The fragment molecular orbital method: theoretical development, implementation in GAMESS , and applications

Use of caps in the auxiliary basis set formulation of the fragment molecular orbital method

An auxiliary polarization formulation of the fragment molecular orbital (FMO) method is developed, combining a basis set correction computed for capped isolated fragments with a polarization obtained from uncapped fragments. For a set of organic and inorganic test systems, it is shown that the total energy and atomic charges are accurately reproduced with respect to full unfragmented calculations. It is demonstrated that the method is accurate for computing electronic excited states. The developed approach is applied to rank the isomers of chignolin from experimental NMR data (PDB: 1UAO) according to their relative energy. Contributions of polarization and basis set effects to pair interactions between fragments are elucidated.

Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme

The fragment molecular orbital (FMO) scheme is one of the popular fragmentation-based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU-accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled-cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen-bonded (FH)3 $$ {}_3 $$ and (FH)2 $$ {}_2 $$ -H2 $$ {}_2 $$ O systems with the STO-3G basis set. VQE-UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size-consistency and orbital-invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH)2 $$ {}_2 $$ -H2 $$ {}_2 $$ O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7-7.7 for 18 qubit systems.

Unraveling the Hydration Shell Structure and Dynamics of Group 10 Aqua Ions

We present ab initio simulations based on subsystem DFT of group 10 aqua ions accurately compared against experimental data on hydration structure. Our simulations provide insights into the molecular structures and dynamics of hydration shells, offering recalibrated interpretations of experimental results. We observe a soft, but distinct second hydration shell in Palladium (Pd) due to a balance between thermal fluctuations, metal-water interactions, and hydrogen bonding. Nickel (Ni) and platinum (Pt) exhibit more rigid hydration shells. Notably, our simulations align with experimental findings for Pd, showing axial hydration marked by a broad peak at about 3 Å in the Pd-O radial distribution function, revising the previously sharp "mesoshell" prediction. We introduce the "hydrogen bond dome" concept to describe a resilient network of hydrogen-bonded water molecules around the metal, which plays a critical role in the axial hydration dynamics.

Enhancement of energy decomposition analysis in fragment molecular orbital calculations

Energy decomposition analysis is one of the most attractive features of fragment molecular orbital (FMO) calculations from the point of view of practical applications. Here we report some enhancements for PIEDA in the ABINIT-MP program. One is a separation of the dispersion-type stabilization from the electron correlation energy, traditionally referred to as the "dispersion interaction" (DI). Another is an alternative evaluation of the electrostatic (ES) interaction using the restrained electrostatic potential (RESP) charges. The GA:CT stacked base pair and the Trp-Cage miniprotein were used as illustrative examples.

Discovery of a novel SHP2 allosteric inhibitor using virtual screening, FMO calculation, and molecular dynamic simulation

CONTEXT

SHP2 is a non-receptor protein tyrosine phosphatase to remove tyrosine phosphorylation. Functionally, SHP2 is an essential bridge to connect numerous oncogenic cell-signaling cascades including RAS-ERK, PI3K-AKT, JAK-STAT, and PD-1/PD-L1 pathways. This study aims to discover novel and potent SHP2 inhibitors using a hierarchical structure-based virtual screening strategy that combines molecular docking and the fragment molecular orbital method (FMO) for calculating binding affinity (referred to as the Dock-FMO protocol). For the SHP2 target, the FMO method prediction has a high correlation between the binding affinity of the protein-ligand interaction and experimental values (R2 = 0.55), demonstrating a significant advantage over the MM/PBSA (R2 = 0.02) and MM/GBSA (R2 = 0.15) methods. Therefore, we employed Dock-FMO virtual screening of ChemDiv database of ∼2,990,000 compounds to identify a novel SHP2 allosteric inhibitor bearing hydroxyimino acetamide scaffold. Experimental validation demonstrated that the new compound (E)-2-(hydroxyimino)-2-phenyl-N-(piperidin-4-ylmethyl)acetamide (7188-0011) effectively inhibited SHP2 in a dose-dependent manner. Molecular dynamics (MD) simulation analysis revealed the binding stability of compound 7188-0011 and the SHP2 protein, along with the key interacting residues in the allosteric binding site. Overall, our work has identified a novel and promising allosteric inhibitor that targets SHP2, providing a new starting point for further optimization to develop more potent inhibitors.

METHODS

All the molecular docking studies were employed to identify potential leads with Maestro v10.1. The protein-ligand binding affinities of potential leads were further predicted by FMO calculations at MP2/6-31G* level using GAMESS v2020 system. MD simulations were carried out with AmberTools18 by applying the FF14SB force field. MD trajectories were analyzed using VMD v1.9.3. MM/GB(PB)SA binding free energy analysis was carried out with the mmpbsa.py tool of AmberTools18. The docking and MD simulation results were visualized through PyMOL v2.5.0.

The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems

The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree-Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. The accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, Rcut. Rcut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small Rcut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.

FMO-guided design of darunavir analogs as HIV-1 protease inhibitors

The prevalence of HIV-1 infection continues to pose a significant global public health issue, highlighting the need for antiretroviral drugs that target viral proteins to reduce viral replication. One such target is HIV-1 protease (PR), responsible for cleaving viral polyproteins, leading to the maturation of viral proteins. While darunavir (DRV) is a potent HIV-1 PR inhibitor, drug resistance can arise due to mutations in HIV-1 PR. To address this issue, we developed a novel approach using the fragment molecular orbital (FMO) method and structure-based drug design to create DRV analogs. Using combinatorial programming, we generated novel analogs freely accessible via an on-the-cloud mode implemented in Google Colab, Combined Analog generator Tool (CAT). The designed analogs underwent cascade screening through molecular docking with HIV-1 PR wild-type and major mutations at the active site. Molecular dynamics (MD) simulations confirmed the assess ligand binding and susceptibility of screened designed analogs. Our findings indicate that the three designed analogs guided by FMO, 19-0-14-3, 19-8-10-0, and 19-8-14-3, are superior to DRV and have the potential to serve as efficient PR inhibitors. These findings demonstrate the effectiveness of our approach and its potential to be used in further studies for developing new antiretroviral drugs.

