Theoretical Study of Protein–Ligand Interactions Using the Molecules-in-Molecules Fragmentation-Based Method

Toward Post-Hartree-Fock Accuracy for Protein-Ligand Affinities Using the Molecules-in-Molecules Fragmentation-Based Method

The complexity and size of large molecular systems, such as protein-ligand complexes, pose computational challenges for accurate post-Hartree-Fock calculations. This study delivers a thorough benchmarking of the Molecules-in-Molecules (MIM) method, presenting a clear and accessible strategy for layer/theory selections in post-Hartree-Fock computations on substantial molecular systems, notably protein-ligand complexes. An approach is articulated, enabling augmented computational efficiency by strategically canceling out common subsystem energy terms between complexes and proteins within the supermolecular equation. Employing DLPNO-based post-Hartree-Fock methods in conjunction with the three-layer MIM method (MIM3), this study demonstrates the achievement of protein-ligand binding energies with remarkable accuracy (errors <1 kcal mol-1), while significantly reducing computational costs. Furthermore, noteworthy correlations between theoretically computed interaction energies and their experimental equivalents were observed, with R2 values of approximately 0.90 and 0.78 for CDK2 and BZT-ITK sets, respectively, thus validating the efficacy of the MIM method in calculating binding energies. By highlighting the crucial role of diffuse or small Pople-style basis sets in the middle layer for reducing energy errors, this work provides valuable insights and practical methodologies for interaction energy computations in large molecular complexes and opens avenues for their application across a diverse range of molecular systems.

Reformulation of All ONIOM-Type Molecular Fragmentation Approaches and Many-Body Theories Using Graph-Theory-Based Projection Operators: Applications to Dynamics, Molecular Potential Surfaces, Machine Learning, and Quantum Computing

We present a graph-theory-based reformulation of all ONIOM-based molecular fragmentation methods. We discuss applications to (a) accurate post-Hartree-Fock AIMD that can be conducted at DFT cost for medium-sized systems, (b) hybrid DFT condensed-phase studies at the cost of pure density functionals, (c) reduced cost on-the-fly large basis gas-phase AIMD and condensed-phase studies, (d) post-Hartree-Fock-level potential surfaces at DFT cost to obtain quantum nuclear effects, and (e) novel transfer machine learning protocols derived from these measures. Additionally, in previous work, the unifying strategy discussed here has been used to construct new quantum computing algorithms. Thus, we conclude that this reformulation is robust and accurate.

Investigation of the interactions of HSA and SARS-CoV-2 papain-like protease against eugenol for novel COVID-19 drug discovery: spectroscopic and insilico study

Coronavirus family consist of a member known as SARS-CoV-2, spread drastically in 2019 (Covid-19), affecting millions of people worldwide. Till date there is no clear-clinical therapy or drug, targeted to cure this serious disease. Researches are going on to prevent this corona virus. Here, we tried to explore a novel SARS-CoV-2 papain-like protease as a potential inhibitor. Finally, eugenol was docked with this protease to find prime SARS-inhibitors. In silico studies revealed that eugenol binds to the active site of SARS-CoV-2 papain-like protease with appropriate binding. Moreover, the MD simulation for 100 ns and MMPBSA calculation reveals that eugenol possess potential phytotherapeutic properties against COVID-19. The interaction of eugenol with human serum albumin has been examined by using fluorescence, UV-vis spectroscopy, circular dichroism as well as computational techniques such as molecular docking, molecular dynamic simulation and MMPBSA calculation. Overall investigation shows eugenol having good affinity for HSA Ka 6.80 × 106 M-1.Communicated by Ramaswamy H. Sarma.

