme with a second-order many-body expansion (MBE) that consistently accounts for all fragment-fragment, fragment-cap, and cap-cap interactions, while retaining the overall simplicity of the MFCC scheme with its chemically meaningful fragments. We show that with the resulting MFCC-MBE(2) scheme, the errors in the total energies of selected polypeptides and proteins can be reduced by up to one order of magnitude and relative energies of different protein conformers can be predicted accurately.

Machine-learning assisted scheduling optimization and its application in quantum chemical calculations

Easy and effective usage of computational resources is crucial for scientific calculations, both from the perspectives of timeliness and economic efficiency. This work proposes a bi-level optimization framework to optimize the computational sequences. Machine-learning (ML) assisted static load-balancing, and different dynamic load-balancing algorithms can be integrated. Consequently, the computational and scheduling engine of the ParaEngine is developed to invoke optimized quantum chemical (QC) calculations. Illustrated benchmark calculations include high-throughput drug suit, solvent model, P38 protein, and SARS-CoV-2 systems. The results show that the usage rate of given computational resources for high throughput and large-scale fragmentation QC calculations can primarily profit, and faster accomplishing computational tasks can be expected when employing high-performance computing (HPC) clusters.

Data-Driven Many-Body Potential Energy Functions for Generic Molecules: Linear Alkanes as a Proof-of-Concept Application

We present a generalization of the many-body energy (MB-nrg) theoretical/computational framework that enables the development of data-driven potential energy functions (PEFs) for generic covalently bonded molecules, with arbitrary quantum mechanical accuracy. The "nearsightedness of electronic matter" is exploited to define monomers as "natural building blocks" on the basis of their distinct chemical identity. The energy of generic molecules is then expressed as a sum of individual many-body energies of incrementally larger subsystems. The MB-nrg PEFs represent the low-order n-body energies, with n = 1-4, using permutationally invariant polynomials derived from electronic structure data carried out at an arbitrary quantum mechanical level of theory, while all higher-order n-body terms (n > 4) are represented by a classical many-body polarization term. As a proof-of-concept application of the general MB-nrg framework, we present MB-nrg PEFs for linear alkanes. The MB-nrg PEFs are shown to accurately reproduce reference energies, harmonic frequencies, and potential energy scans of alkanes, independently of their length. Since, by construction, the MB-nrg framework introduced here can be applied to generic covalently bonded molecules, we envision future computer simulations of complex molecular systems using data-driven MB-nrg PEFs, with arbitrary quantum mechanical accuracy.

Quantum Biochemistry Screening and In Vitro Evaluation of Leishmania Metalloproteinase Inhibitors

Leishmanolysin, also known as major promastigote protease (PSP) or gp63, is the most abundant surface glycoprotein of Leishmania spp., and has been extensively studied and recognized as the main parasite virulence factor. Characterized as a metalloprotease, gp63 can be powerfully inactivated in the presence of a metal chelator. In this study, we first used the structural parameters of a 7-hydroxycoumarin derivative, L1 compound, to evaluate the theoretical-computational experiments against gp63, comparing it with an available metal chelator already described. The methodology followed was (i) analysis of the three-dimensional structure of gp63 as well as its active site, and searching the literature and molecular databases for possible inhibitors; (ii) molecular docking simulations and investigation of the interactions in the generated protein-ligand complexes; and (iii) the individual energy of the gp63 amino acids that interacted most with the ligands of interest was quantified by ab initio calculations using Molecular Fraction with Conjugated Caps (MFCC). MFCC still allowed the final quantum balance calculations of the protein interaction to be obtained with each inhibitor candidate binder. L1 obtained the best energy quantum balance result with -2 eV, followed by DETC (-1.4 eV), doxycycline (-1.3 eV), and 4-terpineol (-0.6 eV), and showed evidence of covalent binding in the enzyme active site. In vitro experiments confirmed L1 as highly effective against L. amazonensis parasites. The compound also exhibited a low cytotoxicity profile against mammalian RAW and 3T3 cells lines, presenting a selective index of 149.19 and 380.64 µM, respectively. L1 induced promastigote forms' death by necrosis and the ultrastructural analysis revealed disruption in membrane integrity. Furthermore, leakage of the contents and destruction of the parasite were confirmed by Spectroscopy Dispersion analysis. These results together suggested L1 has a potential effect against L. amazonensis, the etiologic agent of diffuse leishmaniasis, and the only one that currently does not have a satisfactory treatment.

Fragment-Based Quantum Mechanical Calculation of Excited-State Properties of Fluorescent RNAs

