Electrostatic field-adapted molecular fractionation with conjugated caps for energy calculations of charged biomolecules

The Quality of Embedding Charges Is Critical for Convergence of Many-Body Expansions When BSSE Is Absent

There is conflicting evidence in the literature concerning the benefits of charge embedding on the convergence of many-body expansions (MBEs). Using a systematic series of water and ion-water clusters of varying size, this study indicates that the effects of charge embedding can be masked by basis set superposition error (BSSE). When BSSE is removed, this study demonstrates that charge embedding can significantly accelerate MBE convergence, where the electrostatically embedded two-body method, EE-MBE(2), can often yield accuracy close to the four-body method, MBE(4). Contrary to previous studies on smaller systems, this work shows that the performance of EE-MBE is highly sensitive to the charge model, with the best performance obtained when the natural population analysis (NPA) charge model is used and generated at the same level of theory used in the subsystem and supersystem calculations. It was demonstrated that the "3c" composite method, PBEh-3c, yields NPA atomic charges that are in excellent agreement with those obtained from supersystem density functional theory calculations. The linear-scaling X-Polarization method provides a more general approach to estimating these supersystem QM atomic charges, but its performance depends on how the fragments are defined.

Toward an extreme-scale electronic structure system

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

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

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

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.

Extending multi-layer energy-based fragment method for excited-state calculations of large covalently bonded fragment systems

Recently, we developed a low-scaling Multi-Layer Energy-Based Fragment (MLEBF) method for accurate excited-state calculations and nonadiabatic dynamics simulations of nonbonded fragment systems. In this work, we extend the MLEBF method to treat covalently bonded fragment ones. The main idea is cutting a target system into many fragments according to chemical properties. Fragments with dangling bonds are first saturated by chemical groups; then, saturated fragments, together with the original fragments without dangling bonds, are grouped into different layers. The accurate total energy expression is formulated with the many-body energy expansion theory, in combination with the inclusion-exclusion principle that is used to delete the contribution of chemical groups introduced to saturate dangling bonds. Specifically, in a two-layer MLEBF model, the photochemically active and inert layers are calculated with high-level and efficient electronic structure methods, respectively. Intralayer and interlayer energies can be truncated at the two- or three-body interaction level. Subsequently, through several systems, including neutral and charged covalently bonded fragment systems, we demonstrate that MLEBF can provide accurate ground- and excited-state energies and gradients. Finally, we realize the structure, conical intersection, and path optimizations by combining our MLEBF program with commercial and free packages, e.g., ASE and SciPy. These developments make MLEBF a practical and reliable tool for studying complex photochemical and photophysical processes of large nonbonded and bonded fragment systems.

Treating Polarization Effects in Charged and Polar Bio-Molecules Through Variable Electrostatic Parameters

Polarization plays important roles in charged and hydrogen bonding containing systems. Much effort ranging from the construction of physics-based models to quantum mechanism (QM)-based and machine learning (ML)-assisted models have been devoted to incorporating the polarization effect into the conventional force fields at different levels, such as atomic and coarse grained (CG). The application of polarizable force fields or polarization models was limited by two aspects, namely, computational cost and transferability. Different from physics-based models, no predetermining parameters were required in the QM-based approaches. Taking advantage of both the accuracy of QM calculations and efficiency of molecular mechanism (MM) and ML, polarization effects could be treated more efficiently while maintaining the QM accuracy. The computational cost could be reduced with variable electrostatic parameters, such as the charge, dipole, and electronic dielectric constant with the help of linear scaling fragmentation-based QM calculations and ML models. Polarization and entropy effects on the prediction of partition coefficient of druglike molecules are demonstrated by using both explicit or implicit all-atom molecular dynamics simulations and machine learning-assisted models. Directions and challenges for future development are also envisioned.

Characterization of the binding interaction between atrazine and human serum albumin: Fluorescence spectroscopy, molecular dynamics and quantum biochemistry

Atrazine (ATR), one of the most used herbicides worldwide, causes persistent contamination of water and soil due to its high resistance to degradation. ATR is associated with low fertility and increased risk of prostate cancer in humans, as well as birth defects, low birth weight and premature delivery. Describing ATR binding to human serum albumin (HSA) is clinically relevant to future studies about pharmacokinetics, pharmacodynamics and toxicity of ATR, as albumin is the most abundant carrier protein in plasma and binds important small biological molecules. In this work we characterize, for the first time, the binding of ATR to HSA by using fluorescence spectroscopy and performing simulations using molecular docking, classical molecular dynamics and quantum biochemistry based on density functional theory (DFT). We determine the most likely binding sites of ATR to HSA, highlighting the fatty acid binding site FA8 (located between subdomains IA-IB-IIA and IIB-IIIA-IIIB) as the most important one, and evaluate each nearby amino acid residue contribution to the binding interactions explaining the fluorescence quenching due to ATR complexation with HSA. The stabilization of the ATR/FA8 complex was also aided by the interaction between the atrazine ring and SER454 (hydrogen bond) and LEU481(alkyl interaction).

