RI-MP2 Gradient Calculation of Large Molecules Using the Fragment Molecular Orbital Method

Quantum Chemistry-Based Protein-Protein Docking without Empirical Parameters

This study developed a novel protein-protein docking approach based on quantum chemistry. To judge the appropriateness of complex structures, we introduced two criterion values, EV1 and EV2, computed using the fragment molecular orbital method without any empirical parameters. These criterion values enable us to search complex structures in which patterns of the electrostatic potential of the two proteins are optimally aligned at their interface. The performance of our method was validated using 53 complexes in a benchmark set provided for protein-protein docking. When employing bound state structures, docking success rates reached 64% for EV1 and 76% for EV2. On the other hand, when employing unbound state structures, docking success rates reached 13% for EV1 and 17% for EV2.

High-Performance Multi-GPU Analytic RI-MP2 Energy Gradients

This article presents a novel algorithm for the calculation of analytic energy gradients from second-order Møller-Plesset perturbation theory within the Resolution-of-the-Identity approximation (RI-MP2), which is designed to achieve high performance on clusters with multiple graphical processing units (GPUs). The algorithm uses GPUs for all major steps of the calculation, including integral generation, formation of all required intermediate tensors, solution of the Z-vector equation and gradient accumulation. The implementation in the EXtreme Scale Electronic Structure System (EXESS) software package includes a tailored, highly efficient, multistream scheduling system to hide CPU-GPU data transfer latencies and allows nodes with 8 A100 GPUs to operate at over 80% of theoretical peak floating-point performance. Comparative performance analysis shows a significant reduction in computational time relative to traditional multicore CPU-based methods, with our approach achieving up to a 95-fold speedup over the single-node performance of established software such as Q-Chem and ORCA. Additionally, we demonstrate that pairing our implementation with the molecular fragmentation framework in EXESS can drastically lower the computational scaling of RI-MP2 gradient calculations from quintic to subquadratic, enabling further substantial savings in runtime while retaining high numerical accuracy in the resulting gradients.

Improving the accuracy of the FMO binding affinity prediction of ligand-receptor complexes containing metals

Polarization and charge transfer strongly characterize the ligand-receptor interaction when metal atoms are present, as for the Au(I)-biscarbene/DNA G-quadruplex complexes. In a previous work (J Comput Aided Mol Des2022, 36, 851-866) we used the ab initio FMO2 method at the RI-MP2/6-31G* level of theory with the PCM [1] solvation approach to calculate the binding energy (ΔEFMO) of two Au(I)-biscarbene derivatives, [Au(9-methylcaffein-8-ylidene)2]+ and [Au(1,3-dimethylbenzimidazole-2-ylidene)2]+, able to interact with DNA G-quadruplex motif. We found that ΔEFMO and ligand-receptor pair interaction energies (EINT) show very large negative values making the direct comparison with experimental data difficult and related this issue to the overestimation of the embedded charge transfer energy between fragments containing metal atoms. In this work, to improve the accuracy of the FMO method for predicting the binding affinity of metal-based ligands interacting with DNA G-quadruplex (Gq), we assess the effect of the following computational features: (i) the electron correlation, considering the Hartree-Fock (HF) and a post-HF method, namely RI-MP2; (ii) the two (FMO2) and three-body (FMO3) approaches; (iii) the basis set size (polarization functions and double-ζ vs. triple-ζ) and (iv) the embedding electrostatic potential (ESP). Moreover, the partial screening method was systematically adopted to simulate the solvent screening effect for each calculation. We found that the use of the ESP computed using the screened point charges for all atoms (ESP-SPTC) has a critical impact on the accuracy of both ΔEFMO and EINT, eliminating the overestimation of charge transfer energy and leading to energy values with magnitude comparable with typical experimental binding energies. With this computational approach, EINT values describe the binding efficiency of metal-based binders to DNA Gq more accurately than ΔEFMO. Therefore, to study the binding process of metal containing systems with the FMO method, the adoption of partial screening solvent method combined with ESP-SPCT should be considered. This computational protocol is suggested for FMO calculations on biological systems containing metals, especially when the adoption of the default ESP treatment leads to questionable results.

