Efficient and accurate fragmentation methods

Dataset for quantum-mechanical exploration of conformers and solvent effects in large drug-like molecules

We here introduce the Aquamarine (AQM) dataset, an extensive quantum-mechanical (QM) dataset that contains the structural and electronic information of 59,783 low-and high-energy conformers of 1,653 molecules with a total number of atoms ranging from 2 to 92 (mean: 50.9), and containing up to 54 (mean: 28.2) non-hydrogen atoms. To gain insights into the solvent effects as well as collective dispersion interactions for drug-like molecules, we have performed QM calculations supplemented with a treatment of many-body dispersion (MBD) interactions of structures and properties in the gas phase and implicit water. Thus, AQM contains over 40 global and local physicochemical properties (including ground-state and response properties) per conformer computed at the tightly converged PBE0+MBD level of theory for gas-phase molecules, whereas PBE0+MBD with the modified Poisson-Boltzmann (MPB) model of water was used for solvated molecules. By addressing both molecule-solvent and dispersion interactions, AQM dataset can serve as a challenging benchmark for state-of-the-art machine learning methods for property modeling and de novo generation of large (solvated) molecules with pharmaceutical and biological relevance.

Understanding the Photoprocesses in Biological Systems: Need for Accurate Multireference Treatment

Light-matter interaction is crucial to life itself and revolves around many of the central processes in biology. The need for understanding these photochemical and photophysical processes cannot be overemphasized. Interaction of light with biological systems starts with the absorption of light and subsequent phenomena that occur in the excited states of the system. However, excited states are typically difficult to understand within the mean field approximation of quantum chemical methods. Therefore, suitable multireference methods and methodologies have been developed to understand these phenomena. In this Perspective, we will describe a few methods and methodologies suitable for these descriptions and discuss some persisting difficulties.

Coupled-Cluster Density-Based Many-Body Expansion

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

Competition between Solvent···Solvent and Solvent···Solute Interactions in the Microhydration of the Tetrafluoroborate Anion, BF4-(H2O)n=1,2,3,4

This study systematically examines the interactions of the tetrafluoroborate anion (BF4-) with up to four water molecules (BF4-(H2O)n=1,2,3,4). Full geometry optimizations and subsequent harmonic vibrational frequency computations are performed using a variety of density functional theory (DFT) methods (B3LYP, B3LYP-D3BJ, and M06-2X) and the MP2 ab initio method with a triple-ζ correlation consistent basis set augmented with diffuse functions on all non-hydrogen atoms (cc-pVTZ for H and aug-cc-pVTZ for B, O, and F; denoted as haTZ). Optimized structures and harmonic vibrational frequencies were also obtained with the CCSD(T) ab initio method and the haTZ basis set for the mono- and dihydrate (n = 1, 2) structures. The 2-body:Many-body (2b:Mb) technique, in which CCSD(T) computations capture the 1- and 2-body contributions to the interactions and MP2 computations recover all higher-order contributions, was used to extend these demanding computations to the tri- and tetrahydrate (n = 3, 4) systems. Four, five, and eight new stationary points have been identified for the di-, tri-, and tetrahydrate systems, respectively. The global minimum of the monohydrate adopts a symmetric double ionic hydrogen bond motif with C2v symmetry and an electronic dissociation energy of 13.17 kcal mol-1 at the CCSD(T)/haTZ level of theory. This strong solvent···solute interaction, however, competes with solute···solute interactions in the lowest-energy BF4-(H2O)n=2,3,4 minima that are not seen in the other di-, tri-, or tetrahydrate minima. The latter interactions help increase the 2b:Mb dissociation energies to more than 26, 41, and 51 kcal mol-1 for n = 2, 3, and 4, respectively. Structures that form hydrogen bonds between the solvating water molecules also exhibit the largest shifts in the harmonic OH stretching frequencies for the waters of hydration. These shifts can exceed -280 cm-1 relative to an isolated H2O molecule at the 2b:Mb/haTZ level of theory.

The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures

The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Best practices for the maintenance and distribution of GAMESS are also discussed.

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.