Hydrogen Sulfide Ligation in Hemoglobin I of Lucina pectinata─A QM/MM and Local Mode Study

In this study, we investigated the interaction between the H2S ligand and the heme pocket of hemoglobin I (HbI) of Lucina pectinata for the wild-type protein; three known mutations where distal glutamine is replaced by hydrophobic valine (Gln64Val) and hydrophilic histidine in both protonation forms (Gln64Hisϵ and Gln64Hisδ); five known mutations of the so-called phenyl cage, replacing the hydrophobic phenylalanines Phe29 and Phe43 with tyrosine (Tyr), valine (Val), or leucine (Leu); and two additional mutations, Phe68Tyr and Phe68Val, in order to complement previous studies with new insights about the binding mechanism at the molecular level. A particular focus was on the intrinsic strengths of the chemical bonds involved, utilizing local vibrational force constants based on combined quantum mechanical-molecular mechanical calculations. Wild-type protein and mutations clustered into two distinct groups: Group 1 protein systems with a proton acceptor in the distal protein pocket, close to one of the H2S bonds, and Group 2 protein systems without a hydrogen acceptor close by in the active site of the protein. According to our results, the interactions between H2S and HbI of Lucina pectinata involve two important elements, namely, binding of H2S to Fe of the heme group, followed by the proton transfer from the HS bond to the distal residue. The distal residue is additionally stabilized by a second proton transfer from the distal residue to COO- of the propionate group in heme. We could identify the FeS bond as a key player and discovered that the strength of this bond depends on two mutual factors, namely, the strength of the HS bond involved in the proton transfer and the electrostatic field of the protein pocket qualifying the FeS bond as a sensitive probe for monitoring changes in H2S ligation upon protein mutations. We hope our study will inspire and guide future experimental studies, targeting new promising mutations such as Phe68Tyr, Phe68Val, or Phe43Tyr/Phe68Val.

Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions

Electronic structure calculations on enzymes require hundreds of atoms to obtain converged results, but fragment-based approximations offer a cost-effective solution. We present calculations on enzyme models containing 500-600 atoms using the many-body expansion, comparing to benchmarks in which the entire enzyme-substrate complex is described at the same level of density functional theory. When the amino acid fragments contain ionic side chains, the many-body expansion oscillates under vacuum boundary conditions but rapid convergence is restored using low-dielectric boundary conditions. This implies that full-system calculations in the gas phase are inappropriate benchmarks for assessing errors in fragment-based approximations. A three-body protocol retains sub-kilocalorie per mole fidelity with respect to a supersystem calculation, as does a two-body calculation combined with a full-system correction at a low-cost level of theory. These protocols pave the way for application of high-level quantum chemistry to large systems via rigorous, ab initio treatment of many-body polarization.

Accurate and Cost-Effective NMR Chemical Shift Predictions for Nucleic Acids Using a Molecules-in-Molecules Fragmentation-Based Method

We have developed, implemented, and assessed an efficient protocol for the prediction of NMR chemical shifts of large nucleic acids using our molecules-in-molecules (MIM) fragment-based quantum chemical approach. To assess the performance of our approach, MIM-NMR calculations are calibrated on a test set of three nucleic acids, where the structure is derived from solution-phase NMR studies. For DNA systems with multiple conformers, the one-layer MIM method with trimer fragments (MIM1trimer) is benchmarked to get the lowest energy structure, with an average error of only 0.80 kcal/mol with respect to unfragmented full molecule calculations. The MIMI-NMRdimer calibration with respect to unfragmented full molecule calculations shows a mean absolute deviation (MAD) of 0.06 and 0.11 ppm, respectively, for 1H and 13C nuclei, but the performance with respect to experimental NMR chemical shifts is comparable to the more expensive MIM1-NMR and MIM2-NMR methods with trimer subsystems. To compare with the experimental chemical shifts, a standard protocol is derived using DNA systems with Protein Data Bank (PDB) IDs 1SY8, 1K2K, and 1KR8. The effect of structural minimizations is employed using a hybrid mechanics/semiempirical approach and used for computations in solution with implicit and explicit-implicit solvation models in our MIM1-NMRdimer methodology. To demonstrate the applicability of our protocol, we tested it on seven nucleic acids, including structures with nonstandard residues, heteroatom substitutions (F and B atoms), and side chain mutations with a size ranging from ∼300 to 1100 atoms. The major improvement for predicted MIM1-NMRdimer calculations is obtained from structural minimizations and implicit solvation effects. A significant improvement with the explicit-implicit solvation model is observed only for two smaller nucleic acid systems (1KR8 and 7NBK), where the expensive first solvation shell is replaced by the microsolvation model, in which a single water molecule is added for each solvent-exposed amino and imino protons, along with the implicit solvation. Overall, our target accuracy of ∼0.2-0.3 ppm for 1H and ∼2-3 ppm for 13C has been achieved for large nucleic acids. The proposed MIM-NMR approach is accurate and cost-effective (linear scaling with system size), and it can aid in the structural assignments of a wide range of complex biomolecules.