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.

The FMO2 analysis of the ligand-receptor binding energy: the Biscarbene-Gold(I)/DNA G-Quadruplex case study

In this work, the ab initio fragment molecular orbital (FMO) method was applied to calculate and analyze the binding energy of two biscarbene-Au(I) derivatives, [Au(9-methylcaffein-8-ylidene)₂]⁺ and [Au(1,3-dimethylbenzimidazol-2-ylidene)₂]⁺, to the DNA G-Quadruplex structure. The FMO2 binding energy considers the ligand-receptor complex as well as the isolated forms of energy-minimum state of ligand and receptor, providing a better description of ligand-receptor affinity compared with simple pair interaction energies (PIE). Our results highlight important features of the binding process of biscarbene-Au(I) derivatives to DNA G-Quadruplex, indicating that the total deformation-polarization energy and desolvation penalty of the ligands are the main terms destabilizing the binding. The pair interaction energy decomposition analysis (PIEDA) between ligand and nucleobases suggest that the main interaction terms are electrostatic and charge-transfer energies supporting the hypothesis that Au(I) ion can be involved in π-cation interactions further stabilizing the ligand-receptor complex. Moreover, the presence of polar groups on the carbene ring, as C = O, can improve the charge-transfer interaction with K⁺ ion. These findings can be employed to design new powerful biscarbene-Au(I) DNA-G quadruplex binders as promising anticancer drugs. The procedure described in this work can be applied to investigate any ligand-receptor system and is particularly useful when the binding process is strongly characterized by polarization, charge-transfer and dispersion interactions, properly evaluated by ab initio methods.

Quantification and Neutralization of the Interfacial Electrostatic Potential and Visualization of the Dispersion Interaction in Visualization of the Interfacial Electrostatic Complementarity

Visualization of the interfacial electrostatic complementarity (VIINEC) is a quantum chemistry-based method to examine protein-protein interactions (PPI). In VIINEC, the electrostatic complementarity between proteins at the interface is visually and quantitatively evaluated using the partial electrostatic potential (pESP), which is defined based on the fragment molecular orbital method. In this work, new quantification and neutralization methods of the pESP were proposed together with a method to visualize the dispersion interaction. The reliability and efficiency of these methods were evaluated using 17 models of the complex. It was found that the quantification of the electrostatic complementarity with the pESP using the new neutralization method has a high correlation with the interaction energy, supporting the reliability of VIINEC. As an illustrative example, the PPI between a major histocompatibility complex class I molecule and a T-cell receptor was examined, which demonstrated the value of VIINEC in chemical and biological research.

Homodimeric complexes of the 90-231 human prion: a multilayered computational study based on FMO/GRID-DRY approach

The molecular interaction properties and aggregation capabilities disclosed by PrP-E200K, a pathogenic mutant of the human prion protein, were investigated in detail using multilayered computational approaches. In a previous work, we reported that the electrostatic complementarity between region1 (negative) and region3 (positive) has been assumed to lead to a head-to tail interaction between 120 and 231 PrP-E200K units and to initiation of the aggregation process. In this work, we extended the PrP-E200K structure by including the unstructured 90-120 segment which was found to assume different conformations. Plausible models of 90-231 PrP-E200K dimers were calculated and analyzed in depth to identify the nature of the involved protein-protein interactions. The unstructured 90-120 segment was found to extend the positively charged region3 involved in the association of PrP-E200K units which resulted to be driven by hydrophobic interactions. The combination of molecular dynamics, protein-protein docking, grid-based mapping, and fragment molecular orbital approaches allowed us to provide a plausible mechanism of the early state of 90-231 PrP-E200K aggregation, considered a preliminary step of amyloid conversion.