Spatial Decay and Limits of Quantum Solute-Solvent Interactions

Molecular excitations in the liquid-phase environment are renormalized by the surrounding solvent molecules. Herein, we employ the GW approximation to investigate the solvation effects on the ionization energy of phenol in various solvent environments. The electronic effects differ by up to 0.4 eV among the five investigated solvents. This difference depends on both the macroscopic solvent polarizability and the spatial decay of the solvation effects. The latter is probed by separating the electronic subspace and the GW correlation self-energy into fragments. The fragment correlation energy decays with increasing intermolecular distance and vanishes at ∼9 Å, and this pattern is independent of the type of solvent environment. The 9 Å cutoff defines an effective interacting volume within which the ionization energy shift per solvent molecule is proportional to the macroscopic solvent polarizability. Finally, we propose a simple model for computing the ionization energies of molecules in an arbitrary solvent environment.

An Embedded Fragment Method for Molecules in Strong Magnetic Fields

An extension of the embedded fragment method for calculations on molecular clusters is presented, which includes strong external magnetic fields. The approach is flexible, allowing for calculations at the Hartree-Fock, current-density-functional theory, Møller-Plesset perturbation theory, and coupled-cluster levels using London atomic orbitals. For systems consisting of discrete molecular subunits, calculations using London atomic orbitals can be performed in a computationally tractable manner for systems beyond the reach of conventional calculations, even those accelerated by resolution-of-the-identity or Cholesky decomposition methods. To assess the applicability of the approach, applications to water clusters are presented, showing how strong magnetic fields enhance binding within the clusters. However, our calculations suggest that, contrary to previous suggestions in the literature, this enhanced binding may not be directly attributable to strengthening of hydrogen bonding. Instead, these results suggest that this arises for larger field strengths as a response of the system to the presence of the external field, which induces a charge density build up between the monomer units. The approach is embarrassingly parallel and its computational tractability is demonstrated for clusters of up to 103 water molecules in triple-ζ basis sets, which would correspond to conventional calculations with more than 12 000 basis functions.

General, Rigorous Approach for the Treatment of Interfragment Covalent Bonds

A generalized, projection-based transformation of the method-agnostic Fock operator in various ab initio fragment-based quantum chemistry methods has been developed for the treatment of interfragment covalent bonds. This transformation freezes the relevant localized molecular orbital associated with each interfragment bond, thereby restricting the variational subspace of the fragment wave functions, in order to maintain the proper physical characteristics of the involved covalent bonds. In addition, sets of orbitals that would lead to multiple occupancy of certain orbitals are explicitly removed from the variational space. The transformation is developed for the specific case of mutually orthonormal frozen and unfrozen orbitals within each fragment. The newly developed approach is then used to study model systems with two popular ab initio fragment-based methods, and the results of these calculations are compared to those obtained by existing methodologies. Analysis is focused on both quantitative and qualitative accuracy as well as computational scalability and stability. Other methods for which the developed formalisms are appropriate are outlined, and future extensions of the methods are discussed.

Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree-Fock Methods Corrected with Atom-Centered Potentials

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

A simple fragment-based method for van der Waals corrections over density functional theory

Modeling intermolecular noncovalent interactions between large molecules remains a challenge for the electron structure theory community due to the high cost. Fragment-based methods usually fare well in reducing the cost...

Accurate Quantum Chemical Prediction of Gas-Phase Anion Binding Affinities and Their Structure-Binding Relationships

This paper systematically examines the performance of contemporary wavefunction and density functional theory methods to identify robust and cost-efficient methods for predicting gas-phase anion binding energies. This includes the local coupled cluster LNO-CCSD(T) and DLPNO-CCSD(T), as well as double-hybrid DSD-PBEP86-D3(BJ) and various hybrid functionals M06-2X, B3LYP-D3(BJ), ωB97M-V, and ωB97X-V. The focus is on dual-hydrogen-bonding anion receptors that are commonly found in supramolecular chemistry and organocatalysis, namely, (thio)ureas, deltamides, (thio)squaramides, and croconamides as well as the yet-to-be-explored rhodizonamides. Of the methods examined, M06-2X emerged as the overall best performing method as the other functionals including DSD-PBEP86-D3(BJ) and the local coupled cluster DLPNO-CCSD(T) method displayed systematic errors that increase with the degree of carbonylation of the receptors. Hybrid ONIOM models that employed semiempirical methods (PM7, GFN1-xTB, and GFN2-xTB) and "threefold"-corrected small-basis set potentials (HF-3c, B97-3c, and PBEh-3c) were explored, and the best models resulted in 50- to 500-fold reduction in CPU time compared to W1-local. These calculations provide important insight into the structure-binding relationships where there is a direct correlation between Brønsted acidity and anion binding affinity, though the strength of the correlation also depends on other factors such as hydrogen-bonding geometry and the geometrical distortion that the receptor needs to undergo to bind the anion.

