Benchmark Relative Energies for Large Water Clusters with the Generalized Energy-Based Fragmentation Method

Analysis of two overlapping fragmentation approaches in density matrix construction: GMBE-DM vs. ADMA

In this study, we conduct a comparative analysis of two density matrix construction methods: the generalized many-body expansion for building density matrices (GMBE-DM) based on the set-theoretical principle of inclusion/exclusion and the adjustable density matrix assembler (ADMA) based on the Mulliken-Mezey ansatz. We apply these methods to various noncovalent clusters, including water clusters, ion-water clusters, and ion-pair clusters, using both small 6-31G(d) and large def2-TZVPPD basis sets. Our findings reveal that the GMBE-DM method, particularly when combined with the purification scheme and truncation at the one-body level [GMBE(1)-DM-P], exhibits superior performance across all test systems and basis sets. In contrast, all ADMA set of methods show reasonable results only with small and compact basis sets. For example, GMBE(1)-DM-P outperforms the best ADMA method by at least 4 and 16 times with small and large basis sets, respectively, in the case of (H2O)N=6-55. This highlights the significance of the basis set choice for ADMA, which is even more critical than the fragmentation scheme, such as the size of subsystems, while GMBE-DM consistently produces accurate results irrespective of the chosen basis set. Consequently, the efficient and robust GMBE(1)-DM-P approach is recommended as a fragmentation method for generating accurate absolute and relative energies across different binding patterns and basis sets for noncovalent clusters.

Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration

The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a controllable way, but unfavorable combinatorics often defeats this in practice and applications with n ≥ 4 are rare. Here, we outline an algorithm to overcome this combinatorial bottleneck, based on a bottom-up approach to energy-based screening. This is implemented within a new open-source software application ("Fragme∩t"), which is integrated with a lightweight semi-empirical method that is used to cull subsystems, attenuating the combinatorial growth of higher-order terms in the graph that is used to manage the calculations. This facilitates applications of unprecedented size, and we report four-body calculations in (H2O)64 clusters that afford relative energies within 0.1 kcal/mol/monomer of the supersystem result using less than 10% of the unique subsystems. We also report n-body calculations in (H2O)20 clusters up to n = 8, at which point the expansion terminates naturally due to screening. These are the largest n-body calculations reported to date using ab initio electronic structure theory, and they confirm that high-order n-body terms are mostly artifacts of basis-set superposition error.

Combining fragmentation method and high-performance computing: Geometry optimization and vibrational spectra of proteins

Exploring the structures and spectral features of proteins with advanced quantum chemical methods is an uphill task. In this work, a fragment-based molecular tailoring approach (MTA) is appraised for the CAM-B3LYP/aug-cc-pVDZ-level geometry optimization and vibrational infrared (IR) spectra calculation of ten real proteins containing up to 407 atoms and 6617 basis functions. The use of MTA and the inherently parallel nature of the fragment calculations enables a rapid and accurate calculation of the IR spectrum. The applicability of MTA to optimize the protein geometry and evaluate its IR spectrum employing a polarizable continuum model with water as a solvent is also showcased. The typical errors in the total energy and IR frequencies computed by MTA vis-à-vis their full calculation (FC) counterparts for the studied protein are 5-10 millihartrees and 5 cm-1, respectively. Moreover, due to the independent execution of the fragments, large-scale parallelization can also be achieved. With increasing size and level of theory, MTA shows an appreciable advantage in computer time as well as memory and disk space requirement over the corresponding FCs. The present study suggests that the geometry optimization and IR computations on the biomolecules containing ∼1000 atoms and/or ∼15 000 basis functions using MTA and HPC facility can be clearly envisioned in the near future.