Fluorescent RNA aptamers have been successfully applied to track and tag RNA in a biological system. However, it is still challenging to predict the excited-state properties of the RNA aptamer–fluorophore complex with the traditional electronic structure methods due to expensive computational costs. In this study, an accurate and efficient fragmentation quantum mechanical (QM) approach of the electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) scheme was applied for calculations of excited-state properties of the RNA aptamer–fluorophore complex. In this method, the excited-state properties were first calculated with one-body fragment quantum mechanics/molecular mechanics (QM/MM) calculation (the excited-state properties of the fluorophore) and then corrected with a series of two-body fragment QM calculations for accounting for the QM effects from the RNA on the excited-state properties of the fluorophore. The performance of the EE-GMFCC on prediction of the absolute excitation energies, the corresponding transition electric dipole moment (TEDM), and atomic forces at both the TD-HF and TD-DFT levels was tested using the Mango-II RNA aptamer system as a model system. The results demonstrate that the calculated excited-state properties by EE-GMFCC are in excellent agreement with the traditional full-system time-dependent ab initio calculations. Moreover, the EE-GMFCC method is capable of providing an accurate prediction of the relative conformational excited-state energies for different configurations of the Mango-II RNA aptamer system extracted from the molecular dynamics (MD) simulations. The fragmentation method further provides a straightforward approach to decompose the excitation energy contribution per ribonucleotide around the fluorophore and then reveals the influence of the local chemical environment on the fluorophore. The applications of EE-GMFCC in calculations of excitation energies for other RNA aptamer–fluorophore complexes demonstrate that the EE-GMFCC method is a general approach for accurate and efficient calculations of excited-state properties of fluorescent RNAs.

Computational and data driven molecular material design assisted by low scaling quantum mechanics calculations and machine learning

Electronic structure methods based on quantum mechanics (QM) are widely employed in the computational predictions of the molecular properties and optoelectronic properties of molecular materials. The computational costs of these QM methods, ranging from density functional theory (DFT) or time-dependent DFT (TDDFT) to wave-function theory (WFT), usually increase sharply with the system size, causing the curse of dimensionality and hindering the QM calculations for large sized systems such as long polymer oligomers and complex molecular aggregates. In such cases, in recent years low scaling QM methods and machine learning (ML) techniques have been adopted to reduce the computational costs and thus assist computational and data driven molecular material design. In this review, we illustrated low scaling ground-state and excited-state QM approaches and their applications to long oligomers, self-assembled supramolecular complexes, stimuli-responsive materials, mechanically interlocked molecules, and excited state processes in molecular aggregates. Variable electrostatic parameters were also introduced in the modified force fields with the polarization model. On the basis of QM computational or experimental datasets, several ML algorithms, including explainable models, deep learning, and on-line learning methods, have been employed to predict the molecular energies, forces, electronic structure properties, and optical or electrical properties of materials. It can be conceived that low scaling algorithms with periodic boundary conditions are expected to be further applicable to functional materials, perhaps in combination with machine learning to fast predict the lattice energy, crystal structures, and spectroscopic properties of periodic functional materials.

Molecular Dynamics Driven by the Many-Body Expansion (MBE-MD)

We present a protocol for classical and nuclear quantum dynamics, in which the energies and forces are generated by the many-body expansion (MBE), and apply it to water clusters using the TTM2.1-F and MB-Pol interaction potentials at various temperatures. We carry out MBE-molecular dynamics (MD) classical and nuclear quantum dynamical simulations, in which the energies and forces of the full system are approximated by the two-, three-, and four-body terms of the MBE, and compare the average potential and the vibrational density of states with the full simulation, i.e., the one for which no MBE is used. Our results indicate that the thermally averaged potential energy from the MBE up to the four-body term converges with near-identical behavior to the one from the full simulation. The three-body makes a substantial contribution (∼20%) to the energy, whereas the four-body is necessary for obtaining quantitatively accurate energetics and forces, albeit making a small contribution to each (∼2%). We further show that the harmonic frequencies are reproduced to within a few wavenumbers (cm^-1) at the four-body level and that the slowest modes to converge with the MBE rank are those involving the strongest hydrogen bonds. Anharmonicity exacerbates this effect, so that a four-body description of the energies and forces is needed to achieve accurate anharmonic vibrational frequencies in the hydrogen-bonded OH-stretching region. We also discuss the asymptotic scaling of the MBE-MD protocol with respect to the cost of the underlying potential energy evaluation, suggesting that electronic structure methods that scale at least as N⁴, N being the size of the system, are needed to result in savings over the traditional full MD simulation. We anticipate that the MBE-MD protocol can evolve into a powerful and practical method, which will allow for highly accurate ab initio MD simulations on a much broader range of molecular systems than can be currently handled.

Building quantum mechanics quality force fields of proteins with the generalized energy-based fragmentation approach and machine learning

We combined our generalized energy-based fragmentation (GEBF) approach and machine learning (ML) technique to construct quantum mechanics (QM) quality force fields for proteins. In our scheme, the training sets for a protein are only constructed from its small subsystems, which capture all short-range interactions in the target system. The energy of a given protein is expressed as the summation of atomic contributions from QM calculations of various subsystems, corrected by long-range Coulomb and van der Waals interactions. With the Gaussian approximation potential (GAP) method, our protocol can automatically generate training sets with high efficiency. To facilitate the construction of training sets for proteins, we store all trained subsystem data in a library. If subsystems in the library are detected in a new protein, corresponding datasets can be directly reused as a part of the training set on this new protein. With two polypeptides, 4ZNN and 1XQ8 segment, as examples, the energies and forces predicted by GEBF-GAP are in good agreement with those from conventional QM calculations, and dihedral angle distributions from GEBF-GAP molecular dynamics (MD) simulations can also well reproduce those from ab initio MD simulations. In addition, with the training set generated from GEBF-GAP, we also demonstrate that GEBF-ML force fields constructed by neural network (NN) methods can also show QM quality. Therefore, the present work provides an efficient and systematic way to build QM quality force fields for biological systems.