Interaction between the Human OX2 Orexin Receptor and Suvorexant and Some of Its Analogues: SAPT (DFT) Interaction Energy Decomposition Analysis

In this study, the interaction energy (E_int) of suvorexant (as an orexin receptor antagonist) and some of its analogues with the important residues of the human OX2 orexin receptor, determined by molecular docking, is calculated using the symmetry-adapted perturbation theory-density functional theory (SAPT (DFT)) method. Also, the important residues with the dominant interaction with each ligand are determined based on the obtained SAPT (DFT) interaction energies. To analyze the interaction of the receptor with each ligand, the decomposition of E_int to its constituent components including electrostatic (E_ele), exchange (E_ex), induction (E_ind), and exchange-induction (E_ex-ind), dispersion (E_disp), and exchange-dispersion (E_ex-disp) is performed. The change of interaction energy components with the replacement of the benzoxazole part of suvorexant by pyrimidine containing different functional groups, thieno pyrimidine, and furo pyrimidine is also investigated, separately. It is found that the change in E_int, due to these replacements, is controlled more by the variation of the electrostatic interaction energy component of E_int than by the other interaction energy components. A linear correlation (R² = 0.91) is found for the variation of E_int versus experimental ligand-binding affinities. Also, the existence of the linear correlation for the variation of the interaction energy components with experimental ligand-binding affinities is investigated. The variation of the electrostatic component versus experimental ligand-binding affinities shows a more linear correlation compared to the other interaction energy components.

Comparative assessment of QM-based and MM-based models for prediction of protein-ligand binding affinity trends

Methods which accurately predict protein-ligand binding strengths are critical for drug discovery. In the last two decades, advances in chemical modelling have enabled steadily accelerating progress in the discovery and optimization of structure-based drug design. Most computational methods currently used in this context are based on molecular mechanics force fields that often have deficiencies in describing the quantum mechanical (QM) aspects of molecular binding. In this study, we show the competitiveness of our QM-based Molecules-in-Molecules (MIM) fragmentation method for characterizing binding energy trends for seven different datasets of protein-ligand complexes. By using molecular fragmentation, the MIM method allows for accelerated QM calculations. We demonstrate that for classes of structurally similar ligands bound to a common receptor, MIM provides excellent correlation to experiment, surpassing the more popular Molecular Mechanics Poisson-Boltzmann Surface Area (MM/PBSA) and Molecular Mechanics Generalized Born Surface Area (MM/GBSA) methods. The MIM method offers a relatively simple, well-defined protocol by which binding trends can be ascertained at the QM level and is suggested as a promising option for lead optimization in structure-based drug design.

Reliable Prediction of the Protein-Ligand Binding Affinity Using a Charge Penetration Corrected AMOEBA Force Field: A Case Study of Drug Resistance Mutations in Abl Kinase