Hydrogen bond networks of dimethylsulfoxide (DMSO) pentamer

Understanding of clusters of dimethylsulfoxide (DMSO) is important in several applications in Chemistry. Despite its importance, very few studies of DMSO clusters, (DMSO)_n, have been reported in comparison to systems such as water clusters or methanol clusters. In order to provide further understanding of DMSO clusters, we investigated the structures and non-covalent interactions of the (DMSO)_n, n=5. Therefore, the potential energy surface (PES) of the DMSO pentamer has been examined using classical molecular dynamics. The structures generated using classical molecular dynamics are further optimized at the PW6B95D3/aug-cc-pVDZ level of theory. To comprehend the non-covalent bondings in the DMSO pentamer, we carried out a quantum theory of atoms in molecule (QTAIM) analysis. In addition, the effects of temperature on the structural stability is investigated between 20 and 500K. It comes out that seven different kind of non-covalent bondings can be found in DMSO pentamers.

A unified and flexible formulation of molecular fragmentation schemes

We present a flexible formulation for energy-based molecular fragmentation schemes. This framework does not only incorporate the majority of existing fragmentation expansions but also allows for flexible formulation of novel schemes. We further illustrate its application in multi-level approaches and for electronic interaction energies. For the examples of small water clusters, a small protein, and protein-protein interaction energies, we show how this flexible setup can be exploited to generate a well-suited multi-level fragmentation expansion for the given case. With such a setup, we reproduce the electronic protein-protein interaction energy of ten different structures of a neurotensin and an extracellular loop of its receptor with a mean absolute deviation to the respective super-system calculations below 1 kJ/mol.

Energies, structures, and harmonic frequencies of small water clusters from the direct random phase approximation

The binding energies, structures, and vibrational frequencies of water clusters up to 20 molecules are computed at the direct random phase approximation (RPA) level of theory and compared to theoretical benchmarks. Binding energies of the WATER27 set, which includes neutral and positively and negatively charged clusters, are predicted to be too low in the complete basis set limit by an average of 7 kcal/mol (9%) and are worse than the results from the best density functional theory methods or from the Møller-Plesset theory. The RPA shows significant basis set size dependence for binding energies. The order of the relative energies of the water hexamer and dodecamer isomers is predicted correctly by the RPA. The mean absolute deviation for angles and distances for neutral clusters up to the water hexamer are 0.2° and 0.6 pm, respectively, using quintuple-ζ basis sets. The relative energetic order of the hexamer isomers is preserved upon optimization. Vibrational frequencies for these systems are underestimated by several tens of wavenumbers for large basis sets, and deviations increase with the basis set size. Overall, the direct RPA method yields accurate structural parameters but systematically underestimates binding energies and shows strong basis set size dependence.

Electrostatically embedded molecules-in-molecules approach and its application to molecular clusters

We report the application of our fragment-based quantum chemistry model MIM (Molecules-In-Molecules) with electrostatic embedding. The method is termed "EE-MIM (Electrostatically Embedded Molecules-In-Molecules)" and accounts for the missing electrostatic interactions in the subsystems resulting from fragmentation. Point charges placed at the atomic positions are used to represent the interaction of each subsystem with the rest of the molecule with minimal increase in the computational cost. We have carefully calibrated this model on a range of different sizes of clusters containing up to 57 water molecules. The fragmentation methods have been applied with the goal of reproducing the unfragmented total energy at the MP2/6-311G(d,p) level. Comparative analysis has been carried out between MIM and EE-MIM to gauge the impact of electrostatic embedding. Performance of several different parameters such as the type of charge and levels of fragmentation are analyzed for the prediction of absolute energies. The use of background charges in subsystem calculations improves the performance of both one- and two-layer MIM while it is noticeably important in the case of one-layer MIM. Embedded charges for two-layer MIM are obtained from a full system calculation at the low-level. For one-layer MIM, in the absence of a full system calculation, two different types of embedded charges, namely, Geometry dependent (GD) and geometry independent (GI) charges, are used. A self-consistent procedure is employed to obtain GD charges. We have further tested our method on challenging charged systems with stronger intermolecular interactions, namely, protonated ammonia clusters (containing up to 30 ammonia molecules). The observations are similar to water clusters with improved performance using embedded charges. Overall, the performance of NPA charges as embedded charges is found to be the best.