On the Accuracy of QM/MM Models: A Systematic Study of Intramolecular Proton Transfer Reactions of Amino Acids in Water

This work presents a systematic assessment of QM/QM' and QM/MM models with respect to direct QM calculations for the tautomerization (neutral to zwitterion) reactions of amino acids (glycine, alanine, valine, aspartate, and neutral and protonated histidine) solvated in a 160 water cluster. The effect of varying QM region size and choice of embedding potentials, including fixed-charge and polarizable molecular mechanics force fields (TIP3P and EFP) and various semiempirical QM methods (PM7, GFN2-xTB, DFTBA, DFTB3, HF-3c, and PBEh-3c), on the accuracy of the models was examined. A surprising finding was that molecular mechanics force fields outperformed many of the semiempirical methods. Generally, the errors in the QM/QM' and QM/MM models converge slowly with respect to the QM region size, requiring 50 or more waters to be included in the QM region before the error in the model falls below 1 kcal mol^-1 of its pure QM result. Different QM region selection schemes were also compared, and it was found that selection based on Natural Population Analysis (NPA) atomic charges significantly reduced the error in the QM/QM' and QM/MM models particularly if a low-quality embedding potential was used. It is envisaged that these results will be useful for the development of future hybrid QM models.

Accurate Prediction of Absorption Spectral Shifts of Proteorhodopsin Using a Fragment-Based Quantum Mechanical Method

Many experiments have been carried out to display different colors of Proteorhodopsin (PR) and its mutants, but the mechanism of color tuning of PR was not fully elucidated. In this study, we applied the Electrostatically Embedded Generalized Molecular Fractionation with Conjugate Caps (EE-GMFCC) method to the prediction of excitation energies of PRs. Excitation energies of 10 variants of Blue Proteorhodopsin (BPR-PR105Q) in residue 105GLN were calculated with the EE-GMFCC method at the TD-B3LYP/6-31G* level. The calculated results show good correlation with the experimental values of absorption wavelengths, although the experimental wavelength range among these systems is less than 50 nm. The ensemble-averaged electric fields along the polyene chain of retinal correlated well with EE-GMFCC calculated excitation energies for these 10 PRs, suggesting that electrostatic interactions from nearby residues are responsible for the color tuning. We also utilized the GMFCC method to decompose the excitation energy contribution per residue surrounding the chromophore. Our results show that residues ASP97 and ASP227 have the largest contribution to the absorption spectral shift of PR among the nearby residues of retinal. This work demonstrates that the EE-GMFCC method can be applied to accurately predict the absorption spectral shifts for biomacromolecules.

Density-Based Many-Body Expansion as an Efficient and Accurate Quantum-Chemical Fragmentation Method: Application to Water Clusters

Fragmentation methods based on the many-body expansion offer an attractive approach for the quantum-chemical treatment of large molecular systems, such as molecular clusters and crystals. Conventionally, the many-body expansion is performed for the total energy, but such an energy-based many-body expansion often suffers from a slow convergence with respect to the expansion order. For systems that show strong polarization effects such as water clusters, this can render the energy-based many-body expansion infeasible. Here, we establish a density-based many-body expansion as a promising alternative approach. By performing the many-body expansion for the electron density instead of the total energy and inserting the resulting total electron density into the total energy functional of density functional theory, one can derive a density-based energy correction, which in principle accounts for all higher-order polarization effects. Here, we systematically assess the accuracy of such a density-based many-body expansion for test sets of water clusters. We show that already a density-based two-body expansion is able to reproduce interaction energies per fragment within chemical accuracy and is able to accurately predict the energetic ordering as well as the relative interaction energies of different isomers of water clusters.

Three-Layer Multiscale Approach Based on Extremely Localized Molecular Orbitals to Investigate Enzyme Reactions

Quantum mechanics/molecular mechanics (QM/MM) calculations are widely used embedding techniques to computationally investigate enzyme reactions. In most QM/MM computations, the quantum mechanical region is treated through density functional theory (DFT), which offers the best compromise between chemical accuracy and computational cost. Nevertheless, to obtain more accurate results, one should resort to wave function-based methods, which however lead to a much larger computational cost already for relatively small QM subsystems. To overcome this drawback, we propose the coupling of our QM/ELMO (quantum mechanics/extremely localized molecular orbital) approach with molecular mechanics, thus introducing the three-layer QM/ELMO/MM technique. The QM/ELMO strategy is an embedding method in which the chemically relevant part of the system is treated at the quantum mechanical level, while the rest is described through frozen ELMOs. Since the QM/ELMO method reproduces results of fully QM computations within chemical accuracy and with a much lower computational effort, it can be considered a suitable strategy to extend the range of applicability and accuracy of the QM/MM scheme. In this paper, other than briefly presenting the theoretical bases of the QM/ELMO/MM technique, we will also discuss its validation on the well-tested deprotonation of acetyl coenzyme A by aspartate in citrate synthase.

Fragment-Based Ab Initio Molecular Dynamics Simulation for Combustion

We develop a fragment-based ab initio molecular dynamics (FB-AIMD) method for efficient dynamics simulation of the combustion process. In this method, the intermolecular interactions are treated by a fragment-based many-body expansion in which three- or higher body interactions are neglected, while two-body interactions are computed if the distance between the two fragments is smaller than a cutoff value. The accuracy of the method was verified by comparing FB-AIMD calculated energies and atomic forces of several different systems with those obtained by standard full system quantum calculations. The computational cost of the FB-AIMD method scales linearly with the size of the system, and the calculation is easily parallelizable. The method is applied to methane combustion as a benchmark. Detailed reaction network of methane reaction is analyzed, and important reaction species are tracked in real time. The current result of methane simulation is in excellent agreement with known experimental findings and with prior theoretical studies.