Differential molecular mechanisms of substrate recognition by selenium methyltransferases, INMT and TPMT, in selenium detoxification and excretion

It is known that the recommended dietary allowance of selenium (Se) is dangerously close to its tolerable upper intake level. Se is detoxified and excreted in urine as trimethylselenonium ion (TMSe) when the amount ingested exceeds the nutritional level. Recently, we demonstrated that the production of TMSe requires two methyltransferases: thiopurine S-methyltransferase (TPMT) and indolethylamine N-methyltransferase (INMT). In this study, we investigated the substrate recognition mechanisms of INMT and TPMT in the Se-methylation reaction. Examination of the Se-methyltransferase activities of two paralogs of INMT, namely, nicotinamide N-methyltransferase and phenylethanolamine N-methyltransferase, revealed that only INMT exhibited Se-methyltransferase activity. Consistently, molecular dynamics simulations demonstrated that dimethylselenide was preferentially associated with the active center of INMT. Using the fragment molecular orbital method, we identified hydrophobic residues involved in the binding of dimethylselenide to the active center of INMT. The INMT-L164R mutation resulted in a deficiency in Se- and N-methyltransferase activities. Similarly, TPMT-R152, which occupies the same position as INMT-L164, played a crucial role in the Se-methyltransferase activity of TPMT. Our findings suggest that TPMT recognizes negatively charged substrates, whereas INMT recognizes electrically neutral substrates in the hydrophobic active center embedded within the protein. These observations explain the sequential requirement of the two methyltransferases in producing TMSe.

The Pivotal Distinction between Antagonists' and Agonists' Binding into Dopamine D4 Receptor-MD and FMO/PIEDA Studies

The dopamine D4 receptor (D4R) is a promising therapeutic target in widespread diseases, and the search for novel agonists and antagonists appears to be clinically relevant. The mechanism of binding to the receptor (R) for antagonists and agonists varies. In the present study, we conducted an in-depth computational study, teasing out key similarities and differences in binding modes, complex dynamics, and binding energies for D4R agonists and antagonists. The dynamic network method was applied to investigate the communication paths between the ligand (L) and G-protein binding site (GBS) of human D4R. Finally, the fragment molecular orbitals with pair interaction energy decomposition analysis (FMO/PIEDA) scheme was used to estimate the binding energies of L-R complexes. We found that a strong salt bridge with D3.32 initiates the inhibition of the dopamine D4 receptor. This interaction also occurs in the binding of agonists, but the change in the receptor conformation to the active state starts with interaction with cysteine C3.36. Such a mechanism may arise in the case of agonists unable to form a hydrogen bond with the serine S5.46, considered, so far, to be crucial in the activation of GPCRs. The energy calculations using the FMO/PIEDA method indicate that antagonists show higher residue occupancy of the receptor binding site than agonists, suggesting they could form relatively more stable complexes. Additionally, antagonists were characterized by repulsive interactions with S5.46 distinguishing them from agonists.

Binding Free Energy Calculation Based on the Fragment Molecular Orbital Method and Its Application in Designing Novel SHP-2 Allosteric Inhibitors

The accurate prediction of binding free energy is a major challenge in structure-based drug design. Quantum mechanics (QM)-based approaches show promising potential in predicting ligand-protein binding affinity by accurately describing the behavior and structure of electrons. However, traditional QM calculations face computational limitations, hindering their practical application in drug design. Nevertheless, the fragment molecular orbital (FMO) method has gained widespread application in drug design due to its ability to reduce computational costs and achieve efficient ab initio QM calculations. Although the FMO method has demonstrated its reliability in calculating the gas phase potential energy, the binding of proteins and ligands also involves other contributing energy terms, such as solvent effects, the 'deformation energy' of a ligand's bioactive conformations, and entropy. Particularly in cases involving ionized fragments, the calculation of solvation free energy becomes particularly crucial. We conducted an evaluation of some previously reported implicit solvent methods on the same data set to assess their potential for improving the performance of the FMO method. Herein, we develop a new QM-based binding free energy calculation method called FMOScore, which enhances the performance of the FMO method. The FMOScore method incorporates linear fitting of various terms, including gas-phase potential energy, deformation energy, and solvation free energy. Compared to other widely used traditional prediction methods such as FEP+, MM/PBSA, MM/GBSA, and Autodock vina, FMOScore showed good performance in prediction accuracies. By constructing a retrospective case study, it was observed that incorporating calculations for solvation free energy and deformation energy can further enhance the precision of FMO predictions for binding affinity. Furthermore, using FMOScore-guided lead optimization against Src homology-2-containing protein tyrosine phosphatase 2 (SHP-2), we discovered a novel and potent allosteric SHP-2 inhibitor (compound 8).

High-Throughput Structure-Based Drug Design (HT-SBDD) Using Drug Docking, Fragment Molecular Orbital Calculations, and Molecular Dynamic Techniques

Structure-based drug design (SBDD) is rapidly evolving to be a fundamental tool for faster and more cost-effective methods of lead drug discovery. SBDD aims to offer a computational replacement to traditional high-throughput screening (HTS) methods of drug discovery. This "virtual screening" technique utilizes the structural data of a target protein in conjunction with large databases of potential drug candidates and then applies a range of different computational techniques to determine which potential candidates are likely to bind with high affinity and efficacy. It is proposed that high-throughput SBDD (HT-SBDD) will significantly enrich the success rate of HTS methods, which currently fluctuates around ~1%. In this chapter, we focus on the theory and utility of high-throughput drug docking, fragment molecular orbital calculations, and molecular dynamics techniques. We also offer a comparative review of the benefits and limitations of traditional methods against more recent SBDD advances. As HT-SBDD is computationally intensive, we will also cover the important role high-performance computing (HPC) clusters play in the future of computational drug discovery.