Electronic Structure Theory Calculations Using Modern Architectures: KNL vs Haswell

The time to solution and parallel efficiency of several commonly used electronic structure methods (Hartree-Fock, density functional theory, second order perturbation theory, resolution of the identity second order perturbation theory, coupled cluster) are evaluated on both the Intel Xeon Haswell and the Intel Xeon Phi Knights Landing (KNL) architectures. The Haswell completes the benchmark calculations with a faster time to solution than the KNL for all molecules and methods tested. While the Haswell exhibits an average speedup of at least 3.5 relative to the KNL for all nonthreaded computations, the KNL has a better parallel efficiency than the Haswell with increasing core counts. The architectures are further tested using a more computationally costly coupled cluster method on a transition state reaction. The Haswell appears to be the best choice to minimize the time to solution, though for very large systems and high levels of theory that require memory intensive processes the superior memory hierarchy and larger on node memory of the KNL can make it a better choice. These results are used to showcase aspects of novel architectures that will increase efficiency for quantum chemistry applications.

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

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

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

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

Efficient treatment of molecular excitations in the liquid phase environment via stochastic many-body theory

Accurate predictions of charge excitation energies of molecules in the disordered condensed phase are central to the chemical reactivity, stability, and optoelectronic properties of molecules and critically depend on the specific environment. Herein, we develop a stochastic GW method for calculating these charge excitation energies. The approach employs maximally localized electronic states to define the electronic subspace of a molecule and the rest of the system, both of which are randomly sampled. We test the method on three solute-solvent systems: phenol, thymine, and phenylalanine in water. The results are in excellent agreement with the previous high-level calculations and available experimental data. The stochastic calculations for supercells containing up to 1000 electrons representing the solvated systems are inexpensive and require ≤1000 central processing unit hrs. We find that the coupling with the environment accounts for ∼40% of the total correlation energy. The solvent-to-solute feedback mechanism incorporated in the molecular correlation term causes up to 0.6 eV destabilization of the quasiparticle energy. Simulated photo-emission spectra exhibit red shifts, state-degeneracy lifting, and lifetime shortening. Our method provides an efficient approach for an accurate study of excitations of large molecules in realistic condensed phase environments.

Combined quantum Monte Carlo - effective fragment molecular orbital method: fragmentation across covalent bonds

The previously developed combined Quantum Monte Carlo-Effective Fragment Molecular Orbital (QMC-EFMO) method is extended to systems in which the fragmentation process cuts across covalent molecular bonds. The extended QMC-EFMO capability is demonstrated on a few model systems: the glycine tetramer, the diglycine reaction to form a dipeptide, silica-based rings, and polyalanine chains of increasing length. The agreement between full QMC and QMC-EFMO for the correlation energy is within 2 kcal mol^-1 and for the correlation energy differences is within 1 kcal mol^-1.

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

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

Embedding Quantum Statistical Excitations in a Classical Force Field

Quantum-mechanically driven charge polarization and charge transfer are ubiquitous in biomolecular systems, controlling reaction rates, allosteric interactions, ligand-protein binding, membrane transport, and dynamically driven structural transformations. Molecular dynamics (MD) simulations of these processes require quantum mechanical (QM) information in order to accurately describe their reactive dynamics. However, current techniques-empirical force fields, subsystem approaches, ab initio MD, and machine learning-vary in their ability to achieve a consistent chemical description across multiple atom types, and at scale. Here we present a physics-based, atomistic force field, the ensemble DFT charge-transfer embedded-atom method, in which QM forces are described at a uniform level of theory across all atoms, avoiding the need for explicit solution of the Schrödinger equation or large, precomputed training data sets. Coupling between the electronic and atomistic length scales is effected through an ensemble density functional theory formulation of the embedded-atom method originally developed for elemental materials. Charge transfer is expressed in terms of ensembles of ionic state basis densities of individual atoms, and charge polarization, in terms of atomic excited-state basis densities. This provides a highly compact yet general representation of the force field, encompassing both local and system-wide effects. Charge rearrangement is realized through the evolution of ensemble weights, adjusted at each dynamical time step via chemical potential equalization.