Interaction Analysis on the SARS-CoV-2 Spike Protein Receptor Binding Domain Using Visualization of the Interfacial Electrostatic Complementarity

Visualization of the interfacial electrostatic complementarity (VIINEC) is a recently developed method for analyzing protein-protein interactions using electrostatic potential (ESP) calculated via the ab initio fragment molecular orbital method. In this Letter, the molecular interactions of the receptor-binding domain (RBD) of the SARS-CoV-2 spike protein with human angiotensin-converting enzyme 2 (ACE2) and B38 neutralizing antibody were examined as an illustrative application of VIINEC. The results of VIINEC revealed that the E484 of RBD has a role in making a local electrostatic complementary with ACE2 at the protein-protein interface, while it causes a considerable repulsive electrostatic interaction. Furthermore, the calculated ESP map at the interface of the RBD/B38 complex was significantly different from that of the RBD/ACE2 complex, which is discussed herein in association with the mechanism of the specificity of the antibody binding to the target protein.

The transcriptional corepressor CtBP2 serves as a metabolite sensor orchestrating hepatic glucose and lipid homeostasis

Biological systems to sense and respond to metabolic perturbations are critical for the maintenance of cellular homeostasis. Here we describe a hepatic system in this context orchestrated by the transcriptional corepressor C-terminal binding protein 2 (CtBP2) that harbors metabolite-sensing capabilities. The repressor activity of CtBP2 is reciprocally regulated by NADH and acyl-CoAs. CtBP2 represses Forkhead box O1 (FoxO1)-mediated hepatic gluconeogenesis directly as well as Sterol Regulatory Element-Binding Protein 1 (SREBP1)-mediated lipogenesis indirectly. The activity of CtBP2 is markedly defective in obese liver reflecting the metabolic perturbations. Thus, liver-specific CtBP2 deletion promotes hepatic gluconeogenesis and accelerates the progression of steatohepatitis. Conversely, activation of CtBP2 ameliorates diabetes and hepatic steatosis in obesity. The structure-function relationships revealed in this study identify a critical structural domain called Rossmann fold, a metabolite-sensing pocket, that is susceptible to metabolic liabilities and potentially targetable for developing therapeutic approaches.

Visualization of the Interfacial Electrostatic Complementarity: A Method for Analysis of Protein-Protein Interaction Based on Ab Initio Quantum Chemical Calculations

In this study, we report a method for analyzing the protein-protein interaction based on ab initio quantum chemical calculations, which we refer to as "Visualization of the interfacial electrostatic complementarity (VIINEC)." This method visually provides the electrostatic complementarity at the protein-protein interface; in addition, the ratio of the attractive interaction is calculated. Illustrative calculations revealed that VIINEC could successfully quantify the electronic induced fit owing complex formation, which was responsible for 5%-10% of the total electrostatic complementarity. Furthermore, the contribution of each amino acid to the electrostatic complementarity was evaluated, providing useful information for various applications, including rational antibody designs. Interestingly, a part of the mechanism causing the specificity of the protein-protein bindings was also demonstrated using VIINEC. This is an important achievement of this study because the specificity of the biomolecular interactions is essential for biological functions.

Resolution of the identity approximation applied to PNOF correlation calculations

In this work, the required algebra to employ the resolution of the identity approximation within the Piris Natural Orbital Functional (PNOF) is developed, leading to an implementation named DoNOF-RI. The arithmetic scaling is reduced from fifth-order to fourth-order, and the memory scaling is reduced from fourth-order to third-order, allowing significant computational time savings. After the DoNOF-RI calculation has fully converged, a restart with four-center electron repulsion integrals can be performed to remove the effect of the auxiliary basis set incompleteness, quickly converging to the exact result. The proposed approach has been tested on cycloalkanes and other molecules of general interest to study the numerical results, as well as the speed-ups achieved by PNOF7-RI when compared with PNOF7.