Cluster-in-Molecule Local Correlation Method for Dispersion Interactions in Large Systems and Periodic Systems

ConspectusThe noncovalent interactions, including dispersion interactions, control the structures and stabilities of complex chemical systems, including host-guest complexes and the adsorption process of molecules on the solid surfaces. The density functional theory (DFT) with empirical dispersion correction is now the working horse in many areas of applications. Post-Hartree-Fock (post-HF) methods have been well recognized to provide more accurate descriptions in a systematic way. However, traditional post-HF methods are mainly limited to small- or medium-sized systems, and their applications to periodic condensed phase systems are still very limited due to their expensive computational costs.To extend post-HF calculations to large molecules, the cluster-in-molecule (CIM) local correlation approach has been established, allowing highly accurate electron correlation calculations that are routinely available for very large systems. In the CIM approach, the electron correlation energy of a large molecule could be obtained from electron correlation calculations on a series of clusters, each of which contains a subset of occupied and virtual localized molecular orbitals. The CIM method could be massively and efficiently parallelized on general computer clusters. The CIM method has been implemented at various electron correlation levels, including second-order Mo̷ller-Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), CCSD with perturbative triples correction [CCSD(T)], etc. The CIM-MP2 energy gradient algorithm was developed and applied to the geometry optimizations of large systems. The CIM method has also been extended to condensed-phase systems under periodic boundary conditions (PBC-CIM). For periodic systems, the correlation energy per unit cell could be evaluated with correlation energy contributions from a series of clusters that are built with localized Wannier functions.CIM-based electron correlation calculations have been employed to investigate a number of chemical problems in which the dispersion interaction is important. CIM-based post-HF methods including CIM domain-based local pair natural orbital (DLPNO) CCSD(T) are applied to compute the relative or binding energies of biological systems or supramolecular complexes, the reaction barrier in a relatively complex chemical reaction. The CIM-MP2 method is used to obtain the optimized geometry of large systems. CIM-based post-HF calculations have also been used to compute the cohesive energies of molecular crystals and adsorption energies of molecules on the solid surfaces. The CIM and its PBC variant are expected to become a powerful theoretical tool for accurate calculations of the energies and structures for a broad range of large systems and condensed-phase systems with significant dispersion interactions.

Accelerating Coupled-Cluster Calculations with GPUs: An Implementation of the Density-Fitted CCSD(T) Approach for Heterogeneous Computing Architectures Using OpenMP Directives

An algorithm is presented for the coupled-cluster singles, doubles, and perturbative triples correction [CCSD(T)] method based on the density fitting or the resolution-of-the-identity (RI) approximation for performing calculations on heterogeneous computing platforms composed of multicore CPUs and graphics processing units (GPUs). The directive-based approach to GPU offloading offered by the OpenMP application programming interface has been employed to adapt the most compute-intensive terms in the RI-CCSD amplitude equations with computational costs scaling as O ( N O 2 N V 4 ) , O ( N O 3 N V 3 ) , and O ( N O 4 N V 2 ) (where NO and NV denote the numbers of correlated occupied and virtual orbitals, respectively) and the perturbative triples correction to execute on GPU architectures. The pertinent tensor contractions are performed using an accelerated math library such as cuBLAS or hipBLAS. Optimal strategies are discussed for splitting large data arrays into tiles to fit them into the relatively small memory space of the GPUs, while also minimizing the low-bandwidth CPU-GPU data transfers. The performance of the hybrid CPU-GPU RI-CCSD(T) code is demonstrated on pre-exascale supercomputers composed of heterogeneous nodes equipped with NVIDIA Tesla V100 and A100 GPUs and on the world's first exascale supercomputer named "Frontier", the nodes of which consist of AMD MI250X GPUs. Speedups within the range 4-8× relative to the recently reported CPU-only algorithm are obtained for the GPU-offloaded terms in the RI-CCSD amplitude equations. Applications to polycyclic aromatic hydrocarbons containing 16-66 carbon atoms demonstrate that the acceleration of the hybrid CPU-GPU code for the perturbative triples correction relative to the CPU-only code increases with the molecule size, attaining a speedup of 5.7× for the largest circumovalene molecule (C66H20). The GPU-offloaded code enables the computation of the perturbative triples correction for the C60 molecule using the cc-pVDZ/aug-cc-pVTZ-RI basis sets in 7 min on Frontier when using 12,288 AMD GPUs with a parallel efficiency of 83.1%.

Site-Specific Ionization Potentials and Electron Affinities in Large Molecular Systems at Coupled Cluster Level

A many-body expansion of ionization potentials and electron affinities is developed based on a combination of the fragment molecular orbital method and equation-of-motion coupled-cluster (EOM-CC). In addition to site-specific values, obtained as one-body properties, pair and triple corrections are added to account for nonlocal EOM-CC contributions of the molecular environment of a chromophore. The developed method is applied to carboxylic acids, alkyl cations, a protein ubiquitin (Protein Data Bank ID 1UBQ), and a nano ribbon of white graphene elucidating the effect of environment on ionization potential and electron affinity.

Coupled-Cluster Density-Based Many-Body Expansion

While CCSD(T) is often considered the "gold standard" of computational chemistry, the scaling of its computational cost as N7 limits its applicability for large and complex molecular systems. In this work, we apply the density-based many-body expansion [ Int. J. Quantum Chem. 2020, 120, e26228] in combination with CCSD(T). The accuracy of this approach is assessed for neutral, protonated, and deprotonated water hexamers, as well as (H2O)16 and (H2O)17 clusters. For the neutral water clusters, we find that already with a density-based two-body expansion, we are able to approximate the supermolecular CCSD(T) energies within chemical accuracy (4 kJ/mol). This surpasses the accuracy that is achieved with a conventional, energy-based three-body expansion. We show that this accuracy can be maintained even when approximating the electron densities using Hartree-Fock instead of using coupled-cluster densities. The density-based many-body expansion thus offers a simple, resource-efficient, and highly parallelizable approach that makes CCSD(T)-quality calculations feasible where they would otherwise be prohibitively expensive.