Directional Proton Transfer in the Reaction of the Simplest Criegee Intermediate with Water Involving the Formation of Transient H3O. J Phys Chem Lett 2021;12:3379-3386. [PMID: 33784110 DOI: 10.1021/acs.jpclett.1c00448]

The reaction of Criegee intermediates with water vapor has been widely known as a key Criegee reaction in the troposphere. Herein, we investigated the reaction of the smallest Criegee intermediate, CH₂OO, with a water cluster through fragment-based ab initio molecular dynamics simulations at the MP2/aug-cc-pVDZ level. Our results show that the CH₂OO-water reaction could occur not only at the air/water interface but also inside the water cluster. Moreover, more than one reactive water molecules are required for the CH₂OO-water reaction, which is always initiated from the Criegee carbon atom and ends at the terminal Criegee oxygen atom via a directional proton transfer process. The observed reaction pathways include the loop-structure-mediated and stepwise mechanisms, and the latter involves the formation of transient H₃O⁺. The lifetime of transient H₃O⁺ is on the order of a few picoseconds, which may impact the atmospheric budget of the other trace gases in the actual atmosphere.

Accuracy of DLPNO-CCSD(T): Effect of Basis Set and System Size

The DLPNO-CCSD(T) method is designed to study large molecular systems at significantly reduced cost relative to its canonical counterpart. However, the error in this approach is also size-extensive and relies on cancellation of errors for the calculation of relative energies. This work provides a direct comparison of canonical CCSD(T) and TightPNO DLPNO-CCSD(T) calculations of reaction energies and barriers of a broad range of chemical reactions. The dataset includes acidities, anion binding affinities, enolization, Diels-Alder, nucleophilic substitution, and atom transfer reactions and complements existing theoretical datasets in terms of system size as well as new reaction types (e.g., anion binding affinities and chlorine atom transfer reactions). The performance of DLPNO-CCSD(T) was further examined with respect to systematic variation of basis set and system size and amounts of nonbonded interaction present in the system. The errors in the DLPNO-CCSD(T) were found to be relatively insensitive to the choice of basis set for small systems but increase monotonically with system size. Additionally, calculations of barriers appear to be more challenging than reaction energies with errors exceeding 5 kJ mol^-1 for many Diels-Alder reactions. Further tests on three realistic organic reactions reveal the impact of the DLPNO approximation in calculating absolute and relative barriers that are important for predictions such as stereoselectivity.

Energy-Based Molecular Orbital Localization in a Specific Spatial Region

We present a novel energy-based localization procedure able to localize molecular orbitals into predefined spatial regions. The method is defined in a multiscale framework based on the multilevel Hartree-Fock approach. In particular, the system is partitioned into active and inactive fragments. The localized molecular orbitals are obtained maximizing the repulsion between the two fragments. The method is applied to several cases including both conjugated and non-conjugated systems. Our multiscale approach is compared with reference values for both ground-state properties, such as dipole moments, and local excitation energies. The proposed approach is useful to extend the application range of high-level electron correlation methods. In fact, the reduced number of molecular orbitals can lead to a large reduction in the computational cost of correlated calculations.

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.

Complexity Reduction in Density Functional Theory Calculations of Large Systems: System Partitioning and Fragment Embedding

With the development of low order scaling methods for performing Kohn-Sham density functional theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an increase in the size of the system treated comes an increase in complexity, making it challenging to analyze such large systems and determine the cause of emergent properties. To address this issue, in this paper, we present a systematic complexity reduction methodology which can break down large systems into their constituent fragments and quantify interfragment interactions. The methodology proposed here requires no a priori information or user interaction, allowing a single workflow to be automatically applied to any system of interest. We apply this approach to a variety of different systems and show how it allows for the derivation of new system descriptors, the design of QM/MM partitioning schemes, and the novel application of graph metrics to molecules and materials.

Quantum Mechanical Modeling of the Interactions between Noble Metal (Ag and Au) Nanoclusters and Water with the Effective Fragment Potential Method

Explicit solvent interactions can significantly alter the physical and chemical properties of noble metal (e.g., gold and silver) nanoclusters. In order to compute these solvent interactions at a reasonable computational cost, a quantum mechanical (QM)/molecular mechanics (MM) approach, where the metal nanocluster is treated with full QM and the water molecules are treated with a MM force field, can be used. However, classical MM force fields were typically parameterized using molecules containing main group elements as the reference. The accuracy of noble metal-solvent interactions obtained with these force fields therefore remains unpredictable. The effective fragment potential (EFP) force field, designed to model explicitly solvated systems, represents an attractive method to simulate solvated noble metal nanoclusters because it is derived from first principles and contains few or no fitted parameters, depending on implementation. At the density functional theory-optimized geometries, good correlation is obtained between the nanocluster-water interaction energies computed with EFP and those computed with the reference coupled cluster singles, doubles, and perturbative triples method. It is shown that the EFP method gives qualitatively accurate interaction energies at medium-large intermolecular distances for various molecular configurations. In order to achieve higher quantitative accuracy, the first solvation shell should be treated with full QM, if possible. EFP is therefore a promising method for the QM modeling of explicitly solvated silver and gold nanoclusters.