Protein mutations that directly impair drug binding are related to therapeutic resistance, and accurate prediction of their impact on drug binding would benefit drug design and clinical practice. Here, we have developed a scoring strategy that predicts the effect of the mutations on the protein-ligand binding affinity. In view of the critical importance of electrostatics in protein-ligand interactions, the charge penetration corrected AMOEBA force field (AMOEBA_CP model) was employed to improve the accuracy of the calculated electrostatic energy. We calculated the electrostatic energy using an energy decomposition analysis scheme based on the generalized Kohn-Sham (GKS-EDA). The AMOEBA_CP model was validated by a protein-fragment-ligand complex data set (Abl236) constructed from the co-crystal structures of the cancer target Abl kinase with six inhibitors. To predict ligand binding affinity changes upon protein mutation of Abl kinase, we used sampling protocol with multistep simulated annealing to search conformations of mutant proteins. The scoring strategy based on AMOEBA_CP model has achieved considerable performance in predicting resistance for 8 kinase inhibitors across 144 clinically identified point mutations. Overall, this study illustrates that the AMOEBA_CP model, which accurately treats electrostatics through penetration correction, enables the accurate prediction of the mutation-induced variation of protein-ligand binding affinity.

Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

We present a multitopology molecular fragmentation approach, based on graph theory, to calculate multidimensional potential energy surfaces in agreement with post-Hartree-Fock levels of theory but at the density functional theory cost. A molecular assembly is coarse-grained into a set of graph-theoretic nodes that are then connected with edges to represent a collection of locally interacting subsystems up to an arbitrary order. Each of the subsystems is treated at two levels of electronic structure theory, the result being used to construct many-body expansions that are embedded within an ONIOM scheme. These expansions converge rapidly with the many-body order (or graphical rank) of subsystems and capture many-body interactions accurately and efficiently. However, multiple graphs, and hence multiple fragmentation topologies, may be defined in molecular configuration space that may arise during conformational sampling or from reactive, bond breaking and bond formation, events. Obtaining the resultant potential surfaces is an exponential scaling proposition, given the number of electronic structure computations needed. We utilize a family of graph-theoretic representations within a variational scheme to obtain multidimensional potential surfaces at a reduced cost. The fast convergence of the graph-theoretic expansion with increasing order of many-body interactions alleviates the exponential scaling cost for computing potential surfaces, with the need to only use molecular fragments that contain a fewer number of quantum nuclear degrees of freedom compared to the full system. This is because the dimensionality of the conformational space sampled by the fragment subsystems is much smaller than the full molecular configurational space. Additionally, we also introduce a multidimensional clustering algorithm, based on physically defined criteria, to reduce the number of energy calculations by orders of magnitude. The molecular systems benchmarked include coupled proton motion in protonated water wires. The potential energy surfaces and multidimensional nuclear eigenstates obtained are shown to be in very good agreement with those from explicit post-Hartree-Fock calculations that become prohibitive as the number of quantum nuclear dimensions grows. The developments here provide a rigorous and efficient alternative to this important chemical physics problem.

<i>In silico </i>Identification of Peptide as Epidermal Growth Factor Receptor Tyrosine Kinase Inhibitors in Lung Cancer Treatment

BACKGROUND AND OBJECTIVE

Epidermal growth factor receptor (EGFR) is the biomarker for lung cancer in which the protein has the most active mutated genes in lung cancer patients. Peptides have pharmacological potential as drugs because of their bioactivity and accessibility. The research objective was to obtain peptide compounds drug candidates with good interaction and pharmacological properties that can act as an inhibitor for EGFR for lung cancer treatment by using in silico method.

MATERIALS AND METHODS

EGFR protein structure was obtained from Protein Data Bank and the peptide compounds were retrieved from PubChem. Optimization and energy minimization process were done to prepare the peptides for the simulation. Protein-Ligand Interaction Fingerprint (PLIF) was used to determine the pharmacophore features in the EGFR binding site. Both proteins and ligands underwent a virtual screening through rigid and flexible molecular docking simulation and the best ligands were subjected to a computational ADME-Tox properties prediction.

RESULTS

After screening through molecular docking simulation, nine best compounds were identified to have a good interaction with EGFR protein according to its binding energy and RMSD value. The compounds were identified to form hydrogen bond interactions with the macromolecule.

CONCLUSION

Two peptide compounds (PubChem ID: 20832941 and 9805315) have been predicted as the best ligands with desired pharmacological properties for the inhibition of EGFR tyrosine kinase.