The C-terminal tail of Rad17, iVERGE, binds the 9‒1‒1 complex independently of AAA+ ATPase domains to provide another clamp-loader interface

The ATR pathway plays a crucial role in maintaining genome integrity as the major DNA damage checkpoint. It also attracts attention as a therapeutic target in cancer treatment. The Rad17-RFC2-5 complex loads the Rad9-Hus1-Rad1 (9-1-1) DNA clamp complex onto damaged chromatin to activate the ATR pathway. We previously reported that phosphorylation of a polyanionic C-terminal tail of human Rad17, iVERGE, is essential for the interaction between Rad17 and the 9-1-1 complex. However, the molecular mechanism has remained unclear. Here, we show that iVERGE directly interacts with the Hus1 subunit of the 9-1-1 complex through Rad17-S667 phosphorylation independently of the AAA+ ATPase domains. An exogenous iVERGE peptide interacted with the 9-1-1 complex in vivo. The binding conformation of the iVERGE peptide was analyzed by de novo modeling with docking simulation, simulated annealing-molecular dynamics simulation, and the fragment molecular orbital method. The in silico analyses predicted the association of the iVERGE peptide with the hydrophobic and basic patches on the Hus1 protein, and the corresponding Hus1 mutants were deficient in the interaction with the iVERGE peptide in vivo. The iVERGE peptide occupied the same position as the C-terminus of Saccharomyces cerevisiae RAD24 on MEC3. The interaction energy calculation suggested that the Rad17 KYxxL motif and the iVERGE peptide are the primary and secondary interaction surfaces between the Rad17-RFC2-5 and 9-1-1 complexes. Our data reveal a novel molecular interface, iVERGE, between the Rad17-RFC2-5 and 9-1-1 complexes in vertebrates and implicate that Rad17 utilizes two distinct molecular interfaces to regulate the 9-1-1 complex.

How E-, L-, and P-Selectins Bind to sLex and PSGL-1: A Quantification of Critical Residue Interactions

Selectins and their ability to interact with specific ligands are a cornerstone in cell communication. Over the last three decades, a considerable wealth of experimental and molecular modeling insights into their structure and modus operandi were gathered. Nonetheless, explaining the role of individual selectin residues on a quantitative level remained elusive, despite its importance in understanding the structure-function relationship in these molecules and designing their inhibitors. This work explores essential interactions of selectin-ligand binding, employing a multiscale approach that combines molecular dynamics, quantum-chemical calculations, and residue interaction network models. Such an approach successfully reproduces most of the experimental findings. It proves to be helpful, with the potential for becoming an established tool for quantitative predictions of residue contribution to the binding of biomolecular complexes. The results empower us to quantify the importance of particular residues and functional groups in the protein-ligand interface and to pinpoint differences in molecular recognition by the three selectins. We show that mutations in the E-, L-, and P-selectins, e.g., different residues in positions 46, 85, 97, and 107, present a crucial difference in how the ligand is engaged. We assess the role of sulfation of tyrosine residues in PSGL-1 and suggest that TyrSO3- in position 51 interacting with Arg85 in P-selectin is a significant factor in the increased affinity of P-selectin to PSGL-1 compared to E- and L-selectins. We propose an original pharmacophore targeting five essential PSGL-binding sites based on the analysis of the selectin···PSGL-1 interactions.

Corrigendum: Coupled cluster theory on modern heterogeneous supercomputers

[This corrects the article DOI: 10.3389/fchem.2023.1154526.].

Coupled cluster theory on modern heterogeneous supercomputers

This study examines the computational challenges in elucidating intricate chemical systems, particularly through ab-initio methodologies. This work highlights the Divide-Expand-Consolidate (DEC) approach for coupled cluster (CC) theory-a linear-scaling, massively parallel framework-as a viable solution. Detailed scrutiny of the DEC framework reveals its extensive applicability for large chemical systems, yet it also acknowledges inherent limitations. To mitigate these constraints, the cluster perturbation theory is presented as an effective remedy. Attention is then directed towards the CPS (D-3) model, explicitly derived from a CC singles parent and a doubles auxiliary excitation space, for computing excitation energies. The reviewed new algorithms for the CPS (D-3) method efficiently capitalize on multiple nodes and graphical processing units, expediting heavy tensor contractions. As a result, CPS (D-3) emerges as a scalable, rapid, and precise solution for computing molecular properties in large molecular systems, marking it an efficient contender to conventional CC models.

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.

SophosQM: Accurate Binding Affinity Prediction in Compound Optimization

The optimization of compounds' binding affinity for a biological target is a crucial aspect of the drug development process. Being able to accurately predict binding energies in advance of synthesizing compounds would have a massive impact on the speed of the drug discovery process. The ideal binding affinity prediction method should combine accuracy, reliability, and speed. In this paper, we present SophosQM, a quantum mechanics (QM)-based approach, which can accurately predict the binding affinities of compounds to proteins. The binding affinity predictive models generated by SophosQM are based on the fragment molecular orbital (FMO) method to estimate the enthalpic component of the binding free energy, and a macroscopic descriptor, clog P, is used as an approximation of the entropic component. The affinity prediction is performed using multilinear regression, fitting the experimental values against the FMO-computed enthalpic term and clog P. The quality of the prediction can be assessed in terms of the correlation coefficient between experimental and predicted values. In this work, the method's reliability and accuracy are exemplified by applying SophosQM to 70 compounds binding to six different targets of pharmaceutical relevance. Overall, the results show a very satisfactory performance with a global correlation coefficient in the order of 0.9. Our predictions also show a satisfactory performance compared to data based on free energy perturbation. Finally, SophosQM can also be applied in high-throughput mode by using semiempirical QM methods to evaluate large portions of chemical space, while retaining a good level of accuracy, but decreasing the computing time to just a few seconds per compound.