How accurate are approximate quantum chemical methods at modelling solute-solvent interactions in solvated clusters?

In this paper, the performance of a wide range of DFT methods is assessed for the calculation of interaction energies of thermal clusters of a solute in water. Three different charge states (neutral, proton transfer transition state and zwitterion) of glycine were solvated by 1 to 40 water molecules as sampled from molecular dynamics simulations. While some ab initio composite methods that employ insufficiently large basis sets incurred significant errors even for a cluster containing only 5 water molecules relative to the W1X-2 benchmark, the DLPNO-CCSD(T)/CBS and DSD-PBEP86 (triple zeta basis set) levels of theory predicted very accurate interaction energies. These levels of theory were used to benchmark the performance of 16 density functionals from different rungs of Jacob's Ladder. Of the Rung 4 functionals examined, the ωB97M-V and ωB97X-V functionals stood out for predicting absolute interaction energies in 40-water clusters with mean absolute deviations (MAD) ∼4 kJ mol-1. The B3LYP-D3(BJ) functional performed exceptionally well with a MAD ∼1.7 kJ mol-1 and is the overall best performing method. Calculations of relative interaction energies allow for cancellation of systematic errors, including basis set truncation and superposition errors, and the ωB97M-V and B3LYP-D3(BJ) double zeta basis set calculations yielded relative interaction energies that are within ∼3 kJ mol-1 of the benchmark. The ONIOM approximation provides another strategy for accelerating the calculation of accurate absolute interaction energies provided that the calculations have converged with respect to the size of the "high-level-layer".

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.

Embedding Methods for Quantum Chemistry: Applications from Materials to Life Sciences

Quantum mechanical embedding methods hold the promise to transform not just the way calculations are performed, but to significantly reduce computational costs and improve scaling for macro-molecular systems containing hundreds if not thousands of atoms. The field of embedding has grown increasingly broad with many approaches of different intersecting flavors. In this perspective, we lay out the methods into two streams: QM:MM and QM:QM, showcasing the advantages and disadvantages of both. We provide a review of the literature, the underpinning theories including our contributions, and we highlight current applications with select examples spanning both materials and life sciences. We conclude with prospects and future outlook on embedding, and our view on the use of universal test case scenarios for cross-comparisons of the many available (and future) embedding theories.

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.

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

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

Do Better Quality Embedding Potentials Accelerate the Convergence of QM/MM Models? The Case of Solvated Acid Clusters

This study examines whether the use of more accurate embedding potentials improves the convergence of quantum mechanics/molecular mechanics (QM/MM) models with respect to the size of the QM region. In conjunction with density functional theory calculations using the ωB97X-D functional, various embedding potentials including the TIP3P water model, the effective fragment potential (EFP), and semi-empirical methods (PM6, PM7, and DFTB) were used to simulate the deprotonation energies of solvated acid clusters. The calculations were performed on solvated neutral (HA) and cationic (HB⁺) acids clusters containing 160 and 480 water molecules using configurations sampled from molecular dynamics simulations. Consistently, the ωB97X-D/EFP model performed the best when using a minimal QM region size. The performance for the other potentials appears to be highly sensitive to the charge character of the acid/base pair. Neutral acids display the expected trend that semi-empirical methods generally perform better than TIP3P; however, an opposite trend was observed for the cationic acids. Additionally, electronic embedding provided an improvement over mechanical embedding for the cationic systems, but not the neutral acids. For the best performing ωB97X-D/EFP model, a QM region containing about 6% of the total number of solvent molecules is needed to approach within 10 kJ mol^-1 of the pure QM result if the QM region was chosen based on the distance from the reaction centre.

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.