Accurate and cost-effective NMR chemical shift predictions for proteins using a molecules-in-molecules fragmentation-based method

We have developed an efficient protocol using our two-layer Molecules-in-Molecules (MIM2) fragmentation-based quantum chemical method for the prediction of NMR chemical shifts of large biomolecules. To investigate the performance of our fragmentation approach and demonstrate its applicability, MIM-NMR calculations are first calibrated on a test set of six proteins. The MIM2-NMR method yields a mean absolute deviation (MAD) from unfragmented full molecule calculations of 0.01 ppm for 1H and 0.06 ppm for 13C chemical shifts. Thus, the errors from fragmentation are only about 3% of our target accuracy of ∼0.3 ppm for 1H and 2-3 ppm for 13C chemical shifts. To compare with experimental chemical shifts, a standard protocol is first derived using two smaller proteins 2LHY (176 atoms) and 2LI1 (146 atoms) for obtaining an appropriate protein structure for NMR chemical shift calculations. The effect of the solvent environment on the calculated NMR chemical shifts is incorporated through implicit, explicit, or explicit-implicit solvation models. The expensive first solvation shell calculations are replaced by a micro-solvation model in which only the immediate interaction between the protein and the explicit solvation environment is considered. A single explicit water molecule for each amine and amide proton is found to be sufficient to yield accurate results for 1H chemical shifts. The 1H and 13C NMR chemical shifts calculated using our protocol give excellent agreement with experiments for two larger proteins, 2MC5 (the helical part with 265 atoms) and 3UMK (33 residue slice with 547 atoms). Overall, our target accuracy of ∼0.3 ppm for 1H and ∼2-3 ppm for 13C has been achieved for the larger proteins. The proposed MIM-NMR method is accurate and computationally cost-effective and should be applicable to study a wide range of large proteins.

SQM/COSMO Scoring Function: Reliable Quantum-Mechanical Tool for Sampling and Ranking in Structure-Based Drug Design

Quantum mechanical (QM) methods have been gaining importance in structure-based drug design where a reliable description of protein-ligand interactions is of utmost significance. However, strategies i. e. QM/MM, fragmentation or semiempirical (SQM) methods had to be pursued to overcome the unfavorable scaling of QM methods. Various SQM-based approaches have significantly contributed to the accuracy of docking and improvement of lead compounds. Parametrizations of SQM and implicit solvent methods in our laboratory have been instrumental to obtain a reliable SQM-based scoring function. The experience gained in its application for activity ranking of ligands binding to tens of protein targets resulted in setting up a faster SQM/COSMO scoring approach, which outperforms standard scoring methods in native pose identification for two dozen protein targets with ten thousand poses. Recently, SQM/COSMO was effectively applied in a proof-of-concept study of enrichment in virtual screening. Due to its superior performance, feasibility and chemical generality, we propose the SQM/COSMO approach as an efficient tool in structure-based drug design.

Quantum Mechanical Investigation of Three-Dimensional Activity Cliffs Using the Molecules-in-Molecules Fragmentation-Based Method

The concept of activity cliff (AC) (i.e., a small structural modification resulting in a substantial bioactivity change) is widely encountered in medicinal chemistry during compound design. Whereas the study of ACs is of high interest as it provides a wealth of opportunities for effective drug design, its practical application in the actual drug development process has been difficult because of significant computational challenges. To provide some understanding of the ACs, we have carried out a rigorous quantum-mechanical investigation of the electronic interactions of a wide range of ACs (205 cliffs formed by 261 protein-ligand complexes covering 37 different receptor types) using multilayer molecules-in-molecules (MIM) fragmentation-based methodology. The MIM methodology enables performing accurate high-level quantum mechanical (QM) calculations at a substantially lower computational cost, while allowing for a quantitative decomposition of the protein-ligand binding energy into the contributions from individual residues, solvation, and entropy. Our investigation in this study is mainly focused on whether the QM binding energy calculation can correctly identify the higher potency cliff partner for a given ligand pair having a sufficiently high activity difference. We have also analyzed the effect of including crystal water molecules as a part of the receptor as well as the impact of ligand desolvation energy on the correct identification of the more potent ligand in a cliff pair. Our analysis reveals that, in the majority of the cases, the AC prediction could be significantly improved by carefully identifying the critical crystal water molecules, whereas the contribution from the ligand desolvation also remains essential. Additionally, we have exploited the residue-specific interaction energies provided by MIM to identify the key residues and interaction hot-spots that are responsible for the experimentally observed drastic activity changes. The results show that our MIM fragmentation-based protocol provides comprehensive interaction energy profiles that can be employed to understand the distinctiveness of ligand modifications, for potential applications in structure-based drug design.