Systematic Partitioning of Proteins for Quantum-Chemical Fragmentation Methods Using Graph Algorithms

Quantum-chemical fragmentation methods offer an efficient approach for the treatment of large proteins, in particular if local target quantities such as protein-ligand interaction energies, enzymatic reaction energies, or spectroscopic properties of embedded chromophores are sought. However, the accuracy that is achievable for such local target quantities intricately depends on how the protein is partitioned into smaller fragments. While the commonly employed naı̈ve approach of using fragments with a fixed size is widely used, it can result in large and unpredictable errors when varying the fragment size. Here, we present a systematic partitioning scheme that aims at minimizing the fragmentation error of a local target quantity for a given maximum fragment size. To this end, we construct a weighted graph representation of the protein, in which the amino acids constitute the nodes. These nodes are connected by edges weighted with an estimate for the fragmentation error that is expected when cutting this edge. This allows us to employ graph partitioning algorithms provided by computer science to determine near-optimal partitions of the protein. We apply this scheme to a test set of six proteins representing various prototypical applications of quantum-chemical fragmentation methods using a simplified molecular fractionation with conjugate caps (MFCC) approach with hydrogen caps. We show that our graph-based scheme consistently improves upon the naı̈ve approach.

Automated fragmentation quantum mechanical calculation of 13C and 1H chemical shifts in molecular crystals

In this work, the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach was applied to calculate the ¹³C and ¹H nuclear magnetic resonance (NMR) chemical shifts in molecular crystals. Two benchmark sets of molecular crystals were selected to calculate the NMR chemical shifts. Systematic investigation was conducted to examine the convergence of AF-QM/MM calculations and the impact of various density functionals with different basis sets on the NMR chemical shift prediction. The result demonstrates that the calculated NMR chemical shifts are close to convergence when the distance threshold for the QM region is larger than 3.5 Å. For ¹³C chemical shift calculations, the mPW1PW91 functional is the best density functional among the functionals chosen in this study (namely, B3LYP, B3PW91, M06-2X, M06-L, mPW1PW91, OB98, and OPBE), while the OB98 functional is more suitable for the ¹H NMR chemical shift prediction of molecular crystals. Moreover, with the B3LYP functional, at least a triple-ζ basis set should be utilized to accurately reproduce the experimental ¹³C and ¹H chemical shifts. The employment of diffuse basis functions will further improve the accuracy for ¹³C chemical shift calculations, but not for the ¹H chemical shift prediction. We further proposed a fragmentation scheme of dividing the central molecule into smaller fragments. By comparing with the results of the fragmentation scheme using the entire central molecule as the core region, the AF-QM/MM calculations with the fragmented central molecule can not only achieve accurate results but also reduce the computational cost. Therefore, the AF-QM/MM approach is capable of predicting the ¹³C and ¹H NMR chemical shifts for molecular crystals accurately and effectively, and could be utilized for dealing with more complex periodic systems such as macromolecular polymers and biomacromolecules. The AF-QM/MM program for molecular crystals is available at https://github.com/shiman1995/NMR.

Forecasting System of Computational Time of DFT/TDDFT Calculations under the Multiverse Ansatz via Machine Learning and Cheminformatics

With the view of achieving a better performance in task assignment and load-balancing, a top-level designed forecasting system for predicting computational times of density-functional theory (DFT)/time-dependent DFT (TDDFT) calculations is presented. The computational time is assumed as the intrinsic property for the molecule. Based on this assumption, the forecasting system is established using the "reinforced concrete", which combines the cheminformatics, several machine-learning (ML) models, and the framework of many-world interpretation (MWI) in multiverse ansatz. Herein, the cheminformatics is used to recognize the topological structure of molecules, the ML models are used to build the relationships between topology and computational cost, and the MWI framework is used to hold various combinations of DFT functionals and basis sets in DFT/TDDFT calculations. Calculated results of molecules from the DrugBank dataset show that (1) it can give quantitative predictions of computational costs, typical mean relative errors can be less than 0.2 for DFT/TDDFT calculations with derivations of ±25% using the exactly pretrained ML models and (2) it can also be employed to various combinations of DFT functional and basis set cases without exactly pretrained ML models, while only slightly enlarge predicting errors.