Appropriate clusterset selection for the prediction of thermodynamic properties of liquid water with QCE theory

Evident in many physical and chemical phenomena, thermodynamics is the study of how energy is stored, transformed and transferred in a molecule or material. However, prediction of these properties with simulation techniques is a non-trivial task as several factors such as composition and intermolecular interactions come into play. While molecular dynamics and ab initio molecular dynamics are the most common techniques for the prediction of thermodynamic properties, there exists many shortcomings associated with their use. Therefore, in this work we instead apply QCE theory to predict the thermodynamic properties of liquid water. This theory assumes that a condensed phase system can be represented as a 'mixture' of varying sized clusters rather than as a continuum. As QCE theory relies on first-principle simulations and statistical thermodynamics to determine the thermodynamic behavior of a system, appropriate selection of clusters is a crucial step towards achieving accurate predictions. In this study, we use molecular dynamics and ab initio calculations to obtain initial configurations of 400 water clusters, Wn where n = 3 to 10 and contrast their stability using two different criteria. The role of entropy towards cluster stabilization is investigated by comparing the binding (ΔE_BIND/mol) and Gibbs free binding energy per molecule (ΔG_BIND/mol) of various Wn at 298.15 K. Initial clustersets are constructed by exploring two-, three-, four and five-combinations of clustersets using the minimum ΔG_BIND/mol structures of Wn. We also expand the ΔG_BIND/mol criteria for Wn of sizes 3 to 7 to include values larger than 0.0 kJ mol^-1 and smaller than 3.0 kJ mol^-1 as a means of improving thermodynamic predictions. 37 of the 459 resulting clustersets predicted the correct boiling point of water and its thermodynamic properties with an accuracy of 95%. A scaled population-weighted infrared spectrum was compared to experimental results to validate the composition of the top 5 clustersets. The predicted spectra showed an exact match within the low frequency range (<1000 cm^-1) with some discrepancy at the high frequency range (>3400 cm^-1). This work highlights that ΔG_BIND/mol is so far the best criteria to apply when determining an appropriate clusterset for QCE theory.

Accurate Prediction of Three-Body Intermolecular Interactions via Electron Deformation Density-Based Machine Learning

This work extends the electron deformation density-based descriptor, originally developed in the electron deformation density-based interaction energy machine learning (EDDIE-ML) algorithm to predict dimer interaction energies, to the prediction of three-body interactions in trimers. Using a sequential learning process to select the training data, the resulting Gaussian process regression (GPR) model predicts the three-body interaction energy within 0.2 kcal mol^-1 of the SRS-MP2/cc-pVTZ reference values for the 3B69 and S22-3 trimer data sets. A hybrid kernel function is introduced, which combines contributions from the average and individual atomic environments, allowing the total trimer interaction energy to be predicted in addition to the three-body contribution using the same descriptor. To extend the range and diversity of trimer interaction energies available in the literature, a new data set based on a protein-ligand crystal structure is introduced, consisting of 509 structures of a central ligand with two protein fragments. Benchmark calculations are provided for the new data set, which contains significantly larger molecular interactions than current databases in the literature in addition to charged fragments. Compared to density funtional theory (DFT)- and wavefunction-based methods for calculating the three-body interaction energy, our model makes predictions in a significantly shorter time frame by reducing the number of required SCF calculations from 7 to 4 performed at the PBE0 level of theory, showcasing the utility and efficiency of our Δ-ML method particularly when applied to larger systems.

Quantum Chemical Modeling of Propellant Degradation

An ab initio quantum chemical approach for the modeling of propellant degradation is presented. Using state-of-the-art bonding analysis techniques and composite methods, a series of potential degradation reactions are devised for a sample hydroxyl-terminated-polybutadiene (HTPB) type solid fuel. By applying thermochemical procedures and isodesmic reactions, accurate thermochemical quantities are obtained using a modified G3 composite method based on the resolution of the identity. The calculated heats of formation for the different structures produced presents an ∼2 kcal/mol average error when compared against experimental values.

Analytic Gradient for Time-Dependent Density Functional Theory Combined with the Fragment Molecular Orbital Method

The analytic energy gradient of energy with respect to nuclear coordinates is derived for the fragment molecular orbital (FMO) method combined with time-dependent density functional theory (TDDFT). The response terms arising from the use of a polarizable embedding are derived. The obtained analytic FMO-TDDFT gradient is shown to be accurate in comparison to both numerical FMO-TDDFT and unfragmented TDDFT gradients, at the level of two- and three-body expansions. The gradients are used for geometry optimizations, molecular dynamics, vibrational calculations, and simulations of IR and Raman spectra of excited states. The developed method is used to optimize the geometry of the ground and excited electronic states of the photoactive yellow protein (PDB: 2PHY).

Divide-and-Conquer Linear-Scaling Quantum Chemical Computations

Fragmentation and embedding schemes are of great importance when applying quantum-chemical calculations to more complex and attractive targets. The divide-and-conquer (DC)-based quantum-chemical model is a fragmentation scheme that can be connected to embedding schemes. This feature article explains several DC-based schemes developed by the authors over the last two decades, which was inspired by the pioneering study of DC self-consistent field (SCF) method by Yang and Lee (J. Chem. Phys. 1995, 103, 5674-5678). First, the theoretical aspects of the DC-based SCF, electron correlation, excited-state, and nuclear orbital methods are described, followed by the two-component relativistic theory, quantum-mechanical molecular dynamics simulation, and the introduction of three programs, including DC-based schemes. Illustrative applications confirmed the accuracy and feasibility of the DC-based schemes.

Ca2+-Triggered Coelenterazine-Binding Protein Renilla: Expected and Unexpected Features

Ca²⁺-triggered coelenterazine-binding protein (CBP) is a natural form of the luciferase substrate involved in the Renilla bioluminescence reaction. It is a stable complex of coelenterazine and apoprotein that, unlike coelenterazine, is soluble and stable in an aquatic environment and yields a significantly higher bioluminescent signal. This makes CBP a convenient substrate for luciferase-based in vitro assay. In search of a similar substrate form for the luciferase NanoLuc, a furimazine-apoCBP complex was prepared and verified against furimazine, coelenterazine, and CBP. Furimazine-apoCBP is relatively stable in solution and in a frozen or lyophilized state, but as distinct from CBP, its bioluminescence reaction with NanoLuc is independent of Ca²⁺. NanoLuc turned out to utilize all the four substrates under consideration. The pairs of CBP-NanoLuc and coelenterazine-NanoLuc generate bioluminescence with close efficiency. As for furimazine-apoCBP-NanoLuc pair, the efficiency with which it generates bioluminescence is almost twice lower than that of the furimazine-NanoLuc. The integral signal of the CBP-NanoLuc pair is only 22% lower than that of furimazine-NanoLuc. Thus, along with furimazine as the most effective NanoLuc substrate, CBP can also be recommended as a substrate for in vitro analytical application in view of its water solubility, stability, and Ca²⁺-triggering "character".