Geometry Optimization, Transition State Search, and Reaction Path Mapping Accomplished with the Fragment Molecular Orbital Method

Recent development of the fragment molecular orbital (FMO) method related to energy gradients, geometry optimization, transition state search, and chemical reaction mapping is summarized. The frozen domain formulation of FMO is introduced in detail, and the structure of related GAMESS input files for FMO is described.

What Next for Quantum Mechanics in Structure-Based Drug Discovery?

There is significant potential for electronic structure methods to improve the quality of the predictions furnished by the tools of computer-aided drug design, which typically rely on empirically derived functions. In this perspective, we consider some recent examples of how quantum mechanics has been applied in predicting protein-ligand geometries, protein-ligand binding affinities and ligand strain on binding. We then outline several significant developments in quantum mechanics methodology likely to influence these approaches: in particular, we note the advent of more computationally expedient ab initio quantum mechanical methods that can provide chemical accuracy for larger molecular systems than hitherto possible. We highlight the emergence of increasingly accurate semiempirical quantum mechanical methods and the associated role of machine learning and molecular databases in their development. Indeed, the convergence of improved algorithms for solving and analyzing electronic structure, modern machine learning methods, and increasingly comprehensive benchmark data sets of molecular geometries and energies provides a context in which the potential of quantum mechanics will be increasingly realized in driving future developments and applications in structure-based drug discovery.

Energy-Screened Many-Body Expansion: A Practical Yet Accurate Fragmentation Method for Quantum Chemistry

We introduce an implementation of the truncated many-body expansion, MBE(n), in which the n-body corrections are screened using the effective fragment potential force field, and only those that exceed a specified energy threshold are computed at a quantum-mechanical level of theory. This energy-screened MBE(n) approach is tested at the n = 3 level for a sequence of water clusters, (H₂O)_N=6-34. A threshold of 0.25 kJ/mol eliminates more than 80% of the subsystem electronic structure calculations and is even more efficacious in that respect than is distance-based screening. Even so, the energy-screened MBE(3) method is faithful to a full-system quantum chemistry calculation to within 1-2 kJ/mol/monomer, even in good quality basis sets such as aug-cc-pVTZ. These errors can be reduced by means of a two-layer approach that involves a Hartree-Fock calculation for the entire cluster. Such a correction proves to be necessary in order to obtain accurate relative energies for conformational isomers of (H₂O)₂₀, but the cost of a full-system Hartree-Fock calculation remains smaller than the cost of three-body subsystem calculations at correlated levels of theory. At the level of second-order Møller-Plesset perturbation theory (MP2), a screened MBE(3) calculation plus a full-system Hartree-Fock calculation is less expensive than a full-system MP2 calculation starting at N = 12 water molecules. This is true even if all MBE(3) subsystem calculations are performed on a single 40-core compute node, i.e., without significant parallelization. Energy-screened MBE(n) thus provides a fragment-based method that is accurate, stable in large basis sets, and low in cost, even when the latter is measured in aggregate computer time.

Fantasy versus reality in fragment-based quantum chemistry

Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.

Solvent Screening in Zwitterions Analyzed with the Fragment Molecular Orbital Method

Based on induced solvent charges, a new model of solvent screening is developed in the framework of the fragment molecular orbital combined with the polarizable continuum model. The developed model is applied to analyze interactions in a prototypical zwitterionic system, sodium chloride in water, and it is shown that the large underestimation of the interaction in the original solvent screening based on local charges is successfully corrected. The model is also applied to a complex of the Trp-cage (PDB: 1L2Y ) miniprotein with an anionic ligand, and the physical factors determined protein-ligand binding in solution are unraveled.

Variational Formulation of the Generalized Many-Body Expansion with Self-Consistent Charge Embedding: Simple and Correct Analytic Energy Gradient for Fragment-Based ab Initio Molecular Dynamics

The many-body expansion (MBE) and its extension to overlapping fragments, the generalized (G)MBE, constitute the theoretical basis for most fragment-based approaches for large-scale quantum chemistry. We reformulate the GMBE for use with embedding charges determined self-consistently from the fragment wave functions, in a manner that preserves the variational nature of the underlying self-consistent field method. As a result, the analytic gradient retains the simple "sum of fragment gradients" form that is often assumed in practice, sometimes incorrectly. This obviates (without approximation) the need to solve coupled-perturbed equations, and we demonstrate stable, fragment-based ab initio molecular dynamics simulations using this technique. Energy conservation fails when charge-response contributions to the Fock matrix are neglected, even while geometry optimizations and vibrational frequency calculations may yet be accurate. Stable simulations can be recovered by means of straightforward modifications introduced here, providing a general paradigm for fragment-based ab initio molecular dynamics.

Exploring Reaction Energy Profiles Using the Molecules-in-Molecules Fragmentation-Based Approach

The Molecules-in-Molecules (MIM) fragmentation-based approach has been successfully used in previous studies to obtain the energies, optimized geometries, and spectroscopic properties of large molecular systems. The present work delineates a protocol to study the potential energy profiles for multistep chemical reactions using the MIM methodology. In a complex multistep chemical reaction, the fragmentation scheme needs to be changed as the reacting species transition into a new reaction step, resulting in a discontinuity in the potential energy curve of the reaction. In our approach, the fragmentation scheme for a particular step in a reaction is chosen on the basis of the nature of the bonding changes associated with that step. Thus, the reactant, transition state, and product are treated consistently throughout the reaction step, leading to an accurate energy barrier for that step. The discontinuity now occurs in describing the energies of reaction intermediates at the transition point between two reaction steps that are treated by two different fragmentation schemes. To address this issue, we propose a systematic procedure for obtaining continuous potential energy curves that are least shifted from their initial positions. The corrected MIM potential energy curves are continuous with activation energies preserved. Following this approach, energy profiles of complex reactions involving large molecular species can be obtained at high levels of theory with a reasonable computational cost.

The Fragment Molecular Orbital Method Based on Long-Range Corrected Density-Functional Tight-Binding

The presently available linear scaling approaches to density-functional tight-binding (DFTB) based on the fragment molecular orbital (FMO) method are severely impacted by the problem of artificial charge transfer due to the self-interaction error (SIE), which hampers the simulation of zwitterionic systems such as biopolymers or ionic liquids. Here we report an extension of FMO-DFTB where we included a long-range corrected (LC) functional designed to mitigate the DFTB SIE, called the FMO-LC-DFTB method, resulting in a robust method which succeeds in simulating zwitterionic systems. Both energy and analytic gradient are developed for the gas phase and the polarizable continuum model of solvation. The scaling of FMO-LC-DFTB with system size N is shown to be almost linear, O( N^1.13-1.28), and its numerical accuracy is established for a variety of representative systems including neutral and charged polypeptides. It is shown that pair interaction energies between fragments for two mini-proteins are in excellent agreement with results from long-range corrected density functional theory. The new method was employed in long time scale (1 ns) molecular dynamics simulations of the tryptophan cage protein (PDB: 1L2Y ) in the gas phase for four different protonation states and in stochastic global minimum structure searches for 1-ethyl-3-methylimidazolium nitrate ionic liquid clusters containing up to 2300 atoms.

Simulations of infrared and Raman spectra in solution using the fragment molecular orbital method

Calculation of IR and Raman spectra in solution for large molecular systems made possible with analytic FMO/PCM Hessians.