Analyzing GPCR-Ligand Interactions with the Fragment Molecular Orbital (FMO) Method

G-protein-coupled receptors (GPCRs) have enormous physiological and biomedical importance, and therefore it is not surprising that they are the targets of many prescribed drugs. Further progress in GPCR drug discovery is highly dependent on the availability of protein structural information. However, the ability of X-ray crystallography to guide the drug discovery process for GPCR targets is limited by the availability of accurate tools to explore receptor-ligand interactions. Visual inspection and molecular mechanics approaches cannot explain the full complexity of molecular interactions. Quantum mechanics (QM) approaches are often too computationally expensive to be of practical use in time-sensitive situations, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed, and the ability to reveal key interactions that would otherwise be hard to detect. Integration of GPCR crystallography or homology modelling with FMO reveals atomistic details of the individual contributions of each residue and water molecule toward ligand binding, including an analysis of their chemical nature. Such information is essential for an efficient structure-based drug design (SBDD) process. In this chapter, we describe how to use FMO in the characterization of GPCR-ligand interactions.

The Principles of protein surgery and its application to the logical drug design for the treatment of neurodegenerative diseases

Here we describe the principles of protein surgery and its application to the molecular design for regulating the protein conformation. We initially describe the Poincare duality that defines the basis of complementarity in the time-dependent geometrical space. Next we introduce the theory of protein surgery consisting of "dissection" and "suture," which correspond to differentiation and integration in a phase space, respectively. Then we introduce the surgical (pan-manifold) differential equation and solve several simple cases. In this way, we constructed "medical quantization" strategy which makes a bridge between quantum mechanics and molecular biology. As the application of this theory, here we describe a logical drug design methodology in detail, and its application to anti-prion drug design. Finally, we propose a plan for logical drug (and medical device) design center, in which all the necessary procedures could be done in one place.

Double hybrid DFT calculations with Slater type orbitals

On a comprehensive database with 1,644 datapoints, covering several aspects of main-group as well as of transition metal chemistry, we assess the performance of 60 density functional approximations (DFA), among them 36 double hybrids (DH). All calculations are performed using a Slater type orbital (STO) basis set of triple-ζ (TZ) quality and the highly efficient pair atomic resolution of the identity approach for the exchange- and Coulomb-term of the KS matrix (PARI-K and PARI-J, respectively) and for the evaluation of the MP2 energy correction (PARI-MP2). Employing the quadratic scaling SOS-AO-PARI-MP2 algorithm, DHs based on the spin-opposite-scaled (SOS) MP2 approximation are benchmarked against a database of large molecules. We evaluate the accuracy of STO/PARI calculations for B3LYP as well as for the DH B2GP-PLYP and show that the combined basis set and PARI-error is comparable to the one obtained using the well-known def2-TZVPP Gaussian-type basis set in conjunction with global density fitting. While quadruple-ζ (QZ) calculations are currently not feasible for PARI-MP2 due to numerical issues, we show that, on the TZ level, Jacob's ladder for classifying DFAs is reproduced. However, while the best DHs are more accurate than the best hybrids, the improvements are less pronounced than the ones commonly found on the QZ level. For conformers of organic molecules and noncovalent interactions where very high accuracy is required for qualitatively correct results, DHs provide only small improvements over hybrids, while they still excel in thermochemistry, kinetics, transition metal chemistry and the description of strained organic systems.

Characterization of PD-L1 binding sites by a combined FMO/GRID-DRY approach

The programmed cell death protein 1 (PD-1) and its ligand, PD-L1, constitute an important co-inhibitory immune checkpoint leading to downregulation of immune system. Tumor cells developed a strategy to trigger PD-1/PD-L1 pathway reducing the T cell anticancer activity. Anti-PD-L1 small drugs, generally with improved pharmacokinetic and technological profiles than monoclonal antibodies, became an attractive research topic. Nevertheless, still few works have been published on the chemical features of possible binding sites. In this work, we applied a novel computational protocol based on the combination of the ab initio Fragment Molecular Orbital (FMO) method and a newly developed GRID-DRY approach in order to characterize the PD-L1 binding sites, starting from PD-1/PD-L1 and PD-L1/BMS-ligands (Bristol-Mayers Squibb ligands) complexes. The FMO method allows the calculation of the pair-residues as well as the ligand-residues interactions with ab initio accuracy, whereas the GRID-DRY approach is an effective tool to investigate hydrophobic interactions, not easily detectable by ab initio methods. The present GRID-DRY protocol is able to determine the energy contributions of each ligand atoms to each hydrophobic interaction, both qualitatively and quantitatively. We were also able to identify the three specific hot regions involved in PD-1/PD-L1 protein-protein interaction and in PD-L1/BMS-ligand interactions, in agreement with preceding theoretical/experimental results, and to suggest a specific pharmacophore for PD-L1 inhibitors.