Structures and Spectroscopic Properties of Large Molecules and Condensed-Phase Systems Predicted by Generalized Energy-Based Fragmentation Approach

ConspectusThe structures and spectroscopic properties of molecules and condensed-phase systems are usually experimentally characterized by X-ray, infrared (IR), Raman, nuclear magnetic resonance (NMR), and electronic absorption/emission spectra. Quantum mechanics (QM) calculations are critical in quantitatively understanding the relationship between the structure and physicochemical properties of various chemical systems. However, it is very challenging to apply traditional QM methods to large molecules and condensed-phase systems with large unit cells due to their steep computational scaling with the system size. To overcome this difficulty, theoretical chemists have developed various linear (or low) scaling QM methods, among which energy-based fragmentation methods have achieved great success for large molecules or clusters. One of the most popular energy-based fragmentation methods is the generalized energy-based fragmentation (GEBF) approach developed by us.In this approach, the ground-state energy of a large molecule can be evaluated from the ground-state energies of a series of embedded subsystems. In this Account, we focus on the recent developments and applicability of the GEBF approach for the structures and spectroscopic properties of complicated large molecules and condensed-phase systems. With new fragmentation schemes, the GEBF approach can now describe ionic liquid clusters and metal-containing supramolecular systems accurately and can provide accurate binding energies for host-guest complexes. In addition, the GEBF approach is now available for describing the localized excited states of large systems including a chromophore. More importantly, the GEBF approach under periodic boundary conditions (PBC-GEBF) has been developed to deal with periodic molecular crystals and liquids. Then, the ground-state energy (or property) per unit cell of a periodic condensed phase system can be predicted with QM calculations on nonperiodic embedded subsystems. This feature enables accurate electron correlation calculations on molecular crystals and liquids to be feasible on ordinary workstations. The PBC-GEBF approach has been applied to predict the crystal structures, lattice energies, and spectroscopic properties of some typical molecular crystals and solutions. By combining the GEBF method and machine learning (ML) method, a GEBF-ML force field has been developed for long normal alkanes, and the IR spectra of long alkanes can be obtained from the GEBF-ML molecular dynamics (MD) simulations. The GEBF and its periodic variant are expected to play increasingly important roles in investigating real-life chemical systems of broad interests at the ab initio levels.

A quantum biochemistry investigation of the protein-protein interactions for the description of allosteric modulation on biomass-degrading chimera

The worldwide dependence of population on fossil fuels continues to have several harmful implications for the environment. Bioethanol is an excellent option for renewable fuel to replace the current greenhouse gas emitters. In addition, its production by enzymatic route has gained space among the industrial processes because it replaces the traditional acid treatment. Due to its high versatility, the xylanase family is used in this process as an accessory enzyme for degrading the lignocellulosic substrate of biomass. A chimera built by a xylanolytic domain (Xyl) and a xylose-binding protein (XBP) showed an experimentally improved catalytic efficiency and interdomain allosteric modulation after xylose binding. In this context, we performed a quantum biochemistry characterization of the interactions between these domains and dynamic cross-correlation (DCC) analysis after performing molecular dynamics (DM) simulations of the systems in the presence and absence of xylose in the XBP active site. We used the density functional theory (DFT) within the molecular fractionation with the conjugated caps (MFCC) approach to describe the pair energies, and the corresponding energy difference between the chimera domains responsible for the allosteric effect and amino acid DCC to evaluate the interdomain coupling differences between the energy states. The detailed energetic investigation together with the related structural and dynamics counterparts revealed the molecular mechanisms of chimeric improvement of the xylanase activity observed experimentally. This mechanism was correlated with greater stability and high connectivity at the interdomain interface in the xylose bound relative to the free chimera. We identify the contributions of hydrogen bonds, hydrophobic interactions and water-mediated interactions in the interdomain region responsible for stability together with the structural and dynamical elements related to the allosteric effect. Taken together, these observations led to a comprehensive understanding of the chimera's modulatory action that occurs through the formation of a highly connected interface that makes the essential movements related to xylanolytic activity in xylanase correlated to those of the xylose-binding protein.

Polarizable Density Embedding for Large Biomolecular Systems

We present an efficient and robust fragment-based quantum-classical embedding model capable of accurately capturing effects from complex environments such as proteins and nucleic acids. This is realized by combining the molecular fractionation with conjugate caps (MFCC) procedure with the polarizable density embedding (PDE) model at the level of Fock matrix construction. The PDE contributions to the Fock matrix of the core region are constructed using the local molecular basis of the individual fragments rather than the supermolecular basis of the entire system. Thereby, we avoid complications associated with the application of the MFCC procedure on environment quantities such as electronic densities and molecular-orbital energies. Moreover, the computational cost associated with solving self-consistent field (SCF) equations of the core region remains unchanged from that of purely classical polarized embedding models. We analyze the performance of the resulting model in terms of the reproduction of the electrostatic potential of an insulin monomer protein and further in the context of solving problems related to electron spill-out. Finally, we showcase the model for the calculation of one- and two-photon properties of the Nile red molecule in a protein environment. Based on our analyses, we find that the combination of the MFCC approach with the PDE model is an efficient, yet accurate approach for calculating molecular properties of molecules embedded in structured biomolecular environments.

Fragment Quantum Mechanical Method for Excited States of Proteins: Development and Application to the Green Fluorescent Protein

Understanding the excited-state properties of luminescent biomolecules is of central importance to their biophysical applications. In this study, we develop the Electrostatically Embedded Generalized Molecular Fractionation with Conjugate Caps (EE-GMFCC) method for quantitatively characterizing properties of covalently bonded systems with localized excitations (i.e., involving a single chromophore), such as fluorescent proteins. The excitation energy, transition dipole moment, and oscillator strength of wild-type Green Fluorescent Protein (wt-GFP) calculated by EE-GMFCC are found to be in excellent agreement with full system time-dependent density functional theory results. We also applied the Polarized Protein-Specific Charge model to wt-GFP, and found that electronic polarization of the protein is critical in stabilizing hydrogen bonding interactions in wt-GFP, which influences its absorption spectrum. The predicted absorption spectra of wt-GFP in the A and B states qualitatively agree with experiment. The fragmentation approach further allows a straightforward per residue decomposition of the excitation which reveals the influence of the protein environment on the absorption spectra of wt-GFP A and B states. Our results demonstrate that the EE-GMFCC method is both accurate and efficient for excited-state property calculations on proteins.