Linear-Scaling Open-Shell MP2 Approach: Algorithm, Benchmarks, and Large-Scale Applications

A linear-scaling local second-order Møller–Plesset (MP2) method is presented for high-spin open-shell molecules based on restricted open-shell (RO) reference functions. The open-shell local MP2 (LMP2) approach inherits the iteration- and redundancy-free formulation and the completely integral-direct, OpenMP-parallel, and memory and disk use economic algorithms of our closed-shell LMP2 implementation. By utilizing restricted local molecular orbitals for the demanding integral transformation step and by introducing a novel long-range spin-polarization approximation, the computational cost of RO-LMP2 approaches that of closed-shell LMP2. Extensive benchmarks were performed for reactions of radicals, ionization potentials, as well as spin-state splittings of carbenes and transition-metal complexes. Compared to the conventional MP2 reference for systems of up to 175 atoms, local errors of at most 0.1 kcal/mol were found, which are well below the intrinsic accuracy of MP2. RO-LMP2 computations are presented for challenging protein models of up to 601 atoms and 11 000 basis functions, which involve either spin states of a complexed iron ion or a highly delocalized singly occupied orbital. The corresponding runtimes of 9–15 h obtained with a single, many-core CPU demonstrate that MP2, as well as spin-scaled MP2 and double-hybrid density functional methods, become widely accessible for open-shell systems of unprecedented size and complexity.

Degradation mechanism for Zearalenone ring-cleavage by Zearalenone hydrolase RmZHD: A QM/MM study

The danger of zearalenone (ZEN) as an endocrine disruptor to humans and the environment has aroused increasing attention. In this study, we implemented the quantum mechanics/molecular mechanics (QM/MM) method to investigate the degradation mechanism of ZEN hydrolase (RmZHD) toward ZEN at the atomic level. The degradation process involves two concerted reaction pathways, where the active site contains a Ser-His-Glu triplet as a proton donor. With the Boltzmann-weighted average potential barriers of 18.1 and 21.5 kcal/mol, the process undergoes proton transfer and nucleophilic-substituted ring opening to form a hydroxyl product. Non-covalent interaction analyses elucidated hydrogen bonding between key amino acids with ZEN. The electrostatic influence analysis of 16 amino acids proposes residues Asp34 and His128 as the possible mutation target for future mutation design of enzyme RmZHD. An in-depth investigation of the protein environment of RmZHD can improve the bioremediation efficiency of endocrine disrupting chemicals.

Large-Sized Ammonia Clusters and Solvation Energies of the Proton in Ammonia

The absolute solvation energies (free energies and enthalpies) of the proton in ammonia are used to compute the pK_a of species embedded in ammonia. They are also used to compute the solvation energies of other ions in ammonia. Despite their importance, it is not possible to determine experimentally the solvation energies of the proton in a given solvent. We propose in this work a direct approach to compute the solvation energies of the proton in ammonia from large-sized neutral and protonated ammonia clusters. To undertake this investigation, we performed a geometry optimization of neutral and protonated ammonia 30-mer, 40-mer, and 50 mer to locate stable structures. These structures have been fully optimized at both APFD/6-31++g(d,p) and M06-2X/6-31++g(d,p) levels of theory. An infrared spectroscopic study of these structures has been provided to assess the reliability of our investigation. Using these structures, we have computed the absolute solvation free energy and the absolute solvation enthalpy of the proton in ammonia. It comes out that the absolute solvation free energy of the proton in ammonia is calculated to be -1192 kJ mol^-1 , whereas the absolute solvation enthalpy is evaluated to be -1214 kJ mol^-1 . © 2019 Wiley Periodicals, Inc.

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.

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.