Parametrized quantum-mechanical approaches combined with the fragment molecular orbital method

Fast parameterized methods such as density-functional tight-binding (DFTB) facilitate realistic calculations of large molecular systems, which can be accelerated by the fragment molecular orbital (FMO) method. Fragmentation facilitates interaction analyses between functional parts of molecular systems. In addition to DFTB, other parameterized methods combined with FMO are also described. Applications of FMO methods to biochemical and inorganic systems are reviewed.

The Importance of Charge Transfer and Solvent Screening in the Interactions of Backbones and Functional Groups in Amino Acid Residues and Nucleotides

Quantum mechanical (QM) calculations at the level of density-functional tight-binding are applied to a protein–DNA complex (PDB: 2o8b) consisting of 3763 atoms, averaging 100 snapshots from molecular dynamics simulations. A detailed comparison of QM and force field (Amber) results is presented. It is shown that, when solvent screening is taken into account, the contributions of the backbones are small, and the binding of nucleotides in the double helix is governed by the base–base interactions. On the other hand, the backbones can make a substantial contribution to the binding of amino acid residues to nucleotides and other residues. The effect of charge transfer on the interactions is also analyzed, revealing that the actual charge of nucleotides and amino acid residues can differ by as much as 6 and 8% from the formal integer charge, respectively. The effect of interactions on topological models (protein -residue networks) is elucidated.

Promising SARS-CoV-2 main protease inhibitor ligand-binding modes evaluated using LB-PaCS-MD/FMO

Parallel cascade selection molecular dynamics-based ligand binding-path sampling (LB-PaCS-MD) was combined with fragment molecular orbital (FMO) calculations to reveal the ligand path from an aqueous solution to the SARS-CoV-2 main protease (M^pro) active site and to customise a ligand-binding pocket suitable for delivering a potent inhibitor. Rubraxanthone exhibited mixed-inhibition antiviral activity against SARS-CoV-2 M^pro, relatively low cytotoxicity, and high cellular inhibition. However, the atomic inhibition mechanism remains ambiguous. LB-PaCS-MD/FMO is a hybrid ligand-binding evaluation method elucidating how rubraxanthone interacts with SARS-CoV-2 M^pro. In the first step, LB-PaCS-MD, which is regarded as a flexible docking, efficiently samples a set of ligand-binding pathways. After that, a reasonable docking pose of LB-PaCS-MD is evaluated by the FMO calculation to elucidate a set of protein-ligand interactions, enabling one to know the binding affinity of a specified ligand with respect to a target protein. A possible conformation was proposed for rubraxanthone binding to the SARS-CoV-2 M^pro active site, and allosteric inhibition was elucidated by combining blind docking with k-means clustering. The interaction profile, key binding residues, and considerable interaction were elucidated for rubraxanthone binding to both M^pro sites. Integrated LB-PaCS-MD/FMO provided a more reasonable complex structure for ligand binding at the SARS-CoV-2 M^pro active site, which is vital for discovering and designing antiviral drugs.

BAY-069, a Novel (Trifluoromethyl)pyrimidinedione-Based BCAT1/2 Inhibitor and Chemical Probe

The branched-chain amino acid transaminases (BCATs) are enzymes that catalyze the first reaction of catabolism of the essential branched-chain amino acids to branched-chain keto acids to form glutamate. They are known to play a key role in different cancer types. Here, we report a new structural class of BCAT1/2 inhibitors, (trifluoromethyl)pyrimidinediones, identified by a high-throughput screening campaign and subsequent optimization guided by a series of X-ray crystal structures. Our potent dual BCAT1/2 inhibitor BAY-069 displays high cellular activity and very good selectivity. Along with a negative control (BAY-771), BAY-069 was donated as a chemical probe to the Structural Genomics Consortium.

Computational methods for calculation of protein-ligand binding affinities in structure-based drug design

Drug design is an expensive and time-consuming process. Any method that allows reducing the time the costs of the drug development project can have great practical value for the pharmaceutical industry. In structure-based drug design, affinity prediction methods are of great importance. The majority of methods used to predict binding free energy in protein-ligand complexes use molecular mechanics methods. However, many limitations of these methods in describing interactions exist. An attempt to go beyond these limits is the application of quantum-mechanical description for all or only part of the analyzed system. However, the extensive use of quantum mechanical (QM) approaches in drug discovery is still a demanding challenge. This chapter briefly reviews selected methods used to calculate protein-ligand binding affinity applied in virtual screening (VS), rescoring of docked poses, and lead optimization stage, including QM methods based on molecular simulations.

Accurate Binding Free Energy Method from End-State MD Simulations

Herein, we introduce a new strategy to estimate binding free energies using end-state molecular dynamics simulation trajectories. The method is adopted from linear interaction energy (LIE) and ANI-2x neural network potentials (machine learning) for the atomic simulation environment (ASE). It predicts the single-point interaction energies between ligand–protein and ligand–solvent pairs at the accuracy of the wb97x/6-31G* level for the conformational space that is sampled by molecular dynamics (MD) simulations. Our results on 54 protein–ligand complexes show that the method can be accurate and have a correlation of R = 0.87–0.88 to the experimental binding free energies, outperforming current end-state methods with reduced computational cost. The method also allows us to compare BFEs of ligands with different scaffolds. The code is available free of charge (documentation and test files) at https://github.com/otayfuroglu/deepQM.