Fragment-based quantum mechanical approach to biomolecules, molecular clusters, molecular crystals and liquids

To study large molecular systems beyond the system size that the current state-of-the-art ab initio electronic structure methods could handle, fragment-based quantum mechanical (QM) approaches have been developed over the past years, and proved to be efficient in dealing with large molecular systems at various ab initio levels. According to the fragmentation approach, a large molecular system can be divided into subsystems (fragments), and subsequently the property of the whole system can be approximately obtained by taking a proper combination of the corresponding terms of individual fragments. Therefore, the standard QM calculation of a large system could be circumvented by carrying out a series of calculations on small fragments, which significantly promotes computational efficiency. The electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method is one of the fragment-based QM approaches which has been developed by our research group in recent years. This Perspective presents the theoretical framework of this fragmentation method and its applications in biomolecules, molecular clusters, molecular crystals and liquids, including total energy calculation, protein-ligand/protein binding affinity prediction, geometry optimization, vibrational spectrum simulation, ab initio molecular dynamics simulation, and prediction of excited-state properties.

Combining the Fragmentation Approach and Neural Network Potential Energy Surfaces of Fragments for Accurate Calculation of Protein Energy

Accurate and efficient all-atom quantum mechanical (QM) calculations for biomolecules still present a challenge to computational physicists and chemists. In this study, an extensible generalized molecular fractionation with a conjugate caps method combined with neural networks (NN-GMFCC) is developed for efficient QM calculation of protein energy. In the NN-GMFCC scheme, the total energy of a given protein is calculated by taking a proper combination of the high-precision neural network potential energies of all capped residues and overlapping conjugate caps. In addition, the two-body interaction energies of residue pairs are calculated by molecular mechanics (MM). With reference to the GMFCC/MM calculation at the ωB97XD/6-31G* level, the overall mean unsigned errors of the energy deviations and atomic force root-mean-squared errors calculated by NN-GMFCC are only 2.01 kcal/mol and 0.68 kcal/mol/Å, respectively, for 14 proteins (containing up to 13,728 atoms). Meanwhile, the NN-GMFCC approach is about 4 orders of magnitude faster than the GMFCC/MM method. The NN-GMFCC method could be systematically improved by inclusion of two-body QM interaction and multibody electronic polarization effect. Moreover, the NN-GMFCC approach can also be applied to other macromolecular systems such as DNA/RNA, and it is capable of providing a powerful and efficient approach for exploration of structures and functions of proteins with QM accuracy.

QM Implementation in Drug Design: Does It Really Help?

Computational chemistry allows one to characterize the structure, dynamics, and energetics of protein-ligand interactions, which makes it a valuable tool in drug discovery in both academic research and pharmaceutical industry. Molecular mechanics (MM)-based approaches are widely utilized to assist the discovery of new drug candidates. However, the complexity of protein-ligand interactions challenges the accuracy and efficiency of the commonly used empirical methods. Aiming to provide better accuracy in the description of protein-ligand interactions, quantum mechanics (QM)-based approaches are becoming increasingly explored. In principle, QM calculation includes all contributions to the energy, accounting for terms usually missing in empirical force fields, and provides a greater degree of transferability. The usefulness of QM in drug design cannot be overemphasized. In this chapter, we present recent developments and applications of fragment-based QM method in studying the protein-ligand and protein-protein interactions. We critically discuss the performance of the fragment-based QM method at different ab initio levels while trying to answer a critical question: do QM-based methods really help in drug design?

GPU-Accelerated Large-Scale Excited-State Simulation Based on Divide-and-Conquer Time-Dependent Density-Functional Tight-Binding

The present study implemented the divide-and-conquer time-dependent density-functional tight-binding (DC-TDDFTB) code on a graphical processing unit (GPU). The DC method, which is a linear-scaling scheme, divides a total system into several fragments. By separately solving local equations in individual fragments, the DC method could reduce slow central processing unit (CPU)-GPU memory access, as well as computational cost, and avoid shortfalls of GPU memory. Numerical applications confirmed that the present code on GPU significantly accelerated the TDDFTB calculations, while maintaining accuracy. Furthermore, the DC-TDDFTB simulation of 2-acetylindan-1,3-dione displays excited-state intramolecular proton transfer and provides reasonable absorption and fluorescence energies with the corresponding experimental values. © 2019 Wiley Periodicals, Inc.

Quantum Mechanics/Extremely Localized Molecular Orbital Method: A Fully Quantum Mechanical Embedding Approach for Macromolecules

The development of methods for the quantum mechanical study of macromolecules has always been an important challenge in theoretical chemistry. Nowadays, the techniques proposed in this context can be used to investigate very large systems and can be subdivided into two main categories: fragmentation and embedding strategies. In this paper, by modifying and improving the local self-consistent field approach originally proposed for quantum mechanics/molecular mechanics techniques, we introduce the new multiscale embedding quantum mechanics/extremely localized molecular orbital (QM/ELMO) method. The new strategy enables treatment of chemically relevant regions of large biological molecules through usual methods of quantum chemistry while describing the remaining parts of the systems by means of frozen extremely localized molecular orbitals transferred from properly constructed libraries. Test calculations have shown the correct functioning and the high reliability of the new approach, thus anticipating its possible applications to different fields of physical chemistry, such as rational drug design and structural refinements of proteins.