Pragmatic Many-Body Approach for Economic MP2 Energy Estimation of Molecular Clusters

We propose a procedure, within the many-body analysis (MBA) framework, for an economic yet accurate estimation of the correlated method-based energies of large molecular clusters employing Dunning's augmented basis sets. The basis of the procedure is to segregate the Hartree-Fock ( E_HF) and correlation energy ( E_C) estimations. E_HF is found to differ by tens of millihartrees (mH) from its full-calculation (FC) counterpart on truncating the MBA expansion at the two-body (MBA-2) level. On the contrary, E_C is estimated with smaller error on modest hardware with limited computation time at the (MBA-2) level. In view of this, we adopt a pragmatic method wherein the E_HF (accurate to five decimal places) is taken from the FC, whereas E_C is estimated at the MBA-2 level. This method is applied to a variety of medium to large molecular clusters at the MP2 level. Preliminary results at the CCSD(T) level for (H₂O)₁₆ and (H₂O)₁₇ are also reported with tremendous savings in wall-clock time and resources. The typical errors in MP2 and CCSD(T) energies per monomer are up to 0.1 and 0.2 mH, respectively. Thus the present method, balancing accuracy and computational economy, opens a way for estimating energies of large molecular clusters using correlated theories with large basis sets.

Structures, relative stability and binding energies of neutral water clusters, (H2O)2–30

We have revised the structures of neutral water clusters, (H₂O)_n=2–30, with the affordable M06-2X functional, presenting up to 25 isomers for each cluster size.

Harmonizing accuracy and efficiency: A pragmatic approach to fragmentation of large molecules

Fragmentation methods offer an attractive alternative for ab initio treatment of large molecules and molecular clusters. However, balancing the accuracy and efficiency of these methods is a tight-rope-act. With this in view, we present an algorithm for automatic molecular fragmentation within Molecular Tailoring Approach (MTA) achieving this delicate balance. The automated code is tested out on a variety of molecules and clusters at the Hartree-Fock (HF)- and Møller-Plesset second order perturbation theory as well as density functional theory employing augmented Dunning basis sets. The results show remarkable accuracy and efficiency vis-à-vis the respective full calculations. Thus the present work forms an important step toward the development of an MTA-based black box code for implementation of HF as well as correlated quantum chemical calculations on large molecular systems.

AMOEBA Polarizable Force Field Parameters of the Heme Cofactor in Its Ferrous and Ferric Forms

We report the first parameters of the heme redox cofactors for the polarizable AMOEBA force field in both the ferric and ferrous forms. We consider two types of complexes, one with two histidine side chains as axial ligands and one with a histidine and a methionine side chain as ligands. We have derived permanent multipoles from second-order Møller-Plesset perturbation theory (MP2). The sets of parameters have been validated in a first step by comparison of AMOEBA interaction energies of heme and a collection of biologically relevant molecules with MP2 and Density Functional Theory (DFT) calculations. In a second validation step, we consider interaction energies with large aggregates comprising around 80 H₂O molecules. These calculations are repeated for 30 structures extracted from semiempirical PM7 DM simulations. Very encouraging agreement is found between DFT and the AMOEBA force field, which results from an accurate treatment of electrostatic interactions. We finally report long (10 ns) MD simulations of cytochromes in two redox states with AMOEBA testing both the 2003 and 2014 AMOEBA water models. These simulations have been carried out with the TINKER-HP (High Performance) program. In conclusion, owing to their ubiquity in biology, we think the present work opens a wide array of applications of the polarizable AMOEBA force field on hemeproteins.

Accurate prediction of the structure and vibrational spectra of ionic liquid clusters with the generalized energy-based fragmentation approach: critical role of ion-pair-based fragmentation

The GEBF method with the ion-pair-based fragmentation has been developed to facilitate ab initio calculations of general ionic liquid clusters.

Structures and properties of large supramolecular coordination complexes predicted with the generalized energy-based fragmentation method

The generalized energy-based fragmentation (GEBF) method has been extended to facilitate ab initio calculations of large supramolecular coordination complexes.