A Quadratic Pair Atomic Resolution of the Identity Based SOS-AO-MP2 Algorithm Using Slater Type Orbitals

We report a production level implementation of pair atomic resolution of the identity (PARI) based second-order Møller-Plesset perturbation theory (MP2) in the Slater type orbital (STO) based Amsterdam Density Functional (ADF) code. As demonstrated by systematic benchmarks, dimerization and isomerization energies obtained with our code using STO basis sets of triple-ζ-quality show mean absolute deviations from Gaussian type orbital, canonical, basis set limit extrapolated, global density fitting (DF)-MP2 results of less than 1 kcal/mol. Furthermore, we introduce a quadratic scaling atomic orbital based spin-opposite-scaled (SOS)-MP2 approach with a very small prefactor. Due to a worst-case scaling of [Formula: see text], our implementation is very fast already for small systems and shows an exceptionally early crossover to canonical SOS-PARI-MP2. We report computational wall time results for linear as well as for realistic three-dimensional molecules and show that triple-ζ quality calculations on molecules of several hundreds of atoms are only a matter of a few hours on a single compute node, the bottleneck of the computations being the SCF rather than the post-SCF energy correction.

Development of the FMO/RI-MP2 Fully Analytic Gradient Using a Hybrid-Distributed/Shared Memory Programming Model

The fully analytic gradient of the second-order Møller-Plesset perturbation theory (MP2) with the resolution-of-the-identity (RI) approximation in the fragment molecular orbital (FMO) framework is derived and implemented using a hybrid multilevel parallel programming model, a combination of the general distributed data interface (GDDI) and the OpenMP API. The FMO/MP2 analytic gradient contains three parts, i.e., the internal fragment component, the electrostatic potential (ESP) component, and the response terms. The RI approximation is applied to the internal fragment MP2 gradient term, whose MP2 densities and monomer MP2 Lagrangians are shared with the ESP and the response terms. The FMO/RI-MP2 analytic gradient implementation is validated against the numerical gradient (with errors ∼10^-6-10^-5 Hartree/Bohr) and the energy conservation in molecular dynamics (MD) simulations using NVE ensembles. The RI approximation introduces an error of ∼10^-5 Hartree/Bohr with a speedup of 4.0-8.0× compared with the currently available GDDI FMO/MP2 gradient. The node linear scaling of the fragmentation framework due to multilevel parallelism is well-preserved and is demonstrated in single-point gradient calculations of large water clusters (e.g., 1120 and 2165 molecules) using 300-800 KNL compute nodes with a parallel efficiency of more than 90%.

Characterising GPCR-ligand interactions using a fragment molecular orbital-based approach

There has been fantastic progress in solving GPCR crystal structures. However, the ability of X-ray crystallography to guide the drug discovery process for GPCR targets is limited by the availability of accurate tools to explore receptor-ligand interactions. Visual inspection and molecular mechanics approaches cannot explain the full complexity of molecular interactions. Quantum mechanical approaches (QM) are often too computationally expensive, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed and the ability to reveal key interactions that would otherwise be hard to detect. Integration of GPCR crystallography or homology modelling with FMO reveals atomistic details of the individual contributions of each residue and water molecule towards ligand binding, including an analysis of their chemical nature.