Prediction of Excited-State Properties of Oligoacene Crystals Using Fragment-Based Quantum Mechanical Method

A fundamental understanding of the excited-state properties of molecular crystals is of central importance for their optoelectronics applications. In this study, we developed the electrostatically embedded generalized molecular fractionation (EE-GMF) method for the quantitative characterization of the excited-state properties of locally excited molecular clusters. The accuracy of the EE-GMF method is systematically assessed for oligoacene crystals. Our result demonstrates that the EE-GMF method is capable of providing the lowest vertical singlet (S₁) and triplet excitation energies (T₁), in excellent agreement with the full-system quantum mechanical calculations. Using this method, we also investigated the performance of different density functionals in predicting the excited-state properties of the oligoacene crystals. Among the 13 tested functionals, B3LYP and MN15 give the two lowest overall mean unsigned errors with reference to the experimental S₁ and T₁ excitation energies. The EE-GMF approach can be readily utilized for studying the excited-state properties of large-scale organic solids at diverse ab initio levels.

A Fragment Quantum Mechanical Method for Metalloproteins

An accurate energy calculation of metalloprotein is of crucial importance and also a theoretical challenge. In this work, a metal molecular fractionation with conjugate caps (metal-MFCC) approach is developed for efficient linear-scaling quantum calculation of potential energy and atomic forces of metalloprotein. In this approach, the potential energy of a given protein is calculated by a linear combination of potential energies of the neighboring residues, two-body interaction energy between non-neighboring residues that are spatially in close contact and the potential energy of the metal binding group. The calculation of each fragment is embedded in a field of point charges representing the remaining protein environment. Numerical studies were carried out to check the performance of this method, and the calculated potential energies and atomic forces all show excellent agreement with the full system calculations at the M06-2X/6-31G(d) level. By combining the energy calculation with molecular dynamic simulation, we performed an ab initio structural optimization for a zinc finger protein with high efficiency. The present metal-MFCC approach is linear-scaling with a low prefactor and trivially parallelizable. The individual fragment typically contains about 50 atoms, and it is thus possible to be calculated at higher levels of the quantum chemistry method. This fragment method can be routinely applied to perform structural optimization and ab initio molecular dynamic simulation for metalloproteins of any size.

Libraries of Extremely Localized Molecular Orbitals. 3. Construction and Preliminary Assessment of the New Databanks

The fast and reliable determination of wave functions and electron densities of macromolecules has been one of the goals of theoretical chemistry for a long time, and in this context, several linear scaling techniques have been successfully devised over the years. Different approaches have been adopted to tackle this problem, and one of them exploits the fact that, according to the traditional chemical perception, molecules can be seen as constituted of recurring units (e.g., functional groups) with well-defined chemical features. This has led to the development of methods in which the global wave functions or electron densities of macromolecules are obtained by simply transferring density matrices or fuzzy electron densities associated with molecular fragments. In this context, we propose an alternative strategy that aims at quickly reconstructing wave functions and electron densities of proteins through the transfer of extremely localized molecular orbitals (ELMOs), which are orbitals strictly localized on small molecular units and, for this reason, easily transferable from molecule to molecule. To accomplish this task we have constructed original libraries of ELMOs that cover all the possible elementary fragments of the 20 natural amino acids in all their possible protonation states and forms. Our preliminary test calculations have shown that, compared to more traditional methods of quantum chemistry, the transfers from the novel ELMO databanks allow to obtain wave function and electron densities of large polypeptides and proteins at a significantly reduced computational cost. Furthermore, notwithstanding expected discrepancies, the obtained electron distributions and electrostatic potentials are in very good agreement with those obtained at Hartree-Fock and density functional theory (DFT) levels. Therefore, the results encourage to use the new libraries as alternatives to the popular pseudoatom-databases of crystallography in the refinement of crystallographic structures of macromolecules. In particular, in this context, we have already envisaged the coupling of the ELMO databanks with the promising Hirshfeld atom refinement technique to extend the applicability of the latter to very large systems.

An Ab Initio QM/MM Study of the Electrostatic Contribution to Catalysis in the Active Site of Ketosteroid Isomerase

The electric field in the hydrogen-bond network of the active site of ketosteroid isomerase (KSI) has been experimentally measured using vibrational Stark effect (VSE) spectroscopy, and utilized to study the electrostatic contribution to catalysis. A large gap was found in the electric field between the computational simulation based on the Amber force field and the experimental measurement. In this work, quantum mechanical (QM) calculations of the electric field were performed using an ab initio QM/MM molecular dynamics (MD) simulation and electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method. Our results demonstrate that the QM-derived electric field based on the snapshots from QM/MM MD simulation could give quantitative agreement with the experiment. The accurate calculation of the electric field inside the protein requires both the rigorous sampling of configurations, and a QM description of the electrostatic field. Based on the direct QM calculation of the electric field, we theoretically confirmed that there is a linear correlation relationship between the activation free energy and the electric field in the active site of wild-type KSI and its mutants (namely, D103N, Y16S, and D103L). Our study presents a computational protocol for the accurate simulation of the electric field in the active site of the protein, and provides a theoretical foundation that supports the link between electric fields and enzyme catalysis.