The catalytic activity and adsorption in faujasite and ZSM-5 zeolites: the role of differential stabilization and charge delocalization

Adsorption and chemical reactions occurring on industrially important ZSM-5 and faujasite zeolite catalysts are investigated with the quantum-mechanical fragment molecular orbital method combined with periodic boundary conditions. Suitable fragmentation patterns are devised and tested providing important case studies of computing real materials with fragmentation methods. A good accuracy is demonstrated in comparison to full calculations, and a good agreement with the available experimental data is obtained. The full production cycle of p-xylene on faujasite zeolite is mapped. The catalytic role of the zeolite in the dehydration reaction, analyzed with the partition analysis, is attributed to the delocalization of the negative charge over the zeolite. On the other hand, an increase of the barrier in the Diels-Alder reaction by the zeolite is attributed to the preferential stabilization of the reactants over the transition state as demonstrated by the guest-zeolite interaction energy.

Halogenated Baicalein as a Promising Antiviral Agent toward SARS-CoV-2 Main Protease

The coronavirus disease pandemic is a constant reminder that global citizens are in imminent danger of exposure to emerging infectious diseases. Therefore, developing a technique for inhibitor discovery is essential for effective drug design. Herein, we proposed fragment molecular orbital (FMO)-based virtual screening to predict the molecular binding energy of potential severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) main protease inhibitors. The integration of quantum mechanical approaches and trajectory analysis from a microsecond molecular dynamics simulation was used to identify potential inhibitors. We identified brominated baicalein as a potent inhibitor of the SARS-CoV-2 main protease and confirmed its inhibitory activity in an in vitro assay. Brominated baicalein did not demonstrate significant toxicity in either in vitro or in vivo studies. The pair interaction energy from FMO-RIMP2/PCM and inhibitory constants based on the protease enzyme assay suggested that the brominated baicalein could be further developed into novel SARS-CoV-2 protease inhibitors.

Structure- and Interaction-Based Design of Anti-SARS-CoV-2 Aptamers

Aptamer selection against novel infections is a complicated and time-consuming approach. Synergy can be achieved by using computational methods together with experimental procedures. This study aims to develop a reliable methodology for a rational aptamer in silico et vitro design. The new approach combines multiple steps: (1) Molecular design, based on screening in a DNA aptamer library and directed mutagenesis to fit the protein tertiary structure; (2) 3D molecular modeling of the target; (3) Molecular docking of an aptamer with the protein; (4) Molecular dynamics (MD) simulations of the complexes; (5) Quantum-mechanical (QM) evaluation of the interactions between aptamer and target with further analysis; (6) Experimental verification at each cycle for structure and binding affinity by using small-angle X-ray scattering, cytometry, and fluorescence polarization. By using a new iterative design procedure, structure- and interaction-based drug design (SIBDD), a highly specific aptamer to the receptor-binding domain of the SARS-CoV-2 spike protein, was developed and validated. The SIBDD approach enhances speed of the high-affinity aptamers development from scratch, using a target protein structure. The method could be used to improve existing aptamers for stronger binding. This approach brings to an advanced level the development of novel affinity probes, functional nucleic acids. It offers a blueprint for the straightforward design of targeting molecules for new pathogen agents and emerging variants.

Free Energy Decomposition Analysis Based on the Fragment Molecular Orbital Method

A decomposition of the free energy is developed in the many-body expansion framework of the fragment molecular orbital (FMO) method combined with umbrella sampling molecular dynamics (MD). In FMO/MD simulations, performed with density-functional tight-binding and periodic boundary conditions, all atoms are treated quantum mechanically. The free energy is computed and decomposed for a series of S_N2 Menshutkin reactions in water. The barrier lowering by the solvent is attributed to the competition between the solvent polarization and the solute-solvent interactions including charge transfer.

Analysis of Guest Adsorption on Crystal Surfaces Based on the Fragment Molecular Orbital Method

For gaining insights into interactions in periodic systems, an analysis is developed based on the fragment molecular orbital method combined with periodic boundary conditions. The adsorption energy is decomposed into guest and surface polarization and deformation energy, guest-surface and guest-guest interactions, and the vibrational free energy. The analysis is applied to the adsorption of guest molecules to Ih (001) ice surface. The cooperativity effects result in a non-linear change in the adsorption energy with coverage due to many-body effects. The role of dispersion is found to be dominant for guests with long hydrophobic tails. A rule is proposed relating the length of the alkyl tail with the formation of the guest layer. The computed binding enthalpies are in good agreement with experimental values. For high coverage, adsorbed molecules can form an ordered layer known as self-assembled monolayer.

Scalable ab initio fragmentation methods based on a truncated expansion of the non-orthogonal molecular orbital model

An alternative formulation of the non-orthogonal molecular orbital model of electronic structure theory is developed based on the expansion of the inverse molecular orbital overlap matrix. From this model, a hierarchy of ab initio fragment-based quantum chemistry methods, referred to as the nth-order expanded non-orthogonal molecular orbital methods, are developed using a minimal number of approximations, each of which is frequently employed in intermolecular interaction theory. These novel methods are compared to existing fragment-based quantum chemistry methods, and the implications of those significant differences, where they exist, between the methods developed herein and those already existing methods are examined in detail. Computational complexities and theoretical scaling are also analyzed and discussed. Future extensions for the hierarchy of methods, to account for additional intrafragment and interfragment interactions, are outlined.

Fragment molecular orbital calculations for biomolecules

Exploring biomolecule behavior, such as proteins and nucleic acids, using quantum mechanical theory can identify many life science phenomena from first principles. Fragment molecular orbital (FMO) calculations of whole single particles of biomolecules can determine the electronic state of the interior and surface of molecules and explore molecular recognition mechanisms based on intermolecular and intramolecular interactions. In this review, we summarized the current state of FMO calculations in drug discovery, virology, and structural biology, as well as recent developments from data science.

Special Features of COVID-19 in the FMODB: Fragment Molecular Orbital Calculations and Interaction Energy Analysis of SARS-CoV-2-Related Proteins

SARS-CoV-2 is the causative agent of coronavirus (known as COVID-19), the virus causing the current pandemic. There are ongoing research studies to develop effective therapeutics and vaccines against COVID-19 using various methods and many results have been published. The structure-based drug design of SARS-CoV-2-related proteins is promising, however, reliable information regarding the structural and intra- and intermolecular interactions is required. We have conducted studies based on the fragment molecular orbital (FMO) method for calculating the electronic structures of protein complexes and analyzing their quantitative molecular interactions. This enables us to extensively analyze the molecular interactions in residues or functional group units acting inside the protein complexes. Such precise interaction data are available in the FMO database (FMODB) (https://drugdesign.riken.jp/FMODB/). Since April 2020, we have performed several FMO calculations on the structures of SARS-CoV-2-related proteins registered in the Protein Data Bank. We have published the results of 681 structures, including three structural proteins and 11 nonstructural proteins, on the COVID-19 special page (as of June 8, 2021). In this paper, we describe the entire COVID-19 special page of the FMODB and discuss the calculation results for various proteins. These data not only aid the interpretation of experimentally determined structures but also the understanding of protein functions, which is useful for rational drug design for COVID-19.

Quantum-Mechanical Structure Optimization of Protein Crystals and Analysis of Interactions in Periodic Systems

A fast quantum-mechanical approach, density-functional tight-binding combined with the fragment molecular orbital method and periodic boundary conditions, is used to optimize atomic coordinates and cell parameters for a set of protein crystals: 1ETL, 5OQZ, 3Q8J, 1CBN, and 2VB1. Good agreement between experimental and calculated structures is obtained for both atomic coordinates and cell parameters. Sterical clashes present in the experimental structures are corrected by simulations. The partition analysis is extended to treat periodic boundary conditions and applied to analyze protein-solvent interactions in crystals.

The role of SAXS and molecular simulations in 3D structure elucidation of a DNA aptamer against lung cancer

Aptamers are short, single-stranded DNA or RNA oligonucleotide molecules that function as synthetic analogs of antibodies and bind to a target molecule with high specificity. Aptamer affinity entirely depends on its tertiary structure and charge distribution. Therefore, length and structure optimization are essential for increasing aptamer specificity and affinity. Here, we present a general optimization procedure for finding the most populated atomistic structures of DNA aptamers. Based on the existed aptamer LC-18 for lung adenocarcinoma, a new truncated LC-18 (LC-18t) aptamer LC-18t was developed. A three-dimensional (3D) shape of LC-18t was reported based on small-angle X-ray scattering (SAXS) experiments and molecular modeling by fragment molecular orbital or molecular dynamic methods. Molecular simulations revealed an ensemble of possible aptamer conformations in solution that were in close agreement with measured SAXS data. The aptamer LC-18t had stronger binding to cancerous cells in lung tumor tissues and shared the binding site with the original larger aptamer. The suggested approach reveals 3D shapes of aptamers and helps in designing better affinity probes.

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.

Identification of key stabilizing interactions of amyloid-β oligomers based on fragment molecular orbital calculations on macrocyclic β-hairpin peptides

Analyzing the electronic states and inter-/intra-molecular interactions of amyloid oligomers expand our understanding of the molecular basis of Alzheimer's disease and other amyloid diseases. In the current study, several high-resolution crystal structures of oligomeric assemblies of Aβ-derived peptides have been studied by the ab initio fragment molecular orbital (FMO) method. The FMO method provides comprehensive details of the molecular interactions between the residues of the amyloid oligomers at the quantum mechanical level. Based on the calculations, two sequential aromatic residues (F19 and F20) and negatively charged E22 on the central region of Aβ have been identified as key residues in oligomer stabilization and potential interesting pharmacophores for preventing oligomer formation.

Partitioning of the Vibrational Free Energy

Vibrational energies are partitioned into the contributions of molecular parts called segments, for instance, residues in proteins. The fragment molecular orbital method is used to facilitate vibrational calculations of large systems at the DFTB and HF-3c levels. The vibrational analysis is combined with the partitioning of the electronic energy, yielding free-energy contributions of segments to the binding energy, pinpointing hot spots for drug discovery and other studies. The analysis is illustrated on two protein-ligand complexes in solution.

A Massively Parallel Implementation of the CCSD(T) Method Using the Resolution-of-the-Identity Approximation and a Hybrid Distributed/Shared Memory Parallelization Model

A parallel algorithm is described for the coupled-cluster singles and doubles method augmented with a perturbative correction for triple excitations [CCSD(T)] using the resolution-of-the-identity (RI) approximation for two-electron repulsion integrals (ERIs). The algorithm bypasses the storage of four-center ERIs by adopting an integral-direct strategy. The CCSD amplitude equations are given in a compact quasi-linear form by factorizing them in terms of amplitude-dressed three-center intermediates. A hybrid MPI/OpenMP parallelization scheme is employed, which uses the OpenMP-based shared memory model for intranode parallelization and the MPI-based distributed memory model for internode parallelization. Parallel efficiency has been optimized for all terms in the CCSD amplitude equations. Two different algorithms have been implemented for the rate-limiting terms in the CCSD amplitude equations that entail O(NO2NV4) and O(NO3NV3)-scaling computational costs, where N_O and N_V denote the number of correlated occupied and virtual orbitals, respectively. One of the algorithms assembles the four-center ERIs requiring N_V⁴ and N_O²N_V²-scaling memory costs in a distributed manner on a number of MPI ranks, while the other algorithm completely bypasses the assembling of quartic memory-scaling ERIs and thus largely reduces the memory demand. It is demonstrated that the former memory-expensive algorithm is faster on a few hundred cores, while the latter memory-economic algorithm shows a better strong scaling in the limit of a few thousand cores. The program is shown to exhibit a near-linear scaling, in particular for the compute-intensive triples correction step, on up to 8000 cores. The performance of the program is demonstrated via calculations involving molecules with 24-51 atoms and up to 1624 atomic basis functions. As the first application, the complete basis set (CBS) limit for the interaction energy of the π-stacked uracil dimer from the S66 data set has been investigated. This work reports the first calculation of the interaction energy at the CCSD(T)/aug-cc-pVQZ level without local orbital approximation. The CBS limit for the CCSD correlation contribution to the interaction energy was found to be -8.01 kcal/mol, which agrees very well with the value -7.99 kcal/mol reported by Schmitz, Hättig, and Tew [ Phys. Chem. Chem. Phys. 2014, 16, 22167-22178]. The CBS limit for the total interaction energy was estimated to be -9.64 kcal/mol.