A Force Balanced Fragmentation Method for ab Initio Molecular Dynamic Simulation of Protein

A force balanced generalized molecular fractionation with conjugate caps (FB-GMFCC) method is proposed for ab initio molecular dynamic simulation of proteins. In this approach, the energy of the protein is computed by a linear combination of the QM energies of individual residues and molecular fragments that account for the two-body interaction of hydrogen bond between backbone peptides. The atomic forces on the caped H atoms were corrected to conserve the total force of the protein. Using this approach, ab initio molecular dynamic simulation of an Ace-(ALA)₉-NME linear peptide showed the conservation of the total energy of the system throughout the simulation. Further a more robust 110 ps ab initio molecular dynamic simulation was performed for a protein with 56 residues and 862 atoms in explicit water. Compared with the classical force field, the ab initio molecular dynamic simulations gave better description of the geometry of peptide bonds. Although further development is still needed, the current approach is highly efficient, trivially parallel, and can be applied to ab initio molecular dynamic simulation study of large proteins.

pyEFP: Automatic decomposition of the complex molecular systems into rigid polarizable fragments

We present an open source tool able to describe intermolecular electrostatic interactions within the framework of the effective fragment potential (EFP) method. Complex molecular structure is subdivided into compact rigid fragments and parameters of their interactions are obtained from ab initio calculations. Automatic procedure allows for searching of these parameters into the existing database and merge new fragments into it. A set of standard fragments useful for the studies of organic semiconductors is also provided. Input files both for purely EFP and hybrid QM/MM calculations can be generated. The program is written in python and freely available on GitHub: https://github.com/ale-odinokov/pyEFP © 2017 Wiley Periodicals, Inc.

Benchmarking the Effective Fragment Potential Dispersion Correction on the S22 Test Set

The usual modeling of dispersion interactions in density functional theory (DFT) is often limited by the use of empirically fitted parameters. In this study, the accuracies of the popular empirical dispersion corrections and the first-principles derived effective fragment potential (EFP) dispersion correction are compared by computing the DFT-D and HF-D equilibria interaction energies and intermolecular distances of the S22 test set dimers. Functionals based on the local density approximation (LDA) and generalized gradient approximation (GGA), as well as hybrid functionals, are compared for the DFT-D calculations using coupled cluster CCSD(T) at the complete basis set (CBS) limit as the reference method. In general, the HF-D(EFP) method provides accurate equilibrium dimerization energies and intermolecular distances for hydrogen-bonded systems compared to the CCSD(T)/CBS reference data without using any empirical parameters. For dispersion-dominant and mixed systems, the structures and interaction energies obtained with the B3LYP-D(EFP) method are similar to or better than those obtained with the other DFT-D and HF-D methods. Overall, the first-principles derived -D(EFP) correction presents a robust alternative to the empirical -D corrections when used with the B3LYP functional for dispersion-dominant and mixed systems or with Hartree-Fock for hydrogen-bonded systems.

Photophysical properties and the NO photorelease mechanism of a ruthenium nitrosyl model complex investigated using the CASSCF-in-DFT embedding approach

A complete state-averaged active space self-consistent field (SA-CASSCF) calculation by means of the SA-CASSCF(18,14)-in-BP86 Miller-Manby embedding approach was performed to explore the ground and excited electronic states of the trans-[RuCl(NO)(NH₃)₄]²⁺ complex. Insights into the NO photodissociation mechanism and Ru-NO bonding properties are provided. In addition, spin-orbit (SO) interactions were taken into account to describe and characterize the spin-forbidden transitions observed at the low-energy regions of the trans-[RuCl(NO)(NH₃)₄]²⁺ UV-Vis spectrum. The SA-CASSCF(18,14)-in-BP86 electronic spectrum is in great agreement with the experimental data of Schreiner [Schreiner et al., Inorg. Chem., 1972, 11, 880].

Trends in Two- and Three-Body Effects in Multiscale Clusters of Ionic Liquids

Applications of higher correlated levels of ab initio theory to condensed systems require a significant amount of computational resources. The recent development of the fragment molecular orbital (FMO) approach alleviates this issue by splitting the system into individual fragments and achieves the accuracy of the method by accounting for all possible two-body and three-body interactions. In this work a comprehensive application of the FMO approach in combination with a second order of Møller-Plesset perturbation theory method, MP2, is presented for multiscale clusters of ionic liquids such as [C₁mim]X, [C₁mpyr]X, [C₂py]X, and [NMe₄]X, where X = chloride and tetrafluoroborates, BF₄^-, with the clusters varying in size from 4, 8, 16, to 32 ion pairs. Reliable cutoff criteria for the inclusion of two-body and three-body interactions are identified for both HF energy and MP2 correlation energy to achieve the desired accuracy of 1 kJ mol^-1. The importance of two-body and three-body interactions in ionic liquids is also discussed.