Recognition of repulsive and attractive regions of selected serotonin receptor binding site using FMO-EDA approach

The complexes of selected long-chain arylpiperazines with homology models of 5-HT_1A, 5-HT_2A, and 5-HT₇ receptors were investigated using quantum mechanical methods. The molecular geometries of the ligand-receptor complexes were firstly optimized with the Our own N-layered Integrated molecular Orbital and molecular Mechanics (ONIOM) method. Next, the fragment molecular orbitals method with an energy decomposition analysis scheme (FMO-EDA) was employed to estimate the interaction energies in binding sites. The results clearly showed that orthosteric binding sites of studied serotonin receptors have both attractive and repulsive regions. In the case of 5-HT_1A and 5-HT_2A two repulsive areas, located in the lower part of the binding pocket, and one large area of attraction engaging many residues at the top of all helices were identified. Additionally, for the 5-HT₇ receptor, the third area of destabilization located at the extracellular end of the helix 6 was found.

An insight of early PrP-E200K aggregation by combined molecular dynamics/fragment molecular orbital approaches

Unveiling the events leading to the formation of prion particles is a nowadays challenge in the field of neurochemistry. Pathogenic mutants of prion protein (PrP) are characterized by both an intrinsic tendency to aggregation and scrapie conversion propensity. However, the question about a possible correlation between these two events lasts still unanswered. Here, a multilayered computational workflow was employed to investigate structure, stability, and molecular interaction properties of a dimer of PrP^C -E200K, a well-known mutant of the PrP that represents a reduced model of early aggregates of this protein. Based on the combination of molecular dynamics and quantum mechanical approaches, this study provided for an in depth insight of PrP^C -E200K dimer in terms of residue-residue interactions. Assembly hypotheses for the early aggregation of PrP^C -E200K are paved and compared with PrP^Sc models reported in the literature to find a structural link between early and late (scrapie) aggregates of this protein.

RI-MP3 calculations of biomolecules based on the fragment molecular orbital method

In this study, the third-order Møller-Plesset perturbation (MP3) theory using the resolution of the identity (RI) approximation was combined with the fragment molecular orbital (FMO) method to efficiently calculate a high-order electron correlation energy of biomolecular systems. We developed a new algorithm for the RI-MP3 calculation, which can be used with the FMO scheme. After test calculations using a small molecule, the FMO-RI-MP3 calculations were performed for two biomolecular systems comprising a protein and a ligand. The computational cost of these calculations was only around 5 and 4 times higher than those of the FMO-RHF calculations. The error associated with the RI approximation was around 2.0% of the third-order correlation contribution to the total energy. However, the RI approximation error in the interaction energy between the protein and ligand molecule was insignificantly small, which reflected the negligible error in the inter fragment interaction energy. © 2018 Wiley Periodicals, Inc.

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.

Low-scaling first-order properties within second-order Møller-Plesset perturbation theory using Cholesky decomposed density matrices

An efficient implementation of energy gradients and of hyperfine coupling constants in second-order Møller-Plesset perturbation theory (MP2) is presented based on our fully atomic orbital (AO)-based approach. For the latter, an unrestricted AO-based MP2 formulation is introduced. A reduction in the dependency of the computational efficiency on the size of the basis set is achieved by a Cholesky decomposition and the prefactor is reduced by the resolution-of-the-identity approximation. Significant integral contributions are selected based on distance-including integral estimates (denoted as QQR-screening) and its reliability as a fully controlled screening procedure is demonstrated. The rate-determining steps are shown via model computations to scale cubically in the computation of energy gradients and quadratically in the case of hyperfine coupling constants. Furthermore, a significant speed-up of the computational time with respect to the canonical formulation is demonstrated.

MPI/OpenMP hybrid parallel algorithm for resolution of identity second-order Møller-Plesset perturbation calculation of analytical energy gradient for massively parallel multicore supercomputers