Geometry optimizations with the incremental molecular fragmentation method

Nuclear energy gradients for the incremental molecular fragmentation (IMF) method presented in our previous work [Meitei OR, Heßelmann A, Molecular energies from an incremental fragmentation method, J Chem Phys 144(8):084109, 2016] have been derived. Using the second-order Møller–Plesset perturbation theory method to describe the bonded and nonbonded energy and gradient contributions and the uncorrelated Hartree–Fock method to describe the correction increment, it is shown that the IMF gradient can be easily computed by a sum of the underlying individual derivatives of the energy contributions. The performance of the method has been compared against the supermolecular method by optimizing the structures of a range of polyglycine molecules with up to 36 glycine residues in the chain. It is shown that with a sensible set of parameters used in the fragmentation the supermolecular structures can be fairly well reproduced. In a few cases the optimization with the IMF method leads to structures that differ from the supermolecular ones. It was found, however, that these are more stable geometries also on the supermolecular potential energy surface.

Quantum chemical studies on anion specificity of CαNN motif in functional proteins

Anion binding C^αNN motif is found in functionally important regions of protein structures. This motif based only on backbone atoms from three adjacent residues, recognizes free sulphate or phosphate ion as well as phosphate groups in nucleotides and in a variety of cofactors. The mode of anion recognition and microscopic picture of binding interaction remains unclear. Here we perform self-consistent quantum chemical calculations considering sulphate and phosphate bound C^αNN motif fragments from crystal structures of functional proteins in order to figure out microscopic basis of anion recognition. Our calculations indicate that stability and preference of the anion in the motif depends on the sequence of the motif. The stabilization energy is larger in case of polar residue containing motif fragment. Nitrogen atom of the polar residue of motif mainly participates in the coordination at the lowest energy levels. Anion replacement decreases stabilization energy along with coordination between motif atoms and oxygen atoms of anion shifted to higher energies, suggesting preference of the motif residues to specific anion. Our analysis may be helpful to understand microscopic basis of interaction between proteins and ionic species.

Fragment-based quantum mechanical calculation of protein-protein binding affinities

The electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method has been successfully utilized for efficient linear-scaling quantum mechanical (QM) calculation of protein energies. In this work, we applied the EE-GMFCC method for calculation of binding affinity of Endonuclease colicin-immunity protein complex. The binding free energy changes between the wild-type and mutants of the complex calculated by EE-GMFCC are in good agreement with experimental results. The correlation coefficient (R) between the predicted binding energy changes and experimental values is 0.906 at the B3LYP/6-31G*-D level, based on the snapshot whose binding affinity is closest to the average result from the molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) calculation. The inclusion of the QM effects is important for accurate prediction of protein-protein binding affinities. Moreover, the self-consistent calculation of PB solvation energy is required for accurate calculations of protein-protein binding free energies. This study demonstrates that the EE-GMFCC method is capable of providing reliable prediction of relative binding affinities for protein-protein complexes. © 2018 Wiley Periodicals, Inc.

Structure of liquid water - a dynamical mixture of tetrahedral and 'ring-and-chain' like structures

The nature of the dynamical hydrogen-bond network of liquid water under ambient conditions has challenged both experimental and theoretical researchers for decades and remains a topic of intense debate. In this work, we addressed the structural issue of the hydrogen-bond network of liquid water based on an accurate ab initio molecular dynamics simulation. The present work showed clearly that liquid water is neither accurately described by a static picture of mostly tetrahedral water molecules nor dominated by "ring-and-chain" like structures. Instead, the structure of water is a dynamical mixture of tetrahedral and 'ring-and-chain' like structures with a slight bias toward the former. On average, each water molecule forms about three hydrogen bonds with the surrounding water molecules. The present accurate ab initio molecular dynamics simulation of liquid water was made possible by using a fragment-based second-order Møller-Plesset perturbation theory (MP2) with a large basis set to treat a large body of water molecules. This level of ab initio theory is sufficiently accurate for describing water interactions, and the simulated structural and dynamical properties of liquid water, including radial distribution functions, diffusion coefficient, dipole moment, etc., are uniformly in excellent agreement with experimental observations.

Charge-patching method for the calculation of electronic structure of polypeptides

Based on the CPM method, the charge densities of polypeptides can be generated and their electronic structure can be further calculated.

Outlining migrainous through dihydroergotamine–serotonin receptor interactions using quantum biochemistry

We present the electronic structure of the complex dihydroergotamine–serotonin receptor to unveil new medications to treat migraine and related diseases.

The Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-LT-RIMP2) theory method

The divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation (DEC-RI-MP2) theory method introduced in Baudin et al. [J. Chem. Phys. 144, 054102 (2016)] is significantly improved by introducing the Laplace transform of the orbital energy denominator in order to construct the double amplitudes directly in the local basis. Furthermore, this paper introduces the auxiliary reduction procedure, which reduces the set of the auxiliary functions employed in the individual fragments. The resulting Laplace transformed divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation method is applied to the insulin molecule where we obtain a factor 9.5 speedup compared to the DEC-RI-MP2 method.