A double exponential coupled cluster theory in the fragment molecular orbital framework

Fragmentation-based methods enable electronic structure calculations for large chemical systems through partitioning them into smaller fragments. Here, we have developed and benchmarked a dual exponential operator-based coupled cluster theory to account for high-rank electronic correlation of large chemical systems within the fragment molecular orbital (FMO) framework. Upon partitioning the molecular system into several fragments, the zeroth order reference determinants for each fragment and fragment pair are constructed in a self-consistent manner with two-body FMO expansion. The dynamical correlation is induced through a dual exponential ansatz with a set of fragment-specific rank-one and rank-two operators that act on the individual reference determinants. While the single and double excitations for each fragment are included through the conventional rank-one and rank-two cluster operators, the triple excitation space is spanned via the contraction between the cluster operators and a set of rank-two scattering operators over a few optimized fragment-specific occupied and virtual orbitals. Thus, the high-rank dynamical correlation effects within the FMO framework are computed with rank-one and rank-two parametrization of the wave operator, leading to significant reduction in the number of variables and associated computational scaling over the conventional methods. Through a series of pilot numerical applications on various covalent and non-covalently bonded systems, we have shown the quantitative accuracy of the proposed methodology compared to canonical, as well as FMO-based coupled-cluster single double triple. The accuracy of the proposed method is shown to be systematically improvable upon increasing the number of contractible occupied and virtual molecular orbitals employed to simulate triple excitations.

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

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

iOI: An Iterative Orbital Interaction Approach for Solving the Self-Consistent Field Problem

An iterative orbital interaction (iOI) approach is proposed to solve, in a bottom-up fashion, the self-consistent field problem in quantum chemistry. While it belongs grossly to the family of fragment-based quantum chemical methods, iOI is distinctive in that (1) it divides and conquers not only the energy but also the wave function and that (2) the subsystem sizes are automatically determined by successively merging neighboring small subsystems until they are just enough for converging the wave function to a given accuracy. Orthonormal occupied and virtual localized molecular orbitals are obtained in a natural manner, which can be used for all post-SCF purposes.

Fragment-Based Local Coupled Cluster Embedding Approach for the Quantification and Analysis of Noncovalent Interactions: Exploring the Many-Body Expansion of the Local Coupled Cluster Energy

Herein, we introduce a fragment-based local coupled cluster embedding approach for the accurate quantification and analysis of noncovalent interactions in molecular aggregates. Our scheme combines two different expansions of the domain-based local pair natural orbital coupled cluster (DLPNO-CCSD(T)) energy: the many-body expansion (MBE) and the local energy decomposition (LED). The low-order terms in the MBE are initially computed in the presence of an environment that is treated at a low level of theory. Then, LED is used to decompose the energy of each term in the embedded MBE into additive fragment and fragment-pairwise contributions. This information is used to quantify the total energy of the system while providing at the same time in-depth insights into the nature and cooperativity of noncovalent interactions. Two different approaches are introduced and tested, in which the environment is treated at different levels of theory: the local coupled cluster in the Hartree-Fock (LCC-in-HF) method, in which the environment is treated at the HF level; and the electrostatically embedded local coupled cluster method (LCC-in-EE), in which the environment is replaced by point charges. Both schemes are designed to preserve as much as possible the accuracy of the parent local coupled cluster method for total energies, while being embarrassingly parallel and less memory intensive. These schemes appear to be particularly promising for the study of large and complex molecular aggregates at the coupled cluster level, such as condensed phase systems and protein-ligand interactions.

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

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

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

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

Polarizable Density Embedding for Large Biomolecular Systems

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

Elongation method with intermediate mechanical and electrostatic embedding for geometry optimizations of polymers

The elongation method with intermediate mechanical and electrostatic embedding (ELG-IMEE) is proposed. The electrostatic embedding uses atomic charges generated by a charge sensitivity analysis (CSA) method and parameterized for three different population analyses, namely, the Merz-Singh-Kollman scheme, the charge model 5, and the atomic polar tensor. The obtained CSA models were tested on two model systems. Test calculations show that the electrostatic embedding provides several times of decrease in the difference of energies of testing and reference calculations in comparison with the conventional elongation approach (ELG). The mechanical embedding is implemented in a combination of the conventional elongation method and the ONIOM approach. Moreover, it was demonstrated that the geometry optimization with the ELG-IMEE reduces the errors in the optimized structures by about one order in root-mean-square deviation, when compared to ELG.

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

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

Integrating Machine Learning with the Multilayer Energy-Based Fragment Method for Excited States of Large Systems

In this work we have combined machine learning techniques with our recently developed multilayer energy-based fragment method for studying excited states of large systems. The photochemically active and inert regions are separately treated with the complete active space self-consistent field method and the trained models. This method is demonstrated to provide accurate energies and gradients leading to essentially the same excited-state potential energy surfaces and nonadiabatic dynamics compared with full ab initio results. Furthermore, in conjunction with the use of machine learning models, this method is highly parallel and exhibits low-scaling computational cost. Finally, the present work could encourage the marriage of machine learning with fragment-based electronic structure methods to explore photochemistry of large systems.

A multi-layer energy-based fragment method for excited states and nonadiabatic dynamics

We developed a multi-layer energy-based fragment (MLEBF) method within the many-body energy expansion framework. It supplies accurate energies and gradients, and accurately reproduces excited-state topological structures. Moreover, MLEBF-based nonadiabatic dynamics simulations give nearly the same results compared with full ab initio ones. The present work could stimulate developing energy-based fragment methods for photochemistry of large systems.

Outlining migrainous through dihydroergotamine–serotonin receptor interactions using quantum biochemistry

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

Simulations of molecular self-assembled monolayers on surfaces: packing structures, formation processes and functions tuned by intermolecular and interfacial interactions

Simulations using QM and MM methods guide the rational design of functionalized SAMs on surfaces.

H2 Adsorption in a Porous Crystal: Accurate First-Principles Quantum Simulation

A general method is presented for constructing, from ab initio quantum chemistry calculations, the potential energy surface (PES) for H2 absorbed in a porous crystalline material. The method is illustrated for the metal-organic framework material MOF-5. Rigid body quantum diffusion Monte Carlo simulations are used in the construction of the PES and to evaluate the quantum ground state of H2 in MOF-5, the zero-point energy, and the enthalpy of adsorption at 0 K.

Electrostatically Embedded Many-Body Correlation Energy, with Applications to the Calculation of Accurate Second-Order Møller-Plesset Perturbation Theory Energies for Large Water Clusters

The electrostatically embedded many-body expansion (EE-MB), previously applied to the total electronic energy, is here applied only to the electronic correlation energy (CE), combined with a Hartree-Fock calculation on the entire system. The separate treatment of the Hartree-Fock and correlation energies provides an efficient way to approximate correlation energy for extended systems. We illustrate this here by calculating accurate Møller-Plesset second-order perturbation theory (MP2) energies for a series of clusters ranging in size from 5 to 20 water molecules. In this new method, called EE-MB-CE, where MB is pairwise additive (PA) or three-body (3B), the full Hartree-Fock energy of a system of N monomers is calculated (i.e., the many-body expansion is carried out to the Nth order), while the EE-MB method is used to calculate the correlation energy of the system. We find that not only does this new method lead to better energetics than the original EE-MB method but also that one is able to obtain excellent agreement with full MP2 calculations by considering only a two-body expansion of the correlation energy, leading to a considerable savings in computational time as compared to the three-body expansion. Additionally, we propose the use of a cutoff to further reduce the number of two-body terms that must be calculated, and we show that if a cutoff of 6 Å is used, then one can eliminate up to 44% of the pairs and still calculate energies to within 0.1% of the net interaction energy of the full cluster.

Molecular forces, geometries, and frequencies by systematic molecular fragmentation including embedded charges

The accuracy of energies, energy gradients, and hessians evaluated by systematic molecular fragmentation is examined for a wide range of neutral molecules, zwitterions, and ions. A protocol is established that may employ embedded charges in conjunction with fragmentation to provide accurate evaluation of minimum energy geometries and vibrational frequencies in an automated procedure.

Generalized energy-based fragmentation approach and its applications to macromolecules and molecular aggregates

Conspectus The generalized energy-based fragmentation (GEBF) approach provides a very simple way of approximately evaluating the ground-state energy or properties of a large system in terms of ground-state energies of various small "electrostatically embedded" subsystems, which can be calculated with any traditional ab initio quantum chemistry (X) method (X = Hartree-Fock, density functional theory, and so on). Due to its excellent parallel efficiency, the GEBF approach at the X theory level (GEBF-X) allows full quantum mechanical (QM) calculations to be accessible for systems with hundreds and even thousands of atoms on ordinary workstations. The implementation of the GEBF approach at various theoretical levels can be easily done with existing quantum chemistry programs. This Account reviews the methodology, implementation, and applications of the GEBF-X approach. This method has been successfully applied to optimize the structures of various large systems including molecular clusters, polypeptides, proteins, and foldamers. Such investigations could allow us to elucidate the origin and nature of the cooperative interaction in secondary structures of long peptides or the driving force of the self-assembly processes of aromatic oligoamides. These GEBF-based QM calculations reveal that the structures and stability of various complex systems result from a subtle balance of many types of noncovalent interactions such as hydrogen bonding and van der Waals interactions. The GEBF-based ab initio molecular dynamics (AIMD) method also allows the investigation of dynamic behaviors of large systems on the order of tens of picoseconds. It was demonstrated that the conformational dynamics of two model peptides predicted by GEBF-based AIMD are noticeably different from those predicted by the classical force field MD method. With the target of extending QM calculations to molecular aggregates in the condensed phase, we have implemented the GEBF-based multilayer hybrid models, which could provide satisfactory descriptions of the binding energies between a solute molecule and its surrounding waters and the chain-length dependence of the conformational changes of oligomers in aqueous solutions. A coarse-grained polarizable molecular mechanics model, furnished with GEBF-X dipole moments of subsystems, exhibits some advantages of treating the electrostatic polarization with reduced computational costs. We anticipate that the GEBF approach will continue to develop with the ultimate goal of studying complicated phenomena at mesoscopic scales and serve as a practical tool to elucidate the structure and dynamics of chemical and biological systems.

Density functional calculations of extended, periodic systems using Coulomb corrected molecular fractionation with conjugated caps method (CC-MFCC)

A consistent DFT based formulation of the order-N molecular fractionation with conjugated caps method in which a molecular system is calculated considering a set of finite fragments, is proposed. Here we apply the method and test its performance on a periodic metal–organic framework system.

Analysis of the Errors in the Electrostatically Embedded Many-Body Expansion of the Energy and the Correlation Energy for Zn and Cd Coordination Complexes with Five and Six Ligands and Use of the Analysis to Develop a Generally Successful Fragmentation Strategy

In the present paper, we apply the electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE) to the calculation of zinc-ligand and cadmium-ligand bond dissociation energies, and we analyze the errors due to various fragmentation schemes in a variety of neutral, positively charged, and negatively charged Zn²⁺ and Cd²⁺ coordination complexes. As a result of the analysis, we are able to present a new, simple, and unambiguous fragmentation strategy. Following this strategy, we show that both methods perform well for zinc-ligand and cadmium-ligand bond dissociation energies for all systems studied in the paper, including a model of the catalytic site of the zinc-bearing anthrax toxin lethal factor (LF), which has garnered substantial attention as a target for drug development. To draw general conclusions we consider ten pentacoordinate and hexacoordinate zinc and cadmium containing coordination complexes, each with 10 or 15 different fragmentation schemes. By analyzing errors, we developed a prescription for the optimal fragmentation strategy. With this scheme, and using MP2 correlation energies as a test, we find that the electrostatically embedded three-body expansion of the correlation energy (EE-3B-CE) method is able to reproduce all 53 conventionally calculated bond energies with an average absolute error of only 0.59 kcal/mol. The paper also presents EE-MB-CE calculations using the CCSD(T) level of theory on an LF model system. With CCSD(T), EE-3B-CE has an average error of 0.30 kcal/mol.

Electrostatically embedded generalized molecular fractionation with conjugate caps method for full quantum mechanical calculation of protein energy

An electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method is developed for efficient linear-scaling quantum mechanical (QM) calculation of protein energy. This approach is based on our previously proposed GMFCC/MM method (He; et al. J. Chem. Phys. 2006, 124, 184703), In this EE-GMFCC scheme, the total energy of protein is calculated by taking a linear combination of the QM energy of the neighboring residues and the two-body QM interaction energy between non-neighboring residues that are spatially in close contact. All the fragment calculations are embedded in a field of point charges representing the remaining protein environment, which is the major improvement over our previous GMFCC/MM approach. Numerical studies are carried out to calculate the total energies of 18 real three-dimensional proteins of up to 1142 atoms using the EE-GMFCC approach at the HF/6-31G* level. The overall mean unsigned error of EE-GMFCC for the 18 proteins is 2.39 kcal/mol with reference to the full system HF/6-31G* energies. The EE-GMFCC approach is also applied for proteins at the levels of the density functional theory (DFT) and second-order many-body perturbation theory (MP2), also showing only a few kcal/mol deviation from the corresponding full system result. The EE-GMFCC method is linear-scaling with a low prefactor, trivially parallel, and can be readily applied to routinely perform structural optimization of proteins and molecular dynamics simulation with high level ab initio electronic structure theories.