A massively parallel algorithm of the analytical energy gradient calculations based the resolution of identity Møller-Plesset perturbation (RI-MP2) method from the restricted Hartree-Fock reference is presented for geometry optimization calculations and one-electron property calculations of large molecules. This algorithm is designed for massively parallel computation on multicore supercomputers applying the Message Passing Interface (MPI) and Open Multi-Processing (OpenMP) hybrid parallel programming model. In this algorithm, the two-dimensional hierarchical MP2 parallelization scheme is applied using a huge number of MPI processes (more than 1000 MPI processes) for acceleration of the computationally demanding O(N⁵ ) step such as calculations of occupied-occupied and virtual-virtual blocks of MP2 one-particle density matrix and MP2 two-particle density matrices. The new parallel algorithm performance is assessed using test calculations of several large molecules such as buckycatcher C₆₀ @C₆₀ H₂₈ (144 atoms, 1820 atomic orbitals (AOs) for def2-SVP basis set, and 3888 AOs for def2-TZVP), nanographene dimer (C₉₆ H₂₄ )₂ (240 atoms, 2928 AOs for def2-SVP, and 6432 AOs for cc-pVTZ), and trp-cage protein 1L2Y (304 atoms and 2906 AOs for def2-SVP) using up to 32,768 nodes and 262,144 central processing unit (CPU) cores of the K computer. The results of geometry optimization calculations of trp-cage protein 1L2Y at the RI-MP2/def2-SVP level using the 3072 nodes and 24,576 cores of the K computer are presented and discussed to assess the efficiency of the proposed algorithm. © 2017 Wiley Periodicals, Inc.

[Applications of the Fragment Molecular Orbital Method in Drug Discovery]

  Recently, ab initio quantum mechanical calculations have been applied to large molecules, including biomolecular systems. The fragment molecular orbital (FMO) method is one of the most efficient approaches for the quantum mechanical investigation of such molecules. In the FMO method, dividing a target molecule into small fragments reduces computational effort. The clear definition of inter-fragment interaction energy (IFIE) as an expression of total energy is another valuable feature of the FMO method because it provides the ability to analyze interactions in biomolecules. Thus, the FMO method is expected to be useful for drug discovery. This study demonstrates applications of the FMO method related to drug discovery. First, IFIE, according to FMO calculations, was used in the optimization of drug candidates for the development of anti-prion compounds. The second example involved interaction analysis of the human immunodeficiency virus type 1 (HIV-1) protease and a drug compound that used a novel analytical method for dispersion interaction, i.e., fragment interaction analysis based on LMP2 (FILM).

Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide-expand-consolidate RI-MP2 model

The Resolution of the Identity second-order Møller-Plesset perturbation theory (RI-MP2) method is implemented within the linear-scaling Divide-Expand-Consolidate (DEC) framework. In a DEC calculation, the full molecular correlated calculation is replaced by a set of independent fragment calculations each using a subset of the total orbital space. The number of independent fragment calculations scales linearly with the system size, rendering the method linear-scaling and massively parallel. The DEC-RI-MP2 method can be viewed as an approximation to the DEC-MP2 method where the RI approximation is utilized in each fragment calculation. The individual fragment calculations scale with the fifth power of the fragment size for both methods. However, the DEC-RI-MP2 method has a reduced prefactor compared to DEC-MP2 and is well-suited for implementation on massively parallel supercomputers, as demonstrated by test calculations on a set of medium-sized molecules. The DEC error control ensures that the standard RI-MP2 energy can be obtained to the predefined precision. The errors associated with the RI and DEC approximations are compared, and it is shown that the DEC-RI-MP2 method can be applied to systems far beyond the ones that can be treated with a conventional RI-MP2 implementation.

Electron-correlated fragment-molecular-orbital calculations for biomolecular and nano systems

Recent developments in the fragment molecular orbital (FMO) method for theoretical formulation, implementation, and application to nano and biomolecular systems are reviewed. The FMO method has enabled ab initio quantum-mechanical calculations for large molecular systems such as protein-ligand complexes at a reasonable computational cost in a parallelized way. There have been a wealth of application outcomes from the FMO method in the fields of biochemistry, medicinal chemistry and nanotechnology, in which the electron correlation effects play vital roles. With the aid of the advances in high-performance computing, the FMO method promises larger, faster, and more accurate simulations of biomolecular and related systems, including the descriptions of dynamical behaviors in solvent environments. The current status and future prospects of the FMO scheme are addressed